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- Permanent Link:
- https://ufdc.ufl.edu/UFE0021766/00001
## Material Information- Title:
- Development of a Rational Design Approach (LRFD phi) for Drilled Shafts Considering Redundancy, Spatial Variability, and Testing Cost
- Creator:
- Otero, Johanna Karina
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2007
- Language:
- english
- Physical Description:
- 1 online resource (161 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Civil Engineering
Civil and Coastal Engineering - Committee Chair:
- Ellis, Ralph D.
- Committee Co-Chair:
- McVay, Michael C.
- Committee Members:
- Herbsman, Zohar
Gurley, Kurtis R. Liu, Xueli - Graduation Date:
- 12/14/2007
## Subjects- Subjects / Keywords:
- Civil and Coastal Engineering -- Dissertations, Academic -- UF
City of Apalachicola ( local ) Soils ( jstor ) R factors ( jstor ) Standard error ( jstor ) - Genre:
- Electronic Thesis or Dissertation
born-digital ( sobekcm ) Civil Engineering thesis, Ph.D.
## Notes- Abstract:
- New designs move toward larger single shaft; thus the need to improve LRFD resistance factors, and phi for nonredundant shaft. In general, geotechnical design practice involves analysis using representative values of design parameters (strength, recoveries, etc.), usually an average or lowest value obtained from field and laboratory test results. It is followed by an application of a suitable factor of safety. In nature, soil parameters vary horizontally and vertically, so our research used the same soil boring parameters, but this time used information obtained from sites localized close to the design site instead using the whole site average. Random soil models were created based on geostatistics analysis using soil parameters. The created random soil models were used on a finite element program that modeled a 3-foot-diameter, 20-foot-long drilled shaft, giving the drilled shaft capacity for each random soil model and a suitable phi factor. ( en )
- General Note:
- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2007.
- Local:
- Adviser: Ellis, Ralph D.
- Local:
- Co-adviser: McVay, Michael C.
- Statement of Responsibility:
- by Johanna Karina Otero.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Otero, Johanna Karina. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Classification:
- LD1780 2007 ( lcc )
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endloop end hist gp zdis 15,15,40 hist gp zvel 15,15,40 hist zs~top hist zone szz 15,15,39.9 hist zone szz 15,15,20 set mech damp comb set udmax = -le-4 ncut 15000 step 112500 plot create history plot add hist 4 vs -2 save pile2.say 250[ 160.000 140.000 120.000 ,_ 100.000 80 000 40.000 20.000 0.0 -0.5000 2 50C Figure 4-6. WINSLB SGS Example Results Graph. prescribed boundary conditions are set forth. The program will produce displacements and stress changes associated in addition to many other quantities of interest for geotechnical design. To select the appropriate for each case it is necessary to survey within the wide number of options and to select one that fit to each case. At this time there are three approaches to model engineering problems: Continuum, Discrete, and Hybrid. In the Continuum approach, there is no chance for a failure surface to be explicitly developed since model elements cannot separate at the boundaries except on pre-defined boundaries like "interfaces" (see Figure 4-4). In the Discrete approach, elements are ready to separate on boundaries but discontinuity (failure surface) cannot propagate through the elements, they are still modeled as continuum (see Figure 4-4 c). Finally, the Hybrid approach, as the name implies, incorporates both the Discrete and Continuum approaches (see Figure 4-4 e). The numerical solution methods include: Continuum methods: * Finite Difference Method (FDM). * Finite Element Method (FEM). * Boundary Element Method (BEM). Discrete methods * Discrete Element Method (DEM). * Discrete Fracture Network (DFN) methods. Hybrid continuum/discrete models * Hybrid FEM/BEM. * Hybrid FEM/DEM. * Other hybrid models. CHAPTER 6 COST ANALYSIS The principal initiative of the cost analysis is to find a cost comparison between the different $ factors obtained from this Geostatistics study. This study compared results from the three correlation lengths to the deterministic result. The first one used the soil parameter from the borings made around the specific drilled shaft, and the deterministic used the design parameters from soil borings over the whole site. Moreover, the cost analysis is divided in two stages. The first stage includes the materials, labor and equipment cost of the drilled shaft construction and the second stage includes the costs of additional borings around each drilled shaft. Factor Influencing Cost Several factors influence the final costs of a drilled shaft construction, among them are: Subsurface and site conditions Geometry of Drilled Shaft Specification, including inspection procedures Weather conditions Location of work as related to travel and living cost of crew Governmental regulation Availability of optimum equipment Experience of the contractor Insurance and bonding These factors are just a sample of all the variables that could influence a drilled shaft construction costs. This cost analysis assembles most of these influence variables in three big groups. Those are: 1) Drilled Shaft Construction, 2) Drilled Shaft Excavation and 3) Boring Test Costs. The drilled shaft construction includes the costs of: concrete, steel, temporary casing, labor, materials, equipment and incidentals necessary to complete the drilled shaft. The second group includes all the work related to the drilled shaft excavation. Finally, the boring test cost To my parents Maria Isabel Sanchez and Rafael Otero who have supported me all the way since the beginning of my studies, and to Enrique who accompanied me on this last stage BIOGRAPHICAL SKETCH Johanna Otero was born in Monteria, Colombia, to Maria Isabel Sanchez and Rafael Otero. She graduated from Colegio la Sagrada Familia High School in Monteria Colombia in December 1992. She received his Bachelor of Science in civil engineering in the fall of 1998 from the University EAFIT, Medellin Colombia.. After graduation as an Engineer, she worked on the transportation area on Pereira Colombia for almost four years. Johanna continued her education by entering graduate school to pursue a Master of Engineering in the Construction Management Group of the Civil and Coastal Engineering Department at the University of Florida in the fall 2003. She received his Master of Engineering in the fall of 2004. Currently, she is pursuing a Doctorate of Philosophy at the same institution. capacity at a site that does not have a site-specific soil boring by using the properties of the offshore field as a whole. This paper does the introduction to the development of a site-specific model for predicting axial side capacity, which is the first step for a achieving the same level of reliability in design at a site whether or not a soil boring has been drilled at that site by using the properties of the offshore fields as a whole. This paper developed a similar procedure to the "Static and Dynamic Field Testing of Drilled Shaft" analysis. But, instead predicting axial side capacity the named study predicted end bearing capacity. The model provides a methodology to predict site specific pile capacity profiles with depth and to quantify the uncertainty associated with these predictions. The process of model development consists of the following steps: (1) establish a conceptual geological model; (2) compile geotechnical data to relate the geological model to pile capacity; (3) develop a quantitative model describing spatial trends and variability in pile capacity; and (4) calibrate the quantitative model with geotechnical data. The models are part of a reliability-based methodology for design offshore pile foundations without site-specific geotechnical data that could be used on a lot of cases. The paper is completed with three examples of the application of the model on real cases. Reliability-Based Foundation Design for Transmission Line Structures The Electric Power Research Institute published on 1988, three volumes on Reliability- Based Foundation Design for Transmission Line Structure, Volume 1 "Geotechnical Site Characterization Strategy"; and Volume 3 "Uncertainties in Soil Property Measurement". Each of those volumes focused on geotechnical problems. The first volume explained on its second chapter "Geotechnical Material Variability" a guide for to do Geotechnical modeling having into 4 GEOSTATISTICS AND NUMERICAL MODEL .............. ...............45.... Geostati sti cs ................. ...............45......_.._ .... (Semi) Variogram ............ ..... ..__ ...............46... Semivariogram models............... ...............47. Anisotropy ................. .......... ...............48....... Covariance and correlogram .............. ...............49.... Kriging ................. ....._ ...............49...... Types of Kriging .............. ...............51.... Stochastic Simulation .................. ...............53.. Sequential Gaussian simulation .............. ...............53.... Software ................. ...............54................. Numerical M odels ............... .. ............. ...............5 FLAC3D (Fast Lagrangian Analysis of Continua) .............. ...............57.... 5 DATA ANALYSIS .............. ...............65.... Cases Studies .............. ...............65.... Full er Warren ................. ...............65................. Summary Statistics .............. ...............65.... Spatial Continuity ................. ...............66.......... ...... Fuller Warren Semivariogram ............ .......__ ...............67.. 17th Street Brid ge ............ ...... ._ ...............68.. Summary Statistics .............. ...............68.... 17th Street Bridge Semivariogram .............. ...............68.... 17th Street Bridge Simple Kriging ..................... ...............69 .... 17th Street Bri dge S equential Gaus si an Simul ati on ................. ............... 69........... 17th Street Bridge Random Field Model ................. ...............69........... .. 17th Street Bridge Finite Elements Analysis............... ...............70 17th Street Bridge Determinist Capacity ................. ...............71............... 17th Street Brid ge Parametric Study ................ ... .......... ........... ........7 17th Street Bridge Comparison of Deterministic and Predicted End Bearing .................73 17th Street Bridge LRFD Phi Factors .............. ...............73.... 6 COST ANALYSIS .............. ...............95.... Factor Influencing Cost .............. ...............95.... Drilled Shaft Cost and Excavation .............. ...............96.... Soil Boring Test Costs ............ ..... ._ ...............97... Relative Costs Analysis .............. ...............97.... Drilled Shaft Cost ............ ..... ._ ...............97... Drilled Shaft Excavation .............. ...............98.... Boring Test Cost............... ...............98.. 7 CONCLUSIONS AND RECOMMENDATIONS .......___......... .........___......105 40 ft 55 ft35f Figure 5-1. Fuller Warren Soil Boring Location. CB-1 Elevation vs. qu, qt,RQD,qb 160.00 140.00 120.00 ' 100.00 80.00 60.00 ~ 'i 40.00 20.00 0 I -20.00 -' n -40 -4 -50 -5 -00 -05 - Elevation (ft) -* qu (tsf) -=- qt (tsf) -a- Recovery qb(tsf) (FDOT) -a- quqt Figure 5-2. Fuller Warren Histogram CBl. range, the distance at which the semi variance reaches 95% of the sill value. The Gaussian model, with its parabolic behavior at the origin, represents very smoothly varying properties. (However, using the Gaussian model alone without a nugget effect can lead to numerical instabilities in the kriging process.) The spherical and exponential models exhibit linear behavior the origin, appropriate for representing properties with a higher level of short-range variability. Examples of this model are showed in Figure 4-2. Anisotropy The omni directional semivariogram is that one that for which the directional tolerance is larger enough that the direction of any particular separation vector become unimportant. It contains all possible directions combined into a single variogram. The calculation of the omnidirectional semivariogram does not imply that the spatial continuity is the same in all directions. It provides a starting point for to establishing some of the parameter required for sample semivariogram calculations. In many cases, a random variable shows different autocorrelation structures in different directions, and an anisotropic semivariogram model should be developed to reflect these differences. The most commonly employed model for anisotropy is geometric anisotropy, with the semivariogram reaching the same sill in all directions, but at different ranges. In geological settings, the most prominent form of anisotropy is a strong contrast in ranges in the (stratigraphically) vertical and horizontal directions, with the vertical semivariogram reaching the sill in a much shorter distance than the horizontal semivariogram. In some settings, there may also be significant lateral anisotropy, often reflecting prominent directionality in the depositional setting. Table 6-9. Average Cost for a 1 foot length and 4 feet Diameter Drilled Shaft, (One Soil Boring) Average Drilled Shaft Cost / LF $267.97 Average Drilled Shaft Excavation Cost/ LF $173.92 Average of four Soil Tests Cost/ LF $24.5(*) Average of Auger Soil Boring/ LF $30.63 TOTAL/ LF $497.02 (*) Assuming a set of soil tests every 10 ft. Table 6-10. Average Cost for a 1 foot length 4 feet Diameter Drilled Shaft, (Five Soil Boring) Average Drilled Shaft Cost / LF $267.97 Average Drilled Shaft Excavation Cost/ LF $173.92 Average of four Soil Tests Cost/ LF $122.5 Average of Auger Soil Boring/ LF $153.15 TOTAL/ LF $717.54 Table 6-11i. LRFD $ Factors, Probability of Failure and Fs Based on Reliability, P for Nearest Boring Approach (McVay and Ellis 2001) Reliability, P LRFD, $ PR%) Factor of Safety 2.0 0.86 8.5 1.65 2.5 0.71 1.0 1.98 3.0 0.60 0.1 2.37 3.5 0.50 0.01 2.84 4.0 0.42 0.002 3.40 4.5 0.35 0.0002 4.07 showed in Figure 5-2 to Figure 5-4. These three boring histograms illustrate clearly a difference tendency on properties values from elevation 55 feet and below. This behavior suggests a limit for two different layers on the soil. Additionally, an example of frequency distribution (for qu, qt and RQD), and statistics summary for all new borings (CB 1, CB2 and CB3) is showed in Figure 5-5. It shows that the most suitable frequency distribution is the lognormal. The complete set of graphs showing each of the boring data in all sites for the same bridge are showed in APPENDIX D. The frequency distributions comparing all data (past FDOT research), new data (CB 1,CB2 and CB3) and a combination of both is showed in Figure 5-6. The Eigure showed how the standard deviation from the combination of old and new data is reduced from 25.66 to 20.32-tsf when more data values (new data) are added. Several attempts have been made to obtain the classical statistical properties of the soil, such as the mean value, COV, and probability distribution, throughout geotechnical engineering practice. These statistical characteristics have been discussed by several authors and most of them have implemented distribution models like normal, lognormal, and beta for to curve fit results of Hield data. This implies that these distributions are can be used to fitted soil properties distribution results obtained under Hield conditions. Accorded to the obtained results showed in Figure 5-5, the maj ority of the "closes fitted" distribution model selected for the Fuller Warren site were Lognormal and Beta. Spatial Continuity Spatial continuity exists in most earth science data sets. Two data sets close to each other are more likely to have similar values than two data sets that are far apart. When we look at a data graph or posting, the values do not appear to be randomly located, but rather, low values tend to be near and high values tend to be near other high values. That is the case for each of the Table 5-2. Fuller Warren Soil Boring Modified Data. Name of Boring CB-1 (New) CB-2 (New) CB-3 (New) Distance from Load Test (ft) 30 EL. (ft) -40.5 -40.5 -40.5 -45.5 -45.5 -45.5 -45.5 00-45.5 -50.5 -50.5 -50.5 -50.5 -50.5 -55.5 15 EL. ~i (psi) (ft) 48974.00 -41 -41 30083.74 -41 75668.97 -46 -46 -46 81523.95 -46 75899.59 -51 38959.02 -51 52082.74 -51 15682.83 -51 69402.72 -51 24923.43 -51 14642.92 -51 qu qt (tsf) (tsf) 15.36 31.21 96.14 2.14 6.36 143.30 9.07 59.24 7.21 52.29 15.85 68.09 18.33 13.65 113.41 18.62 11.95 1.86 0.89 1.44 12.56 1.37 qu qt (tsf) (tsf) 42.57 25.23 4.36 18.66 3.54 56.42 1.76 15.32 10.34 64.77 18.36 65.12 8.41 37.24 8.51 140.06 10.11 8.29 1.91 78.44 0.84 15.68 5.49 10.61 1.82 qt (tsf) 3.00 10.91 26.50 1.69 12.89 13.33 14.08 3.17 0.97 1.94 1.34 0.70 2.37 0.87 qu (tsf) 108.40 56.45 92.70 52.55 67.90 91.39 52.41 8.36 12.28 7.22 RQD 37 37 37 74 74 74 74 74 48 48 48 48 48 77 Ei (psi) EL. (ft) 20725.93 -37.58 93362.29 -37.58 -42.58 108694.81 -42.58 20329.10 -42.58 50938.20 -42.58 87522.73 -47.58 163837.76 -47.58 143167.10 -47.58 -47.58 -47.58 -47.58 -52.58 16123.94 -52.58 RQD 23 23 52 52 52 52 87 87 87 87 87 87 98 98 E RQD 50 50 50 67 67 67 67 92 92 92 92 92 92 92 Ei (psi) 139525.37 55345.75 102818.36 64868.52 81761.47 136076.85 56192.28 19141.58 18051.95 13564.22 1 Table 6-5. Summary of Drilled Shaft Cost (Material, labor) for $ Factors FOSM Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 1 $346.66 $391.77 $442.93 $500.88 5 $369.10 $423.33 $484.58 $555.95 12 $407.25 $467.66 $535.94 $616.02 Table 6-6. Summary of Drilled Shaft Cost (Material, labor) for $ Factors FOSM (Modified) Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 1 $280.01 $302.11 $326.00 $351.67 5 $308.72 $340.06 $374.78 $412.26 12 $341.36 $377.42 $416.75 $460.43 Table 6-7. Summary of Drilled Shaft Cost Excavation for $ Factors FOSM Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 1 $224.99 $254.27 $287.47 $325.08 5 $239.56 $274.76 $314.50 $360.83 12 $264.32 $303.53 $347.84 $399.82 Table 6-8. Summary of Drilled Shaft Cost Excavation for $ Factors FOSM (Modified) Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 $181.73 $200.37 $221.55 $196.08 $220.71 $244.96 $211.58 $243.24 $270.48 $228.24 $267.57 $298.83 LIST OF TABLES Table page 2-1 LRFD $ Factors, Probability of Failure (Pf) and Fs Based on Reliability $ for Nearest Boring Approach. ............. ...............34..... 2-2 LRFD $ Factors, Probability of Failure (Pf) and Fs Based on Reliability $ for Random Selection ................ ...............34................. 3-1 Measured Unit End Bearing from Load Tests. ............. ...............39..... 3-2 17th Street Bridge Soil Boring Data (State Proj ect No. 86180-1522) ............... .... ...........40 3-3 Fuller Warren State Materials Office Soil Laboratory Data ................. ............. .......41 4-1 Commercially Available Numerical Programs for Rock Mechanics Study. .....................59 4-2 Sequential Gaussian Simulation Data Values ................. ........._.. ...... 60_._. ... 4-3 WINTSLIB SGS Example Results............... ...............60 5-1 Fuller Warren Bridge Soil Boring Information. ............. ...............77..... 5-2 Fuller Warren Soil Boring Modified Data. .............. ...............78.... 5-3 Table 17th Street Bridge Soil Boring Information. ............. ...............80..... 5-4 17th Street Bridge Wingslib Results ................. ...............81........... .. 5-5 M material Properties............... ..............8 5-6 17TH Street Bridge Cohesion Mean Results Values from Simulations ................... ...........81 5-7 17TH Street Bridge End Bearing Capacity Mean Values from FLAC3D ................... .......81 5-8 17TH Street Mean, Standard, and COV of Predicted End Bearing Capacity Bias .............81 5-9 17TH Street Bridge $ Values for different Reliability Index P FOSM (Traditional). .........82 5-10 17TH Street Bridge $ Values for different Reliability Index P FOSM (Modified) ............82 5-11 17th Street Bridge COV and h............... ...............82... 6-1 FDOT Item Average Unit Cost Database. ............. ...............99..... 6-2 Summary of Drilled Shaft of 48" Diameter (0455 88 5). ............. .....................9 6-3 Summary of Excavation Shaft of 48" Diameter (0455 122 5) ................. ............... ....99 Table 3-3. Fuller Warren State Materials Office Soil Laboratory Data. State Materials Office Foundations Laboratory Rock Core Unconfined Compression-Split Tensile Effective/Revised: 4/27/05 By: G.J. Wet Unit Wt. (pcf) 149.1 142.6 125.2 132.0 150.2 117.1 154.9 150.3 143.5 146.7 139.1 143.3 151.0 143.3 150.0 140.2 135.9 132.5 132.0 118.9 124.2 125.3 124.1 126.9 133.5 Page 1 of 1 Corr. Factor 1.00 1.01 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 L/D Rati o 2.02 1.86 1.05 1.02 0.99 1.05 1.83 0.98 2.02 0.99 2.04 0.98 2.04 0.99 2.06 1.06 1.03 2.09 1.07 1.05 2.06 1.03 0.91 2.00 1.02 Samp. No. lU 2U 3T 4T 5T IT 2U 3T 4U 5T 6U 7T 8U IT 2U 3T 4T 5U 6T 7T 8U 9T 10T 11U 12T Depth Top (ft) Depth Bot. (ft) Length Test Date (in) 8/21/2006 4.8380 4.4327 2.4345 2.4350 2.3500 8/21/2006 2.4165 4.3357 8/22/2006 2.3220 4.8068 2.3535 4.8825 2.3395 4.8715 8/22/2006 2.3315 4.8632 2.4395 2.4330 4.8955 2.4855 2.4545 4.8125 2.3865 2.1210 4.7020 2.4110 Wet Wt. (g) 853.2 740.4 335.2 375.0 409.9 308.4 774.8 406.1 806.8 400.6 799.2 393.8 865.4 380.8 838.4 376.5 378.1 734.4 366.7 328.7 672.7 332.8 291.7 676.5 369.5 Boring /Core CB-3/1 CB-3/2 CB-3/3 Dia. (in) 2.3950 2.3835 2.3100 2.3785 2.3730 2.2995 2.3655 2.3760 2.3820 2.3720 2.3895 2.3870 2.3890 2.3510 2.3610 2.3110 2.3555 2.3430 2.3285 2.3375 2.3360 2.3230 2.3185 2.3455 2.3595 Types of Kriging Classical types of kriging are: Simple kriging assuming a known constant trend: CL(x) = 0. Ordinary kriging assuming an unknown constant trend: CL(x) = CL. * Universal Kriging assuming a general linear trend model k-0 * IRFk-Kriging assuming CL(x) to be an unknown polynomial in x. * Indicator Kriging using indicator functions instead of the process itself, in order to estimate transition probabilities. * Multiple indicator kriging is a version of indicator kriging working with a family of indicators. However, MIK has fallen out of favor as an interpolation technique in recent years. This is due to some inherent difficulties related to operation and model validation. Conditional Simulation is fast becoming the accepted replacement technique in this case. * Disjunctive Kriging is a nonlinear generalization of kriging. * Lognormal Kriging interpolates positive data by means of logarithms. For this research we were focused in two of theses types, Simple and Ordinary Kriging Simple Kriging Simple kriging is the most basic form of kriging in the sense that the model is the simplest in its mathematical formulation. The kriging weights of simple kriging have no unbiasedness condition and are given by the simple kriging equation system: ~(xl~ ~n> *Simple Kriging Interpolation The interpolation by simple kriging is given by: C (~t~l, ~O~I C(-~,, 2O) 2d~l i w, cj=Az,) ~(l~lr .111r S~~) = Figure 3-3. Fuller Warren Bridge during Site Inspection. Figure 3-4. 17th Street Bridge Load Test Location. 17th Street Bridge 11 I I 1 1 1 4/1 1T 1000 1053 1375 2 1485 00527 100/77 754 411 9 381 3 2U 977 1056 3357 2 741 4 00425 092 "755 7105 654 3U 990 1139 5394 3 11953 00505 1 06 "762 778 8 7155 4T 12 15 107 8 1498 2 168 4 0 0398 "75 411 374 6 5U 964 1233 7650 7 1693 3 00548 1 11 "77 861 7 792 7 ST 11 33 1128 438 4 451 00319 "764 455 8 4172 7U 1013 1134 4492 3 989 3 00344 077 "749 726 6661 8U 730 1256 7813 1732 9 00623 1 30 "756 838 2 786 3 9T 702 1236 2047 2 279 4 00643 "77 381 8 361 8 10U 609 1257 6338 7 1403 5 00486 098 "755 840 8 796 9 11T 800 1192 1733 3 2199 00443" 756 394 3 370 7 4/2 1T 321 982 14142 1504 01128 90/48 777 377 367 7 2U 308 101 0 1978 9 439 0 00355 081 "759 595 4 579 9 3T 433 1044 1262 1 1287 00891 "76 401 6 388 1 4T 1079 1190 3328 353 7 00556 "76 9 467 429 5U 8 51 109 5 2030 7 454 7 0 0354 0 90 "76 585 9 545 9 6T 433 1140 2302 1 252 9 00906 "757 405 8 392 1 7T 702 1238 2290 3 252 8 00902 "775 450 9 426 4 8T 1064 1128 2816 1 281 6 00969 "76 1 454 5 418 1 9U 5 61 119 5 3170 6 711 5 0 0553 1 15 "75 1 780 8 743 3 4/3 1T 309 978 12801 1839 00246 82/14 779 294 5 288 2U 222 1490 6791 7 1447 0 00489 1 35 "749 700 686 4 3U 075 1444 9992 7 21348 00458 1 27 "748 691 7 6871 4T 076 1053 1260 9 144 1 00434 "75 352 3 350 2 5T 1 28 1002 8129 91 3 00452 "775 354 4 350 9 4/4 1T 495 1228 2832 6 322 7 00400 87/34 762 430 3 4136 2U 9 54 109 4 2457 9 567 9 0 0247 0 49 "75 756 696 7 3T 6 11 111 6 1563 5 1796 00658 "755 384 8 367 4U 650 97 1 1591 8 341 7 00329 096 "754 486 6 461 5 5T 448 101 2 1743 1 205 7 00986 "779 353 1 341 3 6T 331 942 688 7 842 00312 "77 1 327 1 319 1 7T 3 95 97 9 963 8 105 5 0 0704 "75 8 362 8 351 9 8U 4 70 97 8 1058 1 239 1 0 0223 0 49 "76 9 607 4 583 6 9T 626 979 1296 7 1567 01132 "779 339 4 324 4/5 1U 284 1457 10309 5 2256 4 00540 125 58/25 755 832 4 8115 2U 283 1478 10395 3 2262 9 00506 1 21 "75 1 826 805 3 3T 2 01 152 4 4593 437 5 0 0638 "757 587 1 577 4T 1 76 1491 39134 437 5 00460 "76 503 1 495 7 5T 205 1443 2823 3 354 2 00309 "769 445 3 437 9 6T 357 1350 3007 5 368 4 00760 "777 435 422 7 4/6 1U 186 1465 10446 5 22921 00512 115 775 865 4 851 2U 196 1474 10971 3 2351 0 00473 129 756 727 2 7147 3T 1 46 1372 3324 5 367 7 00283 755 471 3 465 6 4/7 1T 152 1468 4003 3 402 9 00483 42/20 77 5391 532 2 2U 1 32 1447 16231 4 3598 5 00498 1 00 "76 1 9104 899 5 3U 234 1459 10079 6 2161 3 00438 1 10 "749 786 6 770 3 I I I I I I I I 12/O Location: Date Received: Tested by: Table B-1. Continued. Project Number: Lab Number: Bridge Number: LIMS Number: Table E-3. Continued. VV X Y PSF PSF PSF Mean 44963.57643 Mean 42967.49829 Mean 47554.61147 Standard Error 222.873721 Standard Error 222.1398912 Standard Error 248.1298149 Median 41800 Median 39449. 822 Median 43413.186 Mode 49700 Mode 49700 Mode 11399.9996 Standard Deviation 21448.04963 Standard Devbition 21377.4302 Standard Devbition 23878. 54684 Sample Variance 460018833 Sample Variance 456994521.B Sarnple Variance 570184999.2 Kurtosis -0.664903412 Kurtosis -0.588149668 Kurtosis -0.886393787 Skewness 0.400653996 Skewness 0.47779941 Skewness 0.30788879 Range 98933.37236 Range 98727.84014 Range 99288.7588 Minimum 1062.49964 Minimum 1192.01386 Minimum 707.5792 Maximum 99995.872 Maximum 9991 9. 854 Maximum 99996. 338 Sum 416407681.4 Sum 397922001.7 Sum 440403256..9 Count 9261 Count 9261 Count 9261 the bridges showed on the Figure 3-1 with a white shadow. The principal two recurrent failed details were that the load test locations were offshore, and that the load test results did not reach the tip movement (end bearing failure criteria).After the preliminary selection the finally four selected sites or bridges were: * Apalachicola River Bridge (District 3) * Victory Bridge (District 3) * Fuller Warren Bridge (District 2) * 17th Street Bridge (District 4) The field exploration was accomplished by Universal a soil exploration company in Jacksonville and Fort Lauderdale. And the rock cores obtained from Universal were tested at the State Materials Office soil lab district 2 (Gainesville Fl.). Consequently, strength values, recoveries and compressibility records were obtained from them and subsequently were used to establish LRFD resistance factors for end bearing for each specific site location. From the pre-selected sites name above, just two of them were tested. It is the case of Fuller Warren Bridge Jacksonville (District 2) and 17th Street Bridge Fort Lauderdale (District 4). The data obtained from each bridge is showed in the APPENDIX B but an example of the data obtained from the State Material Office lab is showed in the Table 3-3. In this table is illustrated the information for each rock core took from the field, as length, diameter, depth, unit mass, qu, qt, recovery, RQD, density, etc. The data obtained from theses tables was used on the simulation of random fields and later on the model on the finite element program. The next couple of paragraphs are dedicated to relevant information about the two bridges selected for the research. The Fuller Warren Bridge (District 2) It is localized over the St. Johns River in downtown Jacksonville on the Interstate Highway 95 (1-95). It replaced the old Gilmore Street Bridge. It has four Load tests LT-1, LT-2, LT-3 and 20 30 Fuller Warren MEAN = 30.9569 4.2200 77.3793 STD = 33.1697 6.0748 20.3354 SKEW = 1.1429 2.3112 -0.2341 KURT = 2.8870 7.9730 1.4244 MNPDFEXP = 26.9212 4.1906 28.6658 STDPDFEXP= 23.9281 4.0814 25.3287 SKPDFEXP = 1.2791 1.9112 1.5975 KUPDFEXP = 4.0327 7.5835 3.8601 MNPDFLOG = 23.4179 3.5494 60.1970 STDPDFLOG = 21.6499 4.0810 16.9897 SKPDFLOG = 1.7166 2.6733 1.4052 KUPDFLOG = 5.5971 11.9322 2.7615 MNPDFGAM= 27.2903 4.1714 61.5707 STDPDFGAM = 23.7335 4.2676 16.9482 SKPDFGAM = 1.2574 1.9894 1.2835 KUPDFGAM= 4.0039 7.7753 2.6131 sqerrorNORM = 1.0e-004 0.2302 0.0009 0.0131 sqerrorEXP = 1.0e-004 0.1278 0.0024 0.0073 sqerrorLOGN= 1.0e-005 0.7795 0.0204 0.0453 sqerrorGAM = 1.0e-004 0.1260 0.0028 0.0077 0.06 0.04~ 0.02 0 0 0.05- 0.04 0.03 0.02 0.01 0 0 50 100 1 Figure D-10. Fuller Warren New Boring CB3 0.3 0.2 0.1 0 10 geostatistical functions and there is a range of commercial geostatistical packages. Before starting using the WINGSLIB software, a manual check test was realized. All the steps described on the Sequential Gaussian Simulation process, were followed and the results were positive. The data required for to do simulation using SGS in WINGSLB software were: * The variable to be simulated (Cohesion Values) * The Semivariogram structure to be used * The maximum and minimum of original data that should be used to simulate a grid node. * Data Variance * X, Y and Z coordinates for the available data * Definition of the grid system * The number of previously simulated point to use for the simulation of another node. * Type of kriging to be used. This manual check was realized to demonstrate that the results obtained from the Wingslib software are the same or similar to those obtained doing the process manually. The example in 2D used eight data values, showed in Table 4-2. The location on a plan view of data values is illustrated in Figure 4-5. The WINGSLB results values are in Table 4-3 and those same results are represented in Figure 4-6. As you observe in Table 4-3 the last two values correspond to the coordinates X,Y (0,2) and X,Y (2,0). Using WINSLIB the results were 198.95 and 5.52 respectively. And doing the process manually the results are 198.52 and 5.95 respectively. The difference is very small comparing the two results. So, it was proved that using WINGSLB the results obtained are similarly to those that are obtained doing the process manually. Numerical Models Numerical models are available for the user in form of computer codes or programs. A numerical model program is capable of: (1) solving the equations of equilibrium, (2) satisfying the strain compatibility equations, and (3) following certain constitutive equations when Sequential Gaussian Simulation is the most straightforward algorithm for generating realizations of a multivariate Gaussian field. It is provided by the sequential simulation principle of including all data available within a neighborhood of the point on question, including the original data and all previously simulated values. Each variable is simulated sequentially according to its normal cdf fully characterized through a Simple Kriging system. The detailed steps in Sequential Gaussian Simulation are: * Determine the univariate cdf representative of the entire study area and not only of the sample data available. * Transform data to "normal space" * Establish grid network and coordinate system (Zrel-space) * Assign data to the nearest grid node (take the closest of multiple data assigned to the same node) * Determine a random path through all of the grid nodes * Find nearby data and previously simulated grid nodes * Construct the conditional distribution by kriging * Draw simulated value from conditional distribution * Check results * Back transform (Statios 2001) By using different random number seeds the order of visiting locations is varied and, therefore, multiple realizations can be obtained. In other words, since the simulated values are added to the data set, the values available for use in simulation are partly dependent on the locations at which simulations have already been made and, because of this, the values simulated at any one location vary as the available data vary. Software The wide range of public domain and low cost software now available means that the tools of Geostatistics are readily available to the geotechnical. Widely used public domain software packages include WINTGSLIB Geostatistical Software Library, and Gstat the first one used for the case studies presented in this research. In addition, several commercial GISystems include LIST OF FIGURES Figure page 1-1 Location of Boundaries between Materials. ............. ...............26..... 1-2 Litho Logical Heterogeneity. ............. ...............26..... 1-3 Inherent Spatial Soil Variability. ............. ...............26..... 3-1 Load Test Bridge Locations ........._.__ ......._._ ...............43.. 3-2 Fuller Warren Bridge Shaft Locations. .............. ...............43.... 3-3 Fuller Warren Bridge during Site Inspection ................. ...............44........... .. 3-4 17th Street Bridge Load Test Location. .............. ...............44.... 4-1 Semivariogram Model. ............. ...............61..... 4-2 Most popular Semivariogram Models. ............. ...............61..... 4-3 Semivariogram and Covariance. .............. ...............62.... 4-4 Numerical Approaches to Model an Excavation in a Rock Mass .............. ...................63 4-5 WINTSLIB SGS Example Location Data Values. ............. ...............63..... 4-6 WINTSLIB SGS Example Results Graph............... ...............64. 5-1 Fuller Warren Soil Boring Location. ............. ...............83..... 5-2 Fuller Warren Histogram CBl1................. ...............83.___ ... 5-3 Fuller Warren Histogram CB2 ................. ...............84........... ... 5-4 Fuller Warren Histogram CB3 ................ ...............84........... ... 5-5 Fuller Warren New Borings Frequency Distribution qu, qt and RQD. ............. ................85 5-6 Frequency Distribution for quqt ................. ...............86........... ... 5-7 Fuller Warren Bridge quqt and E Correlation............... ..............8 5-8 17th Street Soil Boring Locations ................. ...............87........... .. 5-9 17th Street Frequency Distribution............... ..............8 5-10 17th Street Semivariogram .............. ...............89.... 10 Table B-1. Continued. STATE MATERIALs Rock Core Effective/Revised Date: OFFICE 12/22/05 Unconfined Compression- Foundations Laboratory By: B.W. Page 1 of 1 Split Tensile II ~ i I' I I .I I i I I I 1- .i I I ." I 9/1 1T 52.0 2.3675 2.3758 274.8 99.7 1.00 2U 4.8455 2.3993 734.1 127.7 2.02 1.00 3T 2.5725 2.3918 357.3 117.8 1.08 4U 3.8405 2.3895 623.0 137.8 1.61 1.03 5T 2.2010 2.3723 364.2 142.6 0.93 7U 4.1760 2.3723 631.5 130.3 1.76 1.02 8T 1.9400 2.4003 299.0 129.8 0.81 9T 2.2845 2.3838 357.8 133.7 0.96 10U 57.0 3.6120 2.3605 616.1 148.5 1.53 1.04 9/2 2U 57.0 4.0595 2.3835 642.7 135.2 1.70 1.02 3T 2.4610 2.4002 426.2 145.8 1.03 4T 2.1900 2.3923 384.5 148.8 0.92 5T 62.0 2.3480 2.3793 372.9 136.1 0.99 9/3 1T 62.0 2.3540 2.3748 382.8 139.9 0.99 2T 2.3030 2.3762 411.0 153.3 0.97 3U 4.7730 2.3712 853.7 154.3 2.01 1.00 4T 2.3620 2.3657 413.8 151.8 1.00 5U 4.5455 2.3710 806.2 153.0 1.92 1.01 6T 2.2490 2.3638 355.2 137.1 0.95 7U 3.9055 2.3790 647.2 142.0 1.64 1.03 8T 67.0 2.0000 2.3515 243.9 107.0 0.85 9/4 1T 67.0 2.0470 2.3715 332.2 140.0 0.86 2U 4.8350 2.3870 751.7 132.4 2.03 1.00 3T 2.0110 2.3808 227.2 96.7 0.84 4T 2.2550 2.3907 274.4 103.3 0.94 5T 2.0905 2.3708 248.0 102.4 0.88 6U 3.6590 2.3763 436.6 102.5 1.54 1.04 7T 72.0 1.9035 2.3728 228.5 103.4 0.80 9/5 1T 72.0 2.1880 2.3832 366.2 142.9 0.92 2U 4.5405 2.3837 780.4 146.7 1.90 1.01 3T 2.2630 2.3797 404.8 153.2 0.95 4U 4.4335 2.3853 712.6 137.0 1.86 1.01 5U 77.0 4.8720 2.3825 861.7 151.1 2.04 1.00 9/6 1U 77.0 3.6205 2.3862 662.8 156.0 1.52 1.04 2T 2.4180 2.3888 439.7 154.6 1.01 3T 82.0 1.9630 2.3873 356.4 154.5 0.82 9/7 1U 82.0 87.0 4.2860 2.3872 770.9 153.1 1.80 1.01 ) 20 40 60 0.03 0 50 100 RQD FullerWarren MEAN= 56.6495 8.4384 63.0673 STD = 78.6970 10.6514 25.6656 SKEW = 4.0955 1.8064 -0.1906 KURT = 24.6259 6.3517 1.9980 MNPDFEXP = 56.6321 8.3339 29.6672 STDPDFEXP= 56.5155 8.0886 25.1402 SKPDFEXP = 1.9848 1.7879 1.4168 KUPDFEXP = 8.7361 6.8332 3.5806 MNPDFLOG= 53.7941 6.7613 46.0365 STDPDFLOG = 66.7919 8.8546 20.5086 SKPDFLOG = 3.1883 2.5116 1.2676 KUPDFLOG = 16.7575 9.8725 3.1364 sqerrorNORM = 1.0e-005 0.1896 0.0147 0.0008 sqerrorEXP = 1.0e-006 0.4337 0.0909 0.0524 sqerrorLOGN= 1.0e-006 0.0867 0.1634 0.1023 0.025 0.02 0.015 0.01 0.005 0 0 200 400 0.04 Figure D-3. Fuller Warren Bridge Old and New Borings. Q PSF R PSF S PSF PSF PSF PSF Table E-3. Continued. PSF PSF PSF Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 51470.31861 236.2322652 49608.578 49700 22733.59697 516816431.2 -0. 913495054 0.171190865 99976.04256 18.9974382 99995.04 476666620.7 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 41320.25623 206.1301759 38500 32200 19836.74982 393496643.2 -0.37199239 0.55984348 99177.92682 734.86918 99912.796 382666892.9 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 40438.14456 215.9221412 37335.826 11399.9996 20779.07069 431769778.5 -0.492837597 0.533478348 99853.50113 94.534874 99948.036 374497656.8 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 47042.63871 223.6413497 43499.474 48900.002 21521.92168 463193112.9 -0.740545222 0.319788177 97029.068 2876.152 99905.22 435661877.1 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 44797.74259 231.159873 41342.338 38500 22245.45993 494860487.6 -0.671942245 0.424328387 99524.53918 393.21682 99917.756 414871894.1 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 45763.25705 222.6925403 42281.89 48900.002 21430.61387 459271211 -0.75114585 0.319107618 99124.16976 841.91824 99966.088 423813523.6 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 44061.74486 218.5590664 41032.302 48900.002 21032.83278 442380054.7 -0.626614687 0.424741976 99303.45 617.266 99920.716 408055819.2 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 48102.4208 221.9101921 44215.9 38500 21355.32531 456049919.2 -0.74765644 0.29905297 98855.61356 1139.09244 99994.706 445476519 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 37070.10498 198.1461848 34927.44 15199. 9998 19068.4177 363604553.7 -0.200228081 0.659719139 99517.49996 375.12404 99892.624 343306242.2 9261 resistance are modeled as lognormal random variables. This limits the load and resistance values to only positive numbers. The next equation is used to calibrate the resistance factor using the FOSM method. It is dependent on the target reliability index and the ratio of dead to live load. (1+(C`OV[QD])2 + (COV[QL])2) D E[il AR QD + QL (1+(C`OV[R,]i)2 L qD fly-qln[(1+(COVR~~(CV[Ry]2)(+(COV[Q]2+CV[L) (E[ilQD]- + E[il, ]) -e In the 17th Street Bridge instead using it for to calibrate the resistance factor as a method, it was used for to account for differences or variability based on correlation lengths. The FOSM equation was used for to get Phi factor for different correlation length, but instead using a measured value it was used the deterministic value obtained from the same finite element program. It allows seeing the differences on the phi factor, based on spatial variability and reliability index. To account for spatial variability on the 17th Street Bridge, a total of forty End bearing values were predicted for five and twelve feet correlation length, and thirty values for the one foot length case. Additionally, the deterministic value was obtained using the same program. From the predicted and deterministic values at all the correlation length, the mean hP, Standard deviationoP, and coefficient of variation COVR, WeTO found for the design approach (Table 5-8). Using the computed mean, hP, and coefficient of variation COVR, for each correlation length, the LRFD resistance factor, 5, were determined for different values of reliability index, P. The results are shown in Table 5-9. Location nap CannumContinuum wijth method miumeeet Carinunnlo 1o t-fel Bousa n eierenR Bondary lement ~ ~ ~ ~ ~ ~ ~ la tomuIurdr nthiddr Figure 44 ueia prahst oe nEcvto naRc as(ig20) 2.50_ 1.50_ 200.000 180.000 160.000 140.000 120.000 100.000 80.000 40.000 20.000 0 + O g g? + O + ' l I I ' .50 1.50 2.50 Figure 4-5. WINTSLIB SGS Example Location Data Values. CB-3/1 1U 41' 8/21/2006 4.8380 2.3950 853.2 149.1 2.02 1.00 2U 4.4327 2.3835 740.4 142.6 1.86 1.01 3T 2.4345 2.3100 335.2 125.2 1.05 4T 2.4350 2.3785 375.0 132.0 1.02 5T 46' 2.3500 2.3730 409.9 150.2 0.99 CB-3/2 1T 46' 8/21/2006 2.4165 2.2995 308.4 117.1 1.05 2U 4.3357 2.3655 774.8 154.9 1.83 1.01 3T 8/22/2006 2.3220 2.3760 406.1 150.3 0.98 4LJ 4.8068 2.3820 806.8 143.5 2.02 1300 5T 2.3535 2.3720 400.6 146.7 0.99 6U 4.8825 2.3895 799.2 139.1 2.04 1300 7T 2.3395 2.3870 393.8 143.3 0.98 8U 51' 4.8715 2.3890 865.4 151.0 2.04 1.00 CB-3/3 1T 51' 8/22/2006 2.3315 2.3510 380.8 143.3 0.99 2U 4.8632 2.3610 838.4 150.0 2.06 1300 3T 2.4395 2.3110 376.5 140.2 1.06 4T 2.4330 2.3555 378.1 135.9 1.03 5U 4.8955 2.3430 734.4 132.5 2.09 1.00 6T 2.4855 2.3285 366.7 132.0 1.07 7T 2.4545 2.3375 328.7 118.9 1.D5 8U 4.8125 2.3360 672.7 124.2 2.06 1.00 9T 2.3865 2.3230 332.8 125.3 1.03 10T 2.1210 2.3185 291.7 124.1 0.91 11U 4.7020 2.3455 676.5 126.9 2.00 1.00 12T 56' 2.4110 2.3595 369.5 133.5 1.02 CB-3/4 1T 56' 8/25/2006 2.4285 2.3140 361.2 134.7 1.05 2T 2.4045 2.3495 360.4 131.7 1.02 3U 4.7600 2.3470 716.7 132.6 2.03 1.00 4T 2.3475 2.3350 351.6 133.2 1.01 5U 4.8043 2.3400 701.4 129.3 2.05 1.00 6U 4.8840 2.3575 697.0 124.5 2.07 1.00 7T 2.4785 2.3545 368.8 130.2 1.05 8T 61' 2.4740 2.3655 330.1 115.7 1.D5 CB-3/5 1T 61' 8/29/2006 2.3695 2.3380 291.2 109.1 1.01 2U 4.7328 2.3555 593.2 109.6 2.01 1300 3T 2.2640 2.3445 282.7 110.2 0.97 4U 4.7637 2.3380 606.0 112.9 2.04 1.00 5U 4.5473 2.3420 570.4 110.9 1.94 1.00 6U 4.7163 2.3305 605.3 114.6 2.02 1.00 7T 2.3420 2.5030 330.6 109.3 0.94 8U 4.7265 2.3425 626.8 117.2 2.02 1.00 9T 2.3560 2.3405 313.9 118.0 1.D1 10U 4.6853 2.3125 627.2 121.4 2.03 1.00 11U 4.6542 2.2635 600.2 122.1 2.06 1.00 12T 66' 2.5205 2.3035 313.7 113.8 1.09 CB-3/6 1T 66' 8/29/2006 2.3570 2.3525 329.7 122.6 1.00 2U 4.5855 2.3315 637.4 124.0 1.97 1.00 3T 2.4500 2.3325 331.8 120.7 1.05 4U 71' 4.7435 2.3535 651.6 120.3 2.02 1.00 Table B-2. Continued. APPENDIX F FLAC3D PROGRAMMING MODELS Table F-1. FLAC Results. 