Analytical analysis of cylindrical cavity expansion considering particle breakage effect of sand and its application for cone penetration tests

Abstract

The particle breakage effect in sand exerts a significant influence on the design of underground space structure. However, the existing theories seldom consider the breakage effect and often lack accurate descriptions of void ratio changes, leading to substantial errors in the numerical calculations compared to the actual scenario. This study employs the simple critical state sand model (SIMSAND) to account for the particle breakage effect and transforms the drained cylindrical cavity expansion problem into a set of first‐order ordinary differential equations described by the Lagrangian method. The analytical solution of the cylindrical cavity expansion problem is calculated using Matlab programming codes. Firstly, Fontainebleau sand is investigated to analyse the influence of initial stress, void ratio and specific volume around the cavity. The combined effects of initial stress and particle breakage on the soil around the cavities result in dilatancy characteristics and a reduction in void ratio. The stress path analysis reveals that the soil around the cavities only reaches a critical state under high initial stresses. Secondly, a plane strain numerical model is established for twice expansion to verify the calculation outcomes from the cylindrical cavity expansion theory. Finally, an axisymmetric cone penetration test (CPT) model is developed to analyse the theoretical and numerical solutions for expansion stress and sleeve friction. The research results indicate that the CPT in sand need to consider the particle breakage effect, especially under high stress conditions. Without considering particle breakage, the sleeve friction is overestimated. These research findings can offer guidance for geotechnical engineering applications, such as CPT, pressuremeter tests and predictions of bearing capacity for pile foundations in sand.