Stress integration algorithm of the small-strain Unified Hardening model for soils based on multistage Homotopy continuation method

The small-strain Unified Hardening (SSUH) model considers the high initial stiffness and rapid stiffness degradation of soils during the loading process. When its stress integration is implemented by an implicit algorithm in the finite element analysis, a key issue lies in how to solve the highly nonlinear constitutive equations. This paper proposes multistage Homotopy continuation method (MHCM), which progressively optimizes the initial guess by several stages of Homotopic deformation, to ensure the successful solution of the constitutive equations using Newton-Raphson iteration. An adaptive Homotopic deformation rate is introduced to prevent the subsequent stage of Homotopic deformation from repeating the previous failure. Compared with the original single-stage Homotopy continuation method, MHCM improves the convergence and efficiency without compromising the accuracy. Based on the SSUH model and the proposed stress integration algorithm, the ground displacement induced by the excavation of Crossrail tunnels can be reasonably predicted.