1 (feet) Cap .15(ton) Bias A 200 1.175 0.007300506 B 240 0.979167 0.012186026 C 235 1 0.008020456 D 220 1.068182 0.000456898 E 210 1.119048 0.000869697 F 200 1.175 0.007300506 G 285 0.824561 0.070222666 H 250 0.94 0.022367296 I ~225 1.044444 0=.002035143 J 265 0.886792 0.041113462 K 235 1 0.008020456 L 230 1.021739 0.004599263 LL 185 1.27027 0.032657286 L1 235 1 0.008020456 N 190 1.236842 0.021692902 10 230 1.021739 0.004599263 O 190 1.236842 0.021692902 P 190 1.236842 0.021692902 R 200 1.175 0.007300506 S 235 1 0.008020456 T 215 1.093023 1.20149E.-05 U 235 1 0.008020456 V 240 0.979167 0.012186026 VV 200 1.175 0.007300506 X 187.5 1.253333 0.026822687 Y 195 1.205128 0.013356703 Z 200 1.175 0.007300506 AA 190 1.236842 0.021692902 BB 220 1.068182 0.000456898 Determinis 235 Mean 1.089557 0.407317752 Standar 0.120611204 COV 0.110698 CB-2 Elevation vs. qu, qt,RQD,qb 160.00 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00 -40 -45 -50 -55 -60 -65 Elevation (ft) -* qu (tsf) -=- qt (tsf) -a- Recovery qb(tsf) (FDOT) -a quqt Figure 5-3. Fuller Warren Histogram CB2. CB-3 Elevation vs. qu, qt,RQD,qb 120.00 100.00 AA A 80.00 60.00 40.00 -35 -40 -45 -50 -55 -60 -65 -70 Elevation (ft) qb(tsf) (FDOT) -a- quqt -* qu (tsf) -e qt (tsf) -a Recovery Figure 5-4. Fuller Warren Histogram CB3. ACKNOWLEDGMENTS I would especially thank to my advisor, Dr. Ralph Ellis, for his generous time and commitment. His permanent conviction on my professional capacity during my doctoral work made this research a reality. Also, thanks to Dr. McVay for to share part of his geotechnical knowledge. Special thanks go to Dr. Guerly for his supervision and technical support on the stochastic world. I would like to acknowledge Dr. Horhota and the Florida Department of Transportation (FDOT) State Material Office for providing the funding and help for this research proj ect. Thanks also go to Farouque, Haki and Enrique who assisted me on different stages of the proj ect investigation. Covariance and correlogram There are two other tools used on describing spatial continuity these are the Covariance and Correlation function. Though these two are equally useful, the semivariogram however is the most traditional. Under the condition of second-order stationary (spatially constant mean and variance), the covariance function, correlogram, and semivariogram obey the following relationships: C(0) = Cov(Z(u),Z(u))= Var(Z(u)) p(h) = C(h) C(0) Y (h)= C(0)-C(h) In words, the lag-zero covariance should be equal to the global variance of the variable under consideration; the correlogram should look like the covariance function scaled by the variance, and the semivariogram should look like the covariance function turned upside down. The representation is showed in Figure 4-3. Unlike time series analysts, who prefer to work with either the covariance function or the correlogram, geostatisticians typically work with the semivariogram. This is primarily because the semivariogram, which averages squared differences of the variable, tends to filter the influence of a spatially varying mean. Kriging Kriging technique was named after a South African mining engineer named Daniel Gerhardus Krige who develops the method in an attempt to more accurately predict ore reserves. Kriging is a group of geostatistical techniques to interpolate the value Z(xo) of a random Hield Z(x) (e.g. the elevation Z of the landscape as a function of the geographic location x) at an unobserved location xo from observations Zi Z(i)l i Ir 1 of the random Hield at and for the horizontal direction was 12 feet. Also a nugget effect of 0.3 was used on both directions. Each random field, while having the same semivariogram parameters, will have quite different spatial pattern of cohesion values, due to the dissimilar seed used, and hence a different value of bearing capacity. The software used on the random field, based on semivariogram parameters, calculation was the WINTGSLIB, and a different seed was used in each calculation. Examples of the random field and summary tables are founded in APPENDIX E. On these tables is showed the statistics of the results obtained using different seed values, like mean, standard deviation, etc. It is noticed that having the same parameter, but with different seed, the final results will change. 17th Street Bridge Finite Elements Analysis The load-deflection response of a single concrete pile foundation is calculated for loading in the axial direction. The pile is three feet diameter by twenty feet of length embedded in limestone rock layer. The properties of the concrete pile and the limestone that are kept constant are showed in Table. 5-5. As it was described on CHAPTER 4 the software used for the modeling procedure was FLAC3D. A modified example founded on the FLAC3D manual was used as support of the current model. The soil block model used to simulate our specimen was introduced in the computer program with the following parameter: the coordinates axes were localized on the lower left corner and the z-axis oriented along the pile axis and upward. The top of the model, at z=40 feet is free surface. The base of the model, at z=0, is fixed in the z direction, and roller boundaries are imposed on the sides of the model, at x=30 feet and y=30 feet (see Figure 5-12).The finite element mesh consists of square elements of equal size (1.5 x 1.5 x 2.0 feet). Each element has its own properties, cohesion, bulk, shear and Young modulus. Where vi is a load factor applied to load components Qi and $ is resistance factor applied to the resistance (measured of load carrying capacity) Rn In words it equation says that the capacity of the foundation (modified by the factor 4) must be larger than the total effect of all the loads acting on it. The mention above design formulas are developed by code committees with input from practicing engineers, researchers, and scientists. However, things are changing and there are new requirements that need to be satisfied, for example moving toward larger single shaft construction. New rules are required, for example "field coring of rock at the location of the as built non-redundant shaft" (FDOT Structures Bulletin, 2005). Similar to cycles, new requirement results could improve the formulas over again. The goal of load and resistance factor design (LRFD) analysis is to develop factors that decrease the nominal resistance to give a design with an acceptable and consistent probability of failure. To accomplish this, an equation that incorporates and relates together all of the variables that affect the potential for failure of the structure, must be developed for each limit state. The parameters of load and resistance are considered as random variables, with the variation modeled using the available statistical data. A random variable is a parameter that can take different values that are not predictable. An example is compressive strength of the soil, qu that can be determined using a testing machine. There are three levels of probabilistic design: Levels I, II, and III (Withiam et al. 1998; Nowak and Collins 2000). The Level I method is the least accurate. It is sufficient here to point out that only Level III is a fully probabilistic method. Level III requires complex statistical data beyond what is generally available in geotechnical and structural engineering practice. Level II and Level I probabilistic methods are more viable approaches for geotechnical and structural ~Varogram plot 2 50 2 00 S1.50 1.00 50 .00 .) 10.0 Figure 5-10. 17th Street Semivariogram. r`i 20.0 30.0 40.0 Distance regarding the magnitude of the load and resistance factor selected for a given limit state must consider the adequacy of the data. If the adequacy of the input data is questionable, the final load and resistance factor combination selected should be more heavily weighted toward a level of safety that is consistent with past successful design practice, using the reliability theory results to increase coming as to whether or not past practice is conservative or nonconservative exists (Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design 2005). Current assessment of drilled shaft skin and tip resistance is performed on laboratory rock core samples (unconfined compression, split tension, and intact Young's Modulus) recovered from a site. Generally, all the samples are averaged over the whole site using either a log normal distribution or arithmetic mean throwing out one standard deviation above and below. Unfortunately, these methods don't account for spatial variability of strength and voids, i.e. recoveries at a specific locale, which is important for end bearing for a particular shaft. For this stage a probabilistic approach (Monte Carlo, Bayesian etc.) will be developed to identify the local strength, recovery, etc. for a specific shaft (i.e. use data near location) as well as for the whole site. From the specific locale data, LRFD resistance factors, 4, may be determined for end bearing based. The LRFD resistance factors, 4, for end bearing will also be determined using the geometric mean (lognormal) from the whole site as well. The FDOT online Internet Foundation Database (e.g. Osterberg, Statnamic results) has sufficient laboratory data to determine LRFD resistance factors,$, for end bearing on a site basis, but not for a specific location within a site. Additionally, there are many methods have been developed to calibrate the LRFD resistance factors using statistical data. FOSM (First Order Second Moment) is popular because it does not require a computer program to find the results. FORM (First Order Reliability Method) is more complicated that FOSM and iterates to find a solution. Each of these methods results in a different set of resistance factors. The one used on this research was the FOSM. checks presented in this paper are simple, flexible, and can be easily implemented in other industries. Bearing Capacity of a Rough Rigid Strip Footing on Cohesive Soil-a Probabilistic Study The paper indicates the use of a probabilistic study on the bearing capacity of a rough rigid strip footing on a cohesive soil. The first step on this paper was to use statistics help for to create random Hield model. The parameters used for this purpose were Young modulus E, Poison ratio and undrained shear strength. The first two were held constant and the shear strength is modeled as a random variable. It is assumed to be characterized by a lognormal distribution. And this information was used for to get the spatial correlation function and the correlation coefficient length needed for to generate random fields. After getting the random fields a finite element method was used for to recreated the footing and get the bearing capacity of it. The researcher of this paper was not working with real data if not with assumed statistical properties (our case is using real field data). The last stage of this paper was the Monte Carlo simulation for each set of assumed statistical properties. Each realization, while having the same underlying statistics, had fairly different spatial pattern of shear strength values beneath the footing and hence, a different value of bearing capacity. Our research followed a very similar procedure that the used on this investigation paper, but the differences are that this paper did all the analysis based on assumed statistical properties and our research are real soil properties obtained from the field and instead using a strip footing our is thirty two length drilled shaft. This paper was very helpful in the description of their procedure and the results obtained. Additionally to these papers mentioned are about twenty to thirty more that made contributions to the investigations, the most relevant are, "Observations on Geotechnical reliability-based design development in North America", "Spatial Trends in Rock Strength-can they be Determined from core holes?", and "Drilled Shaft Design for Transmission structures When QN is larger then RN, g() is negative. Therefore, failure can be defined as when g() is less then or equal to zero. However, FOSM assumes that the load and resistance random variables are lognormal random variables, this limits the load and resistance values to only positive numbers. Now considering the relationship between a normally distributed random variable RN, and a lognormal random variable R, R = eRN (1-7) In (R) = R, Writing the g(R,Q) equation in terms of lognormal random variables yields, g(R, Q) = In(R) -InQ) = In R (1-8) This equation is equivalent to the first definition of g(R,Q). When R is less then Q g() will still be negative. The g(R,Q) function is a random variable. G = g(R, Q) = Ini~ (1-9) Yet, R/Q is a lognormal random variable. Therefore the distribution of In(R/Q) is normal. This results in the random variable G having a normal distribution. Reliability index The reliability index (P) is defined as the mean value of G (E[G]) divided by the lognormal standard deviation of G (r(G). E[G] P = (1-10) CG As previously defined, G= In(R) In() (1-11) Table B-2. Continued. Prject Number: CB-3 Location: Fuller Warren Lb Number: Date Received: 8/10/2006 Bridge Number: Tested by: JC LIMS Number: BORING SAMP w DRY MAX ST q (u) DISPL @~ STRAIN %RECO TARE WET DRY NO UNIT WT LOAD STRENGTH FAIL @a FAIL WT WT WT CORE (%~) (pcf) (1bs) (psl) (psl) (In) (%) % RQD (g) (g) (g) CB-3/1 1U 5 32 141 6 6782 1505 6 0 0522 1 08 72/50 430 3 1281 5 1238 5 2U 11 14 128 3 3530 784 1 0 0634 1 43 430 7 1168 7 1094 7 3T 26 01 99 3 368 41 6 00633 366 1 698 4 629 8 4T 16 40 113 4 1378 151 5 0 0687 431 4 805 4 752 7 5T 907 137 8 3224 368 0 00515 428 3 837 2 803 2 CB-312 1T 26 50 92 5 204 23 4 0 0743 77/67 428 1 735 5 671 1 2U 746 144 2 5720 1287 5 00549 1 27 430 2 1196 6 1143 4 3T 8 10 139 0 1552 179 0 00415 430 3 835 8 805 4 4U 11 63 128 5 3252 729 8 0 0541 1 13 431 4 1237 8 1153 8 5T 10 86 132 4 1623 185 1 0 0468 371 5 771 6 732 4 6U 13 79 122 2 4229 943 0 0 0563 1 15 433 1 1230 0 1133 4 7T 11 05 129 0 1715 195 5 00419 312 1 703 9 664 9 8U 8 31 139 4 5690 1269 3 0 0454 0 93 375 9 1239 0 1172 8 CB-313 1T 9 56 130 8 379 44 0 0 0410 100/92 366 0 746 4 713 2 2U 871 138 0 3187 727 9 00630 130 370 8 1207 2 1140 2 3T 454 134 1 120 135 00237 370 6 746 2 729 9 4T 14 37 1188 243 27 0 00276 425 7 802 9 755 5 5U 18 48 111 9 501 116 1 0 0297 0 61 430 6 1164 0 1049 6 6T 19 11 110 8 169 18 6 0 0236 424 6 790 5 731 8 7T 28 86 92 3 88 97 00209 430 4 758 6 685 1 8U 27 47 97 5 731 170 5 0 0455 0 95 302 8 972 4 828 1 9T 24 01 101 1 287 32 9 00422 425 0 756 6 692 4 10T 23 05 100 8 93 12 1 0 0402 410 1 701 0 646 5 11U 23 97 102 3 433 100 3 0 0348 0 74 428 2 1103 6 973 0 12T 17 63 1135 437 48 9 00324 428 4 797 4 742 1 CB-3/4 1T 19 83 112 4 159 18 0 0 0444 85/60 371 3 730 3 670 9 2T 19 85 109 9 361 40 6 00204 377 9 737 8 678 2 3U 20 45 110 1 1627 376 0 0 0503 1 06 304 2 1019 9 898 4 4T 21 49 109 7 328 38 1 0 0311 435 2 786 3 724 2 5U 24 66 103 7 1185 275 5 0 0551 1 15 370 7 1070 4 932 6U 26 73 98 3 873 199 9 0 0708 1 45 419 1113 1 966 7 7T 25 87 103 4 223 24 3 00379 375 9 743 7 668 1 8T 37 81 83 9 181 197 00368 366 695 5 605 1 CB-315 1T 40 81 77 4 131 15 1 0 0392 100/100 366 0 656 5 572 3 2U 41 51 77 4 550 126 2 00528 1 12 371 4 963 6 789 9 3T 40 60 78 4 101 12 1 00494 375 9 657 8 576 4 4U 38 32 81 6 556 129 5 0 0669 1 40 435 3 1039 9 872 4 5U 39 91 79 3 594 137 3 00557 1 22 4190 988 0 825 7 6U 34 81 85 0 581 136 1 00575 1 22 304 2 908 0 752 1 7T 30 13 84 0 175 190 00442 370 6 699 3 623 2 8U 29 44 90 6 485 112 5 0 0492 1 04 377 9 1002 2 860 2 9T 32 05 89 3 159 18 4 0 0365 427 2 740 3 664 3 10U 26 49 96 0 344 81 9 0 0398 0 85 375 3 1001 3 870 2 11U 26 54 96 5 221 55 0 0 0319 0 69 433 0 1032 3 906 6 12T 28 11 88 8 51 5 6 0 0220 371 5 684 6 615 9 CB-3/6 1T 20 39 101 8 98 11 2 0 0234 58/45 431 4 760 8 705 0 2U 21 02 102 5 356 83 1 0 0437 0 95 428 5 1064 8 954 3 3T 24 32 97 1 86 95 00405 428 2 759 4 694 6 4U 24 31 96 8 486 111 7 0 0488 1 03 430 4 1080 9 953 7 0 50 100 RQD FullerWarrenMEAN= 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 SKEW = 1.4909 1.9667 -0.2355 KURT = 4.3762 6.4417 1.9256 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP= 28.4992 4.7548 25.2514 SKPDFEXP = 1.4166 1.8230 1.5131 KUPDFEXP = 4.7127 6.9671 3.7210 MNPDFLOG= 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 SKPDFLOG = 1.8682 2.5286 1.2478 KUPDFLOG = 6.5454 10.3575 2.8813 MNPDFGAM= 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 SKPDFGAM = 1.3825 1.9486 1.0286 KUPDFGAM= 4.6979 7.1993 2.6588 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN= 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 0.04 0.03 0.02 0.01 0 50 100 15 10 20 qt 30 40 0.03 Figure D-5. Fuller Warren Bridge New Borings. corresponds to the use of a specific 5 factor. The complete sets of results are presented in Table 6-5 and Table 6-6. Drilled Shaft Excavation The same procedure followed on the Drilled Shaft Construction Cost section was followed for the Drilled Shaft Excavation. The cost analysis for the excavation item is also based on a one foot length by four feet diameter drilled shaft on lime rock. This excavation cost is $173.92 per linear feet. The complete set of cost results are presented in Table 6-7, and Table 6-8. Boring Test Cost This analysis was based on the influence of number of soil borings around the drilled shaft. The average of the Drilled Shaft construction cost, Excavation, and soil lab test cost presented in Table 6-2 to Table 6-4 are shown in Table 6-9. The total construction cost assuming just one soil boring test was $267.97 per linear feet, the excavation $173.92 and the laboratory soil test costs $24.5 per linear feet. The average auger cost of $30.63 per linear feet was obtained from FDOT District 4 (Table 6-9). The total is $497.02 per linear feet assuming one soil boring per drilled shaft. Under the same circumstances but assuming five soil borings around the drilled shaft, the total cost per linear feet was $717.54 per linear feet (Table 6-10). The difference was $220.52 per linear feet. If the drilled shaft is 20 feet long as the 17th Street Bridge case, the differences will result on $4,410.4. RN = r, AR E[R,]i= r, -E[ilR] (1-16) r=E [R, ] "E[ AR] E [ AR >2 C q (1-17) E [R, ] E[RN] is the expected value of the normally distributed resistance random variable. The next step involves solving the reliability index equation previously derived (equation 1-14) for the E[RN] term. E:[Q, ]- eP'.`Iln[(1+(r,~CO~V[R]))(+(OVQg) E [R, ] = (1-18) (1+(COV[Q, ])2) (1 +(CO V[R, ]) 2 This is then substituted into the fundamental LRFD equitation . (1+(COV[Q, ])2) E [~] ARr, (1+(COV[R, ])2 2 ~= (1-19) E[Q), ]- esO.41n~'-C~I[("'1+(COV[Ry])~2)1(O[]2 NHI 1998 represents the coefficient of variation of the load as, (COV[Q])2 = (COV[QD])2 +(COV[QL])2 (1-20) and rewriting this equation for dead and live loads yields, (1+(COV[QD])2 + (COV[QL])2) E[il AR QD Dy Q L,+y,q (1 +(CO V[R, ]) 2 ~= (1-21) E:[Q, ]- eP'.`Iln[~l~~~(1+j(CO[)2(+CV[D)+CO[L) With, APPENDIX D FREQUENCY DISTRIBUTIONS 0 02 0 00500 550 56 610 620 630 Figure D-1. Total Capacity Frequency Distribution 5 feet Correlation Length 520 540 560 580 600 620 640 Figure D-2. Total Capacity Frequency Distribution 12 feet Correlation Length 131 Table C-2. Fuller Warren Bridge Processed Soil Boring Data. CB-1 (New) 30 EL. (ft) qu (tsf) qt (tsf) Recovery quqt(tsf) Ei (psi) -40.5 15.36 31.21 67 10.95 20725.93 -42.5 96.14 2.14 67 7.18 93362.29 -45.5 143.30 9.07 94 18.02 108694.81 -46.5 59.24 7.21 94 10.34 20329.10 -47.5 52.29 15.85 94 14.40 50938.20 -48.5 68.09 18.33 94 17.67 87522.73 -50.5 113.41 18.62 60 22.97 143167.10 -55.5 12.56 1.37 92 2.07 16123.94 -56.5 22.01 0.91 92 2.24 33646.94 -57.5 22.92 2.58 92 3.85 28351.18 -58.5 11.89 1.77 92 2.29 13580.10 -60.5 7.08 1.05 90 1.37 6509.45 -61.5 7.36 0.66 90 1.10 8173.66 -62.5 8.59 0.25 90 0.73 10247.30 -63.5 7.57 1.05 90 1.41 11768.07 -65.5 3.02 0.40 58 0.55 3832.10 CB-2 (New) 25 EL. ft uts) t(tf Reoey utts) Ei(si -37.58 42.57 25.23 25 16.39 48974.00 -42.58 18.66 3.54 68 4.06 30083.74 -43.58 56.42 1.76 68 4.98 75668.97 -47.58 64.77 18.36 90 17.24 81 523.95 -48.58 65.12 8.41 90 11.70 75899.59 -49.58 37.24 8.51 90 8.90 38959.02 -50.58 140.06 10.11 90 18.82 152082.74 -51.58 8.29 1.91 90 1.99 15682.83 -52 78.44 0.84 90 4.05 69402.72 -52.58 15.68 5.49 98 4.64 24923.43 -53.58 10.61 1.82 98 2.20 14642.92 -54.58 9.08 1.28 98 1.71 13980.61 -55.58 18.88 1.90 98 2.99 21191.30 -56.58 20.99 1.40 98 2.71 20221.36 -57 16.81 1.36 98 2.39 21522.93 -57.58 16.72 1.77 80 2.72 26059.97 -62.58 11.08 1.14 77 1.78 11334.53 -63.58 9.44 1.44 77 1.84 12460.26 -64.58 9.59 1.24 77 1.72 13170.90 -65.58 10.08 0.97 77 1.56 14308.84 -66.58 7.49 0.42 77 0.89 15724.97 CB-3 (New) 15 EL. (t qu(s) q(tf Reoey qqts) Ei(pi -41 108.40 3.00 72 9.01 139525.37 -42 56.45 10.91 72 12.41 55345.75 -46 92.70 1.69 77 6.25 102818.36 -47 52.55 12.89 77 13.01 64868.52 -48 67.90 13.33 77 15.04 81761.47 -49 91.39 14.08 77 17.93 136076.85 -51 52.41 3.17 100 6.44 56192.28 -52 8.36 0.97 100 1.42 19141.58 -53 12.28 1.94 100 2.44 18051.95 -54 7.22 1.34 100 1.55 13564.22 -56 27.07 1.30 85 2.97 35561.05 -57 19.84 2.93 85 3.81 24011.06 -58 14.39 2.74 85 3.14 13791.05 -61 9.09 1.09 100 1.57 11308.89 -62 9.33 0.87 100 1.42 9220.15 -63 9.89 1.37 100 1.84 11249.80 -64 9.80 1.32 100 1.80 11165.85 -65 8.10 0.40 100 0.90 10801.59 -66 5.99 0.81 58 1.10 8732.30 -67 8.04 0.69 58 1.18 10850.17 Table E-1. 17th Street Bridge SGS feetet. A PSF PSF PSF Mean 42503.73487 Standard Error 223.6157448 Median 39001.786 Mode 49700 Standard Deviation 21519.45762 Sample Variance 463087056.4 Kurtosis -0.581050641 Skewness 0.497640383 Range 99866.79713 Minimum 117.150872 Maximum 99983.948 Sum 393627088.6 Count 9261 PSF Mean 42557.4383 Standard Error 220.0553434 Median 39532.284 Mode 11399.9996 Standard Deviation 21176.82563 Sample Variance 448457943.8 Kurtosis -0.580991141 Skewness 0.47042905 Range 98897.99504 Minimum 862.72496 Maximum 99760.72 Sum 394124436.1 Count 9261 APPENDIX E SGS RANDOM FIELD TABLES Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 42562.48642 219.7863813 39538.838 38500 21150.94231 447362360.5 -0.507237829 0.48869983 99365.73316 598.72084 99964.454 394171186.8 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 42658.43886 221.5141441 39514.378 41800 21317.21199 454423526.9 -0.568971001 0.480259697 98794.59432 1077.72768 99872.322 395059802.3 9261 Table 3-2. 17th Street Bridge Soil Boring Data (State Project No. 86180-1522). BB-1 (32+93) S-4 (33+00) EL (ft) qu REC 30 67 RQD 22 28 EL (ft) qu -32 211.2 -36 116.9 REC 68.3 19.4 RQD qt REC RQD REC RQD qt 32.2 27.34 -65 -72 -85 114.2 13 BB-4 (34+81) EL (ft) qu REC -69 32.74 22 -88 28.8 35 BB-9 (35+06) REC RQD EL (ft) qu REC -115 -131 -131 BB-7 (35+44) REC RQD EL (ft) qu REC -49 -65 414 20 -72 37.8 -82 120.8 98 -82 -92 82.98 98 -102 -108 82.44 35 -131 140.6 35 -131 BB-8 (36+10) REC RQD EL (ft) qu REC 38 35 -39 361.3 6 38 38 -46 158.7 48 38 35 -46 272.7 48 RQD qt 5 10 RQD qt 26.5 24.63 32.9 REC 5 43 43 RQD S-12 (35+29) EL (ft) Qu -32 211 -32 -49 117 -49 -72 REC RQD qt RQD qt REC RQD 43.5 18 4 38 26.3 98 38 68.34 19.4 19.6 117.47 66 64.6 35 10 BB-11 EL@ (t -36 (35+53) qu REC 379.4 38 RQD 35 33 60 RQD qt 5 19 55 19 53.99 76.78 12 40.4 14.04 REC RQD qt 143.97 189.01 112.6 26.3 68.7 48 48 48 50 17 -46 23 -56 285.0 50 -95 27.04 140.01 with R and Q being lognormal random variables. This yield, E[G] = E[1n(R)] E[1n(Q)] E [R, ] E[Q, ] E[G=ln1J+(COV[Rhi])2 n-1+(COV[Q,])22 E[G]= In ER J+ CI[(,) (1-12) E[Q, ] J1+(COV[R,])2 With RN and QN being normally distributed, so that E[RN] and E[QN] are the normal means. The coefficients of variation are also calculated using the normal means and normal standard deviations. icG = In[(1+(OIR.~)(1+V[R'T,])2)1+CO[Q])). (1-13) This results in the reliability index being defined as: E[R, ] J1+(C'OV[Q,])2 E[Q, ] 1+(C'OV[R,])2] P = (1-14) IJn[(1+ (CIOV[RI, ]:)2)(1+ (CO V[Q,]) Solving for the resistance factor The following derivation for the resistance factor is based largely on NHI 1998. Solving for the resistance factor begins with the fundamental LRFD equation. 95 r,' > r 9, (1 15) In this equation rn stands for the nominal resistance. Solving for the resistance factor and plugging in the bias yields: 45!i-122- AA Notes Detailed Related Ite~ms Forms Dorcumentatioln UNCLASSIFIED SHAFT EXCAVATION Unit LF; M1 Accuracy Linear Foot; 10th of a Mrleter PlanQuantity? no Intended for the excavation of the drilled shafts Pay Item 40F-88-XAA is required with this Item. Quantity is the depth of excavated hole from ground elevation to tip of shaft. Required 455- 88-AA Recommended Design SHTab~uant COMP 700-050-03 Construction Refer to I:comp Book Design Locate in plans. Summarize quantities by location on tabulation of quantities sheet in the plans, or detail calculations in the computation book. Construction Record -fiinal quantity on the talbulation sheet (plans) or computation "form Compp book). References PPMA Chapter Other SDG's 3.6i Standards Specifications Prep & Doc Manual Chapter(s) 6, 7, 13 Status Struct. 4i56-122- AA UNCLASSIFIED SHAFT EXCAVATION AA = '1 (24'" Diameter ) 2 (30'" Diameter ) 3 (36"" Diameter.) 4 (42'" Diameter.) 5 (48"" Diameter.) 16 (60'" Diameter.) 7 (72'" Diameter.) 8 (54"" Diameter ) Figure 6-2. FDOT Basis of Estimates Handbook Description for the Item 455 122 "Unclassified Shaft Excavation". DEVELOPMENT OF A RATIONAL DESIGN APPROACH (LRFD phi) FOR DRILLED SHAFTS CONSIDERING REDUNDANCY, SPATIAL VARIABILITY, AND TESTING COST by JOHANNA KARINA OTERO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 there is a strong need to assess the LRFD resistance factors, 4, for shaft design, e.g. end bearing, based on the frequency distribution of strengths, recoveries and compressibility data for the whole site vs. a specific location, especially for non-redundant shafts. In addition, there is the question as to the number of cores, samples etc. to ensure a specific reliability. Fortunately, a probabilistic based LRFD resistance factor assessment answers the latter questions. For instance, using a Monte Carlo or Bayesian theory, strength, compressibility, etc., statistical (mean, standard deviation, etc.) properties for a specific shaft or for the whole site may be generated from core and laboratory data near a specific shaft or over the whole site. Using random sampling, kriging, Sequential Gaussian simulation, end bearing, etc. may be computed for a specific shaft or for all the shafts on the site. It is expected that the difference in LRFD resistance factors for end bearing will be significant different if applied at a specific location vs. the whole site. Obj ectives 1. To estimate the influence of the spatial variability of a site on the selection of Load Resistance Factor Design. 2. To assess the resistance factors, 4, for drilled shaft design applying the modified FOSM (First Order Second Moment), based on the frequency distribution of strengths, recoveries, compressibility data and spatial variability. 3. To calculate testing cost and compare those against the final shaft built cost. This comparison will be done by assuming spatial variability testing influences. Methods The method used in this research was the Empirical. It explains the data collected through the development of a model that hypothesizes about the relationship between the data and relevant variables of the environment. The empirical research is grounded in reality rather than in CHAPTER 4 GEOSTATISTICS AND NUMERICAL MODEL Geostatistics Geostatistics were first developed to provide better estimates of ore reserves. In coal mining, they have been used to evaluate energy content, sulfur, ash, and other quality attributes of deposits. In fact, Geostatistics can be used to study many properties that vary in space, but are measured at distinct locations. Field Researches as diverse as hydrology, forestry, air pollution, and global warming have all made extensive use of Geostatistics. (Ledvina et al., 1994; Armstrong, 1998). The Geostatistics term has been used amply in mining design but just a few of times in geotechnical. Since it will be not a clear word, let me recall two definitions: "Geostatistics: study of phenomena that vary in space and/or time" (Deutsch, 2002) and "Geostatistics offers a way of describing the spatial continuity of natural phenomena and provides adaptations of classical regression techniques to take advantage of this continuity." (Isaaks and Srivastava, 1989). Geostatistics deals with spatially auto correlated data. It is data that has correlation between elements of a random variable separated from them by a given interval. The basic idea of Geostatistics is this. Suppose the goal is to determine the cohesion in a limestone field. If two core holes are drilled just 1 ft apart from each other, one would expect that their cohesion values would be very similar. If a third hole is drilled 10 ft away, the cohesion value might be expected to change a little, but still be close the original value. As more holes are drilled further and further away, a distance is eventually reached where the first holes no longer help predict the cohesion value. Between the basic elements of Geostatistics are: *(Semi) variogram analysis characterization of spatial correlation. 8/1 1T 52.0 2.1765 2.3665 290.2 115.5 0.92 2U 3.9035 2.3900 669.1 145.6 1.63 1.03 3T 2.3245 2.3913 249.4 91.0 0.97 4U 4.3995 2.3833 494.8 96.0 1.85 1.01 6U 4.4095 2.3905 745.8 143.6 1.84 1.01 7T 1.5920 2.3745 233.4 126.1 0.67 8U 57.0 3.8605 2.3753 560.6 124.8 1.63 1.03 8/2 1T 57.0 2.3260 2.3933 357.7 130.2 0.97 2U 4.5345 2.3895 712.2 133.4 1.90 1.01 3T 2.0255 2.3955 316.4 132.0 0.85 4U 4.0815 2.3973 631.0 130.5 1.70 1.02 5T 2.3285 2.4045 344.4 124.1 0.97 6U 62.0 4.0865 2.3912 570.2 118.4 1.71 1.02 8/3 1U 62.0 4.4460 2.3633 510.1 99.6 1.88 1.01 2T 2.0945 2.3863 259.6 105.6 0.88 3T 2.3430 2.3708 262.8 96.8 0.99 4T 2.3025 2.3858 254.1 94.0 0.97 5T 1.8790 2.3665 313.8 144.6 0.79 6U 4.7045 2.3860 852.5 154.4 1.97 1.00 7T 2.2252 2.3870 405.1 155.0 0.93 8U 4.3420 2.3868 789.6 154.8 1.82 1.01 9T 2.4615 2.3933 432.8 148.9 1.03 10U 4.71 55 2.3927 801.4 144.0 1.97 1.00 11T 67.0 2.0520 2.3777 327.5 136.9 0.86 8/4 1U 67.0 4.51 65 2.3643 761.0 146.2 1.91 1.01 3T 2.3610 2.3775 283.3 103.0 0.99 4T 2.1220 2.3710 253.2 103.0 0.89 5U 5.0405 2.3805 576.3 97.9 2.12 1.00 6T 72.0 2.0905 2.3848 250.7 102.3 0.88 8/5 1U 72.0 3.9240 2.3735 700.6 153.7 1.65 1.03 2T 2.0870 2.3748 327.2 134.8 0.88 4U 4.2615 2.3708 731.2 148.1 1.80 1.01 5U 4.71 25 2.3745 826.9 151.0 1.98 1.00 6T 1.8625 2.3745 301.7 139.4 0.78 7T 2.1330 2.3822 341.4 136.8 0.90 8U 77.0 3.7315 2.3673 659.3 152.9 1.58 1.03 8/6 77.0 82.0 NA 8/7 1T 82.0 87.0 2.2285 2.3755 406.0 156.6 0.94 8/8 87.0 92.0 NA Table B-1. Continued. 0.8 V10.4 e.2 'r Nugget 0.0 0 2000 Figure 4-1. Semivariogram Model. Linear 4000 6000 8000 Lag (meters) 10000 QClausia Figure 4-2. Most popular Semivariogram Models. *Simple Kriging Error The kriging error is given by: whc lastote eealzd es squares vers=iono h as-Mro hoe (Chiles&Delfine 1999 p. 159) aeweightleads lithnear combin lastio sqae ro of the aviabedaa i s "nbased" sine i ries ohv R ofteerr.Tedsigihfaueoordinary krgng sit imo inmzigte ro variance. In ordinary kriging, it is used a probability model in which the bias and the error variance can both be calculated and then choose weights for the nearby samples that ensure that the average error for our model, mR, iS exactly cero and that our modeled error variance,GR, iS minimized. Table 2-1. LRFD $ Factors, Probability of Failure (Pf) and Fs Based on Reliability $ for Nearest Boring Approach (FDOT & UF 2003). Reliability, P LRFD $ Pc (%) Factor of Safety 2.0 0.86 8.5 1.65 2.5 0.71 1.0 1.98 3.0 0.60 0.1 2.37 3.5 0.50 0.01 2.84 4.0 0.42 0.002 3.40 4.5 0.35 0.0002 4.07 Table 2-2. LRFD $ Factors, Probability of Failure (Pf) and Fs Based on Reliability $ for Random Selection (FDOT & UF 2003). Reliability, P LRFD $ Pc (%) Factor of Safety 2.0 0.56 8.5 2.60 2.5 0.43 1.0 3.32 3.0 0.33 0.1 4.24 3.5 0.26 0.01 5.42 4.0 0.21 0.002 6.92 4.5 0.16 0.0002 8.84 CB-4 (e)CB-5 (e)CB-6(Nw EL. (f) q tf u(s)qq~s) Ei (s) EL. (f) q tf u(s)qq~s) Ei (s) EL. (f) q tf u(s)q~s) Ei(si -52 10.69 53.38 11.94 80829.45 -52 10.98 127.23 18.69 123700.43 -52 16.97 47.39 14.18 174256.09 -53 12.12 86.06 16.15 112508.32 -53 29.82 127.23 30.80 123700.43 -53 25.84 47.39 17.50 174256.09 -54 3.24 121.92 9.95 152060.87 -54 6.25 60.55 9.73 81116.67 -54 29.55 91.31 25.97 180288.98 -55 3.24 71.23 7.60 128709.26 -56 24.65 50.99 17.73 130425.71 -54.5 16.97 40.15 13.05 75248.87 -56 20.11 124.77 25.05 133386.84 -57 12.89 33.58 10.40 261 797.27 -55 20.36 53.19 16.46 116133.00 -57 15.83 101.05 20.00 143472.97 -58 25.35 158.50 31.70 137071.11 -56 6.49 53.19 9.29 116133.00 -57.5 10.83 31.61 9.25 54116.25 -60 13.13 45.58 12.23 46711.83 -57 25.86 67.42 20.88 20587.29 -58 9.27 31.61 8.56 54116.25 -60 15.12 61.29 15.22 24748.90 -59 14.85 67.42 15.82 20587.29 -59 25.47 32.74 14.44 50258.73 -62 9.84 154.63 19.50 166002.00 -60 7.23 67.42 11.04 20587.29 -60 18.21 32.74 12.21 50258.73 -64 31.34 154.63 34.81 166002.00 -60.5 49.11 59.45 27.02 124443.40 -61 20.27 51.23 16.11 61906.50 -65 8.60 154.63 18.23 166002.00 -61.5 17.78 59.45 16.25 124443.40 -62 13.24 104.18 18.57 107548.83 -66 20.18 154.63 27.93 166002.00 -62 19.28 59.45 16.93 124443.40 -65 10.37 153.71 19.96 167965.36 -67 10.89 84.19 15.14 92242.77 -62.5 12.71 153.46 22.09 59292.48 -66 6.57 40.89 8.20 115282.48 -69 4.58 84.19 9.82 92242.77 -63 12.71 74.55 15.39 115316.42 -67 23.23 40.89 15.41 115282.48 -72 2.95 84.19 7.88 92242.77 -64 8.17 31.69 8.04 92628.95 -68 12.93 24.60 8.92 35563.47 -73 22.33 84.19 21.68 92242.77 -65 9.02 39.95 9.49 6111.94 -69 14.81 17.22 7.99 491 75.58 -74 7.20 170.37 17.52 203698.80 -66 11.00 30.02 9.08 60825.36 -70 7.60 17.22 5.72 491 75.58 -75 23.86 51.98 17.61 130769.50 -67 9.18 20.85 6.92 6020.61 -72 11.28 17.22 6.97 491 75.58 -76 20.57 67.79 18.67 8941 0.93 -69 10.90 17.33 6.87 17687.90 -77 26.83 85.80 23.99 116801.38 -71 9.74 17.33 6.50 17687.90 -78 26.83 135.18 30.11 163096.18 -72 14.80 100.35 19.27 136894.81 -80 32.97 157.99 36.09 158144.06 -73 36.71 102.86 30.72 201 41 9.69 -85 44.07 149.30 40.56 159257.64 -75 18.17 37.05 12.97 41673.40 -78 42.72 56.08 24.47 105885.43 -82 34.96 56.08 22.14 105885.43 APPENDIX C SOIL BORING INFORMATION PROCESSED Table C-1. 17th Street Bridge Processed Soil Boring Data. 20.57 105.35 23.28 122375.591 -70 17.33 5.70 17687.90 11.78 43.09 11.26 27136.26 50 100 1 qu (tsf) MEAN= 1.0e+004 0.0033 0.0005 4.0354 STD = 1.0e+004 0.0036 0.0007 4.1662 SKEW = 1.4909 1.9667 1.5006 KURT = 4.3762 6.4417 4.2151 MNPDFEXP = 1.0e+004 0.0031 0.0005 3.6832 STDPDFEXP= 1.0e+004 0.0028 0.0005 3.3610 SKPDFEXP = 1.4166 1.8230 1.3552 KUPDFEXP = 4.7127 6.9671 4.4338 MNPDFLOG = 1.0e+004 0.0028 0.0004 3.3867 STDPDFLOG= 1.0e+004 0.0026 0.0005 2.9839 SKPDFLOG = 1.8682 2.5286 1.7647 KUPDFLOG = 6.5454 10.3575 6.1003 MNPDFGAM= 1.0e+004 0.0031 0.0005 3.8192 STDPDFGAM = 1.0e+004 0.0028 0.0005 3.2012 SKPDFGAM = 1.3825 1.9486 1.2998 KUPDF GAM = 4.6979 7.1993 4.4234 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN= 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 0.04 0.03 0.02 0.01 x 10-s 0 10 20 qt (tsf) 30 40 O 0.5 1 Ei (psi) 1.5 2 x 105 Figure D-7. 17th Street Bridge New Borings. TABLE OF CONTENTS page ACKNOWLEDGMENTS .............. ...............4..... LIST OF TABLES ................. ...............8..___ ..... LIST OF FIGURES .............. ...............10.... AB S TRAC T ............._. .......... ..............._ 12... CHAPTER 1 INTRODUCTION ................. ...............13.......... ...... Introducti on ................. ...............13................. Background .................. ...............13................. Site Characterization .............. ...............14.... Subsoil Exploration ................. ...............14.......... ..... Geotechnical variability ............... ...............14.... Conventional geotechnical modeling ................. ...............15........... .... LRFD ............... ......... .._ .. ......__ .. ...........1 FMOS First Order Second Moment .....__.....___ ..........._ ...........1 Reliability index .................... ...............20. Solving for the resistance factor .....__.....___ ..........._ ............2 Problem Statement ............ ..... ._ ...............23.... Obj ectives ................. ...............24._ ___...... M ethod s .............. ...............24.... 2 LITERATURE REVIEW ............_...... ._ ...............27... Static and Dynamic Field testing of Drilled Shafts ................... .....___ ... ....__........2 Modeling Spatial Variability in Pile Capacity for Reliability-Based Design .......................28 Reliability-Based Foundation Design for Transmission Line Structures ............... .... ...........29 Transportation Research Board Circular E-CO79 ................. ...............30........... ... Estimation for Stochastic Soils Models ............ .....___ ...............31. Practice of Sequential Gaussian Simulation .................. .... ....... ........ ................... .......3 Bearing Capacity of a Rough Rigid Strip Footing on Cohesive Soil-a Probabilistic Study .............. ...............32.... 3 DATA COLLECTION ................. ...............35................ Existent Data Collection ................. ...............35........... .... New Field Data Collection .............. ....... ...............36 The Fuller Warren Bridge (District 2)............... ...............37... 17th Street Bridge Fort Lauderdale (District 4)................... ...............3 Table F-1. Continued. 5 (feet) A B C D E F G H J K L LL M N O P Q R S T U V VV X Y Z AA BB CC DD EE FF GG HH I I JJ KK MM Determinis Cap .15(ton) 235 185 220 215 215 190 230 195 285 225 175 240 240 295 215 200 190 190 265 190 250 230 190 235 240 225 175 200 245 200 190 150 280 220 260 180 180 230 300 160 225 Mean Standar CC)V Bias 1 1.27027 1.068182 1.093023 1.093023 1.236842 1.021739 1.205128 0.824561 1.044444 1.342857 0.979167 0.979167 0.79661 1.093023 1.175 1.236842 1.236842 0.886792 1.236842 0.94 1.021739 1.236842 1 0.979167 1.044444 1.342857 1.175 0.959184 1.175 1.236842 1.566667 0.839286 1.068182 0.903846 1.305556 1.305556 1.021739 0.783333 1.46875 0.01099541 0.027360888 0.001345216 0.000140085 0.000140085 0.01741954 0.006908913 0.010053913 0.078566743 0.003649919 0.056643116 0.015798563 0.015798563 0.095017342 0.000140085 0.00491976 0.01741954 0.01741954 0.047553019 0.01741954 0.02717849 0.006908913 0.01741954 0.01099541 0.015798563 0.003649919 0.056643116 0.00491976 0.021221301 0.00491976 0.01741954 0.213266321 0.07052917 0.001345216 0.040406164 0.040279107 0.040279107 0.006908913 0.103378754 0.13241666 1.104859 1.280593501 0.181206321 0.164009 PSF PSF PSF PSF Table E-4. 17th Street Bridge SGS (20feet). Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 45407.11477 235.5262499 41856.568 48900.002 22665.65424 513731882.1 -01732519328 0.383255739 99920.77422 60.007784 99980.782 420515289.9 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 44728.03485 231.9539298 41280.174 48900.002 22321.87526 498266115 -01718776057 0.39948428 99567.77814 414.47586 99982.254 414226330.7 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 42210.90062 222.0514785 39094.814 49700 21368.92187 456630822.1 -01546710456 0.494754071 99843.95339 84.734612 99928.*B88 390915150.6 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 43657.61793 225.*B671411 39968.552 49700 21716.87187 471622524 -01656686698 0.442924124 99635.08658 222.54142 99857.