Static deformation of a multilayered half-space by internal sources

Singh, Sarva Jit

doi:10.1029/jb075i017p03257

Cited by 98 publications

(85 citation statements)

References 5 publications

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“…Simplified explicit expressions for the elements of the propagator matrix have been obtained for the poroelastic case. This is a generalization of the propagator matrix obtained by Singh (1970) and Singh and Garg (1985) for the elastic case. The propagator matrix can be used for studying the quasi-static plane strain deformation of a multi-layered poroelastic half-space by surface loads or buried sources.…”

Section: Discussionmentioning

confidence: 97%

“…Further references can be found in Wang (2000) and Rudnicki (2001). Singh (1970) used a generalization of the Thomson-Haskell matrix method to study the deformation of a multi-layered elastic half-space by buried sources. The corresponding two-dimensional problem has been discussed by Singh and Garg (1985).…”

Section: Introductionmentioning

confidence: 99%

“…The corresponding two-dimensional problem has been discussed by Singh and Garg (1985). The formulation of Singh (1970) and Singh and Garg (1985) has been used very extensively. Pan (1999) discussed the deformation of a multilayered poroelastic half-space by buried sources.…”

Section: Introductionmentioning

confidence: 99%

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

Singh

Rani

2006

J Earth Syst Sci

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The Biot linearized quasi-static theory of fluid-infiltrated porous materials is used to formulate the problem of the two-dimensional plane strain deformation of a multi-layered poroelastic half-space by surface loads. The Fourier-Laplace transforms of the stresses, displacements, pore pressure and fluid flux in each homogeneous layer of the multi-layered half-space are expressed in terms of six arbitrary constants. Generalized Thomson-Haskell matrix method is used to obtain the deformation field. Simplified explicit expressions for the elements of the 6×6 propagator matrix for the poroelastic medium are obtained. As an example of the possible applications of the analytical formulation developed, formal solution is given for normal strip loading, normal line loading and shear line loading.

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Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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

Singh

Rani

2006

J Earth Syst Sci

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“…As we observed in the last section, the difference between the spectral coefficients for the fully bonded and the spring layer system is that the fully bonded coefficients involve polynomials in k whereas the spring layer system involves rational functions in k (see (15)). By using synthetic division it is possible to reduce all the integrands to the same form as those required in the bonded where…”

Section: Inversion Of the Uasmentioning

confidence: 83%

Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs

Peirce

Siebrits

2008

Num Anal Meth Geomechanics

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SUMMARYWe present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three-layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three-layer-spring medium. Although a closed-form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi-layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo-3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements.

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“…An approximation of Green's function is integrated analytically to obtain the displacements due to a finite rectangular strike-slip fault. Based on the Thomson-Haskell formulation developed by Singh (1970), Rundle (1978) devised a method for computating the displacements due to arbitrary dislocation sources in an elastic layer over a viscoelastic half-space. Matsu'ura et al (1981) and Iwasaki and Matsu'ura (1981) presented a method for the computation of quasi-static surface displacements, strains and tilts due to a dislocation source in a stratified elastic half-space with an intervenient Maxwellian layer.…”

Section: Introductionmentioning

confidence: 99%

Lithospheric Deformation Associated with Two-Dimensional Strike-Slip Faulting.

Singh

Rani

1994

J,Phys,Earth

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To model the coseismic and postseismic lithospheric deformations associated with faulting at a transform plate boundary, the problem of a long inclined strike-slip fault in a layer overlying a uniform half-space is discussed. Closed-form expressions for the static displacements and stresses are obtained when the two media are elastic. These expressions are used to study the effect of the source location and the dip of the fault on the surface deformation. The correspondence principle of linear viscoelasticity is used to obtain the quasi-static field when the layer is elastic and the half-space Maxwell viscoelastic. The coseismic field is modeled by the static response and the postseismic field is modeled by the quasi-static response minus the static response. The variation of the coseismic and postseismic surface displacement and shear stress with the distance from an inclined fault is studied for four source locations: a surface-breaking fault and three buried faults. Both the source location and the dip of the fault are found to influence the deformation field significantly. Contours of constant postseismic displacement and stresses on the distance-time grid are obtained. These contours are useful in examining the spatial and temporal dependence of the displacement and stress fields. It is found that while the nodal lines for the postseismic displacement are independent of time, the nodal lines for the postseismic shear stresses move away from the fault with time after the earthquake.

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Static deformation of a multilayered half-space by internal sources

Cited by 98 publications

References 5 publications

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

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

Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs

Lithospheric Deformation Associated with Two-Dimensional Strike-Slip Faulting.

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