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Suggested Citation:"Chapter 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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 2 - Findings." 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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14 CHAPTER 2 FINDINGS 2.1 STATE OF PRACTICE 2.1.1 Questionnaire and Survey Code development requires examining the state of practice in design and construction in order to address the needs, research the performance, and examine alternatives. The iden- tification of current design and construction methodologies was carried out via a questionnaire along with a survey, which was independently developed and analyzed by Mr. A. Munoz of the FHWA. The questionnaire was distributed to 298 state highway officials, TRB representatives, and state and FHWA geotechnical engineers. A total of 45 surveys were returned and analyzed (43 states and 2 FHWA personnel). The survey elicited information concerning design methodology in geo- technical and structural design, foundation alternatives, and design and constitution considerations for both driven piles and drilled shafts. The questionnaire, the survey, and their analyzed results are presented in Appendix A. A summary analysis of the survey results is presented below. 2.1.2 Major Findings 2.1.2.1 Design Methodology Averaging the responses for driven piles and drilled shafts, about 90% of the respondents used ASD, 35% used AASHTO Load Factor Design (LFD), and 28% used AASHTO Load and Resistance Factors Design (LRFD), suggesting that most of the respondents that use LRFD or LFD use it in parallel with WSD. Among the respondents using ASD to evaluate capacity, 95% used a global safety factor ranging from 2.0 to 3.0, depending on construction control and 5% used partial safety factors of 1.5 to 2.0 for side friction (3.0 for drilled shafts) and 3.0 for end bearing (2.0 to 3.0 for drilled shafts). 2.1.2.2 Foundation Alternatives The majority of the respondents use primarily driven pile foundations (75%), 14% use shallow foundations, and 11% use drilled shafts. Of those responding, 64% prefer the use of driven piles and 5% prefer drilled shafts or other foundation type. When using driven piles, 21% primarily use prestressed concrete piles; 52%, steel H piles; 2%, open-ended steel pipe piles; and 25%, closed-end steel pipe piles. 2.1.2.3 Driven Piles—Design Considerations 1. The most common methods used for evaluating the static axial capacity of driven piles were as follows: • 59%: α-method (Tomlinson, 1987), • 25%: β-method (Esrig & Kirby, 1979), • 5%: λ−method (Vijayvergiya and Focht, 1972), • 75%: Nordlund’s method (Nordlund, 1963), • 5%: Nottingham and Schmertmann’s method: CPT (1975), • 9%: Schmertmann’s method: SPT (Sharp, 1987), • 14%: Meyerhof’s method (1976) modified by Zeitlen and Paikowsky (1982), and • 25%: in-house methods and other less common methods. Of the computer programs used in design, • 39% were developed in-house, • 75% were FHWA developed, and • 20% were from commercial vendors. 2. Of the primary tests used to assess strength parameters in design, 86% used SPT-N values, 11% used CPT data, 2% used Dilatometer data, and none used Pressure- meter data. 3. The majority of the states used Tomlinson’s method to assess the side friction coefficient in cohesive soil (CA − adhesion) and Nordland’s method in cohesionless soil (δ − interfacial friction angle). 4. Pile settlement in the design was considered by 48%, with settlement ranging from 0.25 to 1.0 inches being tolerable. 5. Simplified methods (e.g., Broms, 1964) were used by 34% of the respondents in the lateral pile design meth- ods and/or computer programs, and 88% used methods based on p-y curves. Of the computer programs used in design, 14% were in-house, 82% were from the FHWA, and 55% came from commercial vendors.

15 6. Responses for the estimated risk or failure probability of the group foundation design were as follows: • 27% less than 0.1%, • 4% between 0.1 and 1%, • 1% of the responses were between 1% and 10%, and • 67% were unknown. The assessment for the acceptable maximum failure proba- bility ranged from about 0 to 1%. Pile failure had been expe- rienced by 14% of the respondents. 2.1.2.4 Driven Piles—Construction Considerations 1. Of the respondents, 77% performed static pile load test during construction, and the primary test method was the Quick Method. 2. The most common dynamic methods used for capacity evaluation of driven piles included the following: • Wave Equation Analysis using the program GRL- WEAP (GRL Engineers, Inc. Wave Equation Analy- sis Program) was used by 80% of the respondents. • 45% used the ENR formula, • 16% used Gate’s equation with safety factors rang- ing from 2.0 to 3.5, and • 1 state used its own dynamic formula. 3. Dynamic pile load tests were performed during con- struction by 84 % of respondents, testing 1% to 10% of the piles per bridge. 4. When setting production pile length and driving crite- ria, 82% used EOD conditions, 52% used BOR condi- tions, and 36% did not consider pile freeze or relax- ation effects in determining driving criteria. 2.1.2.5 Drilled Shafts—Design Considerations 1. The most common methods used for evaluating the static axial capacity of drilled shafts were as follows: • 36%: the α-method (total stress approach) (Reese and O’Neill, 1998; Kulhawy, 1989), • 41%: the β-method (effective stress approach) (Reese and O’Neill, 1988), • 9%: the Reese and Wright (1977) approach for side friction in cohesionless soils, • 39%: the FHWA (O’Neill et al., 1996) approach for intermediate geomaterials (soft rock), • 11%: Carter and Kulhawy (1988) approach for inter- mediate geomaterials (soft rock), and • 27%: other methods. Of the computer programs used, 18% were developed in-house, 50% came from the FHWA, 29% from com- mercial vendors, and 20% from others. 2. Of the primary parameters used, 70% were based on SPT values, 7% were obtained from the CPT test, 2% were based on Pressuremeter data, and 2% were based on Dilatometer data. 3. Of the 16% considering the roughness of the borehole wall in rock socket design, all did so by assumption. 4. Shaft settlement was considered by 61% of the respon- dents, with tolerable settlements ranging from 0.25 to 2.0 in. 5. Simplified (e.g., Brooms, 1964) lateral drilled shaft design methods and/or computer programs were used by 27%, and 82% used methods based on p-y curves. 6. For drilled shafts subjected to lateral load, the tolerable deflection ranged from 0.25 to 2.0 in., and the safety factor of lateral pile capacity ranged from 1.5 to 3.0. 7. About 30% of the respondents did not take into account the construction method in design. 8. Concerning the estimated risk or probability of failure of group foundation designs based on the safety factor used, the following responses were made: • 20%: less than 0.1%, • 7%: between 0.1 and 1%, • 2%: between 1 and 10%, and • 71%: unknown. The assessment for the acceptable maximum failure prob- ability ranged from about 0% to 5%. 2.1.2.6 Drilled Shafts—Constructions Considerations 1. 66% performed static load testing during construction. 2. The type of load test used included conventional static load testing (32%), Osterberg load cell (43%), Stat- namic load testing (11%), and Dynamic load testing (7%). 3. The methods used in drilled shaft installations included drilling in dry (64%), wet (52%), and casing methods (86%). 4. For the drilling slurry used during construction, 25% used a mineral slurry of processed Attapulgite, 52% used a mineral slurry of Bentonite clays, and 36% used synthetic polymer slurries. 5. A majority of the States use the AASHTO Specifica- tions for shaft cleanliness, which requires more than 50% of the base to have less than 0.5 in. of sediment and maximum sediment thickness to be less than 1.5 in. 6. 54% performed inspection of the shaft bottom, in which only one State has a specific inspection device. The rest performed inspection by using manual probes or an underwater camera and camcorder. 7. 16% did not perform integrity testing for drilled shaft quality control; 64% used Cross Sonic Logging

