Abstract
We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture.
Highlights
Interfacial, particle, and bulk or continuum models form the majority of approaches used for failure analysis of quasi-brittle materials at continuum level
We propose a stochastic bulk damage model for rock fracture
We employ a stochastic damage model wherein rock cohesion is treated as a random field. This aspect is important for the uniaxial compression examples considered, as due to the lack of macroscopic stress concentration points highly unrealistic fracture patterns will be obtained by using a homogeneous rock mass model
Summary
Interfacial, particle, and bulk or continuum models form the majority of approaches used for failure analysis of quasi-brittle materials at continuum level. Time-relaxed damage formulations possess an internal time parameter which through its interaction with elastic wave speeds introduce a finite length scale for the damage model in transient settings [25,26,27,28] Related to these remedies is the phase field method which closely resembles a gradient-based damage model [29]. We employ a stochastic damage model wherein rock cohesion is treated as a random field This aspect is important for the uniaxial compression examples considered, as due to the lack of macroscopic stress concentration points highly unrealistic fracture patterns will be obtained by using a homogeneous rock mass model.
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