ORIGINAL PAPER Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses Debasis Deb • Kamal C. Das Received: 2 February 2010 / Accepted: 1 April 2010 / Published online: 22 April 2010 Ó Springer Science+Business Media B.V. 2010 Abstract The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element pro- vide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities. Keywords XFEM  Partition of unity  Strong discontinuity  Discontinuous rock mass  Jointed tunnel 1 Introduction Solid mechanics analyses are generally conducted in the context of strict continuum mechanics where continuity of the displacement field is postulated (Oliver 1996a, b). The general principles of rock mechanics are also developed based on continuum solid mechanics concepts. The analysis of discrete joints such as faults, slip or bedding planes, shear zones and others become difficult if the displacement field is assumed to be continuous across the joints. Goodman et al. (1968) formulated a special joint element to be incorporated with the ordinary finite element method. Although this element is being used in modelling discrete joints in rock mechanics problems, it causes numerical difficulties depending on the problem and its boundary conditions, aspect ratio and accuracy of the computer used (Pande et al. 1990). Thus, analysis of cