Abstract Linear Elastic Fracture Mechanics (LEFM) is a widely applied theory to numerically simulate hydraulic fracture initiation and propagation in the subsurface. However, LEFM with the typical fracture toughness measured from unconfined laboratory tests does not apply to hydraulic fracturing applications under subsurface conditions because the fracture toughness is affected by the confining stress and fluid lag at the fracture tip. Thus, the apparent fracture toughness was proposed by Rubin (1993) to consider the contributions of fluid lag and confining stress. The main objective of this study is to validate the applicability of LEFM with the apparent fracture toughness in simulating hydraulic fracture under subsurface conditions. We utilized the finite element models to compare the near-tip stress state between the LEFM approach and the cohesive zone model (CZM), which considers the effect of confining stress and fluid lag. In addition, we compared the analytical solutions of fracture energy between LEFM and CZM. This study showed that the near-tip stress state of CZM outside the fluid lag and cohesive zone is comparable to the stress field predicted by LEFM with the apparent fracture toughness. However, LEFM with the fracture toughness measured from standard unconfined laboratory tests underestimates the near-tip stress state of fractures under confining stress. This study also revealed that the fracture energy of fluid-driven fractures calculated by CZM is identical to the fracture energy estimated from the approach of LEFM with the apparent fracture toughness. Thus, this study demonstrated that LEFM with the apparent fracture toughness is an appropriate and accurate method to simulate hydraulic fracture propagation in the subsurface.

中文翻译：

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LEFM 在水力断裂建模中应用的表观断裂韧性

摘要 线弹性断裂力学（LEFM）是一种广泛应用于数值模拟地下水力裂缝起裂和扩展的理论。然而，具有从无侧限实验室测试中测得的典型断裂韧度的 LEFM 不适用于地下条件下的水力压裂应用，因为断裂韧度受裂缝尖端的围压和流体滞后影响。因此，Rubin (1993) 提出了表观断裂韧性来考虑流体滞后和围压的贡献。本研究的主要目的是验证具有表观断裂韧性的 LEFM 在模拟地下条件下的水力压裂中的适用性。我们利用有限元模型来比较 LEFM 方法和考虑了围压和流体滞后影响的内聚区模型 (CZM) 之间的近尖端应力状态。此外，我们比较了 LEFM 和 CZM 的断裂能解析解。该研究表明，流体滞后和内聚区外的 CZM 的近尖端应力状态与具有表观断裂韧性的 LEFM 预测的应力场相当。然而，具有从标准无侧限实验室测试中测量的断裂韧性的 LEFM 低估了围压下裂缝的近尖端应力状态。该研究还表明，由 CZM 计算的流体驱动裂缝的断裂能与从具有表观断裂韧性的 LEFM 方法估计的断裂能相同。因此，