Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis

Abstract

Stress waves, known as acoustic emissions (AEs), are released by localized inelastic deformation events during the progressive failure of brittle rocks. Although several numerical models have been developed to simulate the deformation and damage processes of rocks, such as non-linear stress-strain behaviour and localization of failure, only a limited number have been capable of providing quantitative information regarding the associated seismicity. Moreover, the majority of these studies have adopted a pseudo-static approach based on elastic strain energy dissipation that completely disregards elastodynamic effects. This paper describes a new AE modelling technique based on the combined finite-discrete element method (FEM/DEM), a numerical tool that simulates material failure by explicitly considering fracture nucleation and propagation in the modelling domain. Given the explicit time integration scheme of the solver, stress wave propagation and the effect of radiated seismic energy can be directly captured. Quasi-dynamic seismic information is extracted from a FEM/DEM model with a newly developed algorithm based on the monitoring of internal variables (e.g. relative displacements and kinetic energy) in proximity to propagating cracks. The AE of a wing crack propagation model based on this algorithm are cross-analysed by traveltime inversion and energy estimation from seismic recordings. Results indicate a good correlation of AE initiation times and locations, and scaling of energies, independently calculated with the two methods. Finally, the modelling technique is validated by simulating a laboratory compression test on a granite sample. The micromechanical parameters of the heterogeneous model are first calibrated to reproduce the macroscopic stress-strain response measured during standard laboratory tests. Subsequently, AE frequency-magnitude statistics, spatial clustering of source locations and the evolution of AE rate are investigated. The distribution of event magnitude tends to decay as power law while the spatial distribution of sources exhibits a fractal character, in agreement with experimental observations. Moreover, the model can capture the decrease of seismic b value associated with the macrorupture of the rock sample and the transition of AE spatial distribution from diffuse, in the pre-peak stage, to strongly localized at the peak and post-peak stages, as reported in a number of published laboratory studies. In future studies, the validated FEM/DEM-AE modelling technique will be used to obtain further insights into the micromechanics of rock failure with potential applications ranging from laboratory-scale microcracking to engineering-scale processes (e.g. excavations within mines, tunnels and caverns, petroleum and geothermal reservoirs) to tectonic earthquakes triggering.

Numerical modelling of microseismicity associated with longwall coal mining

“…The clustering of the microcracks created, both in space and time, is deemed to form an AE event. Lisjak et al (2013) developed a quasi-dynamic technique, whereby the fracture is represented by means of cohesive discrete elements in a FEM/DEM code to model AE activities resulting from brittle failure of rock. Although capable of capturing the intrinsic nature of AE activities, this approach is computationally intensive, which limits its application to field-scale models.…”

“…Many AE simulation methods have been developed to reproduce and interpret laboratory experimental results, including continuum damage models, particle-based discrete element method (DEM) models, lattice models, and the combined finite-discrete element method (FEM/DEM) models (Lisjak et al, 2013).…”

Overview of the numerical methods for the modelling of rock mechanics problems

“…Contrary to Discrete Finite Element Method, the FEM/DEM uses explicit time integration scheme. The FEM/DEM method is used in rock mechanics applications [125,126] and simulation of the behaviour of stone structures [127]. There were some developments of the method considering the reinforcement between discrete elements with application in concrete, but which can be easily used to simulate the rock slopes or tunnel excavations with anchor reinforcements [128].…”

DEM & FEM/DEM MODELS FOR LATERALLY LOADED MASONRY WALLS

“…The height of each element is h = a/2, thus each block has been meshed with 16 elements. In FEM/DEM, the interfaces are made by specific "crack elements", dedicated four nodes cohesive elements which are embedded between the hedges of all adjacent triangular elements pairs since the beginning of simulation [19]. The potential crack path can open everywhere in the mesh, here in order to simulate the behavior of historic masonry panels, in which cracks usually occur mainly in the mortar joints [20,21], two different joints have been used: one inside the blocks and the other between adjacent blocks.…”

“…In order to calibrate the two models, cohesion and friction adopted for joints are the same, whereas the fracture energy in FEM/DEM [19] joints has been evaluated on the base of mortar elastic modulus adopted in DEM. As previously stated, in the DEM, due to rigid block hypothesis, forces are applied at block centers, whereas in the FEM/DEM, forces are lumped at the inner nodes of each block subdivision (Fig.…”