Articles written in Journal of Earth System Science
Volume 101 Issue 3 September 1992 pp 269-282
Closed-form expressions for the displacements and stresses at any point of either of two elastic half-spaces in welded contact caused by a dip-slip line source obtained earlier are integrated analytically to derive the elastic residual field due to a long dip-slip fault of finite width. The results are valid for an arbitrary dip of the fault. The variation of the displacement field with the distance from the fault as well as with the distance from the interface is studied numerically. It is found that the displacement field is heavily dependent on the dip angle. Contour maps showing the residual elastic field in the two half-spaces caused by a vertical dip-slip fault located in one of the half-spaces are also obtained.
Volume 114 Issue 1 February 2005 pp 105-110
Analytical solution for the problem of a surface-breaking long strike-slip fault in an elastic layer overlying an elastic half-space is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. Since the solution is valid for arbitrary values of the fault-depth and the dip angle, the effects of these two important fault parameters can be studied numerically. The variation of the parallel displacement and shear stress with the distance from the fault is studied numerically for different values of the fault-depth and dip angle.
Volume 115 Issue 3 June 2006 pp 277-287
The solution of two-dimensional problem of an interface breaking long inclined dip-slip fault in two welded half-spaces is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. The solution is valid for arbitrary values of the fault-depth and the dip angle. Graphs showing the variation of the displacement field with the distance from the fault, for different values of fault depth and dip angle are presented. Contour maps showing the stress field around a long dip-slip fault are also obtained
Volume 115 Issue 6 December 2006 pp 685-694
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.
Volume 116 Issue 2 April 2007 pp 99-111
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.
Volume 118 Issue 5 October 2009 pp 563-574
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 com-pressibilities 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.
Volume 122 Issue 4 August 2013 pp 1055-1063
The solution of the static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by uniform movement along a long vertical tensile fracture is well known. In this paper, we study the problem of static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by a nonuniform movement along a long vertical tensile fracture of infinite length and finite depth. Four movement profiles are considered: linear, parabolic, elliptic and cubic. The deformation corresponding to the four non-uniform movement profiles is compared numerically with the deformation due to a uniform case, assuming the source potency to be the same. The equality in source potency is achieved in two ways: One, by varying the depth of fracture and keeping the surface discontinuity constant and the other way, by keeping the depth of fracture constant and varying the surface discontinuity. It is found that the effect of non-uniformity in movement in the near field is noteworthy. The far field is not affected significantly by the non-uniformity in movement. In the first case, horizontal displacement is significantly affected rather than vertical displacement. In the second case, non-uniformity in movement changes the magnitude of the displacement at the surface. Also, the displacements around a long vertical tensile fracture for different movement profiles are plotted in three dimensions.