*B28 404313199.7 9261 0 05 60 80 100 Frequency Distnbution New+Old Bonngs 01 0 05 , 0 20 40 60 80 100 1 quqt (tsf) MEAN = 40.4560 11.8474 18.7135 ISTD = 25.6634 12.0870 20.3264 Frequency Distnbution Old Bonngs Frequency Distnbution New bonngs S20 40 60 80 quqt (tsf) 100 1: Figure 5-6. Frequency Distribution for quqt. y = 383.66x + 1E+06 R2 = 0.6645 quqt vs Ei (psf) 25000000 20000000 S15000000 m 10000000 5000000 0 10000 20000 30000 40000 50000 quqt (ps? Figure 5-7 Fuller Warren Bridge quqt and E Correlation 01 0 05 0 0 20 40 [ quqt (Tsf 17th Street Bridge BORING SAMP D MAX ST q (u) DISPL @) STRAIN %RECO TARE WTDRY NO UNIT MS LOAD STRENGTH FAIL @ FAIL W WT WT CORE(~ pf (lbs) (psl) (psl) (m) (%) % RQD (g) (g) (g) 6/1 1T 924 106 5 1758 5 235 6 0 1252 100/62 763 326 9 305 7 2U 839 116 1 2846 5 658 3 0 0200 0 38 "762 830 3 771 9 3T 1453 117 5 3201 6 358 9 0 0836 "754 446 6 399 5 4T 655 132 1 3330 8 410 4 0 0511 "75 4199 398 7 5U 896 123 7 5693 3 1268 2 0 0350 0 70 "769 845 8 782 6 6T 551 129 2 1942 3 235 6 0 0616 "75 408 2 390 8 7U 879 124 3 2542 3 557 7 0 0308 0 74 "76 734 1 680 9 8T 12 07 113 4 2583 7 282 8 0 0851 "763 433 9 395 4 9U 990 122 6 3311 5 738 8 0 0275 0 64 "764 749 688 4 10T 14 18 113 2 788 4 90 1 0 0271 "77 7 414 3 372 5 11T 6 19 133 8 2896 2 359 1 0 0964" 757 398 1 379 3 6/2 1U 260 123 6 4409 9 936 4 0 1758 4 55 72/37 77 5 642 6 628 3 2T 8 56 121 9 1745 3 206 2 0 0705 "75 7 424 5 397 3T 3 87 93 7 871 7 100 4 0 1053 "74 9 329 9 320 4 4T 340 141 9 6055 682 1 0 0486 "756 474 2 461 1 5U 751 124 8 3801 2 825 6 0 0303 0 66 "765 805 5 754 6 6T 11 67 117 9 2097 8 246 9 0 0430 "742 420 5 384 3 7T 512 123 1 2339 3 267 8 0 0591 "757 4101 393 8 6/3 1T 129 100 9 1389 6 176 6 0 0688 80/51 749 325 3 322 1 2U 143 145 5 10020 2 2131 3 0 1268 3 59 "756 679 3 670 8 3U 1 92 143 8 4800 3 1035 5 0 0311 0 90 "76 665 3 654 2 4T 435 87 0 1040 9 113 4 0 1196 "757 332 3 321 6 5U 356 106 4 1966 440 2 0 0205 0 48 "77 7 6189 600 3 6T 3 85 99 8 866 3 125 3 0 1288 "74 2 292 6 284 5 7U 3 51 106 3 2473 7 554 8 0 4020 9 08 "75 7 632 6 613 7 8T 345 997 1302 4 152 7 0 0788 "765 349 339 9 9U 2 83 106 9 1828 4169 0 0357 0 69 "754 722 6 704 8 6/4 1U 263 92 7 1289 8 289 6 0 2128 4 81 68/30 763 552 9 540 7 2T 2 05 105 2 11237 127 5 0 0449 "77 2 370 6 364 7 3T 376 102 5 1072 1 151 4 0 0605 "749 298 2 290 1 4U 2 78 97 8 1081 4 240 7 0 0544 1 36 "77 535 4 523 5T 2 50 98 1 892 6 104 0 0 0590 "76 2 343 1 336 6 6T 318 963 1147 1 131 2 0 0634 "764 345 6 337 3 7T 376 980 11487 135 3 0 0905 "763 343 8 334 1 8T 336 100 3 1509 8 205 6 0 1603 "75 1 303 295 6 6/5 1U 1 23 138 9 6235 5 1393 7 0 0445 1 02 80/60 81 6 796 1 787 4 2T 1 24 152 9 3890 2 509 9 0 0562 "769 445 3 440 8 3U 1 53 124 0 6375 1 1428 6 0 0322 0 71 "75 740 7 730 7 4T 135 143 8 2505 254 6 0 0378 "755 525 4 5194 5T 105 117 5 2201 1 252 3 0 1374 "77 1 395 8 392 5 6U 1 69 110 4 2312 3 514 6 0 0550 1 23 "75 5 660 2 650 5 7T 078 110 8 1209 9 163 6 0 0332 "76 335 2 333 2 8U 165 126 2 27165 598 4 0 0979 221 "762 748 4 737 5 1T 1 80 146 0 5188 1 593 3 0 0366 48 /17 74 8 481 5 474 3 2U 137 143 3 3525 6 778 9 0 0294 0 74 "76 1 750 6 741 5 3T 089 139 7 3676 3 485 5 0 0483 "762 406 1 403 2 Table B-1. Continued. Project Number: Lab Number: Bridge Number: LIMS Number: Location: Date Received: Tested by: Figure 5-12. 17th Street Bridge FLAC Model Grid 91 the site selection. For each available test, a comparison between measured and predicted FDOT failure resistance is made. Furthermore, the same comparison was complete for nearest boring and random selection. The LRFD specifications as approved by AASHTO recommend the use of load factors to account for uncertainty in the load, and resistance factor to account for uncertainty in the materials. Therefore, this research followed the AASHTO recommendation saying that a probabilistic approach for estimating resistance factors be used on a database of measured and predicted values. From that procedure LRFD 4 factors, Probability of failure (Pf) and Fs Based on Reliability 4 for nearest boring and random selection approach were calculated. Table 2-1 and Table 2-2 showed the results obtained in the Static and Dynamic Field testing of drilled shafts research. On the first column is the Reliability for drilled shafts. The Second column is the LRFD factor. And, the fourth and fifth columns pertain to probability of failure and factor of safety . Comparing the LRFD factor from nearest boring and random selection results, the nearest boring has higher resistance factor for the same design approach. Based on this study results evidently, the use of the nearest boring greatly diminished the variability of rock properties and the subsequent mobilized unit end bearing. Modeling Spatial Variability in Pile Capacity for Reliability-Based Design The American Petroleum Institute (API) recommends using site-specific data for soil properties when developing pile capacity profiles for offshore structures (API 1993). However, there are many situations where this site-specific information is not available or would be costly and time consuming to obtain. It is therefore advantageous to be able to predict the expected pile Table 6-1. FDOT Item Average Unit Cost Database. ITEM CATEGORY 100 to 577 Roadway & Bridge 579 to 590 Landscape 600 to 715 Traffic Operations 721 to 770 Peripherals 800 to 899 Mass Transit 900 to 999 Special Use 1000 to 1999 Utility Table 6-2. Summary of Drilled Shaft of 48" Diameter (0455 88 5). Year No. of Contracts Weighted Average Total Quantity (LF) Total Amount 2006 4 $356.66 2456 $875,956.96 2005 3 $204.33 1087 $222,106.71 2004 6 $277.60 2533 $703,106.80 2002-2003 10 $233.29 3488 $813,715.52 Average $267.97 Table 6-3. Summary of Excavation Shaft of 48" Diameter (0455 122 5). Year No. of Contracts Weighted Average Total Quantity (LF) Total Amount 2006 3 $328.19 2380 $781,092.20 2005 2 $170.14 1011 $172,011.54 2004 5 $77.78 2128 $165,515.84 2002-2003 9 $119.58 3270 $391,026.60 Average $173.92 Table 6-4. Summary of Soil Lab from 2003 to 2007 Unconfined Moi sture Specific Split Tensile Compression Test Name Content ($) Gravity ($) ($) ($) Average ($) 2003-2004 8 57.37 89 83.63 238 2004-2005 8.15 55.83 95.83 85.38 245.19 2005-2006 8.43 57.24 95.72 87.80 249.19 2006-2007 8.15 57.34 95.37 86.63 247.49 Average 8.1825 56.945 93.98 85.86 244.9675 : : Varnance =U 0 SSemlvariogram to 1 N SCCVarlance O 2000 4000 6000 8000 10000 Lag (m) Figure 4-3. Semivariogram and Covariance. 71**I I II l* I l *I l I I I II I Il i I II I II II CIB-1/1 1T 40 50 8/10/2006 2 3420 2 4850 463 4 155 4 0 94 2U 48177 2 4610 799 3 132 9 1 96 1 00 3T 2 4465 2 4200 374 3 126 7 1 01 4T 2 3805 2 4200 396 3 137 9 0 98 5U 45 50 4 1642 2 4765 751 1 142 6 1 68 1 02 CIB-1/2 1U 45 50 8/10/2006 3 6302 2 4545 679 5 150 7 1 48 1 04 2T 2 4455 2 4625 442 7 1448 0 99 3U 4 5233 2 4315 750 0 136 0 1 86 1 01 4T 2 3470 2 4250 399 4 140 4 0 97 5U 4 6885 2 4535 805 6 138 5 191 1 01 6T 2 1235 2 4700 384 2 143 9 0 86 7T 2 5135 2 4600 454 9 145 1 1 02 8U 48195 2 4570 848 6 141 5 1 96 1 00 9T 2 5560 2 4640 472 0 147 5 1 04 10U 50 50 4 7962 2 4740 892 8 147 5 194 1 00 CIB-1/3 1T 50 50 8/10/2006 2 4945 2 4510 464 0 150 2 1 02 2U 4 7732 2 4630 911 1 152 6 1 94 1 00 3T 2 4785 2 4495 451 5 147 2 1 01 4T 8/11/2006 2 4555 2 4545 388 3 127 3 1 00 5T 2 3780 2 4340 355 0 122 2 0 98 6T 55 50 2 4080 2 4240 346 0 118 6 0 99 CB-1/4 1U 55 50 8/14/2006 4 7672 2 3530 693 6 127 5 2 03 1 00 2T 2 5350 2 3975 384 2 127 9 1 06 3T 2 5305 2 4060 353 4 1170 1 05 4U 4 8415 2 4215 758 8 129 6 2 00 1 00 5T 2 2020 2 4115 341 0 129 2 0 91 6U 4 8682 2 4230 766 8 130 1 2 01 1 00 7T 2 3085 2 4170 345 1 1241 0 96 8U 4 7217 2 4350 727 1 126 0 1 94 1 00 9T 60 50 2 5060 2 4400 393 8 128 0 1 03 CB-1/5 1T 60 50 8/14/2006 2 3600 2 0160 227 1 114 8 1 17 2T 2 0215 2 1000 207 7 1130 0 96 3T 2 4585 2 2185 285 8 1146 1 11 4U 4 0008 2 0860 420 4 117 1 1 92 1 01 5U 48755 22955 597 1 1127 2 12 1 00 6T 2 4770 2 4000 349 0 1186 1 03 7U 4 8537 2 4230 680 3 1158 2 00 1 00 8U 4 6912 2 4060 665 3 1188 1 95 1 00 9T 65 50 2 4465 2 3815 326 2 1140 1 03 CIB-1/6 1T 65 50 8/15/2006 2 5280 2 3400 328 9 115 3 1 08 2T 2 3860 2 2185 296 0 122 3 1 08 3U 4 8008 2 3850 675 2 1199 2 01 1 00 4T 2 3295 2 4040 344 1 1240 0 97 5T 70 50 2 3140 2 3200 303 5 1182 100 Table B-2. Fuller Warren Soil Boring Data Table B-2. Continued. STATE MATERIALsRokC r Effective/Revised Date: OFFICE 4/27/05 Unconfined Compression- Foundations Laboratory By: G.J. Page 1 of 1 Split Tensile CB-2/1 1U 37 58 8/16/2006 4 0513 2 3715 674 2 143 5 1 71 1 02 2T 2 4250 2 3875 437 6 153 6 1 02 3T 42 58 2 4635 2 3500 390 2 139 1 1 05 CB-2/2 1T 42 58 8/16/2006 2 2305 2 3730 359 4 138 8 O 94 2U 4 8233 2 3865 806 6 142 4 2 02 1 00 3T 2 2735 2 3440 328 3 127 5 0 97 4U 8/17/2006 4 7352 2 3685 756 7 138 2 2 00 1 00 5T 24425 23845 413 1 1443 1 02 6T 47 58 2 4775 2 3770 429 6 148 9 1 04 CB-2/3 1T 47 58 8/17/2006 2 3155 2 3325 393 3 151 4 0 99 2U 46713 2 3815 790 1 1447 1 96 1 00 3T 24450 23890 4152 1443 1 02 4U 2 6913 2 3880 784 5 247 9 1 13 1 09 5T 2 3950 2 3885 401 6 142 6 1 00 6U 4 7383 2 3925 769 6 137 6 1 98 1 00 7T 2 4370 2 3935 401 1 139 4 1 02 8U 4 9098 2 3895 872 3 150 9 2 05 1 00 9T 2 2950 2 3770 310 1 1160 0 97 10U 4 7280 2 3760 630 4 1146 1 99 1 00 11T 2 3950 2 3630 294 3 106 7 1 01 12U 52 58 4 7902 2 3810 834 4 149 0 2 01 1 00 CB-2/4 1T 52 58 8/17/2006 2 3575 2 3365 383 7 144 6 1 01 2U 4 7825 2 3870 798 5 142 1 2 00 1 00 3U 4 7328 2 3500 775 3 143 9 2 01 1 00 4T 8/18/2006 2 3815 2 3675 367 4 133 5 1 01 5U 4 6380 2 3510 701 1 132 7 1 97 1 00 6T 2 3035 2 3635 327 9 123 6 0 97 7U 4 6880 2 3645 655 3 121 3 1 98 1 00 8T 2 2875 2 3445 3126 120 6 0 98 9U 4 7233 2 3485 662 1 123 3 2 01 1 00 10T 2 3315 2 3390 330 5 125 7 1 00 11T 2 3140 2 3530 340 4 128 9 0 98 12U 4 8088 2 3595 699 7 126 8 2 04 1 00 13T 2 5235 2 3475 359 1 125 3 1 07 14T 57 58 2 5360 2 3615 357 3 122 5 107 CB-2/5 1U 57 58 8/18/2006 4 8678 2 3470 705 9 127 7 2 07 1 00 2T 2 4855 2 3655 363 3 126 7 1 05 3U 4 7017 2 3590 677 6 125 6 1 99 1 00 4T 2 3865 2 3325 350 0 130 8 1 02 5U 62 58 4 9502 2 3395 7183 128 6 2 12 1 00 CB-2/6 1T 62 58 8/18/2006 2 3460 2 3535 294 3 109 9 1 00 2U 4 7983 2 3545 623 0 1136 2 04 1 00 3T 2 3445 2 3675 301 1 111 1 0 99 4U 4 7540 2 3515 627 6 1158 2 02 1 00 5T 2 3380 2 3355 311 5 118 5 1 00 6U 46223 2 3500 629 1 1195 1 97 1 00 7U 4 8098 2 3650 654 8 118 1 2 03 1 00 8T 2 3175 2 3130 3128 122 4 1 00 9U 4 8382 2 3155 6541 122 3 2 09 1 00 10T 67 58 2 4185 2 3000 323 1 122 5 1 05 includes the soil boring auger and the laboratory analysis. It will depend basically on the number of tests to be performed. Drilled Shaft Cost and Excavation The analysis is based on the Florida Department of Transportation average unit cost database. The database item descriptions are presented in the Basis of Estimates Handbook (Figure 6-1). This document was created with the purpose of presenting a standard method of documenting the design quantities for construction paid items. The handbook also presents the standard method of calculating quantities for many paid items that require special methods of measurement. The FDOT Item Average Unit Cost Database is numerated from item 000 to 1999 and the items are categorized by paid item range. Table 6-1 shows this categorization. The used items for this research were in the Road &Bridge category from 100 to 577. These items are 455 88 5 Drilled Shaft and 455 122 5 Excavation Unclassified shaft. The item 455 88 5 is specified for a Drilled Shaft of 48" diameter. Figure 6-1 shows the FDOT Basis of Estimates Handbook description for this item. The analyzed drilled shaft in this research was 36" of diameter. However, due to the lack of information for this diameter on the FDOT data base, data from a 48" diameter shaft was used instead. The same procedure was used on the item 455 122 Unclassified Shaft Excavation. Figure 6-2 shows the description of this item. The quantity on this item is measured as the depth of excavation from the ground to tip of the shaft measured in linear feet. The Basis Estimates Handbook is divided by years. Therefore, data from 2002 to 2006 were used. An example of the 2006 Item average Unit Cost for the items 455 88 5 and 455 122 5 are showed in the Figure 6-3. The complete data information is presented in APPENDIX G. CB-7 (e)CB-8 (e)CB-9(Nw EL. (f) q tf u(s) qq~s) Ei (s) EL. (ft) t(s) tf uttf Ei (s) EL. (f) q tf u(s) qq~s) Ei(si -52 27.57 172.01 34.43 123378.55 -52 24.64 171.66 32.52 172341.16 -52 10.43 73.03 13.80 102183.65 -57.5 15.08 101.85 19.59 94451 .43 -54 4.84 17.49 4.60 26327.58 -53 10.05 92.44 15.24 92509.46 -58 26.56 101.85 26.00 94451 .43 -55 12.99 85.93 16.70 133906.89 -54 27.23 69.96 21.82 95248.98 -59 40.44 209.01 45.97 195348.15 -57 12.99 38.71 11.21 38084.20 -55 26.03 69.96 21.34 95248.98 -60 32.97 209.01 41.50 195348.15 -58 27.04 66.36 21.18 120782.02 -55.5 31.48 262.94 45.49 182445.65 -61 30.71 71.84 23.48 116969.04 -60 29.48 83.73 24.84 94551.15 -56 39.88 74.36 27.23 138835.66 -62 34.37 71.84 24.84 116969.04 -61 28.61 51.83 19.26 36950.25 -59 40.03 74.36 27.28 138835.66 -63 17.59 74.79 18.14 165651.22 -62 13.44 17.24 7.61 37794.70 -61 32.21 74.36 24.47 138835.66 -64 23.77 74.79 21.08 165651.22 -63 12.44 17.24 7.32 37794.70 -62 30.01 145.63 33.05 234895.75 -65 11.59 74.79 14.72 165651.22 -64 10.66 146.62 19.77 19631 2.18 -62.5 43.11 145.63 39.62 234895.75 -67 16.03 74.79 17.31 165651.22 -65 34.73 146.62 35.68 19631 2.18 -63.5 33.77 195.44 40.62 218771.42 -72 24.61 171.24 32.46 170366.07 -66 47.32 136.73 40.22 214724.74 -65 24.16 72.42 20.91 60246.07 -73 31.30 171.24 36.61 170366.07 -67 37.73 99.77 30.68 154467.47 -67 16.21 97.22 19.85 144754.85 -74 31.30 188.03 38.36 197601.72 -68 36.27 67.95 24.82 84740.90 -67.5 32.82 97.22 28.24 144754.85 -75 27.34 61.42 20.49 105915.18 -69 15.26 67.95 16.10 84740.90 -68.5 7.68 97.22 13.66 144754.85 -77 27.34 156.86 32.74 186067.63 -70 9.99 17.86 6.68 17126.44 -69 14.00 97.22 18.45 144754.85 -78 54.76 156.86 46.34 186067.63 -72 14.71 158.99 24.18 152286.14 -70 9.13 13.30 5.51 7704.23 -80 31.54 170.90 36.71 158064.46 -73 27.83 141.75 31.40 121415.11 -72 13.88 13.30 6.79 7704.23 -81 31.54 112.80 29.82 83499.76 -76 34.89 99.57 29.47 120236.98 -73 29.54 109.69 28.46 202857.23 -83 49.05 112.80 37.19 83499.76 -77 23.40 156.61 30.27 87842.81 -75 43.37 97.59 32.53 127850.72 -87 30.61 112.80 29.38 83499.76 -87 61.43 156.61 49.04 87842.81 -76 43.37 128.18 37.28 254347.86 -80 43.45 151.17 40.52 187232.64 -82 42.82 142.25 39.02 122014.76 15.60 112.80 20.97 83499.76 Table C-1. Continued. Table 5-9. 17TH Street Bridge $ Values for different Reliability Index P FOSM (Traditional) Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 1 0.773 0.684 0.605 0.535 5 0.726 0.633 0.553 0.482 12 0.658 0.573 0.500 0.435 Table 5-10. 17TH Street Bridge $ Values for different Reliability Index P FOSM (Modified) Correlation Length (ft) p 2.5 p 3.0 p 3.5 p 4.0 1 0.957 0.887 0.822 0.762 5 0.868 0.788 0.715 0.650 12 0.785 0.710 0.643 0.582 Table 5-11. 17th Street Bridge COV and h Correlation Length (ft) COV h 0.1106975 0.1640086 0.17038627 0.1206112 0.18120632 0.17259719 Figure 1-1. Location of Boundaries between Materials. Petles Bedrock Figure 1-2. Litho Logical Heterogeneity. 0.00 -40- -45- -50- 0 -60 -65- -70 - 20.00 40.00 60.00 80.00 100.00 120.00 qu (tsf) Figure 1-3. Inherent Spatial Soil Variability. Phoon, K. K., Kulhawy, F. H. and Grigoriu, M. D. (2003). "Development of a Reliability-Based Design Framework for Transmission Line Structure Foundations." Journal of Geotechnical and Geoenvironmental Engineering, 798-806. Phoon, K.K. and Kulhawy, F.H. (2002). "Observations on Geotechnical Reliability-Based Design Development in North America." Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance, 31-48. Schaeffer, R. and Mcclave, J. (1995). "Probability and Statistics for Engineers." Fourth Edition, 76-83 and 122-164. Consequently, the optimum failure path will be the same as in the uniform material. In our case the result that tends to that result, is the correlation length suggested by the semivariogram. In the APPENDIX G is show all the programming models used on this research, for to obtain the bearing capacity for each one of the soil simulations. Additionally, the results graphs and tables are in this same appendix. 17th Street Bridge Comparison of Deterministic and Predicted End Bearing Table 5-7 shows a comparison of Simulated and deterministic End Bearing capacity from the finite elements program. Each correlation has its own predicted End bearing and it is compared with the End bearing capacity obtained from the deterministic value So, for one, five, and twelve feet correlation lengths the predicted End Bearing are 218.36, 218.375, and 238.125 tons respectively compared to 235 from the deterministic result. 17th Street Bridge LRFD Phi Factors According the explanation in CHAPTER 1, the goal of resistance factor design (LRFD) analysis is to develop factors that decrease the nominal resistance to give a design with an acceptable and consistent probability of failure. Where load components are multiplied by load factors and resistance is multiplied by a resistance factor. The basic equation is: (Rn > Cyi Qi where vi is a load factor applied to load components Qi and $ is resistance factor applied to the resistance (measured of load carrying capacity) Rn. In words it equation says that the capacity of the foundation (modified by the factor 4) must be larger than the total effect of all the loads acting on it. FOSM method has been used (NCHRP 507, 2004) to calibrate LRFD factors using a statistical dataset containing the measured and predicted resistances. It assumes that the load and 6-4 Summary of Soil Lab from 2003 to 2007 .............. ...............99.... 6-5 Summary of Drilled Shaft Cost (Material, labor) for $ Factors FO SM ................... ....... 100 6-6 Summary of Drilled Shaft Cost (Material, labor) for $ Factors FOSM (Modified)........ 100 6-7 Summary of Drilled Shaft Cost Excavation for $ Factors FO SM ................. ............... 100 6-8 Summary of Drilled Shaft Cost Excavation for $ Factors FOSM (Modified). ................ 100 6-9 Average Cost for a 1 foot length and 4 feet Diameter Drilled Shaft, (One Soil Boring) ........... ..... .. ...............101... 6-10 Average Cost for a 1 foot length 4 feet Diameter Drilled Shaft, (Five Soil Boring).......101 6-11 LRFD $ Factors, Probability of Failure and Fs Based on Reliability, P for Nearest Boring Approach ................. ...............101................ A-1 Fuller Warren Bridge Soil Boring Data. .............. ...............107.... A-2 17th Street Bridge Soil Boring Data. .............. ...............109.... B-1 17th Street Soil Boring Data ................. ...............111........... .. B-2 Fuller Warren Soil Boring Data ................. ...............123.............. C-1 17th Street Bridge Processed Soil Boring Data. .............. ...............128.... C-2 Fuller Warren Bridge Processed Soil Boring Data ................. ............................130 E-1 17th Street Bridge SGS feetet. ............. ...............140.... E-2 17th Street Bridge SGS (5feet). ............. ...............142.... E-3 17th Street Bridge SGS (12 feet). ............. ...............144.... E-4 17th Street Bridge SGS (20feet). ............. ...............148.... F-1 FLAC Results.............. .............150. CHAPTER 3 DATA COLLECTION The Data Collection was divided in two different research stages. The first one, the existent data was recollected from diverse resources, like Florida Department of Transportation database, University of Florida past researches, and soil labs maps. And secondly, the data obtained from the soil borings from the Hield and processed on the FDOT Materials lab. Both new and old data was analyzed and it made contribution to the Einal investigation. Existent Data Collection The existent lab data was gathered from different resources like, the FDOT database, University of Florida Geotechnical Department, and Florida Department of Transportation Districts past proj ects. Among the data that was gathered are strengths (qu-qt), recoveries and compressibility, as well as load testing information. The used data was taken from four of the seven proj ects available around Florida that at the time of the initial investigation had available load test information and additionally any soil boring data, which were relevant to the research. These four proj ects that had the requirements described in the last paragraph were Apalachicola Bridge (Calhoun), Victory Bridge (Chattahooch), Fuller Warren Bridge (Jacksonville) and 17th Street Causeway (Fort Lauderdale). The localization around Florida of the mentioned bridges is showed in Figure 3-1. The other three sites that appear in the location map as a white shadow belong to bridges that had some load test information at the time of the initial investigation, but the load test shafts were set in a soil different to limestone. The data obtained from each one of the bridges showed on the Eigure is the Measured Unit End Bearing from Osterberg Load Tests. A summary of this information is showed in the Table 3-1. The table contains in the first column the bridges names, the shaft number and length in the Moreover, the summary of the Drilled Shaft and Excavation shaft of 48' diameter are presented in Table 6-2 and Table 6-3. Soil Boring Test Costs The rates for soil laboratory tests are based on the State Material Office cost database. The available FDOT data from 2003 through 2006 divided annually was used for the analysis. Table 6-4 shows the most common soil test used for Drilled Shaft studies and at the same time used on the 17th Street Bridge. Additionally, the cost of obtaining the soil samples in a rock soil from O' to 50' is $26.25/LF and from 50'-100' is $30.63/LF. These costs are based on actual (2007) cost from FDOT District 4. Relative Costs Analysis The analysis was divided into three groups: 1) Drilled Shaft Cost, 2) Drilled Shaft Excavation and 3) Boring Test Cost. Drilled Shaft Cost All the cost analysis will be based on a one foot length by four feet diameter drilled shaft in lime rock soil. The total Drilled Shaft construction cost was $267.97 per linear feet. This result was compared with the costs generated by the used of the new $ factors presented previously in CHAPTER 5. Those $ factors accounted for three correlation lengths, and four reliability indices (Table 5-10). It is assumed that each 4 factors represent a percentage of the deterministic value. For example from Table 5-10 a value with a correlation length of 5 feet and a reliability index of 3.0 the $ factor is 0.788. Therefore, this value represents the 100/78.88% of the total determinist cost corresponding to this 4 factor. Consequently, the total cost of the determinist value of $267.97 multiply by 1/0.788 will derive on $423.33 per linear feet. This cost TESjT SHIFT LOCATION PLAN ""'~~~~~- --,~ ~Apalachicola (~Calhourg' I GandyBidge H,,,illbrog I~r ~vrLrk C10tka Keys Figure 3-1. Load Test Bridge Locations. I LFrC"" Figure 3-2. Fuller Warren Bridge Shaft Locations. Fuller Warren s t~a ses (acksonville) TitavR~ e homogeneous, that means that the soil profile may vary. Therefore, for estimate the natural soil or rock in-situ properties, it is necessary to pass by two phases; site characterization and subsoil exploration. Site Characterization On this phase, the engineer glances for formation of the soil origin and alterations that usually are caused by the environment processes, like chemical weathering and the introduction of new substances. Those alterations vary on space and time. If the engineer has an understanding of soil formation and later alteration of geotechnical materials, he will have a better acknowledge of the material variability and the behavior that it could have during construction process and structure lifetime. Subsoil Exploration This phase is where the engineer obtains information that assists him/her on calculations of the load bearing capacity of the foundation, estimation of the possible settlement of a structure, establishing foundation problems, choosing the appropriate foundation type, and determining construction methods for changing subsoil condition. The subsoil phase has three basic steps; collection of preliminary information, reconnaissance and site. Geotechnical variability Natural soils are rarely homogeneous and highly variable in their properties. This soil variability can be classified into three main categories. The first is the location of boundaries between materials (see Figure 1-1). The second is litho logical heterogeneity that is the locations of anomalies, or areas of significantly differences properties, within a single material type (see Figure 1-2). And the third is inherent spatial soil variability (see Figure 1-3). Soil and rock material vary so that a property measures at two different points will have different values, assuming no error on measurement. The modified FOSM results are slightly bigger than the traditional, and based on Styler 2006 theory, closer to accurate results. CHAPTER 1 INTTRODUCTION Introduction This research initiative was based on the need to improve the LRFD resistance factors, 4, for non- redundant shaft design, due the new designs methods moves toward larger single shaft design (e.g. Cross -Town, New River, etc). Most geotechnical analysis in general practice involve analysis using representatives values of design parameters,(like strength, recoveries, compressibility, etc), usually an average or the lowest value obtained from field and laboratory test results, and it followed by an application of a suitable factor of safety to get an allowable loading condition. However, in nature soil parameter varies in both horizontally and vertically direction. Our case used the same soil boring parameters than those used on most geotechnical analyses, but this time use information obtained from sites localized close to the design site instead using the whole site average. Random soil models were created based on geostatistics analysis using soil parameters. The created random soil models were used on a finite element program that modeling a six feet diameter, twenty feet long drilled shaft, giving the drilled shaft capacity for each random soil model. Additionally, a cost comparison between using the actual method involving an increment on the drilled shaft construction due to using a bigger LRFD resistance factors, 4. And using the proposed LRFD resistance factors, 5, but with an increment on additional field coring of rock around the location where the shaft will be is accomplished. Background Foundation design depends basically on the engineering properties of the soil or rock that is supporting the foundation. But the soil characteristics at any site frequently are non- Table B-1. Continued. STATE MATERIALs Rock Core Effective/Revised Date: OFFICE 12/22/05 Unconfined Compression- Foundations Laboratory By: B.W. Page 1 of 1 Split Tensile II ~ i I' I I .I I i I I I 1- .i I I ." I 7/1 1T 52.0 1.9905 2.3980 285.2 120.9 0.83 2U 57.0 3.7880 2.3845 633.0 142.6 1.59 1.03 7/2 1T 57.0 2.2260 2.3560 293.3 115.1 0.94 2T 1.9940 2.3500 293.5 129.3 0.85 3U 4.3135 2.3815 693.7 137.5 1.81 1.01 4T 2.2580 2.3835 403.4 152.5 0.95 5U 4.6970 2.3950 841.0 151.4 1.96 1.00 6T 2.0550 2.3970 364.0 149.5 0.86 7T 1.7540 2.3670 254.8 125.8 0.74 8T 2.1750 2.3915 334.1 130.3 0.91 9T 2.4540 2.3975 412.3 141.8 1.02 10U 4.2085 2.3010 612.9 133.4 1.83 1.01 11T 2.4605 2.3720 375.3 131.5 1.04 12U 5.0075 2.3880 763.2 129.6 2.10 1.00 13T 62.0 2.2130 2.3675 337.6 132.0 0.93 7/3 1T 62.0 2.2015 2.2940 223.3 93.5 0.96 2T 67.0 2.3255 2.3015 229.1 90.2 1.01 7/4 67.0 72.0 NA SAND 7/5 1T 72.0 2.4535 2.3843 376.1 130.8 1.03 3T 2.1355 2.3915 366.2 145.4 0.89 4T 2.1765 2.3920 388.8 151.4 0.91 5U 3.8825 2.3842 674.7 148.3 1.63 1.03 6U 4.1465 2.3872 735.6 151.0 1.74 1.02 7U 3.7250 2.3710 576.4 133.5 1.57 1.03 8T 1.4850 2.3715 226.6 131.6 0.63 9U 77.0 3.9970 2.3770 670.0 143.9 1.68 1.02 7/6 1T 77.0 2.0110 2.3840 364.4 154.6 0.84 2T 2.1070 2.3953 378.2 151.7 0.88 3U 3.6625 2.3932 646.9 149.6 1.53 1.04 4U 82.0 3.9280 2.3900 685.7 148.2 1.64 1.03 7/7 1T 82.0 2.1955 2.3965 390.7 150.3 0.92 2T 87.0 2.2945 2.3890 384.8 142.5 0.96 7/8 1T 87.0 92.0 2.3110 2.3970 338.9 123.8 0.96 0.01 E 0. IlI1.. O 100 200 2 quqt/2 0.05 0.041 0.03 0.02 0.01 0 20 40 60 qu(tst) MEAN= 1.0e+004 0.0060 0.0006 6.2192 STD = 1.0e+004 0.0042 0.0006 4.8059 SKEW = 0.5721 0.8510 0.7210 KURT = 2.4376 2.2529 2.3001 MNPDFEXP = 1.0e+004 0.0042 0.0005 4.5972 STDPDFEXP = 1.0e+004 0.0035 0.0004 3.9074 SKPDFEXP = 1.1923 1.2702 1.1766 KUPDFEXP = 3.4116 3.8305 3.4654 MNPDFLOG = 1.0e+004 0.0043 0.0004 4.8072 STDPDFLOG= 1.0e+004 0.0032 0.0004 3.4648 SKPDFLOG = 1.3965 1.6554 1.3606 KUPDFLOG= 4.0138 5.1557 4.1142 MNPDFGAM= 1.0e+004 0.0049 0.0005 5.3568 STDPDFGAM = 1.0e+004 0.0033 0.0004 3.6765 SKPDFGAM= 0.9666 1.2516 0.9698 KUPDFGAM= 3.0719 3.7974 3.1902 sqerrorNORM = 1.0e-005 0.1110 0.0016 0.0279 sqerrorEXP= 1.0e-006 0.1716 0.0205 0.8014 sqerrorLOGN= 1.0e-006 0.0112 0.0037 0.7291 0.015 0.05 Figure D-6. 17th Street Bridge Old and New Borings. 0.04\ 0.03 0 20 40 60 80 qt (tst) Table B-2. Continued. Prject Number: Fuller Warren Location: CB-1 Lb Number: Date Received: 8/9/2006 Bidge Number: Tested by: JC LIMS Number: BORING SAMP w DRY MAX ST q (u) DISPL @~ STRAIN %RECO TARE WET DRY NO UNIT WT LOAD STRENGTH FAIL @a FAIL WT WT WT CORE (%~) (pcf) (1bs) (psl) (psl) (In) (%) % RQD (g) (g) (g) CIB-111 1T 3 35 150 4 3963 2 433 5 0 0640 67/37 427 1 873 8 859 3 2U 16 73 113 8 1017 4 213 3 0 0497 1 03 431 1 1224 3 1110 6 3T 23 01 103 0 276 8 29 8 00464 410 1 781 1 711 7 4T 15 60 119 3 799 8 88 4 0 0445 425 5 821 1 767 7 5U 10 93 128 6 6578 2 1335 3 00609 146 433 1181 1 1107 4 CB-112 1U 8 01 139 5 9815 4 1990 3 0 0699 1 93 94/74 424 3 1098 2 1048 2 2T 10 47 131 1 1191 125 9 0 0443 418 9 861 819 1 3U 14 44 118 9 3855 822 8 0 0496 1 10 302 8 1051 7 957 2 4T 11 77 125 6 896 100 2 00512 370 7 769 5 727 5 5U 14 05 121 4 3453 726 2 0 0672 1 43 435 2 1239 4 1140 3 6T 11 39 129 1 1814 220 2 0 0509 328 3 711 6 672 4 7T 11 43 130 2 2473 254 6 0 0558 434 1 887 6 841 1 8U 11 42 127 0 4494 945 7 0 0522 1 08 368 9 1201 4 1116 1 9T 11 39 132 4 1875 189 6 0 0411 429 5 900 9 852 7 10U #DIV/01 #DIV/01 #VALUEl I#VALUEl CB-113 1T 8 79 138 1 2483 1 258 6 0 0504 60/48 377 8 840 9 803 5 2U 8 31 140 9 7533 1575 1 0 0527 1 10 372 3 1279 6 1210 3T 949 134 5 1582 165 9 00408 428 2 878 2 839 2 4T 16 13 109 6 245 25 9 0 0289 427 1 814 5 760 7 5T 24 16 98 5 112 12 4 0 0213 372 3 726 9 657 9 6T 31 27 90 4 183 19 9 0 0297 435 2 780 7 698 4 CB-114 1U 26 38 100 9 759 174 5 0 0516 1 08 92/77 427 1 1118 4 974 1 2T 23 05 103 9 181 190 00223 372 4 756 2 684 3 3T 30 80 89 5 121 12 7 0 0393 435 3 780 1 698 9 4U 22 23 106 1 1408 305 7 0 0440 0 91 419 1165 6 1029 8 5T 22 22 105 7 299 35 9 00278 364 9 705 4 643 5 6U 22 05 106 6 1468 318 3 0 0547 1 12 308 2 1073 8 935 5 7T 27 86 97 1 215 24 6 00356 313 1 657 8 582 7 8U 25 34 100 5 772 165 1 0 0576 1 22 373 2 1098 8 952 1 9T 23 43 103 7 267 27 8 00440 425 5 819 744 3 CB-115 1T 36 30 84 3 109 14 6 0 0336 90/67 315 2 542 481 6 2T 41 19 80 0 61 92 00242 431 1 6378 577 5 3T 45 34 78 8 29 3 4 0 0173 432 5 716 5 627 9 4U 37 67 85 1 338 98 4 00608 152 3704 789 6 674 9 5U 36 26 82 7 423 102 3 00610 1 25 370 6 965 9 807 5 6T 33 82 88 7 136 14 5 0 0386 376 5724 3 636 4 7U 34 34 86 2 550 1193 00565 1 16 312 990 3 8169 8U 29 72 91 6 479 105 1 0 0420 0 90 300 9965 2 813 9T 30 54 87 4 119 130 00401 371 3 697 620 8 CB-116 1T 29 23 89 2 51 7 5 6 0 0276 58/38 315 2 643 7 569 4 2T 27 22 96 1 46 5 5 0 0407 431 3 726 7 663 5 3U 28 98 93 0 187 41 9 0 0531 1 11 370 4 1045 1 893 5 4T 21 96 101 7 53 60 00284 3649 708 7 646 8 5T 25 61 94 1 30 35 00372 432 5 735 6 673 8 Figure 5-8. 17th Street Soil Boring Locations (SMO 2007). 1 Pier I Pier I I~ I O Ylrr I :r~ I Table 3-1. Measured Unit End Bearing from Load Tests. Shaft Length (ft) 119.4 142.0 100.1 77.5 64.2 101.2 113.9 87.8 85.0 72.0 84.0 134.0 89.2 99.1 41.0 Unknown Friction (ft) 5.2 9.1 11.1 2.6 0 0 0 0 0 0 0 9 0 0 0 Bottom Move. (in) 0.624 1.95 1.89 3.53 4.41 2.97 3.2 5.577 5.977 2.1 1.7 1.3 2.69 4.46 0.23 2.56 2.94 3.12 0.4 2.9 2.5 1.74 Mobilized Bearing (tsf) x x 41.5 x x x x x x 70 60 65 x x 87 x x x x x x x 109 x x 124.4 x FDOT Max. Failure Failure (tsf) (tsf) x x x x x x x 66.4 61.7 90.3 28 39 22.4 30.2 18.5 29.4 72.6 92 x x x x x x 38 40 36 44 x x 80.8 89.5 34 34 34 70 x x Shaft Name LSTSO LSTSO LSTSO LSTSO Test 1 Test 2 Test 4 Test 5A 46-11A 53-2 57-10 59-8 62-5 69-7 LT-1 LT-2 LT-3a LT-4 26-2 52-4 91-4 4-14 3-1 3-2 Failure Status Both Tip Fail Both Tip Fail Tip Fail Tip Fail Tip Fail Tip Fail Both Both Both Both Both Both Skin Fail Both Both Both Skin Fail Both Both Both 17th Street Bridge Acosta Bridge Apalachicola Bridge Fuller Warren Bridge Gandy Bridge Hillsborough Bridge Victory Bridge 27.9 120.7 66.8 38.4 54.5 74.7 70.8 33.2 38.6 46.6 45.0 50.7 0 0 0 9.8 4.33 6.7 7.33 0 9.66 7.7 0 12.14 139.2 42.9 x 0.5 Both 0.4 Skin Fail 2.367 Both 0.528 Both 0.4 Skin Fail 10-2 19-1 19-2 Conventional geotechnical modeling The conventional method of modeling soil structures is to evaluate the results from field testing studies and then to make soil profiles. In theses profiles, each layer is assumed to be homogeneous with singles values for the engineering properties of each layer. This properties information is obtained from in situ soil testing and lab testing. This information is evaluated later by the engineer and a single conservative value is chosen to represent the property of the material. The variability normally is not quantified. The usual design practice for soil design is deterministic. This involves the estimation of ultimate bearing capacity using average values of design parameters and application of a suitable factor of safety (F) to arrive an allowable bearing capacity (Griffiths & Fenton 1999). LRFD The purpose of foundation design is to guarantee that a system achieves adequately in its design life. However, there are some uncertainties on the two phases described above, (site characterization and subsoil exploration) that make it impossible to ensure that any unfortunate performance will occur under all possible circumstances. Foundation failures are always undesirable events. They occur for diverse reasons, negligence, lack of knowledge, greed, etc. The probability of failure is often higher for projects involving new materials, technology, and extreme parameters (larger shaft diameter) for which there is little or no prior experience. Therefore, the design provisions include built-in safety margins: load effects are usually overestimated and resistances are underestimated. In load and resistance factor design (LRFD), load components are multiplied by load factors and resistance is multiplied by a resistance factor. The basic equation is: (Rn Eli Qi (1-1) 45!i- 88- AA DRILLED SHAFT Unit LF; M1 Accuracy Linear Foot; 10th of a Meter PlanQuantity? no Notes Detailed Rlelauted Items Intended to pas for the coest of concrete and steel, temporary casing, all labor, materials, equipment and incidentals necessary to complete the drilled shaft. Length Is measured from top-of-shaft elevation to the design tip el~eva~tion shown in the plans. Pay Itern 455- 122-XAA is required with this item. Pay Item 455-122 covers the cost of the shaft excavation. I:lea,~rlr specify in plans CSL testing requirements as required. C0 51~ of Shaft Inspection Device included in cost of drilled shiaft, 455- 88-XAA. CSL tubes Included under 455- 88-XAA1. CSL testing paid for under Item 455-142. Required 455-122 (24.5-122) Recommended~ 455-142 wvhen C: SL testing is required COMVP 7110.0(503-03 I Forms Design SHTabQuant Construction Refer to Comp Book Documentation Design Locate in plans. Summarize quantities by location on tabulation of quantities sheet in the plans, or detail calculations in the computation book. Construction Record finall quantity on the tabulation sheet (plans) or computation forrn Compp book). PPM Clhapter Rleferences SDG's 3.6 Other Standards Specifications Figure 6-1. FDOT Basis of Estimates Handbook Description for the Item 455 88 "Drilled Shaft". PSF PSF PSF PSF Table E-4. Continued. Mean Standard Error Median Mode Standard Oswiation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 41916.56315 215.7209468 39004.65 41800 20759.70892 430965514.3 -01571675821 0.480379812 99964.77187 10.554133 99975.326 388189291.3 9261 Mean Standard Error Median Mode Standard Oswiation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 42862.22371 214.3914192 39756.89 38500 20631.76305 425669646.5 -0.597299848 0.420685131 99763.42888 18.545119 99781.974 396947053.7 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 45380=.61602 235.732166 41800 38500 22685.47038 514630566.5 -01716214975 0.415227363 99922.89606 65.887942 99988.784 420269885 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku dosis Skewness Range Minimum Maximurn Sum Count 41610.78171 222:.7657464 38575.492 32200 21437.6588 459573214.61 -01524411823 0.521869386 99693.49401 158.311992 99851.806 385357449.4 9261 PSF PSF PSF PSF I Table E-2. 17th Street Bridge SGS (5feet). Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 45806.79179 222.6907591 42021.988 49700 21430.44246 459263864 -0.689609294 0.381837804 99308.9843 594.1977 99903.182 424216698.7 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 41246.08288 217.5866605 38500 41800 20939.25418 438452365.5 -0.448952677 0.545106492 98730.14074 1258.95726 99989.098 381979973.5 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 45632.38736 224.5743392 42031.22 30800 21611.70708 467065883.1 -0.69715789 0.35706524 97915.1958 2035.8922 99951.088 422601539.3 9261 Mean Standard Error Median Mode Standard Deviation Sample Variance Ku rtosis Skewness Range Minimum Maximum Sum Count 42598.52685 217.1910467 39472.638 15199.9998 20901.18264 436859435.9 -0.532426787 0.498080027 99879.66534 109.310656 99988.976 394504957.1 9261 APPENDIX A DATA FROM STATIC AND DYNAMIC FIELD TESTING OF DRELLED SHAFTS (FULLER WARREN AND 17TH STREET BRIDGE) Table A-1. Fuller Warren Bridge Soil Boring Data. BL-2 BL-4 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -35 96.5 62 32 -15 54.5 80 47 -35 27.8 62 32 -15 12.5 80 47 -40 70.5 41 8 -20 98.5 43 20 -40 13.7 41 8 -20 6.1 43 20 -25 89 100 -25 9.1 100 BL-11 BL-13 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -35 92 25 25 -45 82 87 51 -35 13.9 25 25 -45 17.2 87 51 -45 68.5 30 17 -45 24.35 30 17 BL-20 BL-23 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -35 56.5 25 17 -20 95 50 47 -35 8.4 25 17 -20 9.9 50 47 -25 82 48 19 -25 12.95 48 19 BL-36 BL-37 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -20 244.5 70 49 -15 258 100 -20 54.05 70 49 -15 25.2 100 -25 104 100 -20 22.5 87 47 -20 5.6 87 47 -22 117.5 77 25 BW-1 BW-3 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -30 92.5 32 17 -45 28.75 -30 16.75 32 17 Table 3-3. Continued. Max. Load (lbs.) 6782 3530 368 1378 3224 204 5720 1552 3252 1623 4229 1715 5690 379 3187 120 243 501 169 88 731 287 93 433 437 S.T. Strength (psi) Displ. @ q(u) Fail (psi) (in) 1505.6 0.0522 784.1 0.0634 0.0633 0.0687 0.0515 0.0743 1287.5 0.0549 0.0415 729.8 0.0541 0.0468 943.0 0.0563 0.0419 1269.3 0.0454 0.0410 727.9 0.0630 0.0237 0.0276 116.1 0.0297 0.0236 0.0209 170.5 0.0455 0.0422 0.0402 100.3 0.0348 0.0324 Strain @ Fail Tare %Recov./ Wt. %RQD (g) 72/50 430.3 72/50 430.7 72/50 366.1 72/5 0 43 1.4 72/50 428.3 77/67 428.1 77/67 430.2 77/67 430.3 77/67 431.4 77/67 371.5 77/67 433.1 77/67 312.1 77/67 375.9 100/92 366.0 100/92 370.8 100/92 370.6 100/92 425.7 100/92 430.6 100/92 424.6 100/92 430.4 100/92 302.8 100/92 425.0 100/92 410.1 100/92 428.2 100/92 428.4 Dry Wt. (g) 1238.5 1094.7 629.8 752.7 803.2 671.1 1143.4 805.4 1153.8 732.4 1133.4 664.9 1172.8 713.2 1140.2 729.9 755.5 1049.6 731.8 685.1 828.1 692.4 646.5 973.0 742.1 Boring Samp. /Core No. CB-3/1 lU 2U 3T 4T 5T CB-3/2 IT 2U 3T 4U 5T 6U 7T 8U CB-3/3 IT 2U 3T 4T 5U 6T 7T 8U 9T 10T 11U 12T Dry Unit Wt.(pcf) 141.6 128.3 99.3 113.4 137.8 92.5 144.2 139.0 128.5 132.4 122.2 129.0 139.4 130.8 138.0 134.1 118.8 111.9 110.8 92.3 97.5 101.1 100.8 102.3 113.5 Wet Wt. (g) 1281.5 1168.7 698.4 805.4 837.2 735.5 1196.6 835.8 1237.8 771.6 1230.0 703.9 1239.0 746.4 1207.2 746.2 802.9 1164.0 790.5 758.6 972.4 756.6 701.0 1103.6 797.4 w(%) 5.32 11.14 26.01 16.40 9.07 26.50 7.46 8.10 11.63 10.86 13.79 11.05 8.31 9.56 8.71 4.54 14.37 18.48 19.11 28.86 27.47 24.01 23.05 23.97 17.63 ( %) 1.08 1.43 1.27 1.13 1.15 0.93 1.30 0.61 0.95 0.74 41.6 151.5 368.0 23.4 179.0 185.1 195.5 44.0 13.5 27.0 18.6 9.7 32.9 12.1 48.9 Table A-1. Continued. BW-5 BW-12 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -25 44.8 -35 31.85 27 -30 32.75 -40 27.4 -35 29.95 BW-14 EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD -30 43 20 42 -30 9.55 20 42 Added Bcring (Hole 1: Near Boring BL-1) Added Boring (Hole 2: Near Boring BL-1) Dep.(ft) qu REC RQD qt REC RQD Dep.(ft) qu REC RQD qt REC RQD -20 596.2 38 38 -23 65.4 15 10 284 -28 30.8 401.6 -28 34.6 52 33 17.4 24.6 60.2 33.3 80.9 14 -25 110.5 11 -30 43.4 63 26 -33 58.5 32.2 52.9 87.7 15.8 6.6 -35 50.4 -35 87.7 73 66 85.1 77.9 20.4 29.4 12 23.6 17.9 18.3 18.2 47.8 -40 55.1 MEAN= 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP= 28.4992 4.7548 25.2514 MNPDFLOG= 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 MNPDFGAM= 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 MNPDFRAYL = 42.9191 7.3741 45.8545 STDPDFRAYL = 22.4075 3.8534 23.3869 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN= 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 sqerrorRAYL = 1.0e-005 0.5839 0.0968 0.0009 Figure 5-5. Fuller Warren New Borings Frequency Distribution qu, qt and RQD. 0" 0 10 20 qt 50 100 qu 30 40 0.03, O 50 RQD QU QT RQD CHAPTER 5 DATA ANALYSIS Cases Studies In this research, two case studies are presented. The first case study is an analysis of the Fuller Warren Bridge in Jacksonville Florida. The second case study is the 17th Street Bridge in Fort Lauderdale Florida. Both of them were field sites with performed Drilled Shaft Load Test in Limestone. The data analysis followed the theory description showed on the CHAPTER 4. The main purpose was to generate random fields using Sequential Gaussian Simulation (SGS) that was based on the best suited Semivariogram. Each realization, while having the same statistics (Semivariogram), will have quite difference spatial pattern properties of cohesion, bulk and shear values on the soil and hence a difference value of end bearing capacity. This was followed by a finite element model analysis using the random fields obtained on the SGS results. Fuller Warren Summary Statistics The data obtained from the FDOT soil labs are shown in APPENDIX B. It was necessary to transforms these tables to a different format accepted by the software (APPENDIX C). Some of the properties showed on these tables, like qu, qt, and, RQD were used on statistics analysis. The Fuller Warren field data was obtained from three different borings, localized strategically near to Load Test LT4 in the Southwest side of the Bridge. Each of these boring CB 1, CB2, and CB3 has its own information like qu, qt, RQD, and depth. An example is showed in Table 5-1. The same data was presented in a different format and it is showed in Table 5-2. Additionally, the soil boring location is showed in Figure 5-1. The raw data for each boring was analyzed through histograms, frequency distribution and summary statistics realization. The histograms for each soil boring CB 1, CB2 and CB3 are *Kriging optimal interpolation; generates best linear unbiased estimate at each location; employs semivariogram model. *Stochastic simulation generation of multiple equally probable images of the variable; also employs semivariogram model. (Semi) Variogram Establishing the spatial correlation structure of a site having erratic variation in its soil properties would require an extensive amount of subsoil exploration, which may not be feasible in many proj ects due to the high costs (Fenton & Griffiths 1999). One of the most common methods for to estimate the correlation coeffieient length is the semivariogram. The semivariogram is a statistic that appraises the average decrease in similarity between two random variables as the distance between the variables increases. It describe how spatial continuity change as a function of distance and direction. Significant terminology is used to describe the important features of the semivariogram model, these terms are: *Sill: The semi variance value at which the variogram levels off. Also it is used to refer to the "amplitude" of a certain component of the semivariogram. For the plot above, "sill" could refer to the overall sill (1.0) or to the difference (0.8) between the overall sill and the nugget (0.2). Meaning depends on context. *Range: The lag distance at which the semivariogram (or semivariogram component) reaches the sill value. Presumably, autocorrelation is essentially zero beyond the range. *Nugget: In theory the semivariogram value at the origin (0 lag) should be zero. If it is significantly different from zero for lags very close to zero, then this semivariogram value is referred to as the nugget. The nugget represents variability at distances smaller than the typical sample spacing, including measurement error. The ratio of the nugget effect to the sill is often referred to as the relative nugget effect and is usually quoted in percentage. *Trend: If the empirical semivariogram continues climbing steadily beyond the global variance value, this is often indicative of a significant spatial trend in the variable, resulting in a negative correlation between variable values separated by large lags. Three options for dealing with lag include: 1) Fit a trend surface and work with residuals from the trend 2) Try to Eind a "trend-free" direction and use the variogram in that direction as the variogram for the "random" component of the variable 3) ignore the problem and use a linear or power variogram. See Figure 4-1. |

