TECHNICAL REPORT STANDARD PAGE

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1 TECHNICAL REPORT STANDARD PAGE 1. Report No. FHWA/LA.08/ Title and Sbtitle Update of Correlations between Cone Penetration and Boring Log Data 2. Government Accession No. 3. Recipient's Catalog No. 5. Report Date March Performing Organization Code 7. Athor(s) Khalid Alshibli, Ph.D., P.E. Ayman M. Okeil, Ph.D., P.E. Bashar Alramahi, Ph.D. 9. Performing Organization Name and Address Department of Civil and Environmental Engineering Loisiana State University Baton Roge, LA Sponsoring Agency Name and Address Loisiana Department of Transportation and Development P.O. Box Baton Roge, LA Performing Organization Report No. 10. Work Unit No. 11. Contract or Grant No. LTRC Project Nmber: 06-6GT State Project Nmber: Type of Report and Period Covered Final Report Febrary 2007 March Sponsoring Agency Code 15. Spplementary Notes Condcted in Cooperation with the U.S. Department of Transportation, Federal Highway Administration 16. Abstract The cone penetration test (CPT) has been widely sed in Loisiana in the last two decades as an in sit tool to characterize engineering properties of soils. In addition, conventional drilling and sample retrieval sing Shelby tbe followed by laboratory testing is still the acceptable practice in identifying soils engineering properties. The main objective of this project is to pdate the correlations that are crrently sed by Loisiana Department of Transportation and Development (LADOTD) to interpret CPT data for engineering design prposes and to assess the reliability of sing CPT data to predict soil shear strength in both the magnitde and spatial variations in the field with respect to the Load and Resistance Factor Design (LRFD) methodology. The reslts of laboratory soil testing were retrieved from borehole logs and were sed as reference measrements in this stdy. The research team collected project data files in paper printot format from LADOTD and soil testing engineers. Most project files did not have spatial coordinates; therefore, aerial images were sed to identify latitde and longitde coordinates of CPT and borehole locations. The borehole data was not available for all the located CPT sondings. Efforts were made to obtain any available data from LADOTD electronic archive as well as paper project docments. A total of 752 CPT tests were docmented in which 503 were matched with adjacent boreholes and 249 did not have adjacent borehole data available. The CPT data was sed to predict soil ndrained shear strength, blk density and classification according to Robertson and Zhang and Tmay methods [1], [2]. The CPT data was then sed to develop a database of ndrained shear strength estimates with corresponding reslts from boreholes. The reslts in the database were preprocessed to apply some constraints on data points inclded in the calibration stdy, sch as setting a maximm threshold on the distance between CPT and borehole locations; a minimm and maximm threshold on ndrained shear strength vales were sed to represent realistic soil properties. The reslting database inclded reslts from 251 CPT sondings with borehole reslts in their vicinity that meet the aforementioned constraints. From these CPT sondings, 862 niqe ndrained shear strength data points were obtained at varios depths. The dataset was analyzed for general as well as specific trends in order to identify appropriate parameters to be inclded in the stdy. Soil classification was clearly the most plasible parameter based on which the CPT ndrained shear strength estimates shold be calibrated. The calibration of the CPT expression for ndrained shear strength was condcted sing two approaches. The first approach is a direct correlation based of the transformation model crrently sed by LADOTD for estimating the shear strength. The First Order Reliability Method (FORM) forms the basis for the second approach, which is more detailed and acconts for all sorces of ncertainty. Optimm CPT coefficient vales were compted for varios target reliability vales. The reslts were smmarized and implementation procedres were recommended for ftre research. 17. Key Words cone penetrometer; soil testing; reliability; geographical information system 18. Distribtion Statement Unrestricted. 19. Secrity Classification (of this report) N/A 20. Secrity Classification (of this page) N/A 21. No. of Pages Price N/A

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3 Project Review Committee Each research project will have an advisory committee appointed by the LTRC Director. The Project Review Committee is responsible for assisting the LTRC Administrator or Manager in the development of acceptable research problem statements, reqests for proposals, review of research proposals, oversight of approved research projects, and implementation of findings. LTRC appreciates the dedication of the following Project Review Committee Members in giding this research stdy to frition. LTRC Administrator/ Manager Zhongjie Doc Zhang, Ph.D., P.E. Pavement Geotechnical Research Administrator Members Dr. Ching Tsai, Geotechnical Section Ben Fernandez, Geotechnical Section Dr. Mrad Abfarsakh, LTRC Dr. Recep Yilmaz, Fgro Geosciences Bert Wintz, Materials Laboratory Kim Carlington, Geotechnical Section Philip Arena, FHWA Gavin Gatrea, LTRC Directorate Implementation Sponsor William B. Temple DOTD Chief Engineer 4

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5 Update of Correlations between Cone Penetration and Boring Log Data by Khalid Alshibli, Ph.D., P.E. Associate Professor Ayman Okeil, Ph.D., P.E. Assistant Professor Bashar Alramahi, Ph.D. Research Associate Department of Civil and Environmental Engineering 3505 Patrick F. Taylor Hall Loisiana State University Baton Roge, LA LTRC Project No. 06-6GT State Project No condcted for Loisiana Department of Transportation and Development Loisiana Transportation Research Center The contents of this report reflect the views of the athor/principal investigator who is responsible for the facts and the accracy of the data presented herein. The contents of do not necessarily reflect the views or policies of the Loisiana Department of Transportation and Development or the Loisiana Transportation Research Center. This report does not constitte a standard, specification, or reglation. 6 March 2008

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7 ABSTRACT The cone penetration test (CPT) has been widely sed in Loisiana in the last two decades as an in sit tool to characterize engineering properties of soils. In addition, conventional drilling and sample retrieval sing Shelby tbe followed by laboratory testing is still the acceptable practice in identifying soils engineering properties. The main objective of this project is to pdate the correlations that are crrently sed by Loisiana Department of Transportation and Development (LADOTD) to interpret CPT data for engineering design prposes and to assess the reliability of sing CPT data to predict soil shear strength in both the magnitde and spatial variations in the field with respect to the Load and Resistance Factor Design (LRFD) methodology. The reslts of laboratory soil testing were retrieved from borehole logs and were sed as reference measrements in this stdy. The research team collected project data files in paper printot format from LADOTD and soil testing engineers. Most project files did not have spatial coordinates; therefore, aerial images were sed to identify latitde and longitde coordinates of CPT and borehole locations. The borehole data was not available for all the located CPT sondings. Efforts were made to obtain any available data from LADOTD electronic archive as well as paper project docments. A total of 752 CPT sondings were docmented in which 503 were matched with adjacent boreholes and 249 did not have adjacent borehole data available. The CPT data was sed to predict soil ndrained shear strength, blk density and classification according to Robertson and Zhang and Tmay methods [1], [2]. The CPT measrements were then sed to develop a database of ndrained shear strength estimates with corresponding reslts from boreholes. The reslts in the database were preprocessed to apply some constraints on data points inclded in the calibration stdy, sch as setting a maximm threshold on the distance between CPT and borehole locations; a minimm and maximm threshold on ndrained shear strength vales were sed to represent realistic soil properties. The reslting database inclded reslts from 251 CPT sondings with borehole reslts in their vicinity that meet the aforementioned constraints. From these CPT sondings, 862 niqe ndrained shear strength data points were obtained at varios depths. The dataset was analyzed for general as well as specific trends in order to identify appropriate parameters to be inclded in the stdy. Soil classification was clearly the most plasible parameter based on which the CPT ndrained shear strength estimates shold be calibrated. iii

8 The calibration of the CPT expression for ndrained shear strength was condcted sing two approaches. The first approach is a direct correlation based of the transformation model crrently sed by LADOTD for estimating the shear strength. The First Order Reliability Method (FORM) forms the basis for the second approach, which is more detailed and acconts for all sorces of ncertainty. Optimm CPT coefficient vales were compted for varios target reliability vales. The reslts were smmarized and implementation procedres were recommended for ftre research. iv

9 ACKNOWLEDGMENTS The athors grateflly acknowledged the financial spport provided by the Loisiana Transportation Research Center (LTRC) and Loisiana Department of Transportation and Development (LADOTD). The athors also acknowledge the assistance of the gradate stdents Chaytanya Mamidala and Ashwin Bommathanahalli who helped in data archiving and analysis. The athors wold also like to thank Benjamin Fernandez from LADOTD geotechnical section and Jesse Raser from Ardaman & Associates, Inc. for providing the CPT and borehole data. The constrctive criticism and sggestions of Dr. Zhongjie Doc Zhang, pavement geotechnical research administrator, and Mark Morvant, associate director of research at LTRC, are highly valed and appreciated. v

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11 IMPLEMENTATION STATEMENT The reslts of this stdy demonstrated the benefit of performing in depth statistical analyses of soil property estimation methods. The cone penetration test has been in service for years, and it is prdent to pdate its coefficients and identify limits on its application so safe design can be achieved. In this stdy, a database of CPT sondings has been compiled with corresponding borehole reslts where available. The developed database shold be pdated as more borehole and CPT data become available for ftre projects. The database is sefl and has been integrated into a Geographic Information Systems (GIS) system so LADOTD engineers may have easy access to its components. Comparison of the ndrained shear strengths obtained from the CPT sondings and nconfined compression test on borehole samples revealed that it is possible to identify niqe trends. These trends were sed in pdating the correlation of the CPT coefficient, N. As a side prodct of this stdy, a procedre for identifying site variability is proposed that does not involve any sbjective interpretation of the reslts. The procedre may be sed when implementing new Load and Resistance Factor Design (LRFD) design codes where some design coefficients are varied based on the site variability. Based on the reslts of this stdy, it is recommended that the findings of this research be implemented for a pilot testing period where LADOTD engineers gradally start sing the newly correlated CPT coefficient, N, for estimating the ndrained shear strength in conjnction with the traditional borehole assessments. Dring this period, it is important to assess the validity of the proposed changes from this stdy and docment its otcome for ftre reference. As the findings get pdated, it is anticipated that LADOTD engineers can gradally move toward replacing the conventional reliance on boreholes for ndrained shear estimates with CPT sondings. This will translate, in the long rn, as a cost benefit to LADOTD. vii

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13 TABLE OF CONTENTS ABSTRACT... III ACKNOWLEDGMENTS... V IMPLEMENTATION STATEMENT... VII TABLE OF CONTENTS... IX LIST OF TABLES... XIII LIST OF FIGURES... XV Part I: Cone Penetration Test (CPT)... 1 Historic Backgrond... 1 Apparats Description and Correction Factors... 3 Soil Classification sing CPT... 6 Strength Characteristics Effective Stress Strength Parameters Stress History Relative Density from CPT Data Correlations with Standard Penetration Test (SPT) Part II: Load and Resistance Factor Design (LRFD) LRFD in Geotechnical Applications OBJECTIVE SCOPE METHODOLOGY CPT Database Locating CPT Sites sing GIS Borehole Data CPT and Borehole Data Analysis and Archiving Reliability Analysis of CPT Direct Correlation of CPT and Boring Reslts 1 st Approach Detailed Reliability Analysis for Correlation of CPT and Boring Reslts 2 nd Approach Preprocessing CPT Data Matching CPT and Borehole Data ix

14 x Averaging CPT Readings Filtering Data Reslts Calibration of CPT Coefficient Limit State Fnction Chi-Sqare Statistical Test Goodness of Fit Reliability-based Calibration DISCUSSION OF RESULTS Repeatability Tests Statistical Characteristics of Repeatability Data Utilizing CPT for Assessment of Site Variability Initial Data Analysis General Trends Specific Parameter Trends CPT Reading Vales ( q c ) vo Chi-Sqare Reslts Calibration of CPT Coefficient for Undrained Shear Strength Calibration 1 st Approach Calibration 2 nd Approach Correlation Between Unit Weight, T, from CPT and Boring Data SUMMARY AND CONCLUSIONS Smmary Conclsions RECOMMENDATIONS ACRONYMS, ABBREVIATIONS, AND SYMBOLS REFERENCES APPENDIX A List of Projects Inclded in Database APPENDIX B First Order Reliability Method (FORM) APPENDIX C Chi-Sqare Statistical Test: Goodness-of-fit Test APPENDIX D

15 Normal and Lognormal Distribtion Types Normal or Gassian Distribtion Lognormal Distribtion The random variable X is a lognormal random APPENDIX E Example Excel Template to Analyze CPT Data xi

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17 LIST OF TABLES Table 1 Nc vales theoretically derived by different researchers (11) Table 2 Constants for determination of D r [65] Table 3 Sggested Q c vales [67] Table 4 Typical I c ranges for different soil types [73] Table 5 Random variables sed in reliability calibration Table 6 Statistical characteristics of transformation model (Robertson classification) Table 7 Statistical characteristics of transformation model (Zhang and Tmay classification) Table 8 Range of parameters covered in reliability stdy Table 9 Discrete tip resistance, q c, readings at 5 ft. intervals Table 10 Discrete nit weight, T, reslts at 5 ft. intervals Table 11 Discrete overbrden pressre readings at 5 ft. intervals Table 12 Effect of soil depth on ncertainty of CPT reslts Table 13 Effect of net difference between CPT readings, qc, on ncertainty of CPT reslts Table 14 Effect of soil classification on ncertainty of CPT reslts Table 15 Effect of soil classification on ncertainty of CPT reslts Table 16 Effect of soil classification on ncertainty of CPT reslts (Robertson) Table 17 Effect of Plasticity Index on ncertainty of CPT reslts Table 18 Smmary of chi-sqare test reslts for transformation model Table 19 Calibrated N vales for different probability of exceedance, P e, vales Table 20 Reliability reslts ( = 0.0, q = 0.10, Robertson classification) T vo c vo Table 21 Reliability reslts ( = , q = 0.10, Robertson classification) T vo Table 22 Reliability reslts ( = , q = 0.10, Robertson classification) Table 23 Optimm Table 24 Optimm Table 25 Optimm T vo c c N vales ( = 0.0, Robertson classification) T N vales ( = , Robertson classification) T N vales ( = , Robertson classification) T Table 26 Reliability reslts ( = 0.0, q = 0.10, Zhang and Tmay classification) T vo c Table 27 Reliability reslts ( T = , q vo c = 0.10, Zhang and Tmay classification) Table 28 Reliability reslts ( T = , q vo c = 0.10, Zhang and Tmay classification) Table 29 Optimm N vales ( = 0.0, Zhang and Tmay classification) T xiii

18 Table 30 Optimm Table 31 Optimm Table 32 Recommended Table 33 Recommended N vales ( = , Zhang and Tmay classification) T N vales ( = , Zhang and Tmay classification) T N vales sing 2 nd approach (Robertson classification) N vales sing 2 nd approach (Zhang and Tmay classification) 113 Table 34 Projects with CPT and borehole data Table 35 Projects with CPT data withot borehole data Table 36 CDF of the chi-sqare distribtion (Nowak and Collins 2000) xiv

19 LIST OF FIGURES Figre 1 Early cone penetrometers (a) Dtch cone with conical mantle, (b) Begemann cone with friction sleeve [11]... 2 Figre 2 Typical Schematic of Piezocone [12]... 4 Figre 3 Typical reslts of CPT... 5 Figre 4 Doglas and Olsen classification chart [18]... 8 Figre 5 Classification charts presented by Robertson et al. [19]... 9 Figre 6 Eslami and Fellenis classification chart [26]... 9 Figre 7 Charts to obtain S from excess pore water pressre measrements [51] Figre 8 Interpretation diagrams for β = 0 and β = -15 o [57] Figre 9 Empirical correlations of OCR vs. normalized PCPT parameters [58] Figre 10 Comparison between the measred and predicted σ`p vales [62] Figre 11 Variation of q c /N with d 50 [19] Figre 12 Uncertainty in soil property estimates [93] Figre 13 CPT data points from LADOTD and STE Figre 14 CPT data points with and withot borehole data from LADOTD and STE Figre 15 Example CPT point information displayed by selecting a CPT location Figre 16 Example CPT classification file displayed by selecting the PDF link Figre 17 Zoomed view of the northern part of Loisiana where a higher nmber of CPT points were available Figre 18 Zoomed view of the sothwestern part of Loisiana where a smaller nmber of CPT points were available Figre 19 Histogram of depths for CPT points inclded in database Figre 20 Depth histograms for different soil classifications [4], [5], [19] Figre 21 Array of CPT repeatability tests Figre 22 Distance threshold between CPT and borehole locations showing nmber of data points inclded in analyses Figre 23 Averaging raw CPT readings Figre 24 Histogram of S freqency in compiled database Figre 25 Effect of thresholds on ncertainty of transformation model S Figre 26 Illstration of the limit state fnction (LSF) sed in this stdy (general case) Figre 27 Illstration of the limit state fnction (LSF) sed in this stdy (special case) Figre 28 Cone data from all repeatability tests Figre 29 Analysis of repeatability data for cone tip resistance xv

20 Figre 30 Stdy of nit weight data scatter from repeatability tests Figre 31 Stdy of overbrden pressre data scatter from repeatability tests Figre 32 Tip resistance, q c, readings from all CPT repeatability tests Figre 33 Stdy of tip resistance data scatter, COV q, vs. soil classification Figre 34 Stdy of nit weight data scatter, COV T, vs. soil classification Figre 35 Stdy of overbrden pressre data scatter, COV, vs. soil classification Figre 36 Comparison of ndrained shear strength, S, from CPT and UC tests UC Figre 37 Analyzing data trends of different CPT readings verss S Figre 38 Comparison of ndrained shear strength, S, from CPT and UC tests Figre 39 Comparison of ndrained shear strength, S, from CPT and UC tests at different CPT readings net difference,, vales qc vo Figre 40 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Zhang and Tmay clay only) Figre 41 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Zhang and Tmay clay and silt) Figre 42 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Robertson) Figre 43 Comparison of ndrained shear strength, S, from CPT and UC tests for different Plasticity Index vales Figre 44 Chi sqare test reslts for transformation model (all data points) Figre 45 Chi sqare test reslts for transformation model (Soil Classification 2) Figre 46 Chi sqare test reslts for transformation model (Soil Classification 3) Figre 47 Chi sqare test reslts for transformation model (Soil Classification 4) Figre 48 Chi sqare test reslts for device ncertainty Figre 49 Histogram of c N vales obtained from eqation (42) all data points Figre 50 Cmlative distribtion fnction (CDF) for vo N vales [all data points] Figre 51 Histogram of N vales obtained from eqation (42) (by Robertson soil classification) Figre 52 Histogram of N vales obtained from eqation (42) (by Zhang and Tmay s soil classification) Figre 53 Determining optimm N vales ( = , q = 0.05) T vo c xvi

21 Figre 54 Unit weight correlation T (CPT vs. boring reslts) Figre 55 Histogram of nit weight ratio T, CPT T, BoreHole Figre 56 Reliability index evalated at design point (Nowak and Collins 2000) Figre 57 Graphical representation of normal distribtion Figre 58 Graphical representation of lognormal distribtion xvii

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23 INTRODUCTION Part I: Cone Penetration Test (CPT) In recent years, the Cone Penetration Test (CPT) has gained poplarity as a fast, inexpensive, and fairly accrate method for in-sit characterization of sb-srface soil layers. This is attribted to its ability to obtain nearly continos measrements providing a mch higher data resoltion than standard soil sampling procedres. The data obtained from a CPT sonding can be sed to determine the soil shear strength (e.g., [3], [4], and [5]), soil classification, in-sit stresses, compressibility, permeability, and other soil properties. The CPT is a simple, qick, and economical test that provides reliable and continos in-sit sondings of sbsrface soil. In a CPT, a series of metal rods with a cone-shaped tip are pshed into the grond at a constant penetration rate. Dring this process, load sensors measre the amont of force reqired to penetrate different soil layers. Mainly, two force components are measred dring a CPT: the force acting on the cone (Q c ) and the total combined force acting on the cone and cylindrical friction sleeve located behind the tip (Q t ). The cone resistance (q c ) is calclated as the force (Q c ) divided by the projected area of the cone (A c ), while the sleeve friction (f s ) is calclated as the net force acting on the friction sleeve (Q t - Q c ) divided by the srface of the sleeve (A s ). To frther improve the interpretation ability of the CPT, pore water pressre transdcers were added to the cone; it is referred to as Piezo-Cone Penetration Test (PCPT). Pressre measrements are sally obtained at three locations: the tip of the cone ( 1 ), behind the cone ( 2 ), and behind the friction sleeve ( 3 ). The following sections present a historic backgrond, a detailed description of the CPT/PCPT, and a brief overview of the measred and calclated parameters sed to interpret CPT/PCPT data. Historic Backgrond The cone penetration test, in its crrent form, was invented in the Netherlands in 1932 by P. Barentsen. It was referred to as the Dtch cone penetrometer. It consisted of a steel rod with a cone tip sliding inside a metal gas pipe. While the rod was manally pshed in the grond, load measrements were performed at different depths. The apparats was mainly sed by Dtch engineers to determine the ltimate capacity of driven piles in sand [6]. The Dtch cone was later improved by Vermeiden and Plantema by adding a conical mantle jst above the cone to prevent soil from entering the gap between the rod and the pipe

24 (Figre 1a) [7], [8]. A major improvement was introdced by Begemann by adding a friction sleeve behind the cone which enabled the measrement of friction as well as the cone resistance (Figre 1b) [9]. Several methods were sed over time to advance the cone into the grond. The development of a cone penetrometer that consisted of a conical point connected to the piston of a small hydralic jack at the base of the rod was reported by Sanglerat [10]. He also reported the development of a hydralic penetrometer by the Centre Expérimental d Bâtiment et des Travax Pblics (CEBTP) in France in These types of mechanical cones are still in se becase of their low cost and simplicity of se [11]. (a) Figre 1 Early cone penetrometers (a) Dtch cone with conical mantle, (b) Begemann cone with friction sleeve [11] (b) 2

25 Apparats Description and Correction Factors A typical CPT apparats consists of a 60 o conical tip with a 10 or 15 cm 2 base and a 150 cm 2 friction sleeve located behind it. Figre 2 illstrates a typical PCPT apparats showing the geometry of the cone and the friction sleeve in addition to the pore water pressre transdcers. As mentioned earlier, the main parameters measred dring a PCPT are the cone resistance (q c ) and the sleeve friction (f s ) in addition to three pore water pressre measrements performed at different locations: 1 measred on the cone tip, 2 measred behind the cone, and 3 measred behind the sleeve. Many methods are employed to obtain the cone resistance and sleeve friction. Most poplarly, two load cells are sed: one is located behind the cone while the other is located behind the sleeve. The cone resistance is directly obtained from the reading of the first load cell while the sleeve friction is calclated from the difference between the first and second load cell readings. This type is called a sbtraction cone and is preferred de to the overall robstness of the penetrometer [13]. Depending on the cone geometry, sensors locations, and temperatre effects among other factors, several correction factors are sggested in order to ensre the qality of the obtained CPT data and to accont for the different types of penetrometers that might be sed. De to the neqal area effect, where the pore water pressre acts on the sholders behind the cone and the sleeve, a cone area ratio (a) is sed to correct the obtained cone resistance. It is approximately eqal to the ratio of the area of the load cell or shaft to the projected area of the cone. The corrected cone resistance is defined as: q t q 2 (1 a) (1) c The sleeve friction is also inflenced by the neqal area effect; therefore, it is also corrected to accont for the difference in the pore water pressre between the front ( 2 ) and the sholder ( 3 ) of the sleeve. The corrected sleeve friction is calclated as: f ( 2 Asb 3 Ast ) t f s (2) As 3

26 where, A sb is the cross sectional area at the bottom of the friction sleeve, A st is the cross sectional area at the top of the friction sleeve, and A s is friction sleeve srface area. Lnne et al. noted that this correction is rarely carried ot becase 3 is seldom measred [11]. On the other hand, the pore water pressre at the front of the cone can be estimated from pore water pressre readings at the tip of the cone sing the following eqation (14): 2 o ( 1 o k ) (3) where, o = hydrostatic or initial in-sit pore pressre, and k = adjstment factor (fnction of soil type and properties) Figre 2 Typical Schematic of Piezocone [12] 4

27 Figre 3 Typical reslts of CPT Another parameter commonly calclated from CPT data is the ratio of the sleeve friction to the tip resistance, known as the friction ratio illstrated in eqation (4). This parameter is particlarly sefl in soil classification becase different soil types exhibit different relative amonts of tip resistance and sleeve friction. Therefore, this ratio provides a sefl tool to determine different soil types. This parameter is sally plotted alongside the tip resistance and sleeve friction when reporting CPT reslts. An example presentation of CPT data is illstrated in Figre 3. f t R f (4) qt 5

28 Soil Classification sing CPT Data obtained from a CPT can be sed to classify the different types of soils along the path of the cone. It was observed that different types of soils exhibit distinctive responses dring cone penetration making it possible to classify the soils based on their response. For example, while sandy soils are characterized by high cone resistance and low friction ratio, soft clays prodce low cone resistance and high friction ratio [11]. Begemann noted that soil type is not a strict fnction of the tip resistance or sleeve friction bt rather a combination of these vales [15]. Several efforts were made to present a dependable classification chart sing cone penetrometer data [16], [17]. Using an extensive database of CPT reslts in different soil types, Doglas and Olsen presented a chart that can be sed to classify different types of soils sing the cone resistance and the friction ratio (Figre 4) [18]. They noted that this classification provides a gide to the soil types based on their behavior and cannot be expected to provide accrate prediction abot the soils grain size distribtion. In the following years, different classification charts were sggested sing broader soil database; most of them still sed the cone resistance and the friction ratio as a basis for classification [19], [20]. However, it was noticed that even with carefl procedres and corrections for pore pressre effects, sleeve friction measrements are often less accrate and less reliable than the cone resistance [21], [22]. Therefore, classification charts have been proposed based on the tip resistance and pore water pressre [23], [24], [25]. A pore water pressre index B q was sed in the classification; it is defined as [11]: B q q o 2 (5) t vo where, 2 = Pore pressre measred between the cone and the friction sleeve, o = eqilibrim pore pressre, vo = total overbrden stress, and q t = cone resistance corrected for neqal end area effects. 6

29 In order to perform a more accrate classification scheme, Robertson et al. as sggested classification charts based on all three pieces of data (q t, f s, and B q ), shown in Figre 5 [19]. These charts classify the soils based on their response to 12 distinct soil types and provide information abot the relative density and over-consolidation ratio (OCR) of the soils. Eslami and Fellenis presented a classification chart based on data obtained from 20 sites in 5 contries [26]. They sed an effective tip resistance parameter ( qe qt 2 ) to provide a more consistent delineation of envelopes than a plot of only the cone resistance. This parameter along with the sleeve friction were sed to classify soils into five main categories as shown in Figre 6. After comparing several soil classification methods sing CPT data, Fellenis and Eslami conclded that the classification methods that do not correct for the pore pressre on the cone sholder may not be relevant otside the areas where they were developed, and the error de to omitting the pore water pressre is highest in fine grained soils [27]. Since soil classification based on CPT data depends on the mechanical properties of the soils, sch as strength and compressibility; Zhang and Tmay arged that de to complicated environmental conditions, the correlation between soil and mechanical properties will never be a simple one-to-one correspondence [2]. They also indicated that the CPT classification charts do not present an accrate prediction of soil types based on compositional properties bt rather a gide to soil behavior type. They sggested an alternative classification method sing statistical and fzzy sbset approaches to calclate a soil classification index (U) from CPT data that is sed to determine probable Unified Soil Classification System (USCS) (compositional) soil types. 7

30 8 Figre 4 Doglas and Olsen classification chart [18]

31 Figre 5 Classification charts presented by Robertson et al. [19] Figre 6 Eslami and Fellenis classification chart [26] 9

32 This alternative classification method tilizes the fzzy sbset approach which aims to release the constraint of soil composition and pt emphasis on the soil behavior instead [28], [29]. Three empirically defined density fnctions that correspond to three soil grops are presented: highly probable clay (HPC), highly probable mixed (HPM), and highly probable sand (HPS). The three fnctions as a whole will reflect the overall perspective of soil properties. This reslts in a classification that does not yield sharp bondaries between layers bt rather a smooth transition from one soil type to another. This statistical approach has been adopted by LADOTD as a standard procedre for the interpretation on CPT data. Strength Characteristics Undrained Shear Strength. Many researchers attempted to develop a dependable correlation between the parameters obtained from cone penetration tests and the ndrained shear strength of cohesive soils. Some of the presented correlations were based on theoretical soltions like the bearing capacity theory, cavity expansion method strain path method and nmerical methods sing linear and non-linear soil models [30], [31], [32], [33], [34]. Other correlations, however, were empirically developed by comparing CPT reslts with laboratory shear strength experiments. In theoretical soltions, the ndrained shear strength is expressed as a fnction of the cone tip resistance sing the following eqation: S q N c (6) c where, N c is a theoretical cone factor, and σ is the in-sit total pressre. Depending on the theory sed to calclate N c, σ can be the total vertical (σ vo ), horizontal (σ ho ), or mean (σ mean ) stress. Table 1 presents a smmary of N c vales theoretically derived by different researchers. Since cone penetration is a complex phenomenon, all theoretical soltions make several simplifying assmptions regarding soil behavior, failre mechanism, and bondary conditions. The theoretical soltions need to be verified from actal field and/or laboratory test data. Theoretical soltions have limitations in modeling the real soil behavior nder conditions of varying stress history, anisotropy, sensitivity, aging and micro fabric. Hence, 10

33 empirical correlations are generally preferred althogh the theoretical soltions have provided a sefl framework of nderstanding. Lnne and Kleven presented an eqation to predict the ndrained shear strength sing the total cone resistance [44]: S q N c vo (7) k where, q c is the measred cone resistance, vo is the in sit vertical stress, and N k denotes the cone factor that incldes the inflence of the cone shape and depth factor; its vale typically ranges from 11 to 19 for normally consolidated clays [11]. Kjekstad et al. reported a N k vale of 17 for over-consolidated clays [45]. Eqation (7) was later modified where the corrected cone resistance (q t ) was sed: S q N t vo (8) Many experiments were performed to estimate the vale (or range of vales) for N [46], [47], [48]. A wide range of vales were reported depending on the type of cone, field conditions, penetration rate and laboratory testing method. However, most of the reported vales of N ranged between 10 and

34 Table 1 Nc vales theoretically derived by different researchers [11] N c 0 i Remarks Reference vo [35] 7.0 vo [36] 9.34 vo Smooth Base [37] 9.74 vo Rogh Base 9.94 vo [38] Spherical cavity Et ln 1 vo expansion, E t : initial [37] 3s tangent modls E 1 ln s 4 E 1 s ln 3 3s s 1 cot vo vo 4 E 1 s ln cot vo 3 s 4 1 ln I R 3 vo 4 1 ln R 3 I mean 1 ln 11 sa 4 s r E 1 r ln s 3 s 3sr E s Er sr sr s E S Er sr I R ho ln 4 3 E s ` ln r o s s E r vo I 1 K 2 : semi apex angle; IR: rigidity index. r vo vo Spherical cavity expansion, E s : secant modls at 50% failre Spherical cavity expansion Spherical cavity expansion, finite strain theory Spherical cavity expansion Spherical cavity expansion Cylindrical cavity expansion Trilinear stress-strain relationship Elastic perfectly plastic- strain path approach [39] [40] [40] [31] [31] [41] [42] [43] 12

35 Another eqation was sggested by Senneset et al. sing the effective in lie of the total cone resistance [49]: S qe qt 2 (9) N ` N ` c c They reported an average vale of 15 for N c ` with a likely variation of ±3. They also noted that S vales are particlarly qestionable for small excess pore pressres corresponding to B q < 0.4 that is for materials coarser than clayey silt. Using the same eqation, Lnne et al. reported N c ` vales of 1 to 13 [50]. Campanella and Robertson noted that althogh this method might work well for some deposits, it is not recommended to se the effective cone resistance to estimate S [51]. They explained that in soft normally consolidated clays, the total pore pressre behind the cone is approximately 90 percent or more of the measred cone resistance. This reslts in a very small vale of q c that is very sensitive to small errors in q or 2 measrement. Several other researchers attempted to se the excess pore water pressre (Δ = 2 o ) to estimate the ndrained shear strength [31], [52], [53], [54], [55]. They sed: S (10) N The obtained vales of the effective cone resistance method is that N were between 2 and 20. One advantage of these methods over can be very large, especially in soft clays, making the effect of measrement errors less significant and reslting in a better accracy for this method. Based on cavity expansion theory, Massarch and Broms presented a semi-empirical soltion that inclded the effects of overconsolidation and sensitivity of soils by sing Skempton s pore pressre parameter at failre (A f ) [55]. They presented a set of charts to obtain S based on excess pore pressre measrements (Figre 7). 13

36 Figre 7 Charts to obtain S from excess pore water pressre measrements [51] Effective Stress Strength Parameters Many correlations were sggested to calclate the effective stress parameters: friction angle φ` and attraction a ( c tan ` ) from CPT data. Using the bearing capacity approach based on the theory of plasticity, Senneset et al. presented a theoretical approach for sing PCPT data to determine the effective stress parameters [49]. However, Campanella and Robertson arged that since this method is based on the bearing capacity theory and as with any method for determining drained parameters from ndrained cone penetration, it can be sbject to serios problems [51]. One of which is the location of the poros element, where different locations give different measres of the total pore pressres. Keaveny and Mitchell sggested another method that ses empirical correlations to estimate the overconsolidation ratio (OCR), Skempton s pore pressre parameter (A f ), lateral earth pressre parameter (K o ), and Vesic s cavity expansion method to estimate the ndrained shear strength (S ) [56]. These parameters are sed to estimate the effective stress at failre, which combined with S to provide an estimate of the effective stress strength parameters. They reported good reslts for silts and overconsolidated clays; however, reslts for normally consolidated clays were poor. Althogh this method acconts for different pore pressre 14

37 measrement locations, it relies on simplified empirical correlations to estimate OCR, A f, and K o, which cold case poor interpretations [51]. Senneset et al. presented another soltion based on the bearing capacity theory [57]. They sggested two parameters that can be calclated from measred PCPT data: The cone resistance nmber: N m qt vo ` a vo (11) The pore pressre ratio: B q 1 o ` a vo (12) where, `vo is the effective overbrden pressre. The friction angle is then fond from an interpretation chart based of the two parameters in addition to the angle of plastification (β) which expresses an idealized geometry of the generalized failre zones arond the advancing cone. Figre 8 presents example interpretation charts. Figre 8 Interpretation diagrams for β = 0 and β = -15 o [57] 15

38 Stress History Stress history can be expressed by either defining the maximm past effective stress σ`p or the over-consolidation ratio OCR ( ` ` ). Many approaches were sggested to correlate p v CPT data to stress history parameters. Based on data collected from high qality ndistrbed specimens; Lnne et al. presented a set of charts to predict OCR from CPT measrements (Figre 9) [58]. They noted that these figres are based on local correlations and shold be pdated as local experience is obtained. Figre 9 Empirical correlations of OCR vs. normalized PCPT parameters [58] 16

39 On the other hand, Slly et al. presented an expression for OCR based solely on pore pressre measrements, which is shown in eqation (13) [59]. This correlation, however, cannot be extended to clays with very high OCR vales. 1 2 OCR (13) o After reviewing the methods sed to obtain OCR from CPT measrements, Mayne sggested an expression based on critical state soil mechanics and cavity expansion theory [60]: OCR q 2 2 t 1.95M 1 ` vo (14) As a first order estimate, Mayne sggested an expression to predict σ`p sing the corrected tip resistance q t, i.e., eqation (15) [61]. While this expression yielded good estimates of σ`p for a wide variety of clays, it nderestimated the vales for fissred clays. Figre 10 presents a comparison between the vales of σ`p obtained from one-dimensional oedometer test and the vales predicted by eqation (15). ` p 0.33 qt `v (15) Figre 10 Comparison between the measred and predicted σ`p vales [62] 17

40 ' Chen and Mayne presented a set of expressions to estimate p incorporating pore water pressre measrements, i.e., eqations (16) throgh (19) [63]. They arged that the redndancy of expressions give an opportnity to confirm the vale of the calclated parameter in case they agree and gives a reason to frther investigate the reslts if a discrepancy exists [62]. `p 0.41( 1 o ) `p 0.53( 2 o ) ` p 0.75( q t 2 ) ` p 0.60( q t 2 ) (16) (17) (18) (19) Not as many correlations were presented for determining OCR for sandy soils. This is becase it is more challenging to determine the stress history for sandy soils. Mayne noted that this challenge is cased by two main reasons: (1) one dimensional oedometric experiments for sandy soils yield a fairly flat e-log(σ`) crve making it difficlt to detect the pre-consolidation pressre, and (2) it is difficlt to obtain ndistrbed specimens of sandy soil deposits [62]. Therefore, a relationship to obtain OCR for clean sands was empirically derived based on data from 24 calibration chamber experiments [11], [64]: OCR 1 sin ` q t pa 1 sin` ` p vo a 0.31 (20) Relative Density from CPT Data The relative density (D r ) of sands is an important engineering index property that gives an indication abot the level of compaction (or density) that can be sed to estimate other properties like the angle of internal friction. It is traditionally calclated as: D r e e max (21) max e e min where, e is the void ratio, and e max and e min are the maximm and minimm void ratios. It is well known that it is difficlt to obtain reliable vales for e max and e min becase of variations 18

41 in sample preparation procedres (e.g., compaction effort) and their dependency on the operator. Therefore, CPT can provide a sefl alternative for determining the in-sit relative density of sands. D r is commonly related to the cone tip resistance (q c ) with consideration to the overbrden pressre (σ`v) and soil compressibility [65]. Baldi et al. performed calibration testing on clean Ticino silica sand that has a moderate compressibility and proposed the following eqation [66]: D r c ln c qc 1 c 2 v ` 3 (22) where, c 1, c 2, and c 3 are constants dependent on the compressibility; their vales for high, moderate, and low compressibility sands are presented in Table 2. Table 2 Constants for determination of D r [65] Compressibility c 1 c 2 c 3 High Moderate Low Based on experiments performed on clean fine to medim silica sands, Klhawy and Mayne sggested the following formla [67]: D 2 r 305 Q c 1 OCR 0.15 Q A q p c a p a ` v 0.5 (23) where, p a = atmospheric pressre; OCR= over-consolidation ratio; Q c = compressibility factor, sggested vales for this factor are smmarized in Table 3; and Q A = Aging factor, defined as: 19

42 t Q A log (24) 100 where, t is time. The previos correlations sed calibration chamber testing withot considering the bondary effects. Jamiolkowski et al. re-examined a large set of calibration chamber tests and presented another expression for D r that incorporates the bondary effects, [68]. Table 3 Sggested Q c vales [67] Compressibility Description Q c Low Medim High Predominantly qartz sands, ronded grains with little or no fines Qartz sands with some feldspar and/or several percent fines High fines content, mica or other compressible materials D R qt pa ln `vo pa (25) Klhawy and Mayne sed a database of 24 sands to establish a simpler correlation that ses an empirical constant of the least-sqare regression Q F, [67]. D 2 r 1 Q q `v p a 0. pa c 5 F (26) Jang et al. arged that althogh the previos methods are based on the compressibility of soils, compressibility itself is not well defined [69]. It is inflenced by mineral type, particle anglarity, particle gradation, particle size, particle srface roghness, and stress history. They also noted that sands with the same mineral type cold be nder different categories of compressibility (low, medim, or high) depending on D r and stress history. 20

