In this study, we aim at investigating the coupling between poroelasticity (including the fluid flow) and gradient damage phenomena in saturated porous media. To this end, we first extend the thermodynamics-based Biot–Coussy theory of poroelasticity in order to incorporate gradient damage processes. Taking advantage of this framework, we establish a variational formulation for the proposed model, expressed as a four-field incremental minimization problem of a total energy functional which includes poroelastic energy as well as dissipated energy related to damage growth together with Darcy-like fluid flow. Moreover, after a careful analysis of the so-called in each increment, the incremental minimization is reduced to that of three fields, namely, the displacement and damage fields of the skeleton phase of the porous media as well as the pore fluid pressure. Subsequently, we proceed to the numerical implementation of the variational problem via a semi-staggered optimization algorithm and apply it to a first benchmark modeling for which corresponding solution as well as numerical results for hydraulic fracturing are available. Finally, we perform an application of the proposed model for the evaluation of an Excavation Damage Zone (EDZ) around an underground waste storage gallery. The model is shown to be able to deliver sufficiently reliable predictions.

中文翻译：

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梯度损伤的增量变分法与饱和介质的孔隙弹性相结合

在本研究中，我们旨在研究饱和多孔介质中孔隙弹性（包括流体流动）与梯度损伤现象之间的耦合。为此，我们首先扩展基于热力学的多孔弹性毕奥-库西理论，以纳入梯度损伤过程。利用这个框架，我们为所提出的模型建立了变分公式，表示为总能量泛函的四场增量最小化问题，其中包括孔隙弹性能量以及与损伤增长相关的耗散能量以及类达西流体流动。而且，经过仔细分析所谓的每个增量，增量最小化为三个场，即多孔介质骨架相的位移场和损伤场以及孔隙流体压力。随后，我们通过半交错优化算法对变分问题进行数值实现，并将其应用于第一个基准模型，该模型提供了相应的解决方案以及水力压裂的数值结果。最后，我们应用所提出的模型来评估地下废物储存廊道周围的开挖损坏区（EDZ）。该模型被证明能够提供足够可靠的预测。