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Load and Resistance Factor Design (LRFD) for Deep Foundations (2004)

Chapter: Chapter 3 - Interpretation, Appraisal, and Applications

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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
×
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2004. Load and Resistance Factor Design (LRFD) for Deep Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13758.
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33 CHAPTER 3 INTERPRETATION, APPRAISAL, AND APPLICATIONS 3.1 ANALYSIS RESULTS AND RESISTANCE FACTORS 3.1.1 Driven Piles—Static Analysis Table 16 presents a summary of the results obtained from the analyses used for static capacity evaluation of driven piles, compared with the nominal resistance based on Davisson’s failure criterion. The information is grouped by soil and pile type and design method. The table includes statistical param- eters and resistance factors for a range of reliability index values, and a ratio of DL to LL of 2.0. The data leading to Table 16 were statistically analyzed to remove outliers (i.e., extreme cases; Section 3.5 provides a discussion of this process); and the table includes only those cases within ±2 standard deviations of the mean. As can be seen, subcategorization based on pile or soil type may result in subsets too small for reasonable statistical analysis. On the other hand, many of the subsets have similar statistics and resistance factors and hence can be combined. It is important to note that many common design methods for all piles in all soils overpredict the actual (i.e., measured) pile-capacity. This explains the traditional need for high factors of safety for static design (e.g., see Table 1). A more complete picture of the performance of a method is obtained by plotting the histogram of observed to predicted capacities and overlaying the best-fitting normal and lognor- mal PDFs. Figures 17 through 26 present such plots for the selected cases of static analyses of driven piles. The figures are arranged in order from the most inclusive logical case, as the data permit, to subsets of the same category. For example, Figure 17 presents the performance of the α-API method for all pile types (52 cases of H, concrete and pipe piles) in clay. Figures 18 and 19 present the performance of the method for subsets of concrete (36 cases) and H piles (16 cases), respectively. Additional graphical presentations of the data are included in Appendix C. 3.1.2 Driven Piles—Dynamic Analysis 3.1.2.1 The Analyzed Cases Time of driving, driving resistance, and area ratio proved to be controlling parameters for the dynamic methods (sec- tion 2.5.3). The PD/LT 2000 database was first separated into design and construction categories. The dynamic methods used in construction were subdivided between methods that use dynamic measurements and those that do not. These, in turn, were subcategorized according to the controlling param- eters. Figure 27 presents the analyzed subsets, the number of case histories in each set, and the mean and standard devia- tion for each. WEAP is utilized in the design stage. The analysis (not included in this research) needs to be carried out for driving stress evaluation, leading to a load factor. The use of the method for the evaluation of pile capacity was examined through the comparison of WEAP results for default input val- ues and the blow count at the EOD with static load test results. The data presented were provided by GRL Inc. (Hannigan et al., 1996). For the construction category, the dynamic analyses meth- ods without dynamic measurements are the ENR, Gates, and FHWA version of Gates. The methods with dynamic measurements are CAPWAP and the Energy Approach. The dynamic methods are broken down into subsets based on time of driving, driving resistance, and area ratios. Judgment and statistical guidelines were used for the inclusion or exclusion of cases. For example, extreme CAPWAP underpredictions (beyond 2 standard deviations) were observed at EOD at one site. All the case histories on that site included easy driving and large area ratios; if included in the general population of the data, the EOD statistics would have become 1.861 ± 1.483 (mean ± 1 S.D.). This site is included only in the subcategory of blow count < 16 BP10cm and AR < 350. 3.1.2.2 The Critical Categories The outcomes of the statistical analyses presented in Figure 27 allow the identification of critical categories that require calibration and development into resistance factors. For exam- ple, the critical CAPWAP cases include (1) all data, (2) EOD, (3) BOR, and (4) the worst combination of soil motion effect (Blow count < 16 BP10cm and AR < 350). Table 17 presents a summary of the major categories of the dynamic methods identified from Figure 27 as those that require calibration for a resistance factor.

34 Resistance Factors for a Given Reliability Index β Soil Type Pile Type N Design Method (1) Details of Method(2) Application Mean Stand. Dev. COV 2.00 2.50 3.00 4 β-Method 11.5 B; T&P(2) 0.61 0.37 0.61 0.23 0.18 0.13 16 λ-Method 11.5B; T&P(2) 2B; T&P(5) 0.74 0.29 0.39 0.43 0.35 0.29 17 α-Tomlinson 2B; T&P(2) 0.82 0.33 0.40 0.46 0.38 0.31 16 α-API 2B; T&P(5) 0.90 0.37 0.41 0.50 0.41 0.33 H-Piles 8 SPT-97 mob 1.04 0.43 0.41 0.57 0.47 0.38 18 λ-Method 2B; Hara (5h) 0.76 0.22 0.29 0.53 0.45 0.38 17 α-API 2B; Hara (5h) 0.81 0.21 0.26 0.60 0.52 0.44 8 β-Method 2B; Hara (5h) 0.81 0.41 0.51 0.37 0.30 0.23 Concrete Piles 18 α-Tomlinson 2B; Hara (5h) 0.87 0.42 0.48 0.42 0.34 0.26 18 α-Tomlinson 2B; T&P (1) 0.64 0.32 0.50 0.30 0.24 0.19 19 α-API 2B; T&P (1) 0.79 0.43 0.54 0.34 0.27 0.20 12 β-Method 2B; T&P (1) 0.45 0.27 0.60 0.17 0.13 0.10 19 λ-Method 2B; T&P (1) 0.67 0.37 0.55 0.28 0.22 0.17 Clay Pipe Piles 12 SP T-97 mob 2B; T&P (1) 0.39 0.24 0.62 0.15 0.11 0.08 19 Nordlund 36; 11.5B,P(6) 0.94 0.38 0.40 0.53 0.43 0.35 18 Meyerhof 0.81 0.31 0.38 0.47 0.39 0.32 19 β-Method 36; 2B; P(5) 0.78 0.40 0.51 0.36 0.28 0.22 H-Piles 18 SPT-97 mob 1.35 0.58 0.43 0.72 0.59 0.47 36 Nordlund 36: 11.5B; P(6) 1.02 0.49 0.48 0.50 0.40 0.31 35 β-Method 36; 2B; P(5) 1.10 0.48 0.44 0.58 0.47 0.38 36 Meyerhof 0.61 0.37 0.61 0.23 0.18 0.13 Concrete Piles 36 SPT-97 mob 1.21 0.57 0.47 0.60 0.48 0.38 19 Nordlund 36; 2B P(5) 1.48 0.77 0.52 0.67 0.52 0.41 20 β-Method 36; 2B P(5) 1.18 0.73 0.62 0.44 0.33 0.25 20 Meyerhof 0.94 0.55 0.59 0.37 0.29 0.22 Sand Pipe Piles 19 SPT-97 mob 1.58 0.82 0.52 0.71 0.56 0.44 20 α-Tomlinson/Nordlund/Thurman 36; 2B; P(5) 0.59 0.23 0.39 0.34 0.28 0.23 34 α-API/Nordlund/Thurman 36; 2B; P(5) 0.79 0.35 0.44 0.41 0.33 0.27 32 β-Method/Thurman 36; 2B; P(5) 0.48 0.23 0.48 0.23 0.19 0.15 H-Piles 40 SP T-97 1.23 0.55 0.45 0.64 0.51 0.41 33 α-Tomlinson/Nordlund/Thurman 36; 2B; P; Hara(5h) 0.96 0.47 0.49 0.46 0.36 0.29 80 α-API/Nordland/Thurman 36; 11.5B; Sch; T&P(8) 0.87 0.42 0.48 0.42 0.34 0.26 80 β-Method/Thurman 36; 11.5B; Sch; T&P(8) 0.81 0.31 0.38 0.47 0.39 0.32 71 SPT-97 mob 1.81 0.91 0.50 0.84 0.67 0.52 Concrete Piles 30 FHWA CPT 0.84 0.26 0.31 0.57 0.48 0.40 13 α-Tomlinson/Nordlund/Thurman 36; 2B; P(5) 0.74 0.44 0.59 0.29 0.22 0.17 32 α-API/Nordland/Thurman 36; 2B; P(5) 0.80 0.36 0.45 0.41 0.33 0.26 29 β-Method/Thurman 36; 2B; P(5) 0.54 0.26 0.48 0.26 0.21 0.16 Mixed Soils Pipe Piles 33 SPT-97 mob 0.76 0.29 0.38 0.45 0.37 0.30 (1)See Table 6 for details; (2) Numbers in parentheses refer to notations used for detailing soil parameters combinations (see Table 7b and Appendix C for more details), See Tables 7a and 8 for soil properties’ correlations to SPT and CPT respectively, 36 = limiting friction angle, B = pile diameter 2B, 11.5B contributing zone to tip resistance. TABLE 16 The performance of the driven piles’ static analysis methods—statistical summary and resistance factors for data using mean ± 2 SD

Histogram and frequency distributions were prepared for the identified critical categories in order to examine the match between the actual data and PDFs. Figures 28 through 35 present histograms of some of the datasets, along with the best-fitting normal and lognormal distributions. By and large, the lognormal distributions seem to match the data well and hence are the preferable choice to the normal distributions. Moreover, the lognormal distribution matches the low end tail of the cases (lower left corner of the data), where the extreme overpredicting cases exist. Appendix B presents detailed graphical presentations of the data and various correlations. 3.1.2.3 Intermediate Conclusions The data presented in Table 17 and Figures 27 through 35 lead to the following intermediate conclusions: (1) Sig- nal matching generally underpredicts pile capacity, while 35 the method performs well for BOR (last restrike) cases and, (2) the simple Energy Approach provides a good prediction for pile capacity during driving (EOD). These conclusions suggest that construction delays due to restrike and costly signal matching analyses need to be examined in light of capacity-time dependency and economic factors. 3.1.3 Drilled Shafts—Static Analysis Table 18 presents a summary of the analysis results used for static capacity evaluation of drilled shafts, compared with the nominal resistance based on the FHWA failure criterion. The data in Table 18 are limited to cases within two standard deviations of the mean of the initial analysis results of all the drilled shafts. The resistance factors for the different target reliability values were calculated for a ratio of dead load to live load of 2.0. Reviewing the information 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API method 0 1 2 3 4 5 6 7 8 9 10 N um be r of Pi le- C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.270 σlnx = 0.428 normal distribution mx = 0.832 σx = 0.349 Figure 17. Histogram and frequency distributions of Ksx for 52 cases of all pile types (concrete, pipe, H) in clay.

