Solution for Perimeter Stresses of Rocks Around a Rectangular Chamber Using the Complex Function of Elastic Mechanics

The analytical solutions for stress distribution of rocks around underground chambers are simply circular and oval in shape.Aiming at this problem,the complex function was used to calculate the surrounding stress of the rectangular chambers.The coefficient only related to the height-width ratio of the chamber was defined by using the conformal transformation to map the geometric boundaries of the chamber on Z-plane to the central circle on ζ-plane and by using the polygonal method to find the mapping function of the rectangular chamber.Through the trial calculation of the height-width ratio,the approximation solution of the mapping function may be obtained.Thus,the basic formula based on complex function for solving the perimeter stress of a rectangular chamber was obtained,making it possible for us to calculate the perimeter stress of a rectangular chamber when only the height and width are given.The case study shows that this method is feasible for calculating perimeter stresses of rock masses around a rectangular underground chamber.