43 Based on these observations, they presented an approach sing fzzy sets to determine D r from CPT data. In this method, the friction ratio R f is sed to calclate three weight factors (W L, W M, and W H ) that correspond to the three compressibility categories (low, medim, and high, respectively). These factors reflect how close the actal compressibility is to each of the three predefined categories. They also calclated three vales of D r corresponding to each of the three categories (Dr L, Dr M, and Dr H ) sing the Klhawi and Mayne model, i.e., eqation (26). A weighted D r vale is then calclated as: D r Dr W L L Dr M W M Dr H W H (27) Correlations with Standard Penetration Test (SPT) The standard penetration test is the most widely sed method for in-sit characterization of sbsrface soils. While CPT is gaining poplarity as a simple, fast and reliable in-sit testing tool, many researchers attempted to develop correlations between CPT measrements and SPT N vale [70], [71], [17], [72]. The relation between CPT and SPT is sally expressed as the ratio of the tip resistance to the N vale ( N ). Robertson et al. compiled the reslts for a nmber of stdies correlating q c q c N to the mean grain size and soil type (Figre 11) and demonstrated that q c N ratio increases with increasing grain size [19]. They also noted that 60 the scatter in reslts also increases with increasing grain size. Eqations (28) and (29) show that q c and N were also correlated with the mean particle size (d 50 ) and the fines content (FC passing sieve #200). Lnne et al. noted that if no grain size distribtion is available for the in-sit soils, classification charts can be sed to estimate d 50 or FC [11]. q p c a qc p N N 5.44 D a 50 (28) FC 4.25 (29) 41.3 Jefferies and Davies developed an algorithm for estimating SPT N 60 vale from PCPT data withot soil sampling [73]. They presented an eqation that ses a soil classification index I c to calclate q c N ratio, i.e., eqation (30). Typical I 60 c ranges for different soil types are presented in Table 4. N 60 qc ( MPa) I c 4.75 (30) ( Blows / 300mm) 21

44 Figre 11 Variation of q c /N with d 50 [19] I c I c < 1.25 Table 4 Typical I c ranges for different soil types [73] Gravelly sand Soil Classification 1.25 < I c < 1.90 Sands clean sand to silty sand 1.90 < I c < 2.54 Sand mixtres silty sand to sandy silt 2.54 < I c < 2.82 Silt mixtres clayey silt to silty sand 2.82 < I c < 3.22 Clays 22

45 Part II: Load and Resistance Factor Design (LRFD) Most civil engineering design codes have been adopting the Load and Resistance Factor Design (LRFD) philosophy and moving away from the Allowable (Working) Stress Design (ASD) approach. This shift may be attribted to the many shortcomings associated with ASD sch as: the inability to address the different levels of ncertainty associated with calclations/estimations of both loads and resistances; the inability of addressing stress concentrations, stress interactions, and residal stresses; the assmption that materials are elastic and are not representative of the condition at failre; the treatment of different kinds of load (e.g., dead and live) as if they share the same variability; and the designed members lack a niform probability of failre. In the U.S., the American Concrete Institte (ACI) was the first to adopt LRFD in its 1963 Bilding Code Reqirements for Concrete Strctres (ACI 318). Today, design codes for concrete (ACI ), steel (AISC 2001), and highway bridges [74] are all based on the LRFD design philosophy. LRFD design codes appear to be deterministic to their ser; while in fact they are probabilistically calibrated to ensre that a target risk level is not exceeded. This is achieved sing a nmber of design coefficients that help accont for excessive overloading conditions (load factors) and nforeseen strength deficiencies (resistance factors). In general, the main design eqation is sally given as: R Q (31) n i i i where, R n is the nominal capacity of the designed member, is a resistance factor, Q i is the demand de to applied loads (dead, live, etc.), and i is the load factor. The development of LRFD codes was initially started for strctral applications. The resistance of strctral components has variabilities associated with it; however, more ncertainty is inherent in loads than in resistance. Geotechnical applications are niqe in the sense that ncertainties 23

46 are high on the resistance side as well. Nevertheless, LRFD research ensed in the geotechnical engineering commnity early on to develop a rational design methodology based on available statistical information of geotechnical applications. LRFD in Geotechnical Applications Hansen investigated the se of independent load and resistance factors for geotechnical applications within a Limit State Design (LSD) framework [75]. This work was later formlated into code where the resistance factors were applied to the soil properties rather than the nominal resistance [76]. Over the last decade, several researchers investigated the application of LRFD in geotechnical applications. The efforts covered a wide range of applications sch as offshore strctres general fondation design and deep fondations [77], [78], [79], [80], [81]. The findings of NCHRP Project established load and resistance factors for transportation fondations that were incorporated in the AASHTO LRFD Bridge Design Specifications [80], [82]. NCHRP Project (Task 88) dealt with LRFD design of retaining walls which was frther investigated in NCHRP Project for earth pressre in general terms [83], [84]. In another effort throgh NCHRP Project 24-17, Paikowsky et al. condcted a stdy to develop resistance factors that focsed on driven piles and drilled shaft fondations, which are recommended for inclsion in Chapter 10 of the latest version of AASHTO-LRFD [74], [85]. Despite the extensive efforts in this field, the geotechnical profession has not flly accepted the new load and resistance factors developed for AASHTO-LRFD. This is one of the most difficlt hindrances of LRFD to implement in geotechnical applications. As a reslt, more research stdies have been condcted to alleviate dobts and overcome the relctance in the geotechnical commnity. For example, Allen developed geotechnical resistance factors and downdrag load factors for LRFD fondation strength limit state design based on the information sed in NCHRP Projects and [86]. These efforts cover a wide range of geotechnical applications inclding shallow fondations, deep fondations, and retaining strctres [86], [87], [88], [89], [90], [91], [92]. There are two main approaches for addressing ncertainties in geotechnical applications. In the first approach, ncertainties are dissected to their main sorces and each sorce is investigated methodically in a rational way. The main sorces of ncertainty for geotechnical applications inclde inherent soil variability, measrement errors, and expression 24

47 (transformation model) ncertainty. Figre 12 shows a schematic of these sorces [93]. Several researchers sed this approach to stdy geotechnical design within a reliability based framework [94], [95]. Figre 12 Uncertainty in soil property estimates [93] Conversely, reliability stdies for geotechnical applications are often condcted at the fondation capacity level rather than the soil property level. In this second approach, the resistance of the component is investigated by comparing analytical estimates with experimental reslts for which a database of available reslts is assembled. This approach helps in overcoming the complexity and lack of information that may exist at the soil property level. Several researchers followed this approach. Investigations of reliability methods as related to Cone Penetration Test (CPT) are relatively limited. Bab et al. stdied cone tip resistance ( q c ) data obtained from a static cone penetration test on a stiff clay deposit [98]. The data from these tests were analyzed by sing random field theory, which estimated statistical parameters sch as the mean, variance, and atocorrelation fnction. These parameters were then sed in evalating the reliability of the allowable bearing capacity of a strip footing fonded on the above deposit. Ab-Farsakh and Nazzal investigated the reliability of seven interpretation methods for the piezocone penetration test (PCPT) in estimating the vertical coefficient of consolidation, c v, of cohesive soils [99]. Six Loisiana sites were inclded in the stdy where piezocone penetrations were condcted and high-qality Shelby tbe samples were collected to serve as reference. Estimates of c v were 25

48 obtained sing six different methods and compared to the oedometer laboratory. The athors conclded that the scatter was generally high. However, two of the six methods appeared to better predict c v than the other methods. Roy et al. compared the reliability of the Selfboring Pressremeter Test (SBPMT), which is often regarded to be less reliable, with the Cone Penetration Test (CPT) for seven sand silt sites in western Canada [100]. They conclded that observations do not spport the notion of a general lack of reliability of the self-boring pressremeter at sand-silt sites. Several researchers stdied the reliability of CPT as a feasible tool for identifying the probability of soil liqefaction for a given factor of safety. For example, Li and Chen sed data from 49 sites (71 cone penetrations) to develop statistical parameters for cone tip resistance, q c, sleeve friction, f s, grondwater Table, GWT, and soil nit weight, [101]. This information was then sed to treat each parameter as a random variable in analyzing both demand (cyclic resistance ratio CRR) and resistance (cyclic stress ratio CSR). Based on this information, Monte Carlo simlations were condcted to determine soil properties in nsampled sites, which were then sed to map the liqefaction potential. Jang et al. also stdied the liqefaction potential sing CPT reslts after acconting for parameter and/or model ncertainties [69]. The First-order Reliability Method (FORM) was sed to estimate the reliability index,, based on a limit state fnction involving CRR, CSR, and the model ncertainty, c1. Each of the six inpt parameters ( q c, f s, v, ' v, a max, and M w ) was considered to be a random variable and correlation between these parameters was acconted for. The stdy sed a database of 96 liqefaction case histories to determine these parameters, where they considered spatial variations sing Bayesian mapping fnctions. The athors conclded that traditional liqefaction bondaries are often biased on the conservative side, which may lead to erroneos post-earthqake investigations. 26

49 OBJECTIVE The main objective of this research is to pdate the correlations that are crrently sed to interpret CPT and PCPT data for engineering design prposes and to assess the reliability of sing CPT and PCPT data to predict soil shear strength in both the magnitde and spatial variations in the field with respect to the LRFD methodology. Specifically the following objectives will be flfilled by this research: 1. Collect the available CPT and PCPT sondings with the corresponding boring log data from the LADOTD and other possible sorces. Process/analyze the data and pdate the correlations of the shear strength and soil classification, which are crrently sed by the design section of LADOTD. 2. Evalate the spatial variations of soil engineering properties in the field. Develop the Loisiana CPT database for corresponding engineering properties as a general gideline for design prposes with reliability consideration in preparation for se in the LRFD method. 27

50 28

51 SCOPE This stdy focses on the tilization of the CPT to estimate ndrained shear strengths, S, which is an important soil property for strctral projects in Loisiana. While methodologies sed in this stdy are applicable to any location where CPT s can be sed, the stdy was limited to data obtained from Loisiana projects; hence, it is a direct representation of soil conditions in the state. Initially, the objective was to perform a complete stdy on the effects of spatial variations on the reliability of CPT reslts. However, becase of the limited amont of data that the research team was able to collect, it was only possible to stdy the soil depth, h, parameter on the reslts. A complete investigation of this parameter shold also cover the geographic location, which was not possible as can be seen from the sparsely covered maps showing CPT locations inclded in the database. The research team compensated for this hrdle by stdying other factors that are somewhat related to spatial variations albeit indirectly (e.g., soil classification). As more CPT data is inclded in the database, it will be possible to extend this stdy and cover sch parameters that were not covered in the crrent stdy. 29

52 30

53 METHODOLOGY CPT Database Three databases were created for this stdy: The first database is GIS-based where all information pertinent to CPT and borehole data was merged sch that they cold be easily retrieved by engineers via a GISbased ser interface. The second database is Excel-based and is a compilation of analyses condcted for each CPT sonding identified for this stdy. The analyses in this database are mainly based on LTRC CPT compter program and a special excel template. The third and final database is an extraction of data points from the second database. This database was sed for the reliability-based calibration of the CPT coefficient, N. The following sections describe the details abot these databases. Locating CPT Sites sing GIS CPT projects data were received from LADOTD in the form of paper docments containing CPT logs, borehole logs, and project maps. The data also inclded electronic raw (voltage) CPT data. The first task was to create an electronic archive of all the CPT sites sing the geographic information system ArcView. However, most of the projects did not inclde the spatial coordinates of the CPT sondings. Therefore, in order to find the CPT coordinates, a procedre was implemented tilizing readily available high resoltion satellite imagery along with digital orthophoto qarter qad (DOQQ) images. In some recent projects, aerial images and/or high resoltion maps of the project location were inclded in the project docments making it fairly easy to identify the location of the CPT sondings; however, in most projects sch maps were missing. The docments only contained a map of the project location with the CPT sondings marked on it. Therefore, to find the accrate coordinates of every CPT point, some specific (stationary) featres in the paper project map were located in the GIS satellite imagery sing Google Earth. Sch featres inclded street intersections, bildings, bridges, and rivers. By determining the 31

54 locations of the CPT tests relative to these featres in the paper project docment, the points were marked on the electronic maps and the Latitde and Longitde data for each CPT sonding were determined and recoded. Moreover, station nmbers of the CPT sondings were sed to confirm the recorded coordinates where the distance between the points were compared to the distance calclated from the station nmbers. In many cases, the satellite imagery provided by Google Earth did not have sfficient resoltion for the featres to be accrately located. This isse was encontered when the projects where in remote locations away from inhabited areas. Therefore, an alternative method was implemented to locate the CPT sondings in sch location. High resoltion DOQQ images were acqired from the LSU ATLAS website for these locations. These images have mch higher resoltion; however, they had very large sizes and small land coverage area per images. Downloading and displaying these images was time-consming and reqired mch more compter storage space. Therefore, this procedre was sed only when locating the CPT coordinates was not possible sing Google Earth. These procedres were sed to attempt to locate the CPT sondings in all the projects from LADOTD as well as LA1 project data received from Soil Testing Engineers (STE) Company. Althogh the mentioned procedres were sccessfl in determining the accrate locations of many CPT sondings, it was not possible to apply this procedre on all the CPT data received from LADOTD for different reasons. For example, some paper project docments cold not be located for the files received in electronic format (raw CPT data), while in other instances, the project docments were located; however, they did not inclde the project maps, so it was not possible to pinpoint the location of the CPT project. After locating all the CPT sondings and recording their coordinates, ArcMap was sed to plot all the CPT locations on a map of Loisiana. Figre 13 displays the CPT projects located sing the mentioned procedres. 32

55 Figre 13 CPT data points from LADOTD and STE Borehole Data The next step was to match the CPT data with adjacent borehole data. Therefore, for every CPT sonding, one or more boreholes were identified based on the distance from the CPT to allow for the comparison of parameters obtained from boreholes and CPT. The borehole data were inclded in the paper project docments; therefore, all the data had to be inpt into the excel spreadsheet to allow for the comparison. For every borehole, the density, water content, Atterberg limits, and ndrained shear strength were recorded at different depths (when available as a measrement in the borehole log) to be later sed in the correlation with the CPT data. Moreover, Atterberg limits were sed to obtain the USCS classification based on the plasticity chart if the soil is fine-grained. 33

56 The borehole data was not available for all the located CPT sondings. Efforts were made to obtain any available data from LADOTD electronic archives as well as paper project docments. Figre 14 illstrates the projects where the borehole data was located along with the projects where the data cold not be located. In smmary, a total of 752 CPT sondings were docmented, of which 503 were matched with adjacent boreholes, and 249 did not have adjacent borehole data available. Appendix A lists a smmary of all projects inclded in this stdy. Table 34 and Table 35 list projects where CPT sondings were paired with boreholes and projects where borehole information cold not be located, respectively. Figre 14 CPT sondings with and withot borehole data from LADOTD and STE 34

57 CPT and Borehole Data Analysis and Archiving In order to be analyzed and compared to the borehole data, every CPT raw data file was inpt into an Excel data template to perform varios calclations and prodce different plots of the CPT data. The spreadsheet starts by converting the inpt voltage vales from the load cells located at the tip and the sleeve of the cone apparats to tip resistance and sleeve friction (pressre) along the depth of the CPT sondings and sed these vales to calclate different parameters. The following paragraph presents a detailed description of the spreadsheet along with the eqations sed to calclate each parameter. An electronic version of all the Excel spreadsheets sed in this stdy, pls others that did not have a matching borehole, are provided to LTRC. Appendix E shows an example excel template. The CPT raw data are imported from the text file that contains raw data and pasted in the Raw data sheet of the template. The following are processed data in the analysis sheet of the template. Colmns A and B inclde the depth vales in meters and feet, respectively, while the tip resistance and sleeve friction in MPa are displayed in colmns C and D. These vales are converted to tons per sqare foot (tsf) and displayed in colmns E and G. In order to redce the random noise (spikes) in q c and f s, a smoothing fnction was sed where every vale was calclated by averaging five points above and below the point. The smoothed vales are listed in colmns F and H; these vales make it easier to select a representative data vales and discreet depths to be sed later in the analysis. The friction ratio (FR) was calclated in colmn I. The estimated shear wave velocity (V s ) is calclated in colmn L sing the correlation presented by Hegazy and Mayne [102]: f * 100 s s( m/s) 10.1log( qc) 11.4 qt V (32) The calclated shear wave velocity was then sed to calclate the soil nit weight (γ T ) sing the eqation proposed by Mayne, i.e., eqation (33). The calclated nit weight vales are listed in colmn M. These vales are converted to ponds per cbic foot and displayed in colmn N. The calclated nit weight along with the depth (z) were then sed to calclate the total overbrden pressre (σ vo ). Colmns O and P contain the calclated σ vo vales in kpa and tsf, respectively. The depth of the grond water table is then sed to calclate the pore water pressre (colmn Q), which is then sed with the overbrden pressre to calclate the 35

58 effective pressre (colmns R and S). Then the net tip resistance q t-net was calclated in colmn T as shown in eqation (34). 3 (kn/m ) 8.32 log( ) 1.61log( z) (33) T V s q (34) tnet q t vo Colmns V, W, and X are the normalized parameters Q, F, and B q, respectively, sed to determine the behavioral soil type; they are calclated sing eqations (35) throgh (37). Next, the soil behavioral type index presented by Robertson et al., in eqation (38), is calclated in colmn Y. The index is then sed to determine the soil Zone Nmber in colmn Z. Similarly, the soil behavioral type index and zone nmbers are determined sing the eqations presented by Jefferies and Davies, i.e., eqation (39), in colmns AA and AB. Finally, The ndrained shear strength (S ) is calclated sing eqation (40) assming a vale of N = 15 in colmn AC. q Q t (35) vo vo` F B q s (36) q t f t vo q o 2 (37) vo 3.47 log( Q) 2 log( F ) I c (38) 3 log( Q (1 B )) log( F) Ic ** q (39) S q N c vo (40) Moreover, the LTRC CPT plotting and classification software were sed to classify the soils sing Zhang and Tmay statistical approach method [2]. Probability Density Fnctions (PDF) files were generated for each CPT sonding. The excel sheets and the PDF 36

59 classification files were sed to generate an electronic archive of the CPT locations sing ArcMap software. The GIS database inclded all the CPT sondings that were located throghot the state. Each point on the map contained the information abot the CPT sondings inclding the job nmber, job location, parish, district, date, and station nmber. Clicking on any point on the map will display all the information of that test. Figre 15 depicts an example record where the information is displayed in a popp window when the location is selected. Sch a database allows for the selection of a point or a grop of points based on any of the mentioned attribtes (e.g., district, job nmber, etc.). Moreover, when selecting a CPT sonding on the CPT map, two links are provided, one for the CPT classification PDF file generated from the LTRC CPT software and the other for the Excel data sheet where the CPT and borehole information are docmented. Clicking on any of the links opens the PDF or Excel data sheet for the location selected. Figre 16 illstrates an example archive where the PDF classification file is displayed by selected the link for that file from the popp window. Figre 15 Example CPT data information displayed by selecting a CPT location 37

60 Figre 16 Example CPT classification file displayed by selecting the PDF link It can be seen from Figre 14 that some regions of Loisiana have a large nmber of CPTs with boreholes while other regions contained a very small nmber of data. The northern and sotheastern parts of the state have higher nmbers of CPT sondings while the sothwestern part of the state have very few CPT sondings. Figre 17 and Figre 18 depict zoomed views of northern and sothwestern parts of the state where the difference in the nmber of CPT and borehole data points can be clearly noticed. 38

61 Figre 17 Zoomed view of the northern part of Loisiana where a higher nmber of CPT sondings were available 39

62 Figre 18 Zoomed view of the sothwestern part of Loisiana where a smaller nmber of CPT sondings were available To frther illstrate the spatial variations in the assembled database of CPT reslts, a histogram of CPT depths of extracted soil engineering data is provided in Figre 19. It can be seen that a wide range of depths of extracted properties from CPT sondings is inclded in the database ranging from 2 ft. to 100 ft. However, the depths are not distribted niformly. This means that the database is biased toward lower depths (< 25 ft.) than higher depths. It will be seen later in this report that for the database sed in this stdy, depth variations do not significantly affect the correlation of the CPT coefficient. Hence, the reslts in the database are still viable for the prpose of this stdy. Similar depth histograms for each soil classification are also plotted in Figre

63 Freqency < CPT Depth, h (ft) Figre 19 Histogram of depths for CPT measrements inclded in database Freqency < Freqency < CPT Depth, h (ft) CPT Depth, h (ft) Classification 2 Classification 3 Freqency < Freqency < CPT Depth, h (ft) CPT Depth, h (ft) Classification 4 Classification 5 Figre 20 Depth histograms for different soil classifications [4], [5], [19] 41

64 Reliability Analysis of CPT Two approaches were followed to correlate the ndrained shear strength reslts obtained from CPTs and adjacent borings. Both approaches relied on the formla (transformation model) crrently sed by LADOTD for estimating the ndrained shear strength from CPT readings, CPT S, which is given as: S CPT q N c vo (41) The first approach was a direct correlation based on the formla in eqation (41). In the second approach, a more detailed investigation in which all sorces of ncertainty were acconted for tilizing the First Order Reliability Method (FORM). Both approaches are described in detail in the following sections. Direct Correlation of CPT and Boring Reslts 1 st Approach In this approach, the crrently sed expression, transformation model given in eqation (41), will be correlated by eqating the ndrained shear strength vales from both tests ( S from CPT and UC S nconfined compression test) to achieve the goal of this stdy. By rearranging the expression, one can obtain N CPT vales for each CPT reslt in the database as follows: N q c vo (42) UC S De to the ncertainties detailed earlier (inherent soil variability, device measrement, and sed expression transformation model), a constant N is not to be expected, bt rather a scatter of reslts. The reslting N vales can be stdied statistically to establish appropriate probability density fnctions (PDF) and cmlative distribtion fnctions (CDF) for N that describe the scatter of N vales. Once these relations (PDF and CDF) are established, they can be sed to determine acceptable N for varios probability of exceedance levels. Here, the probability of exceedance ( P e ) is defined as the probability of the borehole reslt 42

65 (benchmark) exceeding the CPT estimate for ndrained shear strength. A higher probability of exceedance indicates a more conservative estimate of the ndrained shear strength from CPT readings. Detailed Reliability Analysis for Correlation of CPT and Boring Reslts 2 nd Approach The second approach that was adopted in this stdy for calibrating the CPT coefficient N is more involved and acconts for all ncertainties associated with CPT testing. In addition to the ncertainty cased by the sed formla or transformation model, eqation (41) that was covered in the first approach, ncertainties inherent in soil properties and device measrement are also acconted for. Before this approach cold be carried ot, the statistical characteristics of each of these sorces of ncertainty will first need to be determined. In the next few sections, the methodology adopted for qantifying these ncertainties is explained. Statistical Analysis of CPT Repeatability One of the identified sorces of ncertainty is the inherent variations in the device and measrement eqipment (see Figre 12). This ncertainty needs to be acconted for in the reliability analysis forming the basis for the correlation of the CPT coefficient. Lacking readily available repeatability test reslts, a test program was condcted to assess the variability inherent in CPT measrements. In planning the repeatability test program, the following factors were kept in mind: The CPT tests had to be closely spaced since the prpose of these tests was to identify the variations in the recorded readings nder almost identical soil conditions. The CPT penetration shold extend to a depth of 80 ft., which covers most of the LADOTD applications. A single boring is also reqested to provide reference soil information with which the CPT readings can be related. The boring shold be taken after the conclsion of the CPT tests to avoid distrbing the soil. Sixteen CPT penetrations were condcted in dal polar array as shown in Figre 21. This layot was chosen becase it allows a central zone where a soil boring can be taken for frther analysis and comparison with CPT reslts. The minimm distance between adjacent CPT penetrations did not fall below 3 ft., and the farthest distance between penetrations did not exceed 12 ft. Ths, it can be said that the CPT readings are representative of identical 43

66 soil conditions. Figre 21b shows a photograph of the actal site where the 16 repeatability penetrations took place at LTRC s Accelerated Testing Facility (ALF) site. LTRC and LADOTD staff condcted the tests. CPT Bore Hole Radis = 6 ft R = 3.25 ft (a) (b) Figre 21 Array of CPT repeatability tests 44

67 Preprocessing CPT Data The compiled database of CPT reslts was sed to stdy the calibration of ndrained shear strength, S, transformation model for Loisiana soils. The database comprised of reslts from over 700 CPTs. This database was obtained from projects all over Loisiana. The goal of the project is to calibrate the transformation models tilized by geotechnical engineers by comparing CPT reslts to corresponding reslts from borehole tests, specifically the more UC acceptable nconfined compression (UC) ndrained shear strength, S. It was possible to identify boreholes in the vicinity of 334 CPT sondings ot of all those inclded in the database. The distance between the boreholes and the CPT sondings varied from site to site and limits on distance between both locations were set as is described next. Each CPT test provided several data points to the database. The soil properties were compted at the depth intervals that match the reported borehole reslts. In all, 2,630 data points for ndrained shear strength reslts from boreholes were compiled. It was only possible to compte the ndrained shear strength from CPT readings in 1,886 locations and depths. However, the nmber of data points where ndrained shear strength reslts were available from matching CPT and borehole data was 1,814. The following section describes the methodology by which the reslts were preprocessed, analyzed and presented in this stdy. Matching CPT and Borehole Data As expected, the CPT and borehole locations were not exact matches. This was de to many site factors and is now considered historic data that are not changeable at the time of condcting this research. Ths, it was imperative that acceptable criteria be set to jstify the hypothesis of eqal soil properties at both CPT and borehole locations. These criteria address the fact that the distance between the CPTs and boreholes ranged from 1 ft. to 1,844 ft. Frthermore, it was not possible to exactly identify the coordinates of some locations, which had to be exclded from the database. At the same time, more than one borehole existed in the vicinity of some CPTs in the database, and a weighing fnction was needed for these locations. Criteria were set in this project to address these isses: A maximm distance between the CPT and borehole location was set to be 150 ft. Figre 22 shows a plot showing the nmber of matches between CPTs and boreholes 45

68 at different distance intervals. Accordingly, the nmber of data points inclded in sbseqent analyses is 1,263 from 251 CPT sondings. No. of CPT Locations Distance Threshold = 150 ft No. of Data Points 0 < 25' < 50' < 75' < 100' < 125' < 150' < 200' < 300' < 400' < 500' < 800' < 5,000' No. of CPT Locations < 10,000' No. of Data Points Figre 22 Distance threshold between CPT and borehole locations showing nmber of data points inclded in analyses In the case of having more than one borehole in the vicinity of a CPT sonding, a 1 D weight fnction was sed to accont for the proximity of borehole locations to CPT sonding. The weighted average fnction for any qantity, q, based on the reslts from n boreholes at distances D, D, 2, D i,, D can be written as: 1 n q n i1 q i n D j j1 n j1 D D j i (43) This fnction yields the following weighted averages for the cases of two and three boreholes consectively: 1 D2 D2 D2 D1 q 1 q2 D1 D2 D1 D2 D1 D2 D 1 D2 D1 D q q 1 q2 (44) D1 D2 46

69 D D D D D q D D D D D q D D D D D q D D D D D D D q D D D D D D D q D D D D D D D q q (45) For illstration prposes, a scenario of two boreholes at distances 1 D =35 ft. and 2 D =110 ft. wold yield the following weighted average : q q q (46) Averaging CPT Readings CPT readings are known to have spikes de to many factors. One of these factors is the fact that continos readings are recorded at very small intervals which is in many cases smaller than 1.0 in. of depth. Relying on pinpoint data readings wold reslt in nnecessary scatter, especially that soil properties obtained from borehole tests are sally based on specimens of tangible dimensions (8 in. in the case of Shelby Tbe sample). As a reslt, it was deemed necessary to average CPT data readings over a depth similar to what is sed in borehole soil property testing. In this stdy, 11 consective CPT data readings were averaged arond every desired depth where borehole data was available. These readings correspond to a depth of abot 7.8 in. Figre 23 illstrates the averaging of device readings for the cone tip resistance, c q. Figre 23a is a plot of the raw data obtained from the CPT device, while Figre 23b shows the same reslts after averaging them over a depth of abot 7.8 in. It can be seen that localized spikes are almost eliminated withot losing the general trend of the readings. This is the prpose of the averaging and is done for all CPT readings in the assembled database.

70 Tip Resistance, q c (tsf) Tip Resistance, q c (tsf) Depth, h (ft) 50 Depth, h (ft) (a) raw tip resistance readings, q c Figre 23 Averaging raw CPT readings (b) averaged tip resistance readings, q c 48

71 Filtering Data Reslts As is the case with any natral and hence ncontrollable material, a wide range of readings is always expected. Soils fall nder this category of materials. Nevertheless, soil properties are known to fall within a confined physical range albeit it may be a wide range. Vales otside this range represent soil properties that represent soil conditions that may lead to otcast data points. For example, extremely low ndrained shear strength reslts indicate very soft soils that are difficlt to test nder normal laboratory conditions, ths reslts within this low range are in many cases nrepresentative of actal soil conditions. At the other extreme, high ndrained shear strength vales are sally attribted to stiff clays, which flctations in the cone readings may be excessive leading to nreliable CPT estimates of the ndrained shear strength. It was therefore deemed necessary to set limits on the range of ndrained shear strength, S, collected in the database. Vales that exceed a maximm threshold or fall below a minimm threshold were exclded from the database. Figre 24 shows a histogram of the ndrained shear strength complied in the database. The plot shows that the database incldes points of extremely low and extremely high S vales. Based on the literatre, S vales falling below 150 psf and above 2,500 psf were exclded from the database in sbseqent analyses. Freqency (%) 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% Undrained Shear Strength, S (psf) Figre 24 Histogram of S freqency in compiled database 49

72 Figre 25 shows the impact the chosen threshold has on the scatter of the transformation model sed in this stdy. The scatter is measred by the coefficient of variation, COV, of the CPT UC ratio S S. It can be seen that as more data points with high or low ndrained shear strength vales are exclded, the smaller the COV of the transformation model becomes. Filtering the data sing these two threshold reslts in a redction in the nmber of data points sed in the sbseqent analyses. The database inclded 862 data points after applying the aforementioned thresholds. (a) minimm S threshold Effect of S (b) maximm S threshold Figre 25 thresholds on ncertainty of transformation model 50

73 Calibration of CPT Coefficient The calibration of the CPT coefficient, N, to achieve acceptable reliability in ndrained shear strength, S, estimates will be condcted sing the methodology described next. An acceptable reliability can be defined in terms of a probability of exceedance, P e, which is described in detail in the next section. The statistical characteristics of the data in the compiled database of CPT reslts are first analyzed. These characteristics are essential for the reliability-based calibration. Statistical characteristics of random variables not analyzed in this stdy are obtained from the literatre. A limit state fnction is first established, which is then sed to calibrate N. The calibration is performed for different soil classifications, different target reliability levels, and q ratio. vo c Limit State Fnction The limit state fnction is simply the bondary between acceptable and nacceptable performance. In this stdy, the ndrained shear strength estimates from borehole data, UC S, CPT and CPT data, S, shold be identical in ideal circmstances. In real life, the difference between both is inevitable. An acceptable performance is achieved if CPT estimates for the CPT UC ndrained shear strength, S, is less than the borehole reslt, S, and an nacceptable performance is to be expected if the opposite is tre. Since both terms have inherent randomness in their vales, they can be illstrated graphically as can be seen in Figre 26a. If the formla sed in the determining S CPT, transformation model in eqation (41) is conservative, then the mean vale of CTP estimates,, wold be less than the mean vale of borehole reslts, UC S CPT S. Alternatively, this can be described sing a limit state UC CPT fnction (LSF) that represents the difference between both estimates ( Z S S ), which will also be a random variable that can be plotted as can be seen in Figre 26b. The probability of estimating the ndrained shear strength from borehole nconfined compression tests that will be higher than those obtain from the CPT readings is graphically represented by the shaded area. It can be seen that the larger this area, the safer the CPT estimates. An indirect measre of the area is the distance from the mean, Z, to the origin, which can be represented in mltiples of the standard deviation, Z. This mltiple is defined as the reliability index,. The higher the reliability index, the higher the probability of 51

74 exceedance, P e. In the special case of calibrating a formla (transformation model) that reslts in eqal mean vales, i.e., as illstrated in Figre 27a (the probability of CPT S UC S exceedance, P e ) wold be eqal to 50 percent as can be seen in Figre 27b. Hence, the corresponding reliability index wold be eqal to zero, which will be one of the target reliability levels in this stdy. P D F f (s ) CPT S f (s ) UC S P D F Z f (z) Z Probability of Exceedance (Z>0) S CPT S UC UC S, S (a) (b) Figre 26 Illstration of the limit state fnction (LSF) sed in this stdy (general case) CPT Z Z P D F f (s ) S CPT f (s ) S UC f (z) Z P D F Probability of Exceedance (Z>0) CPT S S UC UC CPT Z S, S (a) (b) Figre 27 Illstration of the limit state fnction (LSF) sed in this stdy (special case) Z The reliability calibration condcted in this stdy is based on the limit state fnction (LSF) CPT described above. However, the CPT estimate, S, will be replaced by the transformation model sed to obtain its vales, eqation (41). This allows for inclding the ncertainties inherent in the original CPT readings, namely q c and vo. Eqation (47) shows the details 52

75 the LSF starting with the random variables eqation (47-b), where UC S is replaced by UC S and CPT S. The expanded version is shown in UC S in which is random variable that UC acconts for ncertainty inherent in the soil property, S, which is taken as a deterministic vale representing soils in location nder investigation. The other two newly introdced random variables, and, represent the ncertainties in the transformation model and tip resistance readings, respectively. Z S S (47-a) UC CPT Z UC q c vo S (47-b) N Table 5 lists the statistical characteristics of the random variables sed in this stdy. The characteristics of the random variable are given in Table 6 and Table 7 for both classification techniqes sed in this stdy, namely Robertson and Zhang and Tmay. The bias and standard deviation vales were compted by determining the statistical descriptors (mean and standard deviation) for the ratio between the CPT estimates and borehole reslts, CPT UC S S, in the database. CPT S bias, mean (48) UC S CPT coefficien t of variation, COV standard deviation UC S CPT S mean UC S (49) Several CPT coefficient vales were considered in determining these statistical descriptors. CPT For each vale, the CPT ndrained shear estimates, S, wold change and case the bias and coefficient of variation given above. The varios vales are needed for the optimization step that follows for determining an appropriate CPT coefficient, N. Finally, the tip resistance ncertainty was obtained from the repeatability stdy presented earlier (see page 42) while the overbrden pressre was taken as a deterministic qantity de to its low COV as will be seen later. S 53

76 Table 5 Random variables sed in reliability calibration Variable Mean COV (%) Distribtio n Sorce Soil Uncertainty, Lognormal Phoon and Klhawy (1999) Transformation Model, varies Lognormal Crrent Stdy Tip Resistance, varies Normal Crrent Stdy Overbrden Pressre deterministic Crrent Stdy Table 6 Statistical characteristics of transformation model (Robertson classification) N ALL Cases Bias STDEV Bias STDEV Bias STDEV Bias STDEV

77 Table 7 Statistical characteristics of transformation model (Zhang and Tmay classification) N ALL Cases Clay > 75% Clay = 50-75% Clay = 25-50% Bias STDEV Bias STDEV Bias STDEV Bias STDEV Chi-Sqare Statistical Test Goodness of Fit In addition to the statistical descriptors that were determined in the previos section (bias,, and coefficient of variation, COV), a distribtion type will be needed for the reliability stdy that follows. Statistical distribtions are mathematical expressions that represent the freqency within a dataset continosly over the possible range for the entire poplation. Any random variables can be described sing different distribtion types. The choice of one distribtion over another is based on how well the chosen mathematical distribtion fits the collected data (observations). Many statistical tests can be sed to evalate how well a certain distribtion fits the collected data. In this stdy, the Chi-Sqare Test will be sed. The details of how the test is condcted are given in Appendix C. The random variables in this stdy were tested for two possible distribtion types, namely Normal and Lognormal. Details of both distribtions can be fond in the literatre and are smmarized in the Appendix for convenience. The reslts from condcting these tests are presented next for the two random variables that were determined in this stdy. 55

78 Reliability-based Calibration Calibration of the CPT coefficient, N, will be condcted sing the LSF described earlier. The goal is to identify N vales that reslt in desired reliability levels, which will be measred in terms of a reliability index,, defined as the ratio between the mean vale of the LSF and its standard deviation, which was previosly illstrated in Figre 26b: Z (50) Z The reliability index,, is related to the probability of exceedance, P e, sing the following expression: e is a cmlative distribtion fnction (CDF) for a limit state fnction, Z. The P (51) where, reliability index was evalated for each considered case. In all, a total of 672 cases were considered (14 N vales 4 Soil Classifications 6 q vo c ratios 2 Classification Methods). The ratio of overbrden pressre to the tip resistance, q, in the reliability analyses was considered in the reliability stdy since the reslts shold cover a wide range of possibilities (design space). The First Order Reliability Method (FORM) was sed to compte for all cases. FORM is based on a first order Taylor series expansion of the limit state fnction, which approximates the failre srface by a tangent plane at the point of interest. More details abot FORM and the procedre sed in this stdy are given in A B. Soil Classification Table 8 Range of parameters covered in reliability stdy Parameter Range CPT Coefficient, N 12, 15, 18, 21,, 39, 42, 45, 48 Ratio, q 0.05, 0.10, 0.20, 0.50, 0.80, 0.90 vo c Robertson 2, 3, 4, 5 Zhang and Tmay > 75%, 50-75%, 25-50%, < 25% vo c 56

79 DISCUSSION OF RESULTS Repeatability Tests The data files obtained from the CPT tests were analyzed by rnning the LTRC software for analysis of CPT readings. The main parameters of interest for this repeatability stdy are the variables inclded in the limit state fnction to be sed in the reliability calibration. These parameters are: tip resistance, q c overbrden pressre, vo It shold be noted that the overbrden pressre, vo, is compted sing the estimated nit weight of the soil, T. Hence, the data for the nit weight of the soil, T, was also analyzed in addition to the two aforementioned variables. Each of the three parameters was first plotted from all 16 CPT tests. Figre 28a throgh Figre 28c show the plots for q c, T, and vo, respectively. The vales of each parameter are plotted verss depth. As expected, it is obvios from Figre 28 that the tip resistance, q c, shows more scatter than the other two variables. The variability in the nit weight of the soil, T, is far less than it is for the tip resistance. Conseqently, the variability of the overbrden pressre, vo, is also relatively less than that of the tip resistance. By comparing the plots for the T and vo, it is clear that the variability in the overbrden pressre is almost negligible. This is de to the fact that the depth, h, is inclded in estimating the overbrden pressre, vo. Depth estimates are pretty accrate in CPT tests since they are based on pipe lengths. As the depth increases, so does the overbrden pressre, vo, and local variations in the soil nit weight, T, become small compared to the total overbrden pressre, vo. Another observation from the plots is that a major change in soil characteristics takes place somewhere in between the 40-ft. and 50-ft. depths. This is especially obvios from Figre 28 where the tip resistance sddenly shifts from vales below 40 tsf to vales easily exceeding 100 tsf. This observation will help explain one of the trends of ncertainty that are compted and presented in the next section. 57

80 Tip Resistance, q c (tsf) Unit Weight, T (pcf) Overbrden Pressre, vo (tsf) Depth, h (ft) 40 Depth, h (ft) 40 Depth, h (ft) (a) Tip resistance, q c (b) Unit weight, (c) Overbrden pressre, T vo Figre 28 Cone data from all repeatability tests 58

81 Statistical Characteristics of Repeatability Data The data obtained from the analysis of all 16 CPT sondings were frther analyzed to assess the statistical characteristics of the parameters of interest for the reliability calibration stdy, namely q c, T, and vo. Two spatial variation parameters were stdied to investigate whether the variability inherent in the device cold be related to either of them. The two parameters are the soil depth and the soil classification. Soil Depth. The statistical analysis focsed on discrete locations along the depth of the penetration with a resoltion of 5 ft. intervals. As with the other analyses, the readings were averaged for a depth eqal to 10 in. (5 in. above and 5 in. below) arond each of the chosen depths. Table 9 throgh Table 11 show the data for all three parameters. The maximm and minimm reading for each variable at each depth are identified (highlighted) in the tables. The coefficient of variation, COV, was compted for each variable at each discrete depth, which is defined as: where, COV X i X and i X i (52) X i X i are the standard deviations and the mean vale for the random variable, X i, respectively. The COV is a direct measre of the scatter reslting from the CPT readings nder identical soil conditions. A large COV indicates a wide scatter of the reslts and vice versa. Table 9 throgh Table 11 also list the COV for all three parameters for each depth. The compted COV reslts also plotted in Figre 29 throgh Figre 31 verss depth. The average vale for each of the parameters is plotted next to each of the COV plots as an indicator of the parameter s trend. Based on these plots, it can be said that there is no clear relationship between the variability inherent in the measring device and the soil depth for the first two parameters qc and T. A trend is observed for the overbrden pressre, vo, which decreases steadily from the srface (depth = 0.0 ft.) to a depth of abot 40 ft., after which the COV vo is almost a constant. In both regions, it shold be noted that the variability is extremely low (< 1 percent). The COV q c, on the other hand, is higher with vales close to 40 percent in some cases. On average, the COVs for three stdied parameters are 19.7 percent, 1.50 percent, and 0.51 percent, respectively. These COV vales will be incorporated in the limit state fnction for the reliability calibration to accont for ncertainties inherent in the measring device, the cone for this stdy. 59

