A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture
A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture
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DOI：
10.3390/app9050830
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发表时间：
2019-03-01
影响因子：
2.7
通讯作者：
Clarke, Philip L.
中科院分区：
文献类型：
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作者：
Bahmani, Bahador;Abedi, Reza;Clarke, Philip L.
提出了一种岩石断裂的随机体损伤模型。将应变或应力张量分解为正、负两部分，常用于驱动损伤和计算有效应力张量。然而，它们通常不能正确地模拟压缩中的岩石断裂。我们提出了一个基于莫尔-库仑破坏准则的损伤力模型和一个有效应力关系，弥补了这个问题。一个演化方程规定了损伤趋于其准静态极限的速率。该模型的弛豫时间引入了动态断裂的内在长度尺度，并解决了早期损伤模型的网格敏感性问题。损伤方程的常微分形式使得这种补救相当简单，并且能够捕获应变-应力响应的加载速率敏感性。采用异步时空间断伽辽金（aSDG）方法进行宏观模拟。为了研究岩石非均匀性的影响，采用Karhunen-Loeve方法实现了岩石粘聚力随机场。它表明，非均匀性大大区分从那些均匀的岩石，包括最大损伤区的位置断裂模式。此外，随着随机场的相关长度的减小，断裂模式类似于压缩岩石断裂中观察到的角裂纹。
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.