非圆形洞室应力监测反馈分析的复变函数方法

在地下工程设计中，横截面上二维初始应力场是地下洞室稳定性分析的重要依据，必须首先需要解决的问题之一。初始应力场一般通过现场试验来测定，但费工费时而且往往很难得到理想效果。在洞室开挖时，利用现场监测资料进行反馈计算能得到较理想的初始应力场。20世纪80年代后提出了多种位移反分析方法，用少数的实测数据分析洞室稳定性，获得较为满意的结果，已得到广泛应用。但应力监测的反馈分析仍鲜为人知。采用穆斯海里什维里弹性平面问题的复变函数解法的基本原理，对非圆形地下洞室应力反馈分析进行了探讨，相应地推导了一系列公式。对映射函数的推求采用实际边界上几个控制点的限定方法，简捷又方便。

Complex function method of stress back analysis for a non-circular underground opening

For the design of underground engineering, the 2-dimensional original stress field on its cross section is the important basis for the stability analysis, which is one of the main problems to be solved first. The original stress field is usually determined by field test, which is time-consuming, costly and unable to provide ideal results. The back analysis using the field data of an opening is able to obtain ideal original stress field. Since the 1980s', many methods for displacement back analysis, which require only a few measured data in the stability analysis of an opening, have been developed and extensively applied, and satisfactory results have been achieved. But those for stress back analysis are seldom. By using the basic principle of Muskhelishvili’s complex function method for plane elastic problems, a back analysis of measured stresses of a non-circular underground opening is performed, and a series of formulas for the stress field are derived accordingly. The mapping function can be conveniently determined by the limit method for some controllable points on actual boundary.