presented in Table 18, one can conclude that the resistance factors are within the range of current practice and the sub- categorization provides details regarding both the method of design and construction. The design methods in general pro- vide more accurate predictions than those for driven piles, as indicated by the bias being closer to one where the COVs are of similar magnitudes to those in Table 16. The “mixed” con- struction method represents the combination of other available construction methods. The actual numbers for the mixed case do not necessarily add up to the sum of the individual categories as each set (individual or combined) is treated independently. Figures 36 through 40 present selected subsets from Table 18 as histograms, along with the best-fitting normal and lognormal distributions. Four of the figures relate to the mixed construction case histories that include other construction methods. The smaller subsets’ databases and wider distribu- tions are the result of the variation between the methods and 36 the wide sources of the data. Additional graphical presenta- tion of the data is included in Appendix C. 3.2 INITIAL EXAMINATION OF RESULTS 3.2.1 Overview An initial examination of the results is required in order to assess the magnitude of values and to allow the process of transforming the large number of methods and correlations to meaningful and inclusive categories. This is done by check- ing the number of case histories needed to be eliminated when limiting the set being investigated to those within the two standard deviation band, recalculating the resistance factors for the recommended target reliabilities, evaluating equiv- alent factors of safety, and examining the efficiency of the Figure 18. Histogram and frequency distributions of Ksx for 36 cases of concrete and pipe pile types in clay. 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API method 0 1 2 3 4 5 6 7 8 9 N um be r of Pi le- C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.302 σlnx = 0.414 mx = 0.801 σx = 0.337 normal distribution

methods by comparisons of factors of safety and the efficiency factors. Additional evaluations are described in section 3.5. 3.2.2 FOSM Versus FORM As the existing AASHTO specifications are based on FOSM (see section 1.4.3.4), the relationship between the fac- tors obtained by FOSM and those obtained by the current methodology, FORM, needed to be checked. Figure 41 pre- sents these relationships for the different categories of the ana- lyzed methods for all three databases and for a reliability index of β = 2.33. The data in Figure 41 suggest that FORM results in resistance factors consistently higher than those obtained by FOSM. The ratio between the two suggests that, as a rule of thumb, FORM provides resistance factors approximately 10% higher than those obtained by FOSM. Two practical conclu- sions can be drawn from these data: (1) first evaluation of data 37 can be done by the simplified, closed form FOSM approach, with the obtained resistance factors on the low side; and (2) the resistance factors obtained in this study (as presented in Tables 16 through 18) can be directly compared to the current speci- fications and other LRFD codes based on FOSM. 3.2.3 Equivalent Factors of Safety The fact that the resistance factors using FORM approxi- mate those obtained by FOSM allows the use of a simplified relationship between resistance factor and FS based on FOSM and provided by Barker et al., 1991: (32)FS Q Q Q Q D D L L D L = + +  γ γ φ 1 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API method 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N um be r o f P ile - C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.197 σlnx = 0.464 mx = 0.901 σx = 0.374 normal distribution Figure 19. Histogram and frequency distributions of Ksx for 16 cases of H piles in clay.

using DL/LL = 2, γL = 1.75,and γD = 1.25 (load factors taken from the structural code) for which the resistance factors were calculated, results in: FS  1.4167/φ (33) 3.2.4 Detailed Tables Tables 19, 20, and 21 present detailed evaluations of the analyzed case histories for static analyses of driven piles, dynamic analyses of driven piles, and static analyses of drilled shafts, respectively. The tables include the number of case histories in the subset as well as the number of case histories used in the analysis of resistance factors. The efficiency fac- tors, φ/λ, are calculated and presented with the resistance fac- tors. The approximated factors of safety associated with the calculated resistance factors based on equation 33 are pro- vided as well. The factors of safety are presented along with the mean overprediction ratio (calculated FS × the bias of the 38 method), which in effect represents both the actual FS and a measure of the economic efficiency of the method—the lower the value, the smaller the number of deep foundations required and the lower the cost, therefore the greater eco- nomic efficiency of the method. Table 22 provides a summary of Tables 19 through 21, presenting resistance factors and efficiency measures for select categories of method/pile/soil combinations. The LRFD principles are clearly seen in the obtained values as the application of consistent target reliability produces values related to the individual method. While a method/ condition combination that has large variability (expressed as COV) results in low resistance factors, the resistance factors alone do not provide a measure of the efficiency of the method. For example, SPT 97 for H piles in sand has a resistance fac- tor φ(β = 2.33) = 0.63 while the Nordlund method for the same cat- egory results in a lower resistance factor φ = 0.46. In fact, SPT 97 underestimates the capacity (λ = 1.35), while Nordlund’s method slightly overestimates it (λ = 0.94); as a result, Nord- lund’s method has an efficiency similar to that of SPT 97 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the Nordlund Design Method 0 1 2 3 4 5 6 7 8 9 10 N um be r of Pi le- C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.028 σlnx = 0.544 mx = 1.115 σx = 0.588 normal distribution Figure 20. Histogram and frequency distributions of Ksx for 74 cases of all pile types (Concrete, Pipe, H) in sand.

(COV 0.40 vs. 0.43) in spite of the large difference in the resis- tance factors. Examining the efficiency factors, one clearly sees that the method that provides the highest φ/λ ratio also provides the lowest “actual” factor of safety (FS × λ). The fac- tors of safety presented in Table 22 for β = 3.0 (the lower of the two values in the last column) are in line with what one would expect, ranging from 2.59 to 5.63, with an average of 3.73. The use of lower target reliability for redundant piles (β = 2.33) provided factors of safety ranging from 2.11 to 4.00 (avg. 2.94), which are judged to be reasonable as well. The recommended resistance factors based on Tables 18 through 22 are presented in section 3.4. 3.2.5 Resistance Factors for Pullout of Driven Piles Utilizing the University of Massachusetts Lowell static pile database, a limited number of case histories were identified for which a static pile load test in tension (pullout) was carried out. 39 The available data were analyzed and the resulting statistical parameters and associated resistance factors are presented in Table 23. The results, though based on limited data, seem to be consistent with expected behavior. Comparing the data in Table 23 to that presented in Table 19 for driven piles under compression, the following can be observed: (1) large dis- placement piles in clay develop similar friction under com- pression or tension, (2) friction for small displacement piles (H) is smaller in tension than in compression, and (3) friction under pullout of all piles in sand is smaller than that which develops under compression. The recommended resistance factors for pullout tests are presented and discussed in section 3.4. 3.3 PILE TESTING 3.3.1 Overview Deep foundation testing is carried out as a quality control to check or verify pile capacity and integrity. Quality control 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the β Design Method 0 1 2 3 4 5 6 7 8 9 N um be r of Pi le- C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = 4.53x10-4 σlnx = 0.552 mx = 1.150 σx = 0.596 normal distribution Figure 21. Histogram and frequency distributions of Ksx for 56 cases of pipe and concrete pile types in sand.

of piles and drilled shafts is performed via static load testing, various methods of dynamic (impact) testing, and integrity testing. The first two are carried out to determine pile capacity and integrity while the last is utilized for structural quality assurance only. Two issues need to be addressed: (1) the testing method’s performance and associated resis- tance factors, and (2) the number of tests that need to be car- ried out. Section 3.1 addressed the methods of dynamic analysis most commonly used during driving. The case histories in the extensive PD/LT2000 database have widely varied sub- surface conditions; hence, the direct calibration of the differ- ent analysis method is applicable to all site conditions. The evaluation of the required number of tests needs to assess a single site variability and evaluate how many piles are required to be tested to guarantee a target capacity. A single site vari- ability, therefore, utilizes judgment and assigns categories that cannot be based on firm data. The following sections address issues associated with pile testing. 40 3.3.2 Resistance Factors for Static Pile Load Tests Assigning resistance factors to associate with (in situ) pile (or drilled shaft) static load test results requires an estimate of the corresponding mean bias and COV. By definition, the mean bias is 1.0, since load tests directly measure in situ pile capacity either to failure or to a maximum applied load (proof test). The COV reflects spatial variation from one pile to another at the same site, along with whatever variation is intro- duced by the definition of failure criterion. Empirical data of sufficient quality to estimate within-site variability is lacking. Therefore, an assumption is made to categorize sites as having low, medium, or high variability and to assign coefficient of variations of 0.15, 0.25, and 0.35 to these three cases respectively (Phoon and Kulhawy, 1996; Trautmann and Kulhawy, 1996). In addition to the natural variability within a site, the inter- pretation of failure criterion itself (i.e., Davisson’s criterion 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the Nordlund Design Method 0 0.5 1 1.5 2 2.5 3 3.5 4 N um be r of Pi le- C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 R ela tiv e Fr eq u en cy log-normal distribution mlnx = 0.250 σlnx = 0.561 mx = 1.475 σx = 0.771 normal distribution Figure 22. Histogram and frequency distributions of Ksx for 19 cases of pipe piles in sand.

for driven piles and FHWA for drilled shafts) introduces variability. Analyses reported in sections 2.3.2 and 2.3.4 suggest that this COV due to the failure criterion alone is about 0.10. Adding this to the COV for the natural within- site variability yields COVs of 0.18, 0.27, and 0.36 for low, medium, and high variability sites, respectively. The reduction in COV on the mean pile capacity at the site should decrease in proportion to 1/√n, where n is the number of pile tests (Benjamin and Cornell, 1970). This leads to the results presented in Table 24, which describes the resistance factors as a function of the site variability, number of piles tested, and target reliability. The recom- mended factors assigned are presented in section 3.45. 3.3.3 Numbers of Dynamic Tests Performed on Production Piles Dynamic pile testing is carried out for quality control, tar- get capacity, integrity, and driving system performance. A 41 certain number of production piles are tested to ensure that the piles, as constructed, are satisfactory, in a way that is sim- ilar to quality assurance testing in manufacturing. For specifying a quality assurance testing plan, the number of piles to be dynamically tested and the criterion for accept- ing a set of piles need to be determined. Two concerns are at issue: the chance that poor quality (i.e., under capacity) piles are incorrectly accepted as being good, and the chance that good quality piles are incorrectly rejected as being poor (see Figure 42). For a given level of sampling effort or cost, reduc- ing the chance of one kind of error invariably increases the chance of the other, and thus the two must be balanced. The definition of “poor quality” piles was taken to be that the average pile capacity is less than the design capacity, that is, less than the reciprocal of the factor of safety. The proba- bility chosen as a reasonable chance that such a set of poor quality piles be incorrectly accepted as good was equilibrated to a reliability index of three, or a probability of about 0.001. This is sometimes called the “buyer’s risk” or the “owner’s risk” as demonstrated in Figures 42 and 43. The definition of 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the β Design Method 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N um be r o f P ile - C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.357 σlnx = 0.479 mx = 0.783 σx = 0.395 normal distribution Figure 23. Histogram and frequency distributions of Ksx for 19 cases of H piles in sand.

