Cavity expansion theory with state-dependent mohr-coulomb model and its application to cone penetration tests

The cone penetration test (CPT) is a fast and efficient in-situ testing technique that provides reliable and continuous measurements of soil properties. The CPT calibration chamber test is widely used to investigate soil-pile interactions. To address the boundary effect problem in CPT calibration chamber tests, this paper applies the cavity expansion theory for analysis. In this approach, the stress-strain relationship of soil is modeled using the classical Mohr-Coulomb (M-C) model, where the elastic modulus is associated with the mean stress, and the internal friction angle and dilation angle are related to the void ratio and mean stress. This modification captures the state-dependent characteristics of sand. By combining the stress equilibrium equation and the volume conservation equation, a system of partial differential equations (PDEs) is established to describe the stress-strain behavior of the soil element. The hybrid Eulerian-Lagrangian approach is employed to solve these PDEs, yielding the pressure-expansion curve and the stress distribution curve along the cavity wall during the expansion process of the cylindrical (spherical) cavity. The results of this semi-analytical solution are compared with the exact solution to validate the accuracy of the proposed method. Additionally, the relationship between the cylindrical (spherical) cavity expansion model and the cone penetration resistance in CPT is established. The development curve of critical depth with cone penetration resistance is accurately predicted.