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PAGE 1 1 DEVELOPMENT OF A RATIONAL DESIGN APPROACH (LRFD phi) FOR DRILLED SHAFTS CONSIDERING REDUNDANCY, SPA TIAL VARIABILITY, AND TESTING COST by JOHANNA KARINA OTERO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 2007 Johanna Karina Otero PAGE 3 3 To my parents Maria Isabel Sanchez and Rafael Otero who have supported me all the way since the beginning of my studies, and to Enri que who accompanied me on this last stage PAGE 4 4 ACKNOWLEDGMENTS I would especially thank to my advisor, Dr. Ralph Ellis, for his generous time and commitment. His permanent conviction on my pr ofessional capacity during my doctoral work made this research a reality. Al so, thanks to Dr. McVay for to share part of his geotechnical knowledge. Special thanks go to Dr. Guerly fo r his supervision and technical support on the stochastic world. I would like to acknowledge Dr. Horhota and th e Florida Department of Transportation (FDOT) State Material Office for providing the f unding and help for this research project. Thanks also go to Farouque, Haki and Enrique who assisted me on different stages of the project investigation. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............12 CHAPTER 1 INTRODUCTION..................................................................................................................13 Introduction................................................................................................................... ..........13 Background..................................................................................................................... ........13 Site Characterization.......................................................................................................14 Subsoil Exploration.........................................................................................................14 Geotechnical variability...........................................................................................14 Conventional geotechnical modeling.......................................................................15 LRFD........................................................................................................................... ....15 FMOS First Order Second Moment.........................................................................19 Reliability index.......................................................................................................20 Solving for the resistance factor...............................................................................21 Problem Statement.............................................................................................................. ....23 Objectives..................................................................................................................... ..........24 Methods........................................................................................................................ ..........24 2 LITERATURE REVIEW.......................................................................................................27 Static and Dynamic Field testing of Drilled Shafts................................................................27 Modeling Spatial Variability in Pile Ca pacity for Reliability-Based Design.........................28 Reliability-Based Foundation Design for Transmission Line Structures...............................29 Transportation Research Board Circular E-C079...................................................................30 Estimation for Stochastic Soils Models..................................................................................31 Practice of Sequential Gaussian Simulation...........................................................................31 Bearing Capacity of a Rough Rigid Strip Footing on Cohesive Soil-a Probabilistic Study.......................................................................................................................... .........32 3 DATA COLLECTION...........................................................................................................35 Existent Data Collection....................................................................................................... ..35 New Field Data Collection.....................................................................................................36 The Fuller Warren Bridge (District 2).............................................................................37 17th Street Bridge Fort Lauderdale (District 4)................................................................38 PAGE 6 6 4 GEOSTATISTICS AND NUMERICAL MODEL................................................................45 Geostatistics.................................................................................................................. ..........45 (Semi) Variogram............................................................................................................46 Semivariogram models.............................................................................................47 Anisotropy................................................................................................................48 Covariance and correlogram....................................................................................49 Kriging........................................................................................................................ .....49 Types of Kriging......................................................................................................51 Stochastic Simulation......................................................................................................53 Sequential Gaussian simulation...............................................................................53 Software....................................................................................................................... ....54 Numerical Models............................................................................................................... ...55 FLAC3D (Fast Lagrangian Analysis of Continua).........................................................57 5 DATA ANALYSIS................................................................................................................65 Cases Studies.................................................................................................................. ........65 Fuller Warren.................................................................................................................. ........65 Summary Statistics..........................................................................................................65 Spatial Continuity............................................................................................................66 Fuller Warren Semivariogram.........................................................................................67 17th Street Bridge.................................................................................................................. ..68 Summary Statistics..........................................................................................................68 17th Street Bridge Semivariogram...................................................................................68 17th Street Bridge Simple Kriging...................................................................................69 17th Street Bridge Sequential Gaussian Simulation.........................................................69 17th Street Bridge Random Field Model..........................................................................69 17th Street Bridge Finite Elements Analysis....................................................................70 17th Street Bridge Determinist Capacity..........................................................................71 17th Street Bridge Parametric Study................................................................................71 17th Street Bridge Comparison of Determ inistic and Predicted End Bearing.................73 17th Street Bridge LRFD Phi Factors..............................................................................73 6 COST ANALYSIS.................................................................................................................95 Factor Influencing Cost........................................................................................................ ..95 Drilled Shaft Cost and Excavation.........................................................................................96 Soil Boring Test Costs......................................................................................................... ...97 Relative Costs Analysis........................................................................................................ ..97 Drilled Shaft Cost............................................................................................................97 Drilled Shaft Excavation.................................................................................................98 Boring Test Cost..............................................................................................................98 7 CONCLUSIONS AND RECOMMENDATIONS...............................................................105 PAGE 7 7 APPENDIX A DATA FROM STATIC AND DYNAMIC FIELD TESTING OF DRILLED SHAFTS (FULLER WARREN AND 17TH STREET BRIDGE)........................................................107 B SOIL BORING DATA FROM FIELD I NVESTIGATION PROC ESSED BY MSO.........111 C SOIL BORING INFORMATION PROCESSED................................................................128 D FREQUENCY DISTRIBUTIONS.......................................................................................131 E SGS RANDOM FIELD TABLES........................................................................................140 F FLAC3D PROGRAMMING MODELS..............................................................................150 G UNIT COST DATA.............................................................................................................157 LIST OF REFERENCES.............................................................................................................159 BIOGRAPHICAL SKETCH.......................................................................................................161 PAGE 8 8 LIST OF TABLES Table page 2-1 LRFD Factors, Probability of Failure (Pf) and Fs Based on Reliability for Nearest Boring Approach..................................................................................................34 2-2 LRFD Factors, Probability of Failure (Pf) and Fs Based on Reliability for Random Selection..............................................................................................................34 3-1 Measured Unit End Bearing from Load Tests...................................................................39 3-2 17th Street Bridge Soil Boring Data (State Project No. 86180-1522)...............................40 3-3 Fuller Warren State Material s Office Soil Laboratory Data..............................................41 4-1 Commercially Availabl e Numerical Programs for Rock Mechanics Study......................59 4-2 Sequential Gaussian Simulation Data Values....................................................................60 4-3 WINSLIB SGS Example Results.......................................................................................60 5-1 Fuller Warren Bridge Soil Boring Information.................................................................77 5-2 Fuller Warren Soil Boring Modified Data.........................................................................78 5-3 Table 17th Street Bridge Soil Boring Information.............................................................80 5-4 17th Street Bridge Wingslib Results...................................................................................81 5-5 Material Properties........................................................................................................ .....81 5-6 17TH Street Bridge Cohesion Mean Re sults Values from Simulations..............................81 5-7 17TH Street Bridge End B earing Capacity Mean Values from FLAC3D..........................81 5-8 17TH Street Mean, Standard, and COV of Predicted End Bearing Capacity Bias.............81 5-9 17TH Street Bridge Values for different Reliability Index FOSM (Traditional)..........82 5-10 17TH Street Bridge Values for different Reliability Index FOSM (Modified)............82 5-11 17th Street Bridge COV and ............................................................................................82 6-1 FDOT Item Average Unit Cost Database..........................................................................99 6-2 Summary of Drilled Shaft of 48 Diameter (0455 88 5)...................................................99 6-3 Summary of Excavation Shaf t of 48 Diameter (0455 122 5)...........................................99 PAGE 9 9 6-4 Summary of Soil Lab from 2003 to 2007..........................................................................99 6-5 Summary of Drilled Shaft Cost (Material, labor) for Factors FOSM..........................100 6-6 Summary of Drilled Shaft Cost (Material, labor) for Factors FOSM (Modified)........100 6-7 Summary of Drilled Shaft Cost Excavation for Factors FOSM...................................100 6-8 Summary of Drilled Shaft Cost Excavation for Factors FOSM (Modified).................100 6-9 Average Cost for a 1 foot length and 4 feet Diameter Dril led Shaft, (One Soil Boring)........................................................................................................................ .....101 6-10 Average Cost for a 1 foot length 4 feet Diameter Drilled Shaf t, (Five Soil Boring).......101 6-11 LRFD Factors, Probability of Failure and Fs Based on Reliability, for Nearest Boring Approach..............................................................................................................101 A-1 Fuller Warren Bridge Soil Boring Data...........................................................................107 A-2 17th Street Bridge Soil Boring Data.................................................................................109 B-1 17th Street Soil Boring Data.............................................................................................111 B-2 Fuller Warren Soil Boring Data.......................................................................................123 C-1 17th Street Bridge Processed Soil Boring Data................................................................128 C-2 Fuller Warren Bridge Processed Soil Boring Data..........................................................130 E-1 17th Street Bridge SGS (1feet).........................................................................................140 E-2 17th Street Bridge SGS (5feet).........................................................................................142 E-3 17th Street Bridge SGS (12 feet)......................................................................................144 E-4 17th Street Bridge SGS (20feet).......................................................................................148 F-1 FLAC Results............................................................................................................... ....150 PAGE 10 10 LIST OF FIGURES Figure page 1-1 Location of Boundaries between Materials.......................................................................26 1-2 Litho Logical Heterogeneity..............................................................................................26 1-3 Inherent Spatial Soil Variability........................................................................................26 3-1 Load Test Bridge Locations...............................................................................................43 3-2 Fuller Warren Bridge Shaft Locations...............................................................................43 3-3 Fuller Warren Bridge during Site Inspection.....................................................................44 3-4 17th Street Bridge Load Test Location...............................................................................44 4-1 Semivariogram Model.......................................................................................................61 4-2 Most popular Semivariogram Models...............................................................................61 4-3 Semivariogram and Covariance.........................................................................................62 4-4 Numerical Approaches to Mode l an Excavation in a Rock Mass.....................................63 4-5 WINSLIB SGS Example Location Data Values...............................................................63 4-6 WINSLIB SGS Example Results Graph............................................................................64 5-1 Fuller Warren Soil Boring Location..................................................................................83 5-2 Fuller Warren Histogram CB1...........................................................................................83 5-3 Fuller Warren Histogram CB2...........................................................................................84 5-4 Fuller Warren Histogram CB3...........................................................................................84 5-5 Fuller Warren New Borings Fre quency Distribution qu, qt and RQD..............................85 5-6 Frequency Dist ribution for quqt.........................................................................................86 5-7 Fuller Warren Bridge quqt and E Correlation....................................................................86 5-8 17th Street Soil Boring Locations.......................................................................................87 5-9 17th Street Frequency Distribution.....................................................................................88 5-10 17th Street Semivariogram.................................................................................................89 PAGE 11 11 5-11 17th Street Bridge Correlation quqt vs E............................................................................90 5-12 17th Street Bridge FLAC Model Grid................................................................................91 5-13 17th Street Axial Force vs Pile Displacement....................................................................92 5-14 17th Street Correlation Length vs Cohesion Mean.............................................................93 5-15 17th Street Correlation Length vs Total Bearing Capacity.................................................93 5-16 17TH Street Correlation length vs End Bearing Capacity...................................................94 6-1 FDOT Basis of Estimates Handbook Descript ion for the Item 455 88 Drilled Shaft..102 6-2 FDOT Basis of Estimates Handbook Descri ption for the Item 455 122 Unclassified Shaft Excavation............................................................................................................103 6-3 Example of the 2006 Item Average Unit Cost for the Items 455 88 5 and 455 122 5.....104 D-1 Total Capacity Frequency Distri bution 5 feet Corr elation Length..................................131 D-2 Total Capacity Frequency Dist ribution 12 feet Correlation Length................................131 D-3 Fuller Warren Bridge Old and New Borings...................................................................132 D-4 Fuller Warren Bridge Old Borings..................................................................................133 D-5 Fuller Warren Bridge New Borings.................................................................................134 D-6 17th Street Bridge Old and New Borings.........................................................................135 D-7 17th Street Bridge New Borings.......................................................................................136 D-8 Fuller Warren Bridge New Boring CB1..........................................................................137 D-9 Fuller Warren New Boring CB2......................................................................................138 D-10 Fuller Warren New Boring CB3......................................................................................139 PAGE 12 12 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT OF A RATIONAL DESIGN APPROACH (LRFD phi) FOR DRILLED SHAFTS CONSIDERING REDUNDANCY, SPA TIAL VARIABILITY, AND TESTING COST By Johanna Karina Otero December 2007 Chair: Ralph Ellis Cochair: Michael McVay Major: Civil Engineering New designs move toward larger single shaft, so the need to improve LRFD resistance factors, for nonredundant shaft, emerge. In ge neral geotechnical desi gn practice involve analysis using representatives values of design pa rameters,(like strength, recoveries, etc), usually an average or lowest value obtained from fiel d and laboratory test results. It followed by an application of a suitable factor of safety. In nature soil parameter varies in horizontally and vertically direction, so our rese arch used the same soil boring parameters, but this time use information obtained from sites localized close to the design site instead using the whole site average. Random soil models were created based on geostatistics analysis using soil parameters. The created random soil models were used on a fin ite element program that modeling a three feet diameter, twenty feet long drilled shaft, givi ng the drilled shaft capacity for each random soil model and a suitable, factor. PAGE 13 13 CHAPTER 1 INTRODUCTION Introduction This research initiative was based on the n eed to improve the LRFD resistance factors, for nonredundant shaft design, due the new designs methods moves toward larger single shaft design (e.g. Cross Town, New River, etc). Most geotechnical analysis in general prac tice involve analysis using representatives values of design parameters,(like strength, recoveri es, compressibility, etc), usually an average or the lowest value obtained from field and laborator y test results, and it followed by an application of a suitable factor of safety to get an allowable loading c ondition. However, in nature soil parameter varies in both horizonta lly and vertically direction. Our case used the same soil boring paramete rs than those used on most geotechnical analyses, but this time use information obtained from sites localized close to the design site instead using the whole site av erage. Random soil models were created based on geostatistics analysis using soil parameters. The created random soil models were used on a finite element program that modeling a six feet diameter, twenty feet long drilled shaft, giving the drilled shaft capacity for each random soil model. Additionally, a cost comparison between usi ng the actual method involving an increment on the drilled shaft construction due to us ing a bigger LRFD resistance factors, And using the proposed LRFD resistance factors, but with an increment on additional field coring of rock around the location where the sh aft will be is accomplished. Background Foundation design depends basically on the engineer ing properties of the soil or rock that is supporting the foundation. But the soil characteris tics at any site frequently are non- PAGE 14 14 homogeneous, that means that the soil profile may vary. Therefore, for estimate the natural soil or rock in-situ properties, it is necessary to pass by two phases; site characterization and subsoil exploration. Site Characterization On this phase, the engineer glances for forma tion of the soil origin and alterations that usually are caused by the environment processes, like chemical weatheri ng and the introduction of new substances. Those alterations vary on space and time. If the engineer has an understanding of soil formation and later alterati on of geotechnical materials, he will have a better acknowledge of the materi al variability and the behavi or that it could have during construction process and structure lifetime. Subsoil Exploration This phase is where the engine er obtains information that as sists him/her on calculations of the load bearing capacity of the foundation, estima tion of the possible settlement of a structure, establishing foundation problems, choosing the appropriate foundation ty pe, and determining construction methods for changing subsoil condi tion. The subsoil phase has three basic steps; collection of preliminary information, reconnaissance and site. Geotechnical variability Natural soils are rarely homogeneous and highl y variable in their pr operties. This soil variability can be classified into three main cat egories. The first is the location of boundaries between materials (see Figure 1-1). The second is litho logical heterogeneity that is the locations of anomalies, or areas of significantly differences properties, within a single material type (see Figure 1-2). And the third is inhe rent spatial soil variability (see Figure 1-3). Soil and rock material vary so that a property measures at two different points will have different values, assuming no error on measurement. PAGE 15 15 Conventional geotechnical modeling The conventional method of modeling soil structur es is to evaluate the results from field testing studies and then to make soil profiles. In theses profiles, each layer is assumed to be homogeneous with singles values for the engine ering properties of each layer. This properties information is obtained from in situ soil testi ng and lab testing. This information is evaluated later by the engineer and a single conservative value is chosen to represent the property of the material. The variability normally is not quantified. The usual design practice for soil design is deterministic. This invol ves the estimation of ultimate bearing capacity using average values of design parameters and application of a suitable factor of safety (F) to arrive an allowa ble bearing capacity (Griffiths & Fenton 1999). LRFD The purpose of foundation design is to guarantee that a system achieves adequately in its design life. However, there are some uncertain ties on the two phases described above, (site characterization and subsoil exploration) that ma ke it impossible to ensure that any unfortunate performance will occur under all possible circumstances. Foundation failures are always undesirable ev ents. They occur for diverse reasons, negligence, lack of knowledge, greed etc. The probability of failure is often higher for projects involving new materials, technology, and extreme parameters (lar ger shaft diameter) for which there is little or no pr ior experience. Therefore, the desi gn provisions include built-in safety margins: load effects are usually overestimated and resistances are underestimated. In load and resistance factor design (LRFD), load components are multiplied by load factors and resistance is multiplied by a resistance factor. The basic equation is: Rn > i Qi (1-1) PAGE 16 16 Where i is a load factor applied to load components Qi and is resistance factor applied to the resistance (measured of load carrying cap acity) Rn In words it equation says that the capacity of the foundation (modified by the factor ) must be larger than the total effect of all the loads acting on it. The mention above design formulas are deve loped by code committees with input from practicing engineers, researchers, and scientists However, things are ch anging and there are new requirements that need to be satisfied, fo r example moving toward larger single shaft construction. New rules are required, for example f ield coring of rock at the location of the as built non-redundant shaft (FDOT Structures Bulle tin, 2005). Similar to cycles, new requirement results could improve the formulas over again. The goal of load and resistance factor design (L RFD) analysis is to develop factors that decrease the nominal resistance to give a design with an acceptabl e and consistent probability of failure. To accomplish this, an equation that incor porates and relates togeth er all of the variables that affect the potential for failure of the struct ure, must be developed for each limit state. The parameters of load and resistance are considered as random variables, with the variation modeled using the available statistical data. A random vari able is a parameter that can take different values that are not predictable. An example is compressive strength of the soil, qu that can be determined using a testing machine. There are three levels of probabilistic design : Levels I, II, and III (Withiam et al. 1998; Nowak and Collins 2000). The Level I method is the l east accurate. It is sufficient here to point out that only Level III is a fully probabilistic me thod. Level III requires complex statistical data beyond what is generally available in geotechnical and structural engineering practice. Level II and Level I probabilistic methods are more viable approaches fo r geotechnical and structural PAGE 17 17 design. In Level I design methods; safety is measured in terms of a safety factor, or the ratio of nominal (design) resistance and nom inal (design) load. In Level II, safety is expressed in terms of the reliability index, The Level II approach generally requires iterative techniques best performed using computer algorithms. But for simple cases, there are available closed-form solutions to estimate Closed-form analytical procedures to estimate load and resistance factors should be considered approximate, with the ex ception of very simple cases where an exact closed-form solution exists (Calibration to Determine Load and Resistance Factors for Geotechnical and Stru ctural Design 2005). For LRFD calibration purposes, statistical characterization should focus on the prediction of load or resistance relative to wh at is actually measured in a structure. Theref ore, this statistical characterization is typically applied to the ratio of the measured to predicted value, termed the bias. The predicted (nominal) value is calculated using the design model be ing investigated. Note that the term bias factor (or bi as) is typically defined as the ra tio of the mean of the measured value divided by the nominal (predicted) value. However, for the purpose s described herein, the term bias is used to refer to individual measured values of load or resistance divided by the predicted value corresponding to that measured value. Regardless of the level of proba bilistic design used to perf orm LRFD calibra tion, the steps needed to conduct a calib ration are as follows: Develop the limit state equation to be evaluated, so that th e correct random variables are considered. Each limit state e quation must be developed base d on a prescribed failure. Statistically characterize the data. Key parame ters include the mean, standard deviation, and coefficient of variation (COV) as well as the type of distribution that best fits the data (i.e., often normal or lognormal). Determine load and resistance factors using reli ability theory. It must be recognized that the accuracy of the results of a reliability theory analysis is directly dependent on the adequacy, in terms of quantity and quality, of the input data used. The final decision made PAGE 18 18 regarding the magnitude of the load and resistance factor selected for a given limit state must consider the adequacy of the data. If the adequacy of th e input data is questionable, the final load and resistance factor combinati on selected should be more heavily weighted toward a level of safety that is consistent with past successful design practice, using the reliability theory results to increase coming as to whether or not past practice is conservative or nonconservative exists (Calib ration to Determine Load and Resistance Factors for Geotechnical a nd Structural Design 2005). Current assessment of drilled sh aft skin and tip resistance is performed on laboratory rock core samples (unconfined compression, split te nsion, and intact Youngs Modulus) recovered from a site. Generally, all the samples are averag ed over the whole site us ing either a log normal distribution or arithmetic m ean throwing out one standard deviation above and below. Unfortunately, these methods dont account for spa tial variability of strength and voids, i.e. recoveries at a specific locale, wh ich is important for end bearing fo r a particular shaft. For this stage a probabilistic approach (Monte Carlo, Bayesian etc.) will be developed to identify the local strength, recovery, etc. for a specific shaft (i.e. use data near location) as well as for the whole site. From the specific local e data, LRFD resistance factors, may be determined for end bearing based. The LRFD resistance factors, for end bearing will also be determined using the geometric mean (lognormal) from the whole site as well. The FDOT online Internet Foundation Database (e.g. Osterberg, Statnamic results) has sufficient laboratory data to determine LRFD resistance factors, for end bearing on a site basis, but not for a specific location within a site. Additionally, there are many methods have been developed to calibrate the LRFD resistance factors using statisti cal data. FOSM (First Order Second Moment) is popular because it does not require a computer pr ogram to find the results. FORM (First Order Reliability Method) is more complicated that FOSM and iterates to find a so lution. Each of these methods results in a different set of resistance factors. The one used on this research was the FOSM. PAGE 19 19 FMOS First Order Second Moment FOSM state for First Order Second Moment, Fi rst Order because use the first-order terms in the Taylor series expansion, Second moment because only means and variance are needed. It has been used (NCHRP 507, 2004) to calibrate LRFD factors using a statistical dataset containing the measured and predicted resistances. The bias of member i of the dataset is defined as, n m ir r (1-2) where i is the bias, rm is the measured resistance, and rn is the nominal resistance. Each element in the dataset will have a corresponding bi as. The average of these biases is found with the following equation. N Ei R ] [ (1-3) where N is the number of elements within th e dataset. The standard deviation of the dataset is, 1 ] [2 N ER i R (1-4) The coefficient of variation (COV) of the bias data is, ] [ ] [R R RE COV (1-5) The reliability index is found using a function of the two ra ndom variables R, resistance and Q load. Assuming RN and QN are normally distributed, this combined function would be, N N N NQ R Q R g ) ( (1-6) PAGE 20 20 When QN is larger then RN, g() is negative. Therefore, failure can be defined as when g() is less then or equal to zero. However, FO SM assumes that the load and resistance random variables are lognormal random variables, this limits the load and resistance values to only positive numbers. Now considering the relationship between a normally distributed random variable RN, and a lognormal random variable R, N RR R e RN ln (1-7) Writing the g(R,Q) equation in terms of lognormal random variables yields, Q R Q R Q R g ln ln ln ) ( (1-8) This equation is equivalent to the first defini tion of g(R,Q). When R is less then Q g() will still be negative. The g(R,Q) function is a random variable. Q R Q R g G ln ) ( (1-9) Yet, R/Q is a lognormal random variable. Theref ore the distribution of ln(R/Q) is normal. This results in the random variab le G having a normal distribution. Reliability index The reliability index ( ) is defined as the mean value of G (E[G]) divided by the lognormal standard deviation of G ( G). GG E ] [ (1-10) As previously defined, ) ln( ) ln( Q R G (1-11) PAGE 21 21 with R and Q being lognormal random variables. This yield, 2 2]) [ ( 1 ] [ ln ]) [ ( 1 ] [ ln ] [ )] [ln( )] [ln( ] [N N N NQ COV Q E R COV R E G E Q E R E G E 2 2]) [ ( 1 ] [ ]) [ ( 1 ] [ ln ] [N n N NR COV Q E Q COV R E G E (1-12) With RN and QN being normally distributed, so that E[RN] and E[QN] are the normal means. The coefficients of va riation are also calculated us ing the normal means and normal standard deviations. )] ]) [ ( 1 )( ]) [ ( 1 ln[(2 2 N N GQ COV R COV (1-13) This results in the reliability index being defined as: )] ]) [ ( 1 )( ]) [ ( 1 ln[( ]) [ ( 1 ] [ ]) [ ( 1 ] [ ln2 2 2 2 N N N N N NQ COV R COV R COV Q E Q COV R E (1-14) Solving for the resistance factor The following derivation for the resistance fact or is based largely on NHI 1998. Solving for the resistance factor begins w ith the fundamental LRFD equation. i i nq r (1-15) In this equation rn stands for the nominal resistance. Solving for the resistance factor and plugging in the bias yields: PAGE 22 22 ] [ ] [ ] [ ] [ 1R N n R n N R n N i i nE R E r E r R E r R q r (1-16) i i N Rq R E E ] [ ] [ (1-17) E[RN] is the expected value of the normally di stributed resistance random variable. The next step involves solving the reliability inde x equation previously de rived (equation 1-14) for the E[RN] term. ) ]) [ ( 1 ( ) ]) [ ( 1 ( ] [ ] [2 2 )] ]) [ ( 1 )( ]) [ ( 1 ln[(2 2N N Q COV R COV N NR COV Q COV e Q E R EN N T (1-18) This is then substituted into the fundamental LRFD equitation )] ]) [ ( 1 )( ]) [ ( 1 ln[( 2 22 2] [ ) ]) [ ( 1 ( ) ]) [ ( 1 ( ] [N N TQ COV R COV N i i N N Re Q E q R COV Q COV E (1-19) NHI 1998 represents the coefficient of variation of the load as, 2 2 2]) [ ( ]) [ ( ]) [ ( QL COV QD COV Q COV (1-20) and rewriting this equation for dead and live loads yields, )] ]) [ ( ]) [ ( 1 )( ]) [ ( 1 ln[( 2 2 22 2 2] [ ) ( ) ]) [ ( 1 ( ) ]) [ ( ]) [ ( 1 ( ] [QL COV QD COV R COV N L QL D QD N RN Te Q E q q R COV QL COV QD COV E (1-21) With, PAGE 23 23 L QL D QD Nq E q E Q E ] [ ] [ ] [ (1-22) Where QD and QL are the dead and live load bias fact ors respectively. This results in, )] ]) [ ( ]) [ ( 1 )( ]) [ ( 1 ln[( 2 2 22 2 2]) [ ] [ ( ) ( ) ]) [ ( 1 ( ) ]) [ ( ]) [ ( 1 ( ] [QL COV QD COV R COV QL L D QD QL L D QD N RN Te E q q E q q R COV QL COV QD COV E (1-23) This equation is used to calibrate the resist ance factor using the FOSM method. It is dependent on the target reliability index and the ratio of dead to live load. Problem Statement In the last 20 years, the use of drilled shaft foundations as an alternative to driven piles for supporting bridges has become common practice. R easons for their use are: 1) higher resistance to lateral loads such as wind loads (e.g. hurricane s etc.) and ship impacts, 2) need to minimize construction noise and vibration in urban areas, 3) right of way constrains which require minimal foundation footprints and 4) the ec onomy of replacing large number of piles with a single or few drilled shaft with out pile caps. Also with the introduction of larger and more autonomous equipment, and the aspiration to reduce costs, shaft diameters have been getting larger and larger. Due to the loss of foundation redundancy or the move toward la rger single shaft construction (e.g. Cross-Town, New River, Ringling, etc.), field co ring of rock at the location of the as built non-redundant shaft is now required (F DOT Structures Bulletin, 2005). However, to accurately assess skin and end bearing of a non-redundant shaft, the need for coring in the vicinity of a proposed sh aft during the design phase is also of strong interest. For instance, the thickness of limestone layers, recoveries (voids), strength and compressibility in the near vicinity of the shaft may significantly improv e the LRFD resistance factors, for design. Consequently, PAGE 24 24 there is a strong need to asse ss the LRFD resistance factors, for shaft design, e.g. end bearing, based on the frequency distributi on of strengths, recoveries and compressibility data for the whole site vs. a specific location, especially for non-redundant shaf ts. In addition, there is the question as to the number of cores, sample s etc. to ensure a specific reliability. Fortunately, a probabilistic based LRFD resist ance factor assessmen t answers the latter questions. For instance, using a Mo nte Carlo or Bayesian theory, strength, compressibility, etc., statistical (mean, standard deviation, etc.) properti es for a specific shaft or for the whole site may be generated from core and laboratory data near a specific shaft or over the whole site. Using random sampling, kriging, Sequential Gaussian si mulation, end bearing, etc. may be computed for a specific shaft or for all the shafts on the si te. It is expected that the difference in LRFD resistance factors for end bearing will be significant different if applied at a specific location vs. the whole site. Objectives 1. To estimate the influence of the spatial vari ability of a site on the selection of Load Resistance Factor Design. 