Probabilistic Analysis of Unreinforced Slopes and Reinforced Footings Using the Random Finite Element Method

Abstract

The focus of this thesis was on probabilistic analysis of unreinforced cohesive soil slopes and geosynthetic reinforced and unreinforced footings over cohesive foundations. Two open-source random finite element method (RFEM) programs written in FORTRAN were modified to accommodate larger problem domains analysed in this study. For footing analyses, subroutines were added to model geosynthetic reinforcement layers as linear elastic-plastic bar elements together with two-layer random fields. The modified RFEM code for the foundation problem was used to examine the case of the footing sitting directly on a cohesive soil layer, and the same footing seated on unreinforced and geosynthetic reinforced granular layers. Simulations were carried out assuming different isotropic and anisotropic spatial correlation lengths for the undrained shear strength of the foundation soil. The influence of reinforced and unreinforced granular layers on worst-case spatial correlation lengths was identified. The footing investigation showed that introduction of geosynthetic layers in the granular layer placed between the footing and underlying cohesive soil foundation significantly reduced the probability of footing failure. The correlation lengths for isotropic and anisotropic spatial variability of the foundation undrained shear strength that were at or close to the width of the footing corresponded to worst-case scenarios with respect to probability of failure regardless of the number of reinforcement layers and reinforcement stiffness. The modified slope stability code was used to investigate the sensitivity of RFEM analysis outcomes to numerical parameters used to describe the random fields. The results of RFEM analyses were compared to results using the random limit equilibrium method (RLEM) for the same cohesive slope problem. The conditions that are necessary for the two methods to achieve practical agreement with respect to probability of failure and worst-case correlation lengths were identified. The slope investigation showed that critical correlation lengths deduced from probabilistic analyses using RFEM are sensitive to the precision of variables in numerical computations and to the ratio of random field cell size to finite element mesh size. The probabilities of failure computed using RFEM can be replicated with RLEM using Janbu method of slices and with less computational time.