Comparative Study on Reliability Analysis of Cohesive Soil Slope using Subset Simulation and Other Methods

Abstract

In geotechnical engineering, uncertainties arise due to variation in loads, soil characteristics, ground stratification and so on. Reliability analysis based on probabilistic approaches is particularly suitable to deal with such uncertainties. In this paper, a newly developed reliability analysis method, namely Subset simulation (SS) method has been implemented to study the stability of a cohesive slope. The results of reliability analysis obtained from SS method are also compared with three other methods, namely First order second moment method (FOSM), First order reliability method (FORM) and Direct Monte-Carlo simulation (MCS) method. The various reliability models have been used in a spreadsheet environment using MS-Excel. The developed spreadsheet-based platform implementing all four methods contains two common models i.e. deterministic model and the uncertainty model. The SS method uses another model called uncertainty propagation using subset simulation (UPSS) in addition to the two above-mentioned models. The factor of safety of the slope is determined using ordinary method of slices under undrained condition. The probability of failure ( and its corresponding reliability index of the proposed slope has been determined using all four methods. A software called Geo-Studio (SLOPE/W) has been used to tally the results of reliability analysis of the slope considered herein. The results obtained from the different methods show that the SS method gives better performance in terms of efficiency and resolution especially at low failure probability i.e., . Also, the SS method helps in identifying the significant depth where the most probable critical slip surface is located.

Probabilistic analysis of pile foundations using Monte Carlo and Subset simulations compared with FOSM-based hybrid ANN paradigm

“…and {𝑃(𝑌 < 𝑥i|𝑌 < 𝑥i-1), 𝑖 = 1, 2,…, 𝑛} corresponds to a conditional probability value equals to 0.10 ( Au and Beck, 2001;Au and Wang, 2014;Au et al, 2010;Kar and Roy, 2022) Apart from MCS and SS, FOSM is a widely used approach in the domain of RA. In FOSM, the uncertainties are expressed as reliability index, β.…”

Implementing Reliability Analysis of a Soil Slope using First-Order Second Moment Method, Monte-Carlo Simulation Method and Subset Simulation Method in a MS-Excel Spreadsheet

“…The reliability index (𝛽) and probability of failure $𝑃 ! & of the slope can be estimated by several methods such as firstorder second moment (FOSM) method [11][12][13][14][15][16][17], Monte-Carlo simulation (MCS) method [14][15][16][17][18][19][20][21][22] and Subset simulation (SS) method [21][22][23][24][25].…”

“…The value of correlation distance (𝜆) among the uncertain soil parameters along the vertical direction is taken as 2.0 m. The FOS of the soil slope is determined using limit equilibrium based ordinary method of slices [29]. The analysis has been developed and executed in a MS-Excel spreadsheet, which mainly consists of three parts i.e., deterministic model generation, uncertainty model generation and uncertainty propagation [15][16][17]. It has been seen that SS method has shown better performance as compared to FOSM method and MCS method especially at low failure probability levels.…”