Though a number of formulations have been proposed for phase--field models for hydraulic fracture, the definition of the degraded poroelastic strain energy varies from one model to another. This study explores previously proposed forms of the poroelastic strain energy with diffused fracture and assesses their ability to recover the explicit fracture opening aperture. We then propose a new form of degraded poroelastic strain energy derived from micromechanical analyses. Unlike the previously proposed models, our poroelastic strain energy degradation depends not only on the phase--field variable (damage) but also on the type of strain energy decomposition. Comparisons against closed form solutions suggest that our proposed model can recover crack opening displacement more accurately irrespective of Biot's coefficient or the pore--pressure distribution. We then verify our model against the plane strain hydraulic fracture propagation, known as the KGD fracture, in the toughness dominated regime. Finally, we demonstrate the model's ability to handle complex hydraulic fracture interactions with a pre--existing natural fracture.

翻译：尽管已提出众多液压断裂相场模型的数学表述，但退化后的孔隙弹性应变能定义在不同模型间存在差异。本研究系统分析了已有扩散型断裂孔隙弹性应变能形式的理论框架，并评估其还原显式断裂张开孔径的能力。基于微观力学分析，我们提出了一种全新的退化孔隙弹性应变能形式。与既有模型不同，该孔隙弹性应变能退化不仅依赖于相场变量（损伤），还受应变能分解类型的影响。与封闭解析解的对比表明，无论比奥系数或孔隙压力分布如何，所提模型均能更精确还原裂纹张开位移。随后在韧性主导机制下，我们针对平面应变水力裂缝扩展（即KGD裂缝）完成了模型验证。最终，通过预存天然裂缝的复杂水力裂缝相互作用案例，展示了该模型的工程适用性。