A thermodynamically consistent phase field model that accounts for initial stress state is proposed in this paper to simulate the gas migration process in saturated bentonite. The energy contribution due to the fracturing process is included in Coussy’s thermodynamic framework for unsaturated porous media. The possible effect of the interfaces between different phases on the driving force functional for phase field and the effective stress has been identified from the proposed thermodynamic framework. In addition, the initial stress state is innovatively accounted for in the phase field model by introducing a fictitious strain tensor that is calculated from its corresponding initial stress tensor. It is the sum of the fictitious strain tensor and the strain tensor due to elastic deformation that governs the evolution of the phase field. The simulated results showed that the effect of the swelling pressure (regarded as the initial effective stress for a high swelling clay) on the fracture initiation has been well described by the proposed method. Specifically, the effect of either isotropic or anisotropic stress state on the fracturing process can be well reflected by the phase field approach based on Rankine-type fracture criterion. In contrast, the phase field approach based on the Griffith fracture criterion is more appropriate for the isotropic stress state than the anisotropic stress state because of the Poisson’s effect. Moreover, the gas pressure required to trigger the fracturing process needs to exceed the sum of the porewater pressure and the initial stress. The effect of the boundary condition on the evolution of fluid pressure and total stress has been qualitatively captured. It is found that the boundary with higher stiffness leads to a higher gas pressure in the developed fracture and a higher water pressure and total stress in the surrounding porous matrix. In addition, some key experimental findings, such as the preferential gas flow, the build-up of porewater pressure, the almost fully saturated state and the localized consolidation, have been qualitatively captured by the developed phase field model.

为了模拟饱和膨润土中的气体运移过程，本文提出了一种热力学上一致的，解释初始应力状态的相场模型。由于压裂过程而产生的能量贡献包括在库西针对不饱和多孔介质的热力学框架中。从所提出的热力学框架已经确定了不同相之间的界面对相场驱动力和有效应力的可能影响。此外，通过引入虚拟应变张量在相场模型中创新地解决了初始应力状态，该虚拟应变张量是从其相应的初始应力张量计算得出的。虚拟应变张量与弹性变形引起的应变张量之和决定了相场的发展。模拟结果表明，所提出的方法已经很好地描述了膨胀压力（对于高膨胀黏土的初始有效应力）对断裂的影响。具体而言，各向同性或各向异性应力状态对压裂过程的影响可以通过基于兰金型断裂准则的相场方法很好地反映出来。相比之下，由于泊松效应，基于格里菲斯断裂准则的相场方法比各向异性应力状态更适合于各向同性应力状态。此外，触发压裂过程所需的气压必须超过孔隙水压力和初始应力之和。定性地记录了边界条件对流体压力和总应力的影响。已经发现，具有较高刚度的边界导致所形成的裂缝中的气体压力较高，而周围的多孔基质中的水压力和总应力较高。此外，已开发的相场模型定性地捕获了一些关键的实验发现，例如优先气流，孔隙水压力的建立，几乎完全饱和的状态和局部固结。