深埋隧洞卸荷过程中围岩应力变形的时间效应

深埋圆形隧洞围岩的应力应变状态是深地下工程设计的重要参考依据。针对岩体内部的缺陷引起的应力集中和松弛，建立了局部附加应力与缺陷尺度和卸载时间之间的联系，得到圆形隧洞在卸载时围岩破坏前遵循的一系列方程，进而推导出围岩变形的解析积分表达式。将围岩应力应变的时间效应分为卸载阶段和应力松弛阶段，通过逐步逼近法分别求解了围岩的应力和变形的近似解析表达式。该近似解析式考虑了岩体内部缺陷处应力集中的影响和卸载的时间效应，可用来考察不同半径处缺陷应力集中和卸载快慢对应力变形状态的影响。计算表明，围岩内部在卸载过程中和卸载完成后均存在局部附加拉应力集中，围岩变形在卸载完成后仍会进一步增加。

Time effect of stress and deformation of surrounding rock of circular tunnels during unloading

The stress state and deformation of surrounding rock of deep-seated tunnels are very important to design of underground engineering. With consideration of the stress concentration and relaxation induced by the nonuniformities, a series of equations for the surrounding rock follows in the deforming process, including the relationship between excess stress and nonuniformity size and unloading duration, is established to deduce the analytic expression of deformation of surrounding rock. The whole deforming process is divided into two stages: the unloading stage and the stress relaxation stage. And the approximate analytic expressions of stress and deformation are solved by successive approximation method. The solutions take the stress concentration and time effect of unloading into account; and they reflect the influence of nonuniformity and unloading duration on the stress and deformation of surrounding rock. Analytical results show that the local excess tensile stress concentrations appears in surrounding rocks in and after the unloading process; and the deformation have a additional increase after unloading.