This article revisits the formulation of the J-integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J-integral in finite element models overestimates the length of hydraulic fractures in the viscosity-dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of the J-integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of the J-integral, termed the JHFM$J_{HFM}$ and JAHFM$J_{HFM}^A$-integral, that demonstrate an enhanced ability to predict viscosity-dominated propagation. In particular, such JHFM$J_{HFM}$-integrals accurately extract stress intensity factors in both viscosity and toughness-dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness-viscous propagation regimes. Both techniques are combined to form an implicit front-tracking JHFM$J_{HFM}$-algorithm capable of quickly converging on the location of the fracture front independently to the toughness-viscous regime of propagation. The JHFM$J_{HFM}$-algorithm represents an energy-based alternative to the aperture-based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro-mechanical finite element simulations at the reservoir scale.

中文翻译：

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水力断裂力学的增强 J 积分

本文在水力断裂力学的背景下重新审视了J积分的公式。我们证明，在有限元模型中使用经典的J积分高估了以粘度为主的传播方式中水力裂缝的长度。有限元分析表明，不准确的流体压力数值解是造成J积分精度损失的原因。有了这种理解，提出了两个新颖的贡献。第一个贡献由J积分的两个变体组成，称为ĴHF米$J_{HFM}$和Ĵ一个HF米$J_{HFM}^A$-积分，表明预测粘度为主的传播的能力增强。特别是，这样的ĴHF米$J_{HFM}$-积分准确地提取了以粘度和韧性为主的传播方式中的应力强度因子。第二个贡献包括一种从适用于整个韧性-粘性传播机制的能量释放速率中提取传播速度的方法。两种技术结合起来形成一个隐式的前向跟踪ĴHF米$J_{HFM}$- 算法能够快速收敛于断裂前沿的位置，独立于韧性-粘性传播机制。这ĴHF米$J_{HFM}$-算法代表了一种基于能量的替代方法，它经常与隐式水平集算法一起用于模拟水力压裂的基于孔径的方法。在裂缝的各种分辨率下进行的模拟表明，新方法适用于储层规模的流体力学有限元模拟。