2. To assess the resistance factors, for drilled shaft design a pplying the modified FOSM (First Order Second Moment), based on the freq uency distribution of strengths, recoveries, compressibility data and spatial variability. 3. To calculate testing cost and compare t hose against the final shaft built cost. This comparison will be done by assuming spat ial variability testing influences. Methods The method used in this research was the Empi rical. It explains the data collected through the development of a model that hypothesizes about the relationship between the data and relevant variables of the environment. The empirical research is grounded in reality rather than in PAGE 25 25 some abstract territory. The base for this rese arch was soil data, and was done in five stages. Therefore, the abstract was replaced by collected data. The five research stages were literature review lab and field data collection, data analysis, LRFD resistance factor development and cost comp arison. Each of these stages will be explained in details in further chapters. PAGE 26 26 Figure 1-1. Location of Bounda ries between Materials. Figure 1-2. Litho Logical Heterogeneity. Figure 1-3. Inherent Spatial Soil Variability. -70 -65 -60 -55 -50 -45 -40 0.0020.0040.0060.0080.00100.00120.00 qu (tsf)Depth (ft) Peat lenses Bedrock Material A Material B Material C PAGE 27 27 CHAPTER 2 LITERATURE REVIEW The LRFD resistance factors, for end bearing, is determin ate without have into account spatial variability of strength and voids. On larger single shaft construction, spatial variability is important due to large cost involves on construc tion. The basis for belo w literature review was spatial variability, Reliability-Based Design, LR FD resistance factor design, and limestone parameters. Static and Dynamic Field testing of Drilled Shafts The Static and Dynamic Field testing of drilled shafts (FDOT and UF) past geotechnical research, is the first part of this research. One of the principal founding of that study was the proposed LRFD resistance factor, and ASD factor of safety for ONeill end bearing. However, that research required include a dditional rock properties to th e study (i.e. mass modulus of the rock) or simply add variables that can improve th e LRFD resistance factor that were reached (i.e. spatial variability). The Static and Dynamic Field testing of drilled shafts basically shows the necessity of have into account the drilled sh aft unit bearing on design. It du e many designers either neglected or uses a small nominal value. However, eviden t from the Osterberg tip results significant end bearing has been generated on drille d shaft founded in Florida Limestone. The study follows the ONeill tip resistance m odel, which identify tip resistance vs. tip displacement. The approach is dependent on th e rocks compressibility (i.e., Youngs Modulus, E) and strength (qu) characteristics. The procedure used there was the computation of all the tip resistances vs. tip displacement for the entire Osterberg tests available at that mome nt (six locations in total). It had two different approaches for each location, nearest boring (b etween 100 ft) and Random Selection based on all PAGE 28 28 the site selection. For each available test, a comparison between measur ed and predicted FDOT failure resistance is made. Furthermore, the same comparison was complete for nearest boring and random selection. The LRFD specifications as approved by AASHT O recommend the use of load factors to account for uncertainty in the load, and resistan ce factor to account for uncertainty in the materials. Therefore, this research fo llowed the AASHTO recommendation saying that a probabilistic approach for estimating resistance f actors be used on a database of measured and predicted values. From that procedure LRFD factors, Probability of fa ilure (Pf) and Fs Based on Reliability for nearest boring and random selec tion approach were calculated. Table 2-1 and Table 2-2 showed the results obtained in the Static and Dynamic Field testing of drilled shafts research. On the first column is the Reliab ility for drilled shafts. The Second column is the LRFD factor. And, the fourth and fifth columns pe rtain to probability of failure and factor of safety. Comparing the LRFD factor fr om nearest boring and random se lection results, the nearest boring has higher resistance factor for the same design approach. Based on this study results evidently, the use of the neares t boring greatly diminished the va riability of rock properties and the subsequent mobilized unit end bearing. Modeling Spatial Variability in Pile Ca pacity for Reliability-Based Design The American Petroleum Institute (API) recommends using site-specific data for soil properties when developing pile capacity profile s for offshore structures (API 1993). However, there are many situations where this site-specific information is not available or would be costly and time consuming to obtain. It is therefore advantageous to be ab le to predict the expected pile PAGE 29 29 capacity at a site that does not have a site-s pecific soil boring by using the properties of the offshore field as a whole. This paper does the introduction to the development of a site-specific model for predicting axial side capacity, which is the first step for a ac hieving the same level of reliability in design at a site whether or not a soil boring has been dril led at that site by using the properties of the offshore fields as a whole. This paper develope d a similar procedure to the Static and Dynamic Field Testing of Drilled Shaft analysis. But, instead predicting axial side capacity the named study predicted end bearing capacity. The model provides a methodology to predict site specific pile capacity profiles with depth and to quantify the uncertainty associated w ith these predictions. The process of model development consists of the following steps: (1) establish a conceptu al geological model; (2) compile geotechnical data to relate the geol ogical model to pile capacity; (3) develop a quantitative model describing spatia l trends and variability in pile capacity; and (4) calibrate the quantitative model with geotechnical data. The models are part of a reliability-b ased methodology for design offshore pile foundations without site-specific geotechnical data that could be used on a lot of cases. The paper is completed with three examples of the application of the model on real cases. Reliability-Based Foundation Design for Transmission Line Structures The Electric Power Research Institute pub lished on 1988, three volumes on ReliabilityBased Foundation Design for Transmission Line Structure, Volume 1 Geotechnical Site Characterization Strategy; and Volume 3 Uncertainties in Soil Property Measurement. Each of those volumes focused on geotechnical probl ems. The first volume explained on its second chapter Geotechnical Material Variability a guide for to do Geotechnical modeling having into PAGE 30 30 account the material variability. Al so, explained reasons for geotech nical material variability and random field models that could be helpful for this research. The second chapter titled Geot echnical Material Variability explained topics like reasons for geotechnical variability, conventional subs urface geotechnical modeling, and random field models. Also, shows a procedure (statistical model) for to quantify variability of the soil and measurement errors. It procedure is alternativ e to the conventional subsurface modeling that requires a great deal of engineeri ng judgment to interpret the resu lts of discrete measurement and generalized them over depth and lateral extent The procedure consist on uses a consistent mathematical model, such as a random field mode l. Explanations of some steps that should be followed for to do the model are on that chapter also. The steps are basically to analyze spatial variability, trend, distribution of the property about its mean and correlation. Transportation Research Board Circular E-C079 The Transportation Research Board Circ ular E-C079, published on September 2005, described a complete procedure for to calibrate a nd determine the load and resistance factors for geotechnical and structural design. It included all the steps that will necessary to follow. Also, it provides alternatives for to do the calibration of the model after the factors have been obtained. The circular document guides the reader starti ng in an overview of the calibration approach through the final selection of Load and Resistance Factors. In th e course, explain with examples and applications, the limit state equation develo pment, some calibration concepts, the target reliability index selection, statistical consid eration of calibration and characterization, how estimate the load and resistance factors, and calibrations using the Monte Carlo method with different variables. It text will be useful in the process of de veloping the phi factor. The application of the Monte Carlo method is an option for to have a si mulation of the data obtained. It due the data PAGE 31 31 obtained on the field is reduced due the costs im plied on its acquisition. Also, some guidance on statistical characterization will be used as technique of estimating the load and resistance factor would be applied. Estimation for Stochastic Soils Models The Journal of Geotechnical a nd Geoenvironmental Engineering paper, published in 1999 by Gordon A. Fenton, talked about the uncertainty in spatial soil variati on and how to quantify it rationally. It described how the mean and varian ce are not sufficient for to make a reliability study, that each day more clients and engineers ar e interested in more sophisticated models and rational soil correlation structures. This pape r clarified reasonable correlations models. Explained how soils are best repr esented using fractal or finite scale models. Also, explained how the soil parameters will be estima ted have been selected the model. The papers give solution to questions by looking at a number of tools which aid in selecting appropriate stochastic models. These tools included the sample covariance, spectral density, variance function, variogram, and wavelet variance functions. Additionally, common models, corresponding to finite scale and fract al models, are invest igated and estimation techniques discussed. Practice of Sequential Gaussian Simulation The Geostatistics Banff, published on 2004 a Marek Nowak and Georges Verly paper. It described the practice of sequential Gaussian si mulation within the mining industry. The paper shows a process for simulation with the objectiv e of reducing the mistakes that could be undetected due to the lack of theory of simulatio n in practice. The paper described four of the most important aspects of the process, like, a gradual trend adjustment, a modified bootstrap approach, a number of pre and post simulation check. All of the approaches, solutions and PAGE 32 32 checks presented in this paper are simple, flex ible, and can be easily implemented in other industries. Bearing Capacity of a Rough Rigid Strip Foot ing on Cohesive Soil-a Probabilistic Study The paper indicates the use of a probabilistic study on the bearing capacity of a rough rigid strip footing on a cohesive soil. Th e first step on this paper was to use statistics help for to create random field model. The parameters used for this purpose were Young modulus E, Poison ratio and undrained shear strength. The fi rst two were held constant a nd the shear strength is modeled as a random variable. It is assumed to be ch aracterized by a lognormal distribution. And this information was used for to get the spatial corr elation function and the correlation coefficient length needed for to generate random fields. Af ter getting the random fi elds a finite element method was used for to recreated the footing and get the bearing capacity of it. The researcher of this paper was not working with real data if not with assumed statistical properties (our case is using real field data). The last stage of this paper was the Monte Carlo simulation for each set of assumed statistical properties. E ach realization, while having the same underlying statistics, had fairly different spatial pattern of shear strength values beneath the footi ng and hence, a different value of bearing capacity. Our research followed a very similar procedure that the used on this investigation paper, but the diffe rences are that this paper did all the analysis based on assumed statistical properties and our research are real soil properties obtained from the field and instead using a strip footing our is thir ty two length drilled shaft. This paper was very helpful in the description of their procedur e and the results obtained. Additionally to these papers mentioned are about twenty to thirty more that made contributions to the investigations, the most relevant are, Observations on Geotechnical reliability-based design development in North Am erica, Spatial Trends in Rock Strength-can they be Determined from core holes?, and D rilled Shaft Design for Transmission structures PAGE 33 33 Using LRFD and MRFD and the rest of them are mentioned on the references or through the research. PAGE 34 34 Table 2-1. LRFD Factors, Probability of Failure (Pf) and Fs Based on Reliability for Nearest Boring Approach (FDOT & UF 2003). Reliability, LRFD Pf (%) Factor of Safety 2.0 0.868.51.65 2.5 0.711.01.98 3.0 0.600.12.37 3.5 0.500.012.84 4.0 0.420.0023.40 4.5 0.350.00024.07 Table 2-2. LRFD Factors, Probability of Failure (Pf) and Fs Based on Reliability for Random Selection (FDOT & UF 2003). Reliability, LRFD Pf (%) Factor of Safety 2.0 0.568.52.60 2.5 0.431.03.32 3.0 0.330.14.24 3.5 0.260.015.42 4.0 0.210.0026.92 4.5 0.160.00028.84 PAGE 35 35 CHAPTER 3 DATA COLLECTION The Data Collection was divided in two different research stages. The first one, the existent data was recollected from divers e resources, like Florida Department of Transportation database, University of Florida past rese arches, and soil labs maps. And s econdly, the data obtained from the soil borings from the field and processed on the FDOT Materials lab. Both new and old data was analyzed and it made contribut ion to the final investigation. Existent Data Collection The existent lab data was gathered from di fferent resources like, the FDOT database, University of Florida Geotechnical Department and Florida Department of Transportation Districts past projects. Among the data that was gathered are strengths (q u-qt), recoveries and compressibility, as well as load testing informati on. The used data was taken from four of the seven projects available around Flor ida that at the time of the init ial investigation had available load test information and additionally any soil bo ring data, which were rele vant to the research. These four projects that had th e requirements described in the last paragraph were Apalachicola Bridge (Calhoun), Victory Bridge (Chattahooch), Fuller Warren Bridge (Jacksonville) and 17th Street Causeway (Fort Lauderdale). The localiza tion around Florida of the mentioned bridges is showed in Figure 3-1. The other three sites that app ear in the location map as a wh ite shadow belong to bridges that had some load test information at the time of the initial investigation, but the load test shafts were set in a soil different to limestone. The data obtained from each one of the bri dges showed on the figure is the Measured Unit End Bearing from Osterberg Load Tests. A summ ary of this information is showed in the Table 3-1. The table contains in the first column the bridges names, the shaft number and length in the PAGE 36 36 second and third columns respec tively. The fourth is for th e unknown friction and the bottom movement on the fifth. The last four columns be long to information about the failure status and the values for each type of the failure. The mobili zed bearing is described as a value less than the shaft diameter over thirty shaft displacement value. FDOT failure is when the displacement is exact that displacement rate and Maximum over it. The values used in the investigation from the above table were the Bottom movement, FDOT failure, Maximum failure and Mobilized bear ing value. Those results were compared with the Predicted unit end bearings ob tained from the finite element model for the different random fields created using the informa tion obtained from the soil boring la b results. The lab results used on the random field creation include s strengths (qu-qt), recoveries (REC) and compressibility for to predict the Unit End bearing. An example from the 17th Street Bridge is the Table 3-2. The Figure shows the bridge name with the state project number on the title. The first row includes the soil boring name and location along the bridge. The first column descri bes the elevation of th e sample, and the other six columns show the strengths (qu and qt), reco very and RQD. This is just one unsystematic example but the complete tables used for each on e of the mentioned bridges are illustrated on the APPENDIX A. New Field Data Collection The second stage for data collection was th e information obtained from the new soil borings on the bridges field. The bridge site sele ction was done using a preliminary research for the mentioned bridges. It includes details as the accessibility to the site (not to be under water), that the site were on limestone ro ck, the selected location had to ha ve strength data, that the load test have preferably a FDOT end bearing failure, and last but not lest that the O-Cell were on the tip of the drilled shaft. Due to theses details so me of the seven projects were not used. Those are PAGE 37 37 the bridges showed on the Figure 3-1 with a white shadow. Th e principal two recurrent failed details were that the load test locations were offs hore, and that the load te st results did not reach the tip movement (end bearing failure criteria).Af ter the preliminary selection the finally four selected sites or bridges were: Apalachicola River Bridge (District 3) Victory Bridge (District 3) Fuller Warren Bridge (District 2) 17th Street Bridge (District 4) The field exploration was accomplished by Un iversal a soil exploration company in Jacksonville and Fort Lauderdale. And the rock cores obtained from Universal were tested at the State Materials Office soil lab district 2 (Gai nesville Fl.). Consequently, strength values, recoveries and compressibility r ecords were obtained from them and subsequently were used to establish LRFD resistance factors for end bearing for each specific site location. From the pre-selected sites name above, just two of them were test ed. It is the case of Fuller Warren Bridge Jacksonville (District 2) and 17th Street Bridge Fort Lauderdale (District 4). The data obtained from each bridge is showed in the APPENDIX B but an example of the data obtained from the State Materi al Office lab is showed in the Table 3-3. In this table is illustrated the information for each rock core took from the field, as length, diameter, depth, unit mass, qu, qt, recovery, RQD, density, etc. The data obtained from theses tables was used on the simulation of random fields and later on the model on the finite element program. The next couple of paragraphs are dedicated to relevant information about the two bridges selected for the research. The Fuller Warren Brid ge (District 2) It is localized over the St. Johns River in downtown Jacksonville on th e Interstate Highway 95 (I-95). It replaced the old Gilmore Street Brid ge. It has four Load tests LT-1, LT-2, LT-3 and PAGE 38 38 LT-4. In the Figure 3-2 are showed the plan view and the soil profile indicating the mentioned shaft load tests localization. Only the load test LT-4 was used on this research. Additionally, in the Figure 3-3 are couple of pictures under the Fulle r Warren Bridge during the site inspection. These pictures shows the position of the load te st LT4 where the additional soils boring were realized around. 17th Street Bridge Fort La uderdale (District 4) This is a bascule replacement bridge for the old movable bridge on S.E. 17th Street Causeway over the intercostals waterway in Fort Lauderdale, located on Broward County. The 17th Street Causeway Bridge has four Osterberg Load test s LTSO-1, LTSO-2, LTSO-3 and LTSO-4. The only load test used was the LTSO4. Figure 3-4 shows pictures where the load test LTSO4 is localized. Data collection for the Fuller Warren Bridge was realized by the Jacksonville Universal Engineering Science firm. The soil samples were ta ken to State Materials Office soil lab district 2 (Gainesville Fl.) were all the necessary lab exploration were r ealized. The same procedure was followed with the 17th Street Br idge Fort Lauderdale but the fi rm in charge to do the soil exploration was PSI Engineering. PAGE 39 39 Table 3-1. Measured Unit End Bearing from Load Tests. Shaft Name Shaft Length (ft) Unknown Friction (ft) Bottom Move. (in) Failure Status Mobilized Bearing (tsf) FDOT Failure (tsf) Max. Failure (tsf) LSTSO 1 119.4 5.20.624Both x xx LSTSO 2 142.0 9.11.95Tip Failx xx LSTSO 3 100.1 11.11.89Both 41.5 xx 17th Street Bridge LSTSO 4 77.5 2.63.53Tip Failx x66.4 Test 1 64.2 04.41Tip Failx 61.790.3 Test 2 101.2 02.97Tip Failx 2839 Test 4 113.9 03.2Tip Failx 22.430.2 Acosta Bridge Test 5A 87.8 05.577Tip Failx 18.529.4 46-11A 85.0 05.977Both x 72.692 53-2 72.0 02.1Both 70 xx 57-10 84.0 01.7Both 60 xx 59-8 134.0 91.3Both 65 xx 62-5 89.2 02.69Both x 3840 Apalachicol a Bridge 69-7 99.1 04.46Both x 3644 LT-1 41.0 00.23Skin Fail 87 xx LT-2 27.9 02.56Both x 80.889.5 LT-3a 120.7 02.94Both x 3434 Fuller Warren Bridge LT-4 66.8 03.12Both x 3470 26-2 38.4 9.80.4Skin Fail x xx 52-4 54.5 4.332.9Both x 139.2x Gandy Bridge 91-4 74.7 6.72.5Both x 42.9x Hillsborough Bridge 4-14 70.8 7.331.74Both x xx 3-1 33.2 00.5Both 109 xx 3-2 38.6 9.660.4Skin Fail x xx 10-2 46.6 7.72.367Both x 45x 19-1 45.0 00.528Both 124.4 xx Victory Bridge 19-2 50.7 12.140.4Skin Fail x xx PAGE 40 40 Table 3-2. 17th Street Bridge Soil Boring Data (State Project No. 86180-1522). BB-1 (32+93) S-4 (33+00) EL (ft) qu REC RQD qt REC RQDEL (ft) qu REC RQD qt RECRQD -65 32.23022-32211.268.3 -72 27.346728-36116.919.4 -85 114.213 7 BB-4 (34+81) BB-9 (35+06) EL (ft) qu REC RQD qt REC RQDEL (ft) qu REC RQD qt RECRQD -69 32.7422 5 -115 26.55 -88 28.835 10 -131 24.6343 -131 32.943 S-12 (35+29) BB-7 (35+44) EL (ft) Qu REC RQD qt REC RQDEL (ft) qu REC RQD qt RECRQD -32 211 -49 43.5184 -32 68.34-65414207 -49 117 -7237.8 -49 19.4-82120.89838 -72 19.6-82 26.39838 -9282.989838 -102 117.47667 -10882.44358 -131140.63510 -131 64.63510 BB-11 (35+53) BB-8 (36+10) EL (ft) qu REC RQD qt REC RQDEL (ft) qu REC RQD qt RECRQD -36 379.4 38 35 143.973835-39361.365 -36 189.013838-46158.74819 554819 -36 112.63835-46272.74819 53.994819 -75 26.333-46 76.784819 -98 27.04 60 23 68.76023-56285.05012 40.45012 -98 140.0160 23 -95 14.04175 PAGE 41 Table 3-3. Fuller Warren State Materials Office Soil Laboratory Data. State Materials Office Rock Core Effective/Revised: 4/27/05 Foundations Laboratory Unconfined Compression-Split Tensile By: G.J. Page 1 of 1 Boring /Core Samp. No. Depth Top (ft) Depth Bot. (ft) Test Date Length (in) Dia. (in) Wet Wt. (g) Wet Unit Wt. (pcf) L/D Rati o Corr. Factor CB-3/1 1U 41' 8/21/20064.8380 2.3950 853.2 149.1 2.02 1.00 2U 4.4327 2.3835 740.4 142.6 1.86 1.01 3T 2.4345 2.3100 335.2 125.2 1.05 4T 2.4350 2.3785 375.0 132.0 1.02 5T 46' 2.3500 2.3730 409.9 150.2 0.99 CB-3/2 1T 46' 8/21/20062.4165 2.2995 308.4 117.1 1.05 2U 4.3357 2.3655 774.8 154.9 1.83 1.01 3T 8/22/20062.3220 2.3760 406.1 150.3 0.98 4U 4.8068 2.3820 806.8 143.5 2.02 1.00 5T 2.3535 2.3720 400.6 146.7 0.99 6U 4.8825 2.3895 799.2 139.1 2.04 1.00 7T 2.3395 2.3870 393.8 143.3 0.98 8U 51' 4.8715 2.3890 865.4 151.0 2.04 1.00 CB-3/3 1T 51' 8/22/20062.3315 2.3510 380.8 143.3 0.99 2U 4.8632 2.3610 838.4 150.0 2.06 1.00 3T 2.4395 2.3110 376.5 140.2 1.06 4T 2.4330 2.3555 378.1 135.9 1.03 5U 4.8955 2.3430 734.4 132.5 2.09 1.00 6T 2.4855 2.3285 366.7 132.0 1.07 7T 2.4545 2.3375 328.7 118.9 1.05 8U 4.8125 2.3360 672.7 124.2 2.06 1.00 9T 2.3865 2.3230 332.8 125.3 1.03 10T 2.1210 2.3185 291.7 124.1 0.91 11U 4.7020 2.3455 676.5 126.9 2.00 1.00 41 12T 56' 2.4110 2.3595 369.5 133.5 1.02 PAGE 42 Table 3-3. Continued. Boring /Core Samp. No.w (%) Dry Unit Wt.(pcf) Max. Load (lbs.) S.T. Strength (psi) q(u) (psi) Displ. @ Fail (in) Strain @ Fail (%) %Recov./ %RQD Tare Wt. (g) Wet Wt. (g) Dry Wt. (g) CB-3/1 1U 5.32 141.6 67821505.6 0.0522 1.08 72/50430.31281.51238.5 2U 11.14 128.3 3530784.1 0.0634 1.43 72/50430.71168.71094.7 3T 26.01 99.3 36841.6 0.0633 72/50366.1698.4629.8 4T 16.40 113.4 1378151.5 0.0687 72/50431.4805.4752.7 5T 9.07 137.8 3224368.0 0.0515 72/50428.3837.2803.2 CB-3/2 1T 26.50 92.5 20423.4 0.0743 77/67428.1735.5671.1 2U 7.46 144.2 57201287.5 0.0549 1.27 77/67430.21196.61143.4 3T 8.10 139.0 1552179.0 0.0415 77/67430.3835.8805.4 4U 11.63 128.5 3252729.8 0.0541 1.13 77/67431.41237.81153.8 5T 10.86 132.4 1623185.1 0.0468 77/67371.5771.6732.4 6U 13.79 122.2 4229943.0 0.0563 1.15 77/67433.11230.01133.4 7T 11.05 129.0 1715195.5 0.0419 77/67312.1703.9664.9 8U 8.31 139.4 56901269.3 0.0454 0.93 77/67375.91239.01172.8 CB-3/3 1T 9.56 130.8 37944.0 0.0410 100/92366.0746.4713.2 2U 8.71 138.0 3187727.9 0.0630 1.30 100/92370.81207.21140.2 3T 4.54 134.1 12013.5 0.0237 100/92370.6746.2729.9 4T 14.37 118.8 24327.0 0.0276 100/92425.7802.9755.5 5U 18.48 111.9 501116.1 0.0297 0.61 100/92430.61164.01049.6 6T 19.11 110.8 16918.6 0.0236 100/92424.6790.5731.8 7T 28.86 92.3 889.7 0.0209 100/92430.4758.6685.1 8U 27.47 97.5 731170.5 0.0455 0.95 100/92302.8972.4828.1 9T 24.01 101.1 28732.9 0.0422 100/92425.0756.6692.4 10T 23.05 100.8 9312.1 0.0402 100/92410.1701.0646.5 11U 23.97 102.3 433100.3 0.0348 0.74 100/92428.21103.6973.0 42 12T 17.63 113.5 43748.9 0.0324 100/92428.4797.4742.1 PAGE 43 43 Figure 3-1. Load Test Bridge Locations. Figure 3-2. Fuller Warren Bridge Shaft Locations. LT 1 LT 2 LT 3 LT 4 PAGE 44 44 Figure 3-3. Fuller Warren Bri dge during Site Inspection. Figure 3-4. 17th Street Bridge Load Test Location. PAGE 45 45 CHAPTER 4 GEOSTATISTICS AND NUMERICAL MODEL Geostatistics Geostatistics were first devel oped to provide better estimate s of ore reserves. In coal mining, they have been used to evaluate energy c ontent, sulfur, ash, and other quality attributes of deposits. In fact, Geostatistics can be used to study many properties that vary in space, but are measured at distinct locations. Field Researches as diverse as hydrology, fo restry, air pollution, and global warming have all made extensive us e of Geostatistics. (Ledvina et al., 1994; Armstrong, 1998). The Geostatistics term has been used amply in mining design but just a few of times in geotechnical. Since it will be not a clear word, let me recall two definitio ns: Geostatistics: study of phenomena that vary in space and/or time (D eutsch, 2002) and Geosta tistics offers a way of describing the spatial continuity of natural phenomena and provi des adaptations of classical regression techniques to take advantage of this continuity. (Isaaks and Srivastava, 1989). Geostatistics deals with spatially auto correlated data. It is data that has correlation between elements of a random variable separa ted from them by a given interval. The basic idea of Geostatistics is this. Suppose the goal is to determine the cohesion in a limestone field. If two core holes are drilled just 1 ft apart from each other, one would expect that their cohesion values would be very similar. If a third hole is drilled 10 ft away, the cohesion value might be expected to change a little, but still be close the original value. As more holes are drilled further and further away, a distance is ev entually reached where the first holes no longer help predict the cohesion value. Between the basic elements of Geostatistics are: (Semi) variogram analysis charact erization of spatial correlation. PAGE 46 46 Kriging optimal interpolation; generates best linear unbiased estimate at each location; employs semivariogram model. Stochastic simulation generation of multiple equally probable images of the variable; also employs semivariogram model. (Semi) Variogram Establishing the spatial correla tion structure of a site having erratic variation in its soil properties would require an extens ive amount of subsoil exploration, which may not be feasible in many projects due to the high costs (Fent on & Griffiths 1999). One of the most common methods for to estimate the correlation coefficient length is the semivariogram. The semivariogram is a statistic that appraise s the average decrease in similarity between two random variables as the dist ance between the variables increas es. It describe how spatial continuity change as a functi on of distance and direction. Significant terminology is used to describe th e important features of the semivariogram model, these terms are: Sill: The semi variance value at which the variogram levels off. Also it is used to refer to the amplitude of a certain component of th e semivariogram. For the plot above, sill could refer to the overall sill (1.0) or to the difference (0.8) between the overall sill and the nugget (0.2). Meaning depends on context. Range: The lag distance at which the semivariogram (or semivariogram component) reaches the sill value. Presumably, autocorrelation is essentially zero beyond the range. Nugget: In theory the semivariogram value at the or igin (0 lag) should be zero. If it is significantly different from zero for lags very close to zero, then this semivariogram value is referred to as the nugget. The nugget represen ts variability at dist ances smaller than the typical sample spacing, including measurement e rror. The ratio of the nugget effect to the sill is often referred to as the relative nugget effect and is usually quoted in percentage. Trend: If the empirical semivariogram conti nues climbing steadily beyond the global variance value, this is often indicative of a si gnificant spatial trend in the variable, resulting in a negative correlation between variable values separated by large la gs. Three options for dealing with lag include: 1) Fit a trend surface and work with residuals from the trend 2) Try to find a trend-free direc tion and use the variogram in th at direction as the variogram for the random component of the variable 3) ignore the problem and use a linear or power variogram. See Figure 4-1. PAGE 47 47 Semivariogram models For the sake of kriging (or stochastic simu lation), we need to replace the empirical semivariogram with an acceptable semivariogram mode l. Part of the reason for this is that the kriging algorithm will need access to semivariogram values for lag distances other than those used in the empirical semivari ogram. More importantly, the semi variogram models used in the kriging process need to obey certa in numerical properties in order for the kriging equations to be solvable. (Technically, the semivariogram model n eeds to be non-negative definite, in order the system of kriging equations to be non-singular.) Therefore, geostatisticia ns choose from a palette of acceptable or licit semivariogram models. Using h to represent lag distance, a to represent (practical) range, and c to represent sill, the five most frequently used models are: The nugget model represents the discontinuity at the origin due to sm all-scale variation. On its own it would represent a purely random variable, with no spatial correlation. The spherical model actually reaches the specified sill value, c, at the specified range, a. The exponential and Gaussian approach the sill asymptotically, with a representing the practical PAGE 48 48 range, the distance at which the semi variance reaches 95% of the sill value. The Gaussian model, with its parabolic behavior at the origin, represents very smoothly varying properties. (However, using the Gaussian model alone w ithout a nugget effect can lead to numerical instabilities in the krig ing process.) The spherica l and exponential models e xhibit linear behavior the origin, appropriate for repres enting properties with a higher le vel of short-range variability. Examples of this model are showed in Figure 4-2. Anisotropy The omni directional semivariogram is that on e that for which the directional tolerance is larger enough that the directi on of any particular separation vector become unimportant. It contains all possible directions combined in to a single variogram. The calculation of the omnidirectional semivariogram does not imply that the spatial continuity is the same in all directions. It provides a starti ng point for to establishing some of the parameter required for sample semivariogram calculations. In many cases, a random variable shows different autocorrelation structures in different directions, and an anisotropic semivariogram model should be developed to reflect these differences. The most commonly employed model fo r anisotropy is geometric anisotropy, with the semivariogram reaching the same sill in all di rections, but at different ranges. In geological settings, the most prominent fo rm of anisotropy is a strong contrast in ranges in the (stratigraphically) vertical and horizontal directions, with the vertical semivariogram reaching the sill in a much shorter distan ce than the horizontal semivariogram. In some settings, there may also be significant lateral anisotropy, often refl ecting prominent directi onality in the depositional setting. PAGE 49 49 Covariance and correlogram There are two other tools used on describing sp atial continuity these are the Covariance and Correlation function. Though these two are equa lly useful, the semivariogram however is the most traditional. Under the condition of secondorder stationary (spatia lly constant mean and variance), the covariance function, correlo gram, and semivariogram obey the following relationships: C(0) = Cov(Z(u),Z(u))= Var(Z(u)) (h) = C(h) C(0) (h)= C(0)-C(h) In words, the lag-zero covarian ce should be equal to the glob al variance of the variable under consideration; the correlogram should lo ok like the covariance f unction scaled by the variance, and the semivariogram should look like the covariance function turned upside down. The representation is showed in Figure 4-3. Unlike time series analysts, who prefer to wo rk with either the covariance function or the correlogram, geostatisticians typi cally work with the semivariogr am. This is primarily because the semivariogram, which averages squared differ ences of the variable, tends to filter the influence of a spatially varying mean. Kriging Kriging technique was named after a Sout h African mining engineer named Daniel Gerhardus Krige who develops the method in an a ttempt to more accurately predict ore reserves. Kriging is a group of geostatistical techniques to interpolate the value Z ( x0) of a random field Z ( x ) (e.g. the elevation Z of the landscape as a function of the geographic location x ) at an unobserved location x0 from observations of the random field at PAGE 50 50 nearby locations Kriging computes the best linear unbiased estimator of Z ( x0) based on a stochastic model of the spatial dependence quantified either by the variogram ( x y ) or by expectation ( x ) = E [ Z ( x )] and the covariance function c ( x y ) of the random field. It have been demonstrated that kriging is not pos sible without knowledge of the semivariogram or the covariance. The kriging estimator is given by a linear combination of the observed values zi = Z ( xi) with weights chosen such that the variance (also called kriging va riance or kriging error): (with w0( x0) = 1) of the prediction error is minimized subject to the unbiased ness condition: Depending on the stochastic properties of the ra ndom field different type s of kriging apply. For the different types of kriging the unbiased ness condition is rewritte n into different linear constraints for the weights wi. The kriging variance must not be confused with the variance of the kriging predictor itself. PAGE 51 51 Types of Kriging Classical types of kriging are: Simple kriging assuming a known constant trend: ( x ) = 0. Ordinary kriging assuming an unknown constant trend: ( x ) = Universal Kriging assuming a general linear trend model IRFk-Kriging assuming ( x ) to be an unknown polynomial in x Indicator Kriging using indicator functions instead of the process itself, in order to estimate transition probabilities. Multiple indicator kriging is a version of indicator krig ing working with a family of indicators. However, MIK has fallen out of fa vor as an interpolati on technique in recent years. This is due to some inherent difficu lties related to operation and model validation. Conditional Simulation is fast becoming the acce pted replacement technique in this case. Disjunctive Kriging is a nonlinear generalization of kriging. Lognormal Kriging interpolates positive data by means of logarithms. For this research we were focused in two of theses types, Simple and Ordinary Kriging Simple Kriging Simple kriging is the most basic form of krigi ng in the sense that the model is the simplest in its mathematical formulation. The kriging weights of simple kriging have no unbiasedness conditi on and are given by the simple kriging equation system: Simple Kriging Interpolation The interpolation by simple kriging is given by: PAGE 52 52 Simple Kriging Error The kriging error is given by: which leads to the generalized least squa res version of the Gauss-Markov theorem (Chiles&Delfiner 1999, p. 159): Ordinary Kriging Ordinary kriging is an estimation method th at is often associated with the acronym B.L.U.E. for best linear unbiased estimator. Ordinary kriging is linear because its estimates are weighted linear combinations of the availabl e data; it is unbiased since it tries to have mR, the mean residual or error, equal to 0; it is best because it aims at minimizing R, the variance of the errors. The distinguish f eature of ordinary kriging, is its aim of minimizing the error variance. In ordinary kriging, it is used a pr obability model in which the bias and the error variance can both be calcul ated and then choose weights for th e nearby samples that ensure that the average error for our model, m R, is exactly cero and that our modeled error variance, R, is minimized. PAGE 53 53 Stochastic Simulation Stochastic Simulation is the process of bu ilding alternative, e qually probable, high resolution models of the spatial distribution of the random variab le in study. The simulation is called conditional if the resul ting realizations honor data values at their locations. Simulation differs from krigi ng in two primary aspects: In kriging the goal is to provide a best local es timate of the variable without specific regard to the resulting spatial statistics of the estimates taken together. In simulation, reproduction of global features and statistics take preceden ce over local accuracy. Kriging provides a set of local representations, wher e local accuracy prevails. Si mulation provides alternative global representations, where reproduction of patterns of spatial continuity prevails. Kriging provides only an incomplete measur e of local accuracy and no appreciation of joint accuracy when several lo cations are considered together. Simulations are designed specifically to provide such measures of accuracy, both local and involving several locations. These measures are given by the differences between alternative simulated values at any location (local accuracy)or the alternative simulated fields (global or joint accuracy). Sequential Gaussian simulation There are many algorithms that can be devised to create stochastic simulations (1) matrix approaches (LU Decomposition), which are not exte nsively used because of size restrictions (an N x N matrix must be solved where N, the numbe r of locations, could be in the millions), (2) turning bands methods where the variable is simu lated on 1-D lines and then combined into a 3D model; not commonly used because of artifacts, (3) spectral method using FFTs can be CPU fast, but honoring conditioning data requires an expensive kriging step, (4) fractal which are not used extensively because of the restrictive assu mption of self-similarity, and (5) moving average methods, which are infrequently used due to CPU requirements. The common approach adopted in recent times is the