Theoretical model for evolution of plastic zone of rock mass around deep tunnels and its comparison with in-situ observation

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.