Meshfree analysis of unsaturated porous media including hydraulic hysteresis and large deformations

摘要

An efficient and robust computational algorithm, based on the meshfree method, is developed for fully coupled large deformation analysis of variably saturated geo-materials. The contributions made in the thesis include: i) a new three-point time discretisation scheme with variable time step for numerical solution of parabolic partial differential equations. The proposed method has the advantage that it dampens spurious oscillations of the numerical results, while maintaining the second order accuracy and remaining unconditional stability; ii) a fully coupled meshfree model, based on the radial point interpolation method (RPIM), for flow-deformation analysis of saturated porous media. A vast majority of current meshfree methods for coupled analysis of saturated porous media are based on the moving least square (MLS) approximation for constructing shape functions, which render imposition of the essential boundary condition difficult. In addition, some suffer from inconsistent discretisation of governing equations leading to physically inadmissible results; iii) a meshfree model for multi phase analysis of unsaturated soils including hydraulic hysteresis. In particular, an incremental model is proposed in this work for the evolution of water retention properties of the soil with deformation; iv) finally, a new formulation for large deformation analysis of saturated porous media. The formulation is based on the Jaumann stress rate and transformation of all the state variables to the configuration at last time step. In the proposed method, the nodal shape function derivatives are only calculated once in each time step leading to less computational cost of the algorithm when a meshfree method is used. Furthermore, nonlinear stiffness matrices (due to effects of large deformations) obtained are independent of the stresses in the medium leading to more stable numerical results. Application of the approaches proposed is demonstrated using an exhaustive array of numerical results including saturated and unsaturated soils. Excellent agreements are obtained between the numerical results and baseline data reported in the literature in all the cases considered.