This approach makes it possible to quantify the probability that load (demand) will exceed resistance for each defined limit state. Design can then be carried out to achieve a target probability of reaching a limit state. That target probability, which can also be defined in terms of a reliability index, can be established by code (e.g., AASHTO) or by the owner or other responsible party. This is the promise of LRFD, a design that meets a quantifiable measure of safety. Criteria for Robust RBD Methods Given the advantages of reliability-based design (RBD), it would appear to be a no- brainer for the geotechnical profession to adopt LRFD immediately. However, as for most worthwhile endeavors, the “devil is in the details.” In particular, the process of establishing resistance factors that account for uncertainty and variability in geotech- nical resistances of drilled shafts poses a difficult challenge to researchers, code writers and practitioners. To ‘calibrate’ resis- tance factors using rigorous probability- based methods requires the following: • The design equation for nominal resistance must be exactly the same as that used for calibration. • The load factors used in the design problem coincide with those used in the calibration. • The geomaterial type is the same as that for which the calibration study was conducted. • Soil and rock properties, groundwater conditions, soil response (drained/ undrained), and other inputs used in the analysis must be determined and interpreted in a manner that is consistent with those used in the calibration analysis. Furthermore, resistances against which the factors are calibrated can be determined only from full-scale load tests. For load test results to be suitable for use in a calibration exercise, all of the information above must be well documented, which means that subsurface conditions at the load test location are characterized accurately and the engineering properties of the geomaterials, such as shear strength, be established using the same procedures as 60 • DEEP FOUNDATIONS • MAY/JUNE 2015 Lateral load test on 6-ft diameter drilled shaft used in the design. That is a tall order! Oh, and by the way, if the test results are used to calibrate a design equation for strength limit states, the load test must be taken to the geo- technical strength limit of the foundation. Basis of AASHTO LRFD As described by Withiam et al. (1998) cali- bration, the process of assigning values to load factors and resistance factors, can be carried out by the use of: (1) judgment, (2) fitting to other codes or past practice, (3) probabilistic-based reliability analyses, or (4) a combination of approaches. Only the third approach, reliability-based calibra- tion, satisfies the stated objective, which is to establish load and resistance factors to achieve a defined target probability of failure. So what is the basis of the resistance factors for drilled shafts in the AASHTO LRFD Bridge Design Specifications and the Drilled Shaft Manual? To illustrate, consider the following nominal resistances identi- fied in the AASHTO code as requiring consideration for drilled shaft design at strength limit states: • Lateral geotechnical resistance of soil and rock stratum, for single shafts and shaft groups • Geotechnical axial compression resistance, for single shafts and shaft groups • Geotechnical axial uplift resistance, for single shafts and shaft groups • Structural resistance of shafts, including checks for axial, lateral and flexural resistances • Axial resistance when downdrag occurs Drilled shaft construction for retaining wall, CA For resistance factors established using reliability theory, the target reliability index was b = 3.0, corresponding to a probability of failure of 1 in 1,000. A careful review of the Allen report and previous studies cited by Allen shows that we are nowhere near a The resistance factors in AASHTO (2014) for the above cases are based on recommendations given by Allen (2005) and are described as: “developed using either statistical analysis of shaft load tests combined with reliability theory (Paikowsky et al. 2004), fitting to Allowable Stress Design (ASD), or both. Where the two approaches resulted in a significantly different resistance factor, engineering judgment was used to establish the final resistance factor, considering the quality and quantity of the available data used in the calibration.”
