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10 0.80 y = 1.1267x 0.70 No. of points = 160 Mean = 1.148 Std. Dev. = 0.039 Resistance factors using FORM 0.60 0.50 0.40 0.30 Driven Piles Static Analysis Driven Piles Dynamic Analysis 0.20 Drilled Shafts FOSM = FORM Linear 0.10 0.00 - 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Resistance factors using FOSM Figure 5. Comparison of resistance factors obtained using FOSM versus those obtained using FORM for a target reliability of 2.33 (Paikowsky et al., 2004). If the sum of the indicator function is Nf, i.e., the limit these assumptions should theoretically produce the same state function was gi 0 (in the failure region) for Nf num- results as the closed-form solutions. ber of times out of the total of N simulations carried out, 3. The power of the MCS is its ability to use varying distribu- then the failure probability, pf, can be directly obtained as tions for load and resistance. the ratio Nf /N. In summary, refinement in the calibration should be pur- Using the MCS process, the resistance factor can be calcu- sued, not refinement of the process used to calculate the reli- lated based on the fact that to attain a target failure probabil- ability index. The MCS, as discussed above, is quite adequate ity of pfT, NfT (Number of samples to obtain target failure at and understandable to the practicing engineer. Refinement the limit states) of the limit state must fall in the failure region. should be sought in the determination of the statistical param- Since in the present geotechnical engineering LRFD only one eters of the various components of force effect and resistance resistance factor is used while keeping the load factors constant, and using the load distributions available for the structural a suitable choice for the resistance factor would shift the limit analysis; this means focusing on the statistical parameters of state function so that Nf T samples fall in the failure region. the resistance. The resistance factor derived in this study using MCS is based on this concept. 1.4 Format for Design Kulicki et al. (2007) made several observations regarding Factor Development the process outlined above: 1.4.1 General 1. The solution is only as good as the modeling of the distri- AASHTO development and implementation of LSD and bution of load and resistance. For example, if the load is not LRFD have been driven primarily by the objectives of achiev- correctly modeled or the actual resistance varies from the ing a uniform design philosophy for bridge structural and modeled distribution, the solution is not accurate. In other geotechnical engineering thereby obtaining a more consis- words, if the statistical parameters are not well defined, the tent and rational framework of risk management in geotech- solution is equally inaccurate. nical engineering. 2. If both the distribution of load and resistance are assumed Section 1.3 detailed the principles of LRFD and described to be normally or lognormally distributed, a MCS using the calibration process. The philosophies of attaining this

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11 calibration, however, vary widely: values are chosen based 1.4.3 Code Calibrations on a range of already available parameters, based on expert opinion, based on comprehensive resistance calibration, or A procedure to rationally determine partial factors in the using the material factor approach. A previous effort to cal- design verification formulas based on reliability analysis is ibrate the ULS of deep foundations concentrated on com- termed "code calibration." Section 1.3.2 and the details in prehensive calibration of the resistance models as an integral Sections 1.3.3, 1.3.4, and 1.3.5 presented the analytical mean- entity (Paikowsky et al., 2004). This philosophy was based ing of the calibration in the LRFD methodology. One of the on the fact that in contrast to other engineering disciplines best known and most important studies in this area is by (e.g., structural analysis), the model uncertainty in geotech- Ellingwood et al. (1982) in which load and resistance factors nical engineering is dominant. The specifications provide an were determined based on a reliability analysis using FORM. ideal framework for prescribed comprehensive methodology Since then, a reasonable number of code calibration studies and, hence, direct calibration of the entire methodology, when have been carried out in structural engineering (e.g., Nowak, possible, results in highly accurate LRFD as demonstrated in 1999). However, rational code calibration studies for geo- the following sub-sections. This approach was followed by and technical engineering codes have only begun to be undertaken large in the development of the SLS (NCHRP Project 12-66) in the past decade or so (Barker et al. 1991; Phoon et al., 1995; and is followed (when possible) in this study as well. The Honjo et al., 2002; Paikowsky et al., 2004). calibration of shallow foundations for ULS has, however, Barker et al. (1991) proposed resistance factors for more complex aspects that cannot be (at present time) cal- the AASHTO bridge foundation code published in 1994 ibrated directly. Hence, Section 1.4.2 (based primarily on (AASHTO, 1994). The calibration was based on FOSM but Honjo and Amatya, 2005) is provided as a background to used back-calculation from factors of safety and introduced the diverse approach of the current research. a significant number of engineering judgments in deter- mining the factors along a not-so-clearly described process. Based on the difficulties encountered in using the work of 1.4.2 Material and Resistance Barker et al. (1991), the partial factors for deep foundations Factor Approach in the AASHTO specification were revised by Paikowsky et al. Some of the key issues in developing sound geotechnical (2004). In Paikowsky et al. (2004), a large database was devel- design codes based on LSD and LRFD are definition of char- oped and used in a directly calibrated model (an RFA approach acteristic values and determination of partial factors together together with a reliability analysis by FORM) to determine the with the formats of design verification (Simpson and Driscoll, resistance factors. The SLS calibration (NCHRP Project 12-66) 1998; Orr, 2002; Honjo and Kusakabe, 2002; Kulhawy and was developed in a similar approach, using MCS to determine Phoon, 2002). The characteristic values of the design param- the factors. Examples from both studies are provided in Sec- eters are conveniently defined as their mean values. tions 1.4.4 and 1.4.5. Phoon et al. (1995, 2000) carried out cal- The approach concerning design factor development for- ibration of the factors for transmission line structure founda- mats can be summarized as whether one should take a material tions based on MRFA by reliability analysis. Some simplified factor approach (MFA) or a resistance factor approach (RFA). design formats were employed, and factors were adjusted until In MFA, partial factors are directly applied to the character- the target reliability index was reached. Kobayashi et al. (2003) istic values of materials in the design calculation, whereas in have calibrated resistance factors for building foundations for RFA, a resistance factor is applied to the resulting resistance cal- the Architectural Institute of Japan (AIJ) limit state design culated using the characteristic values of materials. One of the building code (AIJ, 2002). This code provides a set of load and modifications of RFA is a multiple resistance factor approach resistance factors for all aspects of building design in a unified (MRFA) where several resistance factors are employed to be format. FORM was used for the reliability analysis, and MRFA applied to relatively large masses of calculated resistances. was the adopted format of design verification as far as the foun- The advantage of MRFA is claimed to be that it ensures a dation design was concerned. more consistent safety margin in design compared with RFA (Phoon et al. 1995, 2000; Kulhawy and Phoon, 2002). In gen- 1.4.4 Example of Code Calibrations--ULS eral, MFA originated in Europe whereas RFA originated in North America. However, both approaches are now used inter- The capacity of the comprehensive direct model calibra- changeably worldwide; for example, the "German approach" tion resistance factor approach is demonstrated. Large data- to EC7 coincides with RFA while Eurocode 7 allows several bases of pile static load tests were compiled, and the static and design approaches (both MFA and RFA), and the member dynamic pile capacities of various design methods were com- state can define their preference in their National Annex to pared with the nominal strength obtained from the static load the EC7. test. The geotechnical parameter variability was minimized

