Reliability analysis of a cohesive slope in a spreadsheet using FOSM, FORM and Monte-Carlo Simulation

Abstract

In geotechnical engineering uncertainties arises from loads, soil characteristics and their properties, calculation models etc. To minimize these uncertainties in geotechnical problem, various reliability based and (or probabilistic based) approaches have been developed. This abstract presents a MS-Excel spreadsheet environment based practical framework for estimating the reliability index and failure probability of a cohesive finite slope using First-order second moment method, First-order reliability method and Monte Carlo Simulation. The height and the angle of slope is considered to be 5 m and 45º respectively. The inclination of the slope is 2H:1V and the hard stratum is assumed to be present at 15 m below the soil. The values of saturated unit weight and undrained shear strength are assumed to be 18 kN/m3 and 20 kPa respectively. The stability analysis is carried out using Swedish slice method under undrained condition. The excel spreadsheet developed in the study is mainly divided into two forms i.e. deterministic model worksheet for calculating the factor of safety and uncertainty model for generating the random variables of uncertain parameters. The undrained shear strength is considered as an uncertain parameter. The nominal factor of safety value is found out to be 1.248 and the critical slip circle has coordinate (2.6, 8.8), having radius of 16 m. The reliability index is found out using FOSM, FORM and MCS.