An effective and stabilised (u - pl) SPH framework for large deformation and failure analysis of saturated porous media

Abstract

Particle-based methods such as SPH have been proven to be powerful numerical tools for addressing challenges in solving coupled large deformation and failure of porous materials. In these applications, explicit time integration schemes are commonly adopted to integrate the coupled pore-water pressure equation. The Courant–Friedrichs–Lewy condition is required and imposes a strong restriction on the time increment, which is inversely proportional to the water bulk modulus, leading to a significant increase in the overall computational costs. This affects successful applications of SPH in solving field-scale fully coupled large deformation and failure of porous media. To address this problem, this study proposes a computationally efficient three-point integration (TPI) scheme that removes the influence of water bulk modulus from the pore-water pressure equation, enabling larger time increments for the time integration and hence saving computational costs for field-scale applications. Furthermore, a stabilised method is proposed to enable SPH to solve coupled flow-deformation of saturated porous media involving negative excess pore-water developments for the first time. The proposed SPH algorithm is verified against analytical and finite element solutions for small deformation ranges. Thereafter, it is applied to predict challenging problems involving large deformation and retrogressive failure of saturated porous materials, where contractive and dilative responses of porous materials can cause significant variations and instabilities in the development of excess pore-water pressure. The results suggest that the proposed SPH algorithm is stable and suitable for handling field-scale applications.