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12 60 22 0.15 55 0.14 20 0.14 50 0.13 18 0.12 45 0.12 16 0.11 40 0.1 0.1 14 Relative Frequency log normal Number of Pile Cases Number of Pile Cases Relative Frequency 35 distribution 0.09 mlnx = 0.233 12 lnx = 0.387 0.08 30 0.08 x = 0.387 normal distribution mx = 1.368 0.07 10 log normal 25 distribution normal distribution 0.06 0.06 8 mlnx = -0.293 20 lnx = 0.494 0.05 x = 0.620 15 0.04 6 0.04 0.03 10 4 mx = 0.835 0.02 0.02 5 2 0.01 0 0 0 0 0 0.5 1 1.5 2 2.5 >3 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 Ratio of Static Load Test Results over the Pile Capacity Prediction using the -API/Nordlund/Thurman design method Figure 6. Histogram and frequency distributions for Figure 7. Histogram and frequency distribution of all (377 cases) measured over dynamically (CAPWAP) measured over statically calculated pile capacities for calculated pile-capacities in PD/LT2000 (Paikowsky 146 cases of all pile types (concrete, pipe, H) in mixed et al., 2004). soil (Paikowsky et al., 2004). (indirectly) by adhering to a given consistent procedure in soil The first large LRFD bridge design project in New England parameters selection (e.g., NSPT [Number of Blows in a Stan- (including superstructure and substructure) based on AASHTO dard Penetration Test] correction and friction angle correla- 2006 specifications is currently under construction. A large tions), as well as load test interpretation (e.g., establishing the static load test program preceded the design. Identifiable details uncertainty in Davisson's criterion for capacity determina- are not provided, but Tables 2 and 3 present the capacity eval- tion and then using it consistently). Two examples for such uation for two dynamically and statically tested piles (Class A large calibrations are presented in Figures 6 and 7 for given prediction, submitted by the project consultant, Dr. Samuel specific dynamic and static pile capacity prediction methods, Paikowsky, about one month before testing) using the cal- respectively (Paikowsky et al., 2004). ibrated resistance factors for the specific pile/soil/analysis Further subcategorization of the analyses led to detailed method combination versus the "simplified" AASHTO version resistance factor recommendations based on pile type, soil of the resistance factor. In both cases, the calculated factored type, and analysis method combinations. Adherence to the capacity using the "simplified" resistance factor exceeded the uncertainty of each combination as developed from the data- unfactored and factored measured resistance (by the load test) in base and consistent calibrations led to a range of resistance a dangerous way, while the use of the calibrated resistance fac- factors (see, for example, Table 25 of NCHRP Report 507, tors led to consistent and prudent design. The anticipated sub- Paikowsky et al., 2004). Recent versions of the specifications structure additional cost has increased by 100% (in comparison (AASHTO, 2006, 2008) avoided the detailed calibrations and to its original estimate based on the AASHTO specifications), presented one "simplified" resistance factor ( = 0.45) for static exceeded $100 million (at the time of the load test program), analysis of piles, along with one design method (Nordlund/ and delayed the project 1 year. The power of the comprehen- Thurman). sive, direct RFA calibration based on databases versus arbitrary

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13 Table 2. H Pile--summary (14 177, penetration = 112 ft). Static: Static Pile Capacity Combinations: NCHRP 507 NCHRP 507 AASHTO LRFD Estimated resistance Factored resistance Factored specifications Factored Analysis combination capacity (Rn) factor for H resistance factor for H resistance 2006 resistance (kips) piles in sand (Rr) piles in mixed (Rr) resistance (Rr) ( ) soils ( ) factor ( ) -Method/Thurman (Steel Only) 894 268 179 0.30 0.20 Not specified -Method/Thurman (Box Area) 1,076 323 215 Nordlund/Thurman (Steel Only) 841 379 252 379 0.45 0.35 0.45 Nordlund/Thurman (Box Area) 1,023 460 307 460 FHWA Driven Ver. 1.2 (Steel Only) 845 FHWA Driven Ver. 1.2 (Box Area) 1,032 Notes: 1. Resistance Factors taken from the resistance factors for redundant structures listed in Table 25 of NCHRP Report 507 (Paikowsky et al., 2004). Recommended range for preliminary design. Reference: Static Pile Capacity and Resistance Factors for Pile Load Test Program, GTR report submitted to Haley and Aldrich, Inc. (H&A), June 21, 2006 (Paikowsky, Thibodeau, and Griffin). Note: Above DRIVEN values were obtained by inserting the friction values and unit weights directly into DRIVEN, limiting the friction angle to 36 . Dynamic: Sakonnet River Bridge Test Pile Program Portsmouth, RI--Summary of Dynamic Measurement Predictions and Factored Resistance (H Piles) Pile Time of Energy approach CAPWAP type driving EA1 (kips) 2 Rr (kips) CAP1 (kips) 2 Rr (kips) H EOD 481 0.55 265 310 0.65 202 BOR 606 0.40 242 434 0.65 2823 1 Values represent EOD predictions and average of all BOR predictions. 