A statistical damage constitutive rock model based on elastic energy release rate
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摘要:
为了揭示岩石变形的破坏机理以及岩石材料产生损伤的本质原因，文章对岩石材料变形规律和力学特性进行分析后，再以损伤变量作为影响岩石变形和力学性能变化的内变量，采用能量原理、有效应力原理和统计损伤理论构建了一种基于弹性能释放率的新型岩石统计损伤本构模型。该损伤模型进一步完善了岩石损伤本构模型的理论体系，弥补了传统损伤模型无法合理解释引发岩石破坏原因的不足。利用岩石试验数据对损伤模型的参数进行确定，并将损伤演化模型代入弹性能-应变模型中，分析在加载过程中岩石弹性能变化的规律。结果表明：模型曲线与试验曲线在峰前变形阶段几乎重合，说明损伤模型可以很好地反映岩石的变形特性；在初始加载阶段，岩石的损伤变量随着轴向应变的增大而增大，说明在荷载作用下，岩石内部裂隙逐渐发展发育，使得岩石材料的损伤逐步积累；在围压达到10 MPa以上时，损伤-应变曲线基本重合。同时，在初始加载时刻，损伤-应变曲线增长率急剧上升，大约在岩石应变为0.01%时，损伤-应变曲线趋于平稳变化状态；且由于岩石在峰值应力点附近损伤迅速累积，进而使得损伤变量在数值上快速增大到1，这说明了围压的增大使得岩石破坏极限得到显著的提升。
Abstract:In order to truly reveal the mechanism of rock deformation and failure and the nature of rock material damage, based on the analysis of rock material deformation law and mechanical characteristics, a rock damage constitutive model based on elastic energy release rate is established using the energy principle. Taking the damage variable as an internal variable that affected the change of rock performance, a new type of statistical damage constitutive model for rock is established based on the effective stress principle and statistical damage theory. It further improves the theoretical system of rock damage constitutive model and mades up for the shortcomings that traditional damage models cannot reasonably explain the causes of rock failure. The parameters of the damage model are determined using the rock test data, and the feasibility and applicability of the damage model are verified through a comparative analysis of the model curve and the test curve. The damage evolution model is substituted into the elastic energy-strain model to analyze the law of rock elastic energy change during loading. The results show that the model curve and the test curve almost coincide in the deformation phase before the peak, indicating that the damage model perfectly reflects the linear elastic deformation characteristics of the rock. The model curve and the test curve do not agree well at the post-peak stage, but they also have a good description of the nonlinear deformation law of the rock. The damage model also better reflectes the relationship between the accumulation and release of elastic energy and the damage and destruction of rocks, and the characteristics of the degree of rock damage increases with the increasing confining pressure. At the same time, in the initial loading stage, the damage variable of the rock increases with the increasing axial strain. This shows that under the load, the internal cracks in the rock gradually develop, so that the damage of the rock material is gradually accumulated. When the confining pressure reaches above 10 MPa, the damage-strain curves basically coincide. The growth rate of the damage-strain curve rises sharply at the moment of initial loading. When the strain of the rock is about 0.01%, the damage-strain curve changes from rapid growth to steady growth. Because the damage quickly accumulates near the peak stress point of the rock, the damage variable rapidly increases to 1 in value.
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Key words:
- rock /
- elastic energy release rate /
- statistical damage /
- stress-strain /
- elastic energy /
- damage variable
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表 1 三轴压缩试验结果
Table 1. Triaxial compression test results
围压（σ3）/ MPa 峰值应力（σ1c）/ MPa 峰值应变（ε1c） 0 49.96 0.00542 10 75.95 0.00555 20 100.27 0.00657 30 132.63 0.00737 
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表 2 参数计算值
Table 2. Parameter values
围压（σ3）/ MPa 0 10 20 30 m 0.429 0.478 0.509 0.534 F0 1.280 1.340 1.630 1.760 R2 0.956 0.967 0.957 0.978
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