82 Job # Depth (ft) Repeaibiliy (ALF) Soil Classification Table 9 Discrete tip resistance, q c, readings at 5 ft. intervals COV(q c ) % % % % % % % % % % % % % % % % Minimm= 7.2% Average= 19.7% Maximm= 36.5% q c CPT Job # Repeaibiliy (ALF) Depth (ft) Soil Classification Table 10 Discrete nit weight, T, reslts at 5 ft. intervals T CPT COV( T ) % % % % % % % % % % % % % % % % Minimm= 0.73% Average= 1.50% Maximm= 2.62% 60

83 Job # Repeaibiliy (ALF) Depth (ft) Soil Classification Table 11 Discrete overbrden pressre readings at 5 ft. intervals % % % % % % % % % % % % % % % % Minimm= 0.36% Average= 0.51% Maximm= 0.87% vo CPT COV( vo ) 61

84 0 Tip Resistance, q c (tsf) COV(q c ) 0% 10% 20% 30% 40% Depth, h (ft) 40 Depth, h (ft) (a) Average c q c vs. depth Figre 29 Analysis of repeatability data for cone tip resistance q readings (b) COV 62

85 Unit Weight, T (pcf) COV( T ) 0.0% 1.0% 2.0% 3.0% Depth, h (ft) 40 Depth, h (ft) (a) Average T T vs. depth Figre 30 Stdy of nit weight data scatter from repeatability tests readings (b) COV 63

86 Overbrden Pressre, vo (tsf) COV( vo ) 0.0% 0.2% 0.5% 0.8% 1.0% Depth, h (ft) 40 Depth, h (ft) (a) Average vo vo vs. depth Figre 31 Stdy of overbrden pressre data scatter from repeatability tests readings (b) COV Soil Classification. The same statistical reslts were stdied by focsing on the soil classification obtained sing Robertson s method [1].Classifications where obtained along the soil depth for all 16 CPT repeatability tests. These reslts are plotted in Figre 32 which shows that the first 40 ft. of the soil are classified as to be mixtres of silt and clay. The range is from clay (Classification 3) to clayey silt or silty clay (Classification 4). Some readings show silt/sand mixtres (Classification 5). Beyond the first 40 ft., an obvios change can be seen. The soil classification is mainly between Classification 5 and Classification 6 which corresponds to silt/sand mixtre to clean sand, except for a thin layer arond a depth of 50 ft., where it appears that more clay and silt are present. These classifications may be the 64

87 explanation why the trend for COV vo changed at this jnctre (h=40 ft.). It also raises interest in stdying the variability of the measrements as a fnction of the soil classification. Plots of the coefficient of variation, COV, for the same previos parameters are shown in Figre 33 throgh Figre 35 to stdy sch an effect. By analyzing these plots, one can conclde that clays/silty clays (Classification 3) have a narrower range of COV, of the tip resistance, q c, as compared to the same range for silt/sand mixtres (Classification 5). Similar observations may be made for the nit weight, T ; however, the difference is smaller. No clear trend is observed for the overbrden pressre, vo. Again, it shold be noted that the COV of the nit weight, T, and the overbrden pressre, vo are extremely small and that the COV of the tip resistance, q c, will be the main sorce of device/procedral ncertainty in this stdy. 0 Soil Classification Depth, h (ft) Figre 32 Tip resistance, q c, readings from all CPT repeatability tests 65

88 40% 35% 30% 25% COV(qc) 20% 15% 10% 5% 0% Soil Classification Figre 33 Stdy of tip resistance data scatter, COV q 3.0% c, vs. soil classification 2.5% 2.0% COV(T) 1.5% 1.0% 0.5% 0.0% Soil Classification Figre 34 Stdy of nit weight data scatter, COV T, vs. soil classification 66

89 1.0% 0.8% COV( vo) 0.5% 0.2% 0.0% Soil Classification Figre 35 Stdy of overbrden pressre data scatter, COV vo, vs. soil classification Utilizing CPT for Assessment of Site Variability Recent LRFD design codes adopt an approach where design factors are dependent on site variability. The assessment of the site variability is an important step in the overall design process as it greatly inflences the otcomes. In this section, a methodology is proposed to assist geotechnical engineers in determining the site variability from CPT readings. Althogh the goals of this stdy did not inclde developing methods for classification of sites based on their variability, the reslts presented in this report may assist in achieving this goal. It is believed that based on the repeatability stdy, a procedre can be established for the prpose of classifying sites withot the need for any sbjective interference by the designer. The nderlying principal in the proposed approach is that mltiple CPT sondings in a certain site can reveal the ncertainties inherent in the site. These ncertainties inclde those related to the device itself as well as soil variability. If we assme that the overall scatter is CPT presented as the COV S from mltiple CPT sondings from a specific layer at the investigated site, it can be said that this scatter is cased by: 67

90 the device ncertainty, which is mostly cased by the ncertainty in cone tip resistance and measred by COV since the variability in the overbrden pressre is negligible and can be ignored, and the inherent variability in soil properties, which can be obtained from the literatre as the coefficient of variation of the ndrained shear strength for fine soils COV. This assmption leads to the fact that the expected coefficient of variation of the ndrained shear strength can be obtained as a fnction of the coefficient of variation for the two random variables, and. Based on the coefficient of variation of the cone tip resistance that was established earlier (19.7 percent), it is possible to determine the expected coefficient of variation for the ndrained shear strength for different assmed soil variabilities corresponding to low, medim, and high variability. Comparing the expected coefficient of CPT variation, COV S, to what is actally compted from mltiple CPT sondings for the soil layer of interest can be sed to classify the site variability. The proposed procedre that lays ot the framework that can be refined and tested in a ftre research project is otlined next. For illstration prposes, the coefficient of variation, COV, is taken as 6 percent, 25 percent, and 33 percent corresponding to low, medim, and high, respectively. 1. The CPT readings for the site in qestion are collected and soil layers (classifications) are identified. 2. For each layer of interest (e.g., fondation level), the estimate for the design property sch as ndrained shear strength, S, is obtained from all CPT sondings. CPT Statistical analysis of the soil property (e.g., S CPT ) will yield a mean and standard CPT deviation. The coefficient of variation from these reslts, COV compted to be sed for site variability assessment. CPT 4. By comparing S S, is then COV to the coefficient of variation that is expected from the measring device and the inherent soil variability, one can assess the site variability. This can be done in three gropings: a. measred coefficient of variation vales eqal to or smaller than what is

91 expected for the low end of inherent soil variability ( COV 6 CPT expected S 21 CPT b. measred percent); i.e., COV percent, indicate that the site variability is low, COV vales corresponding to what is expected for an average S inherent soil variability ( 20 CPT COV percent); i.e., expected COV 28 percent, indicate that the site variability is medim, and CPT c. Higher COV vales indicate that the site variability is high. S S It shold be noted that this approach is only valid for fine soils if consistent soil layers cold be identified. In the case were soil layers cannot be identified, the site variability assessment shold be atomatically set to high. Initial Data Analysis General Trends Before calibrating the CPT method for ndrained shear strength reslts, data trends are examined to identify any possible relations. The crrent expression (transformation model) sed for estimating the ndrained shear strength is given as S CPT q N c vo (41) Figre 36 shows a preliminary comparison of the ndrained shear strength as obtained from CPTs and boreholes (UC). The plot shows all 862 data points in the database. Two general conclsions may be made at this stage and these are: The data scatter is considerably high (COV=71 percent) CPT reslts are on average higher than the corresponding borehole reslts; i.e., overestimate of UC S. CPT S is an It shold be noted that these reslts were obtained sing eqation (41) assming a N vale of 15. As will be seen later, a single N vale that is valid for all soil types is not the right approach, which has therefore contribted to the wide scatter. An attempt was then made to assess the relationship between the ndrained shear strength and each of the variables involved, q c and vo. 69

92 3000 Underestimate 2500 Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Figre 36 Comparison of ndrained shear strength, S, from CPT and UC tests While stdying the trends in collected data, it was deemed worthy to also stdy the trends of UC the borehole ndrained shear strength vales, S, verss varios CPT readings sed in this stdy. The prpose of this analysis is to shed some light on the performance of eqation (41) in predicting the ndrained shear strength and whether a different expression is needed. UC In Figre 37, three plots for the relation between the ndrained shear strength, S, and the tip resistance, q c, as well as the overbrden pressre, vo, and the net difference, qc vo, are shown. The plots reveal that there is a rising trend in the tip resistance verss ndrained shear strength vales. This confirms the inclsion of the first term in eqation (41) as a first order with a positive sign. Figre 37b shows that the ndrained shear strength drops as the overbrden pressre increases. However, this trend is not as prononced as it is for the tip resistance, which may sggest that inclding both parameters, qc and vo, with eqal slopes in eqation (41) may need to be revisited. Finally, Figre 37c confirms the rising trend of ndrained shear strength, 70 S, as a fnction of the net difference, qc vo, which is a basic UC

93 variable in eqation (41). The figre also shows five ideal trends obtained sing eqation (41) for different N vales ranging from 12 to 30. The prpose of these trends is to provide the reader with a visal representation of which N reslts in a better match to the borehole reslts in the database. It can be seen from these trend lines in Figre 37c that a vale of 12 is biased on one side of the dataset and that a N vale between 25 and 30 better represents the reslts in the database. It shold be noted that these remarks are based on the entire dataset compiled in the database. N Development of a more refined expression wold need to inclde varios factors that may affect the observed trends (e.g., soil classification, depth, etc.) Several attempts were made to come p with other expressions that wold better match the available data. These expressions inclded higher order polynomials; elimination of the overbrden pressre, vo, from the expression; and a constant to address the non-zero intersect that can be seen in the Figre 37. The conclsion from these attempts is that a better bias can be achieved (reslts can be better matched on average); however, the scatter is not mch different, which affects the ncertainty of the transformation model. Therefore, it was decided to keep the crrently sed transformation model, eqation (41), becase of its simplicity. 71

94 25 Tip Resistance - Overbrden Pressre, q c - vo (tsf) 7 6 Overbrden Pressre, vo (tsf) Cone Tip Resistance, qc (tsf) Borehole Undrained Shear Strength, S (psf) (a) cone tip resistance, qc Borehole Undrained Shear Strength, S (psf) (b) overbrden pressre, vo (c) net difference, qc - vo Figre 37 Analyzing data trends of different CPT readings verss S UC Borehole Undrained Shear Strength, S (psf) 2500

95 Specific Parameter Trends Following the initial review of the collected data, the next phase in the stdy was to stdy the reslts in light of specific relevant parameters that may affect the reliability of CPT readings. This section presents the reslts of these analyses which inclde stdying the following parameters: Soil Depth, h CPT Reading Vales, ( qc vo ) Soil Classification: o Zhang and Tmay Method (1999) o Robertson s Method (1990) o Plasticity Index The range of each of the stdied parameters was dissected into small intervals. The CPT reslts in the database within each of the intervals was statistically analyzed to obtain the CPT UC bias,, and coefficient of variation, COV, of the ratio S S as described earlier. Both qantities represent how accrate the CPT reslts are when compared to the borehole reslts. Bias vales close to nity (1.0) indicate an accrate method on average, whereas vales below or above 1.0 mean that the CPT reslts are nderestimating or overestimating the ndrained shear strength, respectively. The scatter of the reslts is reflected in the COV CPT vales. The higher the COV, the more scatter in S is indicated. These reslts are presented next in tablar form for each of the listed parameters. They will form the basis for the reliability-based calibration stdy that follows this section. Also presented in the tables are the average and standard deviation for N within each sbcategory. These characteristics are provided for easier interpretation of the statistical parameters discssed earlier. In addition to the tablated reslts, graphical plots (Figre 38 throgh Figre 43) of ndrained shear strength estimates from CPT and boreholes are presented within each range of the chosen parameters. The prpose of these plots is to provide the reader with a sense of the extent of the scatter and the bias graphically, which may be needed for readers with little exposre to scientific literatre in that area. It shold be noted that the prpose of investigating these trends is to identify any parameters that wold improve CPT estimates of the ndrained shear strength if inclded in the analysis. N 73

96 The trends are determined based on the crrently sed vale of 15. Despite the fact that this N vale is commonly sed, it was picked for this part of the stdy as an arbitrary vale. Other N vales cold have been chosen withot altering the observations made abot the trends; N is only a constant in any case. As will be seen later, other N vales will be determined dring the calibration stdy. Depth, h. Stdying the effect of soil depth on the ncertainties inherent in CPT predicted ndrained shear strength vales can be viewed as part of stdying the effect of spatial variations. The goal of this stdy is to determine whether different soil depths reslt in different overestimation or nderestimation of the ndrained shear strength. Several arbitrary depth intervals were chosen for this prpose. They represent a top layer with a 5 ft. depth followed by layers ending at 20 ft. depth intervals, i.e., h = 5-20, h = 20-40, h = 40-60, and h greater than 60 feet. It shold be noted that each depth range inclded an acceptable nmber of data points that can be analyzed statistically. A higher resoltion of depth ranges might be CPT UC possible in the ftre as more CPT reslts are inclded in the database. The S S ratio within each depth interval was analyzed and the bias and COV were calclated. Table 12 smmarizes the bias and COV reslts for the chosen depth ranges. The reslts do not indicate a clear trend for any of the compted statistical descriptors. For example, the bias increases from a vale of (overestimate) at depths < 5 ft. to for depths between 5 ft. and 20 ft. However, this trend does not contine beyond this depth range. Actally, it flctates arond an almost constant vale. Similarly, the coefficient of variation, COV, also does not seem to follow a clear trend. After dropping from 85 percent to 58 percent at depth range ft., it increases again for higher depths. Based on these observations, it was conclded that no clear trends can be extracted from the available dataset. As a reslt, the reliability-based calibration wold not reslt in a N factor that depends on, or is a fnction of, h. 74

97 Table 12 Effect of soil depth on ncertainty of CPT reslts Depth range, h 1 : h 2 (feet) < > 60 Bias, Standard Deviation, Coefficient of Variation, COV 85% 73% 61% 58% 73% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N

98 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) h < 5 ft. 5 ft. < h < 20 ft Underestimate 2500 Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) 20 ft. < h < 40 ft. 40 ft. < h < 60 ft. Figre 38 Comparison of ndrained shear strength, S, from CPT and UC tests at different depths 76

99 CPT Reading Vales ( qc vo ) The second inflence stdy condcted is related to the net difference between CPT readings, qc. This difference is in the core of the CPT expression for ndrained shear strength, vo eqation (6). Stdying whether the ncertainties in the CPT reslts are inflenced by is done for the prpose of incorporating sch inflence in the calibration stdy to follow. The hypothesis is that if sch a trend exists, the ser can easily compte the net difference and se an appropriate N vale for ndrained shear strength calclations. As with the previos parameter (soil depth), the range of qc vo qc was divided into several ranges. They are: less than 4 tsf, between 4 and 8 tsf, between 8 and 12 tsf, between 12 and 16 tsf, and greater than 16 tsf. The data points that fell within these ranges were statistically analyzed as before. Table 13 smmarizes the reslts of this statistical analysis for each of the qc ranges. vo vo The reslts show that there is a clear trend in the bias for the ratio estimates are conservative on average for the qc vo S CPT S UC. The CPT below 4 tsf. However, nconservative estimates of the ndrained shear strength are indicated for the higher qc vo vales. This COV varies slightly abot an average vale of 68 percent. It appears that the net difference between the CPT readings, present the clearest parameter that inflence the CPT coefficient qc vo N. As more data become available, it may be possible to calibrate fnction of two parameters, one being the net difference between the CPT readings, N as a qc. Therefore, this information shold be considered in any ftre research efforts that bild on the findings of this stdy. vo 77

100 Table 13 Effect of net difference between CPT readings, Net Difference, qc vo qc, on ncertainty of CPT reslts (tsf) < > 16 Bias, Standard Deviation, Coefficient of Variation, COV 72% 62% 67% 70% 69% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N vo 78

101 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) qc vo < 4 tsf 4 < qc vo < 8 tsf Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) 8 < qc vo < 12 tsf 12 < qc vo < 16 tsf Figre 39 Comparison of ndrained shear strength, S, from CPT and UC tests at different CPT readings net difference,, vales qc vo 79

102 Soil Classification. Three soil classification methods were investigated to stdy the ncertainty in CPT ndrained shear strength estimates: Zhang and Tmay Method (1999) Robertson s Method (1990) Plasticity Index (PI) The first method is implemented in the LADOTD s software for CPT data analysis. It provides the probability of existence of three soil types, namely, clay, silt, and sand. The focs of this project is on the ndrained shear strength that is related to clayey soils. Therefore, the predicted probability of clay percentage is chosen as the classification parameter. The second method by Robertson (1990) provides soil classifications as one of six possible types: two for organic soils and peats, three for clays (silty clay to clays), for for silt mixtres (clayey silt to silty clay), five for sand mixtres (silty sand to sandy silt), six for sands (clean sand to silty sand), and seven for gravelly sand to dense sand. The classifications of interest to this stdy are two throgh for where the ndrained shear strength is relevant. Finally, the plasticity index, which is eqal to Liqid Limit (LL) mins the plastic Limit (PL) is also investigated as a possible soil classification method by stdying its correlation to CPT ndrained shear strength estimates. The reslts from stdying these three parameters are described next. Zhang and Tmay Method. This classification approach provides the ser with the probability of existence of clay, silt, and sand from CPT readings. Its major advantage in the context of this stdy is that no borehole reslts will be needed to assist in estimating the ndrained shear strength, nlike the Plasticity Index for example where sch information will be necessary. The data points were groped twice based on: (1) the probability of existence of clay and (2) the probability of existence of clay pls silt combined. The probability of existence of sand was not considered since it is not related to the ndrained shear strength. The reslts from the two gropings are presented next. Table 14 lists the reslts for the first groping of probability of existence of clay in the tested soil. Both silt and sand are exclded in this groping. For ranges of probability of clay existence were chosen for this stdy. They are less than 25 percent, between 25 and 50 percent, between 50 and 75 percent and greater than 75 percent. Data points falling 80

103 within each range were analyzed statistically as before. The bias, standard deviation, and coefficient of variation are given in Table 14. It can be seen that after an initial increase in the bias and coefficient of variation for the first two ranges (< 25 percent and percent), a clear declining trend is noticed. This implies that as the probability of clay existence increases, the CPT becomes a more reliable tool for estimating the ndrained shear strength. This is expected becase the ndrained shear strength is a qantity that describes soils with high clay contents and the existence of coarser materials in the soil adversely affects the CPT readings for ndrained shear strength calclations. Table 15 lists the reslts from the same classification method; however, the probabilities of existence of clay and silt are combined. For ranges were chosen for the investigation. They are less than 80 percent, between 80 and 90 percent, between 90 and 97.5 percent and greater than 97.5 percent. The statistical reslts for the data points within each range showed trend similar to when only clay was considered. An initial rise for the bias between the first and second range was noticed followed by a consistent drop from one range to the other for sbseqent ranges. The coefficient of variation s trend was not as clear. The first two ranges (< 80 percent and percent) had a similar coefficient of variation (68 percent), followed with a rise in the third range to 83 percent and then a drop to 65 percent in the forth range. This indicates that relying on the existence of clay might be a better soltion in ftre calibration efforts de to the clearer trends it offers. Table 14 Effect of soil classification on ncertainty of CPT reslts (Zhang and Tmay clay only) Clay Percentage (%) < > 75 Bias, Standard Deviation, Coefficient of Variation, COV 67% 78% 76% 62% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N

