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- Permanent Link:
- https://ufdc.ufl.edu/UF00100658/00001
## Material Information- Title:
- Load resistance factor design (LRFD) for driven piles based on dynamic methods with assessment of skin and tip resistance from PDA signals
- Creator:
- Perez Perez, Ariel, 1971- (
*Dissertant*) McVay, Michael C. (*Thesis advisor*) Townsend, Frank C. (*Reviewer*) Fagundo, Fernando E. (*Reviewer*) - Place of Publication:
- Florida
- Publisher:
- State University System of Florida
- Publication Date:
- 1998
- Copyright Date:
- 1998
- Language:
- English
## Subjects- Subjects / Keywords:
- Curved bridges ( jstor )
Damping ( jstor ) Databases ( jstor ) Design evaluation ( jstor ) Hammers ( jstor ) R factors ( jstor ) Safety factors ( jstor ) Skin ( jstor ) Standard deviation ( jstor ) Velocity ( jstor ) Civil Engineering thesis, M.E ( lcsh ) Dissertations, Academic -- Civil Engineering -- UF ( lcsh ) City of Tallahassee ( local ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) government publication (state, provincial, terriorial, dependent) ( marcgt ) non-fiction ( marcgt )
## Notes- Abstract:
- Eight dynamic methods to estimate the static capacity of driven piles were evaluated based on a Florida database and Load Resistance Factor Design (LRFD). The dynamic methods investigated were four stress wave approaches (CAPWAP, PDA, Paikowsky Energy, and Sakai Energy) and four driving formulas (ENR, modified ENR, FDOT, and Gates). In the case of the older driving formulas, the database was broken into both small (i.e. Davisson capacity less than 1779 kN) and large (Davisson capacity larger than 1779 kN) capacity piles. It was demonstrated that the modern methods based on wave mechanics, such as CAPWAP, PDA, and Paikowsky's energy method, are more accurate than the old driving formulas. The utilizable measured Davisson capacity, defined as phi/lambdasubscriptR (ratio of resistance / mean capacity), shows that the new dynamic methods are more cost effective to meet a reliability index in comparison with the old methods based on momentum conservation. In addition, the Gates formula, when used separately for Davisson capacity larger than 1779 kN or less than 1779 kN, may have comparable accuracy with the modern methods. A suggested empirical method is presented to calculate the total, skin, and tip static resistance of driven piles. This method has proved to be equally or more accurate than the most widely used method (i.e. PDA, and CAPWAP). Additional features of the suggested method include determining the total, skin, and tip static capacities as the piles are being driven, saving construction time, therefore, saving construction costs. ( , )
- Subject:
- KEYW0RDS: pile foundations, driven piles
- Thesis:
- Thesis (M.E.)--University of Florida, 1998.
- Bibliography:
- Includes bibliographical references (p. 185-186).
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- System requirements: World Wide Web browser and PDF reader.
- System Details:
- Mode of access: World Wide Web.
- General Note:
- Title from first page of PDF file.
- General Note:
- Document formatted into pages; contains x, 188 p.; also contains graphics.
- General Note:
- Vita.
- Statement of Responsibility:
- by Ariel Perez Perez.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 45839443 ( OCLC )
002424962 ( AlephBibNum ) AMD0042 ( NOTIS )
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LOAD RESISTANCE FACTOR DESIGN (LRFD) FOR DRIVEN PILES BASED ON DYNAMIC METHODS WITH ASSESSMENT OF SKIN AND TIP RESISTANCE FROM PDA SIGNALS By ARIEL PEREZ PEREZ A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 1998 Copyright 1998 by Ariel Perez To my parents ACKNOWLEDGMENTS Above all, I would like to thank all the geotechnical engineering staff. With their knowledge, teaching skills, experience, and professionalism, they have provided me with an excellent level of education. I wish to express my sincere appreciation and gratitude to the chairman of my supervisory committee, Dr. Michael C. McVay, for providing me with the opportunity to conduct this research and for his generous assistance and guidance throughout the course of this study. Grateful acknowledgment is also made to Dr. Frank C. Townsend for serving as committee member and sharing with me his extensive experience in the geotechnical field. Special thanks are given to Dr. Fernando E. Fagundo. Besides being a committee member, Dr. Fagundo has offered me his support and friendship from our first meeting before arriving to Gainesville. Lastly, I would like to acknowledge Dr. Limin Zhang, for his continuing guidance and encouragement in the preparation of this manuscript. Without his work, this project would not have been accomplished. I wish to thank all my friends here in Gainesville, especially Alvin Gutierrez, Beatriz Camacho, Elzys Boscan, Nereida Padr6n and Gabriel Alcaraz. Their friendship has provided me with life experiences I could not have gained elsewhere. I am deeply grateful to Paul Bullock and Tanel Esin from Schmertmann & Crapps, Inc. for their assistance in providing useful load test data appearing in this thesis. The help from Dr. Ching L. Kuo from PSI, Inc. is also gratefully appreciated. Dr. Ching Kuo was always willing to help by providing any requested information or by sharing his vast experience in the deep foundation field. The funding of this research by the Florida Department of Transportation is also acknowledged and appreciated. TABLE OF CONTENTS page A C K N O W L E D G M E N T S .................................................................................................. iv A B S T R A C T ............................................................................ ............... ix CHAPTERS 1 IN T R O D U C T IO N ............................... .................. .................................................... 2 REVIEW OF FLORIDA PILE DRIVING PRACTICE............... ........ ................... 4 C u rren t F lo rid a P practice ................................................................................................ 4 B hearing R equirem ents ............................................................... ..... ................... 4 B low count criteria ................. ............................ ... ...... ... .......... 5 P practical refusal ................................. .................. ..............5 Set-checks and pile redrive........................................ ............................ 5 Pile heave .......................................... 6 Piles w ith insufficient bearing................................................ .............. 6 M methods to D term ine Pile Capacity.................................. ......................... 6 W ave equation ...................................... 7 B hearing form ulas ........................................ ........................ .. ............ 9 D ynam ic load tests ...................................... ...................................... 9 Static load tests ...................... ............. ... .............. 9 Evaluation of Florida Practice Changes ............................... ...... ................ 10 B hearing R equirem ents ............................................................. ..... ................... 10 M methods to D term ine Pile Capacity................................ ......................... 11 3 PILE CAPACITY ASSESSMENT USING STATIC AND DYNAMIC METHODS ........................................................ 14 D avisson's C capacity ................................................. ....... .. .......... 14 D ynam ic M ethods R eview ....................................................................... 16 M om entum C conservation .................................................. .......... .............. 16 ENR ................ ..... ......... .. ................................ 16 Modified Engineering News Record formula ............................................... 17 F D O T ........................................ 18 G ates m ethod ............................ .... ................ 19 Combined Wave Mechanics and Energy Conservation................................... 19 Sakai et al. Japanese energy m ethod .............. ............................. ....... ....... 19 P aik ow sky 's m eth o d ........................................................................................ 2 0 Wave Mechanics .............................. ............ .. 21 vi P D A m eth o d ....................................................................... 2 1 C A P W A P program .......................................................................................... 2 5 4 UNIVERSITY OF FLORIDA PILE DATABASE .............................................. 27 G general Inform ation and H istory....................................................... ... ................. 27 P IL E U F In form action ................................................................................................... 2 9 G e n e ra l ............................................................................. 2 9 Soil Classification .. ................. ........................ ................ 29 D driving Inform action ...................................... .............................. ............ .. 30 Dynamic Data (CAPWAP and PDA) .......................................... ............. 31 L oad Test R results .................. ............................. ....... .. ........ .... 31 SPT94 Capacity....................................................... 32 G gathering N ew Inform ation ........................................................................................ 32 Additional Required Information ............................... ............................ 33 C riteria for N ew E ntries ........................................................................................ 33 5 A SD A N D LRFD CON CEPTS......................................................... ... ................. 34 Allowable Stress Design (ASD) M ethod .......................................... ..... ......... 34 Load Resistance Factor Design (LRFD) Method ................................................... 35 Advantages of LRFD Over A SD ................................................. ....... ....... 36 Lim station of LRFD .................. .............................. ....... .. ........ .. 36 Calibration of LRFD .............................. ............ .. 37 E engineering Judgem ent ....................................................................... 37 Fitting A SD to LRFD .................................................................... ..... 37 Reliability Calibration ............................................... ...... .. .......... 39 Statistical data .. ........................................... ......... 39 Probability density function ........................................ ......... .............. 41 LRFD com ponents .................... ................. ...................... .............. 42 6 LRFD DATA PRESENTATION AND ANALYSIS ............................................ 51 Data Reduction......................................... ............ 51 LRFD A analysis of R esults...................................................................... ................. 56 Effect of Bridge Span Length and Probability of Failure.................................. 57 Level of Conservatism and Accuracy Indicators ............................................. 60 / R R atio ...................................................................... ......... 63 M ethods com prison .......................................................... .............. 64 EOD versus BOR ................ ............................. ..... .. ........ .. .... ....... 64 Evaluation of cases with capacity smaller or larger than 1779 kN .............. 64 R ecom m ended Safety Factors ...................................................... ..... ....... .. 65 A SD D esign E valuation ........................ ........................... ...................................... 68 7 SKIN AND TIP STATIC CAPACITY ASSESSMENT OF DRIVEN PILES........... 69 M ethod 1 ................................................ ......................... 70 Method 2 (Suggested) .......................... ..... .... ........ 72 Description and Main Assumptions ................................................................. 72 Case Damping Coefficient, Jo, versus Tip to Skin Ratio................................... 75 Sensitivity Analysis of Case Damping Coefficient, J ....................................... 77 Static and Dynamic Load Test Data................................................................... 78 Automating the Suggested M ethod ............................................... ................. 79 R results and A analysis ............ .............. ........................ .... ....... ........... ... 81 Presentation of R results ........................................................... .... .. .......... .. 81 Analysis of Total Capacity Predictions .............. ........................................... 86 Analysis of Skin and Tip Capacity Predictions................... ................................ 87 Sensitivity of Jc and Pile R esistance............................................ ... ................. 91 8 CONCLUSIONS AND RECOMMENDATIONS ............................................... 94 LRFD Calibration for Eight Dynamic Methods................................................ 94 Conclusions ........................ ...................... 94 Recom m endations ......... .............. ...... .......... .. ................................ .. 95 Suggested Method to Determine Pile Capacity...................................... ......... ........ 96 C conclusions .......................................... ........ ........ ......... . 96 R ecom m endations ................................................. .. .......... .. 98 APPENDICES A LRFD ANALYSIS RESULTS CAPWAP PROCEDURE ...................................... 99 B LRFD ANALYSIS RESULTS PDA METHOD................................................ 104 C LRFD ANALYSIS RESULTS PAIKOWSKY'S ENERGY METHOD .............. 109 D LRFD ANALYSIS RESULTS SAKAIET AL (JAPANESE) METHOD............ 114 E LRFD ANALYSIS RESULTS FDOT METHOD ................................................. 119 F LRFD ANALYSIS RESULTS ENGINEERING NEWS RECORD (ENR).......... 