Pergamon In:. J. Rock Mech. Min. Sci. Vol. 34, No. 6, 953-962, pp. 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: SO148-9062(97)00016-8 0148-9062/97 317.00 + 0.00 Finite Element Formulation and Application of Poroelastic Generalized Plane Strain Problems L. cu1t V. N. KALIAKINf Y. ABOUSLEIMANS A. H.-D. CHENGS A generalized plane strain finite element is developed for the analysis of poroelasticity problems. The validity and accuracy of the special element is demonstrated by analyzing inclined borehole problems in isotropic and transversely isotropic poroelastic materials. For the former, comparison is made with an analytical solution and the latter, with a three-dimensional$nite element solution. A substantial reduction in computational eflort is realizedfor the generalized plane strain finite element, as compared to the three- dimensional finite element. This is achieved without sacrificing the accuracy and the ability to account for the three-dimensional material anisotropy and far-jield stress components. 0 1997 Elsevier Science Ltd 1. INTRODUCTION Many problems in engineering are defined by two- dimensional geometries. In mining and petroleum engineering, tunnels and boreholes are typical examples. However, material properties and stress conditions generally render these problems three-dimensional. Once a three-dimensional solution technique is called upon, the computational effort becomes intensive. Under certain conditions; e.g. two-dimensional vari- ation in material properties and boundary conditions, it is possible to develop two-dimensional solution algor- ithms. One such condition is defined by the generalized plane strain problem. In these problems, three-dimen- sional material anisotropy and far-field stress com- ponents are admitted. However, only a two-dimensional discretization is needed for numerical solution. Signifi- cant savings in computational effort can thus be achieved. The analytical development underlying generalized plane strain for elastic continua has been presented by Lekhnitskii [I] and Amadei [2]. Solutions based on this development have been widely applied to borehole and tunnel problems, e.g. the determination of in situ stresses [2], borehole stability analysis [3,4] and the determi- nation of elastic properties of anisotropic masses [5]. For more complicated geometries and material properties tRock Mechanics Institute, The University of Oklahoma, Norman, Oklahoma 73019, U.S.A. $Department of Civil and Environmental Engineering, 137 DuPont Hall, University of Delaware, Newark, Delaware 19716, U.S.A. @chool of Engineering & Architecture, Lebanese American Univer- sity, Byblos, Lebanon. that preclude the development of analytical solutions, a finite element solution for generalized plane strain is also available [6]. A shortcoming of the above investigations is that the material is assumed to be elastic. The presence of pore pressure is either ignored or not properly taken into account. In practice, many geological formations are fluid saturated. When subjected to an external load, a coupled hydraulic-mechanical response will take place. This interaction requires an extension of the traditional theories of elasticity and flow through porous media to the coupled theory of poroelasticity [7-91. It has been demonstrated that poroelastic solutions can present not only quantitatively, but also qualitatively different predictions, as compared to their elastic counterparts. Analytical solutions for several poroelastic general- ized plane strain problems have recently been presented. Abousleiman et al. [lo] solved cylinder problems in isotropic viscoporoelastic materials: Cui et al. [l l] solved inclined borehole problems in isotropic poroelastic materials; and subsequently, Abousleiman et al. [12] extended the borehole solutions to account for material transverse isotropy under a special orientation. These analytical solutions have been applied to engineering problems, e.g. the designing of mud weight based on stability analysis of an inclined borehole [13]. However, the analytical solutions are limited by their abilities to handle complicated geometries, material anisotropy, heterogeneity and nonlinearity. For such conditions, numerical techniques, e.g. the finite element method must be employed. RMMS 34/&F 953