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104 20 Temperature bias = 1.00 COV = 0.25 calculated lateral pressure (kPa) n = 12 Shrinkage and creep bias = 0.90 COV = 0.20 bias mean = 1.005 Wind (75-year maximum) bias = 0.85 COV = 0.25 bias COV = 0.215 Braking force (railways) bias = 1.00 COV = 0.10 15 There are no exact measurements available, but wind load is similar to other forces and a limited parametric study seems 10 to be reasonable. Experts (A.S. Nowak, personal communi- cation) suggest that a bias of 1.00 and COV of 0.15 should be 5 used for the lateral pressure due to live loads. 4.2.3.3 Summary of Horizontal Loads 0 0 5 10 15 20 Assuming that lateral loading due to dead load (LFD: lateral measured lateral pressure (kPa) force due to dead load) is mostly due to soil and surcharge, Figure 91. Measured versus calculated possibly compacted, the following load distribution and load residual earth pressures. Measured earth factors (load factors from AASHTO, 2007, Table 3.4.1-2) have pressures at Transport and Road Research been chosen for at-rest and active earth pressures: Laboratory experimental concrete retaining wall by Carder et al. (1977) and calculated LFD = bias of lateral loading due to dead load = 1.00, earth pressure using the incremental solution COVLFD = 0.30 and is assumed to follow lognormal proposed by Duncan and Seed (1986) distribution with the following distribution in soil unit (bias = measured/calculated). weight (assumed to follow normal distribution): = bias of soil weight = 1.00, COV = 0.10 for in-situ (natural) soil conditions, The mean of the bias was found to be 1.005 and the bias COV COV = 0.08 for engineered backfill (controlled was 0.215. soil condition) Based on the results obtained in Table 53, it can be con- Load factor for at-rest earth pressure, EH0 = 1.35, cluded that for the compaction case presented in Figure 90, the and load factor for active earth pressure, EHa = 1.50. worst-case calculated COV of multiplier factor R approaches the COV of the friction angle. Incorporating the effect of the Assuming the lateral loading due to live load (LFL: lateral result obtained in Figure 91, the combined COV for the esti- force due to live load) is mostly shear loads from wind, tem- mation of residual lateral earth pressure due to compaction is perature variation, and creep and shrinkage transferred via the ( approximately 0.35 = 0.202 + 0.202 + 0.2152 using the COVs ) bearing pads, the following distributions and load factors have been chosen: of f = 0.20, R = 0.20 and residual earth pressure estimator = 0.215, respectively. Using COVs of f and R as 0.15 and 0.09 LFL = 1.00, COVLFL = 0.15 and assumed to follow lognor- results in a combined COV of 0.27. The range of COV is thus mal distribution 0.27 to 0.35. Hence, it may be said that a bias of 1.00 and COV Load factor for lateral live load, LFL = 1.00 (assumed) of 0.30 would provide a reasonable estimate of the residual earth pressure due to compaction. 4.3 Calibration Methodology 4.2.3.2 Lateral Pressure from Live Loads 4.3.1 Overview of Calibration Procedures In order to assess the horizontal lateral pressure due to live Probability-based limit state designs are presently carried load, uncertainties in different components of the live load out using methods categorized into three levels (Thoft- must be assessed (A.S. Nowak, personal communication, 2006). Christensen and Baker, 1982): ACI 318 (Szerszen and Nowak, 2003) lists the following: Wind (50-year maximum) bias = 0.78 COV = 0.37 Level 3 includes methods of reliability analysis utiliz- Snow bias = 0.82 COV = 0.26 ing full probabilistic descriptions of design variables and Earthquake bias = 0.66 COV = 0.56 the true nature of the failure domains (limit states) to In 1983, the Ontario Ministry of Transport used the fol- calculate the exact failure probability, for example, using lowing for the assessment of lateral forces for the Toronto MCS techniques. Safety is expressed in terms of failure subway (OHBDC, 1979, 1983, 1993): probability.