sequential Gaussian si mulation (SGS) approach. This method is simple, flexible, and reasonable efficient. PAGE 54 54 Sequential Gaussian Simulation is the most straightforward algorithm for generating realizations of a multivariate Gaussian field. It is provided by the sequential simulation principle of including all data availabl e within a neighborhood of the point on question, including the original data and all previously simulated values. Each variable is simulated sequentially according to its normal cdf fully character ized through a Simple Kriging system. The detailed steps in Sequential Gaussian Simulation are: Determine the univariate cdf representative of the entire study ar ea and not only of the sample data available. Transform data to normal space Establish grid network and coordinate system (Zrel-space) Assign data to the nearest grid node (take the closest of multiple data assigned to the same node) Determine a random path through all of the grid nodes Find nearby data and previous ly simulated grid nodes Construct the conditional distribution by kriging Draw simulated value from conditional distribution Check results Back transform (Statios 2001) By using different random number seeds the or der of visiting locati ons is varied and, therefore, multiple realizations can be obtained. In other words, since the simulated values are added to the data set, the values available fo r use in simulation are partly dependent on the locations at which simulations have already been made and, because of this, the values simulated at any one location vary as the available data vary. Software The wide range of public domain and low cost software now available means that the tools of Geostatistics are readily av ailable to the geotechnical. Wide ly used public domain software packages include WINGSLIB Geostatistical Softwa re Library, and Gstat the first one used for the case studies presented in this research. In addition, several comme rcial GISystems include PAGE 55 55 geostatistical functions and ther e is a range of commercial geostatistical packages. Before starting using the WINGSLIB software, a manual check test was realized. All the steps described on the Sequential Gaussian Simulation process, were followed and the results were positive. The data required for to do simulation using SGS in WINGSLIB software were: The variable to be simulated (Cohesion Values) The Semivariogram structure to be used The maximum and minimum of original data that should be used to simulate a grid node. Data Variance X, Y and Z coordinates for the available data Definition of the grid system The number of previously simulated point to use for the simulation of another node. Type of kriging to be used. This manual check was realized to demonstrat e that the results obtained from the Wingslib software are the same or similar to those obtained doing the process manually. The example in 2D used eight data values, showed in Table 4-2. The location on a plan view of data values is illustrated in Figure 4-5. The WINGSLIB results values are in Table 4-3 and those same results are represented in Figure 4-6 As you observe in Table 4-3 the last two values corre spond to the coordinates X,Y (0,2) and X,Y (2,0). Using WINSLIB the results were 198.95 and 5.52 respectively. And doing the process manually the results are 198.52 and 5.95 respectively. The difference is very small comparing the two results. So, it was proved th at using WINGSLIB the results obtained are similarly to those that are obt ained doing the process manually. Numerical Models Numerical models are available for the user in form of computer codes or programs. A numerical model program is capable of: (1) solving the equations of equilibrium, (2) satisfying the strain compatibility equations, and (3) following certain constitutive equations when PAGE 56 56 prescribed boundary conditions are set forth. The program will produce displacements and stress changes associated in addition to many other qua ntities of interest for geotechnical design. To select the appropriate for each case it is n ecessary to survey within the wide number of options and to select one that f it to each case. At this time ther e are three approaches to model engineering problems: Continuum, Discrete, and Hybrid. In the C ontinuum approach, there is no chance for a failure surface to be explicitly deve loped since model elements cannot separate at the boundaries except on pre-defined boundaries like int erfaces (see Figure 4-4). In the Discrete approach, elements are ready to se parate on boundaries but di scontinuity (failure surface) cannot propagate through the elements they are still modeled as continuum (see Figure 4-4 c). Finally, the Hybrid approach, as the name implies, incorporates both the Discrete and Continuum approaches (see Figure 4-4 e). The numerical solution methods include: Continuum methods: Finite Difference Method (FDM). Finite Element Method (FEM). Boundary Element Method (BEM). Discrete methods Discrete Element Method (DEM). Discrete Fracture Network (DFN) methods. Hybrid continuum/discrete models Hybrid FEM/BEM. Hybrid FEM/DEM. Other hybrid models. PAGE 57 57 From a survey made on South Africa (SIMRA C 1999) a list of many numerical models program available for the use in rock mechanics worldwide is showed in Table 4-1. FLAC3D (Fast Lagrangian Analysis of Continua) Flac3D is a powerful Three-dimensional cont inuum program for modeling soil, rock and structural behavior. The FLAC3D can model nonlinear systems as they evolve in time (Itasca 2002). Used interactively or in batch mode, FLAC is a general analysis and design tool for geotechnical, civil, and mining e ngineers that can be applied to a broad range of problems in engineering studies. The explic it finite difference formulati on of the code makes FLAC3D ideally suited for modeling geomechanical problem s that consist of several stages, such as sequential excavation, b ackfilling and loading. The formulation can accommodate large displa cements and strains and non-linear material behavior, even if yield or failu re occurs over a large area or if total collapse occurs. FLAC3D uses an explicit finite difference time-marching scheme to solve the equations of equilibrium. The equation of motion is solved to drive ne w velocities and displacements from stress and forces. Velocities are then used to calculate th e strain rates, from there a new stresses can be calculated through the constitutive equation. These calculations are carried out over one time step, during which velocities ar e assumed to be constant. The advantage of using the explicit formulation is that the numerical scheme stays stable even when the physical system is unstable. This is particularly advantageous, when mode ling non-linear, large strain behavior and actual physical instability. Th e disadvantage of the time-marching explicit scheme of the FLAC3D is that calculation times can be longer than those of implicit formulations. Materials are represented by polyhedral elements within a three-dimensional grid that is adjusted by the user to fit the shape of the object to be modeled. Each element behaves according to a prescribed linear or nonlinea r stress/strain law in response to applied forces or boundary PAGE 58 58 restraints. The material can yiel d and flow and the grid can defo rm (in large-strain mode) and move with the material that is represented. Th e explicit, Lagrangian calculation scheme and the mixed-discretization zoning technique used in FLAC3D ensure that plastic collapse and flow are modeled very accurately. Because no matrices ar e formed, large three-dimensional calculations can be made without excessive memory requirement s. The drawbacks of the explicit formulation are overcome by automatic inertia scaling and automatic damping that does not influence the mode of failure. FLAC3D offers an ideal an alysis tool for solution of three-dimensional problems in geotechnical engineering. The FLAC3D has many constitutive models bui lt in. The user has the option of choosing the most relevant constitutive model for his problem. The following FLAC3D material models are the most used: Elastic, isotropic; Drucker-Prager plasticity; Mohr-Coulomb plasticity; Strain-hardening / softening Mohr-Coulomb plasticity; Bi-linear strain-hardening / softening ubiquitous-joint plasticity PAGE 59 59 Table 4-1. Commercially Available Nume rical Programs for Rock Mechanics Study. Program Source Type(a) Use Complexity BESOL/ MINAP_97 Mining Stress Systems 2D BEM Common Simple BESOL/MS Mining Stress Systems 3D BEM Common Simple CSIR Minap32 CSIR Miningtek 2D BEM Academic Simple DIGS CSIR Miningtek 2D BEM Research Specialist Elfen CSIR Miningtek 2D FE M Testing Beta Mediocre Examine Rocscience Inc. 3D BEM Rare Mediocre FLAC Itasca Consulting Group Inc. 2D FDM Common Advanced FLAC3D Group Inc. 3D FDM Rare Complex Map3D Mine Modeling Ltd. 3D BEM Moderate Mediocre MINIFFT CSIR Miningtek 3D BEM Research Specialist MINSIM CSIR Miningtek 3D BEM Common Simple PFC2D Itasca Consulting Group Inc. 2D DEM Rare Complex PFC3D Itasca Consulting Group Inc. 2D DEM Rare Complex Phase Rocscience Inc. 3D DEM Rare Simple 3DEC Itasca Consulting Group Inc. 2D BEM Rare Complex UDEC Itasca Consulting Group Inc. 3D DEM Moderate Advanced WAVE CSIR Miningtek 2D3D FDM Research Specialist PLAXIS Plaxis BV 2D3D FEM Moderate Moderate ANSYS ANSYS, Inc. 3D FEM Rare Mediocre ABAQUS ABAQUS, Inc. 3D FEM Rare Mediocre ALGOR ALGOR, Inc. 3D FEM Rare Mediocre (a) BEM: Boundary Element Method; FDM: Finite Differe nce Method; DEM: Distinct Element Method; FEM: Finite Element Method. PAGE 60 60 Table 4-2. Sequential Gaussi an Simulation Data Values. X Coordinate Y Coordinate Values 0 0 80 0 1 190 1 0 10 1 1 80 1 2 200 2 1 5 2 2 80 Table 4-3. WINSLIB SGS Example Results. X Coordinate Y Coordinate Values 0 0 80 0 1 190 1 0 10 1 1 80 1 2 200 2 1 5 2 2 80 0 2 198.95 2 0 5.52 PAGE 61 61 Figure 4-1. Semivariogram Model. Figure 4-2. Most popular Semivariogram Models. PAGE 62 62 Figure 4-3. Semivariogram and Covariance. PAGE 63 63 Figure 4-4. Numerical Approach es to Model an Excavation in a Rock Mass (Jing 2003). Figure 4-5. WINSLIB SGS Exam ple Location Data Values. PAGE 64 64 Figure 4-6. WINSLIB SGS Example Results Graph. PAGE 65 65 CHAPTER 5 DATA ANALYSIS Cases Studies In this research, two case studies are presented. The first case study is an analysis of the Fuller Warren Bridge in Jacksonville Fl orida. The second case study is the 17th Street Bridge in Fort Lauderdale Florida. Both of them were field sites with performed Drilled Shaft Load Test in Limestone. The data analysis followed the theory description showed on the CHAPTER 4. The main purpose was to generate random fi elds using Sequential Gaussian Simulation (SGS) that was based on the best suited Semivari ogram. Each realization, while having the same statistics (Semivariogram), will have quite differe nce spatial pattern properties of cohesion, bulk and shear values on the soil and hence a differe nce value of end bearing capacity. This was followed by a finite element model analysis usin g the random fields obtained on the SGS results. Fuller Warren Summary Statistics The data obtained from the FDOT soil labs are shown in APPENDIX B. It was necessary to transforms these tables to a diffe rent format accepted by the software (APPENDIX C). Some of the properties showed on these tables, like qu, qt, and, RQD were used on statistics analysis. The Fuller Warren field data was obtained from three different borings, localized strategically near to Load Test LT4 in the Sout hwest side of the Bridge Each of these boring CB1, CB2, and CB3 has its own information like qu, qt, RQD, and depth. An example is showed in Table 5-1. The same data was presented in a different format and it is showed in Table 5-2. Additionally, the soil bori ng location is showed in Figure 5-1. The raw data for each boring was analyzed th rough histograms, frequency distribution and summary statistics realization. The histogr ams for each soil boring CB1, CB2 and CB3 are PAGE 66 66 showed in Figure 5-2 to Figure 5-4. These three boring histog rams illustrate clearly a difference tendency on properties values from elevation 55 f eet and below. This behavior suggests a limit for two different layers on the soil. Additionally, an example of frequency distribution (for qu, qt and RQD), and statistics summary for all ne w borings (CB1, CB2 and CB3) is showed in Figure 5-5. It shows that the most suitable frequency distribution is the lognormal. The complete set of graphs showing each of the boring data in all sites for the same bridge are showed in APPENDIX D. The frequency distributions comparing all data (past FDOT research), new data (CB1,CB2 and CB3) and a combination of both is showed in Figure 5-6. The figure showed how the standard deviation from the combination of ol d and new data is reduced from 25.66 to 20.32-tsf when more data values (new data) are added. Several attempts have been made to obtain th e classical statistical properties of the soil, such as the mean value, COV, and probability distribution, throughout geotechnical engineering practice. These statistical characteristics have been discussed by severa l authors and most of them have implemented distribution models like normal, lognormal, and beta for to curve fit results of field data. This implies that these dist ributions are can be used to fitted soil properties distribution results obtai ned under field conditions. Accorded to the obtained results showed in Figure 5-5, the majority of the closes fitted distribution model selected for the Fulle r Warren site were Lognormal and Beta. Spatial Continuity Spatial continuity exists in most earth scienc e data sets. Two data sets close to each other are more likely to have similar values than two da ta sets that are far ap art. When we look at a data graph or posting, the values do not appear to be randomly lo cated, but rather, low values tend to be near and high values tend to be near other high values. That is the case for each of the PAGE 67 67 three soil borings that shows a clear vertical di fference between qu, qt and RQD values from -35 to -55 feet depth and -55 to -65 feet depth (Figure 5-2 to Figure 5-4) The h-scatterplot is another tool used for to an alyze vertical spatial continuity. It explains all possible pair of data whose locations are se parated by a certain dist ance in a particular direction. On this research, the h-scatterplots the x-coordinate of a point correspond to the (qu)^.5(qt)^.5/2 value and the y-co ordinate to the (qu)^.5(qt)^.5 value a distance of 1.5 feet away in a vertical direction. One of the essential features of an h-scatterplot is the fatne ss of the cloud of points. And a way to summarizing this feature is the Correlation Coefficient. As the cloud of points gets fatter, we expect the correlation coefficient to decr ease. The relationship be tween the correlation coefficient of an h-scatterplot and h is called the correlogram. Other indices of spatial continuity are the Semivariogram that is the relationship betw een the moment of inertia of an h-scatterplot and h. And the Covariance function that is the re lationship between the covariance of an hscatterplot and h. Although the h-scatterplot contain much more information than any of the three summary statistics (semivariogram, correlogram and cova riance function), it is very common to bypass the actual h-scatterplot and go dire ctly to any of these three to describe spatial continuity. Fuller Warren Semivariogram Due to the small amount of soil boring location (just three CB1,CB2 and CB3) and the big length between them (35 to 45 feet apart), any real representative corr elation length was founded for this bridge data. There are two possibilities to use the Fuller Warren data. The first is to add two or three more soil boring to the site or secondly, to use th e correlation length of 12 feet like that one founded on the 17th Street Bridge. It is not the best solution but it could represent a PAGE 68 68 better approximation. Since, not real correla tion was founded neither Kr iging nor Sequential, Gaussian Simulation was performed on this bridge. 17th Street Bridge Summary Statistics The 17th Street Bridge field data was obtained from six di fferent borings localized strategically near to Load Test LT4 in the Northeast side of the Bridge (see Figure 5-8). Each of these boring has its own information like qu, qt, RQD, and depth (see Table 5-3). The rest of the borings soil data is available in APPENDIX B. The Frequency distributions, for both individual borings, and the complete field site are showed in the Figure 5-9. No pattern like that layers di fferences on the Fuller Warren bridge data was found in this bridge data. It was discovered from the statistic study th at a Proportional Effect is present on the 17th Street bridge data analysis. Proportional effect on statistics is used when the variance or semivariogram of a random variable (qu^0.5*qt^0.5/2 in this case) is prop ortional to the square of its mean. (Hans Wackernagel 2003). This phenomenon is often an argument to postulate the log normality of the random variable. 17th Street Bridge Semivariogram The semivariogram for the 17th Street Bridge was realized using two directions, horizontal and vertical. The initial idea was to use just one semivariogram for all the data, but after reviewing the statistic results it was noted that th ere were two different ra nges for each direction. The semivariogram range was found to be 12 feet distance. The nugget effect s that represent the random measurement error, was fount to be 0.3 of the total sill (Figure 5-10). PAGE 69 69 17th Street Bridge Simple Kriging The Simple kriging was perf ormed using the cohesion (qu)0.5 (qt)0.5 /2 information from the soil borings, for each soil borings. The results obtained from simple kriging were used as a step on the Sequential Gaussian Simulation process. 17th Street Bridge Sequential Gaussian Simulation The Sequential Gaussian Simulation (SGS) for the 17th Street Bridge was done using the WINGSLIB software. A small part of the result s obtained from the Wingslib is showed in Table 5-4, but the complete table is presented in the APPENDIX E. The results showed on these tables, are the coordinates for each grid point on sp ace and the correspondent simulated cohesion value for each grid point. 17th Street Bridge Random Field Model The behavior of a drilled shaft on limestone ro ck is influenced by the strengths parameters, qu and qt, Poisson ratio ( and Young modulus (E). While the parameter E and influence the computed settlement, the bearing capacity de pends primarily on the strengths qu and qt parameters (Gordon & Griffiths 2001). In the pr esent research the Poisson ratio was held constant and the strengths in the forms (qu^0.5qt ^0.5)/2 are modeled as a random variable. After obtaining the random field the E parameter is calculated from the correlation equation E=165.06*(qu^0.5qt^0.5)/2+300000. The correlation square ratio between E and (qu^0.5qt^0.5)/2 for the 17th Street Bridge is 0.6126 (Figure 5-11). The spatial correlation lengths, or the range fr om the semivariogram, describe the distance over which the spatial random values w ill tend to be correlated. From the 17th Street bridge semivariogram the ranges on the horizontal and vert ical direction were taken, like most of the soil field the isotropy was not assumed. The rando m fields were created using the parameters from the semivariogram showed in Figure 5-10. The range for the ve rtical direction was 6 feet PAGE 70 70 and for the horizontal direction was 12 feet. Also a nugget effect of 0.3 was used on both directions. Each random field, while having the same semivariogram parameters, will have quite different spatial pattern of cohe sion values, due to the dissimilar seed used, and hence a different value of bearing capacity. The software used on the random field, ba sed on semivariogram parameters, calculation was the WINGSLIB, and a different seed was used in each calculation. Examples of the random field and summary tables are founded in APPENDIX E. On these tables is showed the statistics of the results obtained using different seed values, like mean, standard deviation, etc. It is noticed that having the same parameter, but with di fferent seed, the final results will change. 17th Street Bridge Finite Elements Analysis The load-deflection response of a single concrete pile foundati on is calculated for loading in the axial direction. The pile is three feet diameter by twenty feet of length embedded in limestone rock layer. The propertie s of the concrete pile and the li mestone that are kept constant are showed in Table. 5-5. As it was described on CHAPTER 4 the software used for the modeling procedure was FLAC3D. A modified example founded on the FL AC3D manual was used as support of the current model. The soil block model used to simulate our specimen was introduced in the computer program with the following parameter: the coordinates axes were localized on the lower left corner and the z-axis oriented along the pile axis and upward. The top of the model, at z=40 feet is free surface. The base of the model, at z=0, is fixed in the z direction, and roller boundaries are imposed on the sides of the model, at x=30 feet and y=30 feet (see Figure 5-12).The finite element mesh consists of square elements of e qual size (1.5 x 1.5 x 2.0 feet). Each element has its own properties, cohesion, bulk, shear and Young modulus. PAGE 71 71 The axial-bearing capacity of a pile is a f unction of the skin friction resistance along the pile shaft and the end-bearing capacity at the pi le tip. The skin friction resistance is modeled by placing an interface between the pile walls and th e rock. The friction and cohesion properties of the interface represent the fricti onal resistance between the concre te and the limestone. For this model a friction angle of 5 and cohesion of 30000 (tsf) are assumed for th e interfaces properties. The ultimate bearing capacity of the pile in th e axial direction is calculated by applying a vertical velocity at the top of the pile. Many thousand of time st eps are required to propagate a loading through the model. If the velocity is applied suddenly, th e inertial effects will dominate initially and make it more difficult to identify the steady state response of the system. The axial stress at the top of the pile is calculated and stored. It is plotted versus the axial displacement at the pile top and an example is showed in the Figure 5-13. Combined damping is used for this stage of th e analysis because this type of damping is more efficient at removing kine tic energy from the model for th e prescribed lo ading condition. Three different correlation lengths were used on this study, 1,5, and 12 feet. The 12 feet was the length that the semivariogram recommend to use, but to see the behavior on the final capacity, it was necessary to compar e the 12 feet with other lengths. 17th Street Bridge Determinist Capacity The estimated total failure bearing and the E nd bearing capacities for the determinist soil properties by the finite element method we re 1260 (tons), and 235 (tons) respectively. Deterministic soil properties mean an average of all soil properties values from the site. 17th Street Bridge Parametric Study Thirty to forty realizations of statistical so il properties for each one of the correlation lengths were completed. Each realization, whil e having the same underlying statistics, will have quite different spatial pattern of cohesion, bulk, and shear, and hence, a different value of bearing PAGE 72 72 capacity. The results obtained from each simu lation were compiled and are showed in the APPENDIX E. A summar y graph is in the Figure 5-14. In the figure th e values on the x direction are the correlation length 1, 5, and 12 feet respectively. On the Y direction are the cohesion mean of forty simulations, for each one of the correlation length. The values used in Figure 5-14 are also showed in Table 5-6. The cohesion means shows a higher value for the correlation length of 12 feet and a small cohesion value for the 1 foot correlation leng th. The row data cohesion mean value is 42647 (PSF), and it is showed that the one foot corr elation length cohesion mean value is the closest one to the raw data, and the twelve feet the isolated. The explanati on for this is that the smallest the correlation length, the smallest the coefficien t of variation of the simulated data from the sequential Gaussian simulation program. The same tendency on the cohesion behavior is showed on the end bearing capacity obtained from the finite element method Figure 5-15. But in this case the deterministic capacity value is 235 (tons). Therefore, this case is i nversed to the cohesion gr aph. The twelve feet capacity value is approximated to the deterministic capacity value and the one foot is far-away. The explanation for the lower capacit y values for one and five feet correlation lengths lies in the fact that as the spatial correlation length d ecreased, the weakest trail becomes increasingly tortuous, and its length correspondi ngly longer. As a result the w eakest trail starts to look for shorter ways cutting through highe r strength materials (Griffiths & Fenton 1999). If there were a correlation length bigger than 12 feet correlation le ngth, the result could be bigger or smaller but in any case far away from the determinist value; it is because it allows enough variability for a failure surface to develop which deviates sign ificantly from the de terministic results. PAGE 73 73 Consequently, the optimum failure path will be th e same as in the uniform material. In our case the result that tends to that result, is the correlation length suggested by the semivariogram. In the APPENDIX G is show all the programming models used on this research, for to obtain the bearing capacity for each one of the so il simulations. Additionally, the results graphs and tables are in this same appendix. 17th Street Bridge Comparison of Det erministic and Predicted End Bearing Table 5-7 shows a comparison of Simulated an d deterministic End Bearing capacity from the finite elements program. Each correlation has its own predicted End bearing and it is compared with the End bearing capacity obtained from the deterministic value So, for one, five, and twelve feet correlation lengths the pred icted End Bearing are 218.36, 218.375, and 238.125 tons respectively compared to 235 from the deterministic result. 17th Street Bridge LRFD Phi Factors According the explanation in CHAPTER 1, the goal of resi stance factor design (LRFD) analysis is to develop factors that decrease th e nominal resistance to give a design with an acceptable and consistent probability of failure Where load components are multiplied by load factors and resistance is multiplied by a resistance factor. The basic equation is: Rn > i Qi where i is a load factor applied to load components Qi and is resistance factor applied to the resistance (measured of load carrying capacity) Rn. In words it equation says that the capacity of the foundation (modified by the factor ) must be larger than the total effect of all the loads acting on it. FOSM method has been used (NCHRP 507, 200 4) to calibrate LR FD factors using a statistical dataset containing the measured and pred icted resistances. It assumes that the load and PAGE 74 74 resistance are modeled as lognormal random variables. This limits the load and resistance values to only positive numbers. The next equation is used to calibrate the resi stance factor using the FOSM method. It is dependent on the target reliability index and the ratio of dead to live load. )] ]) [ ( ]) [ ( 1 )( ]) [ ( 1 ln[( 2 2 22 2 2]) [ ] [ ( ) ( ) ]) [ ( 1 ( ) ]) [ ( ]) [ ( 1 ( ] [QL COV QD COV R COV QL L D QD QL L D QD N RN Te E q q E q q R COV QL COV QD COV E In the 17th Street Bridge instead using it for to calib rate the resistance f actor as a method, it was used for to account for differences or variability based on correlation lengths. The FOSM equation was used for to get Phi f actor for different correlation length, but instead using a measured value it was used the deterministic value obtained from the same finite element program. It allows seeing the differences on the phi factor, based on spatial variability and reliability index. To account for spatial variability on the 17th Street Bridge, a tota l of forty End bearing values were predicted for five and twelve feet correlation length, and thirty values for the one foot length case. Additionally, the deterministi c value was obtained using the same program. From the predicted and deterministic values at all the correlation length, the mean standard deviation and coefficient of variation COVR, were found for the design approach (Table 5-8). Using the computed mean, and coefficient of variation COVR, for each correlation length, the LRFD resistance factor, were determined for different values of reliability index, The results are shown in Table 5-9. PAGE 75 75 Additionally, a Modified FOSM equation was also used, due to a NCHRP 507 report that shows that the resistance factors developed by FO RM (First Order Reliability Method) tend to be 10 to 15% greater than the factors developed using the FOSM method. This means that the FOSM resistance factors ar e conservative (it is re cognized that the FORM resistance factors are more accurate). Since the purpose of LRFD is to design based off of the probability of failure, it is more beneficial to have accurate resistance factors. The modified FOSM equation is based on a past (Styler 2006) research which stated that the published FOSM equation had an error that o ffered results consistently lower than actual resistance factors. The modified equation is: )] ]) [ ( ] [ ] [ 2 ]) [ ( ]) [ ( ]) [ ( ]) [ ( ]) [ ( 1 )( ]) [ ( 1 ln[( 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2]) [ ] [ ( ) ( ) ]) [ ( 1 ( ) ]) [ ( ] [ ] [ 2 ]) [ ( ]) [ ( ]) [ ( ]) [ ( ]) [ ( 1 ( ] [ QL QL QD L D QD L D QL QL QD QD L D TE E E q q E q q COV E COV E q q R COV QL L D QD QL L D QD QL QL QD L D QD L D QL QL QD QD L D Re E q q E q q R COV E E E q q E q q COV E COV E q q E The modified FOSM equation is still in terms of the target reliability index and the dead to live load ratio. Results from the 17TH Street Bridge using the modifi ed equation are illustrated in Table 5-10. It is shown that posi tively the values using the new equation are a little higher than those using the traditional FOSM equation. The results for the phi factors show a proporti onal inversely relations hip with correlation length, a bigger value when the correlation leng th is minor and small value when the length is larger. This result explanation lies in the fact that with smaller correlation distances better knowledge of the proximity soil properties so a bigger factor could be used. PAGE 76 76 The modified FOSM results are slightly bigger than the traditional, and based on Styler 2006 theory, closer to accurate results. PAGE 77 Table 5-1. Fuller Warren Bridge Soil Boring Information. Boring /Core Samp. No.w (%) Dry Unit Wt.(pcf) Max. Load (lbs.) S.T. Strength (psi) q(u) (psi) Displ. @ Fail (in) Strain @ Fail (%) %Recov./ %RQD Tare Wt. (g) Wet Wt. (g) Dry Wt. (g) CB-3/1 1U 5.32 141.6 67821505.6 0.0522 1.08 72/50430.31281.51238.5 2U 11.14 128.3 3530784.1 0.0634 1.43 72/50430.71168.71094.7 3T 26.01 99.3 36841.6 0.0633 72/50366.1698.4629.8 4T 16.40 113.4 1378151.5 0.0687 72/50431.4805.4752.7 5T 9.07 137.8 3224368.0 0.0515 72/50428.3837.2803.2 CB-3/2 1T 26.50 92.5 20423.4 0.0743 77/67428.1735.5671.1 2U 7.46 144.2 57201287.5 0.0549 1.27 77/67430.21196.61143.4 3T 8.10 139.0 1552179.0 0.0415 77/67430.3835.8805.4 4U 11.63 128.5 3252729.8 0.0541 1.13 77/67431.41237.81153.8 5T 10.86 132.4 1623185.1 0.0468 77/67371.5771.6732.4 6U 13.79 122.2 4229943.0 0.0563 1.15 77/67433.11230.01133.4 7T 11.05 129.0 1715195.5 0.0419 77/67312.1703.9664.9 8U 8.31 139.4 56901269.3 0.0454 0.93 77/67375.91239.01172.8 CB-3/3 1T 9.56 130.8 37944.0 0.0410 100/92366.0746.4713.2 2U 8.71 138.0 3187727.9 0.0630 1.30 100/92370.81207.21140.2 3T 4.54 134.1 12013.5 0.0237 100/92370.6746.2729.9 4T 14.37 118.8 24327.0 0.0276 100/92425.7802.9755.5 5U 18.48 111.9 501116.1 0.0297 0.61 100/92430.61164.01049.6 6T 19.11 110.8 16918.6 0.0236 100/92424.6790.5731.8 7T 28.86 92.3 889.7 0.0209 100/92430.4758.6685.1 8U 27.47 97.5 731170.5 0.0455 0.95 100/92302.8972.4828.1 9T 24.01 101.1 28732.9 0.0422 100/92425.0756.6692.4 10T 23.05 100.8 9312.1 0.0402 100/92410.1701.0646.5 11U 23.97 102.3 433100.3 0.0348 0.74 100/92428.21103.6973.0 77 12T 17.63 113.5 43748.9 0.0324 100/92428.4797.4742.1 PAGE 78 Table 5-2. Fuller Warren Soil Boring Modified Data. Name of Boring CB-1 (New) CB-2 (New) CB-3 (New) Distance from Load Test (ft) 30 25 15 EL. (ft) qu (tsf) qt (tsf) RQD Ei (psi) EL. (ft) qu (tsf) qt (tsf) RQD Ei (psi) EL. (ft) qu (tsf) qt (tsf) RQDEi (psi) -40.5 15.36 31.21 37 20725.93-37.5842.5725.2323 48974.00-41108.403.0050139525.37 -40.5 96.14 2.14 37 93362.29-37.58 4.3623 -4156.4510.915055345.75 -40.5 6.36 37 -42.5818.663.5452 30083.74-41 26.5050 -45.5 143.30 9.07 74 108694.81-42.5856.421.7652 75668.97-4692.701.6967102818.36 -45.5 59.24 7.21 74 20329.10-42.58 15.3252 -4652.5512.896764868.52 -45.5 52.29 15.85 74 50938.20-42.58 10.3452 -4667.9013.336781761.47 -45.5 68.09 18.33 74 87522.73-47.5864.7718.3687 81523.95-4691.3914.0867136076.85 -45.5 13.65 74 163837.76-47.5865.128.4187 75899.59-5152.413.179256192.28 -50.5 113.41 18.62 48 143167.10-47.5837.248.5187 38959.02-518.360.979219141.58 -50.5 11.95 48 -47.58140.0610.1187 152082.74-5112.281.949218051.95 -50.5 1.86 48 -47.588.291.9187 15682.83-517.221.349213564.22 -50.5 0.89 48 -47.5878.440.8487 69402.72-51 0.7092 -50.5 1.44 48 -52.5815.685.4998 24923.43-51 2.3792 78 -55.5 12.56 1.37 77 16123.94-52.5810.611.8298 14642.92-51 0.8792 PAGE 79 Table 5 2. Continued. Name of Boring CB-1 (New) CB-2 (New) CB-3 (New) Distance from Load Test (ft) 30 25 15 EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) EL. (ft) -55.5 22.01 0.91 77 33646.94-52.589.081.2898 13980.61-51 3.5292 -55.5 22.92 2.58 77 28351.18-52.5818.881.9098 21191.30-5627.071.306035561.05 -55.5 11.89 1.77 77 13580.10-52.5820.991.4098 20221.36-5619.842.936024011.06 -55.5 2.00 77 -52.5816.811.3698 21522.93-5614.392.746013791.05 -60.5 7.08 1.05 67 6509.45-52.58 1.0498 -56 1.7560 -60.5 7.36 0.66 67 8173.66-52.58 1.6498 -56 1.4260 -60.5 8.59 0.25 67 10247.30-57.5816.721.7747 26059.97-619.091.0910011308.89 -60.5 7.57 1.05 67 11768.07-57.5810.80 47 11899.08-619.330.871009220.15 -60.5 0.93 67 -57.5818.28 47 19700.99-619.891.3710011249.80 -65.5 3.02 0.40 38 3832.10-62.5811.081.1477 11334.53-619.801.3210011165.85 -65.5 0.40 38 -62.589.441.4477 12460.26-618.100.4010010801.59 -65.5 0.43 38 -62.589.591.2477 13170.90-615.90 1009630.65 -65.5 0.25 38 -62.5810.080.9777 14308.84-613.96 1008026.87 -62.587.490.4277 15724.97-665.990.81458732.30 79 -668.040.694510850.17 PAGE 80 Table 5-3. Table 17th Street Bridge Soil Boring Information. Boring /Core Samp. No.w (%) Dry Unit Wt.(pcf) Max. Load (lbs.) S.T. Strength (psi) q(u) (psi) Displ. @ Fail (in) Strain @ Fail (%) %Recov./ %RQD Tare Wt. (g) Wet Wt. (g) Dry Wt. (g) 9/1 1T 6.88 93.3 1279.5144.8 0.1211 98/6476.3349.6332 2U 6.62 119.7 45861014.4 0.0481 0.99 98/6477803.8758.7 3T 9.36 107.7 1349.6139.6 0.1402 98/6475.4429.4399.1 4U 7.87 127.8 5926.11283.9 0.0533 1.39 98/6477.1684.2639.9 5T 6.88 133.4 3102.2378.2 0.0323 98/6475.1435.4412.2 7U 5.95 123.0 4364.8971.6 0.0426 1.02 98/6474.2695.5660.6 8T 5.68 122.8 2644.6361.6 0.1008 98/6477.9373.6357.7 9T 4.30 128.2 3740437.2 0.1115 98/6476.3430.4415.8 10U 1.86 145.8 165703651.9 0.0723 2.00 98/6475.6682.5671.4 9/2 2U 3.66 130.4 4704.71032.8 0.0302 0.74 62/875.5716.1693.5 3T 1.84 143.2 5139.4553.9 0.0406 62/876.3502.5494.8 4T 2.50 145.2 4575.3556.0 0.0323 62/877.1461.8452.4 5T 1.55 134.0 3925.7447.4 0.0201 62/877.9450.6444.9 9/3 1T 0.90 138.6 3660416.8 0.0345 87/3375.1458.1454.7 2T 1.16 151.6 5147.2598.8 0.0344 87/3375.4486.6481.9 3U 1.62 151.8 8931.82022.7 0.0411 0.86 87/3377930.4916.8 4T 1.15 150.1 4117.4469.1 0.0385 87/3376.1489.7485 5U 2.26 149.6 12046.92714.5 0.0564 1.24 87/3377.1881.4863.6 6T 3.71 132.2 1619.8335.6 0.0306 87/3376.5431.4418.7 7U 3.83 136.8 4587.71005.8 0.0652 1.67 87/3381.6724.1700.4 80 8T 2.53 104.3 1663.5225.2 0.1097 87/3375.7318.7312.7 PAGE 81 81 Table 5-4. 17th Street Bridge Wingslib Results. X Coordinate Y Coordinate Z Coordinate Cohesion Simulated 0 009.59 3 1.5018.59 27 3011.10 0 9030.10 9 19.527.38 0 13.5635.32 0 01036.60 22.5 22.51019.25 0 19.51414.42 Table. 5-5 Material Properties Bulk (psf) Shear (psf) Friction Cohesion (psf) 1.40E+07 8.80E+061577421.79 1.40E+07 8.80E+061570154.74 1.40E+07 8.80E+061554409.3 1.40E+07 8.80E+061560513.67 1.40E+07 8.80E+061567786.84 1.40E+07 8.80E+061562980.13 1.40E+07 8.80E+061550742.8 1.40E+07 8.80E+061553058.95 1.40E+07 8.80E+061568361.9 1.40E+07 8.80E+061579498.88 Table 5-6. 17TH Street Bridge Cohesion Mean Re sults Values from Simulations Correlation Length (ft) Cohesion Mean (psf) 1 42695 5 42931 12 43731 Raw Data 42647 Table 5-7. 17TH Street Bridge End Bearing Capacity Mean Values from FLAC3D Correlation Length (ft) End Bearing Capacity (tons)) 1 216.36 5 218.37 12 238.12 Deterministic 235 Table 5-8. 17TH Street Mean, Standard, and COV of Predicted End Bearing Capacity Bias Correlation Length (ft) Mean Standard Deviation COV 1 1.0895570.1206110.110698 5 1.1048590.1812060.164009 12 1.0129760.1725970.170386 PAGE 82 82 Table 5-9. 17TH Street Bridge Values for different Reliability Index FOSM (Traditional) Correlation Length (ft) 1 0.7730.6840.605 0.535 5 0.7260.6330.553 0.482 12 0.6580.5730.500 0.435 Table 5-10. 17TH Street Bridge Values for different Reliability Index FOSM (Modified) Correlation Length (ft) 1 0.9570.8870.822 0.762 5 0.8680.7880.715 0.650 12 0.7850.7100.643 0.582 Table 5-11. 17th Street Bridge COV and Correlation Length (ft) COV 1 0.11069750.1206112 5 0.16400860.18120632 12 0.170386270.17259719 PAGE 83 83 2 3 1 40 ft 35 ft 55 ft N 2 3 1 40 ft 35 ft 55 ft N Figure 5-1. Fuller Warren Soil Boring Location. CB-1 Elevation vs. qu, qt,RQD,qb-20.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 -70 -65 -60 -55 -50 -45 -40 -35 Elevation (ft)qu (tsf), qt (tsf), RQD qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt Figure 5-2. Fuller Warren Histogram CB1. PAGE 84 84 CB-2 Elevation vs. qu, qt,RQD,qb 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 -70 -65 -60 -55 -50 -45 -40 -35 Elevation (ft)qu (tsf), qt (tsf), RQD qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt Figure 5-3. Fuller Warren Histogram CB2. CB-3 Elevation vs. qu, qt,RQD,qb0.00 20.00 40.00 60.00 80.00 100.00 120.00 -70 -65 -60 -55 -50 -45 -40 -35 Elevation (ft)qu (tsf), qt (tsf), RQD qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt Figure 5-4. Fuller Warren Histogram CB3. PAGE 85 85 0 50 100 150 0 0.01 0.02 0.03 0.04 qu 0 10 20 30 40 0 0.1 0.2 0.3 0.4 qt 0 50 100 0 0.01 0.02 0.03 RQD QU QT RQD MEAN = 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP = 28.4992 4.7548 25.2514 MNPDFLOG = 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 MNPDFGAM = 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 MNPDFRAYL = 42.9191 7.3741 45.8545 STDPDFRAYL = 22.4075 3.8534 23.3869 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 sqerrorRAYL = 1.0e-005 0.5839 0.0968 0.0009 Figure 5-5. Fuller Warren New Borings Fr equency Distribution qu, qt and RQD. PAGE 86 86 0 20 40 60 80 100 120 0 0.05 0.1 Frequency Distribution Old Borings quqt (tsf) 0 20 40 60 80 100 0 0.05 0.1 Frequency Distribution New borings quqt (Tsf) 0 20 40 60 80 100 120 0 0.05 0.1 Frequency Distribution New+Old Borings quqt (tsf) MEAN = 40.4560 11.8474 18.7135 STD = 25.6634 12.0870 20.3264 Figure 5-6. Frequency Distribution for quqt. quqt vs Ei (psf)y = 383.66x + 1E+06 R2 = 0.6645 0 5000000 10000000 15000000 20000000 25000000 01000020000300004000050000 quqt (psfE (psf) Figure 5-7 Fuller Warren Bridge quqt and E Correlation PAGE 87 87 Figure 5-8. 17th Street Soil Boring Locations (SMO 2007). PAGE 88 88 0 100 200 300 0 0.005 0.01 0.015 qu0.5qt0.5/2 0 20 40 60 80 0 0.01 0.02 0.03 0.04 0.05 qt(tsf) 0 20 40 60 0 0.01 0.02 0.03 0.04 0.05 qu (tsf) Figure 5-9. 17th Street Frequency Distribution PAGE 89 89 Figure 5-10. 17th Street Semivariogram. PAGE 90 90 quqt vs Ey = 165.06x + 3E+06 R2 = 0.6126 0 5000000 10000000 15000000 20000000 25000000 30000000 35000000 40000000 050000100000150000200000 quqtE Series1 Linear (Series1) Figure 5-11. 17th Street Bridge Corr elation quqt vs E. PAGE 91 91 Figure 5-12. 17th Street Bridge FLAC Model Grid PAGE 92 92 Figure 5-13. 17th Street Axial Force vs Pile Displacement PAGE 93 93 Correlation Length vs Cohesion Mean 42600 42800 43000 43200 43400 43600 43800 02468101214 Correlation Length (feet)Cohesion Mean (lbs) Figure 5-14. 17th Street Correlation Le ngth vs Cohesion Mean Correlation Length vs Total Bearing Capacity Mean 1150.00 1155.00 1160.00 1165.00 1170.00 1175.00 1180.00 1185.00 1190.00 1195.00 1200.00 02468101214 Correlation length (ft)Total Bearing Capcity Mean (tons) Figure 5-15. 17th Street Correlation Length vs Total Bearing Capacity PAGE 94 94 Correlation Length vs End Bearing Capacity Mean 210.00 215.00 220.00 225.00 230.00 235.00 240.00 02468101214 Correlation length (ft)End Bearing Capcity Mean (tons) Figure 5-16. 