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- Permanent Link:
- https://ufdc.ufl.edu/UF00097392/00001
## Material Information- Title:
- Applications of the electronic cone penetration test for the geotechnical site investigation of Florida soils
- Creator:
- Knox, Kenneth James, 1955- (
*Dissertant*) Townsend, Frank C. (*Thesis advisor*) Davidson, John L. (*Reviewer*) McVay, Michael C. (*Reviewer*) Boomquist, David (*Reviewer*) Wilson, Joseph N. (*Reviewer*) Shafer, D. J. (*Degree grantor*) - Place of Publication:
- Gainesville, Fla.
- Publisher:
- University of Florida
- Publication Date:
- 1989
- Copyright Date:
- 1989
- Language:
- English
- Physical Description:
- xvi, 246 leaves : ill. ; 28 cm.
## Subjects- Subjects / Keywords:
- Autocorrelation ( jstor )
Databases ( jstor ) Datasets ( jstor ) Landfills ( jstor ) Modeling ( jstor ) Penetrometers ( jstor ) Regression analysis ( jstor ) Silts ( jstor ) Soil properties ( jstor ) Soils ( jstor ) Civil Engineering thesis Ph. D Dissertations, Academic -- Civil Engineering -- UF Penetrometer ( lcsh ) Soil penetration test ( lcsh ) Soils -- Florida ( lcsh ) Soils -- Testing ( lcsh ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt ) theses ( marcgt )
## Notes- Abstract:
- The purpose of this research project was to evaluate techniques to improve the application of in situ penetration testing to Florida soils, with emphasis on the electronic cone penetrometer test (ECPT). Topics addressed included describing the spatial variability of soil properties, classifying Florida soils with the ECPT, and correlating the ECPT with the standard penetration test (SPT). A collateral purpose was to create an in situ test data base consisting of 97 ECPT soundings and 79 SPT tests. This data base was subsequently evaluated using statistical analysis. The spatial variability study was carried out to evaluate methods of interpolation between test soundings. The techniques studied included three deterministic approaches (the mean, median, and a 10% trimmed average), three distance-weighting methods (two based on reciprocal distances, and linear interpolation), a random field model (a hybrid distance-weighting/regression model), and regression analysis. While none of the approaches stood out as consistently superior predictors, the deterministic approaches were generally inferior to the other, more sophisticated methods. The distance-weighting methods and the random field model performed comparably, but were sensitive to individual test soundings. The regression models predicted slightly better on the average, and with more stability. The ECPT classification study used parametric and nonparametric discriminant analysis of cone data on soils that had been identified from the SPT test. The ECPT was able to group soil accurately into one of seven categories (organics, clay, silt, clayey sand, silty sand, sand, weathered rock) approximately 40% of the time. This percentage increased to 70% when the three sand categories were combined, reflecting the SPT drillers' difficulties in discriminating silty soils. In the SPT-ECPT correlation study, average q^/N ratios for Florida soils were much higher than expected, possibly due to cementation or liquefaction. Regression analysis of the data suggested that the nature of the SPT-ECPT relationship is more a function of the magnitude of the tip resistance, and less of the actual soil type.
- Thesis:
- Thesis (Ph. D.)--University of Florida, 1989.
- Bibliography:
- Includes bibliographical references (leaves 238-243)
- Additional Physical Form:
- Also available on World Wide Web
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Kenneth James Knox.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 001514186 ( alephbibnum )
21887377 ( oclc ) AHC7193 ( notis )
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APPLICATIONS OF THE ELECTRONIC CONE PENETRATION TEST FOR THE GEOTECHNICAL SITE INVESTIGATION OF FLORIDA SOILS By KENNETH JAMES KNOX A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF -THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1989 UNIVERSITY OF FLORIDA I II llI I II2 l 0 ll lllll 1lllll 3 1262 08552 3198 DEDICATED WITH ALL MY LOVE TO MY WIFE, PAT, AND TO MY WONDERFUL CHILDREN, BRIAN AND KELLY, FOR THEIR DEVOTED LOVE, PATIENCE, AND SUPPORT. ACKNOWLEDGMENTS So many people had a direct and significant impact on my studies and research at the University of Florida that I am reluctant to attempt to write the acknowledgments section for fear of omitting a key contributor. Nevertheless, fear must never be allowed to impede progress and worthwhile endeavors; therefore, please forgive my less- than-perfect memory if I fail to acknowledge someone, and know that I am deeply indebted to and appreciative of everyone I have been associated with these past three years. I would like to express my deepest gratitude to the members of my supervisory committee. In particular, I would like to thank Dr. Frank C. Townsend for serving as my chairman, and for being a true friend and professional. While the wealth of knowledge I have managed to glean from him will undoubtedly serve me well in the future, I value even more his perspectives on the responsibilities of a doctorate, and on the future of education in America. I am also grateful to Dr. David Bloomquist not only for serving on my committee, but also for the abundance of help he provided me, especially regarding operation of the cone testing equipment and preparation of this dissertation. "Dave's" amazing breadth of knowledge and his "Let's do it!" attitude are invaluable assets to all who have the pleasure of working with him. I would like to thank Dr. John L. Davidson for serving on my committee, and for being a ready and willing source of information. I also hope to absorb some of Dr. Davidson's superb teaching style in my own return to teaching. Special thanks are extended to Dr. Joseph N. Wilson of the Department of Computer and Information Sciences for being an old friend of the family and for serving as my external committee member. I have purposely left Dr. Michael C. McVay to the end of my committee members. Dr. McVay was singularly instrumental in, and the driving force behind every phase of my research. He insured that I had the resources I needed to accomplish the work. Dr. McVay constantly challenged and encouraged me throughout the project, and the final product is a direct result of his interest not only in the research, but also in me. My deepest thanks are extended to Dr. McVay for his support. I pray that some of Dr. McVay's thirst for knowledge will rub off on me when I depart the University of Florida. Many geotechnical engineers in the State of Florida unselfishly offered extensive help in support of my research, and I am grateful. This project would have been impossible without them. In particular, I would like to thank Dr. Joseph A. Caliendo, Chief Geotechnical Engineer with the Florida Department of Transportation (FDOT). He was a true friend and invaluable resource. Equally invaluable was the unbelievable assistance offered by Mr. William F. Knight and Mr. Sam Weede of the FDOT's Chipley office. They literally opened up their entire operation to me despite a crushing workload. My sincerest thanks are also extended to Mr. Lincoln Morgado and Mr. Bob Raskin of the FDOT's Miami office, Dr. John H. Schmertmann and Dr. David K. Crapps with Schmertmann and Crapps of Gainesville, Mr. Bill Ryan with Ardaman and Associates of Sarasota, Mr. Richard Stone, Jr., with Law Engineering of Naples, Mr. Jay Casper with Jammal and Associates of Orlando, and Mr. Kevin Kett with Law Engineering in Jacksonville. iv A key contributor to my research was Mr. Ed Dobson, Engineering Technician with the Civil Engineering Department. Ed accompanied me on all of the trips, and proved to be a hard and able worker. His humor and contributions are greatly appreciated. The friendship and support of my many graduate student colleagues are also acknowledged. In particular, I would like to thank my mentor, friend, and fellow Air Force officer, Dr. John Gill. His advice and support were instrumental to my success. I also thank my other Air Force friends, including Dr. Charlie Manzione, Greg Coker, and Bill Corson. I thank Dr. Ramon Martinez, Fernando Parra, and Guillermo Ramirez for their support, friendship, and patience with my Spanish. I am also indebted to my friends Bob Casper, Curt Basnett, Chris Dumas, David Springstead, Michelle Warner, and David Seed, all of whom directly contributed to this research. I would like to express my sincerest appreciation to the United States Air Force for making this doctorate possible. In particular, I would like to express my thanks to the U.S. Air Force Academy and Colonel (Dr.) David 0. Swint, Professor and Head of the Academy Department of Civil Engineering. They helped make my dream come true. Lastly, but not least by a long shot, I would like to thank my wonderful family for their endless devotion and support. Completion of my doctorate would not have been possible without my wife Pat's undying love, nurturing, prodding, scolding, supporting, and caring for me. My little buddy, Brian, and my lovely little girl, Kelly, were bottomless sources of joy to me when I most needed a lift. This doctorate truly belongs to all of them. TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................... iii LIST OF TABLES .................................................... ix LIST OF FIGURES .................................................... xi ABSTRACT ........................................................... xv CHAPTERS I INTRODUCTION ................................................ 1 Purpose of Research.......................................... 3 Research Methodology......................................... 4 2 PROJECT DATA BASE ........................................... 6 Introduction ................................................. 6 Extent of Data Base.......................................... 7 Site Descriptions ........................................... 9 Apalachicola River and Bay Bridges (Sites 001 003)....... 9 Overstreet Bridge (Sites 004 005)........................ 10 Sarasota Garage and Condo (Sites 006 008)................ 10 Sarasota Landfill (Site 009) ............................... 14 Fort Myers Interchange (Sites 010 011)................... 14 Fort Myers Airport (Site 012) .............................. 17 Port Orange (Sites 013 014) .............................. 17 West Palm 1-95 (Sites 015 018) ........................... 17 Choctawhatchee Bay (Sites 019 021)....................... 21 White City (Site 022) ...................................... 21 Orlando Arena (Site 023) ................................... 21 Orlando Hotel (Sites 024 026)............................ 24 Jacksonville Terminal (Sites 027 028).................... 24 Archer Landfill (Site 029) ................................. 26 West Bay (Site 030) ........................................ 26 Lake Wauberg (Site 031) .................................... 26 Collection of ECPT Data...................................... 28 Equipment .................................................. 28 Procedures ................................................. 31 Problems Encountered ...................................... 31 3 LOCAL VARIABILITY IN CONE PENETROMETER TEST MEASUREMENTS..... 40 Introduction ................................................. 40 Local Variability Data Base.................................. 41 Data Filter ................................................. 43 Evaluation of Data Scatter................................... 45 4 DESCRIBING THE SPATIAL VARIABILITY OF SOILS ................. 52 Introduction.................................... ............ 52 Descriptive Statistics for Spatial Variability............... 53 Summarizing a Data Set..................................... 53 Describing Variability..................................... 54 Measuring Association...................................... 55 Estimation Models. .......................................... 58 Traditional Choices ....................................... 58 Random Field Models..................... .................. 59 5 EVALUATION OF THE SPATIAL VARIABILITY MODELS................. 68 Application of Estimation Models............................. 68 Evaluation Criteria ........................................ 68 Data Manipulation .......................................... 69 Autocorrelation Function ................................. 71 Model Types ................................................ 72 Sites Investigated ......................................... 76 Results and Discussion ....................................... 83 Choctawhatchee Bay Site .................................... 83 Apalachicola River Site .................................... 97 Archer Landfill Site ....................................... 106 Discussion of Results ...................................... 112 6 COMPARISON OF 10-TON AND 15-TON FRICTION-CONE PENETROMETER TIPS ....................................................... 124 Introduction ................................................ 124 Size Comparability Study Data Base .............. ............ 125 Evaluation of Data Scatter .............................. 126 7 CLASSIFICATION OF FLORIDA SOILS USING THE ECPT............... 129 Introduction ................................................ 129 Current Practice ............................................. 131 Measurement Considerations ................................. 131 Typical Classification Systems ........................... 132 Analysis Approach.................................... 134 Data Base Creation ................................... 134 Discriminant Analysis............................... 139 Results and Discussion............ ......................... .. 141 Data Transformation ........................................ 141 Data Sets .................................................. 142 Laboratory Data Analysis .... ................. 143 Discriminant Analysis of Field Measurements............... 149 Recommended Classification Scheme................ ..... 154 8 SPT-ECPT CORRELATIONS FOR FLORIDA SOILS..................... 159 Introduction ................................................ 159 SPT-ECPT Data Base........................................... 161 Data Analysis ............................................... 163 Exploratory Data Analysis.................................. 163 Regression Analysis........................................ 164 9 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH.......... 168 Summary and Conclusions...................................... 