工程地质学报2024，Vol.32Issue(1)：206-215,10.DOI:10.13544/j.cnki.jeg.2022-0065
非圆形隧洞衬砌支护下应力与位移的新解法
A NEW ANALYTIC SOLUTION OF STRESS AND DISPLACEMENT FOR LINED NON-CIRCULAR TUNNELS
摘要
Abstract
In the past,when employing the plane elastic complex variable method for the mechanical analysis of non-circular tunnels with lining support,the conventional approach involved conformally mapping the outer region of the tunnel to the outer region of the unit circle on the image plane.Additionally,the same mapping function was utilized to map the lining section to the circular area on the image plane.However,this method resulted in non-uni-form thickness of the lining,especially when the lining was relatively thick,causing significant distortion in the sec-tion shape of the lining.To address this issue,this paper introduces two mapping functions to separately map the outer domain of the cavity and the section of the lining to the outer domain of the unit circle and a circular area on the image plane,respectively.This approach is adaptable to different lining thicknesses,ensuring relatively uniform lining thickness,particularly in cases of thicker linings.The traditional power series method is replaced with the boundary collocation method in solving the analytical functions.This method combines the two sets of mapping func-tions to obtain stress and displacement solutions for the problem.Using the horseshoe tunnel as an example,the so-lution results align well with the numerical solution obtained by ANSYS.The paper analyzes the influence of lining thickness on tunnel stress and displacement.With the solutions presented in this paper,the preliminary design of a tunnel under similar conditions can be carried out conveniently and quickly.关键词
复变函数方法/非圆形压力隧洞/均匀厚度衬砌/两套映射函数/边界配点法Key words
Complex variable method/Non-circular pressure tunnel/Uniform thickness lining/Two sets of map-ping functions/Boundary collocation method分类
交通工程引用本文复制引用
吕爱钟,崔耀启,蔡辉,马耀财..非圆形隧洞衬砌支护下应力与位移的新解法[J].工程地质学报,2024,32(1):206-215,10.基金项目
国家自然科学基金项目(资助号:51974124).This research is supported by the National Natural Science Foundation of China(Grant No.51974124). （资助号:51974124）