“good quality” piles was taken to be nominal capacity. The probability chosen as a reasonable chance that such a set of good quality piles be incorrectly rejected as poor was taken to be 0.10. This is sometimes called the “seller’s risk” or the “contractor’s risk.” Given a large total number of piles, N, relative to the num- ber tested, n, the variance of the sample mean, x¯ , is (Benjamin and Cornell, 1970), (34) For sampling fractions, f = n/N, greater than about 10%, the “finite population correction factor,” (N − n)/(N − 1), comes into play. This reduces the sampling variance, because the assumption of sampling without replacement is no longer reasonable. For example, if 100% of the piles are tested, that Var x N nN x n i n i( ) ≅ − − − =∑ 1 1 1 42 is, if f = n/N = 1, then there is no variance in the sample aver- age since all the piles have been accounted for. An assumption, consistent with that projected in section 3.3.2, is made to categorize sites as having low, medium, or high variability and to assign COVs of 0.15, 0.25, and 0.35 to these three cases, respectively. In addition, the dynamic test method also introduces variability. For that, two meth- ods are considered based on the results presented in sections 3.1.2 and 3.2.4, Energy Approach (EA) to be used for capac- ity evaluation at the EOD and signal matching (CAPWAP) to be used during BOR. Setting the owner’s and contractor’s risks on the one hand, and the definitions of “good” and “poor” piles on the other, as defined above, and noting that the sampling variance of the average pile capacity of the tested piles decreases in propor- tion to where n is the number of pile tests, values for the number of piles to be tested can be estimated. The obtained 1 n, 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API/Nordlund/Thurman design method 0 2 4 6 8 10 12 14 16 18 20 22 N um be r o f P ile - C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.293 σlnx = 0.494 normal distribution mx = 0.835 σx = 0.387 Figure 24. Histogram and frequency distributions of Ksx for 146 cases of all pile types (concrete, pipe, H) in mixed soil.

recommendations based on these estimates are presented in section 3.4.3. 3.3.4 Testing Drilled Shafts for Major Defects 3.3.4.1 Overview Drilled shafts require in-field casting and are subject to defects (especially when unlined in cohesionless soils). Accep- tance sampling is used to assess whether an adequate major- ity of a set of shafts is free of major defects. 3.3.4.2 Statistical Background A sample of n from N shafts is tested to identify major defects. Major defects are defined as any defect that signifi- cantly compromises the ability of the shaft to carry the assigned 43 loads. Each tested shaft is categorized as either “good” or “defective.” If no more than c of the n tested shafts are “defective,” the set of shafts is accepted. The test parameter, c, is usually a small number. Suppose that the set of N actual shafts includes m shafts with major defects. The fraction defective is denoted, p = m/N. Among samples of n tested shafts, the frequency distri- bution of the number of defective tested shafts, c, is of the hypergeometric form, (35) in which fc (c | n, N, m) is the frequency distribution, c is the number of defective test results within the sample, m is the number of defectives in the entire set of N shafts, and Ckq is the number of combinations of k out of q things. f c n N m C CCc n c N m c m n N| , ,( ) = − − 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API/Nordlund/Thurman design method 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 N um be r of Pi le- C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.260 σlnx = 0.502 mx = 0.868 σx = 0.416 normal distribution Figure 25. Histogram and frequency distributions of Ksx for 80 cases of concrete piles in mixed soil.

For n/N less than about 10%, this frequency distribution can be reasonably approximated by the more easily calcu- lated binomial distribution, (36) in which p = m /N is the fraction defective (Figure 44). 3.3.4.3 Sample Calculation Presume that the maximum fraction of shafts with a major defect that the owner is willing to tolerate in a large set of N shafts is 5% and that the owner’s risk of incorrectly accept- ing a set of shafts with greater than 5% defects is set at α = 0.10. Let the contractor’s risk of rejecting a set of N shafts with no more than, say, 1% defects be set at β = 0.10. From the nomograph in Figure 44 (see insert), the assur- ance sampling plan is to test n = 110 of the shafts and require f c p n n c n c p pc c n c| , !! !( ) = −( ) −( ) −1 44 that no more than two are defective, (c = 2). This is a very large number of tests, but as can be seen from the nomo- graph, decreasing the tolerable percent defective from the owner’s perspective or reducing either the owner’s or con- tractor’s risk, only increases the number of shafts, n, that must be tested. This calculation assumes that n/N is less than about 10%, but the conclusion that large sample sizes, n, are required also holds for the case of a larger sampling fraction. Per- forming an iterative solution on the hypergeometric model for the same case as above, but assuming a finite N = 100, yields a sample size of about 80. 3.3.4.4 Conclusion The conclusion to be drawn from these simple calculations is that, in order to statistically ensure very low rates of major defects within a set of drilled shafts, a very high proportion of the shafts must be tested. Thus, it seems reasonable practically 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API/Nordlund/Thurman design method 0 1 2 3 4 5 6 7 8 9 10 N um be r o f P ile - C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.333 σlnx = 0.485 mx = 0.796 σx = 0.348 normal distribution Figure 26. Histogram and frequency distributions of Ksx for 66 cases of pipe and H pile types in mixed soil.

45 *All values represent the ratio of the static capacity based on Davisson’s failure criterion over the dynamic methods prediction, mean ± 1 S.D. Dynamic Analysis Design WEAP Drivability Pile Stress Analysis GTR WEAP / Dynamic Measurements Load Factor Resistance/ Capacity GRL EOD – Default WEAP Analysis 1.656 ± 1.199 No. = 99 Construction No Dynamic Measurements WEAP Dynamic Equations Gates Equation 1.787 ± 0.848 No. = 384 FHWA – Mod. Gates 0.940 ± 0.472 No. = 384 ENR Equation 1.602 ± 0.910 No. = 384 BOR (last) 0.833 ± 0.403 No. = 159 EOD 1.073 ± 0.573 No. = 135 ≥ 16 BP10cm 0.809 ± 0.290 No. = 127 ≥ 16 BP10cm 0.929 ± 0.688 No. = 73 < 16 BP10cm 0.876 ± 0.419 No. = 32 < 16 BP10cm 1.306 ± 0.643 No. = 62 Dynamic Measurements Signal Matching (CAPWAP) 1.368 ± 0.620 No. = 377 EOD 1.626 ± 0.797 No. = 125 EOD 1.084 ± 0.431 No. = 128 Field Evaluation Energy Approach 0.894 ± 0367 No. = 371 BOR (last) 0.785 ± 0.290 No. = 153 BOR (last) 1.158 ± 0.393 No. = 162 < 16 BP10cm 1.843 ± 0.831 No. 54 < 16 BP10cm 1.176 ± 0.530 No. = 32 < 16 BP10cm 1.227 ± 0.474 No. = 56 < 16 BP10cm 0.830 ± 0.352 No. = 29 ≥ 16 BP10cm 1.460 ± 0.734 No. = 71 ≥ 16 BP10cm 1.153 ± 0.354 No. = 130 ≥ 16 BP10cm 0.972 ± 0.359 No. = 72 ≥ 16 BP10cm 0.775 ± 0.274 No. = 124 AR < 350 2.589 ± 2.385 No. = 37 AR ≥ 350 1.929 ± 0.698 No. = 22 AR < 350 1.717 ± 0.841 No. = 37 AR ≥ 350 1.181 ± 0.468 No. = 34 AR < 350 1.116 ± 0.362 No. = 22 AR ≥ 350 1.308 ± 0.796 No. = 10 AR < 350 0.736 ± 0.249 No. = 82 AR < 350 1.054 ± 0.459 No. = 39 AR < 350 1.178 ± 0.379 No. = 83 AR < 350 0.764 ± 0.318 No. = 19 AR < 350 1.431 ± 0.727 No. = 39 AR ≥ 350 0.851 ± 0.305 No. = 42 AR ≥ 350 0.954 ± 0.396 No. = 10 AR ≥ 350 0.926 ± 0.320 No. = 34 AR ≥ 350 1.422 ± 0.888 No. = 23 AR ≥ 350 1.110 ± 0.303 No. = 47 Figure 27. Statistical parameters of a normal distribution for the various dynamic analyses (applied to PD/LT2000 database) grouped by the controlling parameters.

46 Resistance Factors for a given Reliability Index, β Method Time of Driving No. of Cases Mean Standard Deviation COV 2.0 2.5 3.0 General 377 1.368 0.620 0.453 0.68 0.54 0.43 EOD 125 1.626 0.797 0.490 0.75 0.59 0.46 EOD - AR < 350 & Bl. Ct. < 16 BP10cm 37 2.589 2.385 0.921 0.52 0.35 0.23 CAPWAP BOR 162 1.158 0.393 0.339 0.73 0.61 0.51 General 371 0.894 0.367 0.411 0.48 0.39 0.32 EOD 128 1.084 0.431 0.398 0.60 0.49 0.40 EOD - AR < 350 & Bl. Ct. < 16 BP10cm 39 1.431 0.727 0.508 0.63 0.49 0.39 D yn am ic M ea su re m en ts Energy Approach BOR 153 0.785 0.290 0.369 0.46 0.38 0.32 ENR General 384 1.602 1.458 0.910 0.33 0.22 0.15 Gates General 384 1.787 0.848 0.475 0.85 0.67 0.53 General 384 0.940 0.472 0.502 0.42 0.33 0.26 EOD 135 1.073 0.573 0.534 0.45 0.35 0.27 D yn am ic Eq ua tio n s FHWA modified Gates EOD Bl. Ct. < 16BP10cm 62 1.306 0.643 0.492 0.60 0.47 0.37 WEAP EOD 99 1.656 1.199 0.724 0.48 0.34 0.25 Notes: EOD = End of Driving; BOR = Beginning of Restrike; AR = Area Ratio; Bl. Ct. = Blow Count; ENR = Engineering News Record Equation; BP10cm = Blows per 10cm; COV = Coefficient of Variation; Mean = ratio of the static load test results (Davisson’s Criterion) to the predicted capacity = KSX = λ =bias TABLE 17 The performance of the dynamic methods: statistical summary and resistance factors 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the CAPWAP method 0 5 10 15 20 25 30 35 40 45 50 55 60 N um be r o f Pi le - Ca se s 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Re la tiv e Fr eq u en cy log-normal distribution mlnx = 0.233 σlnx = 0.387 normal distribution mx = 1.368 σx = 0.620 > Figure 28. Histogram and frequency distributions for all (377) CAPWAP pile-cases in PD/LT2000. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the Energy Approach method 0 5 10 15 20 25 30 35 40 45 50 55 N um be r o f Pi le - Ca se s 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 Re la tiv e Fr eq u en cy log-normal distribution mlnx = -0.187 σlnx = 0.379 normal distribution mx = 0.894 σx = 0.367 Figure 29. Histogram and frequency distributions for all (371) Energy Approach pile-cases in PD/LT2000.

