Consolidation of a Poroelastic Half–Space
Abstract:
A porous medium is an elastic solid permeated by an interconnected network of pores filled with a fluid. Both solid and pore network are assumed to be continuous so as to form two interpenetrating continua. The theory of poroelasticity investigates the time-dependent coupling between the deformation of the elastic solid skeleton and fluid flow within the skeleton. The solid-to-fluid and fluid-to-solid couplings are assumed to occur instantaneously in the quasi-static approximation in which elastic wave propagation is ignored. Consolidation of a poroelastic body takes place when it is acted upon by surface loads. The study of consolidation of a poroelastic half-space or stratum has received much attention due to its geophysical and engineering applications. The aim of the present paper is to review recent work on the subject, indicating the assumptions made, methods used and conclusions drawn.
Author(s):
DOI:
Keywords:
References:
Ai Z Y, Cheng Z Y and Han J (2008) State space solution to three-dimensional consolidation of multilayered soils; Int. J. Eng. Sci. 46 486-498. http://dx.doi.org/10.1016/j.ijengsci.2007.12.003
Ai Z Y and Wang Q S (2008) A new analytical solution to axisymmetric Biot’s consolidation of a finite soil layer; Appl. Math. Mech. 29 1617-1624. http://dx.doi.org/10.1007/s10483-008-1209-9
Ai Z Y, Wang Q S and Han J (2010a) Analytical solutions describing the consolidation of a multilayered soil under circular loading; J. Eng. Math. 66 381-393. http://dx.doi.org/10.1007/s10665-009-9299-6
Ai Z Y, Wang Q S and Han J (2010b) Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils; Acta. Mech. 211 155-172. http://dx.doi.org/10.1007/s00707-009-0224-x
Ai Z Y and Wu C (2009) Plane strain consolidation of soil layer with anisotropic permeability; Appl.Math. Mech. 30 1437-1444. http://dx.doi.org/10.1007/s10483-009-1109-7
Bell M L and Nur A (1978) Strength changes due to reservoir-induced pore pressure and stresses and application to Lake Oroville; J. Geophys. Res. 83 4469-4483. http://dx.doi.org/10.1029/JB083iB09p04469
Biot M A (1941) General theory of three-dimensional consolidation; J. Appl. Phys.12 155–164. http://dx.doi.org/10.1063/1.1712886
Biot M A (1955) Theory of elasticity and consolidation for a porous anisotropic solid; J. Appl. Phys. 26 182-185. http://dx.doi.org/10.1063/1.1721956
Biot M A (1956a) General solutions of the equations of elasticity and consolidation for a porous material; J. Appl. Mech. 78 91–96.
Biot M A (1956b) Theory of deformation of a porous viscoelastic anisotropic soil; J. Appl. Phys. 27 459-467. http://dx.doi.org/10.1063/1.1722402
Booker J R (1974) The consolidation of a finite layer subjected to surface loading; Int. J. Solids Struct. 10 1053-1065. http://dx.doi.org/10.1016/0020-7683(74)90011-0
Booker J R and Carter J P (1986) Long term subsidence due to fluid extraction from a saturated, anisotropic, elastic soil mass; Q. J. Mech. Appl. Math. 39 85-98. http://dx.doi.org/10.1093/qjmam/39.1.85
Booker J R and Carter J P (1987a) Elastic consolidation around a point sink embedded in a half-space with anisotropic permeability; Int. J. Num. Anal. Meth. Geomech. 11 61-77. http://dx.doi.org/10.1002/nag.1610110106
Booker J R and Carter J P (1987b) Withdrawal of a compressible pore fluid from a point sink in anisotropic elastic half-space with anisotropic permeability; Int. J. Solids Struct. 23 369-385. http://dx.doi.org/10.1016/0020-7683(87)90042-4