104 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Clay < 25% 25 % < Clay < 50% Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) 50 % < Clay < 75% Clay > 75% Figre 40 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Zhang and Tmay clay only) 82

105 Table 15 Effect of soil classification on ncertainty of CPT reslts (Zhang and Tmay clay and silt) Clay and Silt Percentage (%) < > 97.5 Bias, Standard Deviation, Coefficient of Variation, COV 68% 68% 83% 65% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N

106 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Clay and Silt < 80% 80 % < Clay and Silt < 90% Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) 90% < Clay and Silt < 97.5% Clay and Silt > 97.5% Figre 41 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Zhang and Tmay clay and silt) 84

107 Robertson s Method. The first for soil types [two for organic soils and peats, three for clays (silty clay to clays), for for silt mixtres (clayey silt to silty clay), and five for sand mixtres (silty sand to sandy silt)] are analyzed in this stdy. The remaining two classifications [six for sands (clean sand to silty sand) and seven for gravelly sand to dense sand)] were not inclded in this analysis becase of the irrelevance of ndrained shear strength to these soil types. The same can be said abot Soil Type 5. It is, however, inclded in the analysis. Table 16 lists the smmary of the reslts that show a consistent trend of a rising bias and a dropping coefficient of variation for the most relevant soil types (2, 3, and 4). This indicates that the CPT overestimates the ndrained shear strength at a lower rate for Soil Type 2 than Type 3, which is also lower than Type 4. This method shows a good potential for inclsion in ftre CPT calibration efforts becase it only relies on CPT data (no boreholes are needed) similar to the previos classification techniqe (Zhang and Tmay). Table 16 Effect of soil classification on ncertainty of CPT reslts (Robertson) Soil classification Bias, Standard Deviation, Coefficient of Variation, COV 71% 67% 63% 87% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N

108 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Classification 2 Classification Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Classification 4 Classification 5 Figre 42 Comparison of ndrained shear strength, S, from CPT and UC tests for different soil classifications (Robertson) 86

109 Plasticity Index. The Plasticity Index (PI) was also analyzed as a classification techniqe in an attempt to relate the accracy of CPT ndrained shear strength estimates to this qantity. Unlike the previos classification techniqes, the PI wold reqire reslts from boreholes if it were to be sed in interpreting CPT test readings. This approach eliminates the possibility of sing the CPT as an independent testing tool. Five ranges of PI were chosen for the stdy, namely, less than 20, between 20 and 30, between 30 and 40, between 40 and 50, and greater than 50. The reslts of the statistical analysis for the accracy of CPT ndrained shear estimates with respect to borehole reslts are smmarized in Table 17 for each of the stdied ranges. There is no clear trend for the bias or the coefficient of variation. Therefore, it can be conclded that there is no jstification for inclding the plasticity index in sbseqent calibration stdies. Table 17 Effect of Plasticity Index on ncertainty of CPT reslts PI range < > 50 Bias, Standard Deviation, Coefficient of Variation, COV 72% 83% 56% 48% 55% Nmber of Points, N Average CPT Coefficient, N Standard Deviation, N

110 Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) PI < < PI < Underestimate Underestimate Bore Hole Undrained Shear Strength, S (psf) Bore Hole Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) Overestimate CPT Undrained Shear Strength, S (psf) < PI < < PI < 50 Figre 43 Comparison of ndrained shear strength, S, from CPT and UC tests for different Plasticity Index vales

111 Chi-Sqare Reslts Transformation Model, S CPT S UC. A Chi-Sqare test was condcted on the CPT UC transformation model reslts, i.e., the ratio S S, following the procedre described in Appendix C. Figre 44 shows a plot of the observed data (862 points) and theoretical lognormal and normal vales. It can be seen that the lognormal distribtion fits the observed data better. The Chi Sqare test revealed that the smmation m i1 ni ei e i 2 is eqal to for the lognormal distribtion and for the normal distribtion. According to Table 36, the lognormal distribtion passes the test, which reqires the smmation to be less than for 6 degrees of freedom (f = m -1-k = = 6) with a significance level of =10 percent ( ). The normal distribtion fails this test. Similar tests were condcted for the data sbsets according to Robertson classification of soils. The conclsions were identical to those obtained from the whole dataset, except for Soil Classification 2 where both normal and lognormal distribtion passed the test, however, at a lower significance level (5 percent). Table 18 Smmary of chi-sqare test reslts for transformation model Dataset Cont m i1 ni ei e i 2 Lognormal Normal All data points Soil Classification Soil Classification Soil Classification

112 Freqency Lognormal Data > 5.6 Bias, Freqency (a) Lognormal Normal Data > 5.6 Bias, (b) Normal Figre 44 Chi sqare test reslts for transformation model (all data points) 90

113 Freqency Lognormal Data > 2.8 Bias, Freqency (a) Lognormal Normal Data > 2.8 Bias, (b) Normal Figre 45 Chi sqare test reslts for transformation model (Soil Classification 2) 91

114 250 Freqency Lognormal Data > 5.6 Bias, Freqency (a) Lognormal Normal Data > 5.6 Bias, (b) Normal Figre 46 Chi sqare test reslts for transformation model (Soil Classification 3) 92

115 Freqency Lognormal Data > 4.2 Bias, Freqency (a) Lognormal Normal Data > 4.2 Bias, (b) Normal Figre 47 Chi sqare test reslts for transformation model (Soil Classification 4) 93

116 Repeatability of Tip Resistance, q c. The other random variable that is determined from this stdy is that related to the inherent ncertainty in the device measrements. The repeatability reslts (see on Page 59) were sed to choose an appropriate distribtion for this random variable. The reslts are plotted in Figre 48 for both distribtion types. The m 2 ni ei smmation was eqal to for the lognormal distribtion and for i1 ei the normal distribtion. This means that a normal distribtion fits this random variable better as it passes the Chi-Sqare test at a significance level,, eqal to 5percent ( ). Freqency Lognormal Data Freqency < > 1.9 Bias, (a) Lognormal Normal Data < > 1.9 Bias, (b) Normal Figre 48 Chi sqare test reslts for device ncertainty 94

117 Calibration of CPT Coefficient for Undrained Shear Strength N Calibration 1 st Approach As described earlier, the 1 st approach adopted in this stdy for calibrating the CPT coefficient, N, is straightforward and relies on direct correlation between ndrained shear strength obtained from CPT and boring reslts. For the 862 points available in the database, N vales were compted. Figre 49 shows a histogram of the N vales compted sing eqation (42). It can be seen that a wide range of N reslted from the data. To illstrate how this plot can be sed, a N vale of 15 is chosen. For this vale, it can be seen that the shear strength for 80.7 percent of the points in the database will be overestimated. Freqency Underestimated Overestimated if N = 15 is sed 80.7% < > 66 CPT Coefficient, N Figre 49 Histogram of N vales obtained from eqation (42) all data points To simplify this plot in sch a way that can be sed to determine N vales for target probabilities of exceedance, the cmlative distribtion fnction (CDF) of the data is constrcted and plotted in Figre 50. This plot can be sed to determine the probability of exceedance for any N vale. For example, the figre shows that if N is set to 15, the probability of exceedance is eqal to 19 percent ( ). Alternatively, N can be determined for a given target probability of exceedance. In the same figre, a N vale can be determined for a desired target probability of exceedance (40 percent in this illstration) 95

118 can be easily determined to be 21. Similar plots can be generated for different soil classifications. Table 19 lists N vale obtained for probability of exceedance, P e, eqal to 50 percent, 55 percent, and 66.7 percent, which will be the target vales throghot this stdy Probability % % Correlated N Figre 50 Cmlative distribtion fnction (CDF) for N vales [all data points] Table 19 Calibrated N vales for different probability of exceedance, P e, vales Probability of Exceedance, Pe CPT Coefficient, N 50.0% % %

119 Plots similar to the histogram seen in Figre 49 can be generated for any sbgrop of data points. For example, Figre 51 and Figre 52 show the histograms for each soil classification sing both methods investigated in this stdy, namely Robertson (1990) and Zhang and Tmay (1999). It can be seen from the plots that the decrease in clay content (lower classification nmber in Robertson s method and higher percentage in Zhang and Tmay method) is translated into an increase in N vale. This is illstrated with the shift in the histogram to higher N vales. Plots similar to the CDF shown in Figre 50 can also be generated for each soil classification. However, de to the limited nmber of data points, a smooth S-crve sch as the one seen in Figre 50 is not achievable. As more data points become available, the development of these charts will be trivial. Freqency Average N = 20.4 < > 70 Freqency Average N = 28.5 < > 70 CPT Coefficient, N CPT Coefficient, N Classification 2 Classification 3 Freqency Average N = 31.0 < > 70 Freqency Average N = 39.6 < > 70 CPT Coefficient, N CPT Coefficient, N Classification 4 Classification 5 Figre 51 Histogram of N vales obtained from eqation (42) (by Robertson soil classification) 97

120 Average N = Average N = 29.3 Freqency Freqency < > 70 0 < > 70 CPT Coefficient, N CPT Coefficient, N > 75% Clay 50% 75% Clay Average N = Average N = 31.7 Freqency Freqency < > 70 0 < > 70 CPT Coefficient, N CPT Coefficient, N 25% 50% Clay < 25% Clay Figre 52 Histogram of N vales obtained from eqation (42) (by Zhang and Tmay s soil classification) It shold be emphasized that this approach does not accont for the variability inherent in soil properties or measring device. In other words, each of the N vales is obtained sing one CPT sonding and one nconfined compression test. In real life, different CPT sondings will reslt in different readings as was demonstrated by the repeatability stdy. Also, variations in soil properties are the norm and shold be acconted for. If these sorces of ncertainty are not acconted for at this level (soil property), proper care shold be taken when sing these properties in the next level of engineering comptations (fondation design). 98

121 N Calibration 2 nd Approach The 2 nd approach for calibration of the CPT coefficient, N, acconts for all ncertainties identified in this stdy sing the limit state fnction eqation (47-b), and applying the First Order Reliability Method (FORM) described in Appendix B. The reslts from this stdy are presented next. Table 20 throgh Table 22 show the reslts for a series of comptations considering q vo c = 0.10 and relying on Robertson s classification. The choice to present the reslts for a q ratio eqal to 0.10 was based on the average vo c q vo c ratio of data points inclded in the database, which is Frthermore, a sensitivity stdy was condcted, and it was determined that the q ratio does not impact the reliability reslts except for high end vo c vales, e.g., q = The tables also show the term 2, which will be sed in vo c the optimization of N. The three tables correspond to the three chosen target probability of exceedance levels, namely 50 percent ( T = 0.0), 55 percent ( T = ), and 66.7 percent ( T = ). As can be seen, targeting higher vales reqires higher N vales so the term 2 T is eqal to zero. An exact zero vale cannot always be achieved de to the discrete N vales chosen in this stdy. Therefore, finding an optimm T N is achieved as can be seen in Figre 53 where the minimm vale of the plot of 2 T verss N corresponds to the desired vale. 99

122 Reliability reslts ( = 0.0, T Table 20 vo q c = 0.10, Robertson classification) ALL Cases N 2 T 2 T 2 T 2 T

123 Reliability reslts ( = , T Table 21 vo q c = 0.10, Robertson classification) ALL Cases N 2 T 2 T 2 T 2 T

124 Reliability reslts ( = , T Table 22 vo q c = 0.10, Robertson classification) ALL Cases N 2 T 2 T 2 T 2 T

125 Optimm N ( T ) CPT Coefficient, N (a) All data ( T ) N (Class 4) N (Class 3) N (Class 2) CPT Coefficient, N (b) by Robertson s classification Determining optimm Figre 53 N vales ( = , q = 0.05) T vo c 103

126 This optimization procedre was repeated for all stdied cases, and the reslts are smmarized in Table 23 throgh Table 25. Optimm Table 23 N vales ( = 0.0, Robertson classification) T q vo c Classification ALL Optimm Table 24 N vales ( = , Robertson classification) T q vo c Classification ALL

127 Optimm Table 25 N vales ( = , Robertson classification) T q vo c Classification ALL N/A N/A Table 26 throgh Table 31 list the reliability calibration reslts for Zhang and Tmay soil classification method that were obtained by repeating the procedre described above. It can be seen that the optimm N vales are also affected by the type of soil (clay content). Nevertheless, the differences between N vales for difference soil types are smaller than those obtained sing the Robertson soil classification. 105

128 Reliability reslts ( = 0.0, T vo Table 26 q c = 0.10, Zhang and Tmay classification) ALL Cases > 75% 50% - 75% 25% - 50% N 2 T 2 T 2 T 2 T

129 Reliability reslts ( = , T vo Table 27 q c = 0.10, Zhang and Tmay classification) ALL Cases > 75% 50% - 75% 25% - 50% N 2 T 2 T 2 T 2 T

130 Reliability reslts ( = , T vo Table 28 q c = 0.10, Zhang and Tmay classification) ALL Cases > 75% 50% - 75% 25% - 50% N 2 T 2 T 2 T 2 T Optimm Table 29 N vales ( = 0.0, Zhang and Tmay classification) T q vo c Classification (clay probability) ALL > 75% 50% - 75% 25% - 50% < 25%

131 Optimm Table 30 N vales ( = , Zhang and Tmay classification) T q vo c Classification (clay probability) ALL > 75% 50% - 75% 25% - 50% < 25% Optimm Table 31 N vales ( = , Zhang and Tmay classification) T q vo c Classification (clay probability) ALL > 75% 50% - 75% 25% - 50% < 25% N/A N/A N/A N/A 0.9 N/A N/A N/A N/A N/A Correlation Between Unit Weight, T, from CPT and Boring Data As a byprodct of this stdy, the correlation between nit weight estimates obtained from CPT and boring data was also investigated. Eqation (33) was sed to compte the nit weight from CPT readings, while direct nit weight vales were available from boring data. A plot of this correlation can be seen in Figre 54. Unlike the ndrained shear strength plots 109

132 presented earlier, this plot shows better correlation between nit weight estimates from CPT CPT UC and boring data. As before, the bias ( ) and COV of the ratio, T T, were compted to assess the accracy of the CPT nit estimates. The reslts showed that the bias is eqal to 0.98, which indicates that the CPT slightly nderestimated the nit weight on average. The COV of the same ratio is compted to be 12.4 percent indicating a scatter in the reslts, which can be seen in Figre 55. However, it shold be noted that these reslts are sbstantially better than those presented earlier for the ndrained shear strength estimates ( = 2.01 and COV = 71 percent for N 15). In smmary, it can be said that the CPT is a valid testing tool for estimating the nit weight of Loisiana soils. 125 Underestimate 100 Bore Hole Unit Weight, T (pcf) Overestimate CPT Soil Unit Weight, (pcf) Figre 54 Unit weight correlation T (CPT vs. boring reslts) Freqency < > 1.65 Unit Weight Ratio, T,CPT / T,BoreHole Figre 55 Histogram of nit weight ratio T, CPT T, BoreHole 110

133 SUMMARY AND CONCLUSIONS Smmary The prpose of this stdy is to pdate the correlations between cone penetration and boring log data. A thorogh literatre review was first condcted. An extensive database of CPT reslts from projects in Loisiana was collected and processed. This database was merged into a GIS software package to facilitate ftre retrieval of information generated from this stdy. A total of 752 CPT points were docmented of which 503 were matched with adjacent boreholes and 249 did not have adjacent borehole data available. The CPT data was sed to predict soil ndrained shear strength, blk density, and classification according to the Robertson (Robertson 1990) and Zhang and Tmay (1999) methods. A reliability based calibration of the CPT reslts with respect to borehole data as benchmarks was then condcted. The calibration considered the ncertainties known to be associated with soil properties, namely, inherent soil variability, device measrement, and analytical expression (transformation model). Finally, recommendations for ftre research and an implementation statement were sggested based on the findings of this research. Conclsions The conclsions from this stdy can be smmarized in the following: 1. A single N vale that is valid for all soil types is nwarranted as it will lead to acceptable reslts for some soil conditions and nacceptable reslts for others, which can be nconservative. 2. Two approaches for the calibration of the CPT coefficient, N, were presented in this stdy. The first approach is a direct correlation between ndrained shear strength reslts in the assembled database from CPT and boring data. The second approach tilizes the First Order Reliability Method (FORM) and acconts for all sorces of ncertainty (soil properties, device measrement, and transformation model) as compared to the first approach, which only acconts for ncertainties in the transformation model, eqation (41). 3. Based on the first approach, a vale of 25 shold be sed for the CPT coefficient, N, to achieve a 50 percent probability of exceedance, i.e., T = 0.0. Safer designs will 111

134 need higher probability of exceedance vales (higher T ), which reslts in N eqal to 27 and 32 for target T vales eqal to (55 percent) and (66.7 percent), respectively. 4. The second approach yielded N vales eqal to 27.5, 31.0, and 42.0 for target vales eqal to 0, (0 percent), (55 percent) and (66.7 percent), respectively. The difference in N vales obtained from both methods is attribted to the fact that the first approach does not accont for the ncertainties inherent in soil properties and the measring device. Both ncertainties add to the overall confidence in the soil property, which was captred by the FORM analysis (2 nd approach) bt cannot be captred sing the first approach. 5. The N reslts presented above are based on the entire dataset compiled for this stdy. The dataset was frther analyzed by groping data points in sbgrops based on different parameters associated with each point. The parameters considered in this stdy for groping the data are: (1) depth, (2) soil classification (three different methods), and (3) CPT readings. It was determined that the soil classification is the only parameter showing clear trends that affect CPT estimates of the ndrained shear strength. Therefore, frther calibrations were warranted taking into accont the soil type. Vales of N for each soil type based on the Robertson (1990) classification and the Zhang and Tmay (1999) classification were obtained. The following tables smmarize the recommended N vales obtained from the FORM analysis for both soil classification techniqes. It is obvios that the N coefficient for soils with higher clay content is lower than those with less clay content. 6. Reslts obtained from this stdy also showed that the nit weight estimates from CPT readings sing eqation (33) are in good agreement with borehole reslts. The expression in eqation (33) slightly nderestimates the nit weight on average by 2 percent. The scatter of the reslts is also limited (COV = 12.4 percent) compared to the ndrained shear strength discssed earlier. T 112

135 Table 32 Recommended N vales sing 2 nd approach (Robertson classification) Probability of Exceedance N vales for different soil Classifications ALL % ( T = 0.0) % ( T = ) % ( T = ) Table 33 Recommended N vales sing 2 nd approach (Zhang and Tmay classification) Probability of Exceedance N vales for different soil classifications (clay probability) ALL > 75% 50% - 75% 25% 50% < 25% 50% ( T = 0.0) % ( T = ) % ( T = ) A procedre for classifying projects based on the site variability was proposed. The procedre bilds on the reslts from the repeatability stdy condcted in this project. It can be sed to obtain a non-sbjective classification for site variability of a certain project (e.g., low, medim, or high) by stdying the coefficient of variation of the CPT ndrained shear strength estimates from mltiple sonding at the project site. This classification can then be sed in conjnction with AASHTO-LRFD design code to se appropriate design coefficients. 113

136 114

137 RECOMMENDATIONS The research team recommends promoting the developed database to LADOTD staff to se it before sending the drilling crew to the field. In some regions, there are a large nmber of borehole and CPT data files which can prove sefl for ftre projects. The research team also recommends expanding the GIS database when ftre measrements become available. The following procedre describes the steps to add more data, i.e., preparing a table of the new data points where each row of the table represents one CPT sonding. The colmn headers shold be similar to the ones in the original database, i.e., Job Nmber, Location, Station, Date, latitde, longitde, etc.; the table shold also inclde the location of the PDF and Excel files of the CPT sondings. This table can then be imported into ArcMap by sing the Add Data fnction. Once the table is added to ArcMap, the new data can be displayed on the map by selecting the Add X, Y data option. This will prompt the ser to select the colmns where the latitde and longitde are located in the table. After selecting the colmn where the coordinates are located, the points will appear on the map. At this point, the data can be converted into a shape file to be saved and sed in ArcMap. Finally, the join fnction can be sed to add the new points to the original database. Based on the statistical stdies performed in this research effort, it is recommended that the LADOTD starts adopting the pdated CPT coefficient in conjnction with borehole reslts for a transition period ntil the proposed vales are validated. Updates of the CPT coefficient are also prdent as more CPT data becomes available, which mentioned earlier, shold be added to the developed database. 115