16 (CSL), 7% used Surface Reflection (Pulse Echo Method), and 7% used Gamma Ray or NX coring. 2.2 DATABASES 2.2.1 General Three major databases were developed for the primary sta- tistical evaluation of resistance factors for the design and construction of driven piles and drilled shafts. Six additional peripheral databases were assembled and/or used for the investigation of specific issues as needed. The major features of the databases are described below. The detailed cases from which the databases were developed are presented in Appen- dix B (dynamic) and Appendix C (static). 2.2.2 Drilled Shaft Database—Static Analysis The soil type and method of construction of the 256 case histories in the drilled shaft database are detailed in Table 2. The database was developed at the University of Florida, mostly through the integration of databases gathered by the Florida DOT, the Federal Highway Administration (FHWA), and O’Neill et al. (1996). 2.2.3 Driven Pile Database—Static Analysis The soil and pile type of the 338 case histories in the driven pile database are detailed in Table 3. The database was developed at the University of Florida, mostly through the integration of databases gathered by the University of Florida, the FHWA (see, e.g., DiMillio, 1999), the University of Massachusetts Lowell (see, e.g., Paikowsky et al., 1994), and the Louisiana Transportation Research Center. 2.2.4 Driven Pile Database—Dynamic Analysis The PD/LT2000 database contains information related to 210 driven piles that have been statically load tested to failure and dynamically monitored during driving and/or restrike (403 analyzed measurements). PD/LT2000 comprises information from the PD/LT database (Paikowsky et al., 1994), the PD/LT2 database (Paikowsky and LaBelle, 1994), and 57 additional pile case histories described by Paikowsky and Stenersen (2000). The data in PD/LT2000 were carefully examined and analyzed following procedures described by Paikowsky et al. (1994), resulting in detailed static and dynamic pile capacity evaluations. Table 4 presents a summary of the data contained in PD/LT2000, broken down according to pile type and capac- ity range, site location, soil type, factors affecting soil inertia, and time of driving (EOD or BOR). 2.3 DEEP FOUNDATIONS NOMINAL STRENGTH 2.3.1 Overview Probabilistic calibration of resistance factors for any pre- dictive method utilizing a database is possible when the nom- inal geotechnical pile strength (i.e., static pile capacity) is defined and compared to the outcome of the calibrated pre- diction method. The definition of ultimate static capacity given static load test results (load-displacement relations) is not unique, and the use of the term “reference static capacity for calibration” (may include judgment) is more appropriate than “nominal strength.” The static load test results depend on the load testing procedures and the applied interpretation method, often being subjective. The following sections examine each of these factors and its influence on the reference static capac- ity, concluding with a recommended unique procedure to be followed in the calibration. 2.3.2 Failure Criterion for Statically Loaded Driven Piles Past work related to driven piles (Paikowsky et al., 1994) has resorted to a representative static pile capacity based on Method of Construction Casing Slurry Dry Soil/Rock Type Total Skin Total Skin Total Skin Sand 13 6 15 4 6 1 Clay 14 3 40 10 Mixed Soils 23 4 12 5 Rock 0 Sand & Rock 4 20 0 Clay & Rock 2 19 7 Mixed Soils & Rock 2 Total (256) 58 Note: Total = skin + tip; Skin = side alone 0 0 13 7 0 0 0 8 0 4 7 5 0 2 0 1 0 0 2 0 32 36 14 91 25 Soil Type Number of Cases Tip Side H-PILES PPC PIPE Clay 0 0 Sand 0 0 Mix 15 3Rock Total 15 3 Clay 0 0 Sand 37 20 Mix 50 19Sand Total 87 39 Clay 19 20 Sand 1 0 Mix 34 15Clay Total 3 12 6 21 0 17 13 30 8 1 36 44 54 35 Insufficient data 0 7 1 All cases (338) 97 163 78 TABLE 2 Summary and breakdown—drilled shafts database TABLE 3 Driven piles database: soil type and number of cases by type of pile

17 the assessment by five interpretation methods; (1) Davisson’s Criterion (Davisson, 1972), (2) Shape of Curve (similar to the procedure proposed by Butler and Hoy, 1977), (3) Lim- iting Total Settlement to 25.4 mm, (4) Limiting Total Settle- ment to 0.1B (Terzaghi, 1942), and (5) the DeBeer log-log method (DeBeer, 1970). A single representative capacity value was then calculated for the analyzed case as the average of the methods consid- ered relevant (i.e., provided reasonable value). The develop- ment of a calibration in a framework suitable for future mod- ifications requires that the evaluated resistance factors be based on an objective, reproducible procedure. In order to do so, the static capacity of each pile in database PD/LT2000 was evaluated according to all five aforementioned criteria and a representative capacity was assigned for each pile. The mean and standard deviations of the ratio of the representative pile capacity to the capacity given by the method being evaluated was then determined. Details of the analyses and their results are presented by Paikowsky and Stenerson in Appendix B. Figure 6 shows the histogram and calculated distributions (normal and lognormal) for Davisson’s failure criterion in which KSD is the ratio of the designated static capacity to that defined by Davisson’s failure criterion. Davisson’s criterion was found to perform the best overall and was therefore cho- sen as the single method to be used when analyzing load- displacement curves. Davisson’s method provides an objec- tive failure criterion and was also found to perform well for piles exceeding a diameter of 610 mm (examined through 30 pile cases). The data presented in Figure 6 demonstrates, however, that (1) a small bias exists in the static capacity being used as a reference for the evaluation of the methods predicting the capacity of driven piles, and (2) this bias (and other considerations) needs to be accounted for when evalu- ating the resistance factor to be used for field static load tests. Pile Types Geographical Location Soil Types Soil Inertia Type of Data Pile Capacities Pile Type No. Location No. Soil Type Side Tip Criteria Blow Ct. AR Time No. Range (kN) No. H –Pile 37 Northeast USA 44 0-445 2 OEP 10 Southeast USA 69 EOD & BOR 92 445-890 CEP 61 North USA 24 ≥ 16 blows /10cm 272 ---- 890-1334 Voided Concrete 35 South USA 10 Clay /Till 67 EOD & BORs 30 1334-1779 44 254 Northwest USA 3 1779-2224 27 305 Southwest USA 14 < 16 blows /10cm 112 ---- EOD 135 2224-2669 25 356 8 Australia 2 2669-3114 15 406 NewBrunswick 3 Rock 0 BOR 239 3114-3559 10 457 Holland 4 ≥ 350 ----- 134 3559-4003 13 508 Hong Kong 4 EOR 11 4003-4448 13 610 Israel 4 4448-4893 11 Sq. Conc 762 Ontario 22 Sand /Silt 140 < 350 ----- 255 DD 4893-5338 6 Sweden 1 5338-5783 5Octagonal Concrete 3 DR 1 5783-6228 4 Timber 2 NA 6 NA 3 1 NA 5 ---- ALT 1 6228-6672 Monotube 2 >6672 6 Total 210 210 210 210 389 389 389 210 Notes: Pile types: OEP = Open Ended Pipe Pile; CEP=Closed Ended Pipe Pile. Geographic Location: Northeast USA = Federal Highway Regions 1, 2 & 3; Southeast USA = Federal Highway Region 4; North USA = Federal Highway Regions 5, 7 & 8; South USA = Federal Highway Region 6; Northwest USA = Federal Highway Region 10; Southwest USA = Federal Highway Region 9. Type of Data: EOD = End of Driving; BOR = Beginning of Restrike; EOR = End of Restrike; DD = During Driving; DR = During Restrike; ALT = Alternate measurement. NA = Non Applicable / unknown 6 17 6 2 61 11 137 9 5 1 8 8 16 5 EOD & BOR = Cases containing both EOD & BOR; EOD & BOR's = Cases containing both EOD & multiple BOR measurements; TABLE 4 The PD/LT2000 database: pile type, geographical location, soil type, soil inertia, type of data, and pile capacities

18 2.3.3 Load Test Procedure for Statically Loaded Driven Piles The influence of the static load testing procedure (load- ing rate) on the designated pile capacity was examined in two ways. Two detailed case histories from a research site in New- buryport, Massachusetts, were evaluated. A pipe pile and prestressed concrete heavily instrumented friction pile were tested over a lengthy period at a bridge reconstruction site. Both piles were tested using three types of static load testing procedures: slow maintained (testing duration of about 45 hrs), short duration (testing duration of about 6 to 8 hrs), and static cyclic (testing duration of about 15 min). Details about the piles and the testing are presented by Paikowsky and Hajduk (1999, 2000) and Paikowsky et al. (1999). The interpretation of the load-displacement relationships in both cases sug- gested that the test type had an insignificant influence on the pile capacity (referring to a failure criterion irrespective of the displacement). The effect of the test type was further investigated utilizing a database containing information related to 75 piles tested under slow maintained and static-cyclic load testing proce- dures. In the static-cyclic procedure, the piles were loaded to failure using a high loading rate and then unloaded. The process was repeated for four cycles. The testing procedure and its interpretation method are presented by Paikowsky et al. (1999). A comparison between the pile capacity based on Davisson’s failure criterion for the slow maintained tests and the static-cyclic capacity is presented in Figure 7. The obtained relations and the associated statistical information suggest that there is no significant influence on the static pile capac- ity based on the applied static load rate. The static-cyclic load test results were also compared to the representative static pile capacity (based on the afore- mentioned five methods), resulting in a mean KSC of 1.023 and a standard deviation of 0.057. These evaluations led to the conclusion that Davisson’s pile failure criterion can be used to determine the reference pile capacity for driven piles, irrespective of the pile’s diam- eter and the static load-testing procedure. 2.3.4 Failure Criterion for Statically Loaded Drilled Shaft Static load tests of small- to medium-capacity drilled shafts (say up to 5 MN) are similar to that of driven piles. It is com- mon, however, for example in the Northeast region of the United States, to design and build high-capacity drilled shafts (10 MN and more), often as an alternative to a large group of small-capacity driven piles. The testing for capacity of such shafts is a challenge that often requires alternatives to the common external reaction testing, for example, the Osterberg load-cell (Osterberg, 1992), statnamic tests (Bermingham and White, 1995, Middendorp and Bielefeld, 1995), and drop 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0 5 10 15 20 25 30 35 40 45 N um be r o f Pi le - Ca se s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Re la tiv e Fr eq u en cylog-normal distribution ^ mx = 1.013 σlnx = 0.0829 normal distribution mx = 1.018 σx = 0.1010 KSD Ratio of Representative Pile Capacity over the Pile Capacity Based on Davisson’s Failure Criterion 0 200 400 600 800 1000 1200 1400 Static Cyclic Load Test Capacity (kN) 1 kN = 0.2248 kips 0 200 400 600 800 1000 1200 1400 Equation Y = 0.924 * X Number of data points used = 75 R2 = 0.978351 Mean KSC = 0.930 Standard Deviation = 0.136 Max KSC = 1.215 Min KSC = 0.577 Sl ow M ai nt ai ne d St at ic Lo ad Te st – D av iss on ’s Cr ite rio n (kN ) Figure 6. Histogram and frequency distributions of KSD for 186 PD/LT2000 pile-cases in all types of soils. (Paikowsky and Stenersen, 2000). Figure 7. Comparison between pile capacity based on Davisson’s criterion for slow maintained load tests and static-cyclic load test capacity for 75 piles. (Paikowsky et al., 1999).