to require 100% of drilled shafts be postconstruction tested for major defects, as this ensures total quality at little addi- tional cost. 3.4 RECOMMENDED RESISTANCE FACTORS 3.4.1 Overview This section presents all the relevant resistance factors and recommendations for the AASHTO LRFD deep foundation design specifications. Tables 25 through 30 are based on material provided in the previous sections and are presented in an integrated format according to similarity of calculated factors, extent of data on which the factors were based, and relevant issues that have to be addressed as comments to the recommended values. The factors are divided based on pile redundancy as discussed in section 2.7.5. The recommended resistance factors represent the most significant attempt to date to develop LRFD code for deep foundations based on empirical data. 47 3.4.2 Static Analysis of Driven Piles Table 25 presents the recommended resistance factors to be used with static analysis of driven piles under compression, as well as the individual efficiency factor of each method, which indicates the method’s relative economic merit. The design methods should be applied based on soil parameters obtained via a subsurface exploration program with the detailed appli- cation and correlations as outlined in Tables 6, 7, 8, and 19 and further detailed in Appendices B and D. Table 26 presents the recommended factors to be used under tension (pullout) con- ditions, analyzing the skin friction in the same way as it was for compression loads, excluding tapered piles. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the CAPWAP method 0 5 10 15 20 N um be r o f Pi le - Ca se s 0 0.04 0.08 0.12 0.16 Re la tiv e Fr eq u en cy log-normal distribution mlnx = 0.384 σlnx = 0.444 normal distribution mx = 1.626 σx = 0.797 > Figure 30. Histogram and frequency distributions for all EOD (125) CAPWAP pile-cases in PD/LT2000. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the Energy Approach method 0 5 10 15 20 25 N um be r o f Pi le - Ca se s 0 0.04 0.08 0.12 0.16 Re la tiv e Fr eq u en cy log-normal distribution mlnx = 0.011 σlnx = 0.366 normal distribution mx = 1.084 σx = 0.431 Figure 31. Histogram and frequency distributions for all EOD (128) Energy Approach pile-cases in PD/LT2000. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the CAPWAP method 0 5 10 15 20 25 30 35 40 45 N um be r o f Pi le - Ca se s 0 0.04 0.08 0.12 0.16 0.2 0.24 Re la tiv e Fr eq u en cy log-normal distribution mlnx = 0.100 σlnx = 0.295 normal distribution m x = 1.158 σx = 0.393 > Figure 32. Histogram and frequency distributions for all BOR-last (162) CAPWAP pile-cases in PD/LT2000. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the GRLWEAP method 0 5 10 15 20 N um be r o f Pi le - Ca se s 0 0.05 0.1 0.15 0.2 Re la tiv e Fr eq u en cy log-normal distribution mlnx = 0.330 σlnx = 0.549 normal distribution mx = 1.656 σx = 1.199 > Figure 33. Histogram and frequency distributions for EOD default value GRLWEAP pile-cases, (99), data provided by GRL (see Hannigan et al., 1996).

The assigned resistance factors are based on the LRFD principle of a consistent prescribed reliability for either a redundant or a nonredundant pile cap configuration. The rec- ommended values should not be affected by the quality con- trol procedure to be implemented in the construction stage other than through the relationship with the anticipated ulti- mate capacity as explained in item 3 of section 3.4.7. 3.4.3 Dynamic Analysis of Driven Piles Table 27 presents the recommended resistance factors to be used for dynamic monitoring of driven piles and the rele- vant method’s efficiency factors. The dynamic methods are categorized according to the controlling parameter and the time of driving. Table 28 presents the recommended number of tests required during production, with values rounded to the next highest integer. Dynamic tests at EOD are carried out for capacity evaluation, monitoring the performance of the driving system, and establishing driving criteria. As such, EOD tests are of great importance beyond the capacity eval- uation alone. The following comments relate to the way site variability is being established: 1. Site variability relates to the variability within similar subsurface conditions of the same site, not between sites. For example, when piers are based on substantially dif- ferent subsurface conditions (i.e., in the stratum mostly influencing the pile capacity). The criteria should be applied independently to each pier location as a sepa- rate site. 2. Site variability can be determined by judgment or using the following approximate criteria related to borings representative of the entire site subsurface conditions: 48 a. Relate to each significant bearing layer, average parameters used for strength analysis (e.g., N SPT) at each boring location. b. Check the COV between the average values for each identifiable significant layer obtained at each boring location. c. Categorize site variability in the following way: i) COV < 25%—Low ii) 25% ≤ COV < 40%—Medium iii) 40% ≤ COV—High The following recommendations apply to dynamic tests: 1. Restrike should be scheduled according to the guide- lines provided in section 3.4.6 2. The recommended values in Table 28 relate to similar pile types driven at the same site. 3. For EOD conditions: • If dynamic measurements are available, evaluate pile capacity using the Energy Approach; if dynamic mea- surements are not available, evaluate pile capacity using the Gates or the FHWA modified Gates. • Signal matching is recommended for EOD condi- tions for end bearing piles only. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the Energy Approach method 0 5 10 15 20 25 30 N um be r o f Pi le - Ca se s 0 0.04 0.08 0.12 0.16 Re la tiv e Fr eq u en cy log-normal distribution mlnx = -0.304 σlnx = 0.350 normal distribution mx = 0.785 σx = 0.290 Figure 34. Histogram and frequency distributions for all BOR-last (153) energy approach pile-cases in PD/LT2000. Figure 35. Histogram and frequency distributions for all (384) FHWA modified Gates equation pile-cases in PD/LT2000. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction According to the FHWA modified Gates equation 0 5 10 15 20 25 30 35 40 45 50 55 60 N um be r o f Pi le - Ca se s 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Re la tiv e Fr eq u en cy log-normal distribution mlnx = -0.162 σlnx = 0.435 normal distribution mx = 0.940 σx = 0.472 >

• Restrike data is recommended to be interpreted by dynamic measurements, using signal matching analy- sis (CAPWAP). 4. Systematically, test the number of piles according to Table 28 at the chosen time of driving (EOD or BOR). Restrike tests following EOD tests on the same pile are important for the identification of changes with time (setup and relaxation); however, one test type should not be substituted for the other. 5. Average the results of the tested piles. All tested piles should be included regardless of their performance. No “good” pile result can substitute for a “bad” one, even if a replacement is required. If the average capacity of the tested pile is greater than or equal to 85% of the nominal ultimate capacity, then accept the set of piles as “good”; otherwise reject the set as “poor.” At this stage, alternative solutions are chosen, e.g., reduce the required nominal strength by adding piles, drive piles deeper, etc. 6. The above criteria provide a statistical approximation for the entire pile group. From a practical point of view, a separate criterion should be set as a minimum accepted value for each pile (e.g., 1.25 to 1.5 times the design load). 49 3.4.4 Static Analysis for Drilled Shafts Table 29 provides the recommended resistance factors to be used for the static analysis of drilled shafts. The design meth- ods should be applied based on soil parameters obtained via a subsurface exploration program with the detailed method application and correlations as outlined in section 2.5, and Tables 7 and 8, with further details in Appendix C. All drilled shafts should be tested for structural integrity as recom- mended in section 3.3.4.4. 3.4.5 Static Load Test Table 30 provides the recommended resistance factors for static load tests under any testing procedure for both driven piles and drilled shafts. Testing of driven piles should be scheduled according to the recommendations provided in section 3.4.6. The site variability can be determined accord- ing to the comments listed in section 3.4.3. The nominal strength for driven piles should be determined based on Davisson’s failure criterion or the maximum applied load if the pile does not reach failure. The same criterion should be used for piles tested in tension, omitting the offset displace- ment of the elastic compression line. Drilled shaft capacity Resistance factors for a given reliability index β Capacity Component Soil Type Design Method Construction Method No. of Cases Mean COV 2.0 2.50 3.0 Mixed 32 1.71 0.60 0.66 0.51 0.38 Casing 12 2.27 0.46 1.15 0.92 0.73FHWA Slurry 9 1.62 0.74 0.48 0.35 0.25 Mixed 32 1.22 0.67 0.41 0.31 0.23 Casing 12 1.45 0.50 0.68 0.54 0.42 Sand R&W Slurry 9 1.32 0.62 0.49 0.37 0.28 Mixed 53 0.90 0.47 0.45 0.36 0.28 Casing 13 0.84 0.50 0.39 0.31 0.24Clay FHWA Dry 40 0.88 0.48 0.43 0.34 0.27 Mixed 44 1.19 0.30 0.82 0.69 0.58 Casing 21 1.04 0.29 0.73 0.62 0.52 Dry 12 1.32 0.28 0.94 0.80 0.68FHWA Slurry 10 1.29 0.27 0.94 0.80 0.69 Mixed 44 1.09 0.35 0.68 0.57 0.47 Casing 21 1.01 0.42 0.55 0.45 0.36 Dry 12 1.20 0.32 0.79 0.67 0.56 Sand + Clay R&W Slurry 10 1.16 0.25 0.88 0.76 0.65 Mixed 46 1.23 0.41 0.68 0.56 0.45 C&K Dry 29 1.29 0.40 0.73 0.60 0.49 Mixed 46 1.30 0.34 0.83 0.69 0.57 Skin Friction + End Bearing Rock IGM Dry 29 1.35 0.31 0.91 0.77 0.65 FHWA Mixed 11 1.09 0.51 0.50 0.40 0.31 Sand R&W Mixed 11 0.83 0.54 0.36 0.28 0.22 Clay F HWA Mixed 13 0.87 0.37 0.52 0.43 0.36 FHWA Mixed 14 1.25 0.29 0.87 0.75 0.63 Sand + Clay R&W Mixed 14 1.24 0.41 0.69 0.56 0.46 FHWA Mixed 39 1.08 0.41 0.60 0.49 0.40 All Soils R&W Mixed 25 1.07 0.48 0.52 0.42 0.33 C&K Mixed 16 1.18 0.46 0.60 0.48 0.38 Skin Rock IGM Mixed 16 1.25 0.37 0.75 0.62 0.51 TABLE 18 The performance of the drilled shafts’ static analysis methods—statistical summary and resistance factors for data using mean ± 2 SD

should be determined based on the smaller of the two, the FHWA criterion or the maximum applied load on the pile. The relationship between the number of tests and the resis- tance factor is based on similar piles (geometry and size) tested at the same site (see section 3.4.3). The recommended resistance factors should be applied to the mean capacity determined for all tests. 3.4.6 Pile Test Scheduling Static or dynamic tests (restrikes) should be performed no sooner than before the pile has gained 75% of its capacity. This can be established as follows: For piles embedded completely in clay: For static testing purpose: t75 = 1540 × r2 (37) For dynamic testing purpose: t75 = 85 × r (38) 50 For piles embedded in alternating soil conditions (granu- lar and cohesive): For dynamic testing purpose: t75 = 39 × r (39) Where: t75 = time to reach 75% of maximum capacity in hours r = pile radius (or equivalent) in feet. 3.4.7 Design Considerations Figure 3 outlines the process of deep foundation design and construction. The following sequence of comments address several of the steps in that process in relation to the previous sections: 1. When analyzing the field and laboratory testing for strength and deformation parameters, two additional 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Shaft Capacity Prediction using the FHWA Method for Dry Construction 0 1 2 3 4 5 6 7 8 9 N um be r o f P ile - C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.232 σlnx = 0.480 mx = 0.884 σx = 0.424 normal distribution Figure 36. Histogram and frequency distributions for Ksx for 40 cases of drilled shafts in clay.