138 116

139 ACRONYMS, ABBREVIATIONS, AND SYMBOLS a AASHTO A c ACI A f ALF A s A s A sb ASD A st B q Β B q c v c1 c 1, c 2, and c 3 COV CPT CRR CSR D 50 D i Significance level Cone area ratio The American Association of State Highway and Transportation Officials The projected area of the cone American Concrete Institte Skempton s pore pressre parameter at failre LTRC s Accelerated Loading Facility The srface area of the sleeve Friction sleeve srface area Cross sectional area at the bottom of the friction sleeve Allowable Stress Design Cross sectional area at the top of the friction sleeve The pore pressre ratio Angle of plastification Reliability Index Pore water pressre index Coefficient of consolidation Model ncertainty Constants dependent on the compressibility The coefficient of variation Cone Penetration Test Cyclic resistance ratio Cyclic stress ratio Mean particle size Distance between CPT and borehole 117

140 DOQQ D r Dr L, Dr M, Dr H Δ e E t E s e max, e min f t FC FORM F s f s φ` ft. i T GIS h HPC HPM HPS I c In. IR Digital orthophoto qarter qad images Relative density Relative densities corresponding to low, medim, and high compressibility conditions Excess pore water pressre Void ratio Initial tangent modls Secant modls at 50 percent failre The maximm and minimm void ratios Resistance factor The corrected sleeve friction Fines content The First Order Reliability Method The force acting on the friction sleeve The sleeve friction Friction angle Feet The load factor Soil nit weight Geographic information system Depth in feet highly probable clay highly probable mixed highly probable sand Soil classification index Inch Rigidity index 118

141 k K o kpa LADOTD LRFD LSD LTRC Adjstment factor (fnction of soil type and properties) Earth pressre coefficient at rest Kilo Pascal The bias X i The mean Loisiana Department of Transportation and Development Load and Resistance Factor Design Limit State Design Loisiana Transportation Research Center MPa N c, N k, N, N c, N Δ NCHRP OCR p a PCPT PDF PI psf q q E Q i Q A Q c q c Q F q t q t-net Mega Pascal Theoretical cone factor The National Cooperative Highway Research Program over-consolidation ratio Atmospheric pressre Piezo-Cone Penetration Test Portable docment format Plasticity index Ponds per sqare foot Weighted average Effective tip resistance parameter The demand de to applied loads (dead, live, etc.) Aging factor The total force acting on the cone The cone resistance Empirical constant of the least-sqare regression Cone resistance corrected for neqal end area effects Net tip resistance 119

142 R n The nominal capacity of the designed member R f σ ho σ mean vo Friction ratio Horizontal pressre Mean stress total overbrden stress Pre-consolidation pressre `p X i Standard deviation UC S Unconfined compression ndrained shear strength CPT S Undrained shear strength calclated from CPT data SBPMT SPT SPT-N STE S tsf U o USCS V s W L, W M, and W H X i Self-boring Pressremeter Test Standard penetration test Nmber of blows in SPT for 300 mm penetration Soil Testing Engineers, Inc. Undrained shear strength Semi-apex angle Tons per sqare foot soil classification index Pore water pressre at the tip of the cone Pore water pressre behind the cone Pore water pressre behind the friction sleeve Hydrostatic or initial in-sit pore pressre Unified Soil Classification System Shear wave velocity Weight factors Random variable 120

143 REFERENCES 1. Robertson, P.K. (1990), Soil Classification Using the Cone Penetration Test. Canadian Geotechnical Jornal, Vol. 27, No. 1. pp Zhang, Z. and Tmay, M.T. (1999), Statistical to Fzzy Approach Toward CPT Soil Classification. Jornal of Geotechnical and Geoenvironmental Engineering, Vol. 125 (3), pp Villet, W.C.B and Mitchell, J.K. (1981), Cone Resistance, Relative Density and Friction Angle. Cone Penetration Testing and Experience; Session at the ASCE National Convention, St. Lois, , American Society of Engineers (ASCE). 4. Robertson, P.K. and Campanella, R.G. (1983a), Interpretation of Cone Penetrometer Test: Part I: Sand. Canadian Geotechnical Jornal, 20(4), pp Robertson, P.K. and Campanella, R.G. (1983b), Interpretation of Cone Penetrometer Test: Part II: Clay. Canadian Geotechnical Jornal, 20(4), pp Meigh, A. C. (1987), Cone penetration testing. CIRIA Rep., Btterworth s, London, U.K. 7. Vermeiden, J. (1948), Improved Sonding Apparats as Developed in Holland since Proceedings of the Second International Conference on Soil Mechanics and Fondation Engineering, Rotterdam, 1, pp Plantema, G. (1948), Constrction and Method of Operating a New Deep Sonding Apparats. Proceedings of the 2nd International Conference on Soil Mechanics and Fondation Engineering, Rotterdam, 1, pp Begemann, H.K.S. Ph. (1953), Improved Method for Determining Resistance to Adhesion by Sonding Throgh a Loose Sleeve Placed Behind the Cone. Proceedings of the 3rd International Conference on Soil Mechanics and Fondation Engineering, Zrich, 1, pp

144 10. Sanglerat, G. (1972), The Penetrometer and Soil Exploration. Elsevier, Amsterdam, 464 pp. 11. Lnne, T.; Robertson, P.K.; and Powell J.J.M. (1997), Cone Penetration Testing in Geotechnical Practice. Blackie Academic, EF Spon/Rotledge Pblishers, New York, 312 pp. 12. Krp, P. U.; Voyiadjis, G. Z.; and Tmay, M. T. (1994), Calibration Chamber Stdies of Piezocone Test in Cohesive Soils. J. Geotechnical Engineering, American Society of Civil Engineers (ASCE), 120(1), pp Schaap, L.H.J. and Zidberg, H.M. (1982), Mechanical and Electrical Aspects of the Electric Cone Penetrometer Tip. Proceedings of the 2nd Eropean Symposim on Penetration Testing, ESOPT-II, Amsterdam, 2, Balkema Pb. Rotterdam. 14. Sandven, R.; Senneset, K.; and Janb, N. (1988), Interpretation of Piezocone Tests in Cohesive Soils. Proceedings of the International Symposim on Penetration Testing, ISOPT-1, Orlando, 2, , Balkema Pb., Rotterdam. 15. Begemann, H.K.S. Ph. (1965), The Friction Jacket Cone an Aid in Determining the Soil Profile. Proceedings of the 6th International Conference on Soil Mechanics and Fondation Engineering, Montréal, 1, Sanglerat, G.; Nhim, T. V.; Sejorne, M.; and Andina, R. (1974), Direct Soil Classification by Static Penetrometer with Special Friction Sleeve. Proceedings of the First Eropean Symposim on Penetration Testing, ESOPT-1, Jne 5-7, Stockholm, Vol. 2.2, pp Schmertmann, J.H. (1970), Static Cone to Compte Static Settlement Over Sand. Jornal of the Soil Mechanics and Fondations Division, American Society of Civil Engineers (ASCE), 96(SM3), pp Doglas, B.J. and Olsen, R.S. (1981), Soil Classification Using Electric Cone Penetrometer. Cone Penetration Testing and Experience. Proceedings of the ASCE National Convention, St. Lois, American Society of Civil Engineers (ASCE), pp

145 19. Robertson, P.K.; Campanella, R.G.; Gillespie, D.; and Greig, J. (1986), Use of Piezometer Cone Data. Proceedings of the ASCE Specialty Conference In Sit 86: Use of In Sit Tests in Geotechnical Engineering, Blacksbrg, American Society of Civil Engineers (ASCE), pp Olsen, R.S. and Farr, J.V. (1986), Site Characterization Using the Cone Penetration Test. Proceedings of the ASCE Specialty Conference In Sit 86: Use of In Sit Tests in Geotechnical Engineering, Blacksbrg, American Society of Civil Engineers (ASCE), pp Lnne, T.; Eidsmoen, T.; Gillespie, D.; and Howland, J.D. (1986), Laboratory and Field Evalation of Cone Penetrometers. Proceedings of the ASCE Specialty Conference In Sit 86: Use of In Sit Tests in Geotechnical Engineering, Blacksbrg, American Society of Civil Engineers (ASCE), pp Gillespie, D.G. (1990), Evalating Velocity and Pore Pressre Data from the Cone Penetration Test. Ph.D. thesis, Department of Civil Engineering, University of British Colmbia, Vancover, BC. 23. Jones G.A. and Rst, E. (1982), Piezometer Penetration Testing, CUPT. Proceedings of the Second Eropean Symposim on Penetration Testing, ESOPT-2, Amsterdam, May 24-27, Vol. 2, pp Baligh, M.M.; Vivatrat, V.; and Ladd, C.C. (1980), Cone Penetration in Soil Profiling. Jornal of the Geotechnical Engineering Division, American Society of Civil Engineers (ASCE), 106(GT4), pp Senneset K. and Janb, N. (1985), Shear Strength Parameters Obtained from Static Cone Penetration Tests In Sit Measrements. Symposim, San Diego, 1984, American Society for Testing and Materials (ASTM) special technical pblication, STP 883, pp Eslami, A. and Fellenis, B.H. (1997), Pile Capacity by Direct CPT and CPT methods applied to 102 Case Histories. Canadian Geotechnical Jornal, Vol. 34, No. 6, pp

146 Fellenis, B.H. and Eslami, A. (2000), Soil Profile Interpreted from CPT data. Year 2000 Geotechnics, Geotechnical Engineering Conference, Asian Institte of Technology, Bangkok, Thailand, November 27-30, 2000, 18 pp. 28. Kafmann, A. (1975), Introdction to the Theory of Fzzy Sbsets, I: Fndamental Theoretical Elements. Academic Press, New York. 29. Brown, C.B.; Chamea, J.L.; Palmer, R.; and Yao, J.T.P. (1985). Proceedings, NSF Workshop on Civil Engineering Applications of Fzzy Sets, Prde University, West Lafayette, IN. 30. Hill, R. (1950), The Mathematical Theory of Plasticity. Oxford University Press, Oxford, England. 31. Vesic, A.S., (1972), Expansion of Cavities on the Infinite Soil Masses. Jornal of the Soil Mechanics and Fondation Division, American Society of Civil Engineers (ASCE), Vol. 98, SM3, pp Baligh, M.M. (1985), Strain path method. Jornal of the Geotechnical Engineering Division, American Society of Civil Engineers (ASCE), 111(GT9), pp Teh, C.I. and Holsby, G.T. (1991), An Analytical Stdy of the Cone Penetration Test in Clay. Geotechniqe, 41(1), pp Ab-Farsakh, M.Y.; Voyiadjis, G.Z; and Tmay, M.T. (1998), Nmerical Analysis of the Miniatre Piezocone Penetration Tests (PCPT) in Cohesive Soils. International Jornal for Nmerical and Analytical Methods in Geomechanics. Vol. 22 (10), pp Terzaghi, K. (1943), Theoretical soil mechanics. John Wiley and Sons, New York, 510 pp. 36. Caqot, A. and Kerisel, J. (1956), Traité de Mécaniqe des Sols. Gathier-Villars, Paris. 37. Meyerhof, G.G. (1951), The Ultimate Bearing Capacity of Fondations. Géotechniqe. 2(4), pp

147 38. De Beer, E.E. (1977), Static Cone Penetration Testing in Clay and Loam. Sondeer Symposim, Utrecht. 39. Skempton, A.W. (1951), The Bearing Capacity of Clays. Proceedings of the Bilding Research Congress, London, Division I, Gibson, R.E. (1950), Discssion: G. Wilson. The bearing capacity of screw piles and concrete cylinders. Jornal of the Instittion of Civil Engineers, 34, Baligh, M.M. (1975), Theory of Deep Site Static Cone Penetration Resistance. Massachsetts Institte of Technology, Department of Civil Engineering, Cambridge, Mass., Pblication No. R Ladanyi, B. (1967), Deep Pnching of Sensitive Clays. Proceedings of the Third Oan American Conference on Soil Mechanics and Fondation Engineering, Caracas, 1, pp Teh, C.I. (1987), An Analytical Stdy of the Cone Penetration Test. D.Phil. thesis, Oxford University. 44. Lnne, T. and Kleven, A. (1981), Role of CPT in North Sea Fondation Engineering. Session at the ASCE National Convention: Cone Penetration Testing and Materials, St. Lois, American Society of Civil Engineers (ASCE), pp Kjekstad, O.; Lnne, T.; and Clasen, C.J.F. (1978), Comparison Between In Sit Cone Resistance and Laboratory Strength for Overconsolidated North Sea Clays. Marine Geotechnology, 3(1), pp Aas, G.; Lacasse, S.; Lnne, T.; and Hoeg, K. (1986), Use of In Sit Tests for Fondation Design on Clay. Proceedings of the ASCE Specialty conference In Sit 86: Use of In Sit Tests in Geotechnical Engineering, Blacksbrg, American Society of Civil Engineers (ASCE), pp La Rochelle, P.; Zebdi, P.M.; Leroeil, S.; Tavenas, F.; and Virely, D. (1988), Piezocone Tests in Sensitive Clays of Eastern Canada. Proceedings of the International Symposim on Penetration Testing, ISOPT-1, Orlando, 2 pp , Balkema Pb., Rotterdam. 125

148 48. Rad, N.S. and Lnne, T. (1988), Direct Correlations Between Piezocone Test Reslts and Undrained Shear Strength of Clay. Proceedings if The International Symposim on Penetration Testing ISOPT-1, Orlando, 2, , Balkema Pb., Rotterdam. 49. Senneset, K.; Janb, N.; and Svanǿ, G. (1982), Strength and Deformation Parameters from Cone Penetration Tests. Proceedings of the 2nd Eropean Symposim on Penetration Testing, ESOPT-II, Amsterdam, 2, , Balkema Pb., Rotterdam. 50. Lnne, T.; Christopherson, H.P.; and Tjelta, T.I. (1985), Engineering Use of Piezocone Data in North Sea Clays. Proceedings of the 11th International Conference on Soil Mechanics and Fondation Engineering, San Francisco, 2, , Balkema Pb., Rotterdam. 51. Campanella, R.G. and Robertson, P.K. (1988), Crrent Stats of the Piezocone Test. Proceedings of the International Symposim on Penetration Testing, ISOPT-1, Orlando, 1, , Balkema Pb., Rotterdam. 52. Battaglio, M.; Jamiolkowsi, M.; Lancellotta, R.; and Maniscalco, R. (1981), Piezometer Probe Test in Cohesive Deposits. Cone Penetration Testing and Experience. Proceedings of the Session ASCE National Convention, St. Lois, pp Randolph, M.F. and Wroth, C.P. (1979), An Analytical Soltion for the Consolidation Arond a Driven Pile. Proceedings of the International Jornal for Nmerical and Analytical Methods in Geomechanics, 3(3), Henkel, D.J. and Wade, N.H. (1966), Plane Strain on a Satrated Remolded Clay. ASCE-J, Vol. 92, No Massarsch, K.R. and Broms, B.B. (1981), Pile Driving in Clay Slopes. Proceedings of the 10th International Conference on Soil Mechanics and Fondation Engineering, Stockholm, 3, , Balkema Pb., Rotterdam. 56. Keaveny, J.M. and Mitchell, J.K. (1986), Strength of Fine-Rained Soils Using the Piezocone. Proceedings of the ASCE Specialty Conference in Sit 86: Use of In Sit Tests in Geotechnical Engineering, Blacksbrg, , American Society of Civil Engineers (ASCE). 126

149 57. Lnne, T., Lacasse, S. and Rad, N.S. (1989), SPT, CPT, Pressremeter Testing and Recent Developments on In Sit Testing of Soils. General report from the 12th International Conference on Soil Mechanics and Fondation Engineering, Roi de Janeiro, 4, , Balkema Pb., Rotterdam. 58. Senneset, K.; Sandven, R.; and Janb, N. (1989), The Evalation of Soil Parameters from Piezocone Tests. Transportation Research Record, No. 1235, pp Slly, J.P.; Campanella, R.G.; and Robertson, P.K. (1988), Overconsolidation Ratio of Clays From Penetration Pore Water Pressres. Jornal of Geotechnical Engineering, ASCE, 114(2), pp Mayne, P.W. (1991), Determination of OCR in Clays by Piezocone Tests sing Cavity Expansion and Critical State Concepts. Soils and Fondations, 31(2), pp Mayne, P.W., CPT-Based Prediction of Footing Response. Measred & Predicted Behavior of Five Spread Footings on Sand (GSP 41). ASCE, Reston, Virginia, 1994, pp Mayne, P.W. (2006), The 2nd James K. Mitchell Lectre: Undistrbed Sand Strength from Seismic Cone Tests. Geomechanics & Geoengineering, Taylor & Francis Grop, London, Vol. 1, No. 4, Chen, B.S-Y. and Mayne, P.W. (1996), Statistical Relationships between Piezocone Measrements and Stress History of Clays. Canadian Geotechnical Jornal, Vol. 33, pp Mayne, P.W. (2001), Stress-Strain-Strength-Flow Parameters from Enhanced In-Sit Tests. Proceedings, International Conference on In-Sit Measrement of Soil Properties and Case Histories, Bali, Indonesia, pp Jang, C.H.; Hang, X.H.; Holtz, R.D.; and Chen, J.W. (1996), Determination of Relative Density from CPT Using Fzzy Sets. J. Geotechnical Engineering, American Society of Civil Engineers (ASCE), 122(1). 127

150 Baldi, G.; Bellotti, R.; Ghionna, V.; Jamiolkowski, M.; and Pasqalini, E. (1986), Interpretation of CPTs and CPTUs; 2nd part: Drained Penetration of Sands. Proceedings of the Forth International Geotechnical Seminar, Singapore, pp Klhawy, F.H. and Mayne, P.H. (1990), Manal on Estimating Soil Properties for Fondation Design. Electric Power Research Institte, EPRI, Agst, Jamiolkowski, M.; Swets, Zeitlinger and Lisse. (2001), Where Are We Going. Pre- Failre Deformation Characteristics of Geomaterials, Vol. 2 (Proc. Torino 99), pp Jang, C. H.; Fang, S. Y.; and Khor, E. H. (2006). First-Order Reliability Method for Probabilistic Liqefaction Triggering Analysis Using CPT, Jornal of Geotechnical and Geoenvironmental Engineering, Vol. 132, No. 3, pp Meigh, A.C. and Nixon, I.K. (1961), Comparison of In-Sit Tests for Granlar Soils. Proc. 5th International Conference on Soil Mechanics and Fondation Engineering, Paris, 1961, Vol. 1, pp Thornbrn, S. (1970), Proc. Conference on Behavior of Piles. Instittion Civil Engineers, London, pp Brland, J.B. and Brbridge, M.C. (1985), Settlement of Fondations on Sand and Gravel. Proceedings of the Instittion of Civil Engineers. December (Part 1), pp Jefferies, M.G. and Davies, M.P. (1993), Use of CPT to estimate eqivalent SPT N60. Geotechnical Testing Jornal, GTJODJ, Vol. 15, No. 4, December 1993, pp AASHTO (2004). LRFD Bridge Design Specifications. American Association of State Highway and Transportation Officials, Washington, D.C. 75. Hansen, B. (1956). Limit Design and Safety Factors in Soil Mechanics. Blletin No. 1, Danish Geotechnical Institte, Copenhagen, Denmark. 76. Hansen, B. (1966). Code of Practice for Fondation Engineering. Blletin No. 22, Danish Geotechnical Institte, Copenhagen, Denmark.