19 weight dynamic testing. Another National Cooperative High- way Research Program project, NCHRP-21-08 “Innovative Load Testing Systems,” headed by the principal author of this report, examines such alternative methods. As part of this ongoing project, the static load-test results of statically loaded drilled shafts were examined utilizing the failure cri- teria previously described for driven piles, and the FHWA criterion for drilled shafts (O’Neill and Reese, 1999). The FHWA criterion establishes the failure load as that associ- ated with a displacement of 5% of the diameter at the shaft, if plunging of the shaft cannot be achieved. The results of this preliminary study, presented in Table 5, suggest that the FHWA criterion provides a reliable and simple failure interpretation. For the presented LRFD calibration study, the FHWA failure criterion for drilled shaft (i.e., load at a dis- placement of 0.05 B) was, therefore, adopted. 2.4 DRIVEN PILES—STATIC ANALYSIS METHODS Table 6 presents a summary of the methods used for static capacity evaluation of driven piles detailing the equations for side and tip resistances, required parameters, and constraints on their use. The associated correlations used to evaluate the soil properties from SPT and CPT tests are presented in Tables 7a and 8, respectively. While two internal friction angle inter- pretations are listed in Table 7 and were used initially, only the method proposed by Peck Hansen and Thornburn was found to provide more realistic results, and hence utilized in the calibrated analyses. The methods and the correlations listed in Tables 7a and 8 are based on the state of practice established via the questionnaire (see section 2.1 and Appen- dix A.) Table 7b elucidates the combinations and the manner in which the correlations were applied. The notations used in Table 7b are further noted when the analysis results are reported. The tables were, by and large, prepared as part of the study of static pile capacity at the University of Florida, which is presented in Appendix C. 2.5 DRIVEN PILES—DYNAMIC ANALYSIS METHODS 2.5.1 Overview Prior to detailed analyses leading to the determination of resistance factors, two components must be established: (1) the Statistics for the Ratio between Drilled Shaft Capacity of Different Interpretation Methods and the Representative Capacity Davisson DeBeer Shape of Curve FHWA # mx σx # mx σx # mx σx # mx σx 47 0.862 0.17 39 0.908 0.11 36 0.956 0.09 40 0.999 0.13 Notes: # = no. of cases; mx = mean; σx=standard deviation; loads 0.85 to 20 MN; diameter 0.3 to 1.5m; length 5.3 to 58.5m Method Side resistance Tip resistance Parameters required Constraints α-Tomlinson (Tomlinson, 1980/1995) Su; Db (bearing embedment) +Bearing layer must be stiff cohesive + Number of soil layers ≤ 2 α-API (Reese et al., 1998) qs = αSu Su β in cohesive (AASHTO, 1996/2000) qs = βσ’ λ (US Army Corps of Engineers, 1992) qs = λ(σ’+2Su) qp = 9 Su Su Only for cohesive soils β in cohesionless (Bowles, 1996) βσ’ Dr Nordlund and Thurman (Hannigan et al., 1995) ϖ ϖ+δ σ= δ cos )sin( ’CKq Fs qp = αt N’q σ’ φ Meyerhof SPT (Meyer- hof, 1976/1981) qs = k N qp = 0.4D/BN’ N + For cohesionless soils + SPT data Schmertmann SPT (Lai and Graham, 1995) qs = function(N) qp = fn(N) N SPTdata Schmertmann CPT (McVay and Townsend, 1989) qs = function(fs) p = fn(qc) c, fs CPT data OCR q q TABLE 6 Summary of static capacity methods for driven piles TABLE 5 Evaluation of failure criteria for statically loaded drilled shafts

20 type of the dynamic methods to be evaluated and (2) the con- ditions under which these methods need to be examined. Sec- tions 2.5.2 and 2.5.3 address these issues, respectively, based on a detailed study by Paikowsky and Stenerson provided in Appendix B. 2.5.2 Methods of Analysis 2.5.2.1 General Table 9 presents a summary of the major available dynamic methods for evaluating pile capacity. The methods are sub- divided according to the project stage (i.e., design vs. con- struction) and the need for data obtained through dynamic measurements. The incorporation of dynamic equations and WEAP reflects the need to address the state of practice as described in section 2.1. The methods that require dynamic measurements can be broadly categorized as those that utilize a simplified analysis of an instantaneous pile capacity evaluation for each hammer blow and those that require elaborate calculations (i.e., sig- nal matching) traditionally carried out in the office. 2.5.2.2 WEAP Based on Smith (1960), the use of the WEAP (Goble and Rausche, 1976) during design is of great importance for achieving compatibility between the driving system, the pile, and the soil conditions. Drivability studies and pile stress analyses often determine the pile type and geometry and the adequacy of the proposed equipment. Typically, two analyses are carried out: one by the designer during the design stage (prebid), in which a range of equipment to be specified in the bidding documents is examined, and the other by the contrac- tor, demonstrating the adequacy of the proposed construction equipment. The evaluation of WEAP effectiveness for capac- ity predictions is difficult, as a large range of input parameters is possible and the results are greatly affected by the actual field conditions. Examination of the method through analyses making use of default values is probably the best avenue. Other evaluations, including WEAP analysis adjustments fol- lowing dynamic measurements (e.g., matching energy), seem to be impractical in light of the other methods available and lead to questionable results regarding their quality and mean- ing (Rausche et al., 1997; Rausche, 2000). The WEAP analy- sis is evaluated in this study as a dynamic method for pile capacity prediction, using WEAP default input values and the pile’s driving resistance at EOD compared to the static load test results. The evaluation of WEAP as a pile design method examining the analyzed stresses at the design stage to the measured stresses during construction leads to a strength factor (related to the allowed structural stresses in the pile) that is beyond the scope of the presented research. 2.5.2.3 Dynamic Equations The chosen dynamic equations address the state of practice and reflect a range in equation type and performance. While the Engineering News-Record Equation (Wellington, 1892) Properties From SPT Reference (Kulhawy & Mayne, 1990) Peck, Hanson and Thornburn: ≈ 54 - 27.6034 exp(-0.014N’) Figure 4.12 φ Schmertmann ϕ ≈ tan-1[ N / (12.2 + 20.3 σ’/pa’) ] 0.34 Figure 4.13 and Equation 4.11 Terzaghi and Peck (1967): 0.06 N Equation 4.59 Su (bar) Hara 1974: 0.29 N0.72 Equation 4.60 OCR for clay Mayne and Kemper ≈ 0.5 N / σ’o (σ’o in bar) Figures 3.9 and 3.18 Dr Gibbs and Holtz's F igures Figures 2.13 and 2.14 Notations (1) (2) (3) (4) (5) (6) (7) (8) limit φ below tip 40° 36° contributed zone for tip resistance 2B 11.5B 2B 11.5B 2B 11.5B 2B 11.5B φ, if from SPT, is correlated by Peck, Hanson and Thornburn Schmertmann Peck, Hanson and Thornburn Schmertmann Su, if from SPT, is correlated by Terzaghi and Peck Notations (1h) (2h) (3h) (4h) (5h) (6h) (7h) (8h) limit φ below tip 40° 36° contributed zone for tip resistance 2B 11.5B 2B 11.5B 2B 11.5B 2B 11.5B φ, if from SPT, is correlated by Peck, Hanson and Thornburn Schmertmann Peck, Hanson and Thornburn Schmertmann Su, if from SPT, is correlated by Hara TABLE 7a Correlations of soil properties from SPT TABLE 7b Notations for combinations of correlations between soil parameters and standard penetration test results and their manner of application

