RELIABILITY OF SOIL SLOPES
Abstract
The measure of safety used in this study is the "reliability" (or the "probability of failure"), an a-priori quantitative estimate of the likelihood of the safety (failure) of a slope. A closed form solution to determine the reliability is proposed, in which a material with two resistance parameters (c and tan (phi)) are accommodated. Input to the model consists of a bivariate distribution of "c" and "tan (phi)" for the slope material, and a line, called the "critical boundary" (which is independent of the operative strength parameters), that is the locus of points in the c-tan (phi) plane for which the slope in question is in a state of limiting equilibrium (factor of safety equal to unity). Beta distributions are selected to model the variability of c and tan (phi), and a Bayesian inferential procedure permits their updating (changing) as new information becomes available. The critical boundary is determined from two dimensional and three dimensional slope stability analyses. For the former the Ordinary Method of Slices is adopted because of its simplicity (it requires no iterations) and because it is the only method that does not make the unrealistic assumption that the factor of safety takes the same value along the entire slip surface, thus permitting the analysis to yield some information regarding the failure process. For the three dimensional analysis, Hovland's method is used. In concept it is the 3-D equivalent of the Ordinary Method of Slices. Output from the model is the probability of failure of the slope, which is information dependent, and therefore can vary as new information is obtained. These probabilities can then be used to place the problem in the framework of Decision Theory. The principal conclusions obtained are: (i) different probabilities of failure can be obtained for slopes judged equally safe by conventional factors of safety. Slopes displaying tolerable factors of safety can exhibit very high probabilities of failure. (ii) for a given factor of safety, slopes with smaller values of Janbu's dimensionless parameter (lamda) ((lamda) = (gamma)H tan (phi)/c) have higher probabilities of failure; this is because most of their strength is cohesive in nature, and the "c" parameter abounds in uncertainty. (iii) from the three dimensional analysis, it was found that spherical slip surfaces have higher probabilities of failure than cylindrical ones (with the axis of the cylinder in the same plane as the slope profile); (iv) in materials with low (lamda) values, circular (2D) slip surfaces yield higher probabilities of failure than spherical (3D) slip surfaces, however a 3D analysis is more rational, as it approximates better actual failed surfaces in every case (see section 5.5). Only minor differences were noted between 2D and 3D analyses in the present study; (v) the introduction of in-situ lateral stresses (perpendicular to the slope profile) decreases the probability of failure.
Degree
Ph.D.
Subject Area
Civil engineering
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