流变岩土体中浅埋隧道围岩力学响应的理论解

Analytical Solutions for Shallow Tunnel Excavated in Rheological Geomaterial

浅埋隧道施工不仅会使开挖面周围岩土体发生变形,还会引发明显的地表位移,造成既有建筑物、基础、管线等发生破坏.针对黏弹性流变岩土体中浅埋隧道施工问题,用复变函数方法、Laplace变换、黏弹性叠加关系导出开挖位移和应力场的求解方法和理论解答,并与相同模型下的有限元解进行了比对验证.本文解答可以针对任意黏弹性模型岩土体进行计算,同时可以考虑纵向推进效应和任意时刻施加的任意大小均布内压.根据解答分析了浅埋隧道开挖引发的不同时刻地面沉降槽的大小、范围;位移随深度的变化形式以及洞周变形随角度的变化规律.相比数值方法,本文给出的理论解可更方便地进行参数分析和初步设计,而且给出的位移、应力场的理论解可以用于隧道和基础、地下管线的相互影响分析.

The excavation of shallow tunnel can induce not only the deformation of surrounding rock mass, but also the significant surface settlement, which can cause the damage of the existing buildings, foundations, pipelines, etc. The analytical solutions for shallow tunnel excavation were derived by considering the rheology of geomaterial. The complex variable function method, Laplace transform and superposition principle for viscoelastic cases were used in the derivation of excavation induced displacements and stresses around the tunnel. The solution was validated by FEM method through an example and very good agreement is demonstrated between the analytical and numerical solution. The obtained solutions can be employed to calculate for the cases with any viscoelastic model, as well as considering the longitudinal excavation effect and internal uniform pressures applied at any time. Based on the analytical solutions, the size and range of the surface settlement trough versus time, variations of the horizontal displacements along depth, and variations of displacements on the tunnel boundary versus angle at different time were carried out. Compared with the numerical methods, the solutions presented herein can be applied more conveniently in parametric investigation and preliminary design, and the interaction analysis of tunnel excavation and foundation or pipelines.