Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media
Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media
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DOI：
10.1016/j.cma.2015.09.021
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发表时间：
2016-06-01
影响因子：
7.2
通讯作者：
Mauthe, Steffen
中科院分区：
文献类型：
--
作者：
Miehe, Christian;Mauthe, Steffen
流体和水分驱动的裂纹扩展变形多孔介质中的预测已经取得了越来越多的兴趣，在最近几年，特别是关于水力压裂，所谓的“压裂”的建模。在这里，挑战是链接至少三个建模成分（i）的固体骨架和流体体相的行为和它们的相互作用，（ii）裂纹扩展上不先验已知的路径和（iii）额外的流体流动内开发的裂纹。为此，提出了一个宏观框架的连续相场模拟裂缝在多孔介质中。它提供了一个严格的几何方法的扩散裂纹建模的基础上引入的本构平衡方程的正则化裂纹表面和其模块化的连接到一个Darcy-Biot型散装响应的液压孔隙弹性。该方法克服了与尖锐裂纹不连续性的计算实现相关的困难，特别是当涉及到复杂的裂纹拓扑结构，包括分支。一个模块化的概念，概述了连接的扩散裂纹建模与多孔体材料的流体孔隙弹性响应。这包括一个概括的裂纹驱动力从充满活力的定义对阈值为基础的标准，在有关的固体骨架的流体饱和多孔介质的有效应力。此外，Poiquille型本构连续模拟的额外的流体流动的发展裂缝建议基于变形相关的渗透率，这是缩放的特征长度。该建议的模块化模型结构是利用在数值实现中，通过构建一个强大的有限元方法，基于算法解耦的更新裂纹相场和状态变量的液压孔隙弹性体响应。我们展示了性能的相场制定的骨折的一系列模型问题的水力压裂。稍微修改的框架允许模拟干燥引起的裂纹图案在部分饱和毛细多孔介质。(C)2015 Elsevier B. V.版权所有。
The prediction of fluid-and moisture-driven crack propagation in deforming porous media has achieved increasing interest in recent years, in particular with regard to the modeling of hydraulic fracturing, the so-called "fracking". Here, the challenge is to link at least three modeling ingredients for (i) the behavior of the solid skeleton and fluid bulk phases and their interaction, (ii) the crack propagation on not a priori known paths and (iii) the extra fluid flow within developed cracks. To this end, a macroscopic framework is proposed for a continuum phase field modeling of fracture in porous media. It provides a rigorous geometric approach to a diffusive crack modeling based on the introduction of a constitutive balance equation for a regularized crack surface and its modular linkage to a Darcy-Biot-type bulk response of hydro-poro-elasticity. The approach overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies including branching. A modular concept is outlined for linking of the diffusive crack modeling with the hydroporo-elastic response of the porous bulk material. This includes a generalization of crack driving forces from energetic definitions towards threshold-based criteria in terms of the effective stress related to the solid skeleton of a fluid-saturated porous medium. Furthermore, a Poiseuille-type constitutive continuum modeling of the extra fluid flow in developed cracks is suggested based on a deformation-dependent permeability, that is scaled by a characteristic length. This proposed modular model structure is exploited in the numerical implementation by constructing a robust finite element method, based on an algorithmic decoupling of updates for the crack phase field and the state variables of the hydro-poro-elastic bulk response. We demonstrate the performance of the phase field formulation of fracture for a spectrum of model problems of hydraulic fracture. A slight modification of the framework allows the simulation of drying-caused crack patterns in partially saturated capillar-porous media. (C) 2015 Elsevier B.V. All rights reserved.