128 G LRFD ANALYSIS RESULTS MODIFIED ENR........................ ................. 137 H LRFD ANALYSIS RESULTS GATES FORMULA............................................ 146 I FORCE AND VELOCITY TRACES FROM PDA SIGNAL .................................. 155 J OUTPUT FILE FOR SUGGESTED METHOD & GRL PROCEDURE (F O R T R A N ) ..................................................... 179 LIST O F R EFEREN CE S ................................................... ................................. 185 BIOGRAPHICAL SKETCH........................................ 187 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering LOAD RESISTANCE FACTOR DESIGN (LRFD) FOR DRIVEN PILES BASED ON DYNAMIC METHODS WITH ASSESSMENT OF SKIN AND TIP RESISTANCE FROM PDA SIGNALS By Ariel Perez Perez December, 1998 Chairman: Dr. Michael C. McVay Major Department: Civil Engineering Eight dynamic methods to estimate the static capacity of driven piles were evaluated based on a Florida database and Load Resistance Factor Design (LRFD). The dynamic methods investigated were four stress wave approaches (CAPWAP, PDA, Paikowsky Energy, and Sakai Energy) and four driving formulas (ENR, modified ENR, FDOT, and Gates). In the case of the older driving formulas, the database was broken into both small (i.e. Davisson capacity less than 1779 kN) and large (Davisson capacity larger than 1779 kN) capacity piles. It was demonstrated that the modern methods based on wave mechanics, such as CAPWAP, PDA, and Paikowsky's energy method, are more accurate than the old driving formulas. The utilizable measured Davisson capacity, defined as 0/4R (ratio of resistance / mean capacity), shows that the new dynamic methods are more cost effective to meet a reliability index in comparison with the old methods based on momentum conservation. In addition, the Gates formula, when used separately for Davisson capacity larger than 1779 kN or less than 1779 kN, may have comparable accuracy with the modern methods. A suggested empirical method is presented to calculate the total, skin, and tip static resistance of driven piles. This method has proved to be equally or more accurate than the most widely used method (i.e. PDA, and CAPWAP). Additional features of the suggested method include determining the total, skin, and tip static capacities as the piles are being driven, saving construction time, therefore, saving construction costs. CHAPTER 1 INTRODUCTION Dynamic testing has been a tool for estimating pile capacities and hammer suitability since 1888 when the first driving formula, i.e. the Engineering News formula, was published. From then to the early seventies, many driving formulas were proposed and adopted into codes, all derived on the principles of impulse-momentum conservation. In the sixties, pioneer research investigated predicting both stresses and pile capacities based on wave mechanics. The results were the creation of programs such as, WEAP (GRL, 1993), PDA (Pile Dynamics Inc., 1992), and CAPWAP (GRL, 1996). Recently, energy approaches based on both wave mechanics and energy conservation have been developed to determine the pile capacity. Since the implementation of the PDA and CAPWAP about fifteen years ago, it is unknown the accuracy of these methods in comparison with the older driving formulas. Moreover, it is unknown how the newer energy equations compare to the past and present methods for Florida soil conditions. Recently, the American Association of State Highway and Transportation Officials (AASHTO) has moved from the Allowable Stress Design (ASD) to the Load Resistance Factor Design (LRFD) analysis. The latter method employs resistance factor, 6, based on reliability indexes. However, in order to determine the accurate resistance factors, the LRFD requires a database to assess the probability of failure of a given method. Based on the University of Florida pile database and AASHTO's recommended reliability index, and live to dead load ratios, the resistance factors (LRFD) and equivalent safety factors (ASD) were developed for a number of dynamic pile capacity methods. These parameters served as a tool to evaluate the accuracy and level of prediction of the dynamic methods studied. The dynamic methods investigated were four stress wave approaches (CAPWAP, PDA, Paikowsky Energy, and Sakai Energy) and four driving formulas (ENR, modified ENR, FDOT, and Gates). In the case of the older driving formulas, the database was broken into both small (i.e. Davisson capacity less than 1779 kN) and large (Davisson capacity larger than 1779 kN) capacity piles. Since 1994, the Florida Department of Transportation specifications recommend the use of Wave Equations to determine the suitability of the driving system and to estimate the pile capacity. It is also recommended the use of dynamic and/or static load tests to verify the estimated capacity. For the dynamic procedures, FDOT recommends the use of PDA or CAPWAP only. The capability of CAPWAP to estimate the skin and tip capacity in addition to the distribution of damping through the pile have created a level of confidence in the pile industry over the PDA whose result consists only of the total static capacity. However, the CAPWAP program needs highly trained people to run it, and involves a series of iterations. The latter creates delays in the pile driving operations and increase in foundation costs. A suggested empirical method is presented to calculate the total, skin, and tip static resistance of driven piles using the PDA Case solution. This method has proved to be equally or more accurate than the most widely used methods (i.e. PDA, CAPWAP). In addition, the suggested method allows the users to determine the pile capacities instantly as the piles are driven, saving construction time. Because all the calculations for the suggested method are performed automatically, a technician with a high level of expertise is not required. CHAPTER 2 REVIEW OF FLORIDA PILE DRIVING PRACTICE In this chapter, the pile driving practice in Florida will be presented. Because the Florida Department of Transportation (FDOT) uses a large percentage of driven piles versus the private industry, the information presented herein is based on their recommendations. It is the author's intention to present the current driving practice together with a discussion of the most relevant changes throughout the years. This discussion is focused on aspects such as bearing requirements, and methods to determine pile capacity. Current Florida Practice The information presented is in relation to the current Florida practice, which was obtained from the FDOT Standard Specifications for Road and Bridge Construction of 1999. For more details, the reader is referred to the latest FDOT specifications. Bearing Requirements As a general criterion the engineer in charge of the driving process may accept a driven pile if it has achieved the minimum penetration, the blow count has a tendency to increase and the minimum bearing capacity is obtained for 600 mm of consecutive driving. The engineer may also accept a driven pile if the minimum penetration was reached and the driving has achieved practical refusal in firm strata. Aspects such as practical refusal and others driving criteria will be discussed in detail in the following sections. Blow count criteria Using the Wave Equation Analysis for Piles (WEAP) the engineer can determine the number of blows per specific penetration to reach a design pile capacity. The blow count has to be averaged for every 250 mm of pile penetration or through the last 10 to 20 blows of the hammer. It should be noted that the driving equipment must be selected in order to provide the required resistance at a blow count ranging from 30 blows per 250 mm to 98 blows per 250 mm. Practical refusal Practical refusal is defined as a blow count of 20 blows per 25 mm for 50 mm of driving. The FDOT specifications recommend that driving ceases after driving to practical refusal conditions for 250 mm. If the required penetration can not be achieved by driving without exceeding practical refusal, other alternates should be considered such as jetting or Preformed Pile Holes. Set-checks and pile redrive Set-checks. Set checks are performed in the event that the Contractor has driven the pile up to the point that the pile top elevation is within 250 mm of the cut-off elevation and the pile has not reached the required resistance. Prior to a set check, the driving process is interrupted for 15 minutes. Then, the engineer is provided with a level or other suitable equipment to determine elevation in such a way that the pile penetration during the set-checks could be determine in a very accurate manner. If the initial set- check results are not satisfactory, additional set-checks could be performed. The pile is then accepted if the pile has achieved the minimum required pile bearing. Pile redrive. Pile redrive consists of redriving the pile after 72 hours from original driving. The pile redrive is considered when time effect is important in the pile capacity. Other considerations include the pile heave. Pile heave Pile heave is defined as the upward movement of a pile from its originally driven elevation. In occasions, driving a pile can cause excessive heave and/or lateral displacement of the ground. The previously driven pile should be monitored, and in the event of pile heave (6 mm or more), all piles must be redriven unless the engineer has determined that the heave is not detrimental to the pile capacity. Piles with insufficient bearing In the event that the pile top has reached the cut-off elevation without achieving the required bearing resistance, the FDOT specifications recommends: 1. Splice the pile and continue driving. 2. Extract the pile and drive a pile of greater length. 3. Drive additional piles until reducing the adjusted required bearing per pile to the bearing capacity of the piles already driven. Methods to Determine Pile Capacity The FDOT Specifications recommend the use of Wave Equation to determine pile capacity for all structures or projects. The use of static load tests or dynamic load tests, or both, is recommended to verify the capacity estimated from Wave Equation predictions. Nevertheless, the prediction by the Wave Equation (blow count criteria) could be adjusted to match the resistance determined from the static or dynamic load tests, or both. Wave equation The FDOT Specifications recommends to use the WEAP program to predict the pile capacity. This program allows the engineer to evaluate other aspects of the driving process. In the following paragraphs, a description of these aspects will be presented. Evaluation of driving system. Evaluate the suitability of the driving system (including hammer, follower, capblock and pile cushions. The driving system must be capable of driving the pile to a resistance of 3.0 times the design load, plus the scour and down drag resistance or the ultimate resistance, whichever is higher. Determine pile driving resistance. The pile driving resistance, in blows per 250 mm or blows per 25 mm could be determined. The required driving resistance is defined as the design load multiplied by the appropriate factor of safety plus the scour and down drag resistance or the ultimate bearing capacity, whichever is higher. Evaluate pile driving stresses. The engineer must evaluate the driving system to avoid overstressing the pile at any moment during the driving. If the Wave Equation analyses show that the hammer will overstress the pile, the driving system has to be rejected. The FDOT Specifications 455-5.11.2 presents the allowable stresses for piles made out of concrete, steel and timber. Equation 2-1, 2-2, and 2-3 give the maximum allowable tensile and compression stresses for prestressed concrete piles. The allowable compressive stress is, sC = 0.7fc -0.75fpc (2-1) For piles length less than 15 meters the allowable tensile stress is given by sa = 0.54(fY +1.05fp, (2-2) And for piles length greater than 15 meters spt = 0.27(f + 1.05fp (2-3) where Sapc Maximum Allowable Pile Compressive Stress, MPa Sapt Maximum Allowable Pile Tensile Stress, MPa fcl Specified Minimum Compressive Strength of Concrete, MPa. fpc Effective Prestresses at Time of Driving. For steel piles the maximum allowable compression and tensile stresses are equal to ninety percent (90 %) of the yield strength (0.9 fy) of the steel. While for timber piles the maximum allowable pile compression and tensile stresses are 25 MPa for Southern Pine and Pacific Coast Douglas Fir and 0.9 of the ultimate parallel to the grain strength for piles of other wood. Bearing formulas The FDOT under specification 455-5.11.3 recommends the following bearing formula for temporary timber piles driven with power hammers: 167E R =1 (2-4) s+2.54 where R Safe Bearing Value, in Kilonewtons. s The Average Penetration per Blow, in Millimeters. E Energy per Blow of Hammer, in Kilojoules. The latter specification also clearly states that this formula should not be used to determine pile capacity of any other pile type. No other bearing formula is suggested in the specifications for concrete or steel piles. Dynamic load tests Dynamic load testing consists of predicting pile capacity from blows of the hammers during drive and/or redrive of an instrumented pile. Chapter 3 includes more details of how the dynamic load test is performed (see PDA and CAPWAP sections). Static load tests Static load testing consists of applying a static load to the pile to determine its capacity. The FDOT recommends the Modified Quick Test. For more details about the static load test, the reader is referred to the FDOT specification 455-2.2.1. Some general information about this test, and the procedure to obtain the pile capacity are explained in Chapter 3. Evaluation of Florida Practice Changes In the following sections the most relevant changes in the Florida practice (i.e. bearing requirements and proposed methods to determine pile capacity) for approximately the last 10 years are discussed. For this purpose, the actual practice will serve as a reference for any comparison. To facilitate the comparison process, only the changed criteria will be discussed. The latter does not mean that the aspects not mentioned within this document did not vary (i.e. only the topics related to this thesis will be investigated). Because the largest change in FDOT specifications related to pile foundation were found in the 1994 version versus 1991 version specifications, the discussion will be based on these