factors need to be established (related to the comments in section 3.4.3) (a) the number of different “sites” rec- ognized in the project, and (b) the level of site variabil- ity associated with each site. 2. When performing static analysis for the designed deep foundations, resistance parameters from Tables 25 and 26 should be used for driven piles and from Table 29 for drilled shafts. Resistance parameters from Table 26 should be used for driven piles under tension. Attention should be given to the efficiency factors as a measure of economic scale. The factors should be applied accord- ing to the redundancy status of the pile cap arrangement. Without prebid pile field testing, the testing planned during construction (e.g., static and/or dynamic) should not affect the resistance factors used in the design stage other than as described in the following item (3). 3. For driven piles, a drivability study is carried out dur- ing the design stage in order to assess the pile installa- tion. For this purpose alone, the required ultimate pile capacity can be established through the required design 51 load and the resistance factors to be used during the construction. For example, if the required design load is Fd, the site is of medium variability, and two static load tests will be performed, Table 30 indicates that φ = 0.75. Using equation 33, FS = 1.4167/0.75 = 1.89 and hence the ultimate capacity for the WEAP drivability analysis can be taken as Fu = 1.89 × Fd. If the design load is established via LRFD analysis (i.e., factored design load) than Fu = Fd/φ. In case of scour and/or downdrag, both components should be added to the design load, i.e., Fd + net scour + downdrag. It should be noted that the results of this analysis should not be used for pile capacity prediction in the field. Table 27 provides resistance factors that should be used at EOD if WEAP analysis is required as a prediction method for pile capacity based on measured blow count. That table also provides resistance factors associated with the anticipated testing method that should be used (in the same manner as described above for static load tests) if dynamic testing is to be performed. 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Shaft Capacity Prediction using the FHWA Method for Mixed Construction 0 1 2 3 4 5 6 7 8 9 10 N um be r o f P ile - C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = -0.246 σlnx = 0.477 mx = 0.872 σx = 0.419 normal distribution Figure 37. Histogram and frequency distributions for Ksx for 53 cases of drilled shafts in clay.

4. The determination of the required number of indicator piles can be combined along with the required number of dynamic pile tests presented in Table 28. For sites at which fewer than 100 piles are driven, the number of indicator piles can be used as the number of tested piles (approximately 8). Specifically, at least one pile should be tested under each substructure, using the test results as outlined in section 3.3.3. When more than 100 piles are driven, particularly at sites of high variability, sep- aration can be made between indicator piles and pro- duction piles, with the former used for assigning driv- ing criteria and the latter used for production quality control, as outlined in section 3.3.3. Restrike testing of piles should be scheduled according to equations 37 through 39, as outlined in section 3.4.6. 5. Resistance factors for static load tests of driven piles and drilled shafts should be assigned according to Table 30. The driven pile tests should be scheduled according to equations 37 through 39, as outlined in section 3.4.6. 6. All drilled shafts should be tested using small or high strain integrity testing. 52 3.5 EVALUATION OF THE RESISTANCE FACTORS 3.5.1 Overview Evaluation of the recommended resistance factors to be incorporated into a code is a complex and extensive process. The aim of the process is to compare an existing code of practice to the recommended new factors. Very often this evaluation cannot be done directly, as either the principles behind the factors differ (e.g., WSD vs. LRFD), or the applied methodology is not compatible (e.g., the design and con- struction combined factors of the existing code). As a result, the evaluation can be carried out in two ways: 1. Analyzing design case histories in light of both the new factors and the existing codes. In this way what has been done can be compared with what would have been done; and, if a sufficient number of case histories are analyzed, statistically valid conclusions can be derived regarding the effectiveness and overall performance of the recommendations. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 KSX = Ratio of Static Load Test Results over the Shaft Capacity Prediction using the FHWA Method for Mixed Construction 0 0.5 1 1.5 2 2.5 3 3.5 4 N um be r of Pi le- C a se s 0 0.025 0.05 0.075 0.1 0.125 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = 0.326 σlnx = 0.738 mx = 1.714 σx = 1.027 normal distribution Figure 38. Histogram and frequency distributions for Ksx for 32 cases of drilled shafts in sand.

2. Searching for common factors that can be compared, for example establishing a connection between resistance factors and factors of safety (e.g. see section 3.2.3). The following sections deal with various aspects asso- ciated with the recommended factors and means for their evaluation. 3.5.2 Working Stress Design The traditional factors of safety presented in Table 1 can now be evaluated in light of the available data. For example, the COV for the ENR equation and the WEAP analyses are 0.910 and 0.724, respectively, which practically means that the methods are unsuitable for the purpose of capacity pre- diction (see Figure 33). The reduction in the factor of safety from 3.50 to 2.75 when adding WEAP analysis to static cal- culations (as shown in Table 1) is therefore unfounded. Nor does the use of unspecified CAPWAP (general case) justify the reduction of the factor of safety to 2.25, even though the 53 average prediction is conservative and hence the mean case with an FS = 2.25 relates to an overprediction ratio of 3.1 (1.368 × 2.25). In comparison, the use of FS = 2.25 with a specified CAPWAP at the BOR is reasonable and is associ- ated with an acceptable probability of failure for a single pile application (approximately 1.85%; see Figure 32). The use of a large factor of safety for the static analysis appears to be very sensible, as most of the methods overpredict the actual capacity. The WSD existing factor (FS = 3.5) is probably based on historical cumulative experience and matches the presented results without being excessive or wasteful. The data summarized in Figure 45 are used to demonstrate this issue. For example, the average static capacity analysis of a driven pile in clay results in a mean underprediction ratio of about 0.82 and 0.72 for α and λ methods, respectively. The actual factors of safety in theses cases are 2.87 and 2.52. These factors of safety are in good agreement with the actual factor of safety when using the CAPWAP BOR results con- sidering the bias (FS = 2.61; see Figure 45). However, using CAPWAP results at the EOD, considering the bias, results in 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Shaft Capacity Prediction using the R&W Method for Mixed Construction 0 1 2 3 4 5 6 7 8 9 N um be r of Pi le- C a se s 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = 0.007 σlnx = 0.350 mx = 1.066 σx = 0.351 normal distribution Figure 39. Histogram and frequency distributions for Ksx for 44 cases of drilled shafts in sand + clay.

54 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Shaft Capacity Prediction using the C&K Method for Mixed Construction 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 N um be r of Pi le- C a se s 0 0.02 0.04 0.06 0.08 0.1 0.12 R ela tiv e Fr eq ue n cy log-normal distribution mlnx = 0.101 σlnx = 0.494 mx = 1.229 σx = 0.509 normal distribution Figure 40. Histogram and frequency distributions for Ksx for 46 cases of drilled shafts in rock.

55 a very conservative safety factor (FS = 3.66) relative to the static analysis methods. The major derived conclusions are therefore 1. The absolute value of a safety measure (factor of safety or resistance factor) by itself does not represent the eco- nomics of the method or the progressiveness of the code as suggested in Table 1. 2. An efficiency factor or a similar parameter is required in order to account for the bias of the analysis methods and provide an objective evaluation regarding the effec- tiveness of the capacity prediction method. 3. Databases are essential to assess any design method- ology. 4. The reduction of the factor of safety during design based on the anticipated capacity verification method during construction is unreasonable and unsafe. Specifically, if one uses an FS = 2 for static analysis during design because a static load test is expected to be carried out during construction (see Table 1), the actual mean FS in these cases is about 1.5 (1.45 to 1.62 for α and λ methods, respectively). 3.5.3 Sensitivity Analysis and Factors Evaluation The existing resistance factors of the AASHTO specifica- tions for dynamic evaluation of driven piles are limited and connected to static evaluation methods. The recommended resistance factors, presented in Table 27, are novel in their approach and categorization. Detailed comparisons between the current AASHTO specifications and those recommended are, therefore, not possible. General comparison between the factors presented in Table 27 and those of other codes (e.g., Australia’s) suggests that the proposed resistance factors are comparable. The resistance factors for static analyses of driven piles, pre- sented in Table 25, can be compared to the existing specifica- tions with the application of the λv factor and neglecting the specific method of the recommended values. When compared, the proposed parameters are reasonably in agreement with, but demonstrate the weakness of, the existing specifications. A sensitivity analysis along with a comparison between the parameters of different sources for static analyses of driven piles is presented in Figures 45 through 52. Figure 45 presents a summary of parameters from the existing LRFD code, the Standard (WSD) AASHTO code and the present recommended values. Figures 46 through 48 present a sensi- tivity analysis along with a comparison between the factors for selected cases. For example Figure 46 examines the dataset related to pipe piles in clay, analyzed using the α API method. The use of φ = 0.7 for the α method in the existing LRFD AASHTO specifications is apparently based on a database (Barker et al., 1991) and seem to be incompatible with any other source. The dataset for pipe piles in clay (Fig- ure 46) seem to be sensitive to the elimination of the extreme cases as shown by the relations between the resistance fac- tors and target reliability for a set including 20, 19, 18, and 17 cases, associated with all data, data within the two stan- dard deviation zone, 1.5 SD zone, and 1SD zone respec- tively. When examining the same design method for the data- bases of concrete piles and H piles, the sensitivity of the exclusion of cases does not exist once the extreme cases beyond the zone of two standard deviations are omitted. Figures 49 through 52 relate to the analyses of driven piles in sand. The recommended factors seem to vary in relation to the existing FS according to the pile type; matching the exist- ing WSD for pipe piles, while being substantially higher for concrete piles and lower for H piles. This demonstrates the effect of developing parameters with a consistent probability of failure compared to the parameters of the existing method- ology. The new parameters may appear depending on the case conservative or unsafe compared to existing standards, while actually being consistent. The recommended resistance factors for redundant drilled shafts, presented in Table 29, agree overall with those pro- vided by the existing specifications. The categorization by construction methods in mixed subsurface (sand and clay) can be further evaluated in light of local practices. Specify- ing a construction method before bidding is permitted in some states and not in others. Unspecific bidding specifica- tions eliminate the possibility of a design associated with a specific construction method. The practice of constructing single nonredundant drilled shafts is more common than in the case of driven piles. For nonredundant drilled shafts, the recommended resistance factors are lower than the common practice and need to be further evaluated in light of the pos- sible consequences of failure. 3.5.4 Actual Probability of Failure One advantage of using a large database is that the proba- bility of failure (or the risk) can be directly calculated from the available data, rather than by using the calculated distri- bution function. The procedure is done by applying a certain resistance factor to the calculated resistance (capacity) and examining the number of cases that exceed the actual capac- ity (nominal strength). An example of the process as applied to some of the dynamic methods is presented in Table 31. It should be noted that the values presented in Table 31 are con- servative, as a comprehensive calculation should account for the load factors (on the order of 1.35 depending on the DL to LL ratio); hence further decrease the probability of failure values provided in Table 31. The data in Table 31 suggests that the recommended factors presented in Table 27 would result in target reliabilities higher (lower pf) than those cal- culated for using the distribution functions.