Booker J R and Randolph M F (1984) Consolidation of a cross-anisotropic soil medium; Q. J. Mech. Appl. Math. 37 479-495. http://dx.doi.org/10.1093/qjmam/37.3.479
Booker J R and Small J C (1987) A method of computing the consolidation behavior of layered soils using direct numerical inversion of Laplace transforms; Int. J. Numer. Anal. Meth. Geomech. 11 360-380. http://dx.doi.org/10.1002/nag.1610110405
Chau K T (1996) Fluid point source and point forces in linear elastic diffusive half-spaces; Mech. Mater. 23 241-253. http://dx.doi.org/10.1016/0167-6636(96)00015-4
Chen G J (2003) Analysis of pumping in multilayered and poroelastic half-space; Comput. Geotech. 30 1-26. http://dx.doi.org/10.1016/S0266-352X(02)00034-4
Chen G J (2004) Consolidation of multilayered half-space with anisotropic permeability and compressible constituents; Int. J. Solids Struct. 41 4567-4586. http://dx.doi.org/10.1016/j.ijsolstr.2004.03.019
Chen G J (2005) Steady-state solutions of multilayered and cross-anisotropic poroelastic half-space due to a point sink; Int. J. Geomech. 5 45-57. http://dx.doi.org/10.1061/(ASCE)1532-3641(2005)5:1(45)
Chen G J and Gallipoli D (2004) Steady infiltration from a buried point source into heterogeneous cross-anisotropic unsaturated soil; Int. J. Numer. Anal. Meth. Geomech. 28 1033-1055. http://dx.doi.org/10.1002/nag.370
Chen S L, Chen L Z and Zhang L M (2005a) The axisymmetric consolidation of a semi-infinite transversely isotropic saturated soil; Int. J. Numer. Anal. Meth. Geomech. 29 1249-1270. http://dx.doi.org/10.1002/nag.458
Chen S L, Zhang L M and Chen L Z (2005)b Consolidation of a finite transversely isotropic soil layer on a rough impervious layer; J. Eng. Mech. 131 1279-1290. http://dx.doi.org/10.1061/(ASCE)0733-9399(2005)131:12(1279)
Chen Y, Cheng Z, Ling D and Zhu B (2007) Solutions for a completely saturated porous elastic solid with impeded boundaries; Front. Archit. Civ. Eng. 1 322-328. http://dx.doi.org/10.1007/s11709-007-0042-y
Conte E (1998) Consolidation of anisotropic soil deposits; Soils and Foundations 38 227-237.
Conte E (2006) Plane strain and axially symmetric consolidation in unsaturated soils; Int. J. Geomech. 6 133-135. http://dx.doi.org/10.1061/(ASCE)1532-3641(2006)6:2(131)
Detournay E. and Cheng A H-D (1993) Fundamentals of poroelasticity, in Comprehensive Rock Engineering: Principles, Practice, and Projects, (Hudson, J.A. ed.) Pergamon Press, Oxford 2 113-171.
Ganbe T and Kurashige M (2000) Fundamental solutions for a fluid-saturated poroelastic infinite space of transversely isotropic permeability; JSME Int. J. Series A 43 33-39. http://dx.doi.org/10.1299/jsmea.43.33
Gibson R E, Schiffman R L, and Pu S L (1970) Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base; Q. J. Mech. Appl. Math 23 505-520. http://dx.doi.org/10.1093/qjmam/23.4.505
Kalpna and Chander R (1997) On the 2D plane strain problem for harmonic stress applied to an impervious elastic layer resting on a porous elastic half space; Phys. Earth Planet. Int.103 151-164. http://dx.doi.org/10.1016/S0031-9201(97)00028-9
Kalpna and Chander R (2000) Green’s function based stress diffusion solutions in the porous elastic half space for time-varying finite reservoir loads; Phys. Earth Planet. Int. 120 93-101. http://dx.doi.org/10.1016/S0031-9201(00)00146-1
Lu J F and Hanyga A (2005) Fundamental solution for a layered porous half-space subjected to a vertical point force or a point fluid source; Comput. Mech. 35 376-391.
