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Research Papers

A Reexamination of the Equations of Anisotropic Poroelasticity

[+] Author and Article Information
Yue Gao, Zhuo Zhuang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Zhanli Liu

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: liuzhanli@tsinghua.edu.cn

Keh-Chih Hwang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: huangkz@tsinghua.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 12, 2017; final manuscript received March 7, 2017; published online April 5, 2017. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 84(5), 051008 (Apr 05, 2017) (9 pages) Paper No: JAM-17-1030; doi: 10.1115/1.4036194 History: Received January 12, 2017; Revised March 07, 2017

The anisotropic poroelastic constitutive model is reexamined in this article. The assumptions and conclusions of previous works, i.e., Thompson and Willis and Cheng, are compared and clarified. The micromechanics of poroelasticity is discussed by dividing the medium into connected fluid part and solid skeleton part. The latter includes, in turn, solid part and, possibly, disconnected fluid part, i.e., fluid islands; therefore, the solid skeleton part is inhomogeneous. The constitutive model is complicated both in the whole medium and in the solid skeleton because of their inhomogeneity, but the formulations are simplified successfully by introducing a new material constant which is defined differently by Cheng and by Thompson and Willis. All the unmeasurable micromechanical material constants are lumped together in this constant. Four levels of assumptions used in poroelasticity are demonstrated, and with the least assumptions, the constitutive model is formulated. The number of independent material constants is discussed, and the procedures in laboratory tests to obtain the constants are suggested.

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References

Biot, M. A. , 1941, “ General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12(2), pp. 155–164. [CrossRef]
Biot, M. A. , and Willis, D. G. , 1957, “ The Elastic Coefficients of the Theory of Consolidation,” ASME J. Appl. Mech., 24, pp. 594–601.
Rice, J. R. , and Cleary, M. P. , 1976, “ Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media With Compressible Constituents,” Rev. Geophys., 14(2), pp. 227–241. [CrossRef]
Detournay, E. , and Cheng, A. H.-D. , 1993, “ Fundamentals of Poroelasticity,” Comprehensive Rock Engineering: Principles, Practice and Projects (Analysis and Design Method, Vol. 2), Pergamon Press, Oxford, UK, pp. 113–171.
Cheng, A. H.-D. , 2016, Poroelasticity (Theory and Applications of Transport in Porous Media, Vol. 27), Springer International Publishing, Cham, Switzerland.
Kovalyshen, Y. , 2010, “ Fluid-Driven Fracture in Poroelastic Medium,” Ph.D. thesis, University of Minnesota, Ann Arbor, MI.
Miehe, C. , Mauthe, S. , and Teichtmeister, S. , 2015, “ Minimization Principles for the Coupled Problem of Darcy-Biot-Type Fluid Transport in Porous Media Linked to Phase Field Modeling of Fracture,” J. Mech. Phys. Solids, 82, pp. 186–217. [CrossRef]
Detournay, E. , and Cheng, A. H.-D. , 1988, “ Poroelastic Response of a Borehole in a Non-Hydrostatic Stress Field,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25(3), pp. 171–182. [CrossRef]
Gao, Y. , Liu, Z. , Zhuang, Z. , Hwang, K.-C. , Wang, Y. , Yang, L. , and Yang, H. , 2016, “ Cylindrical Borehole Failure in a Poroelastic Medium,” ASME J. Appl. Mech., 83(6), p. 061005. [CrossRef]
Biot, M. A. , 1955, “ Theory of Elasticity and Consolidation for a Porous Anisotropic Solid,” J. Appl. Phys., 26(2), pp. 182–185. [CrossRef]
Biot, M. A. , 1972, “ Theory of Finite Deformations of Porous Solids,” Indiana Univ. Math. J., 21(7), pp. 597–620. [CrossRef]
Biot, M. A. , 1973, “ Nonlinear and Semilinear Rheology of Porous Solids,” J. Geophys. Res., 78(23), pp. 4924–4937. [CrossRef]
Thompson, M. , and Willis, J. R. , 1991, “ A Reformation of the Equations of Anisotropic Poroelasticity,” ASME J. Appl. Mech., 58(3), pp. 612–616. [CrossRef]
Cheng, A. H.-D. , 1997, “ Material Coefficients of Anisotropic Poroelasticity,” Int. J. Rock Mech. Min. Sci., 34(2), pp. 199–205. [CrossRef]
Hill, R. , 1963, “ Elastic Properties of Reinforced Solids: Some Theoretical Principles,” J. Mech. Phys. Solids, 11(5), pp. 357–372. [CrossRef]
Nur, A. , and Byerlee, J. D. , 1971, “ An Exact Effective Stress Law for Elastic Deformation of Rock With Fluids,” J. Geophys. Res., 76(26), pp. 6414–6419. [CrossRef]
Carroll, M. M. , 1979, “ An Effective Stress Law for Anisotropic Elastic Deformation,” J. Geophys. Res.: Solid Earth, 84(B13), pp. 7510–7512. [CrossRef]
Carroll, M. M. , and Katsube, N. , 1983, “ The Role of Terzaghi Effective Stress in Linearly Elastic Deformation,” ASME J. Energy Resour. Technol., 105(4), pp. 509–511. [CrossRef]
Mesri, G. , Adachi, G. , and Ullrich, C. R. , 1976, “ Pore-Pressure Response in Rock to Undrained Change in All-Round Stress,” Géotechnique, 26(2), pp. 317–330. [CrossRef]
Fjaer, E. , Holt, R. , Raaen, A. , Risnes, R. , and Horsrud, P. , 2008, Petroleum Related Rock Mechanics, 2nd ed., Elsevier, Amsterdam, The Netherlands.

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Grahic Jump Location
Fig. 1

A scheme diagram of poroelastic medium

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