Theoretical model for evolution of plastic zone of rock mass around deep tunnels and its comparison with in-situ observation
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摘要: 在高地应力作用下，深部巷道围岩的变形破坏过程表现出了显著的时空效应，研究围岩塑性区的演化规律有助于支护方案的设计与围岩稳定性分析。深部围岩的变形破坏可以看作是其力学性质由固体向流体转换的过程，具有连续渐进相变的特点。结合统计物理学观点，从能量与变形的角度分析了深部围岩塑性区的演化规律：采用有限差分法求解了围岩塑性区演化的kink波解，分析了各参数对塑性区演化过程的影响规律；通过岩石密度–波速关系曲线以及质量守恒定律，建立了围岩波速与塑性应变之间的定量关系，可反演出围岩的变形与应力状态；通过与现场实测数据进行对比，发现kink波解可以很好地描述围岩塑性区的分布及演化规律，验证了理论模型的准确性，可为深部围岩的稳定性分析及灾害防控提供新的思路。Abstract: Under the action of high geo-stress, the deformation and fracture process of surrounding rock mass near deep tunnels is time-dependent. Studying the evolutionary laws of plastic zone in surrounding rock mass is helpful in the optimization of support schemes and analysis of tunnel stability. The deformation and fracture of surrounding rock mass, showing the characteristics of continuous phase transition, can be regarded as a transition process of mechanical properties from solid to liquid. Based on the statistical physics, the evolutionary process of plastic zone in surrounding mass is analyzed from the viewpoint of energy and deformation. The kink wave solution is solved by using the finite difference method, and the sensitivity analysis of parameters in the governing equation is performed. According to the laws of conservation of mass and the relationship between density and ultrasonic velocity, the quantitative relationship between ultrasonic velocity and plastic strains is established to back-reproduce the stress and deformation state of surrounding rock mass. Compared with the in-situ data, it is noted that the kink wave solution can describe the distribution and evolution of plastic zone well, which validates the accuracy of the proposed theoretical model. The results may provide a novel way for the stability analysis and disaster prevention of deep tunnels.
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图 9 不同时刻下巷道围岩塑性区分布
Figure 9. Distribution of plastic zone of surrounding rock mass at different time
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图 14 围岩塑性区实测数据与理论对比
Figure 14. Comparison between theoretical prediction and in-situ data
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