McNamee J and Gibson R E (1960a) Displacement functions and linear transform applied to diffusion through porous elastic media; Q .J. Mech. Appl. Math. 13 98-111. http://dx.doi.org/10.1093/qjmam/13.1.98
McNamee J and Gibson R E (1960b) Plane strain and the axially symmetric problem of the consolidation of a semi-infinite clay stratum; Q. J. Mech. Appl. Math. 13 210-227. http://dx.doi.org/10.1093/qjmam/13.2.210
Mei G X, Yin J H, Zai J M, Yin Z Z, Ding X L, Zhu G F and Chu L M (2004) Consolidation analysis of a cross-anisotropic homogeneous elastic soil using a finite layer numerical method; Int. J. Numer. Anal. Meth. Geomech. 28 111-129. http://dx.doi.org/10.1002/nag.324
Pan E (1999) Green’s functions in layered poroelastic half-spaces; Int. J. Numer. Anal. Meth Geomech. 23 1631-1653.
http://dx.doi.org/10.1002/(SICI)1096-9853(199911)23:13<1631::AID-NAG60>3.0.CO;2-Q
Rani S, Kumar R and Singh S J (2011) Consolidation of an anisotropic compressible poroelastic clay layer by axisymmetric surface loads; Int. J. Geomech. 11 65-71. http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000073
Rice J R and Cleary M P (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents; Rev. Geophys. Space Phys. 14 227-241. http://dx.doi.org/10.1029/RG014i002p00227
Roeloffs E A (1988). Fault stability changes induced beneath a reservoir with cyclic variations in water level; J. Geophys. Res. 93 2107-2124. http://dx.doi.org/10.1029/JB093iB03p02107
Rudnicki J W (2001) Coupled deformation-diffusion effects in the mechanics of faulting and failure of geomaterials; Appl. Mech. Rev. 54 483-502. http://dx.doi.org/10.1115/1.1410935
Schiffman R L and Fungaroli A A (1965) Consolidation due to tangential loads; Proc. 6th Int. Conf. on Soil Mech. and Foundation Eng. Canada 1 188-192.
Selvadurai A P S and Yue Z Q (1994) On the indentation of a poroelastic layer; Int. J. Numer. Anal. Meth. Geomech. 18 161-175. http://dx.doi.org/10.1002/nag.1610180303
Singh S J (2005) Recent advances in poroelasticity; Mathematics Student 74 49-67.
Singh S J , Kumar R and Rani S (2009) Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading; J. Earth Sys. Sci. 118 563-574. http://dx.doi.org/10.1007/s12040-009-0047-0
Singh S J and Rani S (2006) Plane strain deformation of a multilayered poroelastic half-space by surface loads; J. Earth Sys. Sci. 115 685–694. http://dx.doi.org/10.1111/j.1365-246X.2007.03497.x
Singh S J and Rani S (2007) Quasi-static deformation of a multilayered poroelastic half-space by two dimensional buried sources; Acta Mech. 191 161-179. http://dx.doi.org/10.1007/s00707-007-0452-x
Singh S J, Rani S and Kumar R (2007) Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads; Geophys. J. Int. 170 1311-1327. http://dx.doi.org/10.1111/j.1365-246X.2007.03497.x
Taguchi I and Kurashige M (2002). Fundamental solutions for a fluid-saturated, transversely isotropic, poroelastic solid; Int. J. Numer. Anal. Meth. Geomech. 26 299-321. http://dx.doi.org/10.1002/nag.202
Tarn J Q and Lu C C (1991) Analysis of subsidence due to a point sink in an anisotropic porous elastic half-space; Int. J. Numer. Anal. Meth. Geomech. 15 573-592. http://dx.doi.org/10.1002/nag.1610150805
Terzaghi K (1923) Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen; Sitz. Akad. Wissen. Wien. Math. Naturwiss. Kl. Abt. IIa 132 105-124.
Wang H F (2000). Theory of Linear Poroelasticity; Princeton University Press; Princeton.
Wang J and Fang S (2003) State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media; Int. J. Eng. Sci. 41 1799-1813. http://dx.doi.org/10.1016/S0020-7225(03)00062-4
Wang R and Kuumpel H J (2003) Poroelasticity: Efficient modeling of strongly coupled, slow deformation processes in multilayered half-space; Geophys. 68 705-717. http://dx.doi.org/10.1190/1.1567241
Yue Z Q and Selvadurai A P S (1995) Contact problem for saturated poroelastic solid; J. Eng. Mech. 121 502-512. http://dx.doi.org/10.1061/(ASCE)0733-9399(1995)121:4(502))
Yue Z Q, Selvadurai A P S and Law K T (1994) Excess pore pressure in a poroelastic seabed saturated with a compressible fluid; Can. Geotech. J. 31 989-1003. http://dx.doi.org/10.1139/t94-113
