Brittle and ductile failure of rocks: Embedded discontinuity approach for representing mode I and mode II failure mechanisms

Abstract

SUMMARYIn this work, we present a discrete beam lattice model with embedded discontinuities capable of simulating rock failure as a result of propagating cracks through rock mass. The developed model is a two-dimensional (plane strain) microscale representation of rocks as a two-phase heterogeneous material. Phase I is chosen for intact rock part, while phase II stands for pre-existing microcracks and other defects. The proposed model relies on Timoshenko beam elements enhanced with additional kinematics to describe localized failure mechanisms. The model can properly take into account the fracture process zone with pre-existing microcracks coalescence, along with localized failure modes, mode I of tensile opening and mode II of shear sliding. Furthermore, we give the very detailed presentation for two different approaches to capturing the evolution of modes I and II, and their interaction and combination. The first approach is to deal with modes I and II separately, where mode II can be activated but compression force may still be transferred through rock mass which is not yet completely damaged. The second approach is to represent both modes I and II being activated simultaneously at a point where complete failure is reached. A novel numerical procedure for dealing with two modes failure within framework of method of incompatible modes is presented in detail and validated by a set of numerical examples.

A concrete homogenisation technique at meso-scale level accounting for damaging behaviour of cement paste and aggregates

“…The presence of the voids determines a small degradation of the stiffness of the material, as it is shown in Fig. 24(b), and they have almost no effect on the reduction of the material strength, contrarily to what has been found in the case of bi-phase materials in which the voids represent a significant fraction of the material [76][77][78]. In the model a very small percentage of the voids has been adopted, since the occluded porosity resulting from the drying of the cement paste has been considered embedded in the mortar.…”

Discrete Lattice Element Approach for Rock Failure Modeling

“…The enhanced weak form can be established from the enhanced strain fields, eventually leading to the formulation of the embedded discontinuity, along with a condensed stiffness matrix and a residual vector that incorporates traction at the discontinuity. The full explanation of the 2D and 3D models presented can be found in the literature [11][12]. The presented lattice element model can also be used to solve problems brought about by the failure of fluid-saturated, fractured, poro-plastic materials, using the Biot porous media approach [13], or even to examine the influence of rock specimen shape deviations on uniaxial compressive strength [14].…”

“…This section provides the results of two different numerical simulations, in both 2D and 3D. For the 2D setting, the uniaxial tension test on the 2D Timoshenko beam lattice is chosen to represent the rock specimen [11]. The capabilities of the 3D model are shown using a uniaxial (an unconfined) compression test [12].…”

Geomechanical Model Test and Energy Mechanism Analysis of Zonal Disintegration in Deep Surrounding Rock

“…According to the applied parameters, there are two categories: the stress parameter criterion and the energy parameter criterion [15]. In the stress parameter criterion, a 2D [16] and full 3D [17] discrete beam lattice model with embedded discontinuities were present to simulate cracks propagating through rock mass until complete localized failure. In the energy parameter criterion, the deep rock mass is subjected to processes such as transformation, transmission, dissipation and release of energy during the process of cracks fracture.…”