流变岩体中任意形状隧道分部开挖响应的理论解

针对流变岩体中任意断面形状隧道的任意复杂分部开挖问题,根据复变函数理论结合Laplace变换建立黏弹性位移、应力与复位势之间的关系,给出了各施工阶段力学响应(位移与应力)理论解的一般求解方法和解答。从解答可以看出,各步增量位移是新开挖边界处释放面力作用下的流变位移与之前所有各施工步边界释放面力在本步时段中的增量流变位移的和,与施工路径相关。以圆形断面隧道分两阶段(从半圆形到圆形)任意分部开挖为例,导出了各步开挖过程围岩位移与应力的解析解。为验证解答的正确性,针对圆形断面上下开挖方式,将理论结果与有限元结果进行了对比,两者一致。利用解答对上下开挖、右左开挖两种方案下圆形隧道的位移、应力分布特点进行了分析。根据本文方法,可以得到任意黏弹性模型岩体中,复杂孔型任意分部开挖过程的解答。依据解答可建立快速预测系统,给出更方便、快捷地进行相似工程条件下初步设计的可选方法。

Analytical solutions for tunnels with any shape excavated sequentially in rheological rock at great depth

The analytical solutions are presented for the sequential excavation of the tunnel with any shape in viscoelastic rock subjected to anisotropic stress conditions. The complex variable method and the Laplace transformation are introduced to express the displacement and stress by the two potentials, therefore the methodology and analytical solutions for displacement and stress are derived for the general viscoelastic cases. The incremental displacement after each excavation step is the summation of (1) the rheological displacement due to the released stresses along the new boundary in this step and (2) the incremental rheological displacement due to the released stresses along excavation boundaries in all previous steps. The specific analytical solution is given for the two step sequential excavations of circular tunnel. A good agreement between the results from finite element simulations and the analytical solutions is observed for the specific top-bottom excavation method. The displacement and stress distributions for two excavation methods, top-bottom and left-right excavations, are analyzed by the proposed solutions. According to the analytical solutions, a fast computational system for predicting the mechanical state during tunnel excavation can be established in the future, which may provide a more convenient way for the preliminary design of the tunnel.