流变岩体中支护圆形隧道施工过程的时效理论解

Analytical Solutions for the Construction of Circular Tunnel Accounting for Timedependent Characteristic of the Rheological Rock

摘要:

针对水平和竖向地应力不相等的一般地应力条件下圆形隧道的断面开挖、纵向推进及衬砌施工问题，用任意黏弹性模型模拟不同岩石流变特性，用与时间相关的开挖函数模拟隧道断面开挖过程，用虚拟支护力等效纵向开挖效应，并在隧道开挖完成后的任意时刻施加弹性支护.采用复变函数方法和拉普拉斯变换技术给出用复位势表达的边界条件和围岩、衬砌接触位置协调条件，建立关于复位势中待定项系数的方程.通过求解方程确定待定项系数，从而得到开挖与支护整个施工过程任意时刻围岩位移和应力理论解答，并与相同条件下有限元解进行了对比.根据解答分析了围岩位移和应力的分布规律以及衬砌施加时刻对围岩位移和应力的影响.根据现有解析程序，可以形成快速预测隧道施工力学状态的计算机系统，方便、快捷地进行相似工程条件下的初步设计.

Abstract:

The problems of lined circular tunnel construction subject to nonhydrostatic initial stresses were considered, accounting for crosssection excavation, longitudinal advancement, and any installation time of the elastic liner. In the derivation, linear viscoelastic models were adopted to simulate the rheological properties of the rock, time dependent excavation process and fictitious stresses were considered to simulate sequential excavation and tunnel advancement, respectively. According to the complex variable method and Laplace transform technique, the boundary and compatibility conditions were expressed by the two potentials, and the equations with respect to the coefficients in potentials were established afterwards. The analytical solutions for stress and displacement were then provided for the whole construction process after the determination of the coefficients by solving these equations. A good agreement between results from Finite Element Method and the analytical solutions had been obtained. Based on analytical solutions, a comprehensive parametrical analyses were then carried out to investigate the distribution discipline of displacements and stresses of the rock, as well as the influence of liner installation time on displacements and stresses of the rock. According to presented solutions, a fast predicting system for the mechanical state of the rock can be obtained and the ones provide much convenient way for preliminary design of tunnel construction.