17TH Street Correlation length vs End Bearing Capacity PAGE 95 95 CHAPTER 6 COST ANALYSIS The principal initiative of the cost analysis is to find a cost comparison between the different factors obtained from this Geostatistics study. This study compared results from the three correlation lengths to the deterministic result. The first one used the soil parameter from the borings made around the specific drilled shaft, an d the deterministic used the design parameters from soil borings over the whole si te. Moreover, the cost analysis is divided in two stages. The first stage includes the materials, labor and equi pment cost of the drilled shaft construction and the second stage includes the costs of add itional borings around each drilled shaft. Factor Influencing Cost Several factors influence the final costs of a drilled shaft construction, among them are: Subsurface and site conditions Geometry of Drilled Shaft Specification, including inspection procedures Weather conditions Location of work as related to travel and living cost of crew Governmental regulation Availability of optimum equipment Experience of the contractor Insurance and bonding These factors are just a sample of all the va riables that could influence a drilled shaft construction costs. This cost analysis assembles most of these influence variables in three big groups. Those are: 1) Drilled Shaft Construction, 2) Drilled Shaft Excavation and 3) Boring Test Costs. The drilled shaft construction includes the co sts of: concrete, steel, temporary casing, labor, materials, equipment and incidentals necessa ry to complete the drilled shaft. The second group includes all the work relate d to the drilled shaft excavation. Finally, the boring test cost PAGE 96 96 includes the soil boring auger and the laboratory analysis. It will depend basically on the number of tests to be performed. Drilled Shaft Cost and Excavation The analysis is based on the Florida Department of Tran sportation average unit cost database. The database item descriptions are presented in the Basi s of Estimates Handbook (Figure 6-1). This document was created with th e purpose of presenting a standard method of documenting the design quantities for construction paid items. The handbook also presents the standard method of calculating quantities for many paid items that require special methods of measurement. The FDOT Item Average Unit Cost Database is numerated from item 000 to 1999 and the items are categorized by paid item range. Table 6-1 shows this categorization. The used items for this research were in the Road &Bridge cat egory from 100 to 577. These items are 455 88 5 Drilled Shaft and 455 122 5 Excavation Unclassifi ed shaft. The item 455 88 5 is specified for a Drilled Shaft of 48 diameter. Figure 6-1 shows the FDOT Basis of Estimates Handbook description for this item. The analyzed drilled shaft in this research was 36 of diameter. However, due to the lack of information for this diameter on the FDOT data base, data from a 48 diameter shaft was used instead. The same procedure was used on the item 455 122 Unclassified Shaft Excavation. Figure 6-2 shows the description of this item. The quantity on this item is measured as the depth of excavati on from the ground to tip of the shaft measured in linear feet. The Basis Estimates Handbook is divided by ye ars. Therefore, data from 2002 to 2006 were used. An example of the 2006 Item aver age Unit Cost for the items 455 88 5 and 455 122 5 are showed in the Figure 6-3. The complete data information is presented in APPENDIX G. PAGE 97 97 Moreover, the summary of the Drilled Shaft and Excavation shaft of 48 diameter are presented in Table 6-2 and Table 6-3. Soil Boring Test Costs The rates for soil laboratory tests are based on the State Material Office cost database. The available FDOT data from 2003 through 2006 divided annually was used for the analysis. Table 6-4 shows the most common soil test used for Dri lled Shaft studies and at the same time used on the 17th Street Bridge. Additionally, the cost of obtai ning the soil samples in a rock soil from 0 to 50 is $26.25/LF and from 50-100 is $30.63/ LF. These costs are based on actual (2007) cost from FDOT District 4. Relative Costs Analysis The analysis was divided into three groups: 1) Drilled Shaft Cost, 2) Drilled Shaft Excavation and 3) Boring Test Cost. Drilled Shaft Cost All the cost analysis will be ba sed on a one foot length by four feet diameter drilled shaft in lime rock soil. The total Dri lled Shaft construction cost was $267.97 per linear feet. This result was compared with the costs ge nerated by the used of the new factors presented previously in CHAPTER 5. Those factors accounted for three correlation lengths, and four reliability indices (Table 5-10). It is assumed that each factors represent a percentage of the deterministic value. For example from Table 5-10 a value with a correlation le ngth of 5 feet and a reliability index of 3.0 the factor is 0.788. Therefore, this valu e represents the 100/ 78.88% of the total determinist cost corresponding to this factor. Consequently, the total cost of the determinist value of $267.97 multiply by 1/0.788 will derive on $423.33 per linear feet. This cost PAGE 98 98 corresponds to the use of a specific factor. The complete sets of results are presented in Table 6-5 and Table 6-6. Drilled Shaft Excavation The same procedure followed on the Drilled Sh aft Construction Cost section was followed for the Drilled Shaft Excavation. The cost analys is for the excavation item is also based on a one foot length by four feet diameter drilled shaft on lime rock. This excavation cost is $173.92 per linear feet. The complete set of cost results are presented in Table 6-7, and Table 6-8. Boring Test Cost This analysis was based on the influence of nu mber of soil borings ar ound the drilled shaft. The average of the Drilled Shaft construction cost, Excavation, and soil lab test cost presented in Table 6-2 to Table 6-4 are shown in Table 6-9. The total construction cost assuming just one soil boring test was $267.97 per linear feet, the excavation $173.92 and the laboratory soil test costs $24.5 per linear feet. The average auger cost of $30.63 per linear feet was obtained from FDOT District 4 (Table 6-9). The total is $497.02 per linear feet assuming one soil boring per drilled shaft. Under the same circumstances but assuming fi ve soil borings around the drilled shaft, the total cost per linear feet was $717.54 per linear feet (Table 6-10). The difference was $220.52 per linear feet. If the drilled shaft is 20 feet long as the 17th Street Bridge case, the differences will result on $4,410.4. PAGE 99 99 Table 6-1. FDOT Item Average Unit Cost Database. ITEM CATEGORY 100 to 577 Roadway & Bridge 579 to 590 Landscape 600 to 715 Traffic Operations 721 to 770 Peripherals 800 to 899 Mass Transit 900 to 999 Special Use 1000 to 1999 Utility Table 6-2. Summary of Drilled Sh aft of 48 Diameter (0455 88 5). Year No. of Contracts Weighted Aver ageTotal Quantity (LF) Total Amount 2006 4 $356.66 2456 $875,956.96 2005 3 $204.33 1087 $222,106.71 2004 6 $277.60 2533 $703,106.80 2002-2003 10 $233.29 3488 $813,715.52 Average $267.97 Table 6-3. Summary of Excavation Shaft of 48 Diameter (0455 122 5). Year No. of Contracts Weighted Aver ageTotal Quantity (LF) Total Amount 2006 3 $328.19 2380 $781,092.20 2005 2 $170.14 1011 $172,011.54 2004 5 $77.78 2128 $165,515.84 2002-2003 9 $119.58 3270 $391,026.60 Average $173.92 Table 6-4. Summary of Soil Lab from 2003 to 2007 Test Name Moisture Content ($) Specific Gravity ($) Split Tensile ($) Unconfined Compression ($) Average ($) 2003-2004 8 57.378983.63 238 2004-2005 8.15 55.8395.8385.38 245.19 2005-2006 8.43 57.2495.7287.80 249.19 2006-2007 8.15 57.3495.3786.63 247.49 Average 8.1825 56.94593.9885.86 244.9675 PAGE 100 100 Table 6-5. Summary of Drilled Shaft Cost (Material, labor) for Factors FOSM Correlation Length (ft) 1 $346.66$391.77$442.93 $500.88 5 $369.10$423.33$484.58 $555.9512 $407.25$467.66$535.94 $616.02 Table 6-6. Summary of Drilled Sh aft Cost (Material, labor) for Factors FOSM (Modified) Correlation Length (ft) 1 $280.01$302.11$326.00 $351.67 5 $308.72$340.06$374.78 $412.2612 $341.36$377.42$416.75 $460.43 Table 6-7. Summary of Drilled Shaft Cost Excavation for Factors FOSM Correlation Length (ft) 1 $224.99$254.27$287.47 $325.08 5 $239.56$274.76$314.50 $360.8312 $264.32$303.53$347.84 $399.82 Table 6-8. Summary of Drilled Shaft Cost Excavation for Factors FOSM (Modified) Correlation Length (ft) 1 $181.73$196.08$211.58 $228.24 5 $200.37$220.71$243.24 $267.5712 $221.55$244.96$270.48 $298.83 PAGE 101 101 Table 6-9. Average Cost for a 1 foot length and 4 feet Diameter Drilled Shaft, (One Soil Boring) Average Drilled Shaft Cost / LF $267.97 Average Drilled Shaft Excavation Cost/ LF $173.92 Average of four Soil Tests Cost/ LF $24.5(*) Average of Auger Soil Boring/ LF $30.63 TOTAL/ LF $497.02 (*) Assuming a set of soil tests every 10 ft. Table 6-10. Average Cost for a 1 foot length 4 feet Diameter Drilled Sh aft, (Five Soil Boring) Average Drilled Shaft Cost / LF $267.97 Average Drilled Shaft Excavation Cost/ LF $173.92 Average of four Soil Tests Cost/ LF $122.5 Average of Auger Soil Boring/ LF $153.15 TOTAL/ LF $717.54 Table 6-11. LRFD Factors, Probability of Failure and Fs Based on Reliability, for Nearest Boring Approach (McVay and Ellis 2001) Reliability, LRFD, Pf(%) Factor of Safety 2.0 0.86 8.5 1.65 2.5 0.71 1.0 1.98 3.0 0.60 0.1 2.37 3.5 0.50 0.01 2.84 4.0 0.42 0.002 3.40 4.5 0.35 0.0002 4.07 PAGE 102 102 Figure 6-1. FDOT Basis of Estimates Handbook Desc ription for the Item 455 88 Drilled Shaft. PAGE 103 103 Figure 6-2. FDOT Basis of Estimates Handbook De scription for the Item 455 122 Unclassified Shaft Excavation. PAGE 104 104 Figure 6-3. Example of the 2006 Item Average Unit Cost for the Items 455 88 5 and 455 122 5. PAGE 105 105 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS A probabilistic study on the end bearing capacity of a axially loaded drilled shaft, on soil with randomly varying cohesion, bulk, and shear have been realized. Random field theory using Sequential Gaussian simulation has been combined with a finite element program. The results were compared with the determinis tic result obtained from the same software. The objective of this procedure was to see the variability of the factor with spatial variability. Additional cost analyses based on result were completed. The following conclusions can be made: The cohesion means obtained from the sequential Gaussian simulation program shows a higher value for bigger correla tion length, and a small cohesion mean value for minor correlation length. The expl anation to this phenomenon is that the smallest the correlation length the smallest the coefficient of variation for simulation exist. The end bearing capacity mean, obtained from the finite element program, is bigger for larger correlation lengths, and smalle r for minor correlation lengths. It is because as the spatial correlation length decreased, the weakest trail becomes increasingly tortuous, and its length correspondingly longer. As a result the weakest trail starts to look for shorter ways cutting through higher strength materials A smaller resistance factors, were obtained for larger correlation lengths, it because the bigger uncertainties with distances (spatial variability). Resistance factors, obtained with correlation lengt hs valued bigger than the founded using the semivariogram takes to variable results. The drilled shaft construction costs, like materials, labor and equipment, and excavations are less when using the obtained resistance factors, But, the increase PAGE 106 106 on soil boring cost are ar ound twice bigger than the saving achieved from the construction cost. The research was based in just one bridge information; more investigation should be realized using more sites. The spatial variability can be better define with more information, so as more the number of sampling the better the design parameter definitions and the bigger the resistance factors, used. The number of sampling for to get a bigger factor should be at least four, for a correct semivariogram definition, ad ditionally, the distances between them should be as close as possible. PAGE 107 107 APPENDIX A DATA FROM STATIC AND DYNAMIC FIELD TESTING OF DRILLED SHAFTS (FULLER WARREN AND 17TH STREET BRIDGE) Table A-1. Fuller Warren Bridge Soil Boring Data. EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -3596.56232-1554.58047 -3527.86232-1512.58047 -4070.5418-2098.54320 -4013.7418-206.14320 -2589100 -259.1100 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -35922525-45828751 -3513.92525-4517.28751 -4568.53017 -4524.353017 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -3556.52517-20955047 -358.42517-209.95047 -25824819 -2512.954819 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -20244.57049-15258100 -2054.057049-1525.2100 -25104100-2022.58747 -205.68747 -22117.57725 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -3092.53217-4528.75 -3016.753217 j BL-4 BL-11BL-13 BL-20BL-23 BL-36BL-37 BW-1BW-3 BL-2 PAGE 108 108 Table A-1. Continued. EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -2544.8-3531.8527 -3032.75-4027.4 -3529.95 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -30432042 -309.552042 Dep.(ft)quRECRQDqtRECRQDDep.(ft)quRECRQDqtRECRQD -20596.23838-2365.41510 284-2830.8 401.6-2834.65233 17.424.6 60.233.3 80.914 -25110.511 -3043.46326-3358.5 32.2 52.9 87.7 15.8 6.6 -3550.4 -3587.77366 85.1 77.9 20.4 29.4 12 23.6 17.9 18.3 18.2 47.8 -4055.1 Added Boring (Hole 1: Near Boring BL-1)Added Boring (Hole 2: Near Boring BL-1) BW-5BW-12 BW-14 PAGE 109 109 Table A-2. 17th Street Bridge Soil Boring Data. EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -6532.23022-32211.268.3 -7227.346728-36116.919.4 -85114.2137 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -6932.74225-11526.55 -8828.83510-13124.6343 -13132.943 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -32211-4943.5184 -3268.34-65414207 -49117-7237.8 -4919.4-82120.89838 -7219.6-8226.39838 -9282.989838 -102117.47667 -10882.44358 -131140.63510 -13164.63510 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -36379.43835143.973835-39361.365 -36189.013838-46158.74819554819 -36112.63835-46272.7481953.994819 -7526.333-4676.784819 -9827.04602368.76023-56285.02501240.45012 -98140.016023-9514.04175 j BB-7 (35+44) BB-11 (35+53) BB-9 (35+06) S-12 (35+29) BB-1 (32+93)S-4 (33+00) BB-4 (34+81) BB-8 (36+10) PAGE 110 110 Table A-2. Continued. EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -36283.445.813.5148.7645.813.5-664323328 -3652.6445.813.5-6645.243328 -49444.3693649.846936 -49212.84693660.56936 -4965.76936 -56377.68459 -56381.68459 -56320.68459 -105219.04317 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -4951.4-393896331 -4917.5 -7238.34 -727.7 EL.(ft)quRECRQDqtRECRQDEL.(ft)quRECRQDqtRECRQD -4964.954217-5626.548559 -66152.54524-72281.380 -8258.24524-79331.447 -8212.45113 -92365.45710 -92101.45710 -12519.24531 -12520.954531 -12531.044531 Dep.(ft)quRECRQDqtRECRQDDep.(ft)quRECRQDqtRECRQD -5351.750.550.5 58.5 59.9 86.1 -5858.6 -5820.14740.5 -6446.15353 -64250.156.553 28.2 13.5 8.4 -699.8 -77122.53317 -77357.9 -9014.523.513 -10941.52213 Added Boring (34+81, 10' North+) N-17 (36+19) BB-6 (38+07)N-25 (38+38) S-15 (37+10)N-14 (35+55) BB-10 (36+07) PAGE 111 111 APPENDIX B SOIL BORING DATA FROM FIELD I NVESTIGATION PROCESSED BY MSO Table B-1. 17th Street Soil Boring Data. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 4/11T52.04/9/20072.46152.3955337.2115.81.03 2U4/9/20074.63332.3962635.7115.91.931.00 3U4/9/20074.75352.3960704.3125.21.981.00 4T4/9/20072.37702.3830336.4120.91.00 5U4/9/20074.92102.3985788.7135.12.051.00 6T4/9/20072.59332.3880383.0125.61.09 7U4/9/20074.47552.3945660.8124.91.871.01 8U4/9/20074.79552.3960764.9134.82.001.00 9T4/9/20071.94302.4010305.4132.30.81 10U4/9/20074.96802.3980785.4133.42.071.00 11T57.04/9/20072.09332.3970319.2128.70.87 4/21T57.04/9/20072.49552.3990300.0101.31.04 2U4/9/20074.37602.3830533.4104.11.841.01 3T4/9/20072.62102.3815333.7108.91.10 4T4/9/20072.49202.4035391.4131.91.04 5U4/9/20073.91302.3560532.2118.91.661.02 6T4/9/20072.47352.3430332.9118.91.06 7T4/9/20072.40452.3990378.1132.51.00 8T4/9/20072.65802.3955392.5124.81.11 9U62.04/9/20074.81152.3820710.5126.22.021.00 4/31T62.04/9/20071.87502.3630217.7100.90.79 2U4/9/20073.63452.3990656.7152.31.521.04 3U4/9/20073.60352.3945619.6145.51.501.04 4T4/10/20072.36302.3580287.3106.11.00 5T67.04/10/20072.40102.3610280.1101.51.02 4/41T67.04/10/20072.34992.3780353.1128.90.99 2U4/10/20075.01402.3475682.8119.92.141.00 3T4/10/20072.41702.2935310.4118.41.05 4U4/10/20073.42402.3803413.5103.41.441.05 5T4/10/20072.29452.3507276.5105.80.98 6T4/10/20072.17852.3897249.597.30.91 7T4/10/20072.46602.3578287.5101.71.05 8U4/10/20074.58552.3688543.1102.41.941.00 9T72.04/10/20072.25002.3417264.6104.00.96 BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 4/51U72.04/10/20074.33552.3968769.5149.91.811.01 2U4/10/20074.17552.3973752.0152.01.741.02 3T4/10/20072.79002.3953513.1155.51.16 4T4/10/20072.37202.4007427.7151.80.99 5T4/10/20072.11102.4037370.3147.30.88 6T77.04/10/20072.17052.3942358.7139.80.91 4/61U77.04/10/20074.46152.3982789.5149.21.861.01 2U4/10/20073.66952.3942651.7150.31.531.04 3T82.04/10/20072.40302.3955395.8139.21.00 4/71T82.04/10/20072.62602.4087468.2149.11.09 2U4/10/20074.96952.3965862.9146.62.071.00 3U87.04/10/20073.99102.4072711.8149.31.661.02 4/8NA87.092.04/10/2007Effective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile PAGE 112 112 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 4/11T10.00105.31375.2148.50.0527100 / 7775.4411.9381.3 2U9.77105.63357.2741.40.04250.92"75.5710.5654 3U9.90113.95394.31195.30.05051.06"76.2778.8715.5 4T12.15107.81498.2168.40.0398"75411374.6 5U9.64123.37650.71693.30.05481.11"77861.7792.7 6T11.33112.8438.445.10.0319"76.4455.8417.2 7U10.13113.44492.3989.30.03440.77"74.9726666.1 8U7.30125.678131732.90.06231.30"75.6838.2786.3 9T7.02123.62047.2279.40.0643"77381.8361.8 10U6.09125.76338.71403.50.04860.98"75.5840.8796.9 11T8.00119.21733.3219.90.0443"75.6394.3370.7 4/21T3.2198.21414.2150.40.112890 / 4877.7377367.7 2U3.08101.01978.9439.00.03550.81"75.9595.4579.9 3T4.33104.41262.1128.70.0891"76401.6388.1 4T10.79119.03328353.70.0556"76.9467429 5U8.51109.52030.7454.70.03540.90"76585.9545.9 6T4.33114.02302.1252.90.0906"75.7405.8392.1 7T7.02123.82290.3252.80.0902"77.5450.9426.4 8T10.64112.82816.1281.60.0969"76.1454.5418.1 9U5.61119.53170.6711.50.05531.15"75.1780.8743.3 4/31T3.0997.81280.1183.90.024682 / 1477.9294.5288 2U2.22149.06791.71447.00.04891.35"74.9700686.4 3U0.75144.49992.72134.80.04581.27"74.8691.7687.1 4T0.76105.31260.9144.10.0434"75352.3350.2 5T1.28100.2812.991.30.0452"77.5354.4350.9 4/41T4.95122.82832.6322.70.040087 / 3476.2430.3413.6 2U9.54109.42457.9567.90.02470.49"75756696.7 3T6.11111.61563.5179.60.0658"75.5384.8367 4U6.5097.11591.8341.70.03290.96"75.4486.6461.5 5T4.48101.21743.1205.70.0986"77.9353.1341.3 6T3.3194.2688.784.20.0312"77.1327.1319.1 7T3.9597.9963.8105.50.0704"75.8362.8351.9 8U4.7097.81058.1239.10.02230.49"76.9607.4583.6 9T6.2697.91296.7156.70.1132"77.9339.4324 BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 4/51U2.84145.710309.52256.40.05401.2558 / 2575.5832.4811.5 2U2.83147.810395.32262.90.05061.21"75.1826805.3 3T2.01152.44593437.50.0638"75.7587.1577 4T1.76149.13913.4437.50.0460"76503.1495.7 5T2.05144.32823.3354.20.0309"76.9445.3437.9 6T3.57135.03007.5368.40.0760"77.7435422.7 4/61U1.86146.510446.52292.10.05121.1577.5865.4851 2U1.96147.410971.32351.00.04731.2975.6727.2714.7 3T1.46137.23324.5367.70.028375.5471.3465.6 4/71T1.52146.84003.3402.90.048342 / 2077539.1532.2 2U1.32144.716231.43598.50.04981.00"76.1910.4899.5 3U2.34145.910079.62161.30.04381.10"74.9786.6770.3 12 / 0 DISPL. @ FAIL. DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: 17th Street Bridge Location: Date Received: Tested by: PAGE 113 113 Table B-1. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 5/11T52.02.40152.3885330.1116.91.01 2T2.45102.3675333.5117.71.04 3U4.25352.4005665.8131.81.771.02 4T2.37152.3815380.4137.21.00 5U4.22802.3980677.2135.11.761.02 6T2.18402.3965325.2125.80.91 7U3.92552.3800595.6129.91.651.03 8U4.19902.3780628.0128.31.771.02 9T2.33052.2213342.5144.51.05 10U3.70452.3075486.8119.71.611.03 11T2.54102.3835360.8121.21.07 12T57.02.29452.3860342.5127.20.96 13U3.64252.4065621.9143.01.511.04 5/21U57.04.15402.3005625.3138.01.811.01 2T2.37402.3655353.0128.91.00 3T1.99552.3900278.7118.60.83 4U3.70102.3695529.2123.51.561.03 5T62.02.15602.4000300.6117.40.90 5/31U62.04.86952.3820854.4150.02.041.00 2T2.39202.3970392.7138.61.00 3T2.27002.3490229.588.90.97 4T67.02.17252.3970338.8131.70.91 5/41T67.01.81002.2860195.0100.00.79 2T1.69152.3205155.782.90.73 3T72.01.84652.3020185.091.70.80 BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 5/51T72.01.87502.3860320.2145.50.79 2U3.35132.3965606.8152.91.401.05 3T2.44152.4000345.7119.21.02 4U4.80352.4030881.2154.12.001.00 5U4.90852.4010819.0140.42.041.00 6T1.80252.4070316.5147.00.75 7U4.04552.3900687.6144.31.691.02 8T2.18952.4005385.6148.20.91 9U4.63352.3990826.1150.31.931.00 10U77.03.87152.4000650.9141.61.611.03 5/61T77.02.20602.4065405.9154.10.92 2U4.72552.3990835.7149.01.971.00 3T2.18802.3830357.1139.40.92 4U82.03.69002.3870657.5151.71.551.04 5/71T82.02.22152.3845382.2146.80.93 2U87.03.62502.3885630.9148.01.521.04STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile Effective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 PAGE 114 114 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 5/11T9.04107.21772.1196.70.1135100 / 8275.1405.7378.3 2T8.16108.91390.3152.50.0964"75.5408.2383.1 3U7.50122.65753.41252.00.03150.74"74.9737.4691.2 4T8.21126.83673.9414.10.0638"77456.7427.9 5U8.35124.78109.51767.10.06041.43"77.9751.3699.4 6T7.19117.3713.986.80.0394"76.9401.8380 7U8.49119.83836.9841.00.04071.04"77.5670.7624.3 8U8.10118.73195.3708.20.02280.54"75700.7653.8 9T6.93135.12784.1342.40.0873"75.4416.6394.5 10U5.13113.92008466.40.00660.18"75.8561.1537.4 11T4.94115.51703.3179.00.0854"77.9415.5399.6 12T4.32121.93028.1352.10.0565"77.1417.7403.6 13U1.36141.110398.82201.40.05851.61"76.9696.5688.2 5/21U3.97132.72665.4633.10.05631.3670 / 2077.7700.6676.8 2T0.98127.61608.2182.30.0440"76417413.7 3T1.26117.11573.5210.00.0374"77.5342.1338.8 4U6.90115.63880851.30.12733.44"76.2573.2541.1 5T4.45112.41110.3136.60.0307"75.7362349.8 5/31U1.79147.49570.42147.70.06301.2977 / 1575.7928.5913.5 2T1.21136.93920.7435.30.0381"75.5468.1463.4 3T2.0187.11000.5119.50.0812"75.1303.6299.1 4T1.90129.22292.2280.20.0588"75.6413.6407.3 5/41T3.6296.5982.8151.20.122952 / 076270.8264 2T2.7280.739263.60.1238"75.9226.7222.7 3T4.6187.7273.841.00.0446"75.7259.6251.5 BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 5/51T1.23143.72179.8310.20.017280 / 6377.3397393.1 2U1.90150.15546.21169.20.04251.27"75.6680.2668.9 3T2.38116.5920.9100.10.0247"76.3419.8411.8 4U2.26150.710731.92366.30.05581.16"74.9955.4935.9 5U3.05136.23268.8722.00.02710.55"77894.1869.9 6T2.66143.22258.7331.40.0873"76.4392.7384.5 7U2.77140.44315.8941.50.04261.05"76.2751.7733.5 8T1.96145.42358.6285.70.0325"77.6462.3454.9 9U2.18147.16641.71463.20.05541.20"75.5900.7883.1 10U2.95137.55546.11191.70.03951.02"78.3728709.4 5/61T0.87152.83107.5372.60.030066 / 3076.5482.7479.2 2U1.30147.18502.21877.60.05441.15"75910.9900.2 3T2.21136.43750.5457.90.0485"74.2429.6421.9 4U2.13148.510165.42194.30.05121.39"81.6739.1725.4 5/71T2.44143.35093612.10.038737 / 876458.5449.4 2U2.22144.89645.32073.60.04721.30"76.2707.3693.617th Street Bridge Location: Date Received: Tested by:DISPL. @ FAIL. DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: PAGE 115 115 Table B-1. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 6/11T52.01.98702.3910272.5116.40.83 2U5.29452.3465756.2125.82.261.00 3T2.39952.3670372.9134.51.01 4T2.16952.3813357.0140.80.91 5U4.97552.3908790.4134.82.081.00 6T2.21202.3722349.7136.30.93 7U4.15602.3880660.8135.21.741.02 8T2.47152.3530358.4127.01.05 9U4.32302.3750677.5134.81.821.01 10T2.45152.2730337.6129.31.08 11T57.02.38452.1530323.7142.11.11 6/21U57.03.86502.4130588.3126.81.601.03 2T2.26502.3790349.6132.30.95 3T2.36152.3400259.497.31.01 4T2.37702.3775406.5146.71.00 5U4.56702.4130735.5134.21.891.01 6T2.27302.3795349.3131.60.96 7T62.02.35002.3665351.0129.40.99 6/31T62.02.10802.3765250.8102.20.89 2U3.52752.3957615.8147.51.471.04 3U3.46352.3770591.4146.61.461.04 4T2.48002.3557257.690.81.05 5U4.31402.3707551.0110.21.821.01 6T1.88502.3350219.7103.70.81 7U4.42852.3725565.7110.11.871.01 8T2.28502.3757274.3103.20.96 9U67.05.20802.3627658.6109.92.201.00 6/41U67.04.42352.3710487.795.11.871.01 2T2.36402.3732294.7107.41.00 3T1.90452.3665233.8106.30.80 4U3.99752.3658463.7100.51.691.02 5T2.28502.3908270.8100.60.96 6T2.34702.3717270.599.40.99 7T2.26702.3843270.2101.70.95 8T72.01.97752.3643236.3103.70.84 6/51U72.04.37102.3745714.5140.61.841.01 2T2.04352.3770368.4154.80.86 3U4.54002.3770665.7125.91.911.01 4T2.62102.3900449.9145.81.10 5T2.36952.3440318.7118.71.01 6U4.45402.3820584.7112.21.871.01 7T1.96902.3915259.2111.60.82 8U77.04.43952.3930672.2128.31.861.01 6/61T77.02.33352.3855407.0148.70.98 2U3.99652.3740674.5145.31.681.02 3T82.02.02502.3805333.5141.00.85STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile Effective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 PAGE 116 116 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 6/11T9.24106.51758.5235.60.1252100 / 6276.3326.9305.7 2U8.39116.12846.5658.30.02000.38"76.2830.3771.9 3T14.53117.53201.6358.90.0836"75.4446.6399.5 4T6.55132.13330.8410.40.0511"75419.9398.7 5U8.96123.75693.31268.20.03500.70"76.9845.8782.6 6T5.51129.21942.3235.60.0616"75408.2390.8 7U8.79124.32542.3557.70.03080.74"76734.1680.9 8T12.07113.42583.7282.80.0851"76.3433.9395.4 9U9.90122.63311.5738.80.02750.64"76.4749688.4 10T14.18113.2788.490.10.0271"77.7414.3372.5 11T6.19133.82896.2359.10.0964"75.7398.1379.3 6/21U2.60123.64409.9936.40.17584.5572 / 3777.5642.6628.3 2T8.56121.91745.3206.20.0705"75.7424.5397 3T3.8793.7871.7100.40.1053"74.9329.9320.4 4T3.40141.96055682.10.0486"75.6474.2461.1 5U7.51124.83801.2825.60.03030.66"76.5805.5754.6 6T11.67117.92097.8246.90.0430"74.2420.5384.3 7T5.12123.12339.3267.80.0591"75.7410.1393.8 6/31T1.29100.91389.6176.60.068880 / 5174.9325.3322.1 2U1.43145.510020.22131.30.12683.59"75.6679.3670.8 3U1.92143.84800.31035.50.03110.90"76665.3654.2 4T4.3587.01040.9113.40.1196"75.7332.3321.6 5U3.56106.41966440.20.02050.48"77.7618.9600.3 6T3.8599.8866.3125.30.1288"74.2292.6284.5 7U3.51106.32473.7554.80.40209.08"75.7632.6613.7 8T3.4599.71302.4152.70.0788"76.5349339.9 9U2.83106.91828416.90.03570.69"75.4722.6704.8 6/41U2.6392.71289.8289.60.21284.8168 / 3076.3552.9540.7 2T2.05105.21123.7127.50.0449"77.2370.6364.7 3T3.76102.51072.1151.40.0605"74.9298.2290.1 4U2.7897.81081.4240.70.05441.36"77535.4523 5T2.5098.1892.6104.00.0590"76.2343.1336.6 6T3.1896.31147.1131.20.0634"76.4345.6337.3 7T3.7698.01148.7135.30.0905"76.3343.8334.1 8T3.36100.31509.8205.60.1603"75.1303295.6 6/51U1.23138.96235.51393.70.04451.0280 / 6081.6796.1787.4 2T1.24152.93890.2509.90.0562"76.9445.3440.8 3U1.53124.06375.11428.60.03220.71"75740.7730.7 4T1.35143.82505254.60.0378"75.5525.4519.4 5T1.05117.52201.1252.30.1374"77.1395.8392.5 6U1.69110.42312.3514.60.05501.23"75.5660.2650.5 7T0.78110.81209.9163.60.0332"76335.2333.2 8U1.65126.22716.5598.40.09792.21"76.2748.4737.5 1T1.80146.05188.1593.30.036648 / 1774.8481.5474.3 2U1.37143.33525.6778.90.02940.74"76.1750.6741.5 3T0.89139.73676.3485.50.0483"76.2406.1403.217th Street Bridge Location: Date Received: Tested by:DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: PAGE 117 117 Table B-1. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 7/11T52.01.99052.3980285.2120.90.83 2U57.03.78802.3845633.0142.61.591.03 7/21T57.02.22602.3560293.3115.10.94 2T1.99402.3500293.5129.30.85 3U4.31352.3815693.7137.51.811.01 4T2.25802.3835403.4152.50.95 5U4.69702.3950841.0151.41.961.00 6T2.05502.3970364.0149.50.86 7T1.75402.3670254.8125.80.74 8T2.17502.3915334.1130.30.91 9T2.45402.3975412.3141.81.02 10U4.20852.3010612.9133.41.831.01 11T2.46052.3720375.3131.51.04 12U5.00752.3880763.2129.62.101.00 13T62.02.21302.3675337.6132.00.93 7/31T62.02.20152.2940223.393.50.96 2T67.02.32552.3015229.190.21.01 7/467.072.0NASAND 7/51T72.02.45352.3843376.1130.81.03 3T2.13552.3915366.2145.40.89 4T2.17652.3920388.8151.40.91 5U3.88252.3842674.7148.31.631.03 6U4.14652.3872735.6151.01.741.02 7U3.72502.3710576.4133.51.571.03 8T1.48502.3715226.6131.60.63 9U77.03.99702.3770670.0143.91.681.02 7/61T77.02.01102.3840364.4154.60.84 2T2.10702.3953378.2151.70.88 3U3.66252.3932646.9149.61.531.04 4U82.03.92802.3900685.7148.21.641.03 7/71T82.02.19552.3965390.7150.30.92 2T87.02.29452.3890384.8142.50.96 7/81T87.092.02.31102.3970338.9123.80.96Effective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile PAGE 118 118 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 7/11T3.56116.72871382.90.098652 / 1077359.2349.5 2U1.25140.8110002389.10.07341.94"77.2711703.2 7/21T2.67112.11725.4209.40.151593 / 5074.1366.6359 2T5.61122.42714.9368.80.0663"75.9364348.7 3U4.11132.16379.51414.50.06461.50"74.5765.9738.6 4T3.25147.74748.7561.70.0388"75.9476.1463.5 5U0.53150.613108.82903.00.06981.49"76.1891.1886.8 6T1.68147.13542.8457.90.0347"76.3438.4432.4 7T6.38118.22918.9447.60.0936"75.7329.3314.1 8T5.88123.03484.4426.50.0672"75406.1387.7 9T1.90139.14411.4477.30.0591"76488.2480.5 10U3.85128.54195.6997.80.03590.85"75682659.5 11T2.11128.82239.8244.30.0287"75.4448.7441 12U6.12122.24652.11038.70.03140.63"76.9834.4790.7 13T1.78129.72716.6330.10.0326"76.2408.7402.9 7/31T0.6392.91277.5161.00.132442 / 074297.2295.8 2T0.7589.51871.7222.60.1413"77333.2331.3 7/4 50 / 0 7/51T1.19129.33141.3341.90.041183 / 5474.2448.9444.5 3T1.27143.62780.1346.60.0292"75.7442.1437.5 4T1.09149.83555.4434.80.0262"75.7464.6460.4 5U0.90147.010908.52378.30.05421.40"74.9746.5740.5 6U1.37149.011900.52611.50.05481.32"75.6809.4799.5 7U1.94131.03889.5853.00.03000.81"76.2607.2597.1 8T1.49129.72100.7379.70.0599"74.9300.4297.1 9U1.15142.39887.32178.60.04681.17"76.4743.1735.5 7/61T1.36152.65727.5760.50.045667 2777.7442437.1 2T0.83150.53472.4438.00.0288"77.5456452.9 3U1.16147.911070.32373.70.05501.50"76.5722.2714.8 4U1.02146.77211.31566.70.07371.88"76.3722.8716.3 7/71T1.98147.45630.4681.30.040243 / 776466.8459.2 2T2.15139.53660.1425.10.0219"75.7460.5452.4 7/81T1.38122.11884.9216.60.036823 / 877416411.4 DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: 17th Street Bridge Location: Date Received: Tested by: PAGE 119 119 Table B-1. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 8/11T52.02.17652.3665290.2115.50.92 2U3.90352.3900669.1145.61.631.03 3T2.32452.3913249.491.00.97 4U4.39952.3833494.896.01.851.01 6U4.40952.3905745.8143.61.841.01 7T1.59202.3745233.4126.10.67 8U57.03.86052.3753560.6124.81.631.03 8/21T57.02.32602.3933357.7130.20.97 2U4.53452.3895712.2133.41.901.01 3T2.02552.3955316.4132.00.85 4U4.08152.3973631.0130.51.701.02 5T2.32852.4045344.4124.10.97 6U62.04.08652.3912570.2118.41.711.02 8/31U62.04.44602.3633510.199.61.881.01 2T2.09452.3863259.6105.60.88 3T2.34302.3708262.896.80.99 4T2.30252.3858254.194.00.97 5T1.87902.3665313.8144.60.79 6U4.70452.3860852.5154.41.971.00 7T2.22522.3870405.1155.00.93 8U4.34202.3868789.6154.81.821.01 9T2.46152.3933432.8148.91.03 10U4.71552.3927801.4144.01.971.00 11T67.02.05202.3777327.5136.90.86 8/41U67.04.51652.3643761.0146.21.911.01 3T2.36102.3775283.3103.00.99 4T2.12202.3710253.2103.00.89 5U5.04052.3805576.397.92.121.00 6T72.02.09052.3848250.7102.30.88 8/51U72.03.92402.3735700.6153.71.651.03 2T2.08702.3748327.2134.80.88 4U4.26152.3708731.2148.11.801.01 5U4.71252.3745826.9151.01.981.00 6T1.86252.3745301.7139.40.78 7T2.13302.3822341.4136.80.90 8U77.03.73152.3673659.3152.91.581.03 8/677.082.0NA 8/71T82.087.02.22852.3755406.0156.60.94 8/887.092.0NAEffective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile PAGE 120 120 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 8/11T1.90113.32768.5342.20.061885 / 4075.7364.9359.5 2U2.44142.110983.72384.10.05401.38"77.7744.5728.6 3T10.2982.5587.367.30.0477"75.7324.4301.2 4U7.4489.41094.7243.00.04060.92"74.9567.2533.1 6U7.06134.15410.41193.50.03930.89"76820.8771.7 7T10.37114.31071180.40.0374"74.9305.8284.1 8U11.92111.52448.3537.60.05451.41"76.5630.5571.5 8/21T2.12127.53284.3375.60.047661 / 3874.2431.4424 2U1.46131.54159.5921.60.03460.76"77.2784.8774.6 3T2.34129.03120.2409.40.0254"75.7390.7383.5 4U6.00123.153591162.90.05021.23"75.4703667.5 5T2.24121.43494.8397.40.0457"77420412.5 6U8.08109.53299719.90.07961.95"76.3636.6594.7 8/31U0.8898.81058239.40.02820.6385 / 6376.2579.1574.7 2T1.89103.61465.3186.60.1091"76.4334.8330 3T3.3093.71507.4172.80.1471"75.1334.9326.6 4T3.3291.01277.5148.00.0729"76.3325.4317.4 5T1.00143.23369.1482.30.0248"76.1389.3386.2 6U1.16152.69120.52036.40.04881.04"81.6936.2926.4 7T1.02153.45483.6657.20.0370"76.2481476.9 8U0.92153.48597.71899.00.03840.88"77.1866.5859.3 9T1.12147.24848.9524.00.0444"76.9509.8505 10U1.16142.36241.31385.60.04230.90"74.8875.8866.6 11T0.90135.73860.6503.70.0599"76.1401.7398.8 8/41U1.68143.84166.6943.80.05031.1173 / 4676.3832.3819.8 3T2.74100.21869212.00.0974"75.6352.6345.2 4T3.1099.91096.2138.70.0710"75.5318.4311.1 5U1.6996.21103.9248.00.07301.45"77.9636.9627.6 6T1.76100.51599.8204.30.0898"74.2322.9318.6 8/51U0.78152.5100162208.20.05691.4573 / 3876.1774.6769.2 2T0.80133.83009.1386.50.0311"75.7401.9399.3 4U1.16146.48808.21968.70.06911.62"81.6807.3799 5U1.09149.36129.31382.90.05421.15"76.2902.9894 6T1.00138.03366.1484.50.0270"76.5378.2375.2 7T1.72134.52593.7325.00.1258"75.7412.3406.6 8U0.73151.89882.52175.20.09242.48"77.2727.7723 8/6 23 / 0 8/71T1.91153.77095.3853.30.037330 / 076.9483475.4 8/8 6 / 0 DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: 17th Street Bridge Location: Date Received: Tested by: PAGE 121 121 Table B-1. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEMASSUNIT MASSRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) 9/11T52.02.36752.3758274.899.71.00 2U4.84552.3993734.1127.72.021.00 3T2.57252.3918357.3117.81.08 4U3.84052.3895623.0137.81.611.03 5T2.20102.3723364.2142.60.93 7U4.17602.3723631.5130.31.761.02 8T1.94002.4003299.0129.80.81 9T2.28452.3838357.8133.70.96 10U57.03.61202.3605616.1148.51.531.04 9/22U57.04.05952.3835642.7135.21.701.02 3T2.46102.4002426.2145.81.03 4T2.19002.3923384.5148.80.92 5T62.02.34802.3793372.9136.10.99 9/31T62.02.35402.3748382.8139.90.99 2T2.30302.3762411.0153.30.97 3U4.77302.3712853.7154.32.011.00 4T2.36202.3657413.8151.81.00 5U4.54552.3710806.2153.01.921.01 6T2.24902.3638355.2137.10.95 7U3.90552.3790647.2142.01.641.03 8T67.02.00002.3515243.9107.00.85 9/41T67.02.04702.3715332.2140.00.86 2U4.83502.3870751.7132.42.031.00 3T2.01102.3808227.296.70.84 4T2.25502.3907274.4103.30.94 5T2.09052.3708248.0102.40.88 6U3.65902.3763436.6102.51.541.04 7T72.01.90352.3728228.5103.40.80 9/51T72.02.18802.3832366.2142.90.92 2U4.54052.3837780.4146.71.901.01 3T2.26302.3797404.8153.20.95 4U4.43352.3853712.6137.01.861.01 5U77.04.87202.3825861.7151.12.041.00 9/61U77.03.62052.3862662.8156.01.521.04 2T2.41802.3888439.7154.61.01 3T82.01.96302.3873356.4154.50.82 9/71U82.087.04.28602.3872770.9153.11.801.01STATE MATERIALS OFFICE Foundations LaboratoryRock CoreUnconfined CompressionSplit Tensile Effective/Revised Date: 12/22/05 By: B.W.Page 1 of 1 PAGE 122 122 Table B-1. Continued. BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT MAS S LOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) 9/11T6.8893.31279.5144.80.121198 / 6476.3349.6332 2U6.62119.745861014.40.04810.99"77803.8758.7 3T9.36107.71349.6139.60.1402"75.4429.4399.1 4U7.87127.85926.11283.90.05331.39"77.1684.2639.9 5T6.88133.43102.2378.20.0323"75.1435.4412.2 7U5.95123.04364.8971.60.04261.02"74.2695.5660.6 8T5.68122.82644.6361.60.1008"77.9373.6357.7 9T4.30128.23740437.20.1115"76.3430.4415.8 10U1.86145.8165703651.90.07232.00"75.6682.5671.4 9/22U3.66130.44704.71032.80.03020.7462 / 875.5716.1693.5 3T1.84143.25139.4553.90.0406"76.3502.5494.8 4T2.50145.24575.3556.00.0323"77.1461.8452.4 5T1.55134.03925.7447.40.0201"77.9450.6444.9 9/31T0.90138.63660416.80.034587 / 3375.1458.1454.7 2T1.16151.65147.2598.80.0344"75.4486.6481.9 3U1.62151.88931.82022.70.04110.86"77930.4916.8 4T1.15150.14117.4469.10.0385"76.1489.7485 5U2.26149.612046.92714.50.05641.24"77.1881.4863.6 6T3.71132.21619.8335.60.0306"76.5431.4418.7 7U3.83136.84587.71005.80.06521.67"81.6724.1700.4 8T2.53104.31663.5225.20.1097"75.7318.7312.7 9/41T1.34138.13476.3455.90.040468 / 1776.2408.3403.9 2U1.15130.86042.21350.20.04510.93"76.3823.9815.4 3T4.0193.0802.1106.70.0909"77.2302.8294.1 4T2.98100.31647194.50.1026"75.7348.9341 5T3.2199.2986.8126.80.0723"75.9320.5312.9 6U2.15100.3848.3184.70.08772.40"76.1508.6499.5 7T2.27101.11367.3192.70.0828"76.2301.9296.9 9/51T0.97141.63361410.30.054380 / 3772.2437.2433.7 2U1.04145.26839.41523.50.03410.75"76.6856.4848.4 3T1.09151.65095.1602.30.0367"76.7477.2472.9 4U1.21135.46111.71355.40.04701.06"76.1776.6768.2 5U1.20149.37936.31780.20.03410.70"76.3937.8927.6 9/61U1.97152.99747.72099.60.04061.1247 / 1676.7737.9725.1 2T1.62152.15475.7603.50.0583"76.4515.7508.7 3T1.54152.24377.4594.70.0467"79435.5430.1 9/71U1.09151.48963.41975.70.06941.6230 / 1377.3844.1835.817th Street Bridge Location: Date Received: Tested by:DISPL. @ FAIL.Project Number: Lab Number: Bridge Number: LIMS Number: PAGE 123 123 Table B-2. Fuller Warren Soil Boring Data BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEWT.UNIT WTRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) CB-1/1 1T40.508/10/20062.34202.4850463.4155.40.94 2U4.81772.4610799.3132.91.961.00 3T2.44652.4200374.3126.71.01 4T2.38052.4200396.3137.90.98 5U45.504.16422.4765751.1142.61.681.02 CB-1/2 1U45.508/10/20063.63022.4545679.5150.71.481.04 2T2.44552.4625442.7144.80.99 3U4.52332.4315750.0136.01.861.01 4T2.34702.4250399.4140.40.97 5U4.68852.4535805.6138.51.911.01 6T2.12352.4700384.2143.90.86 7T2.51352.4600454.9145.11.02 8U4.81952.4570848.6141.51.961.00 9T2.55602.4640472.0147.51.04 10U50.504.79622.4740892.8147.51.941.00 CB-1/3 1T50.508/10/20062.49452.4510464.0150.21.02 2U4.77322.4630911.1152.61.941.00 3T2.47852.4495451.5147.21.01 4T8/11/20062.45552.4545388.3127.31.00 5T2.37802.4340355.0122.20.98 6T55.502.40802.4240346.0118.60.99 CB-1/4 1U55.508/14/20064.76722.3530693.6127.52.031.00 2T2.53502.3975384.2127.91.06 3T2.53052.4060353.4117.01.05 4U4.84152.4215758.8129.62.001.00 5T2.20202.4115341.0129.20.91 6U4.86822.4230766.8130.12.011.00 7T2.30852.4170345.1124.10.96 8U4.72172.4350727.1126.01.941.00 9T60.502.50602.4400393.8128.01.03 CB-1/5 1T60.508/14/20062.36002.0160227.1114.81.17 2T2.02152.1000207.7113.00.96 3T2.45852.2185285.8114.61.11 4U4.00082.0860420.4117.11.921.01 5U4.87552.2955597.1112.72.121.00 6T2.47702.4000349.0118.61.03 7U4.85372.4230680.3115.82.001.00 8U4.69122.4060665.3118.81.951.00 9T65.502.44652.3815326.2114.01.03 CB-1/6 1T65.508/15/20062.52802.3400328.9115.31.08 2T2.38602.2185296.0122.31.08 3U4.80082.3850675.2119.92.011.00 4T2.32952.4040344.1124.00.97 5T70.502.31402.3200303.5118.21.00Effective/Revised Date: 4/27/05 By: G.J.Page 1 of 1 STATE MATERIALS OFFICEFoundations LaboratoryRock CoreUnconfined CompressionSplit Tensile PAGE 124 124 Table B-2. Continued. CB-1 8/9/2006BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT WTLOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) CB-1/1 1T3.35150.43963.2433.50.064067/37427.1873.8859.3 2U16.73113.81017.4213.30.04971.03431.11224.31110.6 3T23.01103.0276.829.80.0464410.1781.1711.7 4T15.60119.3799.888.40.0445425.5821.1767.7 5U10.93128.66578.21335.30.06091.464331181.11107.4 CB-1/2 1U8.01139.59815.41990.30.06991.9394/74424.31098.21048.2 2T10.47131.11191125.90.0443418.9861819.1 3U14.44118.93855822.80.04961.10302.81051.7957.2 4T11.77125.6896100.20.0512370.7769.5727.5 5U14.05121.43453726.20.06721.43435.21239.41140.3 6T11.39129.11814220.20.0509328.3711.6672.4 7T11.43130.22473254.60.0558434.1887.6841.1 8U11.42127.04494945.70.05221.08368.91201.41116.1 9T11.39132.41875189.60.0411429.5900.9852.7 10U#DIV/0!#DIV/0!*#VALUE!*#VALUE! CB-1/3 1T8.79138.12483.1258.60.050460/48377.8840.9803.5 2U8.31140.975331575.10.05271.10372.31279.61210 3T9.49134.51582165.90.0408428.2878.2839.2 4T16.13109.624525.90.0289427.1814.5760.7 5T24.1698.511212.40.0213372.3726.9657.9 6T31.2790.418319.90.0297435.2780.7698.4 CB-1/4 1U26.38100.9759174.50.05161.0892/77427.11118.4974.1 2T23.05103.918119.00.0223372.4756.2684.3 3T30.8089.512112.70.0393435.3780.1698.9 4U22.23106.11408305.70.04400.914191165.61029.8 5T22.22105.729935.90.0278364.9705.4643.5 6U22.05106.61468318.30.05471.12308.21073.8935.5 7T27.8697.121524.60.0356313.1657.8582.7 8U25.34100.5772165.10.05761.22373.21098.8952.1 9T23.43103.726727.80.0440425.5819744.3 CB-1/5 1T36.3084.310914.60.033690/67315.2542481.6 2T41.1980.0619.20.0242431.1637.8577.5 3T45.3478.8293.40.0173432.5716.5627.9 4U37.6785.133898.40.06081.52370.4789.6674.9 5U36.2682.7423102.30.06101.25370.6965.9807.5 6T33.8288.713614.50.0386376.5724.3636.4 7U34.3486.2550119.30.05651.16312990.3816.9 8U29.7291.6479105.10.04200.90300.9965.2813 9T30.5487.411913.00.0401371.3697620.8 CB-1/6 1T29.2389.251.75.60.027658/38315.2643.7569.4 2T27.2296.1465.50.0407431.3726.7663.5 3U28.9893.018741.90.05311.11370.41045.1893.5 4T21.96101.7536.00.0284364.9708.7646.8 5T25.6194.1303.50.0372432.5735.6673.8 DISPL. @ FAIL.Fuller Warren Project Number: Lab Number: Bridge Number: LIMS Number:JCLocation: Date Received: Tested by: PAGE 125 125 Table B-2. