Probabilistic Analysis of Finite Slope Stability Using MS-Excel

In slope stability analysis, it is crucial to take into account the inherent spatial variation (ISV) in the soil properties as it affects the analysis and design of the slope. The majority of research work employs a probabilistic based approach to incorporate the variability of soil parameters using a random field to evaluate the reliability analysis (RA) of slope. The reliability of a slope can be evaluated by various methods such as First-order second moment, Monte Carlo simulation (MCS) and Subset simulation (SS). The main drawback of MCS is that, the efficiency of this method is very less for the problems having small failure probability. The SS method can be used more efficiently to estimate the slope reliability at small failure probability. The approach is demonstrated in this paper using a finite soil slope having ISV in the cohesion and angle of internal friction with the depth of soil. The RA has been performed in a MS-Excel spreadsheet platform using Ordinary method of slices. The study investigates the effect of ISV and correlation length \((\uplambda )\) $(\mathrm{\lambda })$ on the probability of failure \({(P}_{f})\) ${(P}_f)$ of the soil slope. The \({P}_{f}\) $P_f$ and reliability index \((\beta )\) $(\beta )$ of the soil slope is evaluated using the above-mentioned methods. It is shown that SS method uses many fewer samples to obtain a given accuracy as compared to the MCS. In addition, this method ensures that samples are generated in the failure region, which is not always achievable with the MCS method. Also, the result shows that the proposed method accurately calculates the slope reliability and greatly improves the efficiency at small failure probability levels, while taking into consideration the ISV in soil properties.