Bubble-enhanced quadrilateral finite element formulation for nonlinear analysis of geotechnical problems

Abstract

We investigate a new numerical procedure based on a bubble-enriched finite element formulation in combination with the implicit backward Euler scheme for nonlinear analysis of strip footings and stability of slopes. The soil body is modeled as a perfect plastic Mohr–Coulomb material. The displacement field is approximated by a 4-node quadrilateral element discretization enhanced with bubble modes. Collapse loads and failure mechanisms in cohesive frictional soil are determined by solving a few Newton–Raphson iterations. Numerical results of the present approach are verified by both analytical solutions and other numerical solutions available in the literature. Keywords: Material nonlinear analysis, Backward Euler scheme, Bearing capacity, Slope stability, Bubble functions, Finite elements