168 Recommendations for Future Research ......................... 172 APPENDICES A INDEX TO IN SITU TEST DATA BASE.............................. 175 B PENETROMETER TIP MEASUREMENTS AND UNEQUAL END AREA CALCULATIONS .............................................. 191 C SUMMARY OF LABORATORY CLASSIFICATION OF SOILS................ 193 D DISCRIMINANT ANALYSIS CLASSIFICATION SUMMARIES............... 197 E COMPUTER PROGRAM LISTINGS .................................... 212 E-1. PROGRAM FILTER......................................... 213 E-2. PROGRAM NORMAL......................................... 214 E-3. PROGRAM RANDOM......................................... 218 E-4. PROGRAM AUTOCOR........................................ 220 E-5. PROGRAM AUTOCOR2....................................... 222 F STEPWISE REGRESSION SUMMARIES................................ 224 BIBLIOGRAPHY ....................................................... 238 BIOGRAPHICAL SKETCH................................................ 244 LIST OF TABLES Table paqe 2-1. Data Base Summary ........................................... 9 3-1. Data Base for Local Variability Study ....................... 43 3-2. Results of Local Variability Study......................... 48 5-1. Deterministic Model Parameters for Choctawhatchee Bay Site.. 86 5-2. Regression Models for the Prediction of Cone Resistance at the Choctawhatchee Bay Site ............................. 87 5-3. Regression Models for the Prediction of Friction Resistance at the Choctawhatchee Bay Site........................... 88 5-4. Results of qc Analysis at Choctawhatchee Bay ............... 89 5-5. Results of fs Analysis at Choctawhatchee Bay ............... 89 5-6. Comparison of Transformed and Nontransformed Approaches at Choctawhatchee Bay ........................................ 93 5-7. Deterministic Model Parameters for Apalachicola River Site.. 99 5-8. Regression Models for the Prediction of the SPT N-Value at the Apalachicola River Site................ ............ 100 5-9. Results of Spatial Variability Study at Apalachicola River.. 101 5-10. Comparison of Transformed and Nontransformed Approaches at Apalachicola River ........................................ 103 5-11. Deterministic Model Parameters for Archer Landfill Site..... 108 5-12. Regression Models for the Prediction of Cone Resistance at the Archer Landfill Site.................. .............. 108 5-13. Regression Models for the Prediction of Friction Resistance at the Archer Landfill Site............................... 109 5-14. Results of Spatial Variability Study at Archer Landfill Site Using Transformed Data .................................... 109 5-15. Comparison of Regression Model RMSE with Prediction RMSE.... 120 6-1. Data Base for Size Comparability Study..................... 126 6-2. Results of Size Comparability Study........................ 128 7-1. Soil Types in Classification Data Base..................... 137 7-2. Soil Classification Data Base ............................ 138 7-3. Summary of Laboratory Tests on SPT Samples ................. 139 7-4. Accuracy of SPT Soil Types................................ 143 7-5. Accuracy of Discriminant Analysis Approaches ............... 153 8-1. SPT-ECPT Data Base .......................................... 162 8-2. Exploratory Data Analysis of qc/N Ratios ................... 164 8-3. Results of SPT-ECPT Regression Analysis .................... 166 8-4. Descriptive'Statistics for log(N) in Units of log(blows/ft). 168 LIST OF FIGURES Figure agqe 2-1. Cities Represented in Pile Data Base ....................... 8 2-2. Apalachicola River Bridge SPTs Used for Spatial Variability Studies ................................................... 11 2-3. Apalachicola River Bridge Pier 3 Tests ....................... 11 2-4. Apalachicola River Bridge Flat Slab Bent 16 Tests........... 12 2-5. Apalachicola Bay Bridge Flat Slab Bent 22 Tests............. 12 2-6. Overstreet Bridge Pier 11 Tests............................. 13 2-7. Overstreet Bridge Pier 16 Tests ............................ 13 2-8. Sarasota Garage Tests ....................................... 15 2-9. Sarasota Condo Tests ........................................ 16 2-10. Fort Myers Interchange Tests ............................. 16 2-11. Port Orange Bent 19 Tests ................................ 18 2-12. Port Orange Bent 2 Tests .................................. 18 2-13. West Palm 1-95 Pier B-4 Tests............................. 19 2-14. West Palm 1-95 Pier B-6 Tests ............................. 19 2-15. West Palm 1-95 Pier B-9 Tests .............................. 20 2-16. West Palm 1-95 Pier C-2 Tests .............................. 20 2-17. Choctawhatchee Bay South Tests............................. 22 2-18. Choctawhatchee Bay North Tests............................. 22 2-19. White City South Tests ...................................... 23 2-20. White City North Tests ...................................... 23 2-21. Orlando Arena Tests ................ ......................... 25 2-22. Orlando Hotel Tests ......................................... 25 xi 2-23. Archer Landfill Tests ....................................... 27 2-24. West Bay Tests .............................................. 27 2-25. Subtraction-Type Electronic Friction-Cone P6netrometer...... 29 2-26. The UF Penetration Testing Vehicle.......................... 29 2-27. Calibration for 5-Ton Friction-Cone Penetrometer............ 34 2-28. Calibration for 10-Ton Friction-Cone Penetrometer........... 35 2-29. Calibration for 15-Ton Friction-Cone Penetrometer........... 36 3-1. Typical Matched Soundings for Local Variability Study....... 42 3-2. Cone Resistance Data for Local Variability Study............ 44 3-3. Friction Resistance Data for Local Variability Study........ 44 3-4. Effect of Average-Value Data Filter ........................ 46 3-5. Cone Resistance Data After Data Filtering .................. 47 3-6. Friction Resistance Data After Data Filtering............... 47 3-7. Residual Analysis and Proposed Standard Deviation for q .... 50 3-8. Residual Analysis and Proposed Standard Deviation for fs.... 51 4-1. Critical t-Values for Two-Sided Confidence Intervals........ 56 4-2. Critical Values for Testing Significance of Correlation Coefficient ............................................... 56 4-3. Random Field Model Concept.................................. 60 4-4. Typical Experimental Semi-Variogram of Normalized Data...... 62 4-5. Typical Experimental Autocorrelation Function............... 64 5-1. Effect of Data Transformation on Cone Resistance Data at Choctawhatchee Bay Site................................. 70 5-2. Spatial Variability Soundings at Choctawhatchee Bay......... 77 5-3. Autocorrelation Function for Normalized Raw Data at Choctawhatchee Bay ........................................ 77 5-4. Spatial Variability Soundings at Apalachicola River......... 80 5-5. Autocorrelation Function for Normalized Raw Data at Apalachicola River ........................................ 80 5-6. Spatial Variability Soundings at Archer Landfill............ 82 5-7. Autocorrelation Function for Normalized Raw Data at Archer Landfill .................................................. 82 5-8. Final Autocorrelation Function for Choctawhatchee Bay....... 84 5-9. Final Autocorrelation Function for Choctawhatchee Bay Using Transformed Data Set................ ................... 84 5-10. Prediction RMSEs for Cone Resistance at Choctawhatchee Bay.. 90 5-11. Prediction RMSEs for Friction Resistance at Choctawhatchee Bay ........................................ 91 5-12. Prediction of fs for Sounding J Using a Weighting Model (a/d) at Choctawhatchee Bay............................... 94 5-13. Prediction of qc for Sounding E Using Various Regression Models at Choctawhatchee Bay.............................. 95 5-14. Prediction of fs for Sounding H Using High Term Regression with Transformed and Regular Data at Choctawhatchee Bay... 96 5-15. Final Autocorrelation Function for Apalachicola River....... 98 5-16. Final Autocorrelation Function for Apalachicola River Using Transformed Data Set ...................................... 98 5-17. Prediction RMSEs for SPT N-Values at Apalachicola River..... 102 5-18. Prediction of N for Sounding #16 Using Various Distance- Weighting Models at Apalachicola River ................... 104 5-19. Prediction of N for Sounding #19 Using Various Regression Models at Apalachicola River.............................. 105 5-20. Final Autocorrelation Function for Archer Landfill Using Transformed Data Set ...................................... 107 5-21. Prediction RMSEs for Cone Resistance at Archer Landfill..... 110 5-22. Prediction RMSEs for Friction Resistance at Archer Landfill. 111 5-23. Prediction of qc for Sounding #5 Using Various Distance- Weighting Models with Transformed Data at Archer Landfill. 113 5-24. Prediction of fs for Sounding #4 Using Various Regression Models with Transformed Data at Archer Landfill........... 114 5-25. Comparison of Prediction Methods (Normalized) .............. 118 5-26. Example of Average Error Estimate--Prediction of qc at Choctawhatchee Bay Sounding J Using Low Term Regression... 123 6-1. Cone Resistance Data for Size Comparability Study .......... 127 6-2. Friction Resistance Data for Size Comparability Study....... 127 7-1. Robertson and Campanella's Simple Soil Classification Chart. 133 7-2. Douglas and Olsen's More Complex Soil Classification Chart.. 133 7-3. Discrete Soil Classification Chart......................... 135 7-4. Soil Classification Chart Normalized for Overburden......... 136 7-5. Laboratory Classification Data Plotted with ECPT Data....... 145 7-6. Laboratory Classification Data Plotted with ECPT Data Normalized for Overburden............................... 146 7-7. Discriminant Analysis of Laboratory Data Using NEIGHBOR Procedure................................................. 147 7-8. Discriminant Analysis Using NEIGHBOR Procedure of Laboratory Data Normalized for Overburden........................... 148 7-9. Discriminant Analysis Using DISCRIM Procedure of Laboratory Data Normalized for Overburden........................... 150 7-10. General Trends of the Soil Classification Data Set.......... 151 7-11. DISCRIM Discriminant Analysis on Data Classified by Category 155 7-12. NEIGHBOR Discriminant Analysis on Data Classified by Category.................................................. 156 7-13. Recommended ECPT Soil Classification Chart for Florida Soils 158 8-1. Variation of qc/N Ratio with Mean Grain Size ............... 160 8-2. Results of qc/N Ratio Study................................. 165 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy APPLICATIONS OF THE ELECTRONIC CONE PENETRATION TEST FOR THE GEOTECHNICAL SITE INVESTIGATION OF FLORIDA SOILS By KENNETH JAMES KNOX August 1989 Chairman: Dr. Frank C. Townsend Major Department: Civil Engineering The purpose of this research project was to evaluate techniques to improve the application of in situ penetration testing to Florida soils, with emphasis on the electronic cone penetrometer test (ECPT). Topics addressed included describing the spatial variability of soil properties, classifying Florida soils with the ECPT, and correlating the ECPT with the standard penetration test (SPT). A collateral purpose was to create an in situ test data base consisting of 97 ECPT soundings and 79 SPT tests. This data base was subsequently evaluated using statistical analysis. The spatial variability study was carried out to evaluate methods of interpolation between test soundings. The techniques studied included three deterministic approaches (the mean, median, and a 10% trimmed average), three distance-weighting methods (two based on reciprocal distances, and linear interpolation), a random field model (a hybrid distance-weighting/regression model), and regression analysis. While none of the approaches stood out as consistently superior predictors, the deterministic approaches were generally inferior to the other, more sophisticated methods. The distance-weighting methods and the random field model performed comparably, but were sensitive to individual test soundings. The regression models predicted slightly better on the average, and with more stability. The ECPT classification study used parametric and nonparametric discriminant analysis of cone data on soils that had been identified from the SPT test. The ECPT was able to group soil accurately into one of seven categories organicc, clay, silt, clayey sand, silty sand, sand, weathered rock) approximately 40% of the time. This percentage increased to 70% when the three sand categories were combined, reflecting the SPT drillers' difficulties in discriminating silty soils. In the SPT-ECPT correlation study, average qc/N ratios for Florida soils were much higher than expected, possibly due to cementation or liquefaction. Regression analysis of the data suggested that the nature of the SPT-ECPT relationship is more a function of the magnitude of the tip resistance, and less of the actual soil type. CHAPTER 1 INTRODUCTION Seeking solutions to the problems of transferring superstructure loads to the supporting ground is typically the responsibility of the geotechnical engineer. Solutions to this interface problem are many and diverse depending on the nature and magnitude of the loads involved; the geology of the site; and the economic, environmental, and political climate of the project. The economic impact of foundations can be considerable. Vanikar reports that nearly 20% of approximately 2.6 billion dollars worth of highway construction by the Federal Highway Administration and the state transportation departments in fiscal year 1984 was spent on foundations (62). In all but the simplest of projects, a site investigation of the underground conditions is necessary. This investigation, which usually costs between 0.5 and 1% of the total construction costs (8), should provide the geotechnical engineer with enough information to characterize the site geology, select the type of foundation required, determine the load capacity of the soil and/or rock, and estimate the settlements of the superstructure. There is a large number of in situ tests and equipment available to help obtain this information, including the standard penetration test (SPT), the cone penetration test (CPT), the Marchetti dilatometer test (DMT), the Menard and the self-boring pressuremeters, the vane shear test, and others. 