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.