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105 Level 2 involves a simplification of Level 3 methods by calculated. The target level is usually taken as the mean of the expressing the uncertainties of the design variables in terms reliability levels of representative designs. Such target reliabil- of mean, standard deviation, and/or COV and may involve ity can be thought of as related to the acceptable risks in cur- either approximate iterative procedures (e.g., FOSM, FORM rent practice and hence an acceptable starting point for code and SORM analyses) or more accurate techniques like MCS revision. The second method is based on the concept that safety to evaluate the limit states. Safety is expressed in terms of a measures are associated with cost; therefore, "safety essentially reliability index. is a matter not only of risk and consensus about acceptable Level 1 is more of a limit state design than a reliability analy- risks, but also of cost" (Schneider, 2000). Even though attempts sis. Partial safety factors are applied to the predefined nom- have been made to determine the cost of failure (Kanda and inal values of the design variables (namely the loads and Shah, 1997), it is hard to assign the cost of failure, especially resistance(s) in LRFD); however, the partial safety factors are when it incorporates human injury or loss of life. derived using Level 2 or Level 3 methods. Safety is measured in terms of safety factors. 4.3.2.2 Target Reliability Based on Current WSD Regardless of the probabilistic design levels described above, It has been found that the reliability levels of foundations the following steps are involved in the LRFD calibration designed using WSD factors of safety can vary considerably process: (e.g., Phoon and Kulhawy, 2002; Honjo and Amatya, 2005). Hence, the recommendation of a target reliability index based 1. Establish the limit state equation to be evaluated. on the reliability levels implied in the current WSD practice 2. Define the statistical parameters of the basic random vari- requires some judgment. ables or the related distribution functions. A literature survey shows that very few authors have dealt 3. Select a target failure probability or reliability value. with the determination of the target reliability of shallow foun- 4. Determine load and resistance factors consistent with the dations. Phoon and Kulhawy (2002) calculated the reliability target value using reliability theory. More applicable to an indexes for different COVs in the operative horizontal stress AASHTO LRFD geotechnical application is a variation in coefficient of soil. Taking the soil property variability into which structural selected load factors are utilized to deter- account, it was shown that reliability indexes lie in an approx- mine resistance factors for a given target value. imate range of 2.6 to 3.7, with an average of 3.15. Designs for square footings with embedment depth ratios (ratio of embed- Chapter 1 of this report reviewed the limit state equations to ment depth to footing width) of 1 and 3 and 50-year return be evaluated, and Chapter 2 developed their evaluation to period wind loads of 50% and 33.33% of the uplift capacity of establish the statistical parameters to be used. The statisti- the footings were evaluated. A target level of 3.2 was decided for ULS. However, this target level is specific only for footings cal parameters to be used are further investigated in the subject to uplift loads. following sections of this chapter to finally establish the In NCHRP Report 343 (Barker et al., 1991), which forms parameters to be used in the calibration. The load charac- a basis for the resistance factor in the current edition of teristics were developed and presented in Section 4.2. The AASHTO LRFD Bridge Design Specifications, it was found following section outlines the selected target reliability and that the reliability indexes obtained using "Rational Theory" develops the resistance factors based on the methodology varied from 1.3 to 4.5 for the bearing capacity of footings on presented in Sections 1.3.5 and 1.4. sand and from 2.7 to 5.7 for footings on clay (Allen, 2005). They concluded that a target reliability of 3.5 should be used 4.3.2 Target Reliability for footings (for the reference, the resistance component was taken equal to the factor of safety times the summation of the 4.3.2.1 Methods of Establishing Target Reliability effect of load combination and the reliability indexes calcu- As has been pointed out in NCHRP Report 507 (Paikowsky lated for a ratio of dead load to live load of 3). et al., 2004), in general, two methods are used to generate A target level of 3.5 was used for the code calibration for target reliability levels: (1) basing them on the reliability lev- foundations in the National Building Code of Canada (NRC, els implicit in current WSD codes and (2) using cost-benefit 1995). Becker (1996) mentions that this target reliability was analysis with optimum reliability proposed on the basis of the average of the range of 3.0 to 4.0 obtained using a semi- minimum total cost, which includes the cost of economic analytical approach to fit WSD for the typical load combina- losses and consequences due to failure. tions in Canadian structural design, with ductile behavior In establishing a target reliability level using the first method, and normal consequence of failure. This range of reliability the reliability levels implied in the current design practice are level matches with the range obtained from an updated

