reliability-based design in geotechnical engineering

2 Kok-Kwang Phoon

unattainable goal in the presence of uncertainty and (b) probability theorycan provide a formal framework for developing design criteria that wouldensure that the probability of ldquofailurerdquo (used herein to refer to exceedingany prescribed limit state) is acceptably small Ideally geotechnical LRFDshould be derived as the logical end-product of a philosophical shift in mind-set to probabilistic design in the first instance and a simplification of rigorousRBD into a familiar ldquolook and feelrdquo design format in the second The needto draw a clear distinction between accepting reliability analysis as a nec-essary theoretical basis for geotechnical design and downstream calibrationof simplified multiple-factor design formats with emphasis on the formerwas highlighted by Phoon et al (2003b) The former provides a consis-tent method for propagation of uncertainties and a unifying frameworkfor risk assessment across disciplines (structural and geotechnical design)and national boundaries Other competing frameworks have been suggested(eg λ-method by Simpson et al 1981 worst attainable value method byBolton 1989 Taylor series method by Duncan 2000) but none has thetheoretical breadth and power to handle complex real-world problems thatmay require nonlinear 3D finite element or other numerical approaches forsolution

Simpson and Yazdchi (2003) proposed that ldquolimit state design requiresanalysis of un-reality not of reality Its purpose is to demonstrate thatlimit states are in effect unreal or alternatively that they are lsquosufficientlyunlikelyrsquo being separated by adequate margins from expected statesrdquo It isclear that limit states are ldquounlikelyrdquo states and the purpose of design is toensure that expected states are sufficiently ldquofarrdquo from these limit states Thepivotal point of contention is how to achieve this separation in numericalterms (Phoon et al 1993) It is accurate to say that there is no consensus onthe preferred method and this issue is still the subject of much heated debatein the geotechnical engineering community Simpson and Yazdchi (2003)opined that strength partial factors are physically meaningful because ldquoit isthe gradual mobilisation of strength that causes deformationrdquo This is con-sistent with our prevailing practice of applying a global factor of safety tothe capacity to limit deformations Another physical justification is that vari-ations in soil parameters can create disproportionate nonlinear variations inthe response (or resistance) (Simpson 2000) In this situation the author feltthat ldquoit is difficult to choose values of partial factors which are applicableover the whole range of the variablesrdquo The implicit assumption here is thatthe resistance factor is not desirable because it is not practical to prescribea large number of resistance factors in a design code However if main-taining uniform reliability is a desired goal a single partial factor for sayfriction angle would not produce the same reliability in different problemsbecause the relevant design equations are not equally sensitive to changes inthe friction angle For complex soilndashstructure interaction problems apply-ing a fixed partial factor can result in unrealistic failure mechanisms In fact