International Journal of Science and Technology Volume 2 No. 1, January, 2013 IJST © 2012 – IJST Publications UK. All rights reserved. 44 Plane Strain Deformation of a Poroelastic Half-Space in Welded Contact with an Isotropic Elastic Half Space Neelam Kumari, Aseem Miglani Department of Mathematics, Chaudhary Devi Lal University Sirsa-125055, Haryana (India) ABSTRACT The Biot linearized theory for fluid saturated porous materials is used to study the plane strain deformation of an isotropic, homogeneous, poroelastic half space in welded contact with an isotropic, homogeneous, perfectly elastic half space caused by an inclined line-load in 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 and poroelastic medium by applying boundary conditions at the interface. The integrals for inclined line-load are solved analytically for the limiting case i.e. undrained conditions in high frequency limit. The undrained displacements, stresses and pore pressure for poroelastic half space are shown graphically. Keywords: Inclined line-load, plane strain, poroelastic, welded half-spaces. 1. INTRODUCTION Poroelasticity is the mechanics of poroelastic solids with fluid filled pores. Its mathematical theory deals with the mechanical behaviour of an elastic porous medium which is either completely filled or partially filled with pore fluid and study the time dependent coupling between the deformation of the rock and fluid flow within the rock. The study of deformation by buried sources of a fluid saturated porous medium is very important because of its applications in earthquake engineering, soil mechanics, seismology, hydrology, geomechanics, geophysics etc. Biot (1941, 1956) developed linearized constitutive and field equations for poroelastic medium which has been used by many researchers (see e.g. Wang (2000) and the references listed there in). When the source surface is very long in one direction in comparison with the others, the use of two dimensional approximation is justified and consequently calculations are simplified to a great extent and one gets a closed form analytical solution. A very long strip-source and a very long line-source are examples of two dimensional sources. Love (1944) obtained expressions for the displacements due to a line-source in an isotropic elastic medium. Maruyama (1966) obtained the displacements and stress fields corresponding to long strike-slip faults in a homogeneous isotropic half-space. The two dimensional problem has also been discussed by Rudnicki (1987), Rudnicki and Roeloffs (1990),Singh and Rani (2006) Rani and Singh(2007),Singh et al. (2007). Different approaches and methods like boundary value method, displacement discontinuity method, Galerkin vector approach, displacement function approach and eigen value approach, Biot stress function approach etc. have been made to study the plane strain (two dimensional) problem of poroelasticity. The use of eigen value approach has the advantage of finding the solutions of the governing equations in the matrix form notations that avoids the complicated nature of the problem. Kumar et al. (2000, 2002), Garg et al. (2003), Kumar and Ailwalia (2005), Selim and Ahmed (2006) , Selim (2007,2008), Chugh et al.(2011) etc. have used this approach for solving plane strain problem of elasticity and poroelasticity. In the present paper we study the plane strain deformation of a two phase medium consisting of an isotropic, homogeneous, poroelastic half space in welded contact with an isotropic, homogeneous, perfectly elastic half space caused by an inclined line-load in elastic half space. Using Biot stress function(Biot 1956d,Roeloffs 1988) and Fourier transform ,we find stresses ,displacement and pore pressure for poroelastic unbounded medium in integral form and using eigen value approach following Fourier transform ,we find stresses and displacement for unbounded elastic medium in integral form. Then we obtain the integral expressions for the displacements and stresses in the two half spaces in welded contact from the corresponding expressions for an unbounded elastic and poroelastic medium by applying suitable boundary conditions at the interface. These integrals cannot be solved analytically for arbitrary values of the frequency We evaluate these integrals for the limiting case i.e. undrained conditions in high frequency limit. The undrained displacements, stresses and pore pressure for poroelastic half space are shown graphically.