2 The Florida Department of Transportation (FOOT) uses the SPT and the CPT in the design of axially loaded pile foundations (53). In the standard penetration test, a standard split-barrel sampler is attached to drill rods and inserted into a predrilled borehole. The sampler is then driven 45.7 cm (18 in) using a 63.6 kg (140 lb) hammer and a 76.2 cm (30 in) drop height. The split-barrel sampler is then withdrawn and opened, providing a physical sample of the soil. The SPT "N-value" equals the number of blows for the final 30.5 cm (12 in) of penetration. These N-values have been correlated to many soil parameters despite considerable criticism as to their reproducibility. The SPT is standardized by the American Society for Testing and Materials (ASTM) Standard Method D 1586 (2). In the cone penetration test using an electronic cone penetrometer (designated ECPT), a cylindrical rod with a conical point is pushed into the ground at a constant, slow rate, and the force on the point is measured by an internal strain gauge. A second strain gauge measures the force caused by friction on a free-floating friction sleeve. The ECPT provides an accurate description of the subsurface stratification and, from simple correlations, an estimate of the soil type. Also, many soil properties have been correlated with the ECPT measurements. The principal disadvantages of the cone penetration test are the lack of a soil sample from the test, and the penetrometer's limited ability to penetrate stiff soil layers. The CPT is standardized by the ASTM Standard Method D 3441 (2). The design procedures for pile foundations depend on an accurate representation of the soil at the location of the pile, both in terms of the measured or estimated soil properties,_and the type of soil. 3 Uncertainty in the input parameters determined by the SPT or CPT will naturally result in uncertainty in the calculated pile load capacity. The need exists to describe and quantify the uncertainty in the input parameters, as well as to use procedures which minimize the uncertainty associated with a site investigation program. Purpose of Research The purpose of this research project is to evaluate methods to improve the use of in situ penetration tests for the geotechnical site investigation of soils indigenous to Florida. In support of the University of Florida's driven pile study, the project concentrates on construction sites employing driven pile foundations. The primary in situ device to be evaluated is the electronic cone penetrometer, which is thought to model a pile foundation. This emphasis is the result of the ECPT's faster speed, better reproducibility, and lower cost relative to the standard penetration test. Specifically, methods to describe the spatial variability of soil properties will be evaluated with the purpose of determining the method which can best interpolate test measurements between soundings. The ability of the ECPT to classify Florida soil types will also be evaluated, and procedures recommended to improve current Florida practice. Finally, correlations between the SPT N-values and the ECPT cone resistance and friction resistance will be determined. These correlations will be valuable in situations when the cone penetrometer test cannot be used due to stiff soil layers or difficult access. A collateral purpose for this research project is to develop a data base of pile load tests and in situ tests for Florida. Such a data base 4 will prove extremely valuable to future geotechnical research on Florida soils. Research Methodoloav The initial phase of the research project involved setting up a data base of pile load tests and in situ tests performed throughout Florida. A letter soliciting data and site access was sent to all of the FDOOT district geotechnical engineers, and to many private geotechnical consulting firms. As a result of the letter and follow-up telephone contacts, a significant amount of information was collected. These data included site plans, pile load tests, pile driving records, standard penetration tests, mechanical and electronic cone penetration tests, wave equation analyses (CAPWAPC), and Marchetti dilatometer data. Numerous trips to sites with driven pile load tests were also made in order to collect electronic cone penetration test (ECPT) data using the University of Florida cone penetration testing vehicle and equipment. In order to handle this large data base and to run statistical analyses on the data, the SASTM System was used (SAS is a registered trademark of the SAS Institute Inc., of Cary, North Carolina). The SAS System is computer software that provides data retrieval and management, reporting and graphics capabilities, and an extensive array of elementary and advanced statistical analysis procedures (47,48,49,51). As the data were collected, they were encoded and stored on a computer for future analysis. To date the encoded data base includes pile load tests (PLTs), electronic cone penetration tests (ECPTs), standard penetration tests (SPTs), and some mechanical cone penetration tests (MCPTs). Additional data are on file at the University of Florida, and 5 can be encoded as required by future research. Chapter 2 describes the data base used by this research project. Once the in situ test data were available to the SAS System, the individual data sets were combined into larger sets (depending on the nature of the study) for statistical analysis. The spatial variability studies were accomplished using the SAS data manipulation and reporting capabilities, coupled with regression analysis and exploratory data analysis. The soil classification study employed the SAS discriminant analysis procedures. The SPT/ECPT correlation study used exploratory data analysis and regression analysis. CHAPTER 2 PROJECT DATA BASE Introduction The data base was created in support of the University of Florida Department of Civil Engineering's Deep Foundations Project, sponsored by the Florida Department of Transportion. The specific focus of this phase of the project is the design of axially-loaded driven piles and pile groups. As a result, data were solicited on construction sites having driven pile load test data. Letters and telephone calls were made to all of the FDOT district geotechnical engineers, and to many geotechnical consultants in Florida. When suitable sites were identified, all available geotechnical data were obtained. In order to obtain electronic cone penetration test (ECPT) data coinciding with the pile load tests (PLTs), site visits were made to perform ECPTs if the data were not otherwise available (which was generally the case). ECPT soundings were made near the pile load tests, and also adjacent to standard penetration test borings that were near the PLTs. These latter soundings were designed to support the classification study of the ECPT. This chapter describes the nature and extent of the entire project data base. Subsequent chapters describe the parts of the data base used for the individual analyses. This chapter also describes the procedures and equipment used for the ECPTs performed by the University of Florida, 7 including a discussion of some of the problems and limitations associated with the electronic cone penetration test. Extent of Data Base Figure 2-1 is a map of the State of Florida, showing the thirteen cities where test data were collected. Table 2-1 summarizes the number of tests at each site that have been entered into the computer data base. Note that multiple pile load tests at a site usually indicate multiple tests on the same pile (either the pile was redriven, or a tension test was performed). Note also that additional data from many of the sites are available, but have not yet been encoded and stored in the computer. These tests are generally either not pertinent to this study (the Marchetti dilatometer tests for instance), or are not close to pile load tests of interest. The majority of these data is comprised of SPT and MCPT data. A more extensive description of the Table 2-1 data base is located in Appendix A, which is an index of the data base. This index is organized by location (generally of the pile load test). Each individual test is identified by a prefix to identify the type of test, a number to identify the location, and a suffix to identify individual tests. The prefixes are shown below the test abbreviations in Table 2-1. For instance, C001B is an electronic cone penetration test (the prefix C) at Pier 3 of the Apalachicola River bridge (the number 001), and is the second test at that location (the suffix B). The index includes information on general soil conditions, a description of the pile used in the pile load test, the file name used by the source of the data, and any important additional comments. The data base itself is contained in Knox (25). :ksonville e \Port Orange Beach C. " Figure 2-1. Cities Represented in Pile Data Base Over3treet White ( Table 2-1. Data Base Summary LOCATION PLTs ECPTs SPTs MCPTs NUMBER SITE P) LCu iSl i(M) 001 Apalachicola River Bridge--Pier 3 1 2 20 4 002 Apalachicola River Bridge--Bent 16 1 2 0 2 003 Apalachicola Bay Bridge--Bent 22 1 2 0 4 004 Overstreet Bridge--Pier 11 1 4 2 0 005 Overstreet Bridge--Pier 16 1 4 4 0 006 Sarasota Garage--SP7 2 4 4 0 007 Sarasota Garage--SP5 2 4 5 0 008 Sarasota Condo 2 2 5 0 009 Sarasota Landfill 0 3 3 0 010 Fort Myers--Concrete Pile 2 8 2 0 011 Fort Myers--Steel Pile 1 0 0 0 012 Fort Myers Airport 0 2 2 0 013 Port Orange--Bent 19 1 2 0 2 014 Port Orange--Bent 2 1 1 1 2 015 West Palm 1-95--Pier B-4 1 3 1 0 016 West Palm I-95--Pier B-6 0 3 1 0 017 West Palm I-95--Pier B-9 1 2 1 0 018 West Palm I-95--Pier C-2 1 0 1 2 019 Choctawhatchee Bay--Pier 1 1 13 3 1 020 Choctawhatchee Bay--Pier 4 1 2 1 2 021 Choctawhatchee Bay--Bent 26 1 4 1 3 022 White City 0 3 3 3 023 Orlando Arena 2 4 5 0 024 Orlando Hotel South 1 2 2 0 025 Orlando Hotel North 1 1 1 0 026 Orlando Hotel Northeast I 1 1 0 027 Jacksonville Terminal B-20 2 3 1 0 028 Jacksonville Terminal B-21 2 2 1 0 029 Archer Landfill 0 7 2 0 030 West Bay Bridge 0 6 6 0 031 Lake Wauberg 0 1 0 0 TOTALS 31 97 79 25 Site Descriptions Apalachicola River and Bay Bridges (Sites 001 003) The Apalachicola River and Bay bridges are replacement structures for older bridges on U.S. Highway 98 in Apalachicola. Both are FOOT projects. The Apalachicola River bridge is a 1153 m (3783 ft) structure 10 running generally east and west,' with a turn to the north on its western end. The Apalachicola Bay bridge is a 4321 m (14175 ft) structure traversing the bay east and west. The available test data for these sites include test pile driving records, CAPWAPC analyses, pile load tests (PLTs), standard penetration tests (SPTs), Marchetti dilatometer tests (DMTs), mechanical cone penetration tests (MCPTs), and University of Florida electronic cone penetration tests (ECPTs). The soils are predominantly clays, sands, and clay/sand mixtures. Figure 2-2 locates the Apalachicola River bridge SPTs used in the spatial variability studies. Figures 2-3 through 2-5 locate the available in situ soil test data available near the pile load tests in the data base. Overstreet Bridge (Sites 004 005) The Overstreet bridge is a 962 m (3157 ft) structure over the Intracoastal Waterway on State Road 386, near the town of Overstreet, Florida. This FDOT project is a replacement for an old floating pivot bridge. The available test data include test pile driving records, PLTs, SPTs, MCPTs, and ECPTs. The soils are mostly sand, with some clayey sand and clay. Figures 2-6 and 2-7 locate the available in situ soil test data near the pile load tests in the data base. Sarasota Garage and Condo (Sites 006 008) The Sarasota parking garage (Sites 006 and 007) and the Sarasota condo site (Site 008) are supported by a pile foundation designed by Ardaman & Associates of Sarasota. The available test data include test pile driving records, PLTs, SPTs, and ECPTs. The soils at the parking BORING NUMBERS 14 16 18 20 . m m 0 m i / 110 I I I -JI LU a Figure 2-2. ! PLT A MCPT STATIONS Cl STATION = 30.5 m) Apalachicola River Bridge SPTs Used for Spatial Variability Studies 0 ECPT 0 DMT S001C * M001A A CO01B ,- 0 22.8 m Figure 2-3. Apalachicola River Bridge Pier 3 Tests . SPTs I I2 22 -m U M00IB P001 O MT C001A c 4.1 m 5.0 m m PLT o ECPT M002R 2.7 m A MCPT 0 C002B POO2 C002A ---- 0 Figure 2-4. Apalachicola River Bridge Flat Slab Bent 16 Tests k PLT C003R 0 ECPT A MCPT Figure 2-5. Apalachicola Bay Bridge Flat Slab Bent 22 Tests 0 C003B o0 P003 M003C A 0" 14.B .I n] i PLT o ECPT U SPT N C0048 S0048 I P004 S0048B C004A o 0 S5C004C 22.1 m 3.8 4.4 : 0 12.3 m Co 0040 Figure 2-6. Overstreet Bridge Pier 11 Tests N A PLT o ECPT U SPT C0050 S0058 * 0058 C05B o S005C a 11.8 m Figure 2-7. Overstreet Bridge Pier 16 Tests 14 garage are mostly sand overlying limestone rock at approximately 7.6 m depth (25 ft). The condo site is predominantly fine sand and clayey sand overlying limestone at approximately 5.5 m depth (18 ft). Figures 2-8 and 2-9 locate the available in situ soil test data near the pile load tests in the data base. Sarasota Landfill (Site 009) The Sarasota (Manatee County) landfill is located north of Sarasota. No pile load tests are available for this site, but Ardaman & Associates of Sarasota provided some SPT data, which were supplemented with UF ECPT soundings. ECPT sounding C009A is 0.76 m (2.5 ft) from SPT sounding S009A; 122 m (400 ft) southeast, C009B is 0.76 m from S009B; 61 m (200 ft) further southeast, C009C is 0.5 m (1.5 ft) from S009C. The soils at the landfill are mostly clayey fine sand, with some clay and sandy clay. Fort Myers Interchange (Sites 010 011) The Fort Myers site is a highway interchange project designed by Greiner Engineering of Tampa, with Law Engineering Testing Company of Naples serving as the geotechnical consultant. Available test data include test pile driving logs, pile load tests, SPTs, and ECPTs. Several of the ECPTs were rate-controlled tests (0.5 to 2.0 cm/s), although the nonstandard tests were not used in this project. The soil is sand and sand/clay mixture overlying cemented clayey sand at a depth of 31 m (102 ft). Figure 2-10 locates the test data in the data base. * PLT *~ UNTESTED PILE 007C 5007C C007B C007A - 0 0 C0070 C007C 0 - 5007R . INSET A C00O60 o - SOO6R INSET B Figure 2-8. Sarasota Garage Tests 0 ECPT * SPT 0078 S007B -0.5 a -0.3 * 0 ECPT POO8T *-E 1, 2.3 m 0 C008R COOBB 0.0 Figure 2-9. Sarasota Condo Tests A PLT 0 ECPT C010C CO100 0 0 P011 S010A _?_ . 