Summary
By use of the theory of poroelasticity, the analytical solutions were obtained for mechanical responses of a water-saturated core sample subjected to opposite diametrical loadings that vary like a step function of time (Problem I) and a linearly increasing function of time (Problem II). These loadings correspond to elastic moduli tests (by Hondros) and indirect tensile strength tests (the Brazilian tests) of dry brittle materials, respectively. The analysis showed how the diffusion of pore fluid affects these tests, if the tests are carried out for fluid-saturated samples. Furthermore, the accuracy of the Stehfest numerical Laplace inversion was checked based on the analysis. In addition, a method of determining poroelastic moduli was proposed.
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References
Veatch, Jr, R. W., Moschovidis, Z. A., Fast, C. R.: An overview of hydraulic fracturing. In Recent advances in hydraulic fracturing (Gidley, J. L., Holditch, S. A., Nierode, D. E., Veatch Jr, R. W., eds) pp. 1–38, Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers: Richardson, TX 1989.
Abe, H., Takahashi, H.: Crustal fracture mechanics for geothermal energy extraction (in Japanese). Energy and Resources4, 515–522 (1983).
Bieniawski, Z. T., Hawkes, I.: Suggested methods for determining tensile strength of rock materials. J. Rock Mech. Min. Sci. Geomech. Abs.15, 99–103 (1978).
Frocht, M. M.: Photoelasticity, vol. 1, p. 129. New York: Wiley 1941.
Hondros, G.: The evaluation of Poisson's ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete. Aust. Appl. Sci.10, 243–268 (1959).
Cleary, M. P.: Fundamental solutions for a fluid-saturated porous solid. Int. J. Solids Struct.13, 785–806 (1977).
Biot, M. A.: General theory of three-dimensional consolidation. J. Appl. Phys.,12, 155–164 (1941).
Stehfest, H.: Numerical inversion of Laplace transforms. Comm. ACM.13, 47–49 (1970).
Timoshenko, S., Goodier, J. N.: Theory of elasticity, 2nd ed., p. 26. New York: McGraw Hill 1951.
ibid.——. p. 377.
Senjuntichai, T., Rajapakse, R. K. N.: Transient response of a circular cavity in a poroelastic medium. Int. J. Num. Anal. Meth. Geomech.17, 375–383 (1993).
Rajapakse, R. K. N., Senjuntichai, T.: Fundamental solutions for a poroelastic half-space with compressive constituents. ASME J. Appl. Mech.60, 847–856 (1993).
Detournay, E., Cheng, A. H.-D.: Fundamentals of poroclasticity. In: Comprehensive rock engineering (Hudson, J. A., ed.); vol. 2: Analysis and design methods (Fairhurst, C. ed.) Oxford: Pergamon Press 1993.
Kobayashi, A.: Mechanics of rocks (in Japanese), p. 64. Tokyo: Maruzen 1993.
Cryer, C. W.: A comparison of the three-dimensional consolidation theories of Biot and Terzaghi. Q. J. Mech. Appl. Math.16, 401–412 (1963).
Cheng, A. H.-D.: Approximate inversion of the Laplace transform. The Mathematica J.4, 76–82 (1994).
Detournay, E., Cheng, A. H.-D.: Poroelastic response of a borehole in a non-hydrostatic stress field. Int. J. Rock Mech. Min. Sci. Geomech. Abs.25, 171–182 (1988).
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Mikami, Y., Kurashige, M. & Imai, K. Mechanical response of a water-saturated core sample under opposite diametrical loadings. Acta Mechanica 158, 15–32 (2002). https://doi.org/10.1007/BF01463166
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DOI: https://doi.org/10.1007/BF01463166