21 has proven to be unreliable through the years—as shown, for example, by Olsen and Flaate (1967)—it was founded on a solid theoretical basis and is still used in construction in about half of the states in the country. The equation’s traditional for- mulation—as used, for example, in the Massachusetts State Building Code (Massachusetts, 1997)—includes an FS of 6, which needs to be recognized. The Gates equation (Gates, 1957), while empirical, was found to provide reasonable results (e.g., Olsen and Flaate, 1967; Long et al., 1998). The equation was further enhanced by Richard Cheney of the FHWA (FHWA, 1988) (see also Fragaszy et al. 1985), based on statistical correlations with static load tests and has the fol- lowing format: (27) where: Ru = Ultimate capacity (tons) E = Gross energy of pile hammer, ft-lb Note: The equation includes an 80% efficiency factor on the rated energy, which is a value between 75% and 85% recommended by Gates (1957) for drop hammers and all other hammers, respectively. N = Number of blows per inch 2.5.2.4 Dynamic Measurement: The Case Method The Case method (Goble et al., 1970 and Rausche et al., 1975) is often used in field evaluations, as it is built into Pile Dynamics Inc.’s Pile Driving Analyzer (PDA), the most commonly used system for obtaining dynamic measurements during pile driving in the United States. The method is based on simplified pile and soil behavior assumptions (free end and plastic soil), resulting in a closed form solution related to the impact and its reflection from the tip. With the years, at least five different variations of the method have evolved (GRL, 1999). The Case method utilizes a damping coeffi- cient (Jc) that is assumed to be associated with soil type. The influence of this factor on predicted static capacity depends on the stress wave reflected from the pile’s tip, hence on the driving resistance. The Case-damping coefficient was inves- R E Nu = × × −1 75 10 100. log Properties From CPT Reference (Kulhawy & Mayne, 1990) φ Robertson and Campanella: atan(0.1+0.38*log(qc/σ’)) Figure 4.14 and Eq. 4.12 Su (bar) Theoretical: ( qc - σo ) / Nk qc and σo in bars. Eq. 4.61 OCR for clay Mayne: 0.29 qc / σ’o qc and σo in bars. Figure 3.10 Dr Jamiolkowski: 68 log(qcn) – 68 qcn = 0a c ’P ’q σ (dimensionless) q’c = qc / Kq Kq = 0.9 + Dr/300 qc and σ’o in bars. Figure 2.24 and Eq. 2.20 TABLE 8 Correlations of soil properties from CPT Category Method Advantages Disadvantages Comment Design Stage WEAP (Smith, 1960, Goble et al., 1976) - Equipment Match - Drivability Study - Structural Stresses - Non unique Analysis - Performance sensitive to field conditions - Required for Construction - Required Evaluation for capacity predictions ENR (Wellington, 1892) - Sound Principles - Common use - Unreliable - Needs to be examined without a built in FS. Gates (Gates, 1957) - Empirical - Common use - Depends on original database - Found to be more reliable than other equations Dynamic Equations FHWA version of Gates Eqn. (FHWA, 1988) - Correction based on additional data - Depends on database - Was found to be reliable Signal Matching (e.g. CAPWAP) (Goble et al., 1970) - Solid principle of matching calculations to measurements by imposing msd. B.C. - Stationary soil forces - Expensive - Requires time - Office Method - Found reliable at BOR Case Method (Goble et al., 1970, Rausche et al., 1975) - Simplified Analysis - Field Method - Requires local calibration - Presumed dependency of soil conditions found baseless - Was found reliable with local calibration - How to obtain national or international calibration? Dynamic Measurements Energy Approach (Paikowsky, 1982, Paikowsky et al., 1994) - Simplified Analysis - Field Method - Shows long-term capacity which may not be present at EOD - Ideal for construction NOTES: ENR = Engineering News Record; FS = Factor of Safety; BOR = Beginning of Restrike; EOD = End of Driving. TABLE 9 Dynamic methods for evaluating pile capacity: advantages, disadvantages, and comments

22 tigated through a back calculation (to match the measured static capacity). The results (see section 2.5.3.2.) suggest that there is no correlation between the soil type and the Case- damping coefficient. The recommended practice is to use the Case method based on a specific site/area calibration (GRL, 1999). This approach, in conjunction with the application of the method for maximum resistance (RMX), has proven worthwhile. Accumulated experience on extensive jobs in the Boston area (e.g., Geosciences Testing and Research, Inc. 1997, 1998) has demonstrated the effectiveness of the Case method, when calibrated. A statistical examination of local calibration was performed in Florida by McVay et al. (2000). The results of this analysis suggest that for 48 case histories, the ratio of the static pile capacity to the Case method pre- diction at EOD was 1.344 ± 0.443 (mean ± 1 SD). As no generic conditions exist for the use of the Case method, international or national calibrations are unrealistic. Because the projection of local calibration (based on good experience and practice) beyond the geographical location may be unwise or unsafe, the Case method was excluded from the dynamic analyses examined for this project. 2.5.2.5 Dynamic Measurement: The Energy Approach The Energy Approach uses basic energy relations in con- junction with dynamic measurements to determine pile capacity. The concept was first presented by Paikowsky (1982) and was examined on a limited scale by Paikowsky and Chernauskas (1992). Extensive studies of the Energy Approach method were carried out by Paikowsky et al. (1994) and Paikowsky and LaBelle (1994). The underlying assumption of this approach is the balance of energy between the total energy delivered to the pile and the work done by the pile/soil system. The basic Energy Approach equation is (28) where Ru = maximum pile resistance, Emax = measured maxi- mum energy delivered to the pile, Dmax = measured maximum pile top displacement, and Set = permanent displacement of the pile at the end of the analyzed blow, or 1/measured blow count. For further details regarding the Energy Approach method see Paikowsky et al. (1994) and Paikowsky (1995). 2.5.2.6 Dynamic Measurement: The Signal Matching Techniques The signal matching technique is often referred to as post- driving analysis or the office method. With the availability of faster, portable computers, it became reasonably simple to conduct the analysis in the field, although the field method analyses cannot be carried out for each blow during driving. R EDu = + −( ) max maxSet Set2 The response of the modeled pile-soil system (e.g., force at the pile top) under a given boundary condition (e.g., mea- sured velocity at the pile top) is compared to the measured response (force measured). The modeled pile-soil system or, more accurately, the modeled soil that brings about the best match (visual graphical match) between the calculated and measured responses, is assumed to represent the actual soil resistance. The static component of that resistance is assumed to be the pile’s capacity and reflects that time of driving. The signal matching procedure was first suggested by Goble et al. (1970), utilizing the computer program CAPWAP. Others developed similar analyses, (e.g., Paikowsky, 1982; Paikow- sky and Whitman, 1990) utilizing the computer code TEPWAP. The TNO program was developed by Midden- drop and van Weel (1986), which led to improvements and to the CAPWAPC program, which is used to date. 2.5.3 The Controlling Parameters 2.5.3.1 Overview Preliminary examination of the parameters controlling the performance of the dynamic analyses was carried out prior to a final detailed evaluation of these methods, leading to the calculation of appropriate resistance factors. Such examina- tion influenced the subcategorization of the dynamic meth- ods (according to the important controlling parameters), hence directing the user to utilize the appropriate resistance factor according to the relevant conditions of the employed method. For example, if soil type is a controlling factor and the accu- racy of the signal matching method is largely affected by soil type, evaluation of the method for different soil types will result in the development of different resistance factors depending on the soil type. Conversely, if soil type does not control the accuracy of the specific dynamic method, cate- gorization based on soil type is neither desired nor pursued. The following sections outline the logic used for the pre- liminary examination of the controlling parameters, the analyses, and the results. The rationale presented in this sec- tion follows previous studies by Paikowsky et al. (1994), Paikowsky (1995), Paikowsky et al. (1995), and Paikowsky and Chernauskas (1996). Paikowsky and Stenersen (2000, 2001) present more detailed results related to the dynamic analyses of this study and are provided in Appendix B. The evaluation of static capacity through data derived from pile driving is based on the concept that the driving operation induces failure in the pile-soil system, (i.e., a very fast load test is carried out under each blow). Dynamic analyses encounter three fundamental difficulties: (1) correct formulation of the penetration process (e.g., soil motion, soil plugging etc.), (2) separation of the static resistance out of the total resis- tance overcome during penetration, and (3) time dependent pile capacity (Paikowsky, 1995). The parameters controlling the accuracy of the dynamic predictions reflect, therefore, the ability of each method to address the above difficulties.

