The behavior of support-surrounding rock interaction considering pre-reinforcement is investigated in this paper. Since previous analyses give little consideration to the influence of pre-reinforcement on the support-surrounding rock interaction, the equivalent material approach is adopted such that the ground strength is improved as the result of pre-reinforcement. The fictitious support pressure is introduced to quantify the spatial effect of excavation face, whose solution varies with the configurations of the surrounding rock based on the plastic zone distributions. The compatibility equations of tunnel displacement and support pressure are established accounting for the tunnel displacement prior to support installation. Using the critical displacements defining the transition of different configurations, an analytical method for the whole process of support and surrounding rock action is proposed. Plane-strain analysis is performed to obtain the tunnel displacement and reaction pressure of primary support along the tunnel axis. The proposed method allows a fast dimensioning of the primary support considering the effect of pre-reinforcement. The analytical results are validated by 3D numerical simulations and in-situ measurement. Additionally, a comparison reveals that the proposed model excels the traditional convergence-confinement method in solving the mentioned problem.

本文研究了考虑预加固的支护围岩相互作用行为。由于先前的分析很少考虑预加固对支护围岩相互作用的影响，因此采用等效材料方法，通过预加固提高地基强度。引入虚拟支护压力来量化开挖面的空间效应，其解随基于塑性区分布的围岩配置而变化。考虑到支护安装前的隧道位移，建立了隧道位移和支护压力的相容性方程。使用定义不同配置过渡的临界位移，提出了支护及围岩作用全过程的分析方法。进行平面应变分析以获得沿隧道轴线的主要支护的隧道位移和反作用压力。考虑到预钢筋的影响，所提出的方法允许快速确定主要支撑的尺寸。分析结果通过 3D 数值模拟和原位测量得到验证。此外，比较表明所提出的模型在解决上述问题方面优于传统的收敛限制方法。考虑到预钢筋的影响，所提出的方法允许快速确定主要支撑的尺寸。分析结果通过 3D 数值模拟和原位测量进行了验证。此外，比较表明所提出的模型在解决上述问题方面优于传统的收敛限制方法。考虑到预钢筋的影响，所提出的方法允许快速确定主要支撑的尺寸。分析结果通过 3D 数值模拟和原位测量得到验证。此外，比较表明所提出的模型在解决上述问题方面优于传统的收敛限制方法。