two references. To simplify the comparison, the FDOT specifications of 1991 and prior to 1991 will be called "old specifications" and any other specification after 1991 will be called the "new specifications." Bearing Requirements In general, there was a great change in the FDOT specifications of 1994 in comparison to the older FDOT specifications. In the old specifications the piles were allowed to be driven to grade. Even if the practical resistance had not been reached at that point, the engineer was able to drive the pile below grade and build up. After driving 12 inches (0.305 m) below grade, a set-check could be performed after 12 hour of initial driving. The latter criterion differs from the new practice in the elevation at which the set-check is recommended. The new practice recommends the set-check to be performed at approximately 10 inches above the cut-off elevation. Another important difference is related to the bearing formulas. In the old specifications, the FDOT recommend the use of bearing formulas to determine the pile bearing capacity for piles made out of timber, concrete, composite concrete-steel and steel. Then, from 1994 to date the specifications limited the use of bearing formulas to timber piles driven with power hammers only. Methods to Determine Pile Capacity It was noted that in the old specifications there was not any requirement for using Wave Equation programs to determine the pile capacity. The same observation applies to the use of dynamic testing as a method to determine the pile capacity. Prior to 1994, the FDOT recommended the use of static load test to determine the pile capacity of any pile that did not reach the required resistance at the end of drive or as directed by the engineer. The new specifications recommend the use of Pile Driving Analyzer (PDA), the Wave Equation Analysis for Pile (WEAP), and the static load test separately or in a combination of each, as recommended by the engineer (the safety factor for design depends upon the number and kind of test performed). The other difference is in the criterion for determining the pile capacity from the static load test. In the old specifications, the failure criterion is given by either or both conditions shown below: 1. One and one-half times the yield load settlement develops. The yield load is defined as that load beyond which the total additional settlement exceeds 0.03 inch per ton, for the last increment applied. 2. The total permanent settlement of the top of the pile is greater than 14 of an inch. The new specifications present two criteria to determine the static pile capacity. Those criteria are as follows: 1. Davisson for shafts with diameter up to 600 mm, the load that causes a shaft top deflection equal to the calculated elastic compression, plus 4 mm, plus /120 of the shaft diameter in millimeters. 2. FHWA for shafts with diameter larger than 600 mm, the load that causes a shaft top deflection equal to the calculated elastic compression, plus 1/30 of the shaft diameter. The changes in criteria for selecting the failure load reflect, first, an increase in the use of larger piles in the construction field, and second, the FDOT recognizes that for larger piles (diameter larger than 600 mm) the capacity according to Davisson's criterion is conservative. As a general observation, the FDOT has abandoned the old methods to determine the bearing capacity of piles (i.e. bearing formulas, based on momentum conservation). At the same time, the FDOT has adopted other prediction methods such as Wave Equation, PDA, and CAPWAP, which are based on piles dynamic and wave propagation through the pile, to estimate the static pile capacity. Other old methods such as Gates, ENR, and Modified ENR are not considered as alternates in estimating the pile capacity, neither are the relatively new methods such as Paikowsky's method and Sakai et. al. method. 13 It was proposed by the FDOT to investigate the new FDOT specifications in relation to the old methods based on momentum conservation (i.e. FDOT, Gates, ENR, Modified ENR). Another important consideration was to evaluate the old methods for large capacity piles, which are used today, separately from small capacity piles (i.e. piles with capacity up to 2000 kN approximately). The latter reflects the magnitude of design loads for which piles were designed in the past in comparison to the present practice. CHAPTER 3 PILE CAPACITY ASSESSMENT USING STATIC AND DYNAMIC METHODS The Florida Department of Transportation (FDOT) under contract No. BB-349 required UF to evaluate the older empirical methods for determining pile capacity and compare them to the modern instrumented methods. In addition, it was required to obtain the resistance factor for each method (Load Resistance Factor Design LRFD). In order to perform the latter, the Davisson's capacity served as the measured capacity for each pile. In the following sections, a brief description of the Davisson criterion together with the description of the empirical methods investigated will be presented. Davisson's Capacity The Davisson method (Davisson, 1972) is one of many methods developed to determine the pile capacity based on a static load test results. Davisson defined the pile capacity as the load corresponding to the movement which exceeds the elastic compression of the pile by a value of 4-mm (0.15 inches) plus a factor equal to the diameter of the pile in millimeter divided by 120. Figure 3-1 presents the load- displacement curve resulting from a static load test. From this curve, the Davisson's pile capacity can be obtained. The steps to obtain the Davisson's capacity are as follow: DAVISSON'S METHOD MOVEMENT (INCHES) Figure 3-1. Construction of Davisson's Pile Capacity 1. Plot a line with slope representing the elastic deformation of the pile (Slope m): m = where A E L Cross-sectional Area of the Pile Elastic Modulus of the Pile Material Pile Length 2. Draw a line parallel to the elastic deformation line with an intercept, x, on the settlement (movement) axis given as (3-1) x=4.0+-- (3-2) 120 where D Diameter of Pile in millimeters x horizontal displacement of elastic deformation line in millimeters 3. The Davisson's capacity (point D on Figure 3-1) is defined as the intersection point between the load-settlement curve and the elastic deformation line. Dynamic Methods Review Eight methods were considered in this study, which are subdivided in three categories: momentum conservation, combined wave mechanics with energy conservation, and wave mechanics alone. The methods are the Engineering News Record (ENR), Modified ENR, FDOT, Gates, Paikowsky, Sakai (Japanese), Pile Driving Analyzer (PDA) and the Case Pile Wave Analysis Program (CAPWAP). In the following sections, a brief description of each method is presented. Momentum Conservation ENR One of the older formulas developed to estimate the driven pile capacity was the formula published in the Engineering News Record (ENR) (Coduto after Wellington, 1994). It has since become known as the Engineering News Record formula: Wh P = (3-3) F(s+0.1) where Pa Allowable Pile Load Wr Hammer Ram Weight h Hammer Stroke (the distance the hammer falls) F Factor of Safety s Pile Set (penetration) per Blow in Inches Wellington (1888) recommended using a Safety Factor of 6.0. Modified Engineering News Record formula In 1961, the Michigan Highway Department (Housel, 1966) performed a series of pile driving tests with the objective of evaluating the accuracy of the ENR formula. After evaluating 88 piles, the investigators found that the ENR formula overpredicted the pile capacities by a factor of 2 to 6. The findings mean that piles designed with a SF of 6 will have a real factor of safety of 1 and 3. Based on their results, the Michigan Highway Department developed the Modified Engineering News Formula: 0.0025E(W, +e2W) (3 a (s+0.1)(W,+Wp) Pa Allowable Pile Load (kips) where E Rated Hammer Energy Per Blow (ft-lb) Wp Weight of Pile plus Driving Appurtenances (lb) Wr Weight of Hammer Ram (lb) s Pile Set (in/blow) e Coefficient of Restitution FDOT The Florida Department of Transportation under specification 455-3.3 (1991) recommends the following bearing formula (FDOT, 1991). 2E R = (3-5) S+0.1+0.01P where R Safe Bearing Value in Tons P Weight of Pile as Driven, in Tons S Average Penetration per Blow, in Inches E Energy per Blow of Hammer, in Foot-Tons The last formula was used for concrete piles, composite concrete-steel piles and steel piles. The bearing capacity obtained using the latter FDOT approach either coincided or exceed the design capacity (suggested FS = 1.0). Gates method The method was the results of a research performed by Marvin Gates, J.M (1957). The basic assumption is that the resistance is directly proportional to the squared root of the net hammer energy. This relationship is presented by S= aeE,(b -logs) (3-6) where Pu Static Pile Resistance eh Hammer Efficiency (0.85 used for all Cases) Eh Hammer Energy a, b 27 and 1.0 Respectively (English units) s Point Permanent Penetration per Blow Set A suggested safety factor equal 3.0 is recommended. Combined Wave Mechanics and Energy Conservation Sakai et al. Japanese energy method Sakai's pile driving formula was developed based on stress-wave theory. According to Sakai, this consideration introduced two advantages, it is theoretically accurate as well as easy to use (Sakai et al., 1996). For a blow by an elastic hammer Sakai et al. recommend S J 2, 1 ) (3-7) LP 2MH ma where A Pile Cross Sectional Area E Young's Modulus of Pile Material Lp Length of the Pile Mp Mass of the Pile Dmax Maximum Penetration of Pile per Blow s Permanent Set Paikowsky's method The Paikowsky method or "Energy Approach" is a simplified energy approach formulation for the prediction of pile resistance based on the dynamic measurements recorded during driving. The basic assumption of the method is an elasto-plastic load displacement pile-soil reaction. The Paikowsky method uses as input parameters the maximum calculated transferred energy and maximum pile displacement from the measured data together with the field blow count. Equation 3-8 presents the solution for the dynamic pile capacity R, (Paikowsky, 1994). R = m- (3-8) Set+ max 2 where R, Dynamic Pile Capacity Em Maximum Energy Entering the Pile Dmax Maximum Pile Top Pile Movement Set Point permanent penetration per blow The static pile resistance P, can be obtained by P= K R (3-9) where Ksp 'Static Pile' Correlation Factor Accounting for all Dynamic Energy Looses. For easy driving of piles with small area ratios, Paikowsky recommends a value of Ksp smaller than 1.0, while for hard driving cases with large area ratios, the recommended Ksp value must be larger than 1.0. A value of Ksp equals 1 was used in our calculations. Wave Mechanics PDA method In the 1960's a new method to determine the pile capacity was developed at the Case Institute of Technology in Cleveland, Ohio. This new method called Pile Driving Analyzer (PDA) is based on electronic measurements of the stress waves occurring in the pile while driving. Some advantages of dynamic pile testing are (GRL, 1996): 1. Bearing Capacity The bearing capacity can be found at the time of testing. For the prediction of a pile's long term bearing capacity, measurements can be taken during restriking (Beginning of Restrike BOR) 2. Dynamic Pile Stresses While the pile is driving the stresses within the pile can be monitored. This avoids any possibility of pile damage due to compression or tension stresses. Bending stresses caused by asymmetry of the hammer impact can be also monitored. 3. Pile Integrity To detect any existing damage within the pile 4. Hammer Performance The performance of the hammer is monitored for productivity and construction control purpose. The PDA is considered as field equipment for measuring the forces and accelerations in a pile during driving. The methodology is standardized and is described in ASTM standard D4945. The equipment includes three components (Coduto, 1994): 1. A pair of strain transducers mounted near the top of the pile on each side. 2. A pair of accelerometers mounted near the top of the pile. 3. A pile driving analyzer (PDA) The main purpose of the PDA is to compute the static resistance of the pile using the Case method as it is driven. To perform the latter, the dynamic capacity has to be separated from the static capacity by mean of a damping value Jc, or Case damping value. In the following paragraph a summary of the basic equations used by PDA is presented. The pile wave speed, c, can be determined prior to pile installation while the pile is still on the ground. The accelerometers are installed and the pile is hit with a hammer. Knowing the pile length and the wave travel time, the wave speed can be calculated using Equation 3-10. (3-10) where Length of the Pile Time Required for the Pulse to Travel Twice the Pile Length The dynamic modulus of the pile material, E, is presented in Equation 3-11. The mass density of the pile material is represented by p and the wave speed c. E= pc2 (3-11 Equation 3-12 presents the impedance, Z, of a pile as a function of the dynamic modulus, E, the wave speed, c, and the pile cross-sectional area, A. EA Z= (3-12 c ) ) The force within the pile can be obtained from the strain transducers and knowing the elastic modulus of the pile material and cross-sectional area, according to Equation 3- 13. P= EA (3-13) The velocity is obtained from the integration of the acceleration signal acquired by the accelerometers. It should be noted that the force and velocity used in the PDA calculation is the result from the average of the two strain transducers and the two accelerometers. The velocity is then converted to force units by multiplying by the pile's impedance (Z). The result of the force and velocity are then plotted in a graph versus time for a given blow. Figure 3-2 shows an example of the force and velocity traces for a given hammer blow. 2500 2000 SForce 1500 .. .... Velocity Z 1000 LL 500 0.01 0.02 0.0o 0_ 4 ,50 )6 -500 -1000 Time (s) Figure 3-2. Typical Force and Velocity Traces from PDA The main equation used by PDA to determine the static capacity of piles was derived assuming that the pile is linearly elastic and has constant cross section properties along the length. This equation is based on the force and velocity records at a time T1 and at a time T2 equal to T1 plus 2L/c, and the Case damping constant. Equation 3-14 presents the PDA equation for