23 Based on the concept of a pile loading to failure under each blow, it has traditionally been assumed that during high driv- ing resistance (i.e., refusal) there is not sufficient pile pene- tration to mobilize the full pile capacity (Chellis, 1961). Therefore the dynamic methods are deficient under high driv- ing resistance, categorized as equal or above 12BPI (Blows Per Inch) or approximately 5BPcm (Blows Per cm) (Massa- chusetts Highway Department, 1988). Soil type is also believed to have a major effect on the dynamic analyses because soil damping parameters are com- monly employed to represent viscous resistance in the model- ing of the soil’s dynamic behavior. This viscosity is assumed to be soil type dependent and associated with intrinsic soil properties. High viscosity values are expected for cohesive soils and low viscosity values are expected, therefore, for cohesionless soils. Naturally, under a given velocity, high vis- cous values are associated with higher dynamic resistance and logically should prove more difficult to accurately define the static resistance. The effect of time is well recognized but poorly quantified. With time, piles undergo a decrease or increase of capacity, known as relaxation and set-up, respectively. While the resis- tance during driving and its static component represent the conditions encountered during penetration, the major inter- est remains the long-term ability of the pile to carry load dur- ing its service life. The examination of the dynamic-method predictions with static load tests (often carried out long after the driving) therefore remains valid. The predictions can be assessed in relation to the time at which the data have been obtained (i.e., EOD or BOR). The following sections provide a short summary of the process in which the importance of each of the above assumed controlling parameters was examined. The results are used to evaluate additional possible controlling factors, laying down the framework for the detailed evaluation of the dynamic methods and the resulting resistance factors. More details are provided by Paikowsky and Stenersen in Appendix B. 2.5.3.2 The Effect of Soil Type The effect of soil type was examined in two ways: (1) the correlation between the parameters assumed to be soil type dependent and soil type, i.e., damping parameters; and (2) the accuracy of the predictive methods relative to the soil type. Figures 8 and 9 present the relationship between soil type and Smith-damping parameters (Smith, 1960) used in approx- imately 370 CAPWAP analyses from PD/LT2000 for the tip and side pile resistances, respectively. Figure 10 presents the back-calculated Case-damping coefficient required to obtain a match between the predicted capacity and the measured sta- tic capacity for 290 case histories from the PD/LT database (Paikowsky et al., 1994). All three figures clearly indicate that no unique relationship exists between soil type and damp- ing parameters, suggesting that mechanisms other than the soil type control the value that should be used as a damping factor. A summary of the statistics obtained when examining the accuracy of the signal matching technique (specifically CAPWAP) based on soil type is presented in Table 10. The sta- tistics shown are the mean and standard deviation of a normal 0 0.5 1 1.5 2 2.5 3 Smith Tip Damping (sec/m) So il Ty pe Gravelly Sand Sandy Gravel Clayey Sand Clay Silty Clay Sandy Clay Clayey Silt Silt Sandy Silt Silty Sand Sand Gravel Rock Till 1 sec/m = 0.3048 sec/f t 5.492 3.412 10.102 4.380 0 0.5 1 1.5 2 2.5 3 Smith Side Damping (sec/m) So il Ty pe Gravelly Sand Sandy Gravel Clayey Sand Clay Silty Clay Sandy Clay Clayey Silt Silt Sandy Silt Silty Sand Sand Gravel Rock Till 1 sec/m = 0.3048 sec/f t 3.048 Figure 8. Soil type at the pile’s tip versus Smith tip damping coefficients used in CAPWAP for 372 PD/LT2000 pile-cases. Figure 9. Soil type at the pile’s side versus Smith side damping coefficients used in CAPWAP for 371 PD/LT2000 pile-cases.

24 distribution function for the ratio of the pile’s static capacity (based on Davisson’s failure criterion) to the pile capacity obtained in the CAPWAP analysis. There are no significant differences between clay and till versus sand and silt that jus- tify analysis categorization based on soil type. Although the case histories for piles found on rock provide different val- ues, the numbers are based on a small subset of 15 pile case histories, compared to 100 and 265 pile case histories for the other soil type categories. Table 10 provides further examination of time of driving and driving resistances as subsets of the soil type categoriza- tion. Two sets are examined based on the time of driving: EOD and last BOR, (i.e., in the case of multiple restrikes, only the last restrike is considered for the analysis). The results suggest that the time of driving significantly affects the performance of the CAPWAP prediction, regardless of soil type. The mean values for the BOR sets are closer to one, while the mean values for the EOD are closer to two. The COVs show values of 0.33 and 0.39 for BOR, while the EOD ratios are 0.55 and 0.85, indicating the existence of a sub- stantial scatter. Again, the cases examined for piles in rock are not indicative and are excluded from being meaningful in respect to soil type effect. Further evaluation of the records was carried out on the basis of driving resistance. The division between cases for which the driving resistance is smaller or greater than 5BPcm (5 blows per centimeter), examines the aforementioned notion of refusal and the expected accuracy of the dynamic methods. The results, shown in Table 10, suggest that analy- ses were less accurate and had larger scatter in cases for which the driving resistance was smaller than 5BPcm than when driving resistance was above 5BPcm. Though driving resis- tance seems to be an important factor, clear understanding of its influence on the accuracy of the dynamic methods calls for additional investigation, which is briefly presented in sec- tion 2.5.3.4. In summary, while the performance of the signal matching analysis (CAPWAP) is not well correlated to soil type, other factors associated with soil type may be important (e.g., low driving resistance in soft cohesive soils or gain of capacity with time); but soil type itself does not appear to be impor- tant. The data presented in Table 10 suggests that time of driv- ing must be considered and driving resistance needs to be further examined. 2.5.3.3 The Effect of Time on Tested Capacity Penetration of piles into fine-grained soils causes compres- sion and disturbance, resulting in soil strength during driving So il Ty pe Clay Silty Clay Sandy Clay Clayey Silt Silt Sandy Silt Clayey Sand Silty Sand Sand Gravelly Sand Sandy Gravel Gravel Rock Till -1.86 -5.04 -2.25 7.04 1.51 1.56 2.22no. of cases = 290 -1.5 0.0 1.5-1.00 -0.50 0.50 1.00 Case Damping Coeff icient, Jc Figure 10. Soil type at the pile’s tip versus back calculated Case-damping coefficient (Jc) based on static load test results for 290 PD/LT pile-cases (Paikowsky et al., 1994). Clay & Till Sand & Silt Rock Mean 1.352 1.517 0.930 Standard Deviation 0.723 1.085 0.172 Number of Cases 100 265 15 Time of Driving EOD BOR(last) EOD BOR(last) EOD BOR(last) Mean 1.634 1.133 2.068 1.193 0.968 0.925 Standard Deviation 0.899 0.444 1.765 0.391 0.132 0.203 Number of Cases 45 40 77 116 7 7 Blow Count (BPcm) < 5 ≥ 5 < 5 ≥ 5 < 5 ≥ 5 < 5 ≥ 5 < 5 ≥ 5 < 5 ≥ 5 Mean 1.127 1.725 0.750 1.315 2.191 1.458 1.126 1.283 1.070 0.952 0.671 0.879 Standard Deviation 0.637 0.807 0.241 1.160 1.901 0.512 0.386 0.355 ----- 0.136 0.163 0.230 Number of Cases 35 35 11 10 64 13 74 40 1 6 3 3 NOTES: EOD = End of Driving; BOR(last) = Beginning of the last restrike; BPcm = Blows per centimeter TABLE 10 Statistical parameters of the ratio between static capacity (Davisson’s Criterion) and signal matching analysis (CAPWAP) categorized according to soil type, time of driving and driving resistance

25 that differs from its long-term strength, thus affecting pile capacity. Although factors such as thixotropy and aging con- tribute to this phenomenon, the migration of pore water is the most significant cause of capacity gain with time. Measure- ments carried out on a model (Paikowsky and Hart, 2000) and full-scale piles (Paikowsky and Hajduk, 1999, 2000) show that pore pressure at magnitudes similar to the total soil pres- sure creates in clays around the pile’s shaft zones of about zero effective stress, resulting in almost a complete loss of frictional resistance. Paikowsky et al. (1995, 1996) examined the static and dynamic gain of capacity with time based on radial consolidation; a normalization process was followed, allowing for comparison between different pile sizes. Table 11 presents a summary of parameters describing the pile capacity gain with time based on static and dynamic testing. The slope of the relation between the static capac- ity and the maximum static capacity (scale of 0 to 1) to the elapsed time after driving (logarithm scale) for a 152.4 mm radius (1 ft diameter) pile is denoted as Cgt. Similar relations for the ratio of dynamic capacity (with time) to the maximum static capacity result in a slope denoted by the parameter Cgtd. The time required for the standard pile to gain 75% of its max- imum capacity is denoted as t75. The time extrapolation for any desired pile size is achieved through the relationship of t75 (pile) = 4r2 t75 (table) (29) For which r = the desired pile radius (ft.) or its equivalent for a pile of different shape. The data in Table 11 show that while the rate of capacity gain is similar according to both analyses (Cgt = 0.389, Cgtd = 0.348), the associated time for achieving 75% of the maxi- mum capacity (normalized for all piles to 304.8 mm diame- ter) is about 20 times greater when analyzed by static meth- ods than when analyzed by dynamic methods. In other words, dynamic testing and analyses (namely CAPWAP), while fol- lowing the physical behavior of capacity gain, exhibit this gain much faster than the actual gain monitored by the static load test results. The ramifications of these conclusions are that (1) actual gain of capacity is much slower than that exhib- ited by the dynamic methods, (2) scheduling of construction or testing based on capacity gain should consider the reason for time evaluation (i.e., actual loading in construction or dynamic testing as part of quality control), and (3) at present, the dynamic methods evaluation should concentrate on the long-term pile capacity. 2.5.3.4 The Effect of Soil Motion Overview. Paikowsky and Chernauskas (1996) show that the stationary soil assumption, under which the soil/pile interac- tion models were developed, does not reflect the physical phenomenon that occurs during pile driving. Pseudo-viscous damping serves as a mechanism to absorb energy; but, as it does not reflect the actual phenomenon, it cannot be corre- lated to physical properties (e.g., soil type) or time of driving. If the motion of the displaced soil is a major factor con- tributing to energy loss during driving, a substantial portion of the dynamic resistance should be a function of two param- eters: (1) acceleration of the displaced soil (especially at the tip) that can be conveniently examined as a function of the driving resistance, and (2) mass/volume of the displaced soil that is a function of the pile geometry, namely, small vs. large displacement piles. A brief summary of the findings described by Paikowsky and Stenersen regarding the above two factors follows. Further details of their research are pro- vided in Appendix B. Soil Acceleration/Driving Resistance. The energy loss through the work performed by the displaced soil mass at the tip is directly related to the acceleration of this mass. The detailed evaluation of the soil’s motion at the tip is beyond the scope of the present research and is described by Hölscher (1995), Hölscher and Barends (1996), and Hajduk et al. (2000). The indirect evaluation of these accelerations can be performed through analysis of the driving resistance, which is the measure of the pile’s final displacement under each hammer blow. With low driving resistance (easy driving), high acceleration and velocity (i.e., free-end analogy) are developed at the tip. In the case of high driving resistance (hard driving), there is small acceleration at the tip, resulting in little, if any, mobilization of the soil mass beyond a radi- ating elastic wave. The corresponding energy loss due to soil motion is, therefore, small. Static Data Sets LTT and PUT/LTT Dynamic Data Set PD/LTT ALL DATA Cgt t75* gtd t75** gt t75** No. of Cases 15 5 7 6 22 11 Average for all piles in set. 0.389 385.0 0.348 21.3 0.376 186.6 Standard De- viation 0.119 226.3 0.068 7.9 0.106 237.9 C C Notes: *closed-ended pipe piles only; **t75 = time for a standard pile (0.3048m radius) to gain 75% of its maximum capacity; Cgt = rate of pile capacity gain with the logarithm of time TABLE 11 Summary of static-and-dynamic-based capacity gain with time parameters based on data sets (Paikowsky et al. 1996)

