Enhancement of an FDEM-Based Geomechanical Simulation Software with Hybrid FEM-FDEM and Elasto-Plastic Modeling Capabilities: Application to Slope Stability Analysis
Authors: Lisjak A. , He L. , Ha J. , Tatone B. S. A. , Mahabadi O. K. 
Published: August 2024

ABSTRACT:
The goal of this paper is to present recent developments aimed at improving computational efficiency and extending the range of material applicability of a 2D/3D FDEM geomechanical simulation software. Firstly, a hybrid FEM-FDEM logic was devised to allow for user-defined regions of the domain to be modeled as a continuum, while the remainder is captured by the FDEM formulation with an intrinsic cohesive zone model explicitly capturing fracturing. Benchmarking results indicate simulation speed-ups of up to 48x when using the new logic versus the traditional full FDEM approach. Secondly, the finite element formulation was enhanced with elasto-plastic constitutive models based on Drucker-Prager and Mohr-Coulomb failure criteria, effectively broadening the range of applicability to materials that exhibit irreversible damage processes under load without breaking. These developments were initially verified by comparing simulated stress distributions against analytical solutions for select boundary value problems. Practical validation of the novel FDEM formulation was achieved by capturing the variation of critical failure mechanism observed in a slope as a function of the type of rock mass jointing. The factors of safety computed with the strength reduction method compared very well with those reported in the literature for commercially available programs based on DEM and FEM. Finally, a direct comparison between FEM-based, elasto-plastic and FDEM-based, brittle-fracture models is presented for the case of a homogeneous rock slope.

1. INTRODUCTION
The finite-discrete element method (FDEM) is a numerical method originally introduced by Munjiza et al. (1995) as a means of combining principles of continuum mechanics, such as the theory of elasticity and non-linear fracture mechanics, with discrete element algorithms to model fracture, fragmentation, and failure of cementitious materials and rocks. Building upon Munjiza's pioneering work, FDEM has been further developed by a multitude of research groups and organizations worldwide, and applied to a variety of rock mechanics and rock engineering problems where consideration of brittle fracturing processes is critical. Over the years, developments of FDEM have focused on several major areas of interest including (i) improvement of the core algorithms for deformation, fracture, interaction, and contact detection (e.g., Lei et al., 2016, Fukuda et al., 2021, Cai et al., 2023), (ii) incorporation of multi-physics capabilities to account for hydraulic and thermal effects (e.g., Yan and Jiao, 2018, Yan et al., 2019, Munjiza et al., 2020), and (iii) reduction of simulation run times by parallel computing (e.g., Lei et al., 2014; Lisjak et al., 2018; Fukuda et al, 2019). In the classic implementation of FDEM (Munjiza, 2004), the numerical representation of fractures is achieved by an intrinsic cohesive zone model (ICZM). With this approach, zero-thickness cohesive crack elements are inserted (at the beginning of the simulation) across pairs of adjacent solid finite elements throughout the entire modelling domain. All irreversible ("plastic") deformations are concentrated in the form of yielding and breakage of the interfaces between the solid finite elements, which remain elastic.