0.5 m CO I OF COIOE0 0 0.3 m C010B o COl0R o0 ' Figure 2-10. Fort Myers Interchange Tests P008 m SPT K PLT Fort Myers Airport (Site 012) The Fort Myers airport site is an interchange project, with Law Engineering Testing Company of Naples serving as the geotechnical consultant. Available test data include SPTs, ECPTs, and some laboratory test data. The soil is comprised of sand and sand/silt/clay mixtures, interbedded with weak to competent limestone layers. Two SPT sites were used, separated by approximately 23 m (75 ft). ECPT sounding C012A is 1.37 m (4.5 ft) from SPT S012A, and C012B is 1.52 m (5 ft) from SO12B. Port Orange (Sites 013 014) The Port Orange site is an FDOT bridge on State Road AlA over the Halifax River. The foundation for this bridge uses driven piles on the approaches and drilled shafts under the main spans. The data base includes PLTs, SPTs, MCPTs, ECPTs (both UF and FDOT), CAPWAPC analyses, and laboratory analyses. The soil is mostly shelly sand and sandy silt, with a 4.5 to 6m (15 to 20 ft) thick clay layer overlying limestone at approximately 26 m (85 ft) in depth. Figures 2-11 and 2-12 identify the test data near the pile load tests in the data base. West Palm 1-95 (Sites 015 018) This recently-completed project consisted of ramps and overpasses for Interstate 95 in Palm Beach County. The data base include test pile driving records, PLTs, SPTs, ECPTs (for the P.G.A. Boulevard ramp, Sites 015 017), and MCPTs (for the Military Trail overpass, Site 018). The soil is fine sand with a small amount of clayey fine sand. Figures 2-13 through 2-16 locate the test data near the pile load tests. w PLT 4/ MO13A A -- o ECPT 18.3 m A MCPT -o CO I 3 P013 -w 0 8 .' m - Figure 2-11. Port Orange Bent 19 Tests PLT 0 ECPT A MCPT SPT M014R C013R 4/ Figure 2-12. Port Orange Bent 2 Tests 0 ECPT C015 ---7-- 0 SPT C015A o o --/E- C 2.4 i P015 \V X 'k a 3.2 m Figure 2-13. A PLT West Palm 1-95 Pier B-4 Tests 0 ECPT n SPT C016C 0 2.2 m SO IBA - .6 m\ 3.7 m o C01OR Figure 2-14. West Palm 1-95 Pier B-6 Tests CD 015B S015A 3.4 m M->* -A x PLT -----x s PLT CO7A 0 S017A 0.4 4m P017 m - IC 0 ECPT * SPT o C017B 4/ Figure 2-15. West Palm 1-95 Pier B-9 Tests U PLT A MrPT U SPT M018B I SO018A Figure 2-16. West Palm 1-95 Pier C-2 Tests ------X---------------------------------------------T-- 21 Choctawhatchee Bay (Sites 019 021) The Choctawhatchee Bay bridge is a replacement structure for an older bridge on State Road 83 (U.S. 331). The bridge portion of this FDOT project is approximately 2296 m (7534 ft) long, running north and south. Available test data include PLTs, SPTs, MCPTs, ECPTs (both FDOT and UF), DMTs (available from FDOT), and laboratory test data performed by both the FDOT and the University of Florida. The soils are predominantly sand overlying some clays and clayey sand on the southern approach to the bridge, with the clays increasing as you proceed north. Many of the ECPTs on the south side of the bridge were used in the spatial variability studies. Figures 2-17 and 2-18 identify the in situ test data in the data base. White City (Site 022) The White City bridge is a replacement structure over the Intracoastal Waterway on State Road 71. The bridge portion of this FDOT project is approximately 549 m (1800 ft) long, running north and south. Available test data include SPTs, MCPTs, ECPTs, and laboratory data. Pile load test data should be available in the near future. The soils are mostly sand, with some clayey sand. Figures 2-19 and 2-20 locate the available test data near the UF ECPTs. Orlando Arena (Site 023) The Orlando Arena is a 15,000 plus-seat structure constructed by the City of Orlando. Jammal & Associates of Orlando performed the geotechnical investigation, and kindly provided all of the test data used in this project. Available data include test pile driving records, " PROPOSED PLT o ECPT * SPT o DMT A MCPT 112 114 118 11 120 STATION (I STATION 30.5 m) Note: See Appendix A for test Identification. Figure 2-17. Choctawhatchee Bay South Tests * PROPOSED PLT o ECPT * SPT A MCPT u an 178 tIo 182 184 188 STATION (I STRTION 30.5 m) Note: See Appendix A for test identification. Figure 2-18. Choctawhatchee Bay North Tests S0 00 A A A 13U.i A MCPT =*z C022A S022R M022R - A 1".5 m Figure 2-19. White City South Tests A MCPT 0 ECPT S022B a SPT M022C A -- Figure 2-20. White City North Tests MO22B A 0 ECPT a SPT 24 PLTs, auger borings, SPTs, ECPTs, and laboratory test data. The site is mainly sand overlying mixed clay and sand at depths of 12 to 18 m (40 to 60 ft), with consolidated clays and silts being encountered at depths of approximately 33.5 m (110 ft). Figure 2-21 locates the in situ test data used in this project. Orlando Hotel (Sites 024 026) The Orlando Hotel is a proposed high-rise structure in downtown Orlando. Jammal & Associates of Orlando performed the geotechnical investigation, and provided all of the test data used in this project. Available data include test pile driving records, PLTs, SPTs, ECPTs, and laboratory test data. The site is comprised of a surficial sand fill overlying fine sand with some silt and clay to a depth of 13 to 16 m (43 to 53 ft). Below this depth are mixed sands, silts, and clays characteristic of the Hawthorn Formation. Figure 2-22 identifies the test data used in this project. Jacksonville Terminal (Sites 027 028) This project was the addition of a coal conveyer system to the St. John's River Coal Terminal on Blount Island. The geotechnical consultant for the project was Law Engineering of Jacksonville. The available data include test pile driving records, PLTs, CAPWAPC analyses, SPTs, and ECPTs. The exact location of the PLTs and SPTs could only be estimated at the time of the electronic cone penetration tests, but all tests are believed to be very near one another. The three ECPTs were spaced in a line at 1.5 m (5 ft) increments for Site 027, whereas the two ECPTs at Site 028 were 1.8 m (6 ft) apart. The soils are predominantly fine sand and silty sand. I PLT 0 GCPT I SPT 0 60 FEET 0 I .3 METERS SCALE Figure 2-21. OECPT 0 20 FEET 0 6.1 METERS SCALE Orlando Arena Tests M SPT v==5 S024B .C0248 4C024B C024R C025R P025 SO26A C02AR P026 Figure 2-22. Orlando Hotel Tests SPLT P024 024 S024A ---I F- 26 Archer Landfill (Site 029) This Alachua County landfill site is covered by ancient sand dunes which overlie limestone at approximately 15 m (50 ft) of depth. The source for the data at this site is a Master's thesis by Basnett (7). The site is remarkably uniform, and was used for the spatial variability studies. Available soils data include SPTs, ECPTs, UF laboratory data, and DMTs. Figure 2-23 identifies the test sites pertinent to this study. West Bay (Site 030) The West Bay site is an FDOOT bridge on State Road 79. All of the in situ test data for this site was provided by the FDOOT, and includes approximately 29 SPTs and 14 ECPTs. Laboratory data from both FDOT and UF are also available. The soils are mostly fine sand with some silts and clays. Some of the silty sand is slightly cemented. Figure 2-24 locates the test data used in this project. Lake Wauberg (Site 031) The Lake Wauberg site is located on University of Florida property south of Gainesville. The ECPT sounding for this site came from Basnett (7). This sounding was correlated with the results of UF laboratory analyses on recovered samples of highly plastic clays and elastic silts, the results of which are included in the classification studies. 0 ECPT I SPT 0 100 FEET 0 30.5 METERS CO29H C02G 0 0 C0201 0 v C0293 CO0L 0 CO29K 0 CO29E 0 C029R 0 C0298 I S02BR Figure 2-23. Archer Landfill Tests o ECPT PT P Z 0 C0300 0 15 v S030C S0300 a o C030E 0 2 12 -. S5030A SG30B 0 C030C ' o 0 c030B S030E C030R S030F .0 0* C030F 0 a 0 282 2B 290 294 298 302 30B 310 STATION (I STATION 30.5 m) Figure 2-24. West Bay Tests I S029B CO29F 0 CO2OC 0 C0290 28 Collection of ECPT Data Equipment All of the electronic cone penetration test data was obtained using University of Florida equipment, with the exception of two of the Port Orange soundings (source: FDOT), the Orlando data (source: private consultant), and the West Bay data (source: FDOT). Three electronic friction-cone penetrometers were used in the research, rated at 5-tons (metric), 10-tons, and 15-tons respectively. All three are subtraction- type friction-cone penetrometer tips marketed by Hogentogler and Company, Inc. of Columbia, Maryland. Figure 2-25 is a schematic drawing of a subtraction-type penetrometer tip. The American Society of Testing and Materials (ASTM) has standardized the cone penetrometer and the cone penetration test in ASTM Standard D 3441 (2). The standard penetrometer tip has a 60 cone with a base diameter of 35.7 mm (1.406 in.), resulting in a projected area of 10 cm2 (1.55 in.2). The standard friction sleeve has the same outside diameter as the cone, and a surface area of 150 cm2 (23.2 in.2). The UF 5-ton and 10-ton penetrometer tips conform to this standard, whereas the 15-ton penetrometer's 60 cone has a base diameter of 43.7 mm (1.72 in.) for a projected area of 15 cm2 (2.33 in.2). The friction sleeve, however, has the standard 150 cm2 surface area. Two primary measurements are made by the friction-cone penetrometer. The cone resistance, qc, is defined as the vertical force applied to the cone divided by its projected area. The friction resistance, fs, is the vertical force applied to the friction sleeve divided by its surface area. The friction resistance is comprised of both frictional and adhesive forces. CONE RESISTANCE STRAIN GAUGE FRICTION SLEEVE CONE RESISTANCE AND FRICTION RESISTANCE STRAIN GAUGE ELECTRONIC CABLE CONE 60' 13.41 cmr (5.28 in) Figure 2-25. Subtraction-Type Electronic Friction-Cone Penetrometer Tip Figure 2-26. The UF Penetration Testing Vehicle I, 'MM 30 One of the advantages of electronic penetrometers is that other electrical measuring devices can be incorporated into the tip housing to provide additional and specialized information about the soil being penetrated. The UF penetrometer tips incorporate two additional devices, an inclinometer and a pore pressure transducer. The precision optical inclinometer is primarily a safety device. It measures the angular deviation of the penetrometer tip from vertical during penetration, warning the operator of possible drifting during penetration of stiff layers. Dynamic pore pressures are measured using a small pressure transducer mounted within the penetrometer tip. The plastic porous filter element is located immediately behind the cone- The filter element is carefully boiled in a water/glycerin mixture to completely saturate it. Saturation of the tip is maintained prior to use by a rubber sheath around the filter element. Insertion of the penetrometer tip and collection of the data were accomplished using the University of Florida's cone penetrometer testing truck. This vehicle includes a 20-metric-ton hydraulic ram assembly, four independently-controlled jacks for leveling, and a computer- operated data acquisition system. The data acquisition system is comprised of a microprocessor with a 128k magnetic bubble memory, a keyboard, a printer, and a graphics plotter. The system permits real time monitoring of the ECPT test, built-in overload factors for safety, and permanent recording of the data. The system is described in detail in Davidson and Bloomquist (11). Figure 2-26 shows the UF penetrometer testing vehicle. Procedures The test procedures used to collect the ECPT data follow the ASTM Standard D 3441 (2) and the manufacturer's recommended guidelines (41). In summary, the porous filter elements for the pore pressure measurements are saturated by boiling in a water/glycerin mixture prior to the test, and stored in the same mixture until needed. At the test site, the truck is positioned over the sounding location and leveled. A friction reducer and the first drill rod are attached to the penetrometer tip, and are hung in the jaws of the hydraulic ram's automatic clamp. After the tip has warmed up for at least 20 minutes, an initial no-load baseline reading is taken of all of the data channels (cone resistance, friction resistance, pore pressure, and inclination). Once the baseline is taken, the actual test may begin. The penetrometer tip is pushed into the ground at a rate of 2 cm/s (0.79 in./s). Measurement signals are constantly being received from the tip, but are actually recorded every 5 cm (1.97 in.). During penetration, the next one-meter length of drill rod can be added, allowing for nearly continuous penetration (except for the time required to raise the automatic clamp to grab the next drill rod). Once the test is complete, the automatic clamp is reversed and the rods retracted. Once the penetrometer tip is clear of the ground, it is quickly wiped off and a final baseline reading taken. This final baseline is compared with the initial one to evaluate the quality of the sounding. Problems Encountered Minor problems. Several difficulties were encountered in the course of collecting the ECPT data for this project. Problems included W 32 numerous instances of reaching the thrust limits of the hydraulic ram system, and of unacceptable inclinations as the probe veered from vertical. These problems were a predictable result of the inherent limitations of the equipment. The cone penetration test is not suitable for all geology, a fact well-understood by experienced operators. In locations having competent near-surface limestone formations, highly cemented sands, heavily overconsolidated clays, and similar stiff subsurface soils, the ECPT will necessarily have to give way to more robust in situ testing methods such as the standard penetration test. More troublesome, however, were the less-predictable problems encountered. The friction reducer is a special rod with small projections welded to it. It follows the tip, and its purpose is to enlarge the hole and reduce the friction on the subsequent drill rods, thus permitting deeper soundings. Twice during testing, the friction reducer cold-welded itself to the penetrometer tip, resulting in costly repairs and equipment downtime. Future problems were avoided by careful attention to cleanliness in the threads of the tip, and by the use of an anti-seize compound on the threads. Calibration. The most insidious problems were associated with the quality of the measurements themselves. The usual method of evaluating a device's accuracy is by calibration against a known quantity. The UF penetration testing vehicle contains a field calibration device. This device employs a hand pump to hydraulically apply a force to either the cone or the friction sleeve. The force is measured with a load cell, and compared with the readings from the data acquisition system. Unfortunately, only standard-size penetrometer tips can be calibrated in this device; therefore the 15-ton tip was calibrated by the 33 