2 All factors taken from NCHRP Report 507 (Paikowsky et al., 2004) 3 Only factors for BOR CAPWAP appear in AASHTO (2006) specifications and are marked by shaded cells Reference: Pile Capacity Based on Dynamic Testing and Resistance Factors for Pile Load Test Program, GTR report submitted to H&A, July 17, 2006 (based on earlier submittals of data and analyses) (Paikowsky, Chernauskas, and Hart). Static Load Test Load Test Capacity (Davisson's Criterion): Qu = 378 kips at 0.68 in Resistance Factors NCHRP Report 507 and AASHTO Specifications: = 0.55 (1 test pile large site variability) = 0.70 (1 pile medium site variability) Factored Resistance: Rr = 208 to 265 kips Reference: Load Test Results presented and analyzed by H&A. assignments of resistance factors is clearly demonstrated in and Lu, 2006), large databases of foundation performance the first significant case of its use in New England. were accumulated and analyzed for direct RFA calibrations (Paikowsky et al., 2009a, 2009b). Examples of databases examining the performance of displacement analyses of 1.4.5 Example of Code Calibrations--SLS shallow foundations are presented in Figures 8 and 9 for the The factors associated with the SLS were evaluated under AASHTO (2008) and Schmertmann et al. (1978) settlement NCHRP Project 12-66. Following the development of ser- analysis methods, respectively. These robust analysis results viceability criteria for bridges (Paikowsky, 2005; Paikowsky allow direct calibration of resistance factors for applied loads

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14 Table 3. 42-in Pipe Pile--summary (diam. = 42 in, wall thickness (w.t.) = 1 in, 2-in tip, penetration = 64 ft). Static: Static Pile Capacity Combinations: Assumed Displaced Soil Volume Based on Uniform Wall Thickness (1.0 in) NCHRP 507 NCHRP 507 AASHTO LRFD resistance resistance Estimated Factored Factored specifications Factored factor for factor for Analysis combination capacity (Rn) resistance resistance 2006 resistance pipe piles in pipe piles in (kips) (Rr) (Rr) resistance (Rr) sand mixed soils factor ( ) ( ) ( ) -Method/Thurman (Steel Only) 924 324 231 - -Method/Thurman (30% Tip Area) 984 345 246 - -Method/Thurman (50% Tip Area) 1,084 0.35 380 0.25 271 Not specified - -Method/Thurman (70% Tip Area) 1,184 415 296 - -Method/Thurman (100% Tip Area, plugged) 1,335 467 334 - Nordlund/Thurman (Steel Only) 690 379 241 310 Nordlund/Thurman (30% Tip Area) 750 412 262 337 Nordlund/Thurman (50% Tip Area) 850 0.55 467 0.35 297 0.45 382 Nordlund/Thurman (70% Tip Area) 950 522 332 427 Nordlund/Thurman (100% Tip Area, plugged) 1,101 605 385 495 Notes: 1. Resistance Factors taken from the resistance factors for redundant structures listed in Table 25 of NCHRP Report 507 (Paikowsky et al., 2004). 2. Tip resistance for steel only included 2-in. wall thickness accounting for the driving shoe. Recommended range for preliminary design soil plug only. Reference: Static Pile Capacity and Resistance Factors for Pile Load Test Program, GTR report submitted to Haley and Aldrich, Inc. (H&A), June 21, 2006 (Paikowsky, Thibodeau, and Griffin). Static Load Test (Open Pipe Pile) Load Test Capacity (Davisson's Criterion): Qu = 320 kips at 0.52 in Resistance Factors NCHRP Report 507 and AASHTO Specifications: = 0.55 (1 pile large site variability) = 0.70 (1 pile medium site variability) Factored Resistance: Rr = 176 to 224 kips Reference: Load Test Results presented and analyzed by H&A. for a given SLS criterion (displacement). The data in Figures 8 The complexity of the ULS of shallow foundations (to be and 9 are related to the following: 1 ft (0.30 m) B 28 ft discussed in the next section) requires a multifaceted approach (8.53 m), Bavg = 8 ft (2.44 m), 1.0 L/B 6.79, L/Bavg = 1.55, in which combinations of calibrations are utilized for obtaining 25.2 ksf (1,205 kPa) qmax 177.9 ksf (8,520 kPa) for which the desired factors. The method of approach is presented in B and L are the footing width and length, respectively, and Chapter 2 of this report. Mutiple approaches are needed for the qmax is the maximum stress applied to the foundations under ULS of shallow foundations because of the following: the measured displacement. 1. The capacity of shallow foundations on granular soils under centric vertical load is calculated via a relatively simple 1.4.6 Perspective of Shallow Foundations model (the bearing capacity model without cohesion-related ULS Calibration factors, modified by shape and depth factors only). This The preceding sections have outlined the available for- type of foundation and loading is commonly tested and, mats of factor development and a powerful implementa- hence can be calibrated using a large database (the database tion via robust databases. The established RFA was utilized is presented in Section 3.2). in two extensive studies: one related to the ULS of deep foun- 2. Determination of the capacity of shallow foundations under dations (NCHRP Project 24-17) and one related to the SLS of combined loading conditions requires a multiparameter all foundations (NCHRP Project 12-66). model. The differentiation between favorable and unfavor-