RELIABILITY OF GEOTECHNICAL SYSTEMS

The main objectives of this study are: (a) to examine the inter-dependence of the failure modes of some common geotechnical structures (i.e., soil slopes, earth retaining structures and shallow foundations); (b) to provide a probabilistic description to the problem of "interference" of two near-by sited structures; and (c) to assess the reliability of one or more geotechnical structures having inter-dependent modes of failure.;The above objectives are achieved within the framework of probability theory and reliability analysis. The measure of safety that is employed throughout the study is the probability of failure, defined as the probability with which the resistance (R) of a structure along a given mode of failure is exceeded by the applied loading (S). The effect of the correlation of R and S on the probability of failure is investigated. Soil strength parameters c and (phi) are introduced as correlated random variables and a probabilistic model is developed for the description of their joint distribution.;A geotechnical structure is considered as a system if it has more than one potential failure modes. The latter constitute the components of the system and are placed together in accordance with their role in the overall stability of the structure. The analysis of such systems is performed in three steps: (a) the probability of occurrence of each individual mode is first determined; (b) if there is interference between two or more modes, then the associated conditional probabilities are calculated; and (c) the overall reliability of the system is obtained by combining the results from the first two steps, in accordance with system reliability theory.;The developed method of analysis is applied to a number of illustrated examples and the results are presented and discussed.;On the basis of the analysis and results of this study, the following conclusions may be drawn: (a) System reliability theory provides a rational approach to the assessment of the safety of neighboring structures with interfering failure modes; or of one structure with several inter-dependent modes of failure. (b) The probability of failure of a structure may be grossly under-estimated, if the inter-dependence of its failure modes is neglected. (c) The commonly made assumption of independence between the resistance and the loading of a soil structure underestimates its probability of failure (p(,f)) if the two are negatively correlated; and overestimates p(,f), if the two are positively correlated. (d) The bivariate beta distribution provides a versatile and useful model for the description of the joint behavior of the two components (c and (phi)) of soil strength.