The state of stress and deformation of surrounding rock in deep-buried tunnels provide important basis in the designing of underground engineering. The relationship of local additional stress and the size of defects as well as unloading time is established. Pointing at the stress concentration and relaxation induced by the internal defects of rocks. Then the integral expression parsing of surrounding rock was derived. The time effect of stress and deformation of surrounding rock was divided into unloading and stress relaxation stage, the approximate analytic expression of stress and deformation of surrounding rock was found out by successive approximation method. The approximate analytic formula considering of the influence of stress concentration in the internal of rock as well as the time effect of unloading, can be used to investigating the influence of stress and deformation form which caused by defects of different radius of stress concentration. Analytical results show that the local excess tensile stress concentrations in surrounding rocks appear during and after the process of unloading, and the deformation have an additional increase after unloading.


The state of stress and strain of underground engineering is an important basis in engineering design, so it has a very practical significance to understand of such a state. Although it often needs to make some idealized assumptions in theoretical analysis, which has a certain distance with the actual situation, the theoretical analysis has an irreplaceable role in providing the understanding of the nature of the researched problems, insight into the role of relevant parameters in the problems, as well as a numerical solution of the reference value (Cai 2001).

The traditional equation for analysis of stress and strain is based on the assumption of continuous and homogeneous. The underground engineering is usually simplified as the plane strain problem of circular section tunnel in isotropic infinite homogeneous medium.

Different researchers analysis the state of stress and strain of underground engineering using different material models and strength criterion, with the considering of the plastic flow rule, which has achieved fruitful results (Browne et al. 1983, Sharan 2005 & 2008, Rodionov & Sizov 1988, Park & Kim 2006, Lee & Pietruszczak 2008).

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