determining the static pile capacity. The reader is referred to the PDA manual for detailed information and more thorough derivation. RSP= (1-J) 1-Z z + Jc) 2 (3-14) 2 2 where RSP Total Static Capacity Jo Case Damping Constant P1,P2 Force at Time T1 and T2 Respectively V1,V2 Velocities at Time T1 and T2 Respectively Z Impedance CAPWAP program The Case Pile Wave Analysis Program (CAPWAP) is a computer program that combines the wave equation's pile and soil model with the Case method of forces and velocities from PDA. The CAPWAP solution includes the static total resistance, skin friction and toe bearing of the pile, in addition to the soil resistance distribution, damping factors, and soil stiffness. The program calculates acceleration, velocities, displacements, waves up, waves down and forces at all points along the pile. The procedure used by CAPWAP includes inputting the force trace obtained from PDA and adjust the soils parameters until the velocity trace obtained from PDA can be recreated. It should be noticed that the opposite procedure (i.e. input velocity trace and generate the force trace) can also be performed. When the match obtained is 26 unsatisfactory, it is necessary to modify the soil parameters, until reaching a satisfactory match results. The process of running CAPWAP is considered an iterative one. CHAPTER 4 UNIVERSITY OF FLORIDA PILE DATABASE General Information and History The University of Florida in conjunction with the Florida Department of Transportation (FDOT) has developed a database on driven piles inside and outside the state of Florida. This database, called PILEUF, is the result of many years of research to predict pile capacity from static and dynamic means. Originally, the database was on a Lotus 123 spreadsheet format. However, the database information was transferred to a Microsoft Excel format for this research. By doing the latter, the automatic tasks (macros) or links from Lotus 123 were eliminated. Also, new pile information was obtained from the original geotechnical reports, as well as new cases studied. Currently, there are 242 piles in the database. Out of these 242 piles, 198 are concrete piles (both square and round), 21 are steel pipe piles, and 9 are H-Piles. Table 4- 1 summarizes the number of piles, classification and diameter for the Florida cases while Table 4-2 summarizes the same information for the Non Florida cases. The Florida State total includes 175 piles obtained from 60 sites and represents 218 cases. The difference between the number of piles and cases is due to the multiple attempts to determine the same pile's capacity. The Non-Florida total from Table 4-2 represents 22 sites. In this occasion the number of cases are equal to the number of piles. Table 4-1. Classification of Florida Driven Piles Pile Number of Piles Diameter Squared Pipe Sub-Total (inches) Concrete Piles 10 4 3 7 12 14 2 16 14 26 8 34 18 34 0 34 20 12 0 12 24 44 0 44 30 26 0 26 36 2 0 2 Sub-Total 162 13 175 Table 4-2. Classification ofNon-Florida Driven Piles Pile Number of Piles Diameter Squared Round Pipe H-Piles Sub-Total (inches) Concrete Concrete Piles 10 3 0 1 6 10 10.75 2 0 0 0 2 12 15 2 0 1 18 12.75 3 0 0 0 3 14 2 0 3 2 7 16 5 0 0 0 5 18 2 0 0 0 2 24 2 0 0 0 2 59.06 0 0 4 0 4 Sub-Total 34 2 8 9 53 It should be noted that for the Non-Florida information in Table 4-2 the total number of piles does not include 14 piles with unspecified diameter. The following sections describe briefly the information gathered in the database PILEUF to date. PILEUF Information General Each pile record contains general description of the site location, together with pier or bent number (if available). Four pile types were selected to describe the piles within the database based on shape and materials. The four categories were: 1. Square concrete pile 2. Round concrete pile 3. Pipe pile 4. H-pile The geometry of the piles was described by the pile width, total length, embedded length, and cross sectional area. In addition, the dates when the piles were driven and tested were recorded. Soil Classification The soil information includes the soil stratigraphy (description and properties) with in-situ tests such as SPT, CPT, etc. Nine soil types were used to allow consideration of several combinations of cohesive and non-cohesive soil. The nine soil categories were presented according to the following numbering: 1. Plastic clay 2. Silt-sand-clay, silts and marls 3. Clean sand 4. Limestone, very shelly sands 5. Clayey sand 6. Sandy Clay 7. Silty clay 8. Rocks 9. Sandy gravel, tills The original database combined the side and tip soil number to form a two-digit code, in which the first digit is the side soil type and the second digit is the tip soil type. Driving Information The driving information includes the driving system type, hammer and pile weight and manufacturer's rated energy together with the efficiency of the hammer. Additional information includes the dynamic modulus, wave speed and the pile impedance. If the impedance was not available from CAPWAP or other results, it was calculated as EA/c. The average set for EOD and BOR was taken as the inverse of the blow counts as near as possible to the blow used in PDA or CAPWAP analysis, although it may represent an average of the last foot of driving in some cases, if inch-by-inch information was not available. A record of the depth of penetration and blows per foot (calculated for penetration intervals less than one foot) facilitated the determination of set, knowing the tip depth at the time of the blow. Dynamic Data (CAPWAP and PDA) The CAPWAP and PDA results were sometimes available only for EOD or BOR. Furthermore, not all CAPWAP analyses have complete PDA results available or vice versa. Having both results was not a requirement during the construction of the database. The PDA results include date, RMX (maximum Case Static Resistance calculated during the blow analysis) or other PDA calculated capacity as listed in the source report. The database also presents the PDA Case damping used for calculating the Total Static Resistance. CAPWAP results include date, tip and friction capacities, total capacity, and Case and Smith damping factors for side and tip, where the Case damping factors were calculated from the Smith damping factors. The latter was performed by dividing the Smith damping value by the impedance and multiplying the result by the side or tip resistance. Load Test Results PILEUF contains load test information, measured at the top of the piles. It includes the load in tons and settlements in inches at failure for a given criterion. The failure criteria presented in the database are: 1. Davisson 2. Fuller-Hoy 3. DeBeer 4. FDOT The database also includes the maximum load in tons from the static load test, in addition to the date at which the load test was performed. SPT94 Capacity SPT94 (most recent version SPT97) is a pile capacity prediction program. It is based on the Research Bulletin 121 (RB-121), "Guidelines for use in the Soils Investigation and Design of Foundations for Bridge Structures in the State of Florida", prepared by Schmertmann in 1967, and the research report "Design of Steel Pipe and H- piles" prepared by Dr. Michael McVay et al in 1994. The method calculates pile capacity based on N values obtained from the Standard Penetration Test. SPT94 is capable of evaluating round and square concrete piles, H-piles, and steel pipe piles (open or close end). It calculates an Estimated Davisson capacity by summing the Ultimate Side Friction and 1/3 of the Ultimate End Bearing (Mobilized End Bearing) capacity of the pile. SPT94 predictions presented in PILEUF include the Ultimate Side Friction, Ultimate Tip Capacity, Mobilized Tip Capacity, Ultimate Total Capacity, and Davisson's Capacity. Other related information presented in the database is the input data for SPT94 program. It includes the layering and the soil properties (i.e. unit weight and SPT blow count). Gathering New Information During the course of evaluating the eight dynamic method (See Chapter 3), some extra information was necessary. In order to acquire it, it was required to restudy the geotechnical reports from which the original information was obtained. Some of these parameters are presented in the next sections. Additional Required Information Two parameters that were not found in the PILEUF database were the maximum displacement and the maximum energy transfer to the pile. They were essential to obtain the Paikowsky and Sakai capacities (See Chapter 3). Both, the maximum energy transfer to the pile and the maximum displacement were obtained from the CAPWAP output printout in the geotechnical reports. Criteria for New Entries As a general criterion, new entries in the database should be within the State of Florida. Pile cases from outside the State of Florida were not considered in this study. Because the evaluation of the dynamic methods was performed in correlation to the Davisson capacity, new entries in the database should have the load test carried to the point in which Davisson capacity could be determined. Other information required will depend of the methods to be evaluated. The more information obtained for a particular record, the more dynamic methods there are to be evaluated in relation to the Davisson capacity. CHAPTER 5 ASD AND LRFD CONCEPTS Over the years, multiple design procedures have been developed which provide satisfactory margins of safety. Safety in design is obtained when the material properties exceed the demand put on them by any load or loads combination. Another way to describe the same principle is that the resistance of the structure must exceed the effect of the loads, i.e.: Resistance 2 Effect of Loads (5-1) When a specific loading condition reaches its limit, failure occurs. Two general states of interest to engineers are Strength and Service Limit. Strength Limit State involves the total or partial collapse of the structure (i.e. bearing capacity failure, sliding, and overall instability). On the other hand, Service Limit State only affects the function of the structure under regular service loading conditions (i.e. excessive settlement and/or lateral deflection, structural deterioration, etc). Allowable Stress Design (ASD) Method In geotechnical engineering, the ASD has been the primary method used in U.S.A. ASD procedures are different for Service Limit and Strength Limit States. For the Strength Limit State, safety is obtained in the foundation elements by restricting the ultimate loads to values less than the ultimate resistance divided by a factor of safety, (FS): R ,> ,_Q' (5-2) FS where Rn Nominal Resistance XQi Load Effect (Dead, Live and Environmental Loads) FS Factor of Safety For the Service Limit State, the deformations (i.e. settlements) are calculated using the unfactored loads, and the values obtained are compared to the allowable deformation for that structure. Load Resistance Factor Design (LRFD) Method The LRFD specifications as approved by AASHTO in 1994 recommend the use of load(s) factors to account for uncertainty in the load(s) and a resistance(s) factor to account for the uncertainty in the material resistance(s). This safety criterion can be written as OR,, = r y, Q, (5-3) e) Statistically Based Resistance Factor where Rn Nominal Resistance 11 Load Modifier to Account for Effects of Ductility, Redundancy and Operational Importance yi Statistically Based Load Factor Qi Load effect Even though the LRFD method differs from the accustomed ASD procedure, it has been widely approved by the geotechnical engineers. Some of the advantages and disadvantages of the LRFD method over the ASD method are presented next (Withiam et al., 1997). Advantages of LRFD Over ASD 1. Account for variability in both resistance and load. 2. Achieves relatively uniform levels of safety based on the strength of soil and rock for different limit states, foundation types, and design methods. 3. Provide more consistent levels of safety in the superstructure and substructure when the same probabilities of failure are employed. 4. Using load and resistance factors provided in the code, no complex probability and statistical analysis is required. Limitation of LRFD 1. Implementation requires a change in design procedures for engineers accustomed to ASD. 2. Resistance factors vary with design methods and are not constants. 