manufacturer. Figures 2-27 through 2-29 show the results of the calibrations on the three UF cone penetrometer tips. The calibration for the 5-ton penetrometer (Figure 2-27) showed that the qc readings were high by generally less than 2%, although the readings were off as much as 10% on the high side for cone resistances less than 7 MPa (73 tsf). The friction resistance "noise" refers to the measured friction when only the cone is loaded. This noise, which was generally linear with increasing qc, would result in friction readings that were too low at the rate of approximately 0.34 kPa/MPa. For example, for a moderate cone resistance of 15 MPa (157 tsf), the friction resistance would be too low by about 5.1 kPa (0.053 tsf) due to the cross-channel noise. The fs calibration was similar, reporting friction resistance values generally 1.5% too low, but ranging as high as 7% low for friction resistances less than 100 kPa. The qc noise rate was a low 0.00018 MPa/kPa. The 10-ton penetrometer tip was calibrated twice during the field testing phase of the project. The qc measurements were generally within 1% on the low side of the actual load for cone resistances greater than 10 MPa (105 tsf), and within 4% for smaller qc's. The friction noise ranged as high as 9 kPa (0.094 tsf). The friction resistance was usually within 1 to 3% of the true value. The qc noise rate was an acceptable 0.00046 MPa/kPa. Overall, the calibration for this penetrometer tip was the most acceptable of the three instruments used in the project. The 15-ton penetrometer tip was calibrated before and after repair by the manufacturer in August, 1988. The cone resistance calibration showed an excellent 0.6% error both before and after repair. The o SEPT 88 CALIBRATION 0 5 10 15 20 25 RCTURL Sc (MPa) (R) Go Calibration o SEPT 88 CRLIBRRTION 0 Gc CHANNEL NOISE D 0.20 -J- S-0.15 ,d' 400 o o 0n 200 30 4 5 ACTURL Fs kP.a) (B) Fe Calibratlon Figure 2-27. Calibration for 5-Ton Friction-Cone Penetrometer Figure 2-27. Calibration for 5-Ton Friction-Cone Penetrometer 0 , no 10,- = FRICTION NOISE o SEPT 88 CALIBRATION A NOV 88 CALIBRATION o SEPT 88 Fe NOISE o NOV 88 Fe NOISE 0- 15 50 *55 I0 0 0 0 40 0 0 a 3 ..5D ACTUAL Go CMPa) (C) Gc Calibration o SEPT 88 CALIBRATION a SEPT 88 Bo NOISE a NOV a CRLIBRATION NOV 88 On NOISE Nr- -t 500- y -0.3 Fge 2. fo 0.1 2 /d g =MO a3 13 1-0.0 oM .--- f -0.1 0 100 200 300 500 amm0 ACTUAL Fs (kPa) (B) Fe Calibration Figure 2-28. Calibration for 10-Ton Friction-Cone Penetrometer 36 o BEFORE RECALIBRATION X( AFTER RECALIBRRTIDN a Fe NOISE BEFORE o Fe NOISE AFTER 30 40 ACTUAL Bc (MPa) (R) Gc Calibration o BEFORE RECRLIBRRTION A AFTER RECALIBRATION 00 a 400 an 8am 1000 1200 RCTURL Fa (kPa) (B) Fe Calibration Figure 2-29. Calibration for 15-Ton Friction-Cone Penetrometer 37 friction noise readings were poor prior to repair, however, reading as much as 23 kPa (0.240 tsf) too high. Following repair, the maximum friction noise was 7 kPa (0.073 tsf). The friction channel read as much as 14 to 20 kPa too high for the higher friction resistance measurements prior to the repair. All friction measurements made by the 15-ton cone penetrometer prior to August 1988 are suspect as a result of the calibration. Baseline drift and negative values. The worst problem encountered in the project was negative friction resistance measurements and friction baseline drifts, primarily in the 15-ton penetrometer tip. Physically, negative friction resistance measurements are impossible since the friction sleeve is free-floating, recording a "true" friction value only when the sleeve bears on a shoulder of the central core, as shown in Figure 2-25. Therefore, some type of measurement error must be present. Several sources of the problems are possible (13,18-23,41,50). Regarding the baseline drift problems, the manufacturer defines an "allowable" drift of 1.0 to 1.5% of the full-scale reading. The 1.5% limit equates to a drift of 1.5 MPa (15.7 tsf) for the qc channel, 15 kPa (0.157 tsf) for the fs channel, and 0.4 bar (5.8 psi) for the pore pressure channel. Only the friction channel even approached this limit, exceeding it on several occasions. While temperature effects on the strain gauges may account for a small portion of the problem, the literature suggests the single biggest cause of baseline drift is soil and water ingress during a sounding. Therefore reasonably rigorous attention to cleanliness (under field conditions) was exercised throughout the project. Despite this care, the 15 kPa limit on friction 38 baseline drift was approached fairly regularly, slightly exceeded occasionally, and on a few occasions was exceeded by a large amount. All baseline drifts slightly exceeding 15 kPa were flagged in the data base index (Appendix A), and all clearly unacceptable baselines were discarded. The negative friction readings (predominantly on the 15-ton penetrometer tip) can be partially explained by the unstable baselines. If the baseline value drifts positively 10 kPa, then a friction reading that would have read 5 kPa under the original baseline now reads -5 kPa. The manufacturer also notes that transient voltage surges may temporarily affect measurement readings, resulting in negative values (22). A third potential source for error is due to the design of the subtraction-type electronic friction-cone penetrometer tip (41). The cone load cell measures the cone resistance, and the friction load cell measures the resistance on both the cone and the friction sleeve. The friction resistance is then determined by subtracting the cone load cell measurement from the friction load cell measurement. While this particular design is rugged and robust, the calculation of a small number (fs) by subtracting two large numbers is not good measurement practice. Weak soils. Accurate measurements in weak soils are extremely difficult to obtain. A potential source of error is due to unequal end areas on the cone and the friction sleeve (41,43,50). Below the water table, pore pressures bear on the horizontal surfaces at the joints in the penetrometer tip. For the UF 10-ton tip, these unequal end areas would increase qc by 0.034 MPa/bar pressure (0.025 tsf/psi), and increase fs by 1.0 kPa/bar (0.00072 tsf/psi). While the change in qc is 39 virtually negligible over the normal range of pore pressures of -2 to 6 bars (-29 to 87 psi), the change in friction could be significant in very weak soils, masking any measurements of friction. The unequal end area calculations for the UF penetrometers are in Appendix B. In order to account for the pore pressure effects on the penetrometer tip joints, pore pressures can be monitored during penetration. Only weak soils are significantly affected by the unequal end area corrections, which is fortunate since less than 0.3% of the ECPT soundings in the U.S. monitor pore pressures (36,42). As a result primarily of problems with baseline drift, compounded by questions relating to temperature compensation, unequal end area effects, and measurement design of the subtraction-type penetrometer, accurate measurements in weak soils are extremely difficult. Even with careful attention to these problems the errors in measurements may be of the same magnitude as the properties being measured. The ECPT can easily identify the soil as weak, but discrimination among various weak soils is less certain. While the electronic friction-cone penetrometer is clearly a superior instrument for "average" soils, alternate testing methods may be required to supplement the ECPT when such discrimination in weak soil is required. CHAPTER 3 LOCAL VARIABILITY IN CONE PENETROMETER TEST MEASUREMENTS Introduction Variability in soil property measurements can have many sources, including measurement errors, signal noise, the innate randomness of soil (on the "micro" scale), and the spatial variability of the soil property (on the "macro" scale). The term "local variability" has been adopted to describe the point-to-point variability of a measured soil property, and encompasses the first three sources mentioned above. This differentiation is important in spatial variability studies because local variability could conceivably mask any area trends, producing inconclusive results. As an example, Baecher notes that typical measurement error variances for in situ measurements can account for 0 to 70% of the total data scatter (4). Without changes in measuring equipment and techniques, the local variability in a measured soil property must be accepted and considered in any design employing the data. The purpose of this phase of the research is to quantify the local variability of cone penetrometer measurements used in the study. The approach used was to identify pairs of CPT soundings in the data base that were close to one another, and used the same size penetrometer. Then using graphical and statistical techniques, the local variance was described and quantified. Finally, a type of "digital filter" was devised to reduce the variance while preserving the essence of the data. 41 Local Variability Data Base The research project data base was searched for pairs of ECPT soundings that met two criteria: the soundings must be no more than 4.6 meters (15 feet) apart, and the same size cone penetrometer must have been used in both soundings. The distance criteria was admittedly somewhat arbitrary, and represented an attempt to include a representative number of sounding pairs in the analysis, while hopefully insuring that the penetrometers were sampling the "same" material. The laboratory-type requirement that the material be the same for a comparative analysis is virtually impossible to achieve in the field, making criticism a certainty. If the soundings are too close, then stress relief and other cross-hole interference may result. If the soundings are too far apart, then "different" soils may be tested due to spatial variability. The minimum spacing was determined to be 36 cm (14 inches), based on Robertson and Campanella's recommendation of 10 hole diameters from open boreholes and excavations, to allow for potential radial stress relief effects (41). As a check on the maximum selected spacing of 4.6 meters, the sounding pairs were graphically overlaid and evaluated as to the likelihood that the material was approximately the same. If reasonable doubt existed, the sounding was discarded from further analysis. A typical comparison is shown in Figure 3-1. The resulting data base used in the local variability study is summarized in Table 3-1, and the actual soundings are identified in Appendix A and Knox (25). Note that separation distances varied between 1.8 and 4.6 m (6 and 15 ft), and all three University of Florida penetrometer tips are represented. At the Fort Myers site, the 5-ton penetrometer tip was paired with the 10-ton tip, both of which are the 42 2- 10 0 2 4 6 8 10 12 14 16 18 20 22 CONE RESISTANCE (MPa) SITE = FT MYERS Figure 3-1. Typical Matched Soundings for Local Variability Study standard 35.6 mm (1.4 inches) in diameter. A check of the results showed that the Fort Myers data fell well within scatter for all penetrometer pairs, so this pairing was judged acceptable. All other pairings involved one cone penetrometer only. For the instances where the friction baseline readings were unacceptable (as discussed in Chapter 2), only the cone resistance data were used. The designation of "Site #1" and "Site #2" was strictly arbitrary; hence any perceived skewness in the plots favoring one sounding or another could easily be reversed by simply switching the designations. Table 3-1. Data Base for Local Variability Study Location (ID) Archer Landfill (ALFa) Archer Landfill (ALFb) Fort Myers (FMYER) Sarasota Condo (SCNDO) Sarasota Garage (SGARa) Sarasota Garage (SGARb) Sarasota Garage (SGARc) Site Site #1 #2 C029A C029B C029C C029D C010D C010E C008A C008B C006C C006D C007A COO07B C007C C007D Distance Penetrometer m (ft) (tons) Comments 3.7 (12.0) 10 4.6 (15.0) 10 2.9 (9.5) 5/10 qc only 2.4 (8.0) 15 1.8 (6.0) 15 2.1 (7.0) 15 2.6 (8.5) 15 qc only Figure 3-2, representing 1287 observations, shows the cone resistance data plotted about the expected 1:1 line. Most of the data are relatively well-behaved about the line. Figure 3-3 shows a similar plot for the friction resistance data, representing 809 observations. Data Filter As can be observed in Figure 3-1, many of the large-magnitude "errors" between Soundings #1 and #2 are due to mismatches in the high- ++4 44- t ^A t 10 20 SITE #2 CONE RESISTANCE (MPa) SITE + + + ALFa 0 0 0 SGARa XX X ALFb A A A SGARb * * FMYER : # # SGARc 0 0 0 SCNDO Figure 3-2. Cone Resistance Data for Local Variability Study 300- D C- C+ S 0 + +0 + 100 + O+6 X U- a 0 20 40 60 80 100 120 140 160 180 200 SITE #2 FRICTION RESISTANCE (kPa) SITE + + + ALFa 0 0 0 SGARa XXX ALFb c FMYER 0 C] 0 SCNDO A A A SGARb 4 4 # SGARc Figure 3-3. Friction Resistance Data for Local Variability Study T 1 1 T 45 frequency (and often high-amplitude) peaks characteristic of some soils, especially stiffer ones. These mismatches result in some of the large magnitude scatter observed in Figures 3-2 and 3-3. To reduce the influence of this high-frequency "noise" in the spatial variability study, a digital filter was sought. Several typical digital filters were tested on sample data sets, including moving average and nonrecursive filters employing parabolic fits (24). However, either inadequate smoothing of the data occurred, or sudden shifts in the data were anticipated too early. The adopted filter used a simple average method. The data were divided into 0.5- meter (1.6-foot) increments, the average value of the increment determined, and this value assigned to the midpoint of the increment. This filter was able to smooth out the high-frequency noise in a sounding, while preserving the essence of the sounding. Figure 3-4 shows one of the soundings from Figure 3-1 before and after filtering. Figures 3-5 and 3-6 are identical to Figures 3-2 and 3-3, except that the data have now been filtered. Note that the scatter has been reduced. The number of data points has also been reduced by a factor of 10 as a result of filtering. In computer-intensive applications where the point-to-point soil properties are not critical, such a filter can greatly reduce computer processing time and storage requirements, while, to a point, still reflect the influence of the entire (unfiltered) data set. Evaluation of Data Scatter To evaluate the data scatter, regression analysis using the REG procedure of the SAS system was used. The models used in the analysis were LJ LI 12- 0 2 4 6 a 10 12 14 16 16 20 22 CONE RESISTANCE (MPa) Solid = Unfiltered Dashed = Filtered Figure 3-4. Effect of Average-Value Data Filter +x +a 30 20 , 20 I- on LCJ 10 0 I- 0A SITE + + + ALFa XXX ALFb 0 0 0 SGARa A A A SGARb * * FMYER 4 4 4 SGARc D 0 0 SCNDO Figure 3-5. Cone Resistance Data After Data Filtering + x + + - 0 20 40 60 80 100 120 140 150 SITE #2 FRICTION RESISTANCE (kPa) SITE + + + ALFa XXX ALFb 0 0 0 SGARa A A A SGARb * * FMYER CE [ SCNDO 4 4 4 SGARc Figure 3-6. Friction Resistance Data After Data Filtering 0 10 20 SITE #2 CONE RESISTANCE (MPa) -? 