Analytical solution of circular tunnel in elastic-viscoplastic rock mass

Abstract This paper deals with a deep circular tunnel excavated in infinite homogeneous and isotropic elasto-viscoplastic rock mass subjected to a hydrostatic initial stresses. The tunnel is divided into the initial plastic, viscoplastic, and elastic zones. By combining the generalized Bingham model with Mohr-Coulomb yield criteria, analytical solutions of the circular tunnel are derived with the consideration of non-associated flow rule and elasto-viscoplasticity. The initial plastic zone is defined as the instantaneous change of rock mass excavation. Based on the initial plastic zone, the stresses in viscoplastic zone are transferred to the deep surrounding rock with time due to the initial earth stresses. The results are compared with the elastic-brittle solution at static conditions, and the solutions of this paper are validated. Moreover, the presented results shows that the stress and displacement of the surrounding rock varies with time, and the solutions can be obtained at different instants of time.摘要 本文针对受静水初始应力作用、开挖于无限均匀各向同性弹黏塑性岩体（elasto-viscoplastic rock mass）中的深埋圆形隧道展开研究。该隧道被划分为初始塑性区、黏塑性区与弹性区。通过将广义宾汉姆模型（generalized Bingham model）与莫尔-库仑屈服准则（Mohr-Coulomb yield criteria）相结合，同时考虑非关联流动法则（non-associated flow rule）与弹黏塑性特性，本文推导得到圆形隧道的解析解。初始塑性区被定义为岩体开挖的瞬时变化区域。基于初始塑性区，受初始地应力影响，黏塑性区内的应力将随时间向深部围岩传递。将本文所得结果与静力学条件下的弹性脆性解进行对比，验证了本文解析解的正确性。此外，研究结果表明围岩应力与位移随时间发生演化，且可在不同时刻获取对应解析解。