3. The most rigorous method for developing and adjusting resistance factors to meet individual situations requires availability of statistical data and probabilistic design algorithms. Calibration of LRFD Calibration is defined as the process of assigning values to resistance factors and load factors, which are indispensable for the LRFD approach. This process can be performed by use of engineering judgement, fitting to other codes (e.g. ASD method), use of reliability theory, or a combination of them. In the following sections these approaches will be discussed. Engineering Judgement The calibration of a code using engineering judgement requires experience. Such experience is usually obtained through years of engineering practice. Sometimes, using such an approach results in certain level of conservatism with little validation. Also under varying conditions where no experience exists both excessive conservatism or ever unconservatism may develop. Fitting ASD to LRFD Fitting ASD to LRFD includes using parameters from LRFD (i.e. resistance factor) that result in equivalent physical dimensions of a substructure or superstructure as by ASD. It does not provide a better or more uniform margin of safety. In order to calibrate the ASD method, the first step is to rewrite equations 5-2 and 5-3 as R SQD+QL FS kRn YLQL + YDQD (5-4) (5-5) It should be noted that the loads only include dead and live loads. Environmental loads (i.e. wind, earthquake, etc) were not taken into consideration for the derivation of the ASD fitting equation. Solving both equations for Rn we obtain R 2 FS(QD+ QL ) R >YLQL + YDQD) e jk (5-6) (5-7) Setting Equation 5-6 equal to Equation 5-7 and solving for 6 SYLQL +YD D FS(Q, +Q QD (5-8) Dividing both the numerator and the denominator of Equation 5-8 by QL QD YD + YL = QL (5-9) Equation 5-9 is the resulting calibration equation for ASD fitting to the LRFD or vice versa. For deep foundation design, the values of yD and YL recommended by LRFD Highway Bridges Design Specifications (AASHTO, 1994) are 1.25 and 1.75 respectively. The QD/QL definition and values will be presented in more detail in latter sections. Calibration by fitting is recommended when there is insufficient statistical data to perform a more sophisticated calibration by optimization. When statistical data is available it is recommended to make use of reliability theory. Reliability Calibration Statistical data In order to perform a reliability calibration for deep foundations (obtain resistance factor, 0), such as piles and drilled shafts, the designer must have available statistical data for the method of interest. This statistical data must include real or measured capacities and the estimated or nominal capacities of the shafts. Next, the bias is defined as =& (5-10) where kRi Bias Factor Rm Measured Resistance Rn Predicted (nominal) Resistance The biases for all history cases using the same design procedure are subsequently determined for the database and the values of mean, standard deviation and coefficient of variance are then found. Equations 5-11, 5-12 and 5-13 are used for this purpose (Withiam et al., 1997). R = (5-11) N R -(5-12) N-I COVR = (5-13) where tR Average Resistance Bias Factor N Number of Cases CYR Resistance Standard Deviation COVR Resistance Coefficient of Variance For calibrations of the methods that predict driven pile capacity, the values of the measured resistance (Rm) were obtained from in-situ load test employing the Davisson's capacity. The nominal resistances (Rn) were obtained from the various dynamic equations under study (Chapter 3). Probability density function For the LRFD design, the probability of failure to occur for a given load and resistance distribution is of fundamental importance. The latter is calculated with the "probability density function" which is defined as the probability that X occurs in the interval x to x + dx asf,(x)dx (see Figure 5-1). The total area under the curvef,(x) must be equal to unity because a probability of 1 includes all possible outcomes. x x+dx x Figure 5-1. Lognormal Probability Density Function Based on the distribution of the resistance data, a lognormal probability distribution was recommended for the resistance data by the AASHTO Specification. A normal function was used to represent the observed distribution of load data. Equation 5- 14 presents the lognormal probability density equation. e- s, 1< I(nx-80 2^x 2^ (5-14) In Equation 5-14 the values of 0 and are the lognormal mean and lognormal standard deviation respectively, =2 In 1+ 1 (5-15) S=ln 1 2 (5-16) 2 Where OR and kR are the standard deviation and the mean of the resistance as defined in prior sections. LRFD components Probability of failure. The LRFD approach defines the probability of failure of a structure based on the load and resistance distribution curves. Figures 5-2 shows the probability density functions for normally distributed load and resistance. The shaded area represents the region of failure where the resistance is smaller than the loads. For the load and resistance curves, the margin of safety can be defined in terms of the probability of survival as p, = P(R > Q) (5-17) fQ(q) I -Q SRELIABILITY R Q R BOUNDARY Figure 5-2. Probability Density Functions for Normally Distributed Load and Resistance And the probability of failure, pf may be represented as Pf = 1- p, = P(R < Q) (5-18) where the right hand of Equation 5-18 represents the probability, P, that R is less than Q. It should be noted that the probability of failure can not be calculated directly from the shaded area in Figure 5-2. That area represents a mixture of areas from the load and resistance distribution curves that have different ratios of standard deviation to mean values. To evaluate the probability of failure, a single combined probability density curve function of the resistance and load may developed based on a normal distribution, i.e. g(R,Q)= R-Q (5-19) If a lognormal distribution is used the limit state function g(R,Q) can be written as g(R, Q) = n(R) ln(Q) = ln(R/Q) (5-20) For both Equation 5-19 and 5-20 the limit state is reached when R=Q and failure will occurs when g(R,Q)<0. Reliability index. The reliability index is a simple method of expressing the probability of failure using function g(R, Q) (Eq. 5-20). The frequency distribution of g(R,Q) would look similar to the curve shown in Figure 5-3. f(g) 0 FAILURE REGION AREA = Pf 0 g= n(JRQ) g= n(RIQ) Figure 5-3. Definition of Reliability Index, 3 for lognormal Distributions of R and Q Evident from the curve is that if the standard deviation is small or the mean value is located further to the right, the probability of failure will be smaller. The reliability index 3, is defined as the number of standard deviations, g, between the mean value, g (average), and the origin, or: f g- (5-21) If the resistance, R, and load, Q, are both lognormally distributed random variables and are statistically independent, it can be shown that the mean values of g(R, Q)is g= In-L (5-22) Q 1+COVR and its standard deviation is = ln[(1+COV2 X1 +COV2) (5-23) Substituting Equations 5-22 and 5-23 into Equation 5-21, the relationship for the reliability index, 3, can be expressed as In [R/Q (1 + COV2 )/( + CO2 ) P = (5-24) ln [(+CO X )(1+COV ) Equation 5-24 is very convenient because it depends only on statistical data and not on the distribution of the combined function g(R, Q). A very precise definition of probability of failure, pf, is in terms of reliability index, Fu(3) (Withiam et al. 1997). =1-F (,) (5-25) Standard Normal Probability Density Distribution 045 040 0 35 0 30 S0.25 0 020 015 010 0 05 0.00 -4 -3 -2 -1 0 1 2 3 4 Reliability Index, 0 Figure 5-4. Reliability Definition Based on Standard Normal Probability Density Function In the latter equation, F,(x) is the standard normal cumulative distribution function. F~(f3>i-J 1 e 1p 2V p3 -2ir -2 } (5-26) A graphical representation of Equation 5-26 is presented in Figure 5-4. The shaded area in Figure 5-4 represents the probability of failure, pf, to achieve a target reliability index, 3T. 47 Another commonly accepted relationship between the reliability index, 3, and the probability of failure, pf, has been developed by Rosenblueth and Esteva (1972) using the relationship for values between 2 and 6. 1 OE+00 1 OE-01 1 OE-02 1 OE-03 1 OE-04 1 OE-05 1 OE-06 1 OE-07 1 OE-08 1 OE-09 1 OE-10 Reliability Index, J, vs. Probability of Failure, pf (Comparison of Methods) S..- p= 460 exp (-4.33) Esteva et al. (1972) True value Withiam et al. (1997) 0 1 2 3 4 5 6 7 Reliability index,1 Figure 5-5. Comparison of Esteva and Withiam Methods to Obtain Reliability Index, P. Pf = 460exp(-4.33) (5-27) Figure 5-5 presents a comparison of the results for both, the Rosenblueth and Esteva method and the Withiam method, to determine the reliability index, P. It can be observed that Rosenblueth and Esteva approximation method will yield good values of probability of failure for values of reliability index between 2.0 and 6.0 as recommended by the author of the method. Resistance factor, 0. Once the reliability index, 3, a resistance factor, 0, may be calculated. Assuming lognormal distributions of load and resistance in Eq. 5-5 substituted into Eq. 5-24 gives the follow resistance equation Q I+COV2o +COV2 Q, 1+ COV2 0= RQ n O +CO +CO )]) (5-28) <(';LQL +D LQL) exp f, ln[(++ CO+VQD +C )] where Resistance Factor kR Resistance Bias Factor COVR Resistance Coefficient of Variance PT Target Reliability Index kQD, kQL Bias (Dead and Live Load) QD/QL Dead to Live Load Ratio The dead to live load ratio (QD/QL) in Eq. 5-28 varies with the bridge span. For any bridge the live load is obtain by a standard procedure, while the dead load is based upon the size of the structure. In other words, for the majority of bridges the live loads are mostly constant while the dead loads vary. The dead to live load ratio has been correlated to the span of the bridges by the following representation (Hansell and Viest, 1971): QD QL = (+IM)(0.0132L) (5-29) where QD/QL Dead to Live Load Ratio IM Dynamic Load Allowance Factor (equal 0.33) L Span Length (feet) Table 5-1 presents typical values of bridges span and the corresponding dead to live load ratios. Table 5-1. Values of QD/QL Based on Bridge Span Length Span Length, L Dynamic Load QD/QL (m) Allowance, IM 9 0.33 0.52 18 0.33 1.06 27 0.33 1.58 36 0.33 2.12 45 0.33 2.64 60 0.33 3.53 O/R definition and importance. The axial design capacity of a pile may be represented as (5-30) PDesign = OR, However, from Eq. 5-10, we know the nominal resistance may be expressed in terms of measured value as Rn= m (5-31) LR, Substituting Equation 5-31 into Equation 5-30 the PDesign becomes PDegn Rm (5-32) Equation 5-32 gives the design capacity of a shaft for a specific site. If the bias kRi is replaced by the bias factor kR, (which represents the average of the bias), then the design capacity is directly related to measured resistance (i.e. Davisson's capacity) and the LRFD fitting parameters 4, and ). The 0//R ratio then represent the percentage of Davisson capacity is allowed for design for a given probability of failure. Obviously the higher the ratio fewer piles required and the better the method. CHAPTER 6 LRFD DATA PRESENTATION AND ANALYSIS Data Reduction Prior to determine the LRFD for each dynamic method, a simple statistical analysis was performed. For all the dynamic methods, graphs of measured capacity (Davisson Capacity) related to the estimated capacity at End of Drive (EOD) and Beginning of Restrike (BOR) were constructed. The number of cases for each method was determined based on the availability of parameters needed to obtain the estimated capacity for the corresponding method. The statistic and some of the LRFD results (tables & graphs) from each method are contained within separated Appendices (i.e. Appendix A for all CAPWAP Procedure results, Appendix B for all PDA results, Appendix C for Paikowsky's Energy Method results, etc...) Figures 6-1 and 6-2 present the plots for the PDA at BOR. Figure 6-1 presents a simple graph of PDA BOR capacity versus Davisson Capacity. A line with slope equal 45 degrees has been drawn to facilitate the comparison between the two methods of determining pile capacity. A regression line with the corresponding equation and R2 is shown in the plot. This latter graph is ideal to visually determine how scattered the predictions are for each method. The second graph (Figure 6-2, PDA at BOR) presents the ratio of measured to predicted capacity on the vertical axis and the measured 8000 7000 y = 0.9966x R2= 0.4851 * 6000 - 5000 - 4000 -4 _ 3000 - 2000 -** 1000 -- 0 0 2000 4000 6000 Davisson Capacity (kN) Figure 6-1. Davisson Capacity vs. PDA BOR Capacity 8000 2.5 Cases=42 c 2.0 _ 2.- Mean=1.036 o Standard Dev.=0.32 0. 1.5 - * * S1.0 (0 5 0.5 0.0 0 1000 2000 3000 4000 5000 6000 7000 Davisson Capacity (kN) Figure 6-2. Measured Over Predicted Capacity for PDA at BOR Davisson capacity on the horizontal axis. On each graph, the number of cases for each dynamic method, the mean (or bias factor, kR), and standard deviation, OR, and the ratio of measured to predicted capacity is presented. Appendices A throughout H present the resulting plots for all the methods studied, while Tables 6-7 and 6-8 summarize the number of cases, mean and standard deviation. In addition to the mean and standard deviation, a lognormal probability density function was computed for each method. To assess the latter, Equations 5-14 to 5-16 were used. Figures 6-3 and 6-4 present a summary of the lognormal probability density functions for the eight dynamic methods at EOD and BOR respectively. The lognormal probability density function is used for a resistance distribution of a single pile. However, if it is used for the ratio of measured to predicted capacity, it is a good indicator of how good the method is to reach a desired capacity. For example, by inspection it can be observed that dynamic methods such as ENR and Modified ENR have a very small mean and standard deviation in comparison to the rest of the methods. On the other hand, the Energy (Paikowsky) method has an excellent mean but with a larger standard deviation. Figure 6-4 presents the same analysis for BOR cases, where the same observations can be obtained. At an early stage of this research, it was noted that the old methods (i.e. Gates, FDOT, ENR, and Modified ENR) gave good estimates of the Davisson capacity for piles with Davisson capacity less than 200 tons (1779 kN). This finding is clearly justified because the range of pile capacity in the past did not exceed 1779 kN for driven piles, primarily because of limitation of construction equipment. 3.50 3.00 2.50 2 2.00 1.50 , \ 5 I.UU T 1 2 3 4 5 6 Davisson Capacity / EOD Capacity 0. 0.50 0.00 0 Figure 6-3. Log Normal Probability Distribution at EOD 0 c C3 LL 0 L. - 1 ENR Cases=77 mean=0.30 std. dev=0.16 2 Modified ENR Cases=61 mean=0.45 std. dev=0.27 3 FDOT Cases=72 mean=2.38 std. dev=1.34 4 Gates Cases=74 mean=1.74 std. dev=0.79 - 5 Energy Cases=27 mean=1.11 std. dev=0.37 6 CAPWAP Cases=44 mean=1.60 std. dev=0.56 - 7 PDA Cases=48 mean=1.34 std. dev=0.44 8 Japanese Energy Cases=21 mean=1.50 std. dev=1.26 6 3 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 8 Davisson Capacity / BOR Capacity Figure 6-4. Log Normal Probability Distribution at BOR 7 I A 1 2 5 >7 - 1 ENR cases=71 mean=0.24 std dev=0.16 -2 Modified ENR cases=63 mean=0.36 std dev=0.25 - 3 FDOT cases=63 mean=2.57 std dev=1.29 - 4 Gates cases=71 mean=1.89 std dev=0.72 5 Energy cases=72 mean=0.84 std dev=0.30 6 CAPWAP cases=79 mean=1.26 std dev.=0.44 - 7 PDA cases=42 mean=1.04 std dev=0.32 - 8 Japanese Energy cases=52 mean=1.46 std dev=0.78 It was then decided to study the old methods under three circumstances, first, for piles with Davisson capacity less than 1779 kN, second, for pile with capacity larger than 1779 kN, and finally for the all cases. Based solely on the statistical analysis and the lognormal probability distribution, the assessment of the eight dynamic methods to determine pile capacity could not be successfully completed (i.e. no criterion). The LRFD resistance factor was then recommended to assess the performance of each method. In the next section, a description of the LRFD results is presented. LRFD Analysis of Results In order to obtain the resistance factor, 0, two approaches were considered. The first approach consists of fitting ASD to LRFD, by use of Equation 5-9. For this approach, the 0 factor depends on the safety factor (ASD) and the ratio of dead load to live load for a given bridge. The second approach used was Reliability Calibration (See Chapter 5) in which the 0 factor was determined based on the covariance of the measured to predicted (k, bias), the reliability index, 3, and the ratio of dead load to live load. In order to perform the LRFD analysis, the statistical result calculated earlier became extremely useful. For example, the bias factor (kR) and standard deviation (oR) of the bias were used in addition to the covariance of the resistance (COVR). These parameters were employed with AASHTO's load statistics (see Chapter 5) and the failure probabilities also recommended by AASHTO to obtain the resistance factor, 4. Additional attention was paid to the target reliability index, 3T. For this study, the reliability index was calculated using the Withiam method instead of the Rosenblueth and Esteva method which is the method recommended by AASHTO in their procedure (See Chapter 5). The values recommended in the Withiam method yield an exact reliability index, while the values obtained using the Rosenblueth and Esteva result in an approximate quantity. Thus, the probability of failure, pf, was back calculated from the AASHTO recommended reliability indexes. Table 6-1 all through Table 6-6 show typical output results for each LRFD analysis performed. Tables 6-1 to 6-3 present the results for PDA at EOD, while tables 6- 4 to 6-6 present the commensurate for PDA at BOR. Tables 6-1 and 6-4 summarize the resistance factors, ), evaluated for four different failure probabilities (i.e. reliability indexes) and eight bridge span lengths based on LRFD calibration of the method. Tables 6-2 and 6-5 show the equivalent ASD safety factors based on the resistance factors calculated using the LRFD calibration method for the same bridge span lengths and failure probabilities. Finally, Tables 6-3 and 6-6 present the resistance factor, reliability index and probability of failure that correspond to the actual safety factor that have been used in current ASD procedures. Appendices A throughout H present in detail the LRFD analysis results for each dynamic method studied. Effect of Bridge Span Length and Probability of Failure The bridge span lengths evaluated in this study range from 9.0 to 60.0 meters, each length corresponding to a recommended (AASHTO) dead to live load ratio. After observing the results for the PDA, EOD and/or BOR it is evident that the bridge span length has negligible effect on the resistance factor, ), or the corresponding safety factor. Table 6-1. ( Values Evaluated for PDA (EOD) Span length Failure Probability pf / Reliability Index PT (m) QD/QL 2.50E-02 6.22E-03 1.22E-03 1.79E-04 1.96 2.5 3.03 3.57 9 0.52 0.856 0.694 0.565 0.458 15 1.00 0.821 0.666 0.542 0.439 18 1.06 0.818 0.663 0.540 0.437 27 1.58 0.796 0.645 0.525 0.426 36 2.12 0.781 0.633 0.515 0.418 45 2.64 0.770 0.625 0.508 0.412 50 3.00 0.765 0.620 0.505 0.409 60 3.53 0.758 0.615 0.500 0.405 Table 6-2. ASD Design Safety Factor Values Evaluated for PDA (EOD) Span length Failure Probability pf / Reliability Index pT (m) QD/QL 2.50E-02 6.22E-03 1.22E-03 1.79E-04 1.96 2.5 3.03 3.57 9 0.52 1.845 2.276 2.796 3.449 15 1.00 1.827 2.253 2.769 3.415 18 1.06 1.825 2.251 2.766 3.412 27 1.58 1.814 2.237 2.749 3.391 36 2.12 1.806 2.228 2.738 3.377 45 2.64 1.801 2.221 2.730 3.367 50 3.00 1.798 2.218 2.725 3.362 60 3.53 1.795 2.214 2.720 3.356 Table 6-3. 0 Factors for Safety Factor 2.50 PDA (EOD) Span length (m) QD/QL PT Pf 9 0.52 0.632 2.742 0.0035 15 1.00 0.600 2.767 0.0031 18 1.06 0.597 2.770 0.0031 27 1.58 0.578 2.786 0.0029 36 2.12 0.564 2.797 0.0028 45 2.64 0.555 2.804 0.0027 50 3.00 0.550 2.808 0.0026 60 3.53 0.544 2.813 0.0026 Table 6-4. ( Values Evaluated for PDA (BOR) Span length Failure Probability pr / Reliability Index PT (m) QD/QL 2.50E-02 6.22E-03 1.22E-03 1.79E-04 1.96 2.50 3.03 3.57 9 0.52 0.682 0.557 0.457 0.373 15 1.00 0.654 0.534 0.438 0.358 18 1.06 0.652 0.532 0.436 0.356 27 1.58 0.634 0.518 0.425 0.347 36 2.12 0.622 0.508 0.417 0.340 45 2.64 0.614 0.501 0.411 0.336 50 3.00 0.609 0.498 0.408 0.333 60 3.53 0.604 0.493 0.404 0.330 Table 6-5. ASD Design Safety Factor Values Evaluated for PDA (BOR) Span length Failure Probability pf / Reliability Index pT (m) QD/QL 2.50E-02 6.22E-03 1.22E-03 1.79E-04 1.96 2.50 3.03 3.57 9 0.52 2.316 2.835 3.458 4.234 15 1.00 2.293 2.807 3.424 4.192 18 1.06 2.291 2.805 3.421 4.188 27 1.58 2.277 2.787 3.400 4.163 36 2.12 2.267 2.776 3.386 4.145 45 2.64 2.260 2.768 3.376 4.133 50 3.00 2.257 2.763 3.370 4.127 60 3.53 2.253 2.758 3.364 4.119 Table 6-6. ( Factors for Safety Factor 2.50 PDA (BOR) Span length (m) QD/QL 0 Pf 9 0.52 0.632 2.164 0.0418 15 1.00 0.600 2.191 0.0373 18 1.06 0.597 2.193 0.0369 27 1.58 0.578 2.210 0.0344 36 2.12 0.564 2.221 0.0328 45 2.64 0.555 2.229 0.0317 50 3.00 0.550 2.233 0.0311 60 3.53 0.544 2.238 0.0304 At a target reliability index of 2.5 for both EOD and BOR, the 0 factor decreases only 6.8% and the safety factor decreases only 1.6% when the span length increased from 15.0 meters to 50.0 meters. The latter phenomenon was observed throughout all the methods evaluated. Thus, for practical purposes the rest of LRFD analysis results are summarized for a 27 meters bridge span length. In terms of the probability of failure, pf, the increase in probability of failure was directly related to a decrease in reliability index, 3, and a diminishment in the resistance factor, 4. This effect could be easily understood, because lowering the probability of failure for a given structure should be accompanied by a reduction of the resistance factor, which means, penalizing the structure resistance and producing a more conservative design. Different to the effect of the bridge span length, the reliability index has a big influence in the resistance factor 4, and the equivalent safety factor. The relation of 0 factor and reliability index, 3, is inversely proportional and linear. For piles AASHTO recommends a reliability index, 3, of 2.0 to 2.5. Level of Conservatism and Accuracy Indicators Similar analyses as those presented in Tables 6-1 to 6-6 were performed for each of the eight dynamic methods, as well as breaking the old methods in terms of Davisson capacity less than 1779 kN and larger than 1779 kN. A summary of the results is presented in Tables 6-7 and 6-8 for EOD and BOR respectively. The results show that the higher the bias factor 4R, for a given method the higher the resulting resistance factor will be. For example, for CAPWAP at BOR the mean is equal to 1.260 and 0 is equal to 0.58 (for 3 = 2.50) while FDOT method shows a mean Table 6-7. Load and Resistance Factor Design (LRFD) of Driven Piles Using Dynamic Methods at EOD Prediction Method Number Mean, XR Standard COVR Pf=0.62% (pT=2.50) Pf=2.50% (PT=1.96) of cases (Dav/Pred) Deviation FS /X1R 0 FS /XR1 CAPWAP 44 1.597 0.559 0.350 0.733 1.970 0.459 0.912 1.584 0.571 PDA 48 1.344 0.443 0.329 0.645 2.237 0.480 0.796 1.814 0.592 Paikowsky Energy 27 1.110 0.372 0.335 0.527 2.740 0.475 0.651 2.216 0.587 Sakai et al Energy 21 1.504 1.256 0.835 0.231 6.254 0.153 0.348 4.150 0.231 FDOT (overall) 72 2.381 1.341 0.563 0.669 2.160 0.281 0.909 1.588 0.382 FDOT (<1779 kN) 34 1.490 0.782 0.525 0.457 3.161 0.307 0.611 2.362 0.410 FDOT (>1779 kN) 38 3.158 1.248 0.395 1.307 1.104 0.414 1.658 0.871 0.525 ENR (overall) 77 0.299 0.159 0.532 0.090 16.024 0.301 0.121 11.935 0.405 ENR (<1779 kN) 34 0.250 0.129 0.515 0.078 18.395 0.314 0.105 13.801 0.419 ENR (>1779 kN) 43 0.338 0.171 0.507 0.108 13.388 0.319 0.143 10.074 0.424 Modified ENR (overall) 61 0.446 0.267 0.599 0.115 12.533 0.258 0.159 9.086 0.357 Modified ENR (<1779 kN) 25 0.325 0.222 0.683 0.069 20.818 0.214 0.099 14.604 0.305 Modified ENR (>1779 kN) 36 0.530 0.321 0.606 0.135 10.720 0.254 0.186 7.749 0.352 Gates (overall) 74 1.742 0.787 0.452 0.633 2.280 0.363 0.822 1.756 0.472 Gates (<1779 kN) 32 1.071 0.351 0.328 0.515 2.802 0.481 0.635 2.272 0.593 Gates (>1779 kN) 42 2.254 0.717 0.318 1.109 1.302 0.492 1.361 1.061 0.604 Table 6-8. Load Resistance Factor Design (LRFD) of Driven Piles Using Dynamic Methods at BOR Prediction Method Number Mean, XR Standard COVR Pf=0.62% (pT=2.50) Pf=2.50% (PT=1.96) of cases (Dav/Pred) Deviation FS 3/XR 0 FS /XR1 CAPWAP 79 1.260 0.438 0.347 0.581 2.485 0.461 0.722 1.999 0.573 PDA 42 1.036 0.322 0.311 0.518 2.787 0.500 0.634 2.277 0.612 Paikowsky Energy 72 0.836 0.301 0.360 0.374 3.857 0.448 0.468 3.086 0.560 Sakai et al Energy 52 1.457 0.784 0.538 0.433 3.334 0.297 0.583 2.477 0.400 FDOT (overall) 63 2.574 1.293 0.502 0.832 1.735 0.323 1.103 1.309 0.429 FDOT (<1779 kN) 8 1.355 0.380 0.280 0.724 1.995 0.534 0.875 1.650 0.646 FDOT (>1779 kN) 55 2.751 1.284 0.467 0.966 1.495 0.351 1.262 1.144 0.459 ENR (overall) 71 0.235 0.160 0.681 0.050 28.597 0.215 0.072 20.080 0.306 ENR (<1779 kN) 9 0.186 0.057 0.306 0.094 15.348 0.505 0.115 12.562 0.617 ENR (>1779 kN) 62 0.242 0.169 0.698 0.050 28.841 0.207 0.072 20.120 0.296 Modified ENR (overall) 63 0.363 0.246 0.676 0.079 18.314 0.217 0.112 12.881 0.308 Modified ENR (<1779 kN) 8 0.277 0.062 0.224 0.166 8.704 0.598 0.196 7.356 0.708 Modified ENR (>1779 kN) 55 0.376 0.260 0.692 0.079 18.321 0.210 0.113 12.810 0.300 Gates (overall) 71 1.886 0.715 0.379 0.810 1.783 0.429 1.020 1.416 0.541 Gates (<1779 kN) 9 1.067 0.201 0.189 0.681 2.121 0.638 0.796 1.815 0.746 Gates (>1779 kN) 62 2.005 0.684 0.341 0.938 1.540 0.468 1.162 1.242 0.580 and resistance factor of 2.574 and 0.97 respectively for the same reliability index. This effect could be explained in terms of the bias factors meaning. As defined in the preceding chapters, the bias factor is the ratio of measured to predicted capacity. Then, a large bias factor means a very conservative method and the result is a higher resistance factor. Although the resistance factor is a good qualitative method to determine the degree of conservatism or unconservatism, it does not indicate the accuracy of the method. The combination of both, mean and standard deviation through the COVR (i.e. ratio of standard deviation to the mean or bias) has proved to be a good indicator of the accuracy of the methods. Under this criterion, the new methods such as PDA, Paikowsky, and CAPWAP have the best accuracy, while ENR and modified ENR have the worst accuracy. )/XR Ratio The efficiency or performance of the dynamic methods can be evaluated by the ratio of 0/4R, indicating the percentage of the measured Davisson capacity that can be utilized for design to reach a pre-defined structure reliability. It must be remembered that the average bias factor XR is an average of each pile bias, therefore, 4/XR ratio is an "approximated" percentage of the measured Davisson capacity. The latter consideration makes the 4/XR ratio remarkably valuable from an economic point of view. The higher the O/XR ratio the more cost effective the method is. Methods comparison From Table 6-7 (LRFD Results for Dynamic Methods at EOD) it can be observed that for the reliability index, 3 = 2.50, the 0//R values for the new methods such as CAPWAP (0/4R=0.459), PDA (4/kR=0.480), and Paikowsky (4/kR=0.475) are by far the highest in the table. In the other hand, the lowest 0//R are represented by the old driving formulas, given by FDOT (4/kR=0.281), ENR (0/4R=0.301), Modified ENR (0/,R=0.258), and the Sakai et al. (4/RR=0.153) method. The same trend is observed for a reliability index of 1.96. In Table 6-8 (LRFD Results for Dynamic Methods at BOR) the prior observations are valid, in terms of the trend that was observed for the EOD results. Only one exception was observed in relation to the Gates method whose 4/XR ratio was equal to 0.541 and compares favorable with the new driving methods. EOD versus BOR In general, the 0/R ratio tends to be a little higher at BOR. This effect is easily explained by the value of 4R, which at BOR decreases due to an increase in capacity prediction from the dynamic methods. This effect can be attributed to pile freezing on the pile or dissipation of pore water pressure that are created during the driving of the pile. Evaluation of cases with capacity smaller or larger than 1779 kN After separating the cases with capacity larger than 1779 kN from the cases with capacity smaller than 1779 kN for the old methods, all the statistical and LRFD analysis was performed for each driving equation method. The results are summarized in Tables 6-7 and 6-8. For Gates and FDOT methods, the bias for cases with capacity smaller than 1779 kN tended to be close to unity in comparison to the overall bias which tended to be a higher value. This results agree with the observations on the measured versus predicted capacity plots. For ENR and Modified ENR a decrease in bias was observed, but because these two methods are very unconservative, the bias for cases with capacity smaller than 1779 kN tends to be even more unconservative. In terms of 4/0R, as a general observation, the piles with capacity larger than 1779 kN have larger values than the overall cases, and the piles with capacity smaller than 1779 kN have smaller values than the overall cases. Therefore, the equivalent ASD factor of safety decreases for cases with capacity larger than 1779 kN. An example of this pattern is shown with the Modified ENR at EOD (3 = 1.96), which safety factors decrease from 14.6 for pile with capacity smaller than 1779 kN to 7.75 for piles with capacity larger than 1779 kN. For a reliability index, 3, equals 2.5 the decrease in safety factor is also by a half. Recommended Safety Factors The factor of Safety shown on Tables 6-7 and 6-8 were calculated using Equation 5-9. This procedure makes the FS depend only on the resistance factor, 4, and the bridge span length. The values of FS obtained for EOD and BOR are summarized on Table 6-9, together with the recommended FS. All values were calculated using a 27 meters bridge span length. The recommended FS are the average of the FS found for probabilities of failure of 0.62 % and 2.50 % respectively. From Table 6-9 it can be observed that ENR and Modified ENR methods use higher safety factor than the actual recommended safety factor (FS=6.0). Factor of Safety are as high as 28.60 for a probability of failure of 0.62 percentage for ENR at BOR. This results show that ENR and Modified ENR are very unconservative method (i.e. overestimate the pile capacity). Table 6-9. Recommended Safety Factors for Dynamic Methods FS at FS at FS at FS at Recommended FS Prediction Method pf=0.62% pf=2.50% pf=0.62% pf=2.50% BOR BOR EOD EOD EOD BOR CAPWAP 2.48 2.00 1.97 1.58 1.80 2.25 PDA 2.79 2.28 2.24 1.81 2.00 2.50 Paikowsky Energy 3.86 3.09 2.74 2.22 2.50 3.50 FDOT (overall) 1.74 1.31 2.16 1.59 1.90 1.50 FDOT (<1779 kN) 2.00 1.65 3.16 2.36 2.75 1.80 FDOT (>1779 kN) 1.49 1.14 1.10 0.87 1.00 1.30 ENR (overall) 28.60 20.08 16.02 11.93 14.00 24.00 ENR (<1779 kN) 15.35 12.56 18.40 13.80 16.00 14.00 ENR (>1779 kN) 28.84 20.12 13.39 10.07 12.00 24.00 Modified ENR (overall) 18.31 12.88 12.53 9.09 11.00 16.50 Modified ENR (<1779 kN) 8.70 7.36 20.82 14.60 17.70 8.00 Modified ENR (>1779 kN) 18.32 12.81 10.72 7.75 9.20 16.50 Gates (overall) 1.78 1.42 2.28 1.76 2.00 1.60 Gates (<1779 kN) 2.12 1.81 2.80 2.27 2.50 2.00 Gates (>1779 kN) 1.54 1.24 1.30 1.06 1.20 1.40 The FDOT method recommends a safety factor equals 1, but according to the database, a higher safety factor must be used during design. It is recommended a FS of 1.50 for BOR and 1.90 for EOD. Other methods such as CAPWAP, PDA, and Gates should use a lower FS. For the Paikowsky's Energy method, it is recommended to modify only the safety factor at BOR from 2.50 to 3.50, while at EOD the actual safety factor of 2.50 is appropriated. Table 6-10. Summary of Results for Fitting the ASD to the LRFD Prediction Method ASD LRFD Equiv. ASD Design (EOD) ASD Design (BOR) FS 4/XR p Pf (%) 4/XR p Pf (%) CAPWAP 2.5 0.578 0.362 3.089 0.100 0.458 2.515 0.596 PDA 2.5 0.578 0.430 2.786 0.267 0.557 2.210 1.357 Paikowsky Energy 2.5 0.578 0.520 2.267 1.171 0.691 1.449 7.374 Sakai et al Energy 2.5 0.578 0.384 1.293 9.810 0.396 1.976 2.411 FDOT (overall) 1.0 1.444 0.606 1.146 12.600 0.561 1.445 7.430 FDOT (<1779 kN) 1.0 1.444 0.969 0.369 35.630 1.065 0.536 29.620 FDOT (>1779 kN) 1.0 1.444 0.457 2.274 1.150 0.525 1.688 4.575 ENR (overall) 6.0 0.241 0.805 0.700 24.210 1.024 0.115 45.440 ENR (<1779 kN) 6.0 0.241 0.963 0.395 34.660 1.293 -0.032 51.300 ENR (>1779 kN) 6.0 0.241 0.713 0.976 16.470 0.994 0.146 44.220 Modified ENR (overall) 6.0 0.241 0.540 1.263 10.340 0.662 0.788 21.550 Modified ENR (<1779 kN) 6.0 0.241 0.741 0.605 27.280 0.868 1.306 9.586 Modified ENR (>1779 kN) 6.0 0.241 0.454 1.534 6.258 0.640 0.815 20.770 Gates (overall) 3.0 0.481 0.276 3.067 0.108 0.255 3.718 0.010 Gates (<1779 kN) 3.0 0.481 0.450 2.676 0.363 0.451 3.703 0.010 Gates (>1779 kN) 3.0 0.481 0.214 4.694 0.0001 0.240 4.177 0.0015 ASD Design Evaluation Because Equation 5-9 relates LRFD to ASD in terms only of the bridge span length, and load factors, all methods that use the same safety factor will have the same load resistance factor, 0. These are not the same findings obtained for the reliability index, 3, which depends on the COVR and 4R. Table 6-10 presents the LRFD equivalent load resistance factor, 0, the 0/R ratio, reliability index, 3, and the corresponding probability of failure, pf (percent) for the actual ASD procedure. Using as a reference value the AASHTO's recommended probability of failure for single piles (i.e. 0.62 % for 3 = 2.50 and 2.50% for 3 = 1.96), a comparison of the probability of failures for each method could be performed. First, the ENR and Modified ENR procedures show extremely high probability of failures, which reflect the level of unconservatism as discussed in preceding sections. On the other hand, Gates method shows a probability of failure as low as 0.010 percent, typical of a very conservative method. Other methods such as CAPWAP, PDA, and Sakai show relative good agreement to the recommended probability of failure from AASHTO. CHAPTER 7 SKIN AND TIP STATIC CAPACITY ASSESSMENT OF DRIVEN PILES As discussed in the previous chapter, the PDA Case method was found to be as accurate as the other dynamic methods such as Paikowsky and CAPWAP procedures. This trend was observed for driven piles at both, EOD and BOR. The PDA Case method results depend on the estimated damping coefficient, J,. The recommended values for Jo vary according to the soil type near the tip of the pile. On the other hand, CAPWAP selects the Coefficient of Damping and the pile resistance in such a way that the force trace can be reproduced from the velocity trace. The latter permit CAPWAP to estimate the skin resistance distribution and the tip resistance for any given pile. The estimate of the skin and tip capacity in addition to the distribution of damping and skin friction along the pile from CAPWAP have resulted in its use (scour areas, etc.) versus the PDA, in which only the total static capacity is obtained. However, CAPWAP is a multi-variable program that requires iterations (i.e. time consuming) and a significant level of expertise by the technician who use it. In the next sections, two methods to determine the skin and the tip static capacity from the PDA traces are presented. The results will be compared to the Davisson's capacity determined by the static load test. Method 1 In this method, the GRL procedure to determine the total dynamic skin capacity is used as starting point. The GRL procedure (Likins et. al., 1988) makes use of the pile top measurements of force and velocity histories during a hammer blow as recorded by the PDA. Figure 7-1 illustrates this procedure. ? I r:C Force ----Velocity Time (s) Figure 7-1. GRL procedure to determine the total skin capacity of a driven pile. To obtain the total dynamic skin friction, the rise time must be determined. The rise time is defined as the time between initial rise and the peak. This rise time is used to determine point "b" which is one rise time earlier than time "a". At time "a", the separation between force and velocity (Fa -Z*Va) represents the total pile skin friction above that point on the pile. The point "a" was moved back one rise time from 2 L/c to exclude any reflections from the pile tip of the initial input wave. The assumption of this method is that the skin friction of the bottom one rise length is the same as the one additional rise time length above. Based on that assumption, the skin resistance is the separation of force and velocity at point "a" added to the increase in resistance from point "b" to point "a" as stated below. SFT = (F ZV)+ [(F-ZV (Fb ZVb )] (7-1) Once the estimate of dynamic skin friction is determined using the GRL procedure, as described above, the static tip and skin capacity were calculated according to the following methodology (Method 1). First, the total dynamic capacity, RTL, is determined using the Case solution for dynamic capacity (Equation 3-14 for Jc equals 0). Then, knowing the total dynamic capacity and the GRL estimate of skin dynamic capacity, the dynamic tip capacity, TT, could be computed. TT = RTL SFT (7-2) where TT Dynamic Tip Capacity RTL Total Dynamic Capacity SFT GRL Estimate of Dynamic Skin Capacity Then, the total tip to skin capacity ratio, T/S, may be determined TT T/S TT (7-3) SFT The static skin and tip resistance can be calculated assuming the tip to skin ratio for the dynamic capacity equals to the tip to skin ratio for the static capacity. It is then necessary to define the total static capacity in order to calculate the skin and tip static capacity. For this purpose, the PDA Rmax obtained from the driving records was used. Method 2 (Suggested) Description and Main Assumptions For this method, the tip/skin ratio is obtained directly from the force and velocity traces of the PDA. Figure 7-2 presents an example of a PDA force and velocity traces. This method differs from method 1 in the procedure to obtain the tip to skin ratio. Instead of determining the dynamic skin resistance (GRL procedure) by extrapolating the skin resistance from the rise time before the tip reflection, the method considers the skin capacity prior the tip reflection and the tip reflection itself. For driven piles, when the hammer suddenly hits the pile, a compression wave is produced. This compression wave travels at a constant speed through the pile, reaches the tip, and, depending on the resistance of the pile tip, reflects back as a tension or a compression wave. Before the compression wave reaches the pile tip, a series of compression waves are reflected back to the top due to the skin resistance of the pile. By measuring the Force and Velocity (and velocity multiplied by impedance) at the pile top, the skin resistance can be calculated as the force minus the velocity (twice the wave up). This principle only applies before any reflection from the tip arrives. 73 6000 2L/c 5000 4000 Force Velocity 3000 P V ( 2000 L. 1000 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04, 0.045 0. 5 -1000 -2000 Time (s) Figure 7-2. Typical Force, Velocity and Double Wave up Traces from PDA. In order to determine the time at which the pile tip reflection arrives to the pile top, the rise time must be considered. The rise time accounts for how fast the tip reflection is developed and it will depend on how fast the hammer transmits the energy to the pile top. The larger the rise time, the more difficult to have an estimate of the skin capacity of the pile. Knowing the rise time allows us to determine the skin resistance at a distance "x" from the top of the pile as RT x = L- (7-4) 2c where Length of Pile Below Gages Wave Speed Rise Time Under this consideration all the skin capacity near the tip of the pile (length equals RT/2c) can not be calculated. Figure 7-3 shows the plot of force minus velocity for the same PDA signal presented in Figure 7-2 (i.e. double wave up). After that point in time (point "b") the reflection from the tip begins to arrive. 2500 b 2000 1500 - 500 - NRT 0- 2 Uc -500 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 Time (s) Figure 7-3. Procedure to Determine Tip to Skin Ratio for the Suggested Method 0.05 From point "b" to a time equals 2L/c from the force peak (point "c"), both skin and tip reflections interact creating an abrupt change in the force up trace. The decrease in the force up trace shown in Figure 7-3 corresponds to the increase in velocity and decrease in the force at time 2L/c (see Figure 7-2). This condition is attributed to piles with small tip capacity, and piles that, although they possess large tip capacity, the energy imparted by the hammer is too large to mobilize the tip capacity. The proposed method makes use of the two concepts mentioned to determine the tip to skin ratio. The basic assumption of this method is that the tip/skin ratio is equal to the decrease in the wave up trace from point "b" (time 2L/c minus rise time) to point "c" (time 2L/c from maximum force) divided by the net increase in the wave up trace from point "a" to point "b". The mathematical expression for the proposed method is Tip (F,-ZVJ-(F -z)] (7-5) m [(Fb )-(F Z )] (75) The use of wave up at point "a" is to account for any error in the instrumentation readings. Because a decrease in the wave up is needed to obtain a tip to skin ratio, the hammer must be able to mobilize the whole pile capacity. Case Damping Coefficient, Jc, versus Tip to Skin Ratio In the process of finding a method to obtain the Case damping coefficient, Jc, directly from the PDA signal, the relation between the tip to skin ratio and the Jc value was studied. To do the latter, the measured Davisson's capacity was substituted as RSP in Equation 3-14, and the Jc coefficient was then determined. Subsequently, this damping value was plotted versus the suggested tip to skin ratio. The results are presented in Figure 7-4. Two observations can be made from Figure 7-4. First, for tip to skin ratios smaller than 1.0, the Jc is on the order of 0.4 to 0.6, and there is a tendency for Jc to decrease as the tip to skin ratio is increased. Second, the values of Case damping are scattered. It is believed that there are two reasons for the latter: 1) the hammer may or may not impart enough energy to mobilize the static pile capacity; and 2) PDA capacity predictions assumes pile damping occurs at pile toe which may not always be true. However, as part of this study a sensitivity analysis was performed on the influence of Jc on the static pile capacity (see next section). An important finding of this study is that a 30% variation in Jc results in only a 10 % variation in static pile capacity. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 2.0 4.0 6.0 8.0 10.0 Suggested Tip / Skin Ratio Figure 7-4. Suggested Tip to Skin Ratio versus Case Damping Coefficient Suggested Regression Curve Jc = -0.09744 In (Tip/Skin) + 0.2686 * * * Figure 7-4 shows the regression curve for the Jc. This curve is significant, because it allows us to obtain a Case damping coefficient, Jc, directly from the PDA traces, without taking into consideration the soil type in which the pile is embedded. The suggested equation to correlate tip to skin ratio to Jc is J =-0.097441n Ti +0.2686 (7-6) Because the latter equation was obtained from a comparison with the Davisson's capacity at BOR, it is only recommended for estimating the pile capacity from dynamic tests performed at BOR. Sensitivity Analysis of Case Damping Coefficient, Jc In order to measure how sensitive the Case method resistance (RSP) solution is to the variation of Jo, the coefficient of variance was used. The following steps were followed to obtain a relation between the coefficient of variance for the resistance and the coefficient of variance for J,. Using the Case method solution for the pile resistance, R, the average (bars for average) resistance based on the average value of J.is given as R= 1 [JXF, + ZV)+ (+ (JXF2 -ZV2)] (7-7) 2 If the standard deviation of the resistance is defined in terms of the standard deviation of the Case damping, we obtain oR = J [- (F + ZV)+(F -Z )] (7-8) 2 r Then the covariance of the resistance can be written as follow: COV _R a J[-(F +ZVI)+(F2-ZV2)] (7-9) R 1([-J, F,+ZVI)+ +JX F2 -ZV2,) If we define the constant r| in terms of the force and velocity at time T1 and time T2 (T1 plus 2L/c), then (F1- ZVI ) (2-Z2) (7-10) S(F,+Zv) Next divide the numerator and denominator of Equation 7-10 by the average J, and making the appropriate substitutions for r1 we obtain COV =COVR 1+- 1+- (7-11) 1 2 1-1 Equation 7-11 allows us to determine the variance in the Jo for a given percent of variance in the resistance, or vice-versa. Static and Dynamic Load Test Data The criteria for selecting a load test pile for this study includes the Davisson's failure load from a static load test, and the PDA force and velocity traces. For the dynamic load test, the selected blow was chosen as close to the static load test date as possible (i.e. neglect freeze). For all the cases, the dynamic load test closer to the static load test was performed after the load test (i.e. the static capacity was compared to the Beginning of Restrike). Other requirements include having a measured skin capacity by mean of a pull out static load test or Osterberg load cell test. For each pile, it was required to know both geometric and driving parameters, such as, wave speed, pile length below the gages, cross-sectional area, and material modulus. Based on the latter requirements, 18 test pile were considered. Table 7-1 summarizes general information of each load test pile. The pile population represents 9 sites and 3 diameters, while the range of depths of the piles below the gages varies from 9.15 to 34.45 meters. Only one test pile is from a location outside the State of Florida. Automating the Suggested Method A Fortran program was developed in order to simplify the calculation process. This program is able to read directly from the PDA record the force and velocity signal and perform the data reduction. The input parameters for this program are the length of the pile below the gages, the wave speed, the material modulus, the cross-sectional area, and the data-sampling interval. The output file contains a general description of the pile itself and the driving information entered previously. In addition, it presents in a tabular form the time increment, velocity, force, velocity times impedance, displacement, and double wave up (P ZV). The latter information can be easily plotted to obtain the PDA traces. Appendix I contains the PDA traces (force, velocity, double force up, and displacement) for the signals studied. At the end of the output file, the results from the suggested Table 7-1. Geometric and Driving Information of Load Test Piles File Site Pile Shaft Shaft Wave Material Cross-Sec. Data Sampling Name Location Location Length Diameter Speed Modulus Area Increment (m) (m) (m/s) (kN/m2) (m2) (s) Pascagoula, Mississippi Vilano Bridge Escambria Bridge Buckman Bridge Buckman Bridge Buckman Bridge Buckman Bridge Acosta Bridge Acosta Bridge Acosta Bridge Vilano West Bridge Vilano East Bridge Buckman Bridge Seebreze Bridge Aucilla Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Test Site 4 Test Site 1 Bent 5 / Pile 27 Test Site 13 Test Site 19 Test Site 24 Test Site 29 Pier F6 / Pile 44 Pier G13 / Pile 95 Pier H2 / Pile 26 STA. 142+74 STA. 183+47 STA. 362+90 STA. 353+15 STA. 494+47 Pier FSB3 / Pile 2 Pier 5 / Pile x Pier 11 / Pile 38 Pier 23 / Pile 13 Pier 29 / Pile 7 Pier 35 / Pile 7 Pier 41 / Pile x FSB 26 / Pile 3 34.45 29.88 26.83 33.84 32.74 30.98 29.27 19.21 17.68 10.64 19.05 10.98 9.15 25.91 20.43 24.36 18.63 29.76 29.27 29.00 27.16 24.09 19.82 0.61 0.61 0.61 0.76 0.76 0.76 0.76 0.61 0.61 0.61 0.46 0.46 0.46 0.46 0.46 0.61 0.76 0.76 0.76 0.76 0.76 0.76 0.61 4325.0 3929.9 4425.0 3935.7 3993.9 3937.1 3984.2 3872.0 4325.0 4116.2 4186.6 3730.2 3900.6 3926.6 3993.8 4172.7 4329.3 4643.0 4520.8 4208.8 4292.1 4412.0 4283.2 44905380 37684870 47005420 37184330 38292260 37211220 39470520 35989530 39470519 40656360 42075920 33402750 36523850 37011970 38291580 41796700 43612000 51750160 49062030 42524060 44224220 46728270 44041520 0.37 0.37 0.37 0.48 0.48 0.48 0.48 0.37 0.37 0.37 0.21 0.21 0.21 0.21 0.21 0.37 0.42 0.42 0.42 0.42 0.42 0.42 0.37 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 TS41 TS1B102 B5RS2 TS13A1-A TS19FRCB TS24ALTA TS29RC F6-58A G13-37 H2-27B VLWA-61 D VLE-32C BKM30J BZ83N AUC63K B1-76F PR5R2 B8-97R2 B14-89R2 B17-94R2 PR35FIN B23-76F2 B27-63F method and the GRL procedure are presented. In addition, the important time records such as the time of maximum force, T1, and time T2 (T1 + 2L/c), rise time, etc, are also presented. Appendix J presents an example of the Fortran output. Only the first five pages and the last page of the output are included. Results and Analysis In the following sections, the results from the suggested method will be presented in addition to the results of other methodologies such as method 1, PDA, and the CAPWAP procedure. The reader is referred to Appendix I for the plots of force, velocity, double wave up, and displacement traces for each case studied. In order to evaluate the accuracy of the methods studied, a series of comparison of total static capacity have been performed in relation to the static load capacity. In addition, the predicted skin capacity of the piles was evaluated for piles with performed pullout tests or Osterberg tests in which skin failure occurred. Presentation of Results Table 7-2 summarizes the results for the suggested method and the load tests. The tip to skin ratio is presented together with the recommended Case damping coefficient, J,. Based on these two parameters and using the PDA Case solution, the total capacity was computed. The load test results include the Davisson's capacity for all compression tests and the skin capacity for piles with a performed tensile load test or an Osterberg test with skin failure. Table 7-3 presents the estimated capacities using Method 1 and CAPWAP. Table 7-2. Suggested Method Results and Static Load Test Results File Suggested Method Static Capacities Load Test Results (kN) Name Location Tip/Skin Jc Total Skin Tip Type of Davisson Ratio (kN) (kN) (kN) Test Total Skin Tip Pascagoula, Mississippi Vilano Bridge Escambria Bridge Buckman Bridge Buckman Bridge Buckman Bridge Buckman Bridge Acosta Bridge Acosta Bridge Acosta Bridge Vilano West Bridge Vilano East Bridge Buckman Bridge Seebreze Bridge Aucilla Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge Choctawhatche Bridge 0.33 0.29 0.24 0.27 0.19 0.34 0.16 0.32 0.26 0.10 0.12 0.26 0.05 0.27 0.15 0.29 0.10 0.38 0.24 0.45 0.35 0.14 0.25 5069.7 4140.9 3256.3 5456.4 5279.6 6599.9 4797.8 4096.2 3990.6 3530.5 1403.8 2722.7 1561.5 3244.8 2419.9 3349.8 3722.9 6618.2 4734.1 3196.9 5013.0 4355.2 3547.6 3261.9 2270.8 1389.9 2772.2 1671.2 4455.8 1207.0 2589.1 1948.9 543.1 246.5 1325.2 153.4 1629.5 558.4 1822.7 570.2 4986.3 1997.2 2752.9 3440.3 942.9 1633.8 1807.8 1870.1 1866.4 2684.2 3608.3 2144.1 3590.8 1507.1 2041.7 2987.3 1157.4 1397.5 1408.1 1615.3 1861.4 1527.1 3152.7 1631.9 2736.9 444.0 1572.7 3412.3 1913.8 Osterb.(T&T) Static (C&T) Static (C) Static (C&T) Static (C&T) Static (C&T) Static (C&T) Static (C) Static (C) Static (C) Osterberg Osterberg Osterberg Osterberg Osterberg Static (C) Static (C) Static (C) Static (C) Static (C) Static (C) Static (C) Static (C) 3282.6 4919.5 3780.8 4092.2 4376.8 4892.8 4519.2 3451.6 4964.0 2570.9 n/a n/a n/a n/a n/a 2215.1 5444.4 6360.6 2846.7 4074.4 6485.2 6253.9 4270.1 1316.6 2775.6 n/a 1601.3 1396.7 2490.9 1734.7 n/a n/a n/a 382.5 1150.3 120.1 1470.5 938.5 n/a n/a n/a n/a n/a n/a n/a n/a 1966.0 2143.9 n/a 2490.9 2980.2 2401.9 2784.4 n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a TS41 TS1B102 B5RS2 TS13A1-A TS19FRCB TS24ALTA TS29RC F6-58A G13-37 H2-27B VLWA-61 D VLE-32C BKM30J BZ83N AUC63K B1-76F PR5R2 B8-97R2 B14-89R2 B17-94R2 PR35FIN B23-76F2 B27-63F 0.57 0.8 1.34 0.97 2.16 0.48 2.98 0.58 1.05 5.50 4.70 1.06 9.18 0.99 3.33 0.84 5.53 0.33 1.37 0.16 0.46 3.62 1.17 Table 7-3. CAPWAP, and Method 1 Results File Method 1 CAPWAP Static Results Name Location Tip/Skin Total (PDA) Skin Tip Tip/Skin Total Skin Tip Ratio (kN) (kN) (kN) Ratio (kN) (kN) (kN) TS41 Pascagoula, Mississippi 1.6 4581.4 1785.4 2796.0 2.6 4518.3 1265.9 3252.4 TS1B102 Vilano Bridge 0.1 3433.9 3116.0 317.8 0.3 3915.1 2930.8 984.3 B5RS2 Escambria Bridge 1.1 2526.5 1217.6 1308.9 0.6 2610.1 1623.1 987.0 TS13A1-A Buckman Bridge 0.9 4803.8 2468.6 2335.3 1.1 4007.6 1950.0 2057.6 TS19FRCB Buckman Bridge 1.9 5640.1 1947.5 3692.5 2.1 6510.1 2087.9 4422.2 TS24ALTA Buckman Bridge 9.0 6636.4 661.8 5974.6 0.5 6240.5 4123.7 2116.8 TS29RC Buckman Bridge 3.1 5239.7 1276.1 3963.6 3.6 5115.2 1123.6 3991.6 F6-58A Acosta Bridge 0.3 3771.9 2926.2 845.7 0.1 3474.8 3052.7 422.1 G13-37 Acosta Bridge 1.1 5177.5 2457.7 2719.8 1.2 4826.1 2224.0 2602.1 H2-27B Acosta Bridge 3.2 3967.6 948.1 3019.6 5.2 4091.3 658.3 3433.0 oo VLWA-61D Vilano West Bridge 1.5 1080.9 430.1 650.8 0.9 916.3 494.6 421.7 VLE-32C Vilano East Bridge 0.8 2570.9 1395.0 1176.0 0.9 2691.0 1400.7 1290.4 BKM30J Buckman Bridge 1.5 1961.6 772.6 1189.0 1.2 1939.3 881.6 1057.7 BZ83N Seebreze Bridge 0.2 2628.8 2183.4 445.4 0.3 2361.9 1774.8 587.1 AUC63K Aucilla Bridge 4.6 1757.0 313.4 1443.6 0.7 1823.7 1045.3 778.4 B1-76F Choctawhatche Bridge 0.0 3220.4 3233.3 -12.9 0.2 2231.6 1907.3 324.3 PR5R2 Choctawhatche Bridge 8.7 3255.9 334.7 2921.2 6.0 2596.3 371.0 2225.3 B8-97R2 Choctawhatche Bridge 1.4 4554.8 1863.6 2691.1 0.2 3621.6 3033.1 588.5 B14-89R2 Choctawhatche Bridge 0.5 3131.4 2029.4 1102.0 0.1 1975.4 1802.3 173.0 B17-94R2 Choctawhatche Bridge 0.0 3700.7 3780.1 -79.4 0.0 3452.5 3288.9 163.7 PR35FIN Choctawhatche Bridge 0.3 4661.5 3650.4 1011.1 0.3 4045.0 3231.9 813.1 B23-76F2 Choctawhatche Bridge -7.9 4448.0 -645.7 5093.7 3.8 2155.9 453.7 1702.2 B27-63F Choctawhatche Bridge 0.8 2673.2 1452.1 1221.2 3.6 2503.3 542.2 1961.1 8000 7000 6000 5000 4000 3000 2000 0 1000 2000 3000 4000 5000 6000 7000 8000 Davisson Capacity (kN) Figure 7-5. Davisson Capacity vs. Suggested Method Capacity 0 1000 2000 3000 4000 5000 6000 7000 8000 Davisson Capacity (kN) Figure 7-6. Davisson Capacity vs. CAPWAP Capacity Number of Cases = 18 Mean = 1.00 Std. Dev. = 0.29 COV = 0.29 8000 7000 6000 z 5000 U 0. S3000 U 4 2000 1000 0 8000 7000 6000 S5000 S 4000 W, 3000 200 Number of Cases = 18 Mean = 1.09 Std. Dev. = 0.35 1000 COV = 0.32 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Davisson Capacity (kN) Figure 7-7. Davisson Capacity vs. PDA Rmax Capacity (used in Method 1) The total dynamic capacity was obtained using the Case solution for time T1 located at the maximum force entering the pile. Then, the tip and the tip to skin ratio were calculated using Equations 7-2 and 7-3. With this tip to skin ratio and the PDA Rmax the static skin and tip capacity for the Method 1 were calculated. A series of figures show the results from the three methods studied, i.e. CAPWAP, Method 1 (using PDA Rmax), and the suggested method in comparison with the measured capacity. Figure 7-5 shows the Davisson's capacity versus the estimated capacity by the suggested method. The CAPWAP estimated capacity versus the Davisson's capacity is presented in Figure 7-6, and the same relation for the PDA estimated capacity is presented in Figure 7-7. Analysis of Total Capacity Predictions For the total capacity analysis, only 18 cases out of 23 cases were used. The bias factor kR, the standard deviation, a, and the coefficient of variance, COVR, were calculated (see bias factor, standard deviation, and coefficient of variance definition on Chapter 5). Table 7-4 presents the findings for the three methods studied. Table 7-4. Comparison of Mean, Standard Deviation, and COVR. Method Mean, XR Std. Dev. o COVR Suggested 1.00 0.29 0.29 Method CAPWAP 1.28 0.58 0.45 Method 1 1.09 0.35 0.32 It should be noted that although the number of cases studied are only 18, the mean, standard deviation, and coefficient of variance for CAPWAP and PDA show good agreement with the database. According to the database, for PDA capacity at BOR the mean, standard deviation, and COV are 1.04, 0.32 and 0.31 respectively. For CAPWAP at BOR the mean is 1.26, the standard deviation is 0.44, and the COVR is 0.35. From Table 7-4, it can be observed that the best method to estimate the Davisson's capacity is the suggested method with a mean value of 1.0 (it is important to remember that the suggested method was calibrated to have a mean value of 1.00). The PDA underestimated the Davisson's capacity by 9 percent, while the CAPWAP procedure underestimated the Davisson's capacity by 26 percent at BOR. In Chapter 6, it has been explained how the coefficient of variance could be a useful tool to measure the accuracy of a dynamic method. Making use of this criterion, the suggested method (COVR equals 0.29) can be considered the most accurate of the three methods followed by the PDA (COVR equals 0.32). The CAPWAP procedure was the less accurate of the three methods (COVR equals 0.45). Analysis of Skin and Tip Capacity Predictions The number of cases to evaluate the skin and tip predictions is much smaller than the number of cases used for total capacity prediction. For the skin prediction, the total number of cases is 10, while for the tip prediction the number of cases drops to only six. The reason for this decrease in number of cases is the limited number of tensile test and Osterberg tests. From the six Osterberg tests, one test failed at the tip and five failed at the skin). The tensile tests are very helpful to determine the skin capacity. With the skin capacity calculated, and knowing the total static capacity the tip capacity can be calculated. Table 7-5. Statistical Analysis for Skin and Tip Predictions Method Skin Capacity Prediction (10 Cases) Tip Capacity Prediction (6 Cases) Mean, XR Std. Dev. o COVR Mean, XR Std. Dev. o COVR Suggested 1.04 0.40 0.39 0.96 0.16 0.17 Method CAPWAP 0.80 0.35 0.43 1.08 0.59 0.55 Method 1 1.29 1.15 0.89 1.94 2.47 1.27 5000 4500 4000 C 3500 c 3000 2500 2000 o b Number of Cases= 10 1500 - 1500 Mean = 1.04 I* Std. Dev. = 0.40 S1000 COV = 0.39 500 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Davisson Skin Capacity (kN) Figure 7-8. Davisson Capacity vs. Suggested Method Capacity (Skin Capacity) 5000 4500 4000 z 3500 ' 3000 o 2500 S2000 - (L Number of Cases = 10 1500 Mean = 0.80 0 Std. Dev. = 0.35 0 1000 COV = 0.43 500 - 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Davisson Skin Capacity (kN) Figure 7-9. Davisson Capacity vs. CAPWAP Capacity (Skin Capacity) 89 5000 4500 4000 3500 3000 ., 2500 0 Number of Cases = 10 V Mean = 1.29 1500 Std. Dev. = 1.15 z 1500 SCOV = 0.89 1000 500 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Davisson Skin Capacity (kN) Figure 7-10. Davisson Capacity vs. Method 1 Skin Capacity 6000 - 5000 z S4000 C-, .E * 3000 "0 2000 20 Number of Cases = 6 SStd. Dev. = 0.16 S1000 COV= 0.17 0 0 1000 2000 3000 4000 5000 6000 Davisson Tip Capacity (kN) Figure 7-11. Davisson Capacity vs. Suggested Method (Tip Capacity) 90 6000 5000 . 4000 .5 U . 3000 CL Number of Cases = 6 2000- Mean = 1.08 2 00 Std. Dev. = 0.59 0 COV= 0.55 1000 * 0 0 1000 2000 3000 4000 5000 6000 Davisson Tip Capacity (kN) Figure 7-12. Davisson Capacity vs. CAPWAP Capacity (Tip Capacity) 6000 - 5000 z , 4000 o a 3000 "o Number of Cases = 6 | 2000 Mean = 1.94 Std. Dev. = 2.47 COV = 1.27 1000 0 0 1000 2000 3000 4000 5000 6000 Davisson Tip Capacity (kN) Figure 7-13. Davisson Capacity vs. Method 1 Capacity (Tip Capacity) |