43_1366

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Back Analysis of Isotropic Elastic Ground with Two Neighboring

Arbitrary Shaped Tunnels without Lining Supports

by

Yukio YAMASHITA*,Toshio FUJIWARA* and Ken-ichi HIRASHIMA**

In works of rock mass excavation such as tunnel constructions etc., the values and directions of in-

itial 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 iso-

tropic 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 easi-

ly 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.

Key words: Back analysis, Complex variable method, Two neighboring tunnels,

Arbitrary shaped tunnel, 2-dimensional analysis, In-plane load

1 Œ¾

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Fig. 1. Geometry of isotropic elastic rock containing

two neighboring tunnels with arbitrary shape

of cross section under applied in-plane initial

stresses.

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Fig. 4. Actual tunnel cross section for

calculating mapping functions and

for putting into analysis.

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43_1366