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEWT.UNIT WTRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) CB-2/1 1U37.588/16/20064.05132.3715674.2143.51.711.02 2T2.42502.3875437.6153.61.02 3T42.582.46352.3500390.2139.11.05 CB-2/2 1T42.588/16/20062.23052.3730359.4138.80.94 2U4.82332.3865806.6142.42.021.00 3T2.27352.3440328.3127.50.97 4U8/17/20064.73522.3685756.7138.22.001.00 5T2.44252.3845413.1144.31.02 6T47.582.47752.3770429.6148.91.04 CB-2/3 1T47.588/17/20062.31552.3325393.3151.40.99 2U4.67132.3815790.1144.71.961.00 3T2.44502.3890415.2144.31.02 4U2.69132.3880784.5247.91.131.09 5T2.39502.3885401.6142.61.00 6U4.73832.3925769.6137.61.981.00 7T2.43702.3935401.1139.41.02 8U4.90982.3895872.3150.92.051.00 9T2.29502.3770310.1116.00.97 10U4.72802.3760630.4114.61.991.00 11T2.39502.3630294.3106.71.01 12U52.584.79022.3810834.4149.02.011.00 CB-2/4 1T52.588/17/20062.35752.3365383.7144.61.01 2U4.78252.3870798.5142.12.001.00 3U4.73282.3500775.3143.92.011.00 4T8/18/20062.38152.3675367.4133.51.01 5U4.63802.3510701.1132.71.971.00 6T2.30352.3635327.9123.60.97 7U4.68802.3645655.3121.31.981.00 8T2.28752.3445312.6120.60.98 9U4.72332.3485662.1123.32.011.00 10T2.33152.3390330.5125.71.00 11T2.31402.3530340.4128.90.98 12U4.80882.3595699.7126.82.041.00 13T2.52352.3475359.1125.31.07 14T57.582.53602.3615357.3122.51.07 CB-2/5 1U57.588/18/20064.86782.3470705.9127.72.071.00 2T2.48552.3655363.3126.71.05 3U4.70172.3590677.6125.61.991.00 4T2.38652.3325350.0130.81.02 5U62.584.95022.3395718.3128.62.121.00 CB-2/6 1T62.588/18/20062.34602.3535294.3109.91.00 2U4.79832.3545623.0113.62.041.00 3T2.34452.3675301.1111.10.99 4U4.75402.3515627.6115.82.021.00 5T2.33802.3355311.5118.51.00 6U4.62232.3500629.1119.51.971.00 7U4.80982.3650654.8118.12.031.00 8T2.31752.3130312.8122.41.00 9U4.83822.3155654.1122.32.091.00 10T67.582.41852.3000323.1122.51.05STATE MATERIALS OFFICEFoundations LaboratoryRock CoreUnconfined CompressionSplit Tensile Effective/Revised Date: 4/27/05 By: G.J.Page 1 of 1 PAGE 126 126 Table B-2. Continued. BORINGSAMPDEPTHDEPTHTESTLENGTHDIA.WETWETL / DCORR. NO.TOPBOT.DATEWT.UNIT WTRATIOFACTOR CORE(ft)(ft)(in)(in)(g)(pcf) CB-3/1 1U41'8/21/20064.83802.3950853.2149.12.021.00 2U4.43272.3835740.4142.61.861.01 3T2.43452.3100335.2125.21.05 4T2.43502.3785375.0132.01.02 5T46'2.35002.3730409.9150.20.99 CB-3/2 1T46'8/21/20062.41652.2995308.4117.11.05 2U4.33572.3655774.8154.91.831.01 3T8/22/20062.32202.3760406.1150.30.98 4U4.80682.3820806.8143.52.021.00 5T2.35352.3720400.6146.70.99 6U4.88252.3895799.2139.12.041.00 7T2.33952.3870393.8143.30.98 8U51'4.87152.3890865.4151.02.041.00 CB-3/3 1T51'8/22/20062.33152.3510380.8143.30.99 2U4.86322.3610838.4150.02.061.00 3T2.43952.3110376.5140.21.06 4T2.43302.3555378.1135.91.03 5U4.89552.3430734.4132.52.091.00 6T2.48552.3285366.7132.01.07 7T2.45452.3375328.7118.91.05 8U4.81252.3360672.7124.22.061.00 9T2.38652.3230332.8125.31.03 10T2.12102.3185291.7124.10.91 11U4.70202.3455676.5126.92.001.00 12T56'2.41102.3595369.5133.51.02 CB-3/4 1T56'8/25/20062.42852.3140361.2134.71.05 2T2.40452.3495360.4131.71.02 3U4.76002.3470716.7132.62.031.00 4T2.34752.3350351.6133.21.01 5U4.80432.3400701.4129.32.051.00 6U4.88402.3575697.0124.52.071.00 7T2.47852.3545368.8130.21.05 8T61'2.47402.3655330.1115.71.05 CB-3/5 1T61'8/29/20062.36952.3380291.2109.11.01 2U4.73282.3555593.2109.62.011.00 3T2.26402.3445282.7110.20.97 4U4.76372.3380606.0112.92.041.00 5U4.54732.3420570.4110.91.941.00 6U4.71632.3305605.3114.62.021.00 7T2.34202.5030330.6109.30.94 8U4.72652.3425626.8117.22.021.00 9T2.35602.3405313.9118.01.01 10U4.68532.3125627.2121.42.031.00 11U4.65422.2635600.2122.12.061.00 12T66'2.52052.3035313.7113.81.09 CB-3/6 1T66'8/29/20062.35702.3525329.7122.61.00 2U4.58552.3315637.4124.01.971.00 3T2.45002.3325331.8120.71.05 4U71'4.74352.3535651.6120.32.021.00Effective/Revised Date: 4/27/05 By: G.J.Page 1 of 1 STATE MATERIALS OFFICEFoundations LaboratoryRock CoreUnconfined CompressionSplit Tensile PAGE 127 127 Table B-2. Continued. CB-3 8/10/2006BORINGSAMP.wDRYMAX.S. T.q (u)STRAIN% RECOV.TAREWETDRY NO.UNIT WTLOADSTRENGTH@ FAIL.WT.WT.WT. CORE(%)(pcf)(lbs)(psi)(psi)(in)(%)% RQD(g)(g)(g) CB-3/1 1U5.32141.667821505.60.05221.0872/50430.31281.51238.5 2U11.14128.33530784.10.06341.43430.71168.71094.7 3T26.0199.336841.60.0633366.1698.4629.8 4T16.40113.41378151.50.0687431.4805.4752.7 5T9.07137.83224368.00.0515428.3837.2803.2 CB-3/2 1T26.5092.520423.40.074377/67428.1735.5671.1 2U7.46144.257201287.50.05491.27430.21196.61143.4 3T8.10139.01552179.00.0415430.3835.8805.4 4U11.63128.53252729.80.05411.13431.41237.81153.8 5T10.86132.41623185.10.0468371.5771.6732.4 6U13.79122.24229943.00.05631.15433.11230.01133.4 7T11.05129.01715195.50.0419312.1703.9664.9 8U8.31139.456901269.30.04540.93375.91239.01172.8 CB-3/3 1T9.56130.837944.00.0410100/92366.0746.4713.2 2U8.71138.03187727.90.06301.30370.81207.21140.2 3T4.54134.112013.50.0237370.6746.2729.9 4T14.37118.824327.00.0276425.7802.9755.5 5U18.48111.9501116.10.02970.61430.61164.01049.6 6T19.11110.816918.60.0236424.6790.5731.8 7T28.8692.3889.70.0209430.4758.6685.1 8U27.4797.5731170.50.04550.95302.8972.4828.1 9T24.01101.128732.90.0422425.0756.6692.4 10T23.05100.89312.10.0402410.1701.0646.5 11U23.97102.3433100.30.03480.74428.21103.6973.0 12T17.63113.543748.90.0324428.4797.4742.1 CB-3/4 1T19.83112.415918.00.044485/60371.3730.3670.9 2T19.85109.936140.60.0204377.9737.8678.2 3U20.45110.11627376.00.05031.06304.21019.9898.4 4T21.49109.732838.10.0311435.2786.3724.2 5U24.66103.71185275.50.05511.15370.71070.4932 6U26.7398.3873199.90.07081.454191113.1966.7 7T25.87103.422324.30.0379375.9743.7668.1 8T37.8183.918119.70.0368366695.5605.1 CB-3/5 1T40.8177.413115.10.0392100/100366.0656.5572.3 2U41.5177.4550126.20.05281.12371.4963.6789.9 3T40.6078.410112.10.0494375.9657.8576.4 4U38.3281.6556129.50.06691.40435.31039.9872.4 5U39.9179.3594137.30.05571.22419.0988.0825.7 6U34.8185.0581136.10.05751.22304.2908.0752.1 7T30.1384.017519.00.0442370.6699.3623.2 8U29.4490.6485112.50.04921.04377.91002.2860.2 9T32.0589.315918.40.0365427.2740.3664.3 10U26.4996.034481.90.03980.85375.31001.3870.2 11U26.5496.522155.00.03190.69433.01032.3906.6 12T28.1188.8515.60.0220371.5684.6615.9 CB-3/6 1T20.39101.89811.20.023458/45431.4760.8705.0 2U21.02102.535683.10.04370.95428.51064.8954.3 3T24.3297.1869.50.0405428.2759.4694.6 4U24.3196.8486111.70.04881.03430.41080.9953.7 DISPL. @ FAIL.Fuller Warren Project Number: Lab Number: Bridge Number: LIMS Number:JCLocation: Date Received: Tested by: PAGE 128 APPENDIX C SOIL BORING INFORMATION PROCESSED Table C-1. 17th Street Bridge Processed Soil Boring Data. 128 123 EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi)EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi)EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi) -5210.6953.3811.9480829.45-5210.98127.2318.69123700.43-5216.9747.3914.18174256.09 -5312.1286.0616.15112508.32-5329.82127.2330.80123700.43-5325.8447.3917.50174256.09 -543.24121.929.95152060.87-546.2560.559.7381116.67-5429.5591.3125.97180288.98 -553.2471.237.60128709.26-5624.6550.9917.73130425.71-54.516.9740.1513.0575248.87 -5620.11124.7725.05133386.84-5712.8933.5810.40261797.27-5520.3653.1916.46116133.00 -5715.83101.0520.00143472.97-5825.35158.5031.70137071.11-566.4953.199.29116133.00 -57.510.8331.619.2554116.25-6013.1345.5812.2346711.83-5725.8667.4220.8820587.29 -589.2731.618.5654116.25-6015.1261.2915.2224748.90-5914.8567.4215.8220587.29 -5925.4732.7414.4450258.73-629.84154.6319.50166002.00-607.2367.4211.0420587.29 -6018.2132.7412.2150258.73-6431.34154.6334.81166002.00-60.549.1159.4527.02124443.40 -6120.2751.2316.1161906.50-658.60154.6318.23166002.00-61.517.7859.4516.25124443.40 -6213.24104.1818.57107548.83-6620.18154.6327.93166002.00-6219.2859.4516.93124443.40 -6510.37153.7119.96167965.36-6710.8984.1915.1492242.77-62.512.71153.4622.0959292.48 -666.5740.898.20115282.48-694.5884.199.8292242.77-6312.7174.5515.39115316.42 -6723.2340.8915.41115282.48-722.9584.197.8892242.77-648.1731.698.0492628.95 -6812.9324.608.9235563.47-7322.3384.1921.6892242.77-659.0239.959.496111.94 -6914.8117.227.9949175.58-747.20170.3717.52203698.80-6611.0030.029.0860825.36 -707.6017.225.7249175.58-7523.8651.9817.61130769.50-679.1820.856.926020.61 -7211.2817.226.9749175.58-7620.5767.7918.6789410.93-6910.9017.336.8717687.90 -7720.57105.3523.28122375.59-707.4917.335.7017687.90 -7726.8385.8023.99116801.38-719.7417.336.5017687.90 -7826.83135.1830.11163096.18-7214.80100.3519.27136894.81 -8032.97157.9936.09158144.06-7336.71102.8630.72201419.69 -8544.07149.3040.56159257.64-7518.1737.0512.9741673.40 -7711.7843.0911.2627136.26 -7842.7256.0824.47105885.43 -8234.9656.0822.14105885.43 CB-6 (New) CB-4 (New)CB-5 (New) PAGE 129 Table C-1. Continued. 129 456 EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi)EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi)EL. (ft)qt (tsf)qu (tsf)quqt(tsf)Ei (psi) -5227.57172.0134.43123378.55-5224.64171.6632.52172341.16-5210.4373.0313.80102183.65 -57.515.08101.8519.5994451.43-544.8417.494.6026327.58-5310.0592.4415.2492509.46 -5826.56101.8526.0094451.43-5512.9985.9316.70133906.89-5427.2369.9621.8295248.98 -5940.44209.0145.97195348.15-5712.9938.7111.2138084.20-5526.0369.9621.3495248.98 -6032.97209.0141.50195348.15-5827.0466.3621.18120782.02-55.531.48262.9445.49182445.65 -6130.7171.8423.48116969.04-6029.4883.7324.8494551.15-5639.8874.3627.23138835.66 -6234.3771.8424.84116969.04-6128.6151.8319.2636950.25-5940.0374.3627.28138835.66 -6317.5974.7918.14165651.22-6213.4417.247.6137794.70-6132.2174.3624.47138835.66 -6423.7774.7921.08165651.22-6312.4417.247.3237794.70-6230.01145.6333.05234895.75 -6511.5974.7914.72165651.22-6410.66146.6219.77196312.18-62.543.11145.6339.62234895.75 -6716.0374.7917.31165651.22-6534.73146.6235.68196312.18-63.533.77195.4440.62218771.42 -7224.61171.2432.46170366.07-6647.32136.7340.22214724.74-6524.1672.4220.9160246.07 -7331.30171.2436.61170366.07-6737.7399.7730.68154467.47-6716.2197.2219.85144754.85 -7431.30188.0338.36197601.72-6836.2767.9524.8284740.90-67.532.8297.2228.24144754.85 -7527.3461.4220.49105915.18-6915.2667.9516.1084740.90-68.57.6897.2213.66144754.85 -7727.34156.8632.74186067.63-709.9917.866.6817126.44-6914.0097.2218.45144754.85 -7854.76156.8646.34186067.63-7214.71158.9924.18152286.14-709.1313.305.517704.23 -8031.54170.9036.71158064.46-7327.83141.7531.40121415.11-7213.8813.306.797704.23 -8131.54112.8029.8283499.76-7634.8999.5729.47120236.98-7329.54109.6928.46202857.23 -8349.05112.8037.1983499.76-7723.40156.6130.2787842.81-7543.3797.5932.53127850.72 -8730.61112.8029.3883499.76-8761.43156.6149.0487842.81-7643.37128.1837.28254347.86 -9015.60112.8020.9783499.76-8043.45151.1740.52187232.64 -8242.82142.2539.02122014.76 CB-7 (New)CB-8 (New)CB-9 (New) PAGE 130 130 Table C-2. Fuller Warren Bridge Processed Soil Boring Data. EL. (ft)qu (tsf)qt (tsf)Recoveryquqt(tsf) Ei (psi) -40.515.3631.216710.9520725.93 -42.596.142.14677.1893362.29 -45.5143.309.079418.02108694.81 -46.559.247.219410.3420329.10 -47.552.2915.859414.4050938.20 -48.568.0918.339417.6787522.73 -50.5113.4118.626022.97143167.10 -55.512.561.37922.0716123.94 -56.522.010.91922.2433646.94 -57.522.922.58923.8528351.18 -58.511.891.77922.2913580.10 -60.57.081.05901.376509.45 -61.57.360.66901.108173.66 -62.58.590.25900.7310247.30 -63.57.571.05901.4111768.07 -65.53.020.40580.553832.10 EL. (ft)qu (tsf)qt (tsf)Recoveryquqt(tsf) Ei (psi) -37.5842.5725.232516.3948974.00 -42.5818.663.54684.0630083.74 -43.5856.421.76684.9875668.97 -47.5864.7718.369017.2481523.95 -48.5865.128.419011.7075899.59 -49.5837.248.51908.9038959.02 -50.58140.0610.119018.82152082.74 -51.588.291.91901.9915682.83 -5278.440.84904.0569402.72 -52.5815.685.49984.6424923.43 -53.5810.611.82982.2014642.92 -54.589.081.28981.7113980.61 -55.5818.881.90982.9921191.30 -56.5820.991.40982.7120221.36 -5716.811.36982.3921522.93 -57.5816.721.77802.7226059.97 -62.5811.081.14771.7811334.53 -63.589.441.44771.8412460.26 -64.589.591.24771.7213170.90 -65.5810.080.97771.5614308.84 -66.587.490.42770.8915724.97 EL. (ft)qu (tsf)qt (tsf)Recoveryquqt(tsf) Ei (psi) -41108.403.00729.01139525.37 -4256.4510.917212.4155345.75 -4692.701.69776.25102818.36 -4752.5512.897713.0164868.52 -4867.9013.337715.0481761.47 -4991.3914.087717.93136076.85 -5152.413.171006.4456192.28 -528.360.971001.4219141.58 -5312.281.941002.4418051.95 -547.221.341001.5513564.22 -5627.071.30852.9735561.05 -5719.842.93853.8124011.06 -5814.392.74853.1413791.05 -619.091.091001.5711308.89 -629.330.871001.429220.15 -639.891.371001.8411249.80 -649.801.321001.8011165.85 -658.100.401000.9010801.59 -665.990.81581.108732.30 -678.040.69581.1810850.17 CB-3 (New) 15 CB-1 (New) 30 CB-2 (New) 25 PAGE 131 131 APPENDIX D FREQUENCY DISTRIBUTIONS Figure D-1. Total Capacity Frequency Di stribution 5 feet Co rrelation Length Figure D-2. Total Capacity Frequency Distribution 12 feet Correlation Length 500 520 540 560 580 600 620 640 660 680 700 0 0.005 0.01 0.015 0.02 0.025 0.03 550 560 570 580 590 600 610 620 630 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 PAGE 132 132 0 200 400 600 0 0.005 0.01 0.015 0.02 0.025 qu 0 20 40 60 0 0.1 0.2 0.3 0.4 qt 0 50 100 0 0.01 0.02 0.03 0.04 RQD FullerWarren MEAN = 56.6495 8.4384 63.0673 STD = 78.6970 10.6514 25.6656 SKEW = 4.0955 1.8064 -0.1906 KURT = 24.6259 6.3517 1.9980 MNPDFEXP = 56.6321 8.3339 29.6672 STDPDFEXP = 56.5155 8.0886 25.1402 SKPDFEXP = 1.9848 1.7879 1.4168 KUPDFEXP = 8.7361 6.8332 3.5806 MNPDFLOG = 53.7941 6.7613 46.0365 STDPDFLOG = 66.7919 8.8546 20.5086 SKPDFLOG = 3.1883 2.5116 1.2676 KUPDFLOG = 16.7575 9.8725 3.1364 sqerrorNORM = 1.0e-005 0.1896 0.0147 0.0008 sqerrorEXP = 1.0e-006 0.4337 0.0909 0.0524 sqerrorLOGN = 1.0e-006 0.0867 0.1634 0.1023 Figure D-3. Fuller Warren Br idge Old and New Borings. PAGE 133 133 0 200 400 600 0 0.005 0.01 0.015 qu 0 20 40 60 0 0.02 0.04 0.06 0.08 qt 0 20 40 60 80 0 0.02 0.04 0.06 RQD FullerWarren MEAN = 84.0846 21.0250 31.8000 STD = 103.4132 12.8320 15.8931 SKEW = 3.1996 0.8896 0.3480 KURT = 14.4114 3.2306 2.1762 MNPDFEXP = 83.5399 16.3554 20.5342 STDPDFEXP = 82.2767 14.0040 17.1492 SKPDFEXP = 1.8272 1.2029 1.2207 KUPDFEXP = 7.2899 3.5943 3.4034 MNPDFLOG = 78.7380 19.3564 27.8348 STDPDFLOG = 79.1172 11.3702 13.9045 SKPDFLOG = 2.4872 1.2153 1.0484 KUPDFLOG = 11.0840 4.0844 3.3541 sqerrorNORM = sqerrorNORM = 1.0e-005 0.1173 0.0002 0.0009 sqerrorEXP = 1.0e-006 0.6094 0.0027 0.0002 sqerrorLOGN = 1.0e-006 0.3260 0.0093 0.0001 Figure D-4. Fuller Warren Bridge Old Borings. PAGE 134 134 0 50 100 150 0 0.01 0.02 0.03 0.04 qu 0 10 20 30 40 0 0.1 0.2 0.3 0.4 qt 0 50 100 0 0.01 0.02 0.03 RQD FullerWarren MEAN = 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 SKEW = 1.4909 1.9667 -0.2355 KURT = 4.3762 6.4417 1.9256 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP = 28.4992 4.7548 25.2514 SKPDFEXP = 1.4166 1.8230 1.5131 KUPDFEXP = 4.7127 6.9671 3.7210 MNPDFLOG = 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 SKPDFLOG = 1.8682 2.5286 1.2478 KUPDFLOG = 6.5454 10.3575 2.8813 MNPDFGAM = 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 SKPDFGAM = 1.3825 1.9486 1.0286 KUPDFGAM = 4.6979 7.1993 2.6588 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 Figure D-5. Fuller Warren Bridge New Borings. PAGE 135 135 0 100 200 300 0 0.005 0.01 0.015 quqt/2 0 20 40 60 80 0 0.01 0.02 0.03 0.04 0.05 qt (tsf) 0 20 40 60 0 0.01 0.02 0.03 0.04 0.05 qu(tsf) MEAN = 1.0e+004 0.0060 0.0006 6.2192 STD = 1.0e+004 0.0042 0.0006 4.8059 SKEW = 0.5721 0.8510 0.7210 KURT = 2.4376 2.2529 2.3001 MNPDFEXP = 1.0e+004 0.0042 0.0005 4.5972 STDPDFEXP = 1.0e+004 0.0035 0.0004 3.9074 SKPDFEXP = 1.1923 1.2702 1.1766 KUPDFEXP = 3.4116 3.8305 3.4654 MNPDFLOG = 1.0e+004 0.0043 0.0004 4.8072 STDPDFLOG = 1.0e+004 0.0032 0.0004 3.4648 SKPDFLOG = 1.3965 1.6554 1.3606 KUPDFLOG = 4.0138 5.1557 4.1142 MNPDFGAM = 1.0e+004 0.0049 0.0005 5.3568 STDPDFGAM = 1.0e+004 0.0033 0.0004 3.6765 SKPDFGAM = 0.9666 1.2516 0.9698 KUPDFGAM = 3.0719 3.7974 3.1902 sqerrorNORM = 1.0e-005 0.1110 0.0016 0.0279 sqerrorEXP = 1.0e-006 0.1716 0.0205 0.8014 sqerrorLOGN = 1.0e-006 0.0112 0.0037 0.7291 Figure D-6. 17th Street Bridge Old and New Borings. PAGE 136 136 0 50 100 150 0 0.01 0.02 0.03 0.04 qu (tsf) 0 10 20 30 40 0 0.1 0.2 0.3 0.4 qt (tsf) 0 0.5 1 1.5 2 x 105 0 2 4 6 x 10-5 Ei (psi) MEAN = 1.0e+004 0.0033 0.0005 4.0354 STD = 1.0e+004 0.0036 0.0007 4.1662 SKEW = 1.4909 1.9667 1.5006 KURT = 4.3762 6.4417 4.2151 MNPDFEXP = 1.0e+004 0.0031 0.0005 3.6832 STDPDFEXP = 1.0e+004 0.0028 0.0005 3.3610 SKPDFEXP = 1.4166 1.8230 1.3552 KUPDFEXP = 4.7127 6.9671 4.4338 MNPDFLOG = 1.0e+004 0.0028 0.0004 3.3867 STDPDFLOG = 1.0e+004 0.0026 0.0005 2.9839 SKPDFLOG = 1.8682 2.5286 1.7647 KUPDFLOG = 6.5454 10.3575 6.1003 MNPDFGAM = 1.0e+004 0.0031 0.0005 3.8192 STDPDFGAM = 1.0e+004 0.0028 0.0005 3.2012 SKPDFGAM = 1.3825 1.9486 1.2998 KUPDFGAM = 4.6979 7.1993 4.4234 sqerrorNORM = 1.0e-005 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 0.3299 0.0037 0.0041 Figure D-7. 17th Street Bridge New Borings. PAGE 137 137 0 50 100 150 0 0.01 0.02 0.03 0.04 0 10 20 30 40 0 0.1 0.2 0.3 0.4 0 20 40 60 80 0 0.02 0.04 0.06 0.08 0.1 FullerWarren MEAN = 40.6770 5.6533 59.0000 STD = 43.8454 7.7969 16.2741 SKEW = 1.1377 1.7369 -0.2460 KURT = 3.0363 5.4691 1.3395 MNPDFEXP = 35.4210 5.5212 22.4767 STDPDFEXP = 31.5161 5.2677 19.7376 SKPDFEXP = 1.2780 1.7062 1.5784 KUPDFEXP = 4.0350 6.2048 3.8275 MNPDFLOG = 29.4949 4.1192 46.3333 STDPDFLOG = 29.1923 5.4296 13.3009 SKPDFLOG = 1.7745 2.4799 1.3628 KUPDFLOG = 5.7006 9.4714 2.7984 MNPDFGAM = 35.1343 5.2196 47.4964 STDPDFGAM = 31.6539 5.8278 13.2912 SKPDFGAM = 1.2908 1.9324 1.2163 KUPDFGAM = 4.0534 6.6096 2.6321 sqerrorNORM = 1.0e-005 0.6799 0.0320 0.0000 sqerrorEXP = 1.0e-005 0.3160 0.0222 0.0074 sqerrorLOGN = 1.0e-005 0.2110 0.0085 0.0160 sqerrorGAM = 1.0e-005 0.3215 0.0209 0.0077 Figure D-8. Fuller Warren Bridge New Boring CB1. PAGE 138 138 0 50 100 150 0 0.02 0.04 0.06 0 10 20 30 0 0.1 0.2 0.3 0.4 0 50 100 0 0.01 0.02 0.03 0.04 0.05 FullerWarren EAN = 30.3093 5.0613 74.5000 STD = 32.0428 6.2900 23.5584 SKEW = 2.0375 1.8282 -0.7659 KURT = 7.0180 5.6542 2.4186 MNPDFEXP = 28.8431 4.9667 28.9120 STDPDFEXP = 27.0370 4.7615 25.2984 SKPDFEXP = 1.5024 1.7542 1.5628 KUPDFEXP = 5.1612 6.4929 3.8012 MNPDFLOG = 27.2953 4.3067 51.6272 STDPDFLOG = 23.2056 4.7122 19.8380 SKPDFLOG = 1.9139 2.3214 1.4651 KUPDFLOG = 7.2505 9.2016 2.9963 MNPDFGAM = 29.8271 4.9493 54.7557 STDPDFGAM = 24.1703 4.8362 19.5059 SKPDFGAM = 1.4061 1.7783 1.2851 KUPDFGAM = 5.1809 6.5286 2.7296 sqerrorNORM = 1.0e-004 0.2195 0.0025 0.0032 sqerrorEXP = 1.0e-004 0.1553 0.0008 0.0003 sqerrorLOGN = 1.0e-005 0.9675 0.0110 0.0006 sqerrorGAM = 1.0e-004 0.1333 0.0025 0.0006 Figure D-9. Fuller Warren New Boring CB2. PAGE 139 139 0 50 100 150 0 0.02 0.04 0.06 0 10 20 30 0 0.1 0.2 0.3 0.4 0 50 100 0 0.01 0.02 0.03 0.04 0.05 FullerWarren MEAN = 30.9569 4.2200 77.3793 STD = 33.1697 6.0748 20.3354 SKEW = 1.1429 2.3112 -0.2341 KURT = 2.8870 7.9730 1.4244 MNPDFEXP = 26.9212 4.1906 28.6658 STDPDFEXP = 23.9281 4.0814 25.3287 SKPDFEXP = 1.2791 1.9112 1.5975 KUPDFEXP = 4.0327 7.5835 3.8601 MNPDFLOG = 23.4179 3.5494 60.1970 STDPDFLOG = 21.6499 4.0810 16.9897 SKPDFLOG = 1.7166 2.6733 1.4052 KUPDFLOG = 5.5971 11.9322 2.7615 MNPDFGAM = 27.2903 4.1714 61.5707 STDPDFGAM = 23.7335 4.2676 16.9482 SKPDFGAM = 1.2574 1.9894 1.2835 KUPDFGAM = 4.0039 7.7753 2.6131 sqerrorNORM = 1.0e-004 0.2302 0.0009 0.0131 sqerrorEXP = 1.0e-004 0.1278 0.0024 0.0073 sqerrorLOGN = 1.0e-005 0.7795 0.0204 0.0453 sqerrorGAM = 1.0e-004 0.1260 0.0028 0.0077 Figure D-10. Fuller Warren New Boring CB3 PAGE 140 140 APPENDIX E SGS RANDOM FIELD TABLES Table E-1. 17th Street Bridge SGS (1feet). A PSF Mean42562.48642 Standard Error219.7863813 Median39538.838 Mode38500 Standard Deviation21150.94231 Sample Variance447362360.5 Kurtosis-0.507237829 Skewness0.48869983 Range99365.73316 Minimum598.72084 Maximum99964.454 Sum394171186.8 Count9261 B PSF Mean42658.43886 Standard Error221.5141441 Median39514.378 Mode41800 Standard Deviation21317.21199 Sample Variance454423526.9 Kurtosis-0.568971001 Skewness0.480259697 Range98794.59432 Minimum1077.72768 Maximum99872.322 Sum395059802.3 Count9261 C PSF Mean42503.73487 Standard Error223.6157448 Median39001.786 Mode49700 Standard Deviation21519.45762 Sample Variance463087056.4 Kurtosis-0.581050641 Skewness0.497640383 Range99866.79713 Minimum117.150872 Maximum99983.948 Sum393627088.6 Count9261 D PSF Mean42557.4383 Standard Error220.0553434 Median39532.284 Mode11399.9996 Standard Deviation21176.82563 Sample Variance448457943.8 Kurtosis-0.580991141 Skewness0.47042905 Range98897.99504 Minimum862.72496 Maximum99760.72 Sum394124436.1 Count9261 PAGE 141 141 Table E-1. Continued. E PSF Mean42518.58199 Standard Error219.4444741 Median39411.644 Mode48900.002 Standard Deviation21118.03918 Sample Variance445971578.7 Kurtosis-0.526496513 Skewness0.488121523 Range99546.9086 Minimum430.7594 Maximum99977.668 Sum393764587.8 Count9261 F PSF Mean43109.75042 Standard Error223.6009188 Median39677.666 Mode38500 Standard Deviation21518.03086 Sample Variance463025652 Kurtosis-0.575002397 Skewness0.468898326 Range99622.97688 Minimum375.72712 Maximum99998.704 Sum399239398.7 Count9261 G PSF Mean42377.27821 Standard Error219.7337363 Median39054.524 Mode15199.9998 Standard Deviation21145.87606 Sample Variance447148074.4 Kurtosis-0.568985276 Skewness0.486387424 Range99352.60342 Minimum622.84458 Maximum99975.448 Sum392455973.5 Count9261 H PSF Mean42587.84604 Standard Error220.7370971 Median39504.638 Mode15199.9998 Standard Deviation21242.43358 Sample Variance451240984.2 Kurtosis-0.544309321 Skewness0.478158775 Range99739.27387 Minimum191.482126 Maximum99930.756 Sum394406042.2 Count9261 I PSF Mean42446.51502 Standard Error221.3665243 Median39289.578 Mode38500 Standard Deviation21303.00593 Sample Variance453818061.7 Kurtosis-0.564645925 Skewness0.495661419 Range99259.75486 Minimum631.13714 Maximum99890.892 Sum393097175.6 Count9261 PAGE 142 142 Table E-2. 17th Street Bridge SGS (5feet). A PSF Mean45806.79179 Standard Error222.6907591 Median42021.988 Mode49700 Standard Deviation21430.44246 Sample Variance459263864 Kurtosis-0.689609294 Skewness0.381837804 Range99308.9843 Minimum594.1977 Maximum99903.182 Sum424216698.7 Count9261 B PSF Mean41246.08288 Standard Error217.5866605 Median38500 Mode41800 Standard Deviation20939.25418 Sample Variance438452365.5 Kurtosis-0.448952677 Skewness0.545106492 Range98730.14074 Minimum1258.95726 Maximum99989.098 Sum381979973.5 Count9261 C PSF Mean45632.38736 Standard Error224.5743392 Median42031.22 Mode30800 Standard Deviation21611.70708 Sample Variance467065883.1 Kurtosis-0.69715789 Skewness0.35706524 Range97915.1958 Minimum2035.8922 Maximum99951.088 Sum422601539.3 Count9261 D PSF Mean42598.52685 Standard Error217.1910467 Median39472.638 Mode15199.9998 Standard Deviation20901.18264 Sample Variance436859435.9 Kurtosis-0.532426787 Skewness0.498080027 Range99879.66534 Minimum109.310656 Maximum99988.976 Sum394504957.1 Count9261 PAGE 143 143 Table E-2. Continued. E PSF Mean44489.19162 Standard Error222.650213 Median41394.268 Mode48900.002 Standard Deviation21426.54054 Sample Variance459096639.7 Kurtosis-0.649152833 Skewness0.41713792 Range99747.25472 Minimum223.29528 Maximum99970.55 Sum412014403.6 Count9261 G PSF Mean41666.77162 Standard Error216.0629871 Median38692.49 Mode49700 Standard Deviation20792.62486 Sample Variance432333248.4 Kurtosis-0.514976359 Skewness0.501212334 Range99806.4971 Minimum67.244902 Maximum99873.742 Sum385875971.9 Count9261 H PSF Mean42756.64801 Standard Error224.632869 Median39366.7 Mode49700 Standard Deviation21617.33964 Sample Variance467309373.1 Kurtosis-0.551513094 Skewness0.508615793 Range99542.12376 Minimum371.65624 Maximum99913.78 Sum395969317.2 I PSF Mean43683.07808 Standard Error222.3762153 Median39940.616 Mode48900.002 Standard Deviation21400.17263 Sample Variance457967388.5 Kurtosis-0.63673678 Skewness0.421260262 Range99744.20568 Minimum158.764318 Maximum99902.97 Sum404548986.1 Count9261 J PSF Mean41831.42157 Standard Error216.718847 Median38761.494 Mode48900.002 Standard Deviation20855.74094 Sample Variance434961930 Kurtosis-0.50047995 Skewness0.533206704 Range99290.7898 Minimum697.6282 Maximum99988.418 Sum387400795.2 Count9261 PAGE 144 144 Table E-3. 17th Street Bridge SGS (12 feet). A BC PSFPSFPSF Mean41584.65934Mean52111.7188Mean39762.78304 Standard Error205.8633641Standard Error233.0037394Standard Error212.0978036 Median38963.996Median49829.998Median36918.004 Mode49700Mode48900.002Mode15199.9998 Standard Deviation19811.07343Standard Deviation22422.90273Standard Deviation20411.03904 Sample Variance392478630.3Sample Variance502786566.9Sample Variance416610514.6 Kurtosis-0.457306535Kurtosis-0.9338627Kurtosis-0.264671923 Skewness0.493885727Skewness0.102754863Skewness0.646850373 Range99151.57972Range99192.8432Range99913.70662 Minimum611.08428Minimum732.4568Minimum62.269382 Maximum99762.664Maximum99925.3Maximum99975.976 Sum385115530.2Sum482606627.8Sum368243133.8 Count9261Count9261Count9261 DEF PSFPSFPSF Mean39355.34143Mean46573.85942Mean40064.89254 Standard Error215.9959574Standard Error232.6746559Standard Error212.0271793 Median36115.68Median42937.85Median37300 Mode11399.9996Mode49700Mode38500 Standard Deviation20786.17431Standard Deviation22391.23368Standard Deviation20404.24257 Sample Variance432065042.7Sample Variance501367345.7Sample Variance416333114.8 Kurtosis-0.386909561Kurtosis-0.802132918Kurtosis-0.443063463 Skewness0.640670637Skewness0.28637968Skewness0.530885072 Range99816.1107Range99937.26621Range99619.43411 Minimum87.5993Minimum14.7757856Minimum97.851888 Maximum99903.71Maximum99952.042Maximum99717.286 Sum364469817Sum431320512.1Sum371040969.8 Count9261Count9261Count9261 GHJ PSFPSFPSF Mean37173.00379Mean47907.34312Mean41663.39521 Standard Error208.7527541Standard Error228.4042742Standard Error220.5532068 Median34311.524Median43876.092Median38535.546 Mode11399.9996Mode49700Mode11399.9996 Standard Deviation20089.13124Standard Deviation21980.27739Standard Deviation21224.73707 Sample Variance403573194.1Sample Variance483132594.2Sample Variance450489463.6 Kurtosis-0.17153857Kurtosis-0.80052981Kurtosis-0.530291652 Skewness0.714709268Skewness0.300035536Skewness0.522353319 Range99077.68402Range98726.572Range99212.07664 Minimum339.23998Minimum1247.8Minimum480.66536 Maximum99416.924Maximum99974.372Maximum99692.742 Sum344259188.1Sum443669904.7Sum385844703.1 Count9261Count9261Count9261 PAGE 145 145 Table E-3. Continued. A A BBZ PSFPSFPSF Mean42900.29827Mean42408.97909Mean46519.50275 Standard Error219.2799472Standard Error218.869694Standard Error223.6012514 Median39601.91Median39127.61Median42316.284 Mode15199.9998Mode48900.002Mode49700 Standard Deviation21102.20608Standard Deviation21062.72574Standard Deviation21518.06286 Sample Variance445303101.5Sample Variance443638415.5Sample Variance463027029.4 Kurtosis-0.643142448Kurtosis-0.538154163Kurtosis-0.695072802 Skewness0.430785494Skewness0.49509214Skewness0.381873107 Range99267.1778Range99698.04192Range99382.08064 Minimum550.6242Minimum212.13808Minimum559.82136 Maximum99817.802Maximum99910.18Maximum99941.902 Sum397299662.3Sum392749555.3Sum430817115 Count9261Count9261Count9261 IKL PSFPSFPSF Mean43704.58521Mean39506.03724Mean44470.57504 Standard Error214.6861676Standard Error199.8427351Standard Error224.9408061 Median39961.776Median37021.622Median41004.174 Mode41800Mode38500Mode49700 Standard Deviation20660.12788Standard Deviation19231.68367Standard Deviation21646.97368 Sample Variance426840884.2Sample Variance369857657Sample Variance468591469.6 Kurtosis-0.585301651Kurtosis-0.35014142Kurtosis-0.659852085 Skewness0.445114079Skewness0.56895775Skewness0.436021337 Range98805.25304Range99826.24379Range99576.18214 Minimum1054.96096Minimum143.53621Minimum260.83786 Maximum99860.214Maximum99969.78Maximum99837.02 Sum404748163.6Sum365865410.8Sum411841995.5 Count9261Count9261Count9261 LLMN PSFPSFPSF Mean52001.27262Mean47226.12953Mean46392.57197 Standard Error231.0221144Standard Error228.5146525Standard Error235.8458747 Median49700Median43423.728Median42452.282 Mode49700Mode41800Mode48900.002 Standard Deviation22232.20286Standard Deviation21990.89954Standard Deviation22696.41304 Sample Variance494270843.9Sample Variance483599662.6Sample Variance515127164.7 Kurtosis-0.875814507Kurtosis-0.743959545Kurtosis-0.793047923 Skewness0.140331985Skewness0.347746576Skewness0.343204355 Range99156.84372Range96633.395Range99050.74032 Minimum837.24428Minimum3327.115Minimum935.39768 Maximum99994.088Maximum99960.51Maximum99986.138 Sum481583785.7Sum437361185.5Sum429641609 Count9261Count9261Count9261 PAGE 146 146 Table E-3. Continued. OP PSFPSFPSF Mean51470.31861Mean41320.25623Mean40438.14456 Standard Error236.2322652Standard Error206.1301759Standard Error215.9221412 Median49608.578Median38500Median37335.826 Mode49700Mode32200Mode11399.9996 Standard Deviation22733.59697Standard Deviation19836.74982Standard Deviation20779.07069 Sample Variance516816431.2Sample Variance393496643.2Sample Variance431769778.5 Kurtosis-0.913495054Kurtosis-0.37199239Kurtosis-0.492837597 Skewness0.171190865Skewness0.55984348Skewness0.533478348 Range99976.04256Range99177.92682Range99853.50113 Minimum18.9974382Minimum734.86918Minimum94.534874 Maximum99995.04Maximum99912.796Maximum99948.036 Sum476666620.7Sum382666892.9Sum374497656.8 Count9261Count9261Count9261 QRS PSFPSFPSF Mean47042.63871Mean44797.74259Mean45763.25705 Standard Error223.6413497Standard Error231.159873Standard Error222.6925403 Median43499.474Median41342.338Median42281.89 Mode48900.002Mode38500Mode48900.002 Standard Deviation21521.92168Standard Deviation22245.45993Standard Deviation21430.61387 Sample Variance463193112.9Sample Variance494860487.6Sample Variance459271211 Kurtosis-0.740545222Kurtosis-0.671942245Kurtosis-0.75114585 Skewness0.319788177Skewness0.424328387Skewness0.319107618 Range97029.068Range99524.53918Range99124.16976 Minimum2876.152Minimum393.21682Minimum841.91824 Maximum99905.22Maximum99917.756Maximum99966.088 Sum435661877.1Sum414871894.1Sum423813523.6 Count9261Count9261Count9261 TUV PSFPSFPSF Mean44061.74486Mean48102.4208Mean37070.10498 Standard Error218.5590664Standard Error221.9101921Standard Error198.1461848 Median41032.302Median44215.9Median34927.44 Mode48900.002Mode38500Mode15199.9998 Standard Deviation21032.83278Standard Deviation21355.32531Standard Deviation19068.4177 Sample Variance442380054.7Sample Variance456049919.2Sample Variance363604553.7 Kurtosis-0.626614687Kurtosis-0.74765644Kurtosis-0.200228081 Skewness0.424741976Skewness0.29905297Skewness0.659719139 Range99303.45Range98855.61356Range99517.49996 Minimum617.266Minimum1139.09244Minimum375.12404 Maximum99920.716Maximum99994.706Maximum99892.624 Sum408055819.2Sum445476519Sum343306242.2 Count9261Count9261Count9261 PAGE 147 147 Table E-3. Continued. WXY PSFPSFPSF Mean44963.57643Mean42967.49829Mean47554.61147 Standard Error222.873721Standard Error222.1398912Standard Error248.1298149 Median41800Median39449.822Median43413.186 Mode49700Mode49700Mode11399.9996 Standard Deviation21448.04963Standard Deviation21377.4302Standard Deviation23878.54684 Sample Variance460018833Sample Variance456994521.8Sample Variance570184999.2 Kurtosis-0.664903412Kurtosis-0.588149668Kurtosis-0.886393787 Skewness0.400653996Skewness0.47779941Skewness0.30788879 Range98933.37236Range98727.84014Range99288.7588 Minimum1062.49964Minimum1192.01386Minimum707.5792 Maximum99995.872Maximum99919.854Maximum99996.338 Sum416407681.4Sum397922001.7Sum440403256.8 Count9261Count9261Count9261 PAGE 148 148 Table E-4. 17th Street Bridge SGS (20feet). A B PSFPSF Mean45407.11477Mean44728.03485 Standard Error235.5262499Standard Error231.9539298 Median41856.568Median41280.174 Mode48900.002Mode48900.002 Standard Deviation22665.65424Standard Deviation22321.87526 Sample Variance513731882.1Sample Variance498266115 Kurtosis-0.732519328Kurtosis-0.718776057 Skewness0.383255739Skewness0.39948428 Range99920.77422Range99567.77814 Minimum60.007784Minimum414.47586 Maximum99980.782Maximum99982.254 Sum420515289.9Sum414226330.7 Count9261Count9261 CD PSFPSF Mean42210.90062Mean43657.61793 Standard Error222.0514785Standard Error225.6671411 Median39094.814Median39968.552 Mode49700Mode49700 Standard Deviation21368.92187Standard Deviation21716.87187 Sample Variance456630822.1Sample Variance471622524 Kurtosis-0.546710456Kurtosis-0.656686698 Skewness0.494754071Skewness0.442924124 Range99843.95339Range99635.08658 Minimum84.734612Minimum222.54142 Maximum99928.688Maximum99857.628 Sum390915150.6Sum404313199.7 Count9261Count9261 PAGE 149 149 Table E-4. Continued. FG PSFPSF Mean41916.56315Mean42862.22371 Standard Error215.7209468Standard Error214.3914192 Median39004.65Median39756.89 Mode41800Mode38500 Standard Deviation20759.70892Standard Deviation20631.76305 Sample Variance430965514.3Sample Variance425669646.5 Kurtosis-0.571675821Kurtosis-0.597299848 Skewness0.480379812Skewness0.420685131 Range99964.77187Range99763.42888 Minimum10.554133Minimum18.545119 Maximum99975.326Maximum99781.974 Sum388189291.3Sum396947053.7 Count9261Count9261 HI PSFPSF Mean45380.61602Mean41610.78171 Standard Error235.732166Standard Error222.7657464 Median41800Median38575.492 Mode38500Mode32200 Standard Deviation22685.47038Standard Deviation21437.6588 Sample Variance514630566.5Sample Variance459573214.6 Kurtosis-0.716214975Kurtosis-0.524411823 Skewness0.415227363Skewness0.521869386 Range99922.89606Range99693.49401 Minimum65.887942Minimum158.311992 Maximum99988.784Maximum99851.806 Sum420269885Sum385357449.4 Count9261Count9261 PAGE 150 150 APPENDIX F FLAC3D PROGRAMMING MODELS Table F-1. FLAC Results. 1 (feet) Cap .15(ton) Bias A 200 1.175 0.007300506 B 240 0.979167 0.012186026 C 235 1 0.008020456 D 220 1.068182 0.000456898 E 210 1.119048 0.000869697 F 200 1.175 0.007300506 G 285 0.824561 0.070222666 H 250 0.94 0.022367296 I 225 1.044444 0.002035143 J 265 0.886792 0.041113462 K 235 1 0.008020456 L 230 1.021739 0.004599263 LL 185 1.27027 0.032657286 M 235 1 0.008020456 N 190 1.236842 0.021692902 230 1.021739 0.004599263 O 190 1.236842 0.021692902 P 190 1.236842 0.021692902 R 200 1.175 0.007300506 S 235 1 0.008020456 T 215 1.093023 1.20149E-05 U 235 1 0.008020456 V 240 0.979167 0.012186026 W 200 1.175 0.007300506 X 187.5 1.253333 0.026822687 Y 195 1.205128 0.013356703 Z 200 1.175 0.007300506 AA 190 1.236842 0.021692902 BB 220 1.068182 0.000456898 Determinis 235 Mean 1.089557 0.407317752 Standar 0.120611204 COV 0.110698 PAGE 151 151 Table F-1. Continued. 5 (feet) Cap .15(ton) Bias A 235 1 0.01099541 B 185 1.27027 0.027360888 C 220 1.068182 0.001345216 D 215 1.093023 0.000140085 E 215 1.093023 0.000140085 F 190 1.236842 0.01741954 G 230 1.021739 0.006908913 H 195 1.205128 0.010053913 I 285 0.824561 0.078566743 J 225 1.044444 0.003649919 K 175 1.342857 0.056643116 L 240 0.979167 0.015798563 LL 240 0.979167 0.015798563 M 295 0.79661 0.095017342 N 215 1.093023 0.000140085 200 1.175 0.00491976 O 190 1.236842 0.01741954 P 190 1.236842 0.01741954 Q 265 0.886792 0.047553019 R 190 1.236842 0.01741954 S 250 0.94 0.02717849 T 230 1.021739 0.006908913 U 190 1.236842 0.01741954 V 235 1 0.01099541 W 240 0.979167 0.015798563 X 225 1.044444 0.003649919 Y 175 1.342857 0.056643116 Z 200 1.175 0.00491976 AA 245 0.959184 0.021221301 BB 200 1.175 0.00491976 CC 190 1.236842 0.01741954 DD 150 1.566667 0.213266321 EE 280 0.839286 0.07052917 FF 220 1.068182 0.001345216 GG 260 0.903846 0.040406164 HH 180 1.305556 0.040279107 II 180 1.305556 0.040279107 JJ 230 1.021739 0.006908913 KK 300 0.783333 0.103378754 MM 160 1.46875 0.13241666 Determinis 225 Mean 1.104859 1.280593501 Standar 0.181206321 COV 0.164009 PAGE 152 152 Table F-1. Continued 12 (feet) Cap .15(ton) Bias A 260 0.903846 0.01190932 B 250 0.94 0.0154095 C 240 0.979167 0.00721962 D 270 0.87037 0.03754473 E 250 0.94 0.0154095 F 215 1.093023 0.00083453 G 200 1.175 0.01229105 H 250 0.94 0.0154095 I 280 0.839286 0.0505572 J 200 1.175 0.01229105 K 235 1 0.0041133 L 265 0.886792 0.03145038 LL 310 0.758065 0.09367914 M 260 0.903846 0.02569251 N 190 1.236842 0.02982774 200 1.175 0.01229105 O 285 0.824561 0.05739551 P 205 1.146341 0.0067579 Q 225 1.044444 0.00038772 R 210 1.119048 0.0030154 S 280 0.839286 0.0505572 T 240 0.979167 0.00721962 U 285 0.824561 0.05739551 V 200 1.175 0.01229105 W 200 1.175 0.01229105 X 285 0.824561 0.05739551 Y 330 0.712121 0.12391371 Z 210 1.119048 0.0030154 AA 225 1.044444 0.00038772 BB 195 1.205128 0.01987908 CC 250 0.94 0.0154095 DD 200 1.175 0.01229105 EE 230 1.021739 0.00179741 FF 225 1.044444 0.00038772 GG 260 0.903846 0.02569251 HH 270 0.87037 0.03754473 II 185 1.27027 0.04249175 JJ 190 1.236842 0.02982774 KK 300 0.783333 0.07884958 MM 165 1.424242 0.12967736 Determinis 235 Mean 1.012976 1.16180183 Standar 0.17259719 COV 0.170386 PAGE 153 153 Table F-2 1 (feet) End Bearing .15(ton) Mean 218.362069 Standard Error 4.689030312 Median 220 Mode 200 Standard Deviation 25.25120102 Sample Variance 637.6231527 Kurtosis 0.124369761 Skewness 0.651972746 Range 100 Minimum 185 Maximum 285 Sum 6332.5 Count 295 (feet) End Bearing .15(ton) Mean 218.375 Standard Error 5.727205375 Median 217.5 Mode 190 Standard Deviation 36.22202723 Sample Variance 1312.035256 Kurtosis 0.226714365 Skewness 0.449655743 Range 150 Minimum 150 Maximum 300 Sum 8735 Count 4012 (feet) End Bearing .15(ton) Mean 238.125 Standard Error 6.175031 Median 237.5 Mode 200 Standard Deviation 39.05433 Sample Variance 1525.24 Kurtosis -0.63762 Skewness 0.310262 Range 165 Minimum 165 Maximum 330 Sum 9525 Count 40 PAGE 154 154 TYPICAL FLAC3D EXAMPLE ;----------------------------------------------; Vertically loaded pile ;----------------------------------------------model mohr prop bulk 8.86E+06 shear 6.10E+06 fric 15 coh 71980.51 range group 1 prop bulk 8.70E+06 shear 5.99E+06 fric 15 coh 70372.78 range group 2 prop bulk 8.00E+06 shear 5.51E+06 fric 15 coh 63234.3 range group 3 prop bulk 8.39E+06 shear 5.78E+06 fric 20 coh 67204.36 range group 7998 prop bulk 7.94E+06 shear 5.47E+06 fric 20 coh 62625.79 range group 7999 prop bulk 7.48E+06 shear 5.15E+06 fric 20 coh 57934.44 range group 8000 ini dens 4.4 range group 1 ini dens 4.4 range group 2 ini dens 4.4 range group 3 ini dens 3.1 range group 7998 ini dens 3.1 range group 7999 ini dens 3.1 range group 8000 ; gen zone brick p0 (13.5,13.5,20) p1 (16.5, 13.5,20) p2 (13.5,16.5,20) p3 (13.5,13.5,40)& p4 (16.5,16.5,20) p5 (13.5,16.5,40) p6 (16.5,13.5,40) p7 (16.5,16.5,40)& size 2 2 20 gen zone brick p0 (13.5,13.5,40) p1 (16.5,13. 5,40) p2 (13.5,16.5,40) p3 (13.5,13.5,40.1)& p4 (16.5,16.5,40) p5 (13.5,16.5,40.1) p6 (16.5,13.5,40.1) p7 (16.5,16.5,40.1)& size 2 2 1 group pile range x=13.5 16.5 y=13.5 16.5 z=20 40.1 save pile_geom.sav ; model elas range group pile prop bulk 6.50E+06 shear 3.00E+06 range group pile interface 1 prop kn 1.8e7 ks 1.8e7 fric 5 coh 30000 ; ini dens 3.1 range group pile model null range z 39.9 40.15 ; fix z range z -.1 .1 fix x range x -.1 .1 fix x range x 29.9 30.1 fix y range y -.1 .1 fix y range y 29.9 30.1 PAGE 155 155 set grav 0 0 -32.18 ini szz 0. grad 0 0 100 range z 0 40 ini sxx 0. grad 0 0 50 range z 0 40 ini syy 0. grad 0 0 50 range z 0 40 ; hist unbal ; solve rat 1.0e-5 save pile0.sav ; model elas range group pile prop bulk 3.10E+08 shear 2.54E+08 range group pile ini dens 4.9 range group pile call find_add.fis solve rat 1.e-5 save pile1.sav ; ini state 0 ini xdis 0 ydis 0 zdis 0 ; ; monitor vertical loading at pile cap def zs_top ad = top_head zftot = 0.0 loop while ad # null gp_pnt = mem(ad+1) zf = gp_zfunbal(gp_pnt) zftot = zftot + zf ad = mem(ad) endloop zs_top = zftot / 9 end fix z range z 40.05 40.15 group pile ; def ramp while_stepping if step < ncut then udapp = float(st ep) udmax / float(ncut) else udapp = udmax endif ad = top_head loop while ad # null gp_pnt = mem(ad+1) gp_zvel(gp_pnt) = udapp ad = mem(ad) PAGE 156 156 endloop end ; hist gp zdis 15,15,40 hist gp zvel 15,15,40 hist zs_top hist zone szz 15,15,39.9 hist zone szz 15,15,20 ; set mech damp comb set udmax = -1e-4 ncut 15000 step 112500 plot create history plot add hist 4 vs -2 save pile2.sav PAGE 157 157 APPENDIX G UNIT COST DATA PAGE 158 158 PAGE 159 159 LIST OF REFERENCES Allen, T., Nowak, A.S. and Bathurst, R.J. (2005). Calibration to Determine Load and Resistance Factors for Geotechnical and Stru ctural Design. Tran sportation Research Board. Ang, H-S. and Tang, W.H. (1975). Probability Concepts in Engineering Planning and Design. Vol. I Basic Principles, 19-45. Fenton, G.A. (1999). Estimation for Stochastic Soil Models. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 125 (6), 470-485. Fenton, G.A. (2002). Probabilistic Foundation Settlement on a Spatially Random Soil. ASCE Journal of Geotechnical and Geoenvironm ental Engineering, 128 (5), 381-390. Fenton, G.A. and Griffiths, D.V. (2003). Bearing Capacity of Spatially Random cSoils. Canadian Geotechnical J ournal, 40(1), 54-65. (Jing 2003). Kulhawy, F.H., Spry M.J. and Grigoriu, M.D. (1988). Reliability-Bas ed Foundation Design for Transmission Line Structures. EPRI Vol. 1. Geotechnical Site Characterization Strategy. Kulhawy, F.H., Filippas O.B. and Grigoriu, M. D. (1988). Reliability -Based Foundation Design for Transmission Line Structures. EPRI Vol. 3. Uncertainties in Soil Property Measurement. Learning Resource Centre at Learning Deve lopment-University of Wollongong (2001). Self Directed Learning Resource. Mark, C., McWilliams, L., Pappas, D. and Rusnak, J. (2004). Spatial Trends in Rock StrengthCan They be Determined from Coreholes? Na tional Institute for Occupational Safety and Health. McVey, M. and Ellis, E. (2003). Static and Dyna mic Field Testing of Drilled Shafts. Florida Department of Transportation No. 99052794. National Cooperative Highway Research Pr ogram (NCHRP) (2004). Load and Resistance Factor Design (LRFD) for Deep Foundations. Report 507. National Highway Institute (1998). Load and Re sistance Factor Design (LRFD) for Highway Bridge Substructures. NHI Course No. 13068, Volume 2. Nowak, A.S. and Collins, K.R. (2000). Reliabili ty of Structures. Chapter 8 Design Codes. Nowak, M. and Verly, G. (2004). The Pr actice of Sequential Gaussian Simulation. Geostatistics Banff, 1, 387-398. PAGE 160 160 Phoon, K. K., Kulhawy, F. H. and Grigoriu, M. D. (2003). Development of a Reliability-Based Design Framework for Transmission Line Stru cture Foundations. Journal of Geotechnical and Geoenvironmental Engineering, 798-806. Phoon, K.K. and Kulhawy, F.H. (2002). Obs ervations on Geotechnical Reliability-Based Design Development in North America. Foundation Design Codes and Soil Investigation in View of Internati onal Harmonization and Performance, 31-48. Schaeffer, R. and Mcclave, J. (1995). Probability and Statistics for Engineers. Fourth Edition, 76-83 and 122-164. PAGE 161 161 BIOGRAPHICAL SKETCH Johanna Otero was born in Monter ia, Colombia, to Maria Isabel Sanchez and Rafael Otero. She graduated from Colegio la Sagrada Familia High School in Monteria Colombia in December 1992. She received his Bachelor of Science in ci vil engineering in the fall of 1998 from the University EAFIT, Medellin Colombia.. After graduation as an Engi neer, she worked on the transportation area on Pereira Colombia for almost four years. Johanna continued her education by entering graduate school to pursue a Master of Engineering in the Construction Management Group of the Civil and Coastal Engineering Department at the University of Florida in th e fall 2003. She received his Master of Engineering in the fall of 2004. Currently, she is pursuing a Doctorate of Philosophy at the same institution. |