56 . y = 1.1267x 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 - 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Resistance factors using FOSM R es is ta nc e fa ct or s us in g FO RM Driven Piles Static Analysis Driven Piles Dynamic Analysis Drilled Shafts Static Analysis FOSM = FORM Linear Best-fit No. of points = 160 Mean = 1.148 Std. Dev. = 0.039 FOSM = FORM Figure 41. Comparison between resistance factors obtained using the First Order Second Moment (FOSM) vs. those obtained by using First Order Reliability Method (FORM) for a target reliability of β = 2.33.

57 β=2.33 β=3.00 Soil Type Pile Type N Total No. of Cases Design Method(1) Details of Method (2) Application No. of Cases ± 2 SD Mean (λ) COV φ φ/λ FS FS x λ φ φ/λ FS FS x λ 4 β-Method 11.5 B;T&P(2) 4 0.61 0.61 0.19 0.32 7.34 4.48 0.13 0.22 10.63 6.48 17 λ-Method 11.5B; T&P(2) 2B; T&P(5) 16 0.74 0.39 0.37 0.50 3.80 2.82 0.29 0.39 4.97 3.68 17 α-Tomlinson 2B; T&P(2) 17 0.82 0.40 0.40 0.49 3.51 2.88 0.31 0.37 4.61 3.78 17 α-API 2B; T&P(5) 16 0.90 0.41 0.43 0.48 3.26 2.93 0.33 0.37 4.30 3.87 H-Piles 9 SPT-97 mob 8 1.04 0.41 0.50 0.48 2.84 2.95 0.38 0.36 3.74 3.89 19 λ-Method 2B; Hara (5h) 18 0.76 0.29 0.48 0.63 2.97 2.26 0.38 0.51 3.69 2.80 19 α-API 2B; Hara (5h) 17 0.81 0.26 0.54 0.67 2.61 2.11 0.44 0.55 3.20 2.59 8 β-Method 2B; Hara (5h) 8 0.81 0.51 0.32 0.39 4.45 3.60 0.23 0.28 6.14 4.97 Concrete Piles 19 α-Tomlinson 2B; Hara (5h) 18 0.87 0.48 0.36 0.41 3.94 3.43 0.26 0.30 5.37 4.67 20 α-Tomlinson 2B; T&P (1) 18 0.64 0.50 0.25 0.40 5.56 3.56 0.19 0.29 7.64 4.89 20 α-API 2B; T&P (1) 19 0.79 0.54 0.29 0.36 4.95 3.91 0.20 0.26 6.96 5.50 13 β-Method 2B; T&P (1) 12 0.45 0.60 0.14 0.32 9.81 4.41 0.10 0.22 14.16 6.37 20 λ-Method 2B; T&P (1) 19 0.67 0.55 0.24 0.36 5.94 3.98 0.17 0.25 8.38 5.62 Clay Pipe Piles 13 SPT-97 mob 2B; T&P (1) 12 0.39 0.62 0.12 0.31 11.70 4.56 0.08 0.21 17.02 6.64 19 Nordlund 36; 11.5B,P(6) 19 0.94 0.40 0.46 0.49 3.08 2.89 0.35 0.37 4.04 3.80 19 Meyerhof 18 0.81 0.38 0.42 0.51 3.41 2.76 0.32 0.39 4.43 3.59 19 β-Method 36; 2B; P(5) 19 0.78 0.51 0.30 0.39 4.69 3.66 0.22 0.28 6.49 5.06 H-Piles 19 SPT-97 mob 18 1.35 0.43 0.63 0.46 2.26 3.05 0.47 0.35 3.01 4.06 37 Nordlund 36: 11.5B; P(6) 36 1.02 0.48 0.42 0.42 3.34 3.41 0.31 0.31 4.55 4.64 37 β-Method 36; 2B; P(5) 35 1.10 0.44 0.50 0.46 2.82 3.10 0.38 0.34 3.76 4.13 37 Meyerhof 36 0.61 0.61 0.19 0.32 7.34 4.48 0.13 0.22 10.63 6.48 Concrete Piles 37 SPT97 mob 36 1.21 0.47 0.51 0.42 2.76 3.34 0.38 0.31 3.75 4.53 20 Nordlund 36; 2B P(5) 19 1.48 0.52 0.56 0.38 2.51 3.71 0.41 0.27 3.49 5.16 20 β-Method 36; 2B P(5) 20 1.18 0.62 0.36 0.31 3.89 4.59 0.25 0.21 5.67 6.69 20 Meyerhof 20 0.94 0.59 0.31 0.33 4.55 4.27 0.22 0.23 6.52 6.13 Sand Pipe Piles 20 SPT-97 mob 19 1.58 0.52 0.60 0.38 2.34 3.70 0.44 0.28 3.26 5.14 22 α-Tomlinson/Nordlund/Thurman 36; 2B; P(5) 20 0.59 0.39 0.30 0.51 4.75 2.80 0.23 0.39 6.20 3.66 37 α-API/Nordlund/Thurman 36; 2B; P(5) 34 0.79 0.44 0.36 0.45 3.98 3.14 0.27 0.34 5.33 4.21 35 β-Method/Thurman 36; 2B; P(5) 32 0.48 0.48 0.20 0.42 7.08 3.40 0.15 0.31 9.65 4.63 H-Piles 41 SPT-97 40 1.23 0.45 0.55 0.45 2.58 3.17 0.41 0.33 3.46 4.25 34 α-Tomlinson/Nordlund/Thurman 36; 2B; P; Hara(5h) 33 0.96 0.49 0.39 0.41 3.62 3.48 0.29 0.30 4.96 4.76 85 α-API/Nordland/Thurman 36; 11.5B; Sch; T&P(8) 80 0.87 0.48 0.36 0.41 3.94 3.43 0.26 0.30 5.37 4.67 85 β-Method/Thurman 36; 11.5B; Sch; T&P(8) 80 0.81 0.38 0.42 0.51 3.41 2.76 0.32 0.39 4.43 3.59 74 SPT-97 mob 71 1.81 0.50 0.72 0.40 1.98 3.58 0.52 0.29 2.72 4.93 Concrete Piles 32 FHWA CPT 30 0.84 0.31 0.51 0.60 2.81 2.36 0.40 0.48 3.52 2.96 13 α-Tomlinson/Nordlund/Thurman 36; 2B; P(5) 13 0.74 0.59 0.24 0.32 5.89 4.36 0.17 0.23 8.49 6.28 34 α-API/Nordland/Thurman 36; 2B; P(5) 32 0.80 0.45 0.36 0.44 3.99 3.19 0.26 0.33 5.36 4.29 31 β-Method/Thurman 36; 2B; P(5) 29 0.54 0.48 0.22 0.41 6.33 3.42 0.16 0.30 8.63 4.66 Mixed Soils Pipe Piles 34 SPT-97 mob 33 0.76 0.38 0.39 0.51 3.62 2.75 0.30 0.40 4.71 3.58 (1)See Table 6 for details; (2)Numbers in parentheses refer to notations used for detailing soil parameter combinations (see Table 7b and Appendix C for more details), See Tables 7a and 8 for soil properties’ correlations to SPT and CPT respectively, 36 = limiting friction angle, B = pile diameter 2B, 11.5B contributing zone to tip resistance. TABLE 19 Statistical details of static analyses of driven piles, resistance factors, efficiency factors, equivalent and “actual” factors of safety

58 β = 2.33 β = 3.0 Method Time of Driving No. of Cases Mean (λ) COV φ φ/λ F.S. F.S.xλ φ φ/λ F.S F.S.xλ General 377 1.368 0.453 0.59 0.43 2.40 3.28 0.43 0.31 3.29 4.51 EOD 125 1.626 0.490 0.64 0.40 2.21 3.60 0.46 0.28 3.08 5.01 EOD - AR < 350 & Bl. Ct. < 16 BP10cm 37 2.589 0.921 0.41 0.16 3.46 8.95 0.23 0.09 6.16 15.95 CAPWAP BOR 162 1.158 0.339 0.65 0.56 2.18 2.52 0.51 0.44 2.78 3.22 General 371 0.894 0.411 0.42 0.47 2.52 2.26 0.32 0.36 4.43 3.96 EOD 128 1.084 0.398 0.53 0.49 2.67 2.91 0.40 0.37 3.54 3.84 EOD - AR < 350 & Bl. Ct. < 16 BP10cm 39 1.431 0.508 0.54 0.38 2.62 3.75 0.39 0.27 3.63 5.20 D yn am ic M ea su re m en ts Energy Approach BOR 153 0.785 0.369 0.41 0.52 3.46 2.71 0.32 0.41 4.43 3.48 ENR General 384 1.602 0.910 0.26 0.16 5.45 8.73 0.15 0.09 9.45 15.13 Gates General 384 1.787 0.475 0.73 0.41 1.94 3.47 0.53 0.30 2.67 4.78 General 384 0.940 0.502 0.36 0.38 3.94 3.70 0.26 0.38 5.45 5.12 EOD 135 1.073 0.534 0.38 0.36 3.73 4.00 0.27 0.25 5.25 5.63 D yn am ic Eq ua tio n s FHWA modified Gates EOD Bl. Ct. < 16BP10cm 62 1.306 0.492 0.51 0.39 2.78 3.63 0.37 0.28 3.83 5.00 WEAP EOD 99 1.656 0.724 0.39 0.24 3.63 6.02 0.25 0.24 5.67 9.38 Notes: Column heads: Mean = ratio of the static load test results (Davisson’s Criterion) to the predicted capacity = Ksx = λ = bias; COV = Coefficient of Variation Methods: ENR = Engineering News Record Equation Time of Driving: EOD = end of driving; BOR = beginning of restrike; AR = area ratio; Bl. Ct. = blow count; BP10cm = blows per 10cm TABLE 20 Statistical details of dynamic analyses of driven piles, resistance factors, efficiency factors, equivalent and “actual” factors of safety