26 To evaluate the blow count that identifies the transition between easy and hard driving (high and low soil acceleration) the ratio between the static capacity and the CAPWAP pre- diction (KSW) by blow count for all pile case histories in PD/LT2000 was determined, as presented in Figure 11a. Fig- ure 11b presents the data separated into intervals of 8 BP10cm (2BPI), with the mean and standard deviation of each group graphed as a point and an error bar against the mid point blow count of the interval. For example, for driving resistance between 0 and 8BP10cm there were 42 case histories with a mean of 2.506 and a standard deviation of 2.217 plotted at the center of the interval, i.e., at 4BP10cm. The data pre- sented in Figure 11b show that for the first two intervals (up to 16BP10cm) the predicted capacity was substantially lower than for all other intervals with a significantly higher scatter. After approximately 16 blows per 10cm, the mean and stan- dard deviation of the individual intervals fall within the range of all case histories. The boundary of the dynamic method evaluation based on driving resistance was defined, there- fore, as 16BP10cm (4BPI). Displaced Soil/Pile Area Ratio. The volume of the displaced soil is identical to the volume of the penetrating pile, except when pile plugging takes place (Paikowsky and Whitman, 1990). The piles, therefore, can be classified as small (e.g., H and unplugged open pipe) and large (e.g., closed pipe and square concrete) displacement piles. Additional classification of open-pipe piles can be made according to a tip-area ratio similar to that used for soil samplers (Paikowsky et al., 1989). As most soil displacement takes place at the tip area, the classification of piles can be better served by looking at the ratio between the pile’s embedded surface area and the area of the pile tip (Paikowsky et al., 1994): (30) Using this ratio, a pile traditionally referred to as a “large dis- placement” pile can behave like a “small displacement pile” if it is driven deeply enough. A quantitative boundary of AR = 350 between “small” and “large” displacement piles was pro- posed by Paikowsky et al. (1994). Figure 12a presents the relationship between AR and the ratio of the static capacity over CAPWAP prediction (KSW) for all pile case histories in PD/LT2000. The data are sepa- rated into AR intervals of 175, with the mean and standard deviation of each group graphed as a point and error bar at A AAR skin tip = = Surface area in contact with soil Area of pile tip (a) (b) 0 8 16 24 32 40 48 56 64 72 80 88 Blow Count (blows/10cm) 0 1 2 3 4 K SW 0 2 4 6 8 10 12 14 16 18 20 Blow Count (blows/inch) 0 40 80 120 160 200 240 280 320 360 400 Blow Count (blows/10cm) 0 1 2 3 4 K SW = Lo ad Te st Re su lts CA PW A P o r TE PW A P Pr ed ic tio n s 0 10 20 30 40 50 60 70 80 90 100 Blow Count (blows/in) no set no set 42 66 64 38 32 25 15 16 8 16 60 no. of cases in 8 blows/10cm interval mean for all cases = 1.452 standard deviation for all cases = 0.985 Total no. of cases = 382 6.85, 11.26, 5.97, 9.38, 5.26, 4.75, 4.41 4.72 LG SM DISP DISP Sand & Silt Clay & Till Rock Figure 11. The ratio of static capacity to dynamic signal matching prediction, KSW versus blow count for all pile- cases in PD/LT2000 (a) all data points, and (b) data grouped in intervals of 8 blows/10cm (2BPI). 0 175 350 525 700 875 1050 1225 1400 1575 Area Ratio, AR 0 1 2 3 4 K SW = Lo ad Te st Re su lts CA PW A P o r TE PW A P Pr ed ict io n s 111 139 18 12 11 5 3 7 no. of cases in intervals of 175 mean for all cases = 1.452 standard deviation for all cases = 0.985 Total no. of cases = 382 76 0 1050 2100 3150 Area Ratio, AR 0 1 2 3 4 K SW = Lo ad Te st Re su lts CA PW A P o r TE PW A P Pr ed ict io n s 16 21 6 8 10 10 no. of cases in intervals mean for all cases = 1.460 standard deviation for all cases = 0.734 Total no. of cases = 71 175350525 (b) (a) Figure 12. KSW versus area ratio, (a) for all pile-cases in PD/LT2000 and (b) for 71 pile-cases with driving resistance exceeding 16 BP10cm (4BPI) at the EOD.

27 the midpoint AR of the interval. For example, for the 139 piles with AR between 175 and 350, the mean KSW, 1.656, and the standard deviation, 1.425, are plotted at the center of the interval (i.e., AR 262.5). Figure 12a suggests that piles with an AR smaller than 350 present less accurate predictions and larger scatters compared to the mean and the scatter of all cases. Above an AR of 350, the mean and standard deviation of the individual intervals fall within the range of all cases. Because driving resistance may affect the data, in Figure 12a the influence of the area ratio was further examined for piles with a driving resistance greater than 16 BP10cm at EOD. Figure 12b presents the relationship between AR and KSW for 71 case histories answering to this criterion. These data suggest even when excluding the easy driving resistance effects, the accuracy of the dynamic predictions are still lower and have a larger scatter for piles with AR smaller than 350. The boundary of AR = 350 between small and large dis- placement piles was therefore confirmed, based on database PD/LT2000. 2.6 DRILLED SHAFTS— STATIC ANALYSIS METHODS Based on the established state of practice in design (reviewed in section 2.1 and presented in Appendix A), the following analysis methods and correlations have been used for the static capacity evaluation of the drilled shaft database: 1. FHWA Method (Reese and O’Neill, 1988)—β method and α method were used for sand and clay respectively. For the undrained shear strength, Su, the SPT correlation given by Terzaghi and Peck (1967) was used. 2. R&W Method (Reese and Wright, 1977)—for sands while for sand and clay mix layers the α method was used for the clay. 3. C&K Method (Carter and Kulhawy, 1988)—for rock. 4. IGM Method (Intermediate Geomaterials) (O’Neill et al., 1996; O’Neill and Reese, 1999). The design assumed a smooth rock socket for skin friction and closed joints for end bearing. Details of the analysis methods, the analyzed case histo- ries, and the obtained results are summarized in Appendix C. 2.7 LEVEL OF TARGET RELIABILITY 2.7.1 Target Reliability and Probability of Failure The utilization of LRFD requires the selection of a set of target reliability levels, which determine the probability of failure and, hence, the magnitude of the load and resistance factors (see section 1.3.1 and Figure 2). The probability of failure represents the probability for the condition at which the resistance multiplied by the resistance factors will be less than the load multiplied by the load factors. When fitting LRFD to ASD, the issue is less significant because, in prac- tice, the factors are established to conform (often conserva- tively) to existing factors of safety. When calibrating for a database, however, the establishment of an acceptable proba- bility of failure is cardinal, including the question of a new design versus the existing state of practice. An approximate relationship between probability of failure and target reliabil- ity for a lognormal distribution was presented by Rosenbleuth and Esteva (1972) and is commonly in use (e.g., Withiam et al., 1998): pf = 460 e−4.3β (31) Baecher (2001) shows, however, that this approximation is not very accurate below β of about 2.5; and Table 12 provides a comparison between the approximation and the “exact” numbers for different values of β that suggests significant errors, especially in the zone of interest for foundation design, (β = 2 to 3). 2.7.2 Concepts for Establishing Target Reliability 2.7.2.1 General Methods of Approach Three accepted methods exist to determine probabilities of an event occurring: (1) historical data providing the results of frequent observations, (2) mathematical modeling derived from probability theory, and (3) quantification of expert sys- tems (Benjamin and Cornell, 1970). Combination of the three, when possible, can lead to a practical tool in design (e.g., Zhang et al., 2002, for dam slope failure). Such knowledge does not exist for foundations, and the selection of target reliability lev- els is a difficult task as these values are not readily available β Rosenbleuth and Estevas’ pf Exact pf Percent Error 2.0 8.4689E- 2 2.2750E-2 272.3% 2.5 9.8649E- 3 6.2097E-3 58.9% 3.0 1.1491E- 3 1.3500E-3 -14.9% 3.5 1.3385E- 4 2.3267E-4 -42.5% 4.0 1.5592E- 5 3.1686E-5 -50.8% 4.5 1.8162E- 6 3.4008E-6 -46.6% 5.0 2.1156E- 7 2.8711E-7 -26.3% 5.5 2.4643E- 8 1.9036E-8 29.5% 6.0 2.8705E- 9 9.9012E-10 189.9% TABLE 12 Comparison between Rosenbleuth and Esteva approximation and series expansion labeled “Exact” of the probability of failure (pf) for different values of reliability index (β) (Baecher, 2001)

