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A deterministic model for the factor of safety of an idealized rock mass for planar mode of failure is developed adopting Limit Equilibrium Method (LEM) using Patton’s shear strength criterion and considering practically occurring conditions such as the effect of tension crack, water filled up in tension crack, horizontal and vertical seismic acceleration, rock bolt stabilizing force and surcharge. In the Pseudo-static analysis horizontal seismic acceleration is taken outward from the slope and vertical seismic acceleration is considered in both the direction i.e. towards the direction of gravity (downward) and opposite to the direction of gravity (upward). An expression of normal stresses as limiting criterion has been derived in order to compare the field normal stresses along the failure surface. A detailed parametric study has been presented to investigate the influence of vertical seismic coefficient for both the direction on the stability of rock slope using developed expression. For high normal stress along the failure plane, it is observed that the factor of safety decreases with increase in the value of vertical seismic coefficient towards the direction of gravity and increases linearly with increase in the value of vertical seismic coefficient against the direction of gravity and the opposite trend has been found for lower normal stress. The vertical seismic coefficient against the direction of gravity has predominant effect on factor of safety of rock slope as the rate of increase/decrease of factor of safety with vertical seismic coefficient is more against the direction of gravity. Hence in determining the critical factor of safety, effect of vertical seismic coefficient against the direction of gravity should be considered.

The paper presents a computational procedure for reliability analysis of earth slopes considering spatial variability of soils under the framework of the Limit Equilibrium Method. In the reliability analysis of earth slopes, the effect of spatial variability of soil properties is generally included indirectly by assuming that the probabilistic critical slip surface is the same as that determined without considering spatial variability. In contrast to this indirect approach, in the direct approach, the effect of spatial variability is included in the process of determination of the probabilistic critical surface itself. While the indirect approach requires much less computational effort, the direct approach is definitely more rigorous. In this context this paper attempts to investigate, with the help of numerical examples, how far away are the results obtained from the indirect approach from that obtained from the direct approach. In both the approaches, it is required to use a model of discretization of random fields into finite random variables. A few such models are available in the literature for onedimensional (1D) as well as two-dimensional (2D) spatial variability. The developed computational scheme is based on the First Order Reliability Method (FORM) coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. The study includes bringing out the computational advantages and disadvantages of the three commonly used discretization models. The sensitivity of the reliability index to the magnitudes of the scales of fluctuation has also been studied.

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