ISSN 1000-3665 CN 11-2202/P

    考虑微裂纹力学行为的岩石单轴压缩损伤模型

    A compressive damage model for a rock considering the microcrack mechanical behavior

    • 摘要: 针对目前岩石压缩损伤模型未能很好地同时考虑微裂纹滑移与扩展对岩石总变形的贡献、微裂纹复合扩展准则及岩石损伤程度对被激活裂纹数量影响等不足,基于细观力学对微裂纹在单轴压缩荷载下的滑移及扩展机理展开研究。首先根据微裂纹滑移模型及能量平衡原理,建立了岩石单轴压缩应力应变关系,并认为微裂纹服从Weibull分布模型;进而以应变能密度准则作为微裂隙扩展判据,采用迭代法求解复合型断裂的翼裂纹扩展长度,并获得用翼裂纹扩展长度表示的岩石损伤变量演化方程,由此提出了一个新的岩石单轴压缩损伤模型,并验证了其合理性;最后,采用参数敏感性分析研究了微裂纹长度及摩擦系数和岩石断裂韧度对岩石力学特性的影响。结果表明:由本模型预测得到的岩石单轴压缩峰值强度与试验结果吻合较好,说明了其合理性。同时发现随着微裂纹长度增加及其摩擦系数减小、岩石断裂韧度增加,岩石单轴抗压峰值强度及峰值应变均随之减小。当微裂纹长度由60 μm增加到120 μm时,岩石单轴抗压峰值强度近似线性降低;而当微裂纹摩擦系数由0.5增加到0.8及岩石断裂韧度由0.3 MPa·m1/2增加到0.6 MPa·m1/2时,岩石单轴抗压峰值强度均是先缓慢增加,而后迅速增加。本研究为岩石压缩损伤本构模型的建立提供了一条新的思路,具有重要的理论意义。

       

      Abstract: The contributions of the microcrack sliding and propagation to the rock total deformation, the mixed propagation criterion of the microcrack, and the influence of the rock damage degree on the number of the activated microcracks are not completely considered in the existing rock compressive damage model. Thus, the microcrack sliding and propagation mechanism under uniaxial compression was studied with the mesoscopic mechanics. Firstly, the uniaxial compression stress-strain relationship was developed according to the microcrack sliding model and energy balance which assumed the microcracks being Weibull distribution. Then the mixed fracture propagation length of the wing-crack was solved with the strain energy density criterion as the microcrack propagation criterion and iteration method. The damage evolution equation was obtained with the wing-crack propagation length. A new damage model for the rock under uniaxial compression was proposed and verified. Finally, the parametric sensitivity analysis was adopted to study the effects of the microcrack length, friction coefficient, and rock fracture toughness on the rock mechanical properties. The results show that the rock climax strength from the proposed model is consistent with the corresponding test result, indicating that the proposed model is reasonable. The uniaxial compression climax strength and strain both decrease with the increase of the microcrack length and the decrease of the microcrack friction coefficient. When the microcrack length increases from 60 μm to 120 μm, the uniaxial compression climax strength almost decreases linearly. When the microcrack friction coefficient increases from 0.5 to 0.8 and the rock fracture toughness increases from 0.3 MPa·m1/2 to 0.6 MPa·m1/2, the uniaxial compression climax strength increases slowly and then rapidly. This study provides new insight into the establishment of the rock damage constitutive model under compression.

       

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