Implementation of a Damage Mechanics Model into the Particle Finite Element Method for Rock Slope Failure Analysis
Authors: Wang Liang , Lei Qinghua 
Published: September 2022

ABSTRACT:
We implement a damage mechanics model into the particle finite element method to simulate the pre- and post-failure processes of rock slopes. In this computational framework, the stress-driven strain localisation and damage evolution are modelled based on a continuum damage mechanics model; discrete discontinuities like faults are represented as thin continuum layers of equivalent properties; the particle finite element method is used to solve and track the large deformation of rock masses. In the paper, we first present the mathematical formulation of the proposed model and then conduct a thorough validation of our model for simulating damage propagation against well-documented experimental data. We further apply the model to simulate progressive failure phenomena of a naturally faulted rock slope including both the pre-failure degradation and post-failure runout, demonstrating the strong capability of our model in capturing the emergence, evolution and consequences of catastrophic rock slope failure. Our work has important implications for understanding the physical mechanisms driving the progressive destabilisation and catastrophic failure phenomena of faulted rock slopes in nature.

1. INTRODUCTION
Landslide phenomena usually involve the movements of a mixture of rock, earth and/or debris downslope (Cruden, 1991), which tend to develop over time through several different stages, from initiation to propagation and to final deposition (Leroueil, 2001). A landslide may exhibit different phases of movements, and one of the most important episodes is the formation of a fully developed slip surface (Hungr et al., 2014), which is often referred to as a failure. Before the failure, the deformation processes are usually controlled by the variation of stresses, showing a progressive destablisation behaviour (Eberhardt, 2008; Leroueil, 2001); during or after the failure, the geomaterials that have undergone a certain degree of stress loss may show a significantly increased mobility, leading to rapid inertia-dominated movements (Hungr et al., 2014). To describe the complex behaviour of geomaterials during these different phases, various approaches have been developed for landslide analysis (Chen, 2007; Denlinger, 2004; Duncan, 1996; Griffiths & Lane, 1999; Savage & Hutter, 1989; Sloan, 2013). For the pre-failure stage, the state of failure has been determined either statically or dynamically: (i) the static stability is mostly analysed using the limit equilibrium method (Duncan, 1996), limit analysis method (Chen, 2007; Sloan, 2013) and strength reduction method (Dawson et al., 1999; Griffiths & Lane, 1999); (ii) the dynamic stability may be assessed by describing the stress-strain relationship of geomaterials under complex conditions (Duncan, 1996), solved using different numerical techniques. As for the post-failure stage involving large deformations, the moving mass is usually characterised by the simplified Navier-Stokes equations for flow-like problems (Savage & Hutter, 1989). These two phases of slope movements (i.e. pre- and post-failure stages) have long been treated separately in geotechnical analyses due to the lack of a unified computational framework for describing the entire landslide process (Soga et al., 2016).