Stress Analysis of Thick‐Walled Reinforced Tunnel
Publication: Journal of Engineering Mechanics
Volume 112, Issue 9
Abstract
Analytic solutions are presented for the interaction of a thick‐walled circular cylindrical structure (tunnel) buried deeply underground. The medium is assumed to be homogeneous, isotropic, and linearly elastic so that Michell's formulation of the Airy stress function can be applied. The general expressions for the stresses and displacements in the cylindrically orthotropic structure are formulated using both the elasticity and shell‐theory approaches. Solutions are then obtained by considering the boundary conditions at the structure inner surface and at the tunnel‐medium interface. The shell theory employed is an improved shear‐deformable version of the well‐accepted Sanders shell theory. A technique is also developed to predict the transverse stresses in the structure. The results show a close agreement with those obtained by the theory of elasticity for a shell with an outer radius‐to‐thickness ratio of 5.
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References
1.
Bert, C. W. (1962). “Complete stress function for nonhomogeneous, anisotropic, plane problems in continuum mechanics.” J. Aerospace Sci., 29(6), 756–757.
2.
Bert, C. W., and Niedenfuhr, F. W. (1963). “Stretching of a polar‐orthotropic disk of varying thickness under arbitrary body forces.” AIAA Journal, 1(6), 1385–1390.
3.
Burns, J. Q., and Richard, R. M. (1964). “Attenuation of stresses for buried cylinders.” Symposium on Soil‐Structure Interaction, Univ. of Arizona, Tucson, Ariz., 378–392.
4.
Dar, S. M., and Bates, R. C. (1974). “Stress analysis of hollow cylindrical inclusions.” J. Geotechnical Engrg. Div., ASCE, 100(GT2), 123–138.
5.
Flügge, W. (1932). “Die stabilität der kreiszylinderschale.” Ingenieur‐Archiv., 3, 463–506.
See also Stresses in Shells, Springer‐Verlag, New York, N.Y., 1966, Chap. 5.
6.
Goldberg, J. E., Baluch, M. H., and Tang, Y. K. (1971). “Analysis of moderately thick shells of revolution.” Proc. First Int. Conference on Structural Mechanics in Reactor Technology, Berlin, 4(G), 37–48.
7.
Goodier, J. N. (1933). “Concentration of stress around spherical and cylindrical inclusions and flaws.” Transactions of ASME, 55, 39–44.
8.
Halpin, J. C., and Tsai, S. W. (1969). “Effects of environmental factors on composite materials.” AFML‐TR 67‐423, Air Force Materials Laboratory, Wright‐Patterson AFB, Ohio. See also Jones, R. M. (1975). Mechanics of Composite Materials, Scripta, Washington, D.C., 114–121.
9.
Hsu, Y. S., Reddy, J. N., and Bert, C. W. (1981). “Thermoelasticity of circular cylindrical shells laminated of bimodulus composite materials.” J. of Thermal Stresses, 4, 155–177.
10.
Liu, K. Y. (1984). “Stress analysis of a thick‐walled reinforced tunnel.” Thesis presented to the University of Oklahoma, at Norman, Okla., in partial fulfillmerit of the requirements for the degree of Master of Science.
11.
Michell, J. H. (1899). “On the direct determination of stress in an elastic solid, with application to the theory of plates.” Proc. London Math. Soc., 31, 100–124.
See also Boresi, A. P., and Lynn, P. P. (1974). Elasticity in Engineering Mechanics, Prentice‐Hall, Englewood Cliffs, N.J., 286.
12.
Sanders, J. L., Jr. (1959). “An improved first approximation theory for thin shells.” NASA TR R‐24, National Aeronautics and Space Administration, Washington, D.C.
13.
Sherrer, R. E. (1967). “Filament‐wound cylinders with axial‐symmetric loads.” J. Composite Materials, 1(4), 344–355.
14.
Szechy, K. (1973). The Art of Tunneling, 2nd Eng. ed., Akadeiai Kiadó, Budapest, Hungary.
15.
Vinson, J. R. (1972). “Method of analysis for very thick walled cylindrical shells.” Report No. CR 73.002, Naval Civil Engrg. Lab., Port Hueneme, Calif.
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Copyright © 1986 ASCE.
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Published online: Sep 1, 1986
Published in print: Sep 1986
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