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

S. Kar, A. Burman, L. B. Roy
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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.
利用FOSM、FORM和蒙特卡罗仿真对电子表格中的粘性边坡进行可靠性分析
在岩土工程中,不确定性来源于荷载、土体特性及其性质、计算模型等。为了尽量减少岩土工程问题中的这些不确定性,人们开发了各种基于可靠性和(或基于概率的)方法。摘要提出了一种基于MS-Excel电子表格环境的实用框架,利用一阶二阶矩法、一阶可靠度法和蒙特卡罗模拟法估算黏聚有限边坡的可靠度指标和失效概率。坡度高度和坡度角度分别取5 m和45º。边坡倾角为2H:1V,假定土壤下15m处存在硬地层。假定饱和单位重量为18 kN/m3,不排水抗剪强度为20 kPa。在不排水条件下,采用瑞典切片法进行了稳定性分析。本研究开发的excel电子表格主要分为计算安全系数的确定性模型工作表和生成不确定参数随机变量的不确定性模型两种形式。不排水抗剪强度是一个不确定参数。计算出安全系数为1.248,临界滑移圈坐标为2.6、8.8,半径为16 m。采用FOSM、FORM和MCS方法确定了可靠性指标。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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