申航 周航 刘汉龙

摘 要：隨着城市建设的发展，矩形隧道的应用越来越多，但针对矩形隧道的理论研究却鲜有见闻。针对矩形隧道，建立了半无限空间矩形隧道的弹性理论计算模型，采用最小二乘迭代方法确定共形映射函数的各项系数，并将计算区域映射为复平面上的一个同心圆环;运用Muskhelishvili复变函数方法，将计算区域内的应力函数展开成为Laurant级数的形式，给定了地表零应力边界和矩形孔口径向位移边界，求得了半无限空间矩形隧道在给定位移条件下的应力场和位移场。分析了不同高宽比、不同泊松比、不同埋深对位移场和应力场的影响，总结了矩形隧道位移场和应力场的一般规律。结果表明：高宽比偏小、泊松比偏大、埋深偏小都会使得沉降槽不再是类高斯曲线的形状，这些参数的变化也会在不同程度上影响应力场和位移场的大小和分布。

关键词：孔收缩;半无限空间;共形映射;位移条件;应力场;位移场

中图分类号：TU431   文献标志码：A   文章编号：2096-6717（2020）04-0001-11

收稿日期：2020-11-27

基金项目：国家自然科学基金（51978105）;重庆市技术创新与应用发展专项（cstc2019jscx-msxmX0107）

作者简介：申航（1996- ），男，主要从事隧道开挖对桩基的影响研究，E-mail：457570774@qq.com。

周航（通信作者），男，副教授，博士生导师，E-mail：zh4412517@163.com。

Received：2020-11-27

Foundation items：National Natural Science Foundation of China （No. 51978105）; Chongqing Technical Innovation and Application Development Special Project （No. cstc2019jscx-msxmX0107）

Author brief：SHEN Hang （1996- ）， main research interest： influence of tunnel excavation on pile foundation， E-mail： 457570774@qq.com.

ZHOU Hang （corresponding author）， associate professor， doctorial supervisor， E-mail： zh4412517@163.com.

Solution of complex function of rectangular hole contraction in elastic semi-infinite space

SHEN Hang， ZHOU Hang， LIU Hanlong

（Key Laboratory of New Technology for Construction of Cities in Mountain Area， Ministry of Education; School of Civil Engineering， Chongqing University， Chongqing 400045， P. R. China）

Abstract： With the development of urban construction in China， more and more applications of rectangular tunnel are emerging， but there are few theoretical studies on rectangular tunnels. In this paper， the elastic theoretical calculation model of the semi-infinite space rectangular tunnel was established. The coefficients of conformal mapping function were determined by the least squares iterative method. And the calculated area was mapped to a concentric ring on the complex plane. Afterwards， The Muskhelishvili complex function method was used to expand the stress function in the calculation area into the form of Laurant series， which gives the zero stress boundary on the ground surface and the radial displacement boundary of the rectangular hole. The stress field and displacement field of the rectangular tunnel in the semi-infinite space under the given displacement condition were also obtained by the method. In this paper， the influence of aspect ratios， Poisson's ratios， and buried depths on the displacement field and stress field was analyzed， and the general rules of the displacement field and stress field of rectangular tunnels has been summarized. The results show that a smaller aspect ratio， a larger Poisson's ratio， and a smaller buried depth will make the settlement curve no longer similar to a Gaussian curve. The variation of these parameters will also affect the size and distribution of the stress field and displacement field to varying degrees.

Keywords：constraction of hole; semi-infinite space; conformal mapping; displacement condition; stress field; displacement field

近年來，中国城市隧道建设突飞猛进，不仅数量上上了新台阶，而且越来越多的隧道类型不断涌现。其中，矩形顶管隧道相较传统圆形隧道，有着埋深浅、断面面积利用率高、施工时对地面交通影响小、无污染、无噪音等优点。……