MATLAB script for slope stability calculations with COMSOL Multiphysics

Abstract

A new MATLAB script was developed and implemented to conduct slope stability analyses with finite element (FE) software COMSOL Multiphysics. The MATLAB script computes a factor of safety based on the finite element stress field calculated with COMSOL. The stresses are calculated based on a linear-elastic behaviour using a Young’s modulus and a Poisson’s ratio. The script is programmed to test a series of circular slip surfaces defined by their centre coordinates and their radius. The script first verifies the intersection between the slope geometry and slip surface. The intersecting part is then divided into a series of equalwidth vertical slices. Stresses are calculated from the COMSOL model at the middle point of the base of each slice along the slip surface. The FE stress tensor is then rotated based on the inclination of the slice base to calculate the normal and shear stresses. The normal stress values are used with Mohr-Coulomb parameters to compute the shear strength. The mobilized shear stress was assumed to be equal to the FE shear stress values. Finally, a global factor of safety is calculated based on the ratio between the sum of resisting forces and the sum of mobilized forces. The new script was verified using FE code SIGMA/W to calculate the stresses and using SLOPE/W for factor of safety calculations. The verification was conducted using four different slopes: a uniform slope, a slope with benches, a steep slope, and a uniform slope in a layered soil deposit. The same critical slip surfaces with similar factor of safety values were obtained with the MATLAB script and with the SLOPE/W analysis. The new MATLAB code extends the realm of potential multiphysics applications in geotechnical engineering that can be studied with COMSOL. The thesis also makes recommendations to further improve the MATLAB script. It is suggested to program a strength reduction method, to verify the code with examples involving a pore water pressure, and to perform the force integration directly in COMSOL using integration couplings.

Date	8 Aug 2017
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	François Duhaime (Supervisor) & Yannic A. Éthier (Co-supervisor)