β = 2.33 β = 3.0 Capacity Component Soil Type N Total No. of Cases Design Method Const. Method No. of Cases ± 2 SD Mean (λ) COV φ φ/λ F.S. F.S. x λ φ φ/λ F.S. F.S. x λ 34 Mixed 32 1.71 0.60 0.55 0.32 2.58 4.41 0.38 0.22 3.73 6.37 14 Casing 12 2.27 0.46 0.99 0.43 1.44 3.26 0.73 0.32 1.94 4.40 14 FHWA Slurry 9 1.62 0.74 0.38 0.24 3.69 5.97 0.25 0.15 5.70 9.23 34 Mixed 32 1.22 0.67 0.34 0.28 4.21 5.13 0.23 0.18 6.29 7.67 14 Casing 12 1.45 0.50 0.58 0.40 2.45 3.56 0.42 0.29 3.37 4.89 Sand 14 R&W Slurry 9 1.32 0.62 0.41 0.31 3.49 4.61 0.28 0.21 5.09 6.72 54 Mixed 53 0.90 0.47 0.38 0.43 3.70 3.33 0.28 0.31 5.02 4.52 14 Casing 13 0.84 0.50 0.33 0.40 4.23 3.56 0.24 0.29 5.82 4.89Clay 40 FHWA Dry 40 0.88 0.48 0.37 0.42 3.87 3.41 0.27 0.31 5.27 4.64 48 Mixed 44 1.19 0.30 0.73 0.61 1.94 2.31 0.58 0.49 2.42 2.88 23 Casing 21 1.04 0.29 0.65 0.63 2.17 2.26 0.52 0.50 2.70 2.81 13 Dry 12 1.32 0.28 0.85 0.64 1.67 2.21 0.68 0.52 2.07 2.73 12 FHWA Slurry 10 1.29 0.27 0.84 0.65 1.68 2.16 0.69 0.53 2.06 2.66 48 Mixed 44 1.09 0.35 0.60 0.55 2.36 2.57 0.47 0.43 3.02 3.29 23 Casing 21 1.01 0.42 0.48 0.47 2.96 2.99 0.36 0.36 3.92 3.96 13 Dry 12 1.20 0.32 0.71 0.59 2.01 2.41 0.56 0.47 2.53 3.04 Sand + Clay 12 R&W Slurry 10 1.16 0.25 0.79 0.68 1.79 2.07 0.65 0.56 2.18 2.53 49 Mixed 46 1.23 0.41 0.60 0.48 2.38 2.93 0.45 0.37 3.13 3.86 32 C&K Dry 29 1.29 0.40 0.64 0.49 2.22 2.86 0.49 0.38 2.91 3.76 49 Mixed 46 1.30 0.34 0.73 0.56 1.94 2.52 0.57 0.44 2.46 3.20 Skin Friction + End Bearing Rock 32 IGM Dry 29 1.35 0.31 0.81 0.60 1.75 2.36 0.65 0.48 2.19 2.96 11 FHWA Mixed 11 1.09 0.51 0.43 0.39 3.33 3.63 0.31 0.28 4.61 5.02Sand 11 R&W Mixed 11 0.83 0.54 0.30 0.37 4.67 3.88 0.22 0.26 6.55 5.44 Clay 16 FHWA Mixed 13 0.87 0.37 0.46 0.53 3.09 2.69 0.36 0.41 3.99 3.47 16 FHWA Mixed 14 1.25 0.29 0.78 0.63 1.81 2.26 0.63 0.50 2.25 2.81Sand + Clay 16 R&W Mixed 14 1.24 0.41 0.60 0.48 2.36 2.93 0.46 0.37 3.11 3.86 40 FHWA Mixed 39 1.08 0.41 0.52 0.48 2.71 2.93 0.40 0.37 3.57 3.86All Soils 27 R&W Mixed 25 1.07 0.48 0.45 0.42 3.18 3.41 0.33 0.31 4.34 4.64 17 C&K Mixed 16 1.18 0.46 0.51 0.43 2.76 3.26 0.38 0.32 3.73 4.40 Skin Rock 17 IGM Mixed 16 1.25 0.37 0.66 0.53 2.15 2.69 0.51 0.41 2.78 3.47 TABLE 21 Statistical details of static analyses of drilled shafts, resistance factors, efficiency factors, equivalent and “actual” factors of safety

60 β = 2.33 β = 3.00 γL = 1.75, γD = 1.2, DL/LL = 2 Category Pile Type or Construction Soil Type or State Method of Analysis φ resistance factor φ/λ efficiency FS factor of safety FS x λ actual mean FS PPC Clay α - API 0.54 0.44 0.67 0.55 2.61 3.20 2.11 2.59 PPC Sand β 0.50 0.38 0.46 0.34 2.82 3.76 3.10 4.13 Static Methods Driven Piles Pipe Mixed α - API Nordlund/Thurman 0.36 0.26 0.44 0.33 3.99 5.36 3.19 4.29 All BOR CAPWAP 0.65 0.51 0.56 0.44 2.18 2.78 2.52 3.22 All Energy Approach 0.53 0.40 0.49 0.37 2.67 3.54 2.91 3.84 Dynamic Methods Driven Piles All EOD FHWA mod Gates 0.38 0.27 0.36 0.25 3.73 5.25 4.00 5.63 Mixed All R&W skin 0.45 0.33 0.42 0.31 3.18 4.34 3.41 4.64 Mixed Rock C&K total 0.60 0.45 0.48 0.37 2.38 3.13 2.93 3.86 Static Methods Drilled Shafts Mixed Sand & Clay FHWA skin 0.78 0.63 0.63 0.50 1.81 2.25 2.26 2.81 Notes: *Top line of column: β = 2.33; **Bottom line of column: β = 3.00; γL = 1.75; γD = 1.2; DL/LL = 2. EOD Resistance Factor φ/λ Pile Type Soil Type Design Method No. λ COV Redundant β = 2.33 Non- redundant β = 3.00 Redundant β = 2.33 Non- redundant β = 3.00 α-API 9 1.11 0.71 0.28 0.18 0.25 0.16 α-Tomlinson 9 0.95 0.57 0.33 0.23 0.35 0.24Clay λ-Method 9 0.72 0.52 0.27 0.20 0.38 0.36 β-Method 7 0.52 0.54 0.19 0.14 0.37 0.27 SPT-97 mob 7 1.18 1.33 0.08 0.04 0.07 0.03 Pipe Sand and Mixed αAPI/Nordlund 7 0.80 0.60 0.26 0.18 0.33 0.23 α-API 3 0.76 0.57 0.26 0.18 0.34 0.24Clay α-Tomlinson 3 0.64 0.54 0.23 0.17 0.36 0.27 β-Method 8 0.23 0.36 0.12 0.10 0.52 0.43H Sand SPT-97 mob 0.43 0.32 0.25 0.20 0.58 0.478 Target Reliability β Site Variation N Mean (λ) (Bias) SD C.O.V. 2.00 2.33 3.00 1 1 0.18 0.18 0.86 0.80 0.67 2 1 0.13 0.13 0.96 0.89 0.78 3 1 0.10 0.10 1.00 0.94 0.83 4 1 0.09 0.09 1.03 0.97 0.86 Low 5 1 0.08 0.08 1.04 0.99 0.88 1 1 0.27 0.27 0.73 0.65 0.53 2 1 0.19 0.19 0.85 0.78 0.66 3 1 0.16 0.16 0.90 0.84 0.72 4 1 0.14 0.14 0.94 0.88 0.76 Medium 5 1 0.12 0.12 0.97 0.90 0.79 1 1 0.36 0.36 0.61 0.54 0.42 2 1 0.25 0.25 0.75 0.68 0.55 3 1 0.21 0.21 0.82 0.75 0.63 4 1 0.18 0.18 0.86 0.80 0.67 High 5 1 0.16 0.16 0.90 0.83 0.71 Note: N = Number of load tests TABLE 22 Resistance factors and associated factors of safety along with efficiency measures for sample methods TABLE 23 Detailed resistance factors for pullout of driven piles—based on static analyses TABLE 24 Resistance factors as a function of number of load tests per site, site variability and target reliability

61 Fr eq ue nc y Fr eq ue nc y Pile Capacity Acceptance criterion x* Seller's risk Buyer's risk Distribution of unac- ceptable set of piles Distribution of ac- ceptable set of piles Figure 42. Frequency distributions of test results taken from sets of unacceptable and acceptable piles, showing contractor’s (seller’s) and owner’s (buyer’s) risks (schematic). 0.00 0.20 0.40 0.60 0.80 1.00 400 500 600 700 800 900 1,000 Mean Pile Capacity (kips) Pr ob ab ili ty o f A cc ep ta nc e Contractor's risk: β=0.10 Owner's risk: 1−α=0.90 Figure 43. Operating characteristics curve for an acceptance sampling plan to ensure the average axial capacity of a set of piles.

62 2 110 0.01 0.1 0.90 0.05 Figure 44. Binomial nomograph for determining sample size, n, and permitted number of defectives, c, for contractor’s risk α and owner’s risk β (Montgomery 1991). The procedure for using the nomograph to design a sampling plan is to (1) draw a line connecting α on the right-hand rule with the corresponding p1 on the left-hand rule, (2) draw a similar line connecting (1-β) and p2, and (3) the point of intersection of the two lines gives the required sample size, n, and the maximum number of defectives permitted within the sample for acceptance.