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106 database included in the final report for NCHRP Project 20-7/ at this stage for leaving the target reliability as a range: (1) using Task 186 (Kulicki et al., 2007)--for a majority (about 120) of the the different resistance factors obtained from the target relia- 124 bridges analyzed, the reliability index for superstructures bility range allows evaluation of the associated range of equiv- was between 3 and 4. A target reliability level of 3.5 is taken alent factors of safety and hence identification of suitability to in the current AASHTO LRFD Bridge Design Specifications WSD and (2) shallow foundation design includes two distinct (1994) (for the structural system) for the most common load groups of foundations for which the controlling limit state is combination, dead load and maximum 75-year live load different. By and large, shallow foundations on soil are con- (Strength I). trolled by the SLS, and, therefore, the target reliability of the Further, a range of 2.5 to 3.0 for drilled shafts and 2.0 to 2.5 ULS and the associated resistance factor are of secondary prac- for a redundant foundation system such as a pile group of tical importance and must be evaluated against the service- more than four piles was suggested by Barker et al. (1991). ability limits. In contrast, for foundations built on rock, the Paikowsky et al. (2004) suggested a target reliability of 3.0 for ULS is by and large the controlling criterion as either struc- a nonredundant deep foundation system (system with four or tural or geotechnical failure will take place before the limit less piles) and, along with the study by Zhang et al. (2001), settlement will be mobilized. As such, the chosen target reli- suggested 2.33 for a redundant deep foundation system. ability actually controls the safety of the structure. An addi- tional aspect affecting the aforementioned discussion is the fact that the uncertainty in the determination of capac- 4.3.2.3 Recommended Target Reliability ity for foundations on rock is of higher complexity (as it is subjected to discontinuities that control the rock strength), General Considerations. It would be logical and conven- and, hence, a possible logical outcome of the proposed range ient to assign at the present stage a target level for foundations is the use of two different target reliabilities: one for shallow equal to that assigned for superstructures. In order to fulfill one foundations on soil and the other for shallow foundations of the main goals of the LRFD, the reliability level of the foun- on rock. dation system should be comparable to that of the structural system. However, the actual resulting reliability level of the Examined Target Reliability Range. Resistance factors for combined system of super- and sub-structures (including soil- three target reliabilities--3.0 (pf = 0.135%), 3.25 (pf = 0.058%), structure interaction) is unknown, even though a target level and 3.5 (pf = 0.023%)--are examined as a first stage in the pres- equal to that obtained for the superstructure is assigned for ent study for the uncertainty established by the databases and substructures. selected methods of analysis. Figure 92 illustrates the range of It may also be of interest to note that due consideration resistance factors calculated based on a typical range of bias and should be given to applying structural safety concepts to geo- a wide range in the uncertainty of the resistance using load technical designs (Phoon and Kulhawy, 2002) for two reasons. characteristics from NCHRP Report 507's calibration for the First, it is unrealistic to assign a single "typical" variation (of three examined target reliabilities. Considering "typical" val- COV) to each soil parameter, even those obtained from direct ues of resistance with a lognormal distribution, with a bias of measurements taking into consideration the inherent soil vari- 1.5, and a COV of 0.3, the resistance factors for the target reli- ability, measurement errors, and transformation uncertain- abilities of 3.00, 3.25, and 3.50 are 0.64, 0.58, and 0.53, respec- ties. Usually, a range has to be provided even for datasets tively. The three resistance factors roughly translate into a cost of satisfactory quality, taking into consideration important difference of 20% between the higher and the lower resistance details like soil type, number of samples per site, distribu- factor (assuming, for simplicity, direct relations among load, tion of depositions and measurement techniques. Second, it size, and cost). is important to consider the vital role of the geotechnical engineer in appreciating and recognizing the complexities 4.3.3 Load Conditions, Distributions, of soil behavior and the inherent limitation of "simplistic" Ratios, and Factors empirical geotechnical models used in the prediction of such behavior. The loading conditions are taken as those presented in Table 49 and Section 4.2.3.3. The actual load transferred from the Current Study Calibrations. For the present calibration superstructure to the foundations is, by and large, unknown of resistance factors for shallow foundations, a target relia- because very little long-term research has been focused on the bility range of 3.0 (pf = 0.135%) to 3.5 (pf = 0.023%) will be subject. The load uncertainties are taken, therefore, as those examined. This range encompasses the nonredundant target used for superstructure analysis. The LRFD Bridge Design Spec- reliability used for deep foundations ( = 3.0) to the target reli- ifications (AASHTO, 2007) provide four load combinations for ability assigned in the current LRFD Bridge Design Specifica- the standard strength limit state (dead, live, vehicular, and tions for shallow foundations. There are two major reasons wind loads) and two for the extreme limit states (earthquake