Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

Abstract

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points. As a result, this problem cannot be solved by the common self-similar-based similarity techniques. This paper proposes a novel, exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils. Considering stress-dependent elastic moduli of soils, new analytical stress and displacement solutions for the non-self-similar problem are developed taking the small strain assumption in the elastic zone. In the plastic zone, the cavity expansion response is formulated into a set of first-order partial differential equations (PDEs) with the combination use of Eulerian and Lagrangian descriptions, and a novel solution algorithm is developed to efficiently solve this complex boundary value problem. The solution is presented in a general form and thus can be useful for a wide range of soils. With the new solution, the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted, which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass. The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

Keywords

• Cavity expansion
• Drained analysis
• Boundary effect
• Critical state soil
• Non-self-similar
• Eulerian-Lagrangian approach