63 Resistance Factor φ φ/λ Pile Type Soil Type Design Method Redundant Non- redundant Redundant Non- redundant Mixed SPT-97 mob 0.70 0.50 0.40 0.29 α-API 0.67 0.55 Clay λ-Method 0.63 0.55 β-Method 0.46 0.34Sand SPT-97 mob 0.42 0.31 FHWA CPT 0.50 0.40 0.60 0.48 β-Method/Thurman 0.51 0.39Mixed αTomlinson/Nordlund/Thurman 0.41 0.30 Sand Nordlund 0.40 0.30 0.42 0.31 Clay α-Tomlinson 0.41 0.30 Mixed α-API/Nordlund/Thurman 0.35 0.25 0.41 0.30 Concrete Pile Sand Meyerhof 0.20 0.15 0.32 0.22 SPT-97 mob 0.38 0.28 Sand Nordlund 0.55 0.45 0.38 0.27 SPT-97 mob 0.40 0.30 0.51 0.40 Mixed α-API/Nordlund/Thurman 0.44 0.31 Sand β-Method 0.35 0.25 0.31 0.21 Clay α-API 0.36 0.26 Sand Meyerhof 0.30 0.20 0.33 0.23 αTomlinson/Nordlund/Thurman 0.32 0.23Mixed β-Method/Thurman 0.41 0.30 α-Tomlinson 0.40 0.29 . Pipe Pile Clay λ-Method 0.25 0.15 0.36 0.25 Mixed SPT-97 mob 0.45 0.33 SPT-97 mob 0.55 0.45 0.46 0.35 Nordlund 0.49 0.37Sand Meyerhof 0.51 0.39 α-API 0.45 0.35 0.48 0.37 α-Tomlinson 0.49 0.37Clay λ-Method 0.40 0.30 0.50 0.39 α-API/Nordlund/Thurman 0.35 0.45 0.34Mixed αTomlinson/Nordlund/Thurman 0.51 0.39 Sand β-Method 0.30 0.25 0.39 0.28 H Piles Mixed β-Method/Thurman 0.20 0.15 0.42 0.31 Notes: φ/λ = efficiency factor, evaluating the relative economic performance of each method (higher ratios indicate a more economical solution). λ = bias = Ksx = Mean of measured over predicted. φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table Redundant = Five piles or more under one pile cap ( β = 2.33 pf = 1.0%) Non-Redundant = Four or fewer piles under one pile cap (β = 3.0 pf = 0.1%) 1Higher values may be applicable for PPC piles but no sufficient data were available to support this. φ (resistance factor) Soil Type Design Method Pile Type Redundant β = 2.33 Non-Redundant β = 3.00 Clay α-API, λ αTomlinson H, Pipe, PPC 0.25 1 0.20 H 0.15 0.10 β Pipe, PPC 0.25 0.20 Sand SPT-97 H, Pipe, PPC 0.25 0.20 Mixed α-API/Nordlund H, Pipe, PPC 0.20 0.15 TABLE 25 Recommended resistance and efficiency factors for static analyses of driven piles TABLE 26 Recommended resistance factors for static analysis of nontapered driven piles under pullout

64 φ (resistance factor) φ/ λ Method Case Redundant Non-Redundant Redundant Non-Redundant EOD 0.65 0.45 0.40 0.28 EOD, AR<350, Bl. Ct.<16BP10cm 0.40 0.25 0.16 0.09 Signal Matching (CAPWAP) BOR 0.65 0.50 0.56 0.44 EOD 0.55 0.40 0.49 0.37 Dynamic Measurements Energy Approach BOR 0.40 0.30 0.52 0.41 ENR General 0.25 0.15 0.16 0.09 Gates General 0.75 0.55 0.41 0.30Dynamic Equations FHWA modified General 0.40 0.25 0.38 0.28 WEAP EOD 0.40 0.25 0.24 0.15 Notes: COV = Coefficient of Variation Column heads: φ/ λ = efficiency factor, evaluating the relative economic performance of each method (higher ratios indicate a more economical solution); φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table; Redundant = Five piles or more under one pile cap.( β = 2.33 pf = 1.0%); λ = bias = KSX = Mean of measured/predicted; Non-Redundant = Four or less piles under one pile cap (β = 3.0 pf = 0.1%) Method: ENR = Engineering News Record Equation. Case: EOD = End of Driving; BOR = Beginning of Restrike; AR = Area ratio; Bl.Ct. = blow count; BP10cm = blows per 10cm Site Variability. Low Medium High Method EA CAPWAP EA CAPWAP EA CAPWAPNo. of Piles Time EOD BOR EOD BOR EOD BOR ≤ 15 4 3 5 4 6 6 16 - 25 5 3 6 5 9 8 26 - 50 6 4 8 6 10 9 51 – 100 7 4 9 7 12 10 101 – 500 7 4 11 7 14 12 > 500 7 4 12 7 15 12 Notes: Site variability – see section 3.4.3, item 4 for the determination of site variability. EA = Energy Approach Analysis; CAPWAP = Signal Matching Analysis; EOD = End of Driving; BOR = Beginning of Restrike TABLE 27 Recommended resistance and efficiency factors for dynamic analyses of driven piles TABLE 28 Recommended number of dynamic tests to be conducted during production

65 φ (resistance Factors) φ/λ Shaft Resistance Soil Type Design Method Construction Method Redundant Non-Redundant Redundant Non- Redundant R&W 0.36 0.29Sand FHWA All 0.50 0.40 0.38 0.31 Clay FHWA All 0.40 0.30 0.43 0.31 Slurry & Dry 0.85 0.70 0.63 0.52FHWA Casing 0.65 0.50 0.63 0.52 Slurry & Dry 0.75 0.60 0.65 0.52 Sand + Clay R&W Casing 0.50 0.35 0.47 0.36 C&K All 0.60 0.60 0.48 0.37 Total Resistance Rock IGM All 0.75 0.75 0.56 0.44 FHWA 0.48 0.40 All Soils R&W All 0.45 0.35 0.42 0.33 C&K 0.50 0.35 0.43 0.32 Skin Resistance Rock IGM All 0.65 0.50 0.53 0.41 Notes: φ/λ = efficiency factor, evaluating the relative economic performance of each method (higher ratios indicate a more economical solution); φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table. Redundant = Five piles or more under one pile cap ( β = 2.33 pf = 1.0%) Non-Redundant = Four or fewer piles under one pile cap (β = 3.0 pf = 0.1%) λ = bias = KSX = mean of measured/predicted FHWA = Reese and O’Neill (1988); R&W = Reese and Wright (1977); C&K = Carter and Kulhawy (1988); IGM = O’Neill and Reese (1999). φ (Resistance Factor) Site Variability No. of Load Tests Per Site Low Medium High 1 0.80 0.70 0.55 2 0.90 0.75 0.65 3 0.90 0.85 0.75 ≥ 4 0.90 0.90 0.80 Note: Site variability: see section 3.4.3 item 4 for the determination of site variability. TABLE 29 Recommended resistance factors for drilled shafts TABLE 30 Recommended resistance factors for static load tests

66 0.40 0.40 0.45 H 0.25 0.25 0.30 Pipe 0.50 0.35 0.50 Concrete λ α α Method Pile Type Recommended φ values for β = 2.33 FS = 3.5 WSD 0.70 λv End Bearing Skempton 0.50 λv β Method and Nordlund applied for clay 0.55 λv λ Method 0.70 λv α Method Existing LRFD φ values 1. Suggest to omit β Method in clay. Not considered Nordlund in clay 2. FHWA CPT mixed soil concrete piles φ = 0.50 No./Mean of Prediction (data ± 2 SD) 0.72 53 0.81 51 0.83 52 Total 0.74 16 0.82 17 0.90 16 H 0.67 19 0.64 18 0.79 19 Pipe 0.76 18 0.87 18 0.81 17 Concrete λ α Tomlinson α API MethodPile Type Actual Mean FS for driven piles in clay α Method = 0.82 x 3.5 = 2.87 λ Method = 0.72 x 3.5 = 2.52 For Comparison CAPWAP - EOD 126 cases Mean = 1.63 BOR 162 Mean = 1.16 Actual FS EOD = 1.63 x 2.25 = 3.66 Actual FS BOR = 1.16 x 2.25 = 2.61 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e F a c to r Pipe Piles - α API 1 SD (17) 1.5 SD (18) 2 SD (19) all data (20) recommendedα Method Exist λ Method Exist Actual Mean FS = 2.77 FS = 3.5 WSD Figure 45. Data summary for parameter evaluation of driven piles in clay. Figure 46. Sensitivity analysis examining the recommended parameters for the design of pipe piles in clay using α API method.

67 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e Fa c to r Concrete Piles - α API α Method Exist λ Method Exist Actual Mean FS = 2.84 FS = 3.5 WSD 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e F a c to r H Piles - α API 1 SD (12) 1.5 SD (15) 2 SD (16) all data (17) recommended α Method Exist λ Method Exist Actual Mean FS = 3.15 FS = 3.5 WSD Figure 47. Sensitivity analysis examining the recommended parameters for the design of concrete piles in clay using α API method. Figure 48. Sensitivity analysis examining the recommended parameters for the design of H piles in clay using α API method.

68 0.45 0.55 0.40 Nordlund 0.550.30.45H 0.55 0.30.30 Pipe 0.50 0.50.20 Concrete SPT 97 β Meyerhof Method Pile Type Recommended φ values for β = 2.33 FS = 3.5WSD 0.45 λv SPT 0.55 λv CPT Existing LRFD φ values skin and end bearing FHWA CPT mixed soil concrete piles φ = 0.50 No./Mean of prediction (data ± 2 SD) 1.18* 0.94 1.48 1.02 74 19 19 36 Nordlund 1.34* 73 1.04* 74 0.75* 74 Total 1.35 18 0.78 19 0.81 18 H 1.58 19 1.18 20 0.94 20 Pipe 1.21 36 1.10 35 0.61 36 Concrete SPT 97 βMeyerhof MethodPile Type Actual mean FS for driven piles in sand Range: pipe piles SPT 97 = 1.58 x 3.5 = 5.53 Meyerhof PPC = 0.61 x 3.5 = 2.14 * - large variation between pile types 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e F a c to r Pipe Piles - β Method 1 SD (13) 1.5 SD (18) 2 SD (20) all data (20) recommended Actual Mean FS = 4.13 FS = 3.5 WSD Figure 49. Data summary for parameter evaluation of driven piles in sand. Figure 50. Sensitivity analysis examining the recommended parameters for the design of pipe piles in sand using the β method.

69 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e F a c to r Concrete Piles - β Method 1 SD (28) 1.5 SD (31) 2 SD (35) all data (37) recommended Actual Mean FS = 3.85 FS = 3.5 WSD 1.5 2 2.5 3 3.5 β - Target Reliability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 φ - R e s is ta n c e F a c to r H Piles - β Method 1 SD (13) 1.5 SD (16) 2 SD (19) all data (19) recommended Actual Mean FS = 2.73 FS = 3.5 WSD Figure 51. Sensitivity analysis examining the recommended parameters for the design of concrete piles in sand using the β method. Figure 52. Sensitivity analysis examining the recommended parameters for the design of H piles in sand using the β method.

70 Resistance factor φ CAPWAP General CAPWAP BOR CAPWAP EOD AR > 350 BL ct. > 16 BP10cm Energy Approach EOD FHWA Mod Gates General 0.5 0.27 0 2.70 1.56 10.42 0.4 0 0 0 0 3.13 0.33 0 0 0 0 0.78 # of cases used 377 162 37 128 384 TABLE 31 Calculated probability of failure [p = (%)] based on direct utilization of database PD/LT 2000 for selected prediction methods

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 507: Load and Resistance Factor Design (LRFD) for Deep Foundations examines resistance factors for driven pile and drilled shaft foundations,and provides a procedure for calibrating deep foundation resistance.

Errata - Table 29 and Figure 47 in the pdf of NCHRP Report 507 contains incorrect information. An update to Table 29 and Figure 47 are available on-line.

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