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Keywords: back-analysis, progressive excavations, arbitrary shape, exact elastic solu-

tion

1.

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o @ T v .

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, Fourier

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Wu, II

}-2 d@nR

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22

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5) Hirashima, K: Stresses in isotropic and anisotropic beams

having holes, Mem. Fac. Eng., Kyoto Univ., Vol. 34, pp. 27

-52, 1972.

6) Muskhelishvilli, NI.: Some Basic Problems of the

Mathematical Theory of Elasticity, Noordhoff, pp. 376-

380, 1963.

7) {wO: f @Y e wI l @1, H,

yw_ W, No. 3, pp. 60`79, pp. 159 74, 1949.

8) Derski, W. et al: Rock and Soil Mechanics, Elsevier,

pp. 237-242, 1989.

9) Heller, SR., Brock, JS., and Bart, R.: The stresses around

a rectangular opening with rounded corners in a uniformly

loaded plate, Proc. 3rd U. S. Nat. Congr. Appl. Mech.,

pp. 357-368, 1958.

10) Kantorovich, LV. and Krylov, VI.: Approximate Methods

of Higher Analyis, Interscience Pub., pp. 451---478, 1964.

1990. 5, 7 t)

ANALYSIS AND BACK-ANALYSIS OF ROCK GROUND WITH ARBITRARY SHAPE

OF TUNNEL CONSIDERING PROGRESSIVE EXCAVATIONS BY MEANS OF EXACT

ELASTIC SOLUTION

Ken-ichi HIRASHIMA, Tetsutaro KAWAKAMI, Toshio FUJIWARA and Toshiyuki RIKIMA

In this paper, we discuss a back-analysismethod for determining the two-dimensional

in-plane initial state of stresses and elastic constants of the ground, from a set of dis-

placements measured during progressive excavations of underground tunnel.

The proposed method of solutions bases on the exact elastic theory by using of com-

plex variable method with a conformal mapping transformation, which can be treated

for an arbitrary shape of the tunnel.

The results of stresses, strains and displacementsat arbitrary locations in rock ground

are exactly computed by the given values of in-plane load, elastic constants and shape

of the tunnel.

In order to verify the practical availavilitiesof this back-analysis,several numerical re-

sults are given in relation to the accuracyof the results.