Probabilistic approach to evaluation of earthquake-induced permanent deformation of slopes

The impact of various sources of uncertainty on the seismic response and performance of slopes is investigated, and probabilistic procedures are developed to model the uncertainties and their impact on the predicted slope deformation under seismic loading. The proposed approach incorporates probabilistic concepts into the classical limit equilibrium methods and the Newmark-type deformation assessment technique. The material properties are treated as random variables whose spatial variations are regarded as the realizations of random fields. Statistics of spatially averaged material properties is reviewed and extended to cover more general cases which also account for the uncertainty arising from measurement errors and the locations of the measurement points. Newly developed formulas for unified treatment of various sources of uncertainty of the material properties are presented. These formulas incorporate sampling and measurement errors as well as spatial variability and its reduced variance due to spatial averaging. The stochastic nature of seismic loading is accounted for by generating a large series of RMS-hazard compatible artificial motions, and by using them in subsequent response analyses. The RMS procedures are capable of generating a large series of ground motions that match target seismic hazard at the site of interest.; A set of example problems with increasing complexity is used to demonstrate the applicability of the developed probabilistic methods, starting from the static stability assessment of a homogeneous slope and ending with the analysis of seismically induced deformations of a waste fill. To determine the risk of slope failure, several computation methods including FORM, SORM, and Monte Carlo simulation are selectively implemented, based on their applicability to the different loading conditions.; The results of analyses confirm that the variability of the local average is always less than that of the point value, and that the variability of the local average always decreases as the dimension of a domain increases. The variance reduction due to areal averaging can be more significant than line averaging. Unlike the inherent uncertainty, errors from the insufficient data and imperfect measurement do not decrease by averaging over the area of space, but depend only on the number of samples. The results of the example analyses show that the risk of failure is sensitive to the choice of the distribution of random soil properties. The results confirm that representing a soil layer as a single random variable with the assumption of point statistics generally leads to very conservative results, often with unrealistically high probability of failure. The scale of fluctuation also has a very significant effect on the reliability of the slope stability and uncertainty arising from sampling and measurement errors can substantially contribute to the risk of failure, especially if the scale of fluctuation is relatively small.; One of the most important findings in this study is that the uncertainty of soil properties can have a significant impact on the computed risk of slope failure at relatively low levels of seismic hazard, but it may have relatively small impact on the computed risk if the slope is exposed to relatively high levels of hazard. These results suggest that in a highly seismically active region, characterization of earthquake hazard is the critical factor, and a moderate variability in soil properties has a relatively small effect on the computed risk of the slope failure.