300 C- LU C-, 200 20 ow LLJ a: 1- CL- 4S 0 LU I- CA 48 (qc)l = bo + b (qc)2 ................................. ............ (3-1) (fs)1 = bo + b1(fs)2 ............................................. (3-2) Besides calculating a slope and intercept using the ordinary least squares approach, the REG procedure also calculates the root mean square error of the model, or RMSE: E(Z Z )2 RMSE = A P .......................................... (3-3) n 2 in which n is the number of observations, Z is the soil property being measured (either qc or fs), and the subscripts A and P refer to actual and predicted values of the soil property, respectively. This RMSE is an unbiased estimate of the standard deviation of the errors about the regression line (9,16). Table 3-2. Results of Local Variability Study Parameter (units) Filter b0 b1 RMSE Cone Resistance No 1.77 0.80 3.44 (MPa) Yes 1.41 0.83 2.91 Friction Resistance No 3.79 1.03 31.1 (kPa) Yes 0.46 1.10 23.9 From Table 3-2 one can see that using the average-value data filter reduced the root mean square error by approximately 15% for qc, and over 23% for fs. Thus the use of the filter appears desirable, especially when one is primarily interested in the most likely value of the soil property in question. 49 Based on the results of this study as summarized in Table 3-2, reasonably conservative values for the local standard deviation of friction-cone penetrometer measurements are estimated to be 3.0 MPa for qc, and 24 kPa for fs. Figures 3-7 and 3-8 plot the residuals from the regression analysis (Actual minus Predicted) as a function of the independent variable for qc and fs, respectively. Only the lower- magnitude values of the data are shown in the figures for amplification. Note that at very low values of qc and fs the variability is lower, increasing with increasing values of the soil property. It is proposed that the following standard deviation be adopted for the spatial variability study, as shown on Figures 3-7 and 3-8: local standard deviation (qc) = 0.5(qc) for qc < 6.0 MPa (62.7 tsf) = 3.0 MPa (31.4 tsf) for qc > 6.0 MPa local standard deviation (fs) = 0.5(fs) for f.s 48 kPa (0.50 tsf) = 24 kPa (0.25 tsf) for fs > 48 kPa The local standard deviation can be interpreted as the minimum precision one can expect from the cone penetrometer measurements used in the spatial variability study. It may be argued that the variability measured in the local variability study was in reality true spatial variability. However this author contends that any variability measured over a horizontal span of less than 4.6 meters (15 feet) in what appear to be nearly identical soils is for most practical applications a "local" phenomenon, and can be treated as such. + X 5 i0 15 SITE #2 CONE RESISTANCE (MPa) SITE + + + ALFa XXX ALFb * FMYER 0 0 0 SGARa AA A SGARb tt a SGARc 7 0 0 SCNDO Figure 3-7. Residual Analysis and Proposed Standard Deviation for qc 90g- 80- 70- + 60- 50- 40- 30- 20- A 0 -10- X -0 i0 A ++, -20- O + + A __ -30- -40 A -50- -60- -70- -60- -90- -30- 0 20. 40 60 80 100 120 SITE #2 FRICTION RESISTANCE (kPa) SITE + + + ALFa X X X ALFb * FMYER E C 0 SCNDO 0 0 0 SGARa A A A SGARb 4 # = SGARc Figure 3-8. Residual Analysis and Proposed Standard Deviation for fs CHAPTER 4 DESCRIBING THE SPATIAL VARIABILITY OF SOILS Introduction Because of the way it is formed, even nominally homogeneous soil layers can exhibit considerable variation in properties from one point to another. This variation is termed spatial variability. Depending on the factors involved in soil formation (source material, transport mechanisms, etc.) and their fluctuations over both time and space, the spatial variability may be large or small. Lumb notes this variability in soil properties tends to be random, although general trends may exist both vertically and horizontally (30). The evaluation of soil variability is important because soil properties must be estimated from a limited number of in situ and laboratory tests. When soil properties are estimated at an unobserved location, the engineer needs to have confidence that his estimates are likely to be representative of the actual soil properties at that location, or at least be able to quantify his confidence in the estimates. In evaluating soil variability, modern statistics and data analysis offer several tools to help achieve these goals. The purpose of this phase of the research is to evaluate these tools, and to develop a field-usable methodology for describing the spatial variability of Florida soils. A word of caution is in order, however. In applying these tools one is reminded of Ralph Peck's admonition that subsurface 52 53 engineering is an art--"...every interpretation of the results of a test boring and every interpolation between two borings is an exercise in geology. If carried out without regard to geologic principles the results may be erroneous or even ridiculous" (37, p.62). Fortunately most of Florida's soils are depositional due to their marine origin, somewhat simplifying the geology and aiding interpolation. Descriptive Statistics for Spatial Variability Summarizing a Data Set Traditionally, a deterministic, or single-valued approach is used in describing soil properties. The most commonly used approach to quantify a measured property, x, of a nominally homogeneous soil layer is to use the average or mean value, R, of the property: n Sx(4-1) x = i=l i .................... .. ............................ (4-1) n in which xi is the measured value of the property at point i, and n is the total number of measurements. This estimator is the best choice for summarizing data if the data are normally distributed. However, this measure is sensitive to nonnormal distributions and to outliers, which are unusually high or low data points that stand out from the rest due to mistakes or other reasons. An alternative to the mean for describing the center of a distribution is the median, defined as the middle value of a data set ordered from smallest to largest value. The median is robust against 54 outliers, and can do a better job of summarizing nonnormal distributions. Siegel (54) offers a compromise between the mean and median for describing a set of data, called the trimmed average. This statistic removes the extremes from a distribution, and averages the remaining data. For example, a 10% trimmed average would remove 10% of the highest values, and 10% of the lowest (rounding down when the sample size is not evenly divisible by 10), and then take the mean of the remaining 80% of the data. Describing Variability The uncertainty in the mean of a data set is described by its variance, V, or the square root of the variance, termed the standard deviation, s: V= Z(x x) S= ................................................ (4-2) s = / .......................................................... (4-3) For normally distributed data, approximately 68% of the data should lie within one standard deviation of the mean, and 95% within two standard deviations. As is true of the mean, the variance and standard deviation are sensitive to outliers and nonnormal distributions. If the variance is comprised of contributions from different, uncorrelated sources (such as from spatial variability, measurement error, signal noise, etc.), then the total variance is equal to the sum of the individual variances (3,26,57,63): VT = VI + V2 + ... + Vn .......................................... (4-4) 55 A more robust measure of variability, related to the median, is the interquartile range. If the data are ordered from smallest to largest, the lower quartile is the 25% value (one-fourth of the data is less that or equal to the lower quartile), the median is the 50% value, and the upper quartile is the 75% value. Therefore interquartile range = upper quartile lower quartile ............(4-5) Using tables for the area beneath a normal distribution, for normally distributed data the standard deviation and interquartile range can be related by interquartile range = 1.46 s ..................................... (4-6) If we have a random sample from a normally distributed population, we can determine a confidence interval on the mean of the sample using the following: t s interval = x n-1 ........................................ (4-7) in which tn-1 is called the t-value. Given the desired confidence level and the number of degrees of freedom (equal to n-1), the t-value can be obtained from standard statistical tables. Figure 4-1 shows the t-value for selected two-sided confidence intervals. Measuring Association If Z is a function of two variables x and y, then the strength of association between the two variables is usually measured by their correlation coefficient, r: 1.2 1.0 0.8 0.8 0.4 0.2 0.0 0.0 N 95Z CONFIDENCE O- -902 CONFIDENCE CONFIDENCE 0.2 0.4 0.8 0.8 1.0 1.2 1.4 1.8 1.8 2.0 LOG (SAMPLE SIZE) Critical t-Values for Two-Sided Confidence Intervals 1.0 0.4 0.2 0.4 0.B 0.8 1.0 1.2 1.4 1.8 1.8 2.0 LOG SIMPLEE SIZE) Source: Siegel f1988) p.430 Figure 4-2. Critical Values for Testing Significance of Correlation Coefficient Figure 4-1. LU W _j t-J z W Z W 0 S[(x x)(y y)] r(Z) = r(x,y) = i i .................. (4-8) /[E(x -_ )2[E(y 7)2]' V i i1 The correlation coefficient ranges between +1 and -1, with +1 indicating perfect 1:1 correlation, 0 indicating no correlation, and -1 indicating perfect inverse correlation (i.e., as one variable increases, the other decreases proportionally). For interpreting other values of the correlation coefficient, Smith (55) suggests the following guide: I|rl 0.8 Strong correlation, assume complete dependence 0.8 > Irl 0.2 Moderate correlation 0.2 Irl Weak correlation, assume complete independence Siegel (54) suggests minimum values of the correlation coefficient for testing that a significant association exists, given the sample size and level of confidence desired. The data must represent a random sample of the population and must be bivariate normal, meaning the two variables come from normal distributions and plot linearly (x versus y) except for randomness. These requirements rule out outliers and nonlinear data sets. Figure 4-2 is a plot of the critical r values for a 90% confidence level. The association between the uncertainty of two variables, x and y, is usually described by their covariance, C: C(x,y) =- [(x x)(y y)] ............... .... (49) n 1 i= i i Note that when x=y, then the covariance equals the variance (i.e., the W 58 diagonal terms in a covariance matrix are the variances, V). It can also be shown that the covariance, correlation coefficient, and standard deviation are related by r(x,y) = s s ............................................... (4-10) x y Estimation Models Traditional Choices When faced with the need for determining a soil property for input into a design process, the conventional or deterministic approach is to assume a homogeneous soil (or soil layer), described by some "average" value for the soil property. This single-value approach is appealing due to the simpler mathematics involved. If a measure of the soil's variability is also desired, the standard deviation of the measured property and perhaps a confidence interval are the usual choices. Often, however, the variability of measured soil properties is so great that a simple "average" could result in needlessly conservative or dangerously nonconservative design. Thus explicit consideration of the spatial variability of soil is required. A model is needed which can predict a soil property at a point i, based on measurements of the property at n other points. Some of the most commonly used estimation techniques seek to interpolate between measured points by fitting linear and higher order regression models to the data using the well-known least squares curve fitting techniques (17,26,46,58). Distance weighting functions, such as a/d and a/d2 (where d is the distance between the measured point and the 59 point to -be estimated, and a is a suitably chosen parameter) are also often used to estimate soil parameters. Regarding the use of these models for estimating properties used in the mining industry, Rutledge criticizes these procedures as being "quite arbitrary and without a sound theoretical basis. The so-called 'principle of gradual change' and the 'rule of nearest points' are an appeal to mysticism, not science" (46, p.300). Rutledge's objections notwithstanding, these methods have been successfully used for many years in designing and constructing innumerable civil structures. Random Field Models In response to the need for an estimation model based at least in part on theoretical principles, numerous researchers have acknowledged the stochastic nature of soil by employing random field models to estimate soil properties (3,5,10,12,26,27,28,30,46,58,59,60,63). Generally, these models are two-part models consisting of a nonstationary and a stationary portion. The nonstationary, or trending portion of the model is generally described by conventional regression analysis. The random field models are used for the stationary, or stochastic portion (i.e., the residuals from the regression analysis). The stationary portion of the model attempts to improve the soil property prediction from the regression analysis (the nonstationary portion) by considering any correlation structure within the residuals. This correlation structure (more properly termed autocorrelation) results from the fact that nearby soil volumes tend to have similar residuals from the regression analysis (i.e., adjacent soil volumes would both tend to be above or below the prediction from regression, 60 whereas more distant soil volumes would more likely follow the expected random variation about the regression prediction). Figure 4-3 describes the Random Field Model concept. While the straight line (determined from regression analysis) predicts the general trend of the data, knowledge of Points #1 and #2--which are correlated with one another--would permit a better prediction of Point #3, thus enhancing the prediction from the regression model. /' I Figure 4-3. Random Field Model Concept Regression analysis. In using the ordinary least squares (OLS) approach to regression analysis, the model used is typically [Z] = [X][b] + [e] ............. ............ . ........... (4-11) in which [Z] = (n x 1) column vector of n observations of the dependent variable Z [X] = (n x p) matrix comprised of I's in the first column to represent the intercept term b1 (i.e., X1 = 1), and of the n observations on (p 1) independent variables X2,...,Xp 61 [b] = (p x 1) column vector of unknown weights to be determined: b1 (the intercept term), b2 ,...,bp [e] is an (n x 1) column vector of n residuals, ei Several key assumptions are made relative to the residual terms in applying the OLS method to regression analysis, namely that they have zero mean, are uncorrelated, have constant variance, and are normally distributed (14). These assumptions are often represented by e = N(0,V) ..................................................... (4-12a) E[C(ei,ej)] = 0 for i / j .................................... (4-12b) in which E[ ] is the expected value of [ ]. As introduced above, though soil is typically considered a random media, soil properties for neighboring soil volumes tend to be more correlated than the properties for more distant volumes, causing the covariance assumption (Equation 4-12b) to be violated for some i j. This feature is termed autocorrelation. The random field models attempt to improve soil property estimation by accounting for the autocorrelation structure of the residuals. Autocorrelation structure. Autocorrelation structure is often described by a semi-variogram (Figure 4-4), which is a graph showing the degree of continuity of a soil property (26,33,40). By graphing the semi-variogram function,Y (r), against separation or lag distance, r, the semi-variogram provides information on how far data may be spatially extrapolated (4). The theoretical semi-variogram function is equal to y(r) = 0.5 V [Z(x + r) Z(x)] ..............................(4-13) 62 + NORMRLIZEO RF DOTR --- FITTED THEORETICAL CURVE 1.8 1.4 Iz ++ ++ // 2 + ,++ M 0.8 ! 0.4 / LAG DISTANCE Cr) Figure 4-4. Typical Experimental Semi-Variogram of Normalized Data in which Z(x) is the value of property Z at point x and V[] is the variance. For random residuals this function will level off to a constant value (the variance of the data set) at r greater than a distance termed the range of the variogram. For finite data sets, Equation 4-13 is estimated by 1 N(r) Y(r) Z [Z(x + r) Z(x )]2 .................... (4-14) 2N(r) i=l i i in which N(r) is the number of observation pairs whose separation distance is r. In working with real data spaced at less than uniform intervals, a band or tolerance is often applied to the separation distance (i.e., r = 50 feet + 10 feet). Tang (59) cautions that the error in the estimated variogram can be substantial if r varies significantly from the discretized average distance. Also, the reliability of the estimate for Y(r) decreases with increasing r, so usually only separation distance values up to one-fourth to one-half the total distance spanned are used in the analysis (26,28). Vanmarcke (63) notes that statistical analysis of actual soil data can often be handled easier if the soil is normalized to be "statistically homogeneous," producing what Lumb calls a "grossly uniform soil" (31). Data can be normalized to have a mean of zero and a standard deviation (and variance) of unity by the following transformation: x = x x ..................................................... (4-15) n s x where xn is the normalized data corresponding to x. For normalized random data, the semi-variogram function should level off to a value of one. Given a data set of normalized residuals, the autocorrelation function, P(r), is complementary to the semi-variogram function, and can be determined by p(r ) = 1 y (r ) ............................................... (4-16) Similar to the correlation coefficient, p(r) can vary between 1 (perfect continuity of the soil property) and 0 (completely random variation). However, as a measure of association between data pairs, the correlation function may seem more familiar to engineers than the semi-variogram function, whose origin lies in mining geology. Figure 4-5 shows the correlation function corresponding to Figure 4-4, and fitted by an 64 + NORMALIZED RAW DATA --- FITTED CRVE 1.0 w \ 0.4 \ -0.8 LAG DISTANCE Cr) Figure 4-5. Typical Experimental Autocorrelation Function exponential expression from Vanmarcke (63). Vanmarcke presents four analytical expressions of many in the literature describing the correlation function, each characterized by a single parameter. He notes that all of the formulas are merely curve fitting expressions with no theoretical basis; hence, they all "work" about equally well--a practical point of view echoed by Tang (59). The correlation function (or the related semi-variogram) is used to account for autocorrelation structure in regression analysis, as described below. It is also a powerful device for estimating the maximum spacing between samples. In order to characterize the autocorrelation structure of a site (and, hence, the spatial variability of the measured soil property), Peters (40) states the maximum spacing between samples is the range of the variogram (or correlation function), with a recommended spacing of two-thirds to three-quarters of the range. A larger spacing would likely miss the correlation structure, and a smaller spacing would be unnecessarily expensive. Naturally, closely- spaced trial samples in the area would be initially required to establish the correlation structure of the soil property. Kulatilake and Miller note that if the purpose of a site investigation is to generally characterize the site while avoiding redundancy (i.e., to describe the general trend of the site), then sample spacing should be greater than the range (27). Incorporation into model. If the nonstationary portion of the regression model is designated Z and the stationary portion Z then the complete model is Z(xi) = Z*(xi) + Z**(xi) ........................................ (4-17) in which Z(xi) is the estimated value of the soil property, Z, at point xi. The nonstationary portion is estimated using conventional regression techniques. The stationary portion is estimated using a method presented by Kulatilake and Ghosh (26). One of the difficulties in applying a random field model is testing for stationarity of the data. Normally replicate testing techniques can be used to insure that the residuals are N(O,V) beyond the range of the semi-variogram; but with destructive tests such as the CPT and SPT, alternate methods are required. Kulatilake and Ghosh proposed examining the form of the semi-variogram at large lag distances. If the normalized semi-variogram function levels off to 1 (or the complementary autocorrelation function to 0), then stationarity can be assumed. However, if leveling-off behavior is not exhibited, then a trend 66 component is apparently remaining in the residuals, and a higher order regression model should be used. They recommend using the lowest order trend (nonstationary) model that results in a satisfactory semi- variogram. In quantifying the stationary portion of the estimation model, Kulatilake and Ghosh employed an approach related to the geostatistical procedure called kriging. Briefly, kriging is a computer-intensive process used to estimate the value of an unknown, autocorrelated property using a linear weighting function. The weights are chosen subject two conditions: the sum of the weights must equal 1, and the sampling variance should be minimized (4,6,10,12,33). Z**(xi) was thus estimated by ** q Z (x ) = (s ) Z a h ....................................... (4-17) i e k=l ki k a = ki ; j = ,2 ... q .............................(4-18) ki ji in which q = the number of measurements within the correlated region around xi se = the standard deviation of the residuals from lowest order regression model resulting in stationary autocorrelation function hk = the normalized residual at location k within the correlated region about point i aki = a suitable weighting coefficient, and 67 mn = value of the correlation function for a separation distance corresponding to the distance between points m and n CHAPTER 5 EVALUATION OF THE SPATIAL VARIABILITY MODELS Application of Estimation Models Five general models for predicting soil properties influenced by spatial variability were evaluated at three sites, as discussed below. In all cases the approach taken was to attempt to predict a sounding. (whether it be an SPT or CPT sounding) by suppressing that sounding from the data base, and using the remaining soundings for the prediction. The three sites selected were Choctawhatchee Bay (CPTs), Apalachicola River (SPTs), and Archer Landfill (CPTs). Evaluation Criteria The root mean square error, RMSE, was used as a criterion to evaluate the accuracy of the various models. The model to predict a soil property, Z, which minimizes the RMSE can likely be judged the best of the evaluated models: RMSE = j=1 A P j ......................................... (5-1) n in which n is the number of observations, and the subscripts A and P refer to actual and predicted values of the soil property, respectively. The RMSE is an estimate of the standard deviation of the errors about the prediction; however it is not a true unbiased estimate (as was used 69 in Chapter 3 to evaluate the local variability of cone penetration test measurements) because the denominator equals the total number of observations, not the number of independent observations. This slightly revised definition of the root mean square error is deliberate to permit true comparison between all of the prediction methods--the affect on the value of the RMSE will be negligible due to the large number of observations involved. In addition to the RMSE criterion, the predictions were graphically overlaid onto the actual soundings and subjectively compared. This was an important check on the root mean square error to insure that the best RMSE did indeed reflect the best prediction. Data Manipulation For the Choctawhatchee Bay and Apalachicola River sites, the five general models were applied to both transformed and nontransformed variables. Only transformed variables were used at the Archer Landfill site. The transformation used was logarithmic (base 10), which has the effect of spreading out small values of the variable while bringing in large values. This was judged potentially beneficial for the Florida data sets used in this analysis because of the relatively large percentage of small values of the variables (whether they be qc, fs, or N), and the large-valued spikes in some of the soundings. It was felt that such a transformation may emphasize the smaller values of the variables, giving a somewhat more conservative estimate. Another potential advantage of the logarithmic transformation was the elimination of any negative predictions, an occasional problem with the regression models. Figure 5-1 compares a typical frequency distribution GC MIDPOINT 0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.S 15.0 16.5 18.0 19.5 21.0 22.5 24.0 25.5 27.0 28.5 30.0 31.5 33.0 34.5 36.0 37.5 I 0 100 200 300 400 500 600 700 600 900 1000 FREQUENCY GC MIDPOINT -0.65 -0.556 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 (a) No Transformation 100 200 300 FREQUENCY (b) Logarithmic Transformation Figure 5-1. Effect of Data Transformation on Cone Resistance Data at Choctawhatchee Bay Site CUM. PCT. PCT. i4.46 14.46 20.90 35.36 13.85 49.21 11.79 61.01 98.5 69.59 6.67 76.26 5.23 81.49 3.61 95.10 2.20 87.30 1.62 86.92 2.01 90.93 1.69 92.62 1.32 94.14 1.01 95.15 0.99 98.14 0.73 96.87 0.76 97.63 0.71 98.34 0.34 98.66 0.40 99.08 0.17 99.24 0.27 99.52 0.15 99.66 0.19 99.85 0.06 99.92 0.06 100.0 CUM. PCT. PCT. 0.04 0.04 0.17 0.21 1.15 1.39 3.29 4.66 5.71 10.4 5.15 15.5 3.865 19.4 4.83 24.2 4.95 29.2 3.59 32.8 4.81 37.6 6.38 43.9 7.22 51.2 8.12 59.3 7.91 67.2 7.66 74.9 7.41 92.3 4.81 87.1 4.01 91.1 3.80 94.9 2.92 97.8 1.59 98.4 0.61 100 of a variable with its associated transformation. While neither distribution is statistically "normal," the transformed variable is much more symmetrical, suggesting that deterministic estimates of the distribution (i.e., the mean and median) may be more representative of the entire data set. In addition to the logarithmic transformations, the cone penetration test data were filtered using the average value over a 0.5 meter increment. As discussed in Chapter 3, this digital filter smoothes out the high-frequency noise seen in many CPT soundings, while preserving the true character of the sounding. As a result the RMSE will be reduced, and will better reflect the standard deviation in the average value of the estimate. Autocorrelation Function As suggested by Anderson et al., the autocorrelation function was estimated for each site by considering the measured soil property values along lines of constant elevation, and pooling vertically (3). The lowest order regression model which demonstrated stationary residuals (using Kulatilake and Ghosh's approach) was used to remove the trend component. Then an equation was fitted to the autocorrelation function exhibited by the residuals. Appendix E contains two BASIC programs for calculating the autocorrelation function: one assuming the soundings are equally spaced, the other assuming irregular spacing. As mentioned above, the autocorrelation function permits rational evaluation of the spacing of soundings during a geotechnical site investigation. Also, two of the estimation models employed in this study make use of the information obtained from the autocorrelation 72 function; specifically the range or correlated distance, and the fitted autocorrelation function. As noted earlier, since the exact form of this equation is of little real significance and has no theoretical basis, a simple exponential form was used for each site: -r/ib p(r) = e .................................................... (5-2) in which r is the lag or separation distance, and Bis the constant which causes the function to best fit the actual data. The range of the autocorrelation function is the distance at which the data become uncorrelated. For the purposes of this research project, data were assumed uncorrelated when the correlation coefficient was approximately 0.1 or less. Model Types Deterministic. A constant value was used to represent the soil for the whole depth. Three deterministic models were evaluated: the mean, the median, and the 10% trimmed average of the entire data set. Distance Weighting. Two distance weighting functions were applied to soundings within the range of the sounding to be predicted. The first used al/d for the weighting function, whereas the second function used a2/d2, where d is the horizontal distance from the sounding in the data base to the sounding to be predicted. The "an" terms were determined so that the sum of the weighting functions equaled 1: n E d a = i=l i ..........................................