28 and need to be generated or selected (Payer et al., 1994). Tar- get reliability levels vary from one application to another due to various factors, including implied reliability levels in cur- rent design practice, failure consequences, public and media sensitivity, types of users and owners, design life of a struc- ture, and other political, economic, and societal factors. For a general view, see Whitman (1984) and Becker (1996). Two approaches to generating target reliability levels are used in general: (1) calibrated reliability levels that are implied in currently used codes, and (2) cost-benefit analysis. The first approach is commonly used to develop reliability- based codified design, such as LRFD. The target reliability levels developed according to this approach are based on cali- brated values of implied levels of uncertainty in a currently used design practice. The argument for using this approach is that a code documents an accepted practice, and, as such, can be used as a launching point for code revision and cali- bration. Any adjustments in the implied levels should be for the purpose of creating consistency in reliability among the resulting designs when using the reliability-based code. Using the same argument, it can be concluded that target reli- ability levels used in one industry might not be fully appli- cable to another industry. Cost-benefit analysis, the second approach to generating target reliability levels, is used effectively in dealing with designs for which failures result only in economic losses and consequences. Since structural failures might result in human injury or loss of life, the use of this method might be very dif- ficult because of its need for assigning a monetary value to human life. One way to avoid the need to measure the mon- etary value of human life is to assign probabilities of failure as a function of both, monitoring cost and loss of lives (see, e.g., Zhang et al., 2002). 2.7.2.2 Calibration A number of efforts for the purpose of calibrating a new generation of structural design codes have resulted in the development of target reliability levels (i.e., safety indices, or β values). The general methodology for code calibration based on specific reliability theories, using second-moment reliability concepts, is outlined by Melchers (1987) and oth- ers. Melchers notes that frequently the information is insuf- ficient for this determination and one must make a “semi- intuitive” judgment in selecting target reliability, βt, values. While the specific reliabilities will be a function of the strength criteria needed for specific materials and load com- binations within designated structures, it is useful to have an indication of the range of possible target reliability levels. 2.7.3 Target Reliability for Structures Ellingwood et al. (1980) present ranges for reliability lev- els for metal structures, reinforced and prestressed concrete, heavy timber, and masonry structures, as well as discussions of issues that should be considered when making the cali- brations. Table 13 provides typical values for βT based on values provided by Ellingwood et al. (1980). The target reli- ability levels shown in Table 14 are used by Ellingwood and Galambos (1982) to demonstrate the development of partial safety factors. Moses and Verma (1987) suggested target reliability levels in calibrating bridge codes (i.e., AASHTO Specifications). Assuming that bridge spans of less than 100 ft are most com- mon, a βT of 2.5 to 2.7 is suggested for redundant bridges, and a βT of 3.5 for nonredundant bridges. Wirsching (1984) estimated the safety index, or β values, implied by the API specifications (American Petroleum Insti- tute, 1989) for fixed offshore structures in fatigue of tubular welded joints to be 2.5. He reported that this value is on the low end, because of the reference wave values. Madsen et al. (1986) discuss target reliability levels that were used by the National Building Code of Canada (National Research Council of Canada, 1977) for hot-rolled steel struc- tures. The values selected were βT = 4.00 for yielding in ten- sion and flexure, βT = 4.75 for compression and buckling Structural Type Target Reliability Level (βt) Metal structures for buildings (dead, live, and snow loads) 3 Metal structures for buildings (dead, live, and wind loads) 2.5 Metal structures for buildings (dead, live, snow, and earthquake loads) 1.75 Metal connections for buildings (dead, live, and snow loads) 4 to 4.5 Reinforced concrete for buildings (dead, live, and snow loads) - ductile failure - brittle failure 3 3.5 Note: The βt values are for structural members designed for 50 years of service. Member, Limit State Target Reliability Level (βt) Structural Steel Tension member, yield Beams in flexure Beams in shear Column, intermediate slenderness 3.0 2.5 3.0 3.5 Reinforced Concrete Beam in flexure Beam in shear Tied column, compressive failure 3.0 3.0 3.5 Masonry, unreinforced Wall in compression, inspected Wall in compression, uninspected 5.0 7.5 Note: The βt values are for structural members designed for 50 years of service. TABLE 14 Target reliability, levels for members, used by Ellingwood and Galambos (1982) TABLE 13 Target reliability levels by structural type [based on Ellingwood et al. (1980)]

29 failure, and βT = 4.25 for shear failures. These values are higher than those in Tables 13 and 14 because they reflect dif- ferent environmental loading conditions and, possibly, differ- ent design life. The Canadian Standard Association presented the following target failure probabilities for developing design criteria for offshore installation in Canadian waters (Mansour et al., 1994): 10−5 per year for failures that would result in great loss of life or have a high potential for envi- ronmental damage; and 10−3 per year for failures that result in small risk to life or a low potential for environmental dam- age. (It is important to note that no direct relationship exists between general probability of failure and annual probability of failure.) Madsen et al. (1986) also discuss target reliability levels that were used by the Nordic Committee on Building Regu- lations (1978). Target reliability values were selected depending on the failure consequences of a building: βT = 3.1 for less serious failure consequences, βT = 5.2 for very seri- ous failure consequences, and βT = 4.3 for common cases. 2.7.4 Geotechnical Perspective The review provided in section 2.7.3 suggests that typical target reliability for members and structures relevant to bridge construction varies between 1.75 and 3.0, with a target relia- bility of 2.5 to 2.7 for relevant bridges. Barker et al. (1991, p. A-51) state the following regarding target reliability index for driven piles: Meyerhof (1970) showed that the probability of failure of foundations should be between 10−3 and 10−4, which corre- sponds to values of β between 3 and 3.6. The reliability index of offshore piles reported by Wu, et al. (1989) is between 2 and 3. They calculated that the reliability index for pile sys- tems is somewhat higher and is approximately 4.0, corre- sponding to a lifetime probability of failure of 0.00005. Tang et al. (1990) reported that offshore piles have a reliability index ranging from 1.4 to 3.0. Reliability indices for driven piles are summarized in Table 5.4 [Table 15 of this report]. Values of β between 1.5 and 2.8 are generally obtained for the lognormal procedure. Thus a target value of β between 2.5 to 3 may be appropriate. How- ever, piles are usually used in groups. Failure of one pile does not necessarily imply that the pile group will fail. Because of this redundancy in pile groups, it is felt that the target relia- bility index for driven piles can be reduced from 2.5 to 3.0 to a value between 2.0 and 2.5. Zhang et al. (2001) used a first order reliability method to evaluate the reliability of axially loaded pile groups designed using the traditional concept of group efficiency. Group effects and system effects were identified as the major causes of the significantly greater observed reliability of pile foundations compared to the calculated reliability of single piles. Group effect relates to the combined action of any number of piles vs. a single pile. A system effect is the contribution of the superstructure stiffness to the load distribution and resistance. The calculated probability of failure of pile groups was found to be 1 to 4 orders of magnitude smaller than that of single piles, depending on the significance of system effects (changing the system bias factor λs from 1 to 2). Based on their study, Zhang et al. (2001) state that the target reliabil- ity index, βT, for achieving a specified reliability level should differ for an isolated single pile (β), an isolated pile group (βTG), and a pile system (βTS). They give the following rec- ommendations based on their research: 1. A βTG value of 3.0 requires a β of 2.0 to 2.8 if no sys- tem effects are considered. 2. A βTG value of 3.0 requires a β of 1.7 to 2.5 if a system effect factor of 1.5 is considered. Additional aspect to the increased reliability of deep foun- dations can be obtained from the limited data available regarding the loads, which actually arrive at the piles during their service. Tang et al. (1994) followed the response of drilled shafts during construction loading and found that, while 44% to 67% of the design load was measured at the pile’s top, only 6% to 13% of the design load arrived at the tip in the rock socket. In the design of drilled shafts the fric- tion or the end bearing are often being neglected, especially in rock sockets. This practice and the observed values sug- gest that piles are often underutilized (over conservative), a fact contributing to the reliability of pile foundations, which rarely fail. These facts, while recognized, cannot be consid- ered when assigning a target reliability value until more data are available and relevant load factors can be directly devel- oped for foundations. 2.7.5 Recommended Target Reliability 2.7.5.1 General Range for Single Piles and Pile Groups Based on the above review and the data presented, it seems reasonable to establish the target reliability between 2.0 and 2.5 for pile groups and as high as 3.0 for single piles. It is clear from the review that, while the redundancy of pile groups serves as the major reason for the decrease in tar- get reliability, no logical distinction was made (when choos- ing target reliability) between the target reliability of single piles and pile groups. One can evaluate the performance of the piles on the basis of their “redundancy.” A nonredundant Reliability Index, β Dead to Live Load Ratio Lognormal Advanced 1.00 1.6 – 2.8 1.6 – 3.0 3.69 1.7 – 3.1 1.8 – 3.3 TABLE 15 Reliability indices for driven piles (Barker et al., 1991)

