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In works of rock mass excavation such as tunnel constructions etc., the values and directions of initial stresses in the ground and the elastic constants of rock mass are usually decided by back analysis using in-situ measuring data for estimating stability of caverns.The present paper shows a highly accurate analytical method utilizing complex variable method and point matching technique for the problems of two neighboring arbitrary shaped tunnels in an isotropic elastic ground under 2-dimensional in-plane loading conditions, and describes the theoretical process of back analysis using this solution.The complex variable method with conformal mapping transformation is a very useful analytical technique for tunnel excavation problems, because stresses and displacements around a tunnel can easily be obtained as exact closed-form solutions of elasticity. Therefore, it is possible to remove some restrictions on calculating time and computer capacity compared with FEM or BEM. The usefulness of this method is additionally shown through some numerical examples in this paper.

Back Analysis of Isotropic Elastic Ground with Two Neighboring Arbitrary Shaped Tunnels without Lining Supports.