Plane strain deformation of a multi-layered poroelastic half-space by surface loads

Singh, Sarva Jit; Rani, Sunita

doi:10.1007/s12040-006-0001-3

Cited by 18 publications

(17 citation statements)

References 12 publications

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“…A 2 is related to B 3 through . For isotropic permeability, c 1 = c 3 and eqs and reduce to Eqs and coincide with the corresponding results given by Singh & Rani (2006) for isotropic permeability.…”

Section: Solution Of the Governing Equationssupporting

confidence: 79%

“…may be functions of k , x = x 1 , z = x 3 and Inserting the expressions for F and p from eqs and in , we find Similarly, implies Eqs , and yield Corresponding to the stresses given by eqs , the displacements are found by integrating the constitutive eqs . We find (Singh & Garg 1985; Singh & Rani 2006) In deriving eqs and , the relation has been used. A 2 is related to B 3 through .…”

Section: Solution Of the Governing Equationsmentioning

confidence: 99%

“…Let a normal load σ 0 per unit length acting in the positive z ‐direction be uniformly distributed over this strip. The boundary conditions yield (Singh & Rani 2006) with the lower solution in eqs . Comparing eqs and , we conclude that the formal solution for normal strip loading is given by eqs with an extra factor (sin kL )/ kL in the integrands.…”

Section: Surface Loadsmentioning

confidence: 99%

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Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

Singh

Rani²,

Kumar³

2007

Geophysical Journal International

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SUMMARY An analytical solution is obtained of the fully coupled diffusion–deformation system of equations governing the quasi‐static plane strain deformation of a poroelastic half‐space with anisotropic permeability and compressible constituents. The stresses and the pore pressure are taken as the basic state variables. Displacements are obtained by integrating the coupled constitutive relations. The problem of surface loads is discussed in detail. Explicit analytical solutions are derived for normal line loading, shear line loading and normal strip loading. The permeability anisotropy is found to have a significant effect on the quasi‐static deformation of the half‐space. However, in the drained and undrained limits, the anisotropy has no effect. The stresses in the drained and undrained states are independent of the poroelastic parameters. Numerical computation of the pore pressure indicates that ignoring permeability anisotropy may lead to an overestimation of the pore pressure at points vertically below the point of normal loading. Further, anisotropy in permeability may lead to a dilution in the theoretical prediction of the Mandel–Cryer Effect.

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Section: Solution Of the Governing Equationssupporting

confidence: 79%

Section: Solution Of the Governing Equationsmentioning

confidence: 99%

Section: Surface Loadsmentioning

confidence: 99%

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Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

Singh

Rani²,

Kumar³

2007

Geophysical Journal International

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“…The plane strain problem for an isotropric poroelastic medium can be solved in terms of Biot's stress function F such that (Biot 1956;Singh and Rani 2006) …”

Section: Solution For Poroelastic Half-spacementioning

confidence: 99%

Quasi-static deformation due to two-dimensional seismic sources embedded in an elastic half-space in welded contact with a poroelastic half-space

Rani

Singh

2007

J Earth Syst Sci

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The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly elastic half-space caused by a twodimensional source in the elastic half-space. The integral expressions for the displacements and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail. The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for the drained case (ω → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically. Diffusion of the pore pressure with time is also studied.

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“…Biot's theory of linear poroelasticity (Biot 1941(Biot , 1956 has been used very extensively to study the consolidation of a homogeneous or layered half-space by surface loads or buried sources (see, e.g., Rudnicki 1986;Pan 1999;Wang and Kuempel 2003;Singh and Rani 2006). However, most of these studies did not take into account the anisotropy in hydraulic permeability.…”

Section: Introductionmentioning

confidence: 99%

Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading

2009

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The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid constituents of the poroelastic medium are compressible and its permeability in the vertical direction is different from its permeability in the horizontal direction. An analytical solution of the governing equations is obtained by taking the displacements and the pore pressure as the basic state variables and using a combination of the Laplace and Hankel transforms. The problem of an axisymmetric normal load is discussed in detail. An explicit analytical solution is obtained for normal disc loading. Detailed numerical computations reveal that the anisotropy in permeability as well as the compressibilities of the fluid and solid constituents of the poroelastic medium have significant effects on the consolidation of the half-space. The anisotropy in permeability may accelerate the consolidation process and may lead to a dilution in the theoretical prediction of the Mandel-Cryer effect. The compressibility of the solid constituents may also accelerate the consolidation process.

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Plane strain deformation of a multi-layered poroelastic half-space by surface loads

Cited by 18 publications

References 12 publications

Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

Quasi-static deformation due to two-dimensional seismic sources embedded in an elastic half-space in welded contact with a poroelastic half-space

Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading

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