30 member is one for which failure will directly affect the ele- ment carried by it (i.e., the column) with limited or no ability of other foundations supporting the same element to mitigate the effect of the failure of the member. Referring to Figure 13, one can intuitively see that, as three points define a plane, a failure of any deep foundation element in such a configura- tion cannot be mitigated by the others. Though details of the foundation scheme are important—see, e.g., Foundation Design Standards in the World (Japanese Geotechnical Soci- ety, 1998)—one can distinguish between a 5-member scheme (clearly redundant) and a 3- or fewer member scheme (non- redundant) for the purpose of establishing a target reliability. The evaluation of the resistance factors in the present study was originally carried out by using reliability indices of 2.0, 2.5, and 3.0 associated with pf = 2.28%, 0.62%, and 0.14%, respectively. This approach provided a reasonable range of values to investigate before the final target reliabil- ity values were set. 2.7.5.2 Recommended Concept and Targets Based on the review of the state of the art, the survey of common practice, and the evaluation of the above values, the following reliability indices and probability of failure were developed and are recommended in conjunction with meth- ods for capacity evaluation of single piles (see Figure 13): 1. For redundant piles, defined as 5 or more piles per pile cap, the recommended probability of failure is pf = 1%, corresponding to a target reliability index of β = 2.33. 2. For nonredundant piles, defined as 4 or fewer piles per pile cap, the recommended probability of failure is pf = 0.1%, corresponding to a reliability index of β = 3.00. 2.8 INVESTIGATION OF THE RESISTANCE FACTORS 2.8.1 Initial Resistance Factors Calculations The factors were evaluated using FORM (First Order Reli- ability Method) with dead load (DL) to live load (LL) ratios ranging from 1 to 4. The results for a bias of one and a coef- ficient of variation of 0.4 and target reliability values of 2.0, 2.5, and 3.0 presented in Figure 14, suggest very little sensi- tivity of the resistance factors to the DL to LL ratio. A simi- lar trend was observed using DL to LL ratio of 10. The large dead-to-live-load ratios represent conditions of bridge con- struction, typically associated with very long bridge spans. The relatively small influence of the dead-to-live-load ratio on the calculated resistance factors suggests that (1) the use of a DL to LL ratio of 2 or 2.5 as a typical value is reason- able, and (2) the obtained factors are, by and large, applica- ble for long span bridges. 2.8.2 Parameter Study—The Limited Meaning of the Resistance Factor Value The use of FORM requires an iterative process and hence a parametric study more easily obtained by using the FOSM relationships, assuming the results of both are within a close range (to be demonstrated in section 3.2.2). Figure 15 pre- sents such relations using Equation 10, the chosen load dis- tribution parameters (Equations 25 and 26), DL to LL ratio of 2.5 and a target reliability β = 2.33 (see section 2.7.5.2). The obtained relationship shows that a perfect prediction (λ = 1, COV = 0) would result with a resistance factor of (φ = 0.80. With a prediction method for which the bias is one but the distribution is greater (COV > 0), the resistance factor would sharply decrease so that for COV = 0.4 the resistance factor would reduce to φ = 0.44. The influence of the bias of the method (λ, or mean ratio of measured over predicted) on the resistance factor is equally important. As seen in the figure, an under predictive method (λ > 1) has a “built in” safety and hence a higher resistance factor is used in order to achieve the same target reliability as would be obtained by using a method which predicts, on average, more accurately (λ ≈ 1). For example, for methods having the same distribution (COV = 0.4), an underpredictive method with a bias of λ = 1.5 would result in a resistance factor φ = 0.67, whereas a method with a bias λ = 1.0 would result in φ = 0.44. Although Redundant Non - Redundant Logically Non-Redundant β = 2.33 Pf = 1.0%β = 3.00 Pf = 0.1% 0 1 2 3 4 5 DL/LL - Dead to Live Load Ratio 0.4 0.6 0.8 Re sis ta n ce Fa ct o r, φ General Case Bias = 1 COV = 0.4 β = 2.0 Pf= 2.28% β = 2.5 pf= 0.62% β = 3.0 Pf= 0.14% Figure 13. Redundant vs. non-redundant pile support and the current research recommendations of target reliability. Figure 14. Calculated resistance factors for a general case showing the influence of the dead-to-live-load ratio.

31 both methods predict the same way (i.e., have the same dis- tribution), the method, which predicts more accurately (lower bias) will result in having a resistance factor lower than the underpredictive method. The judgment of the methods’ eco- nomic value (“efficiency”) on the basis of the resistance value is therefore misleading. The same argument can be made regarding the misleading absolute values of the factor of safety disregarding the bias. The FS values in Table 1 seem to be high (and not attractive economically) for the sta- tic analyses compared to the dynamic prediction methods. Again these values are of limited meaning if the bias of the method is not considered. For example, if the bias of the sta- tic methods (to be discussed further in Chapter 3, section 3.5.2) is lower than 1 (overprediction), while the bias of the dynamic methods is greater than one (underprediction), the methods may have practically a similar “actual” FS (and hence economical viability). 2.8.3 The Design Methods’ Efficiency The values of the resistance factors alone (or the factors of safety) do not provide a measure for evaluating the effi- ciency of the design methods, as previously discussed. Such efficiency can be evaluated through the bias factor, and its COV, or the ratio of the resistance factor to the bias factor, i.e., φ/λ, as proposed by McVay et al. (2000). Figure 16 illus- trates the meaning of the efficiency factor showing that the ratio of φ/λ is systematically higher for methods which pre- dict more accurately regardless of the bias. The value of the 0 0.5 1 1.5 2 2.5 3 Bias (λ) 0.0 0.5 1.0 1.5 2.0 2.5 R es ist a n ce Fa ct o r (φ) FOSM λQL = 1.15 λQD = 1.05 COVQL= 0.2 COVQD =0.1 QD/QL = 2.5 β = 2.33 γD = 1.25, γL = 1.75 CO V = 0 0.2 0.4 0.6 0.8 0.5 COV = 1.00 Figure 15. Calculated resistance factors as a function of the bias and COV for the chosen load distributions and DD/LL ratio of 2.5. 0 0.2 0.4 0.6 0.8 1 COVR 0 0.2 0.4 0.6 0.8 E ffi ci en cy (φ /λ ) FOSM λQL = 1.15 λQD = 1.05 COVQL = 0.2 COVQD = 0.1 QD/QL = 2.5 β = 2.33 γD = 1.25 γL = 1.75 Figure 16. Illustration of the efficiency factor as a measure of the effectiveness of a design method when using resistance factors.

32 efficiency factor remains constant for all bias combinations for a given COV, leading to higher values for methods with a lower COV. Using the example given in section 2.8.2, a method with COV = 0.4, λ = 1.0, and φ = 0.44 will result in φ/λ = 0.44; a second method with COV = 0.4, λ = 1.5, and φ = 0.67 will result in the same φ/λ = 0.44. Thus, although one method presents a resistance factor of 0.67 and the other of 0.44, both methods have identical efficiency and should result in identical design; hence they have the same economic value. The efficiency of a given capacity prediction method can, therefore, be improved only through a reduction in its vari- ability (COV); alternatively, design methods need to be cho- sen based on their COV. This measure of efficiency needs to accompany prescribed resistance factors in order to avoid a misconception of the existence of a correlation between the economy of a design method and high resistance factors when compared to others. Similarly, such misconceptions exist between the economic value of a method and the lower level of a factor of safety, where a mean factor of safety (defined as FS x bias) repre- sents the economic value of the method (the lower the bet- ter), as proposed by Paikowsky et al. (1994).

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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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