Finite-Element Limit Analysis Formulation using Bishop’s Strength Criterion for Anisotropic Undrained Soils

Abstract

This paper presents a novel finite-element limit analysis formulation employing Bishop’s strength criterion—an anisotropic model designed specifically for soils loaded under undrained conditions. The proposed approach employs a three-field mixed finite-element model, previously devised by the authors using the alternating direction method of multipliers (ADMM) framework. In this work, the inherent splitting operator approach associated with ADMM is exploited to seamlessly incorporate the anisotropic criterion. Importantly, the introduction of this new strength criterion does not compromise the formulation’s ability to produce strict lower and upper bounds for the collapse loads of mechanical systems. The paper includes several numerical examples, covering two-dimensional (plane strain conditions) and three-dimensional scenarios, to demonstrate the effectiveness of the computational tool in accurately calculating collapse load limits for problems involving undrained anisotropic soils. In addition, these examples highlight the impact of anisotropy on the bearing capacity and stability of geotechnical structures.