In this study, an analytical model is proposed to calculate earth pressure considering the displacement of a rigid wall, and this model is developed based on the hyperbolic soil stress-strain relationship. By introducing the soil–failure ratio, the classic limit earth pressure theories can be incorporated into this analytical model. Using the axis-translation method, the earth pressure at rest is the initial state without wall movement. As the wall moves away from the soil mass, the earth pressure decreases and reaches the limit active earth pressure if the wall displacement reaches a threshold value. Similarly, the earth pressure increases to the limit passive earth pressure as the wall moves against the soil mass. This analytical model is verified when compared with experimental and numerical results and can predict the nonlinear earth pressure distribution under various modes of wall movement. This proposed analytical model provides an effective approach to predict the variation of earth pressure, with various wall displacements ranging from the limit active state to the limit passive state.

Cavity expansion theory has been well developed in the past few decades, but little progress has been made to cavity expansion theory regarding biaxial in situ stresses. Owing to the two-dimensional nature of cavity expansion under anisotropic in situ stresses, a rigorous analytical or semi-analytical solution is no longer available for such cavity expansion problems. In this paper, a numerical study is performed to investigate the drained expansion responses of a cylindrical cavity under biaxial in situ stresses. The advanced anisotropic S-CLAY1 model integrated by the fully implicit backward Euler algorithm is implemented as a user-defined materials (UMAT) subroutine in the finite element model (FEM) to represent the elastoplastic behaviors of the anisotropic soils during cavity expansion. The FEM is validated by comparing with a benchmark semi-analytical solution under the uniform in situ stress. The expansion responses under biaxial in situ stresses, including the distributions of stress components, the evolutions of expansion pressures, stress paths, and yield surfaces, are subsequently investigated on leverage of the FEM and compared with those from approximate solutions. The present FEM in conjunction with the UMAT subroutine provides a benchmark for the validation of approximate solutions and the outcomes give significant insights into practical geotechnical problems pertaining to cavity expansion under biaxial in situ stresses.

Ground surface settlement (GSS) is one of the major concerns in design and construction of a deep excavation. This paper proposes an analytical approach for the prediction of GSS induced by a braced deep excavation. Considering wall deformation and stress release, the problem investigated is formulated as a system of two second-order partial differential equations (Lame equations) with mixed boundary conditions based on the elastic theory. Taking advantage of the superposition principle, the mixed boundary conditions are decomposed into displacement and stress boundary. The separation of variables method is applied to solve the governing equations with displacement boundary, while the Fourier Transform Method is employed to derive the solution for the governing equations with stress boundary. A novel least-squares based method is proposed to transform the scatter data of wall deflection into a continuous function, which is used to determine the unknown coefficients in the solution. The validity of the proposed solution is checked by predicting the GSS of two well-documented cases and by comparing with some empirical approaches. Parametric studies are conducted to demonstrate the impact of the modulus ratio on the excavation responses.