151 77. Tang, W. (1993). Recent Developments in Geotechnical Reliability. Proceedings, Conference on Probabilistic Methods in Geotechnical Engineering, Balkema, Rotterdam, The Netherlands, Canberra, Astralia, pp Hamilton, J. and Mrff, J. (1992). Selection of LRFD Resistance Factors for Pile Fondation Design. Proceedings, Strctres Congress, American Society of Civil Engineers, San Antonio, TX. 79. Klhawy, F. and Phoon, K. (1996). Engineering Jdgment in the evoltion from Deterministic to Reliability-Based Fondation Design. Proceedings, 1996 Conference on Uncertainty in the Geologic Environment, UNCERTAINTY '96, American Society of Civil Engineers, NY, Madison, WI, pp Barker, R. M.; Dncan, J. M.; Rojiani, K. B.; Ooi, P. S. K.; Tan, C. K.; and Kim, S. G. (1991). Manals for the Design of Bridge Fondations: Shallow Fondations, Driven Piles, Retaining Walls and Abtments, Drilled Shafts, Estimating Tolerable Movements, and Load Factor Design Specifications and Commentary. NCHRP Report No. 343, TRB, National Research Concil, Washington, D.C. 81. O'Neill, M. (1995). LRFD Factors for Deep Fondations throgh Direct Experimentation. Proceedings, US/Taiwan Geotechnical Engineering Collaboration Workshop, Taipei, Taiwan, pp AASHTO (1994). LRFD Bridge Design Specifications. American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C. 83. D'Appolonia (1998). LRFD Specifications for Retaining Walls. NCHRP Project (Task 88), TRB, National Research Concil, Washington, D.C. 84. Withiam, J. L. (2004). Load and Resistance Factors for Earth Pressres on Bridge Sbstrctres and Retaining Walls. NCHRP Project 12-55, TRB, National Research Concil, Washington, D.C. 85. Paikowsky, S. G.; Birgisson, B.; McVay, M.; Ngyen, T.; Ko, C.; Baecher, G.; Ayyb, B.; Stenersen, K.; O'Malley, K.; Chernaskas, L.; and O'Neill, M. (2004). Load and 129

152 Resistance Factor Design (LRFD) for Deep Fondations. NCHRP Report No. 507, TRB, National Research Concil, Washington, D.C. 86. Allen, T. M. (2005). Development of Geotechnical Resistance Factors and Downdrag Load Factors for LRFD Fondation Strength Limit State Design. FHWA-NHI , Federal Highway Administration, Washington, D.C. 87. Phoon, K. K.; Klhawy, F. H.; and Grigori, M. D. (2003). Mltiple Resistance Factor Design for Shallow Transmission Line Strctre Fondations, Jornal of Geotechnical and Geoenvironmental Engineering, Vol. 129, No. 9, pp. 88. Phoon, K. K.; and Klhawy, F. H. (2005). Characterisation of Model Uncertainties for Laterally Loaded Rigid Drilled Shafts, Geotechniqe, Vol. 55, No. 1, pp Abd Alghaffar, M. A. and Dymiotis-Wellington, C. (2005). Reliability Analysis of Retaining Walls Designed to British and Eropean Standards, Strctre and Infrastrctre Engineering, TAYLOR & FRANCIS LTD, Vol. 1, No. 4, pp Low, B. K. (2005). Reliability-Based Design Applied to Retaining Walls, Geotechniqe, Vol. 55, No. 4, pp Goh, A. T. C. and Klhawy, F. H. (2005). Reliability Assessment of Serviceability Performance of Braced Retaining Walls Using a Neral Network Approach, International Jornal for Nmerical and Analytical Methods in Geomechanics, Vol. 29, No. 6, pp Fenton, G. A.; Griffiths, D. V.; and Williams, M. B. (2005). Reliability of Traditional Retaining Wall Design, Geotechniqe, Vol. 55, No. 1, pp Klhawy, F. H. and Phoon, K. K. (2002). Observations on Geotechnical Reliability- Based Design Development in North America. Proceedings, Fondation Design Codes and Soil Investigation in View of International Harmonization and Performance Based Design, Balkema, Lisse, Netherlands, pp Phoon, K. K. and Klhawy, F. H. (1999a). Characterization of Geotechnical Variability, Canadian Geotechnical Jornal, Vol. 36, No. 4, pp

153 95. Phoon, K. K. and Klhawy, F. H. (1999b). Evalation of Geotechnical Property Variability, Canadian Geotechnical Jornal, Vol. 36, No. 4, pp McVay, M. C.; Birgisson, B.; Zhang, L.; Perez, A.; and Ptcha, S. (2000). Load and Resistance Factor Design (LRFD) for Driven Piles Using Dynamic Methods-A Florida Perspective, Geotechnical Testing Jornal, American Society for Testing and Materials, Vol. 23, No. 1, pp Titi, H. H.; Mahamid, M.; Ab-Farsakh, M. Y.; and Elias, M. (2004). Evalation of CPT Methods for Load and Resistance Factor Design of Driven Piles. Geotechnical Engineering for Transportation Projects: Proceedings of Geo-Trans 2004, American Society of Civil Engineers, Reston, VA , United States, Los Angeles, CA, United States, pp Bab, G. L. S.; Srivastava, A.; and Mrthy, D. S. N. (2006). Reliability Analysis of the Bearing Capacity of a Shallow Fondation Resting on Cohesive Soil, Canadian Geotechnical Jornal, Vol. 43, No. 2, pp Ab-Farsakh, M. Y. and Nazzal, M. D. (2005). Reliability of Piezocone Penetration Test Methods for Estimating the Coefficient of Consolidation of Cohesive Soils, Geology and Properties of Earth Materials 2005, No. 1913, pp Roy, D.; Hghes, J. M. O.; and Campanella, R. G. (1999). Reliability of Self-Boring Pressremeter in Sand, Canadian Geotechnical Jornal, Vol. 36, No. 1, pp Li, C. N. and Chen, C. H. (2006). Mapping Liqefaction Potential Considering Spatial Correlations of CPT Measrements, Jornal of Geotechnical and Geoenvironmental Engineering, Vol. 132, No. 9, pp Hegazy, Y.A and Mayne, P.W. (1995). Statistical Correlations Between Vs and CPT Data for Different Soil Types. Proceedings, Cone Penetration Testing (CPT 95), Linkoping, Swedish Geotechnical Society, pp

154

155 APPENDIX A List of Projects Inclded in Database Table 34 Projects with CPT and borehole data Job Nmber District Parish Name Date Job Location Dist 02 St. Bernard 10/1/2006 LA 46 St Bernard Dist 02 Orleans 2/1/2005 Rigolets Pass Bridge & approaches Dist 02 St. Charles 12/23/2004 LA 632 Main Canal Bridge Dist 02 Laforche 12/22/2004 Drain Canal Bridge on LA Dist 02 Jefferson 11/19/2003 Caseway Bolevard Dist 02 Jefferson 11/13/2003 Hey P. Long Bridge Dist 02 Laforche 8/20/2002 T-Bois Bridge Dist 02 Orleans 1/9/2002 US Pass Dist 03 Iberia 5/18/2005 US 90 LA Dist 03 Vermilion 8/17/2004 LA 332 Maree Michel Canal Bridge Dist 03 Iberia 5/28/2003 US 90 Iberia Parish Dist 03 Iberia 8/28/2002 US LA Dist 03 St marys 9/29/1992 Mac drv over mopac rr Dist 03 St. Landry 1/26/2005 LA 363 Drainage Canal Dist 04 Caddo 9/8/2005 LA LA Dist 04 Bossier 1/28/2004 LA Dist 04 Caddo 12/17/2003 LA Bayo Pierre Dist 04 Caddo 3/26/2003 US Dist 04 Bossier 3/25/2003 Benoit Bridge Dist 04 Caddo 10/1/2002 LA

156 Dist 04 Webster 8/7/2002 US Dixie Inn Dist 04 Bossier 12/8/1999 US KCS RR Dist 05 Oachita 5/2/2000 N. 18 St. Ext Seg Dist 05 Union 12/25/2004 LA 33 Creek Bridge Dist 05 Oachita 1/27/2004 Rote US Dist 05 Madison 1/30/2002 Madison Parish Dist 05 Jackson 7/10/2001 LA Dist 05 Jackson 10/25/2000 Chaptham-Eros Dist 05 La Salle 6/28/1995 Lat Long Dist 05 Jackson 6/27/1995 JCT la 34 Jackson ph-line Dist 05 Oachita 10/26/1994 Forsythe Ave Dist 08 Sabine 4/17/2001 Zwolle-noble Dist 08 Rapides 8/5/2002 Ssek Dr. Pineville Dist 08 Natchitoches 8/10/2004 LA 491 str # Dist 08 Natchitoches 4/8/2003 str # Dist 08 Vernon 3/19/2003 Bayo Zorie Dist 08 Natchitoches 3/29/2000 Black Lake LA Dist 08 Rapides 8/19/1998 LA 488 Bayo Boef Dist 08 Winn 10/4/1995 Dgdemona Relief Dist 08 Grant 4/12/1994 Flag on Bayo Grant ph Dist 08 Winn 3/31/1993 LA Dist 08 Rapides 12/15/1992 Red River Bridge Appro Dist 08 Rapides 12/14/1992 Red River Bridge Appro Dist 08 Rapides 12/14/1992 Red River Bridge Appro Dist 58 La Salle 4/2/2003 Hemps Creek West Bridge Dist 58 Franklin 12/13/1994 Bayo Macon 134

157 Dist 61 E. Baton Roge 5/10/2004 Perkins Rd. \ LA Dist 61 Assmption 6/12/1996 Bayo Boef Dist 62 St. Tammany 6/7/2005 LA1088 at I Dist 62 Livingston 4/21/2005 Jban Road Dist 62 Livingston 12/28/2004 LA 64 Amite River Bridge Dist 62 Tangipahoa 11/9/1994 Ward Line Road 135

158 Table 35 Projects with CPT data withot borehole data Job Nmber District Parish Name Date Job Location Dist 02 Jefferson 3/3/2003 US 190 St. Landry Dist 02 Orleans 2/12/2003 LA 158 Bayo Grappe Dist 02 Jefferson 3/22/2000 Bayo Teche Dist 02 Orleans 10/31/2000 US 71/ Dist 02 Terrebonne 6/13/2006 LA Sterlington Dist 02 Orleans 8/4/2004 Caseway Interchange Phase Dist 02 Terrebonne 11/22/2005 Bayo Liberty Dist 03 St. Landry 10/29/2005 Rssell Cemetery Road Dist 03 St. Landry 10/29/2005 Philadelphia Road Dist 03 Lafayette 10/28/2005 Red Ct Loop Road Dist 03 St. Landry 10/28/2005 Bayo Oaks Drive Dist 03 Acadia 10/26/2005 Emmanel mill bayo Dist 03 Iberia 10/25/2005 Mosswood Drive Dist 04 Caddo 10/24/2005 Hapsbrg lane of US 167 Lafayette Dist 04 Caddo 4/20/2005 Creek Bridge of US Dist 04 Caddo 1/26/2005 LA 103 Bayo Cortablea Dist 04 Caddo 1/25/2005 US 165 Oakdale to Glenmora Dist 04 Caddo 12/26/2004 LA 4 Biles Branch Bridge Dist 05 Oachita 12/25/2004 LA 577 Creek Bridge Dist 05 Oachita 12/19/2004 Camp Street Dist 05 Oachita 12/14/2004 Inner Loop Extension Dist 05 Oachita 3/26/2004 Inner Loop Extension Dist 05 Jackson 11/4/2004 Fremeax Interchange- US190b 136

159 Dist 05 W. Carroll 8/11/2004 la 1220 little river bridge Dist 05 Union 6/16/2004 Drain Canal Bridge on LA Dist 05 Union 6/15/2004 Tchopitolas to Soth Peters Dist 05 Lincoln 4/15/2004 LA Dist 05 Union 3/23/2004 Oakland Bayo D'Lotre Bridge Dist 05 W. Carroll 2/4/2004 LA Dist 05 Richland 7/1/2003 LA Dist 07 Calcasie 4/1/2003 Bridge over Bayo D'Arbonne Dist 07 Allen 3/18/2003 LA Dist 07 Allen 3/5/2003 dollar road LA 158 bayo grappe Dist 08 Grant 2/11/2003 LA 127 drain bridge s 71/1 6 7 Dist 08 Rapides 1/29/2002 Cypress Creek Dist 08 Natchitoches 1/29/2002 Lion Creek Bridge Dist 08 Rapides 10/2/2001 LA Dist 08 Natchitoches 3/13/2001 Loreaville Canal Dist 08 Natchitoches 1/4/2001 LA 1153 Allen Ph Dist 08 Vernon 12/18/2000 LA Bayo Macon Dist 08 Vernon 5/8/2000 Bayo Macon LA Dist 08 Rapides 11/18/1998 Black Jack Branch Dist 08 Rapides 11/2/1998 I-10 Lake Pont Dist 08 Rapides 8/26/1998 I-10 relief canal Dist 58 La Salle 11/8/1995 Bayo L'orse Dist 58 Franklin 2/9/1994 Brookwood Drive Dist 61 West Baton Roge 2/7/1994 Richland Parish Road # Dist 62 St. Tammany 5/4/1993 Inner Loop over W70 ST 137

160 Dist 62 St. Tammany 4/29/1993 Inner Loop over Ellerb Dist 62 Washington 11/18/1992 Red River bridge app Dist 62 St. John the Baptist 11/17/1992 Alex Urban sec I49 138

161 APPENDIX B First Order Reliability Method (FORM) FORM is based on a first order Taylor Series expansion of the limit state fnction that approximates the failre srface by a tangent plane at the point of interest. It is not always possible to find a closed form soltion for a non-linear limit state fnction or a fnction inclding more than two random variables. Hence, to convert a non-linear limit state fnction into simple polynomials, Taylor series, eqation (53) is sed. The expansion of a fnction, f X, at a certain point a is given by: f ' X f a X af a 2 X a '' X a n f a... f a (53) 2 n! FORM ses this expansion to simplify the limit state fnction, g Z Z,..., n 1, 2 Z n by considering the expansion of the Taylor series after trncating terms higher than the first * order. The expansion is done at the actal design point X. The design point is a point on the failre srface g Z Z,..., 1, 2 Z n as shown in Figre 56 for the case of two variables in a nonlinear limit state fnction. Figre 56 Reliability index evalated at design point (Nowak and Collins 2000) 139

162 To locate this point on the design space of g Z, Z,..., Z n, an iterative process is needed (Nowak and Collins 2000). For the convergence of a design point throgh iterative procedre reqires solving of a set of (2n + 1) simltaneos eqation with (2n + 1) nknowns * * *, 1, 2,, n, Z1, Z 2,, Z n : where, g Z i evalated at design po int i (54) 2 n g k 1 Z k evalated at design po int g g X i g X Z X Z X i (55) n i i1 * Z i 2 1 i i i i (56) i 1 2 Z n * * * Z, Z,, 0 (57) g (58) i is a nit vector in the direction of a design point from the origin, and design point in transformed space. Eqation (58) is a mathematical statement of the reqirement that the design point mst be on the failre bondary. * Z i is the This procedre was derived with the assmption that the involved random variables are normally distribted. When the probability distribtions for the variables involved in the limit state fnction are not normally distribted, it is reqired to calclate the eqivalent normal vales of the mean and standard deviation for each non-normal random variable. To e e obtain the eqivalent normal mean, X, and standard deviation, X, the CDF and PDF of the actal fnction shold be eqal to normal CDF and normal PDF at the vale of the variable * X on the failre bondary described by g 0. Mathematically it can be expressed asp * e X X F X ( X * ) (59) e X 140

163 f X * e * 1 X X X e e X X (60) where, X is a random variable with mean X and standard deviation X and is described by a CDF (X ) X. is the CDF for the standard normal F X and a PDF f X. Where, distribtion and. is the PDF for the standard normal distribtion. Expressions for e X can be obtained as follows: e X and e * e 1 * X X X FX X (61) 1 e 1 * X F X * X (62) f X X The basic steps in the iteration procedre (Nowak and Collins 2000) to obtain β are as follows: 1. Formlate the limit state fnction. Determine the probability distribtions and appropriate parameters for all random variables, X i i 1,2,, n 2. Obtain an initial design point, X * i involved., by assming vales for n-1 of the random variables. (Mean vales are a reasonable choice.) Solve the limit state eqation g =0 for the remaining random variable which ensres that the design point is on the failre bondary. e e 3. Eqivalent normal mean, X and standard deviation, X is determined sing eqations (61) and (62) for design vales corresponding to a non-normal distribtion. Determine the redced variables X sing Z * i X * i e X i e X i Z corresponding to the design point * i 4. Determine the partial derivatives of the limit state fnction with respect to the redced variables;g is a colmn vector whose elements are the partial derivatives eqation (55), mltiplied by -1. * i (63) 141

164 G G G 1 2 G n where, G 5. Estimate of β is then calclated sing i g (64) Z i evalated at design point * Z 1 T * * G Z * Z 2 where, Z T G G * Z n 6. The direction cosines for the design point to be sed in the sbseqent iteration are then calclated sing G T G G 7. Determine a new design point for n-1 of the variables sing * Z i i (67) 8. Determine the corresponding design point vales in original coordinates for the n-1 vales in Step 7 by X * i e X i * i e X i (65) (66) Z (68) 9. Determine the vale of the remaining random variable by solving the limit state fnction g = Repeat Steps 3 to 10 ntil β and X * i converge. 142

165 APPENDIX C Chi-Sqare Statistical Test: Goodness-of-fit Test The Chi-Sqare test is often sed to assess the goodness-of-fit between an obtained set of freqencies in a random sample and what is expected nder a given statistical hypothesis. To be able to decide which distribtion is better for a particlar random variable, the difference between actal observation vales (observed freqencies) and theoretical distribtion vales (theoretical freqencies) is qantified. The steps to determine the probability distribtion of a random variable are given below. 1. Divide the observed data range into eqal intervals. 2. Find the nmber of observations (Observed Freqency, n i ) within each interval which do not depend on the distribtion type. 3. Assme different distribtion types that will represent the random variable and find the theoretical distribtion vales (Theoretical Freqency, e i ) within each interval for the respective distribtions. If a random variable, X, lies in an interval a to b sch that a X given by b a X b N, then the Theoretical Freqency, e i, for a certain distribtion type is e i P * (69) where, N is the total nmber of observation (data points), and Pa X b PX b PX a The probability of X less than a or b, PX a, and X b (70) P is fond sing the CDF for the respective distribtion. The CDF for different distribtion types can be obtained from the literatre. 4. For each interval, compte the difference between n i and e i, (sqared) as a ratio of e i. 5. Compte the smmation of differences (sqared) as a ratio of e i which is given as m i1 n e i e i i 2 where, m is the total nmber of intervals. (71) 143

166 6. Calclate the degree of freedom, f, for the Chi-Sqare test, which is given by f m 1 k where, k is the nmber of parameters reqired to describe a particlar distribtion. In this stdy, Normal and Lognormal distribtion types are sed for these types, k = The smmation evalated in Step 5 is compared to the Chi-Sqare distribtion for a certain significance level,, which is always taken between 1 and 10 percent. 8. If m i1 enogh. n e i e i i 2 C, f, then the assmed distribtion is fitting statistical data well C, f vales are given in Table 36. Table 36 CDF of the chi-sqare distribtion (Nowak and Collins 2000) 144

167 APPENDIX D Normal and Lognormal Distribtion Types Normal or Gassian Distribtion If a variable is normally distribted then two qantities have to be specified: the mean, X, which coincides with the peak of the PDF crve and the standard distribtion, σ X, which indicates the spread of the bell crve. The PDF for a normal random variable X is given by eqation (72). f X ( X ) 1 1 X X exp 2 2 X X 2 (72) There is no closed-form soltion for the CDF of a normal random variable bt tables have been developed to provide vales of the CDF for the special case in which X = 0 and X = 1 (Nowak and Collins 2000). These tables can be sed to obtain vales for any general normal distribtion. 145

168 Figre 57 Graphical representation of normal distribtion Lognormal Distribtion The random variable X is a lognormal random variable, Figre 58, if Y = ln(x) is normally distribted, FX ( x) FY ( y). The mean and standard deviation for Y are given by eqations (73) and (74). 2 X Y ln( X ) ln 1 (73) X 1 2 Y ln( X ) ln( X ) ln( X ) (74) 2 146

169 Probability Log-normal PDF X Log-normal CDF Probability Figre 58 Graphical representation of lognormal distribtion 147

170

171 APPENDIX E Example Excel Template to Analyze CPT Data 149

172 150