The Park-Paulino-Roesler (PPR) cohesive zone model (CZM) for coal was established for analyzing mixed-mode I/II fractures using semicircular specimens under punch-through shear (PTS) and three-point bending (SCB) tests. In these methods, the main parameters of the fracture were obtained through SCB tests and PTS tests. And according to the experimental results, the coal specimens show obvious characteristics of ductile fracture under mode I and II loading. Moreover, hydraulic and supercritical carbon dioxide (ScCO₂) fracture tests were conducted, and accordingly, it was found that the crack initiation pressure of coal specimens for hydraulic fracturing is 17.76 MPa, about 1.59 times that driven by ScCO₂. And the crack initiation time of coal with ScCO₂ fracturing is 123.73 s, which is 1.58 times that for hydraulic fracturing. A macrocrack eventually formed in the coal specimen due to the hydraulic drive, which penetrated through the entire specimen. Yet, there was no crack penetrating the whole fracture specimen and several widely distributed secondary cracks in the fractured coal specimens by ScCO₂. Furthermore, zero-thickness pore pressure cohesive elements were utilized to investigate multicrack propagation in coals undergoing hydraulic and ScCO₂ fracturing. The constitutive relationships of the established PPR CZM were introduced into the cohesive elements. The obtained results are consistent with the hydraulic and ScCO₂ fracturing experiment results for the coal specimens. This indicates that the established PPR CZMs can accurately represent the crack propagation behavior in coals for hydraulic and ScCO₂ fracturing.

中文翻译：

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水和超临界二氧化碳在煤中压裂的数值模拟与基于潜在的粘性带模型

建立了煤的 Park-Paulino-Roesler (PPR) 粘性带模型 (CZM)，用于在穿通剪切 (PTS) 和三点弯曲 (SCB) 测试下使用半圆形试样分析混合模式 I/II 裂缝。在这些方法中，断裂的主要参数是通过 SCB 测试和 PTS 测试获得的。并且根据实验结果，煤样在I和II型加载下表现出明显的韧性断裂特征。并进行了水力压裂和超临界二氧化碳（ScCO ₂）压裂试验，发现水力压裂煤样的裂纹起裂压力为17.76 MPa，约为ScCO ₂驱动的1.59倍。以及含 ScCO ₂的煤的裂纹萌生时间压裂时间为123.73 s，是水力压裂的1.58倍。由于液压驱动，最终在煤试样中形成宏观裂纹，并贯穿整个试样。然而，ScCO ₂并没有贯穿整个断裂试样的裂纹，并且在断裂煤试样中出现了几个广泛分布的二次裂纹。此外，利用零厚度孔隙压力粘性元素来研究进行水力压裂和 ScCO ₂压裂的煤中的多裂纹扩展。已建立的 PPR CZM 的本构关系被引入到内聚元素中。所得结果与水力和 ScCO ₂一致煤样的压裂实验结果。这表明已建立的 PPR CZM 可以准确地表示水力压裂和 ScCO ₂压裂煤中的裂纹扩展行为。