(5-3) 1 n n Z [ T d /(d )] i=l i=1 i i n 1 d2 a = i=l i ........................................ (5-4) 2 n n E [ H d2/(d2)] i=1 i=1 i i in which di is the distance to sounding i of n total soundings within the range about the sounding to be predicted. If individual observations of a particular sounding were missing for some reason, then the weights were recalculated using the remaining soundings within the correlated region. Regression Analysis. The third general model evaluated was regression analysis, which fits the "best" curve through the given data by minimizing the squared distance between the curve and the data points using the method of least squares. The adequacy of the model fit is usually summarized using the squared multiple correlation coefficient, R2: 2E(Z Z )(5-5) R( Z )- ....1...................... .............. (5-5) R2 = I A P (z z)2 A in which the subscripts A and P refer to actual and predicted soil property values. The R2 value represents the proportion of the total variability in the dependent variable that can be explained by the regression model, and can vary between 0 (no fit) to 1 (perfect fit). As a rule of thumb, Brook and Arnold recommend an R2 of at least 0.5 in order to have much confidence in the model (9). Several levels of regression analysis were used. The lowest level, termed Model 1, was a simple first order (linear) model: 74 P = b0 + blX + b2Y + b3Z + e ..................................... (5-6) in which P is the predicted value, X and Y are perpendicular horizontal distances, and Z is the vertical depth from some selected reference point. Model 2 was similar to Model 1, except that a second order depth term was added: P = bo + biX + b2Y + b3Z + b4Z2 + e .............................. (5-7) The remaining two levels of regression analysis are termed "Low Term Regression" and "High Term Regression," terminology which requires some explanation. To better describe observed trends in the data set, higher order variables are often required. However, part of the difficulty in applying regression analysis to a problem is determining which variables are important and significant in describing the trends. A stepwise variable selection technique, contained in the SAS procedure STEPWISE, was employed for selection of significant higher-order regression variables. The stepwise technique is a well-regarded variable selection method, the details of which can be found in many texts on regression or multivariate analysis (14,16,48,56). Briefly, the stepwise procedure enters and removes predictors one by one until some "best" regression equation is found. The method starts out by entering the variable most highly correlated with the dependent variable (i.e., the predictor having the largest squared correlation coefficient--squared to allow for significant negative correlations). Succeeding variables are added at each step according to the largest F-value, a statistic which measures whether a variable's contribution to the model was significant, or could be explained by chance. A significance level of 0.15 was used to admit predictor variables to the model (meaning there was at most a 15% chance that the variable's contribution was due to chance). After a variable is admitted to the model, all previously admitted variables are then checked for possible removal by calculating their F-values, assuming that they were the last variable admitted to the model. This test eliminates predictors that may be highly correlated with subsequently entered predictors. A significance level of 0.15 was also used to remove variables. The stepwise procedure continues until all variables meeting the required F-value are entered into the model. Lumb (30) and Tabba and Yong (58) note that horizontal trends can generally be described using first or second order variables, whereas depth variables often must be of much higher order. Therefore the variables selected for evaluation by the STEPWISE procedure were depth up to order 8, horizontal distance up to order 2, and depth-distance interaction terms up to order 5 for depth and order 2 for distance. After the STEPWISE procedure completed its analysis, the "High Term Regression Model" was the final step in the procedure, and represented the best model (as measured by the R2 statistic) containing all predictor variables significant at the 0.15 level. The "Low Term Regression Model" was a model from one of the earlier steps in the STEPWISE procedure with an R2 statistic nearly as large as the High Term Model (i.e., subsequent steps reflected the Law of Diminishing Returns in improvement of the model fit). Random Field. The fourth type of model evaluated for predicting soil properties is the random field model. The nonstationary, or trend portion of the model is the lowest order regression equation exhibiting stationary residuals, as determined during evaluation of the 76 autocorrelation function. The stationary, or random portion employs Equations 4-17 and 4-18, using the equation for the fitted autocorrelation function determined above. A BASIC program for calculating the stationary portion of the model is contained in Appendix E. Linear Interpolation. The final general model evaluated in this study was a simple linear interpolation model. For this model, the sounding to be predicted was linearly interpolated from the immediately adjacent soundings, based on separation distance. This model provides an important comparison for the more "sophisticated" attempts to improve on a single-value deterministicc) estimate, because it is the method most likely to be employed by an engineer. Sites Investigated Choctawhatchee Bay. The first site evaluated was a portion of a replacement bridge being built by the Florida Department of Transportation (FDOT) across Choctawhatchee Bay in the Florida panhandle. Twelve friction-cone penetrometer soundings were used, running generally south to north between Stations 110+88 (Sounding A) and 119+47 (Sounding L) on the causeway south of the main channel, a distance of 859 feet. Figure 5-2 shows a plan view of the site. For purposes of evaluating their spatial variability, the twelve soundings were assumed on a straight line (reducing the problem to a two- dimensional problem), except that the autocorrelation function was calculated based on true separation distances. Three soundings were "predicted," located at Stations 114+78 (Sounding E), 117+00 (Sounding H), and 119+00 (Sounding J). a ECPT TO BE PREDICTED STATION (I STATION 30.5 m) Figure 5-2. Spatial Variability Soundings at Choctawhatchee Bay 1.0, 0.4 o o.---- 0.-8 '2 0. / -0.4 0o u I -0.6 -O 2 a Fs -0.8 2 -1.0 '- 0 100 200 300 400 LAG DISTANCE (FEET) Figure 5-3. Autocorrelation Function for Normalized Raw Data at Choctawhatchee Bay 0 ECPT The spatial variability analysis was based on the upper 20 meters of soil. The surface elevation was nearly level at approximately 1.8 m MSL (6.0 ft MSL), with a range of 1.6 m to 2.1 m (5.4 ft to 7.0 ft). The soil is predominantly fine sand and silty sand, with some sandy clay layers. The ECPT soundings show the site, in general, to have low to moderate qc values to a depth of 5-7 meters (16-23 feet), followed by very low qc's. Between 11 and 14 meters (36-46 feet) the cone resistance increases somewhat, becoming moderate to high at depths ranging from 13 to 17 meters (43-56 feet). The friction resistance values remained low throughout the soundings, increasing modestly when the stiffer sand layer was encountered. A subjective evaluation of the site would describe it as reasonably uniform, sounding to sounding. Figure 5-3 is the autocorrelation function for the raw data (normalized using equation 4-15). Autocorrelation was assumed to be a circular function in the horizontal plane (i.e., autocorrelation in the x- direction = autocorrelation in the y-direction). Figure 5-3 supports the subjective description of "reasonably uniform" since it generally leveled off to an average correlation coefficient of around 0.5 to 0.6 for at least 122 meters (400 feet) laterally. Several of the soundings recorded negative friction values in very weak soils, a problem discussed in Chapter 3. Friction resistance values less than -10 kPa (-105 tsf) were deleted from the data base; all other negative friction values were forced to zero (Note: These values were forced to 1 kPa for the transformed fs). Apalachicola River. The second site evaluated for spatial variability was another FDOOT bridge project across the Apalachicola 79 River. Thirteen standard penetration test (SPT) soundings were used, running on a line east to west between Stations 105+00 (Boring 10) and 124+00 (Boring 22) within the boundaries of the Apalachicola River. Figure 5-4 shows a plan view of the site. Three soundings were "predicted," located at Stations 106+00 (Boring 11), 114+00 (Boring 9), and 118+00 (Boring 13). The spatial variability analysis was based on the SPT soundings between elevation -9.1 and -27.4 meters (-30 and -90 feet) MSL. To facilitate the analysis, the individual soundings were slightly adjusted up or down so that the SPT N values (with units of blows per foot) occurred at the same elevation for all soundings. The decision to limit the analysis to elevations between -9.1 and -27.4 meters was due to 1. The SPT measurements display nearly perfect uniformity from the mud line to elevation -9.1 m (with an N=1-2), and hence show virtually no detectable spatial variability; and 2. Data are sparse below elevation -27.4 m. To minimize any undue effect of individual large data values on the analysis, all N values in excess of 150 (such as 50 blows per 3 inches, equivalent to 200 blows per foot) were truncated to 150 blows per foot. This was the only filtering performed on the Apalachicola River data set. The soil profile is typically loose clayey sand overlying stiff clay, which overlies dense sand. The SPT soundings show the site, in general, to have low N values between elevation -9.1 and -27.4 meters (- 30 and -13.7 feet). Between elevation -13.7 and -27.4 meters (-45 and - 90 feet), however, the N values range widely. Adjacent soundings tended to have somewhat similar profiles, but large differences were not o SPTs * PREDICTED SPTs 112 , I 105 : / I I I -ji LU a: BORING NUMBERS 14 18 18 0 0 0 = * 22 1 15 STATIONS (I STATION = 30.5 m) Figure 5-4. Spatial Variability Soundings at Apalachicola River S1.0 0.8 -\ I- S0.0 S-0.2 S-0.4 C3- o SPT -0.68 -0.8 -1.0 0 100 200 300 400 500 800 700 800 900 1000 LAG DISTANCE (FEET) Figure 5-5. Autocorrelation Function for Normalized Raw Data at Apalachicola River 81 uncommon. Figure 5-5 shows the autocorrelation function for the raw SPT data. Note the generally decreasing correlation coefficient up to a lag distance of 500 feet (152 m). The correlation seems to improve slightly beyond 500 feet, but since autocorrelation functions are known to be less reliable at larger lag distances, this improvement is thought to be an artifact of the particular data set. Archer Landfill. The final site evaluated for spatial variability was a future landfill located west of Archer, Florida. Ten electronic cone penetrometer soundings were used, spread out over approximately 0.7 hectares (1.7 acres). Figure 5-6 shows a plan view of the site. For this analysis, the data were located three-dimensionally since the soundings were not in a relatively straight line. Soundings #4, #5, and #8 were "predicted." The source of the data was a University of Florida Master's degree thesis by Basnett (7). The spatial variability analysis was based on the ECPT soundings between elevations 20 and 30 meters (66-98 feet) (data were sparse below elevation 20 meters). The surface elevation averaged 31.85 meters MSL (104.5 ft MSL), with a range of 30.60 to 32.85 meters (100.4 to 107.8 ft). The soil is described as medium to fine-grained quartz sand. No water table was encountered. The ECPT soundings show the site to have cone resistance and friction resistance values that generally increase with depth. The site is remarkably uniform, although measured stresses are somewhat more variable for the lower five meters (16 ft) of the sounding. Figure 5-7 shows the autocorrelation function for the raw SPT data. Autocorrelation was assumed to be a circular function in the horizontal plane. The uniformity of the site is reflected by the leveling off of 1 4 n 2 n2 u3 I 8 6n1 7 0 ECPT I PREDICTED ECPTs 0 100 FEET 0 30.5 METERS COORDINATES C(FT1 1. (95.204) 2. (122.159) 9 3. (124.149) 0 4. (153.195) 10 5. (382.99) 0 6. (404.5B) 7. (408.45) 8. (430.71) 9. (533,100) 10. (580.50) Figure 5-6. Spatial Variability Soundings I 0. LL 0. o. -0. LJ -0. S-0. -0. at Archer Landfill 50 100 150 200 LAG DISTANCE (FEET) 250 300 Autocorrelation Function for Normalized Raw Data at Archer Landfill 84- ', SOc 4 c I Fs I*.I 0 Figure 5-7. no- -} 83 the correlation coefficients to values generally over 0.6 as far as 300 feet (91.4 m) apart. Results and Discussion Choctawhatchee Bay Site Autocorrelation Function. Since the autocorrelation function for the normalized raw data did not level off to zero (Figure 5-3), a nonstationary component was assumed to be present. Following Kulatilake and Ghosh's recommended technique (26), a first order regression model (Model 1) was used to try to describe the trend. However, the autocorrelation function for the residuals from the regression analysis showed little change from Figure 5-3. Again increasing the order of the regression model one step (Model 2), the autocorrelation function began to approach the expected leveling-off behavior. In order to better describe the trend component, the STEPWISE model generator in the SAS system was employed. A four-term model was selected for both qc and fs: qc = bo + biD + b2D2 + b3D8 + b4D5X R2 = 0.55 ..............(5-8) fs = bo + blD2 + b2X2 + b3DX + b4D5X R2 = 0.65 ..............(5-9) in which 0 is the depth in meters, and X is the distance from Sounding A in.feet. This model produced the autocorrelation functions used in the analysis (Figure 5-8): By trial and error an exponential curve corresponding to equation 5-2 was fitted to both the cone resistance and friction resistance data of Figure 5-8 (since the two curves were very similar). A constant (S) of 20, and a range of 50 feet were estimated. The fact that the range |