基于西原模型的圆形隧道黏弹-黏塑性解析解

Viscoelasto-viscoplastic solutions for circular tunnel based on Nishihara model

基于西原模型,假设黏塑性体的偏应变张量的一阶导数与瞬态偏应力张量和稳态偏应力张量之差成正比,得到围岩黏塑性区的本构方程。采用拉普拉斯变换与逆变换,推导了圆形隧道黏弹-黏塑性解析解。当t?0时,该解退化成线弹性本构模型的解答;当t??时,该解退化成理想弹塑性本构模型的解答。通过工程实例,分析了围岩位移场、应力场和黏塑性区半径随时间的变化规律。当支护力保持不变时,围岩不同位置位移、围岩黏塑性区半径将随时间增长而持续增大并趋于稳定;围岩黏弹-黏塑性特征对径向应力和黏弹性区切向应力影响较小,对黏塑性区切向应力影响较大,越靠近洞壁处,切向应力随时间变化越剧烈。此外,不同支护力作用下洞壁处的切向应力在支护初期均较大,因此应采用及时支护的策略;考虑到围岩黏弹-黏塑性特征对支护力的影响,建议采取让压支护技术以保证围岩和衬砌的稳定性。

Based on Nishihara model, the first derivative of the deviatoric strain tensor of the viscoplastic element is assumed to be proportional to the difference between the transient deviatoric stress tensor and the steady-state deviatoric stress tensor. Thus, the constitutive equation of ground in viscoplastic region is obtained. The viscoelasto-viscoplastic solutions are derived by means of Laplace transform and Laplace reverse transform. While the time t is close to 0, the viscoelasto-viscoplastic solutions could be degenerated into linear elastic solutions. While the time t tends to infinity, the solutions could be simplified into perfectly elastic-plastic solutions. The time-dependent performances of ground displacement, ground stress and the plastic zone are investigated through an engineering example. When the support force remains constant, the ground displacement and the radius of plastic zone increase continuously with time and then tend to be stable. The influence of time-dependent behavior on the radial stress and tangential stress of viscoelastic region are not very obvious, while the influence on the tangential stress in viscoplastic region is much larger. For the rock mass around the wall in viscoplastic region, the tangential stress changes faster with time. In addition, the tangential stress of tunnel wall under different supporting forces is larger at the initial stage of support, so the strategy of timely support should be adopted. Considering the influence of ground time-dependent performances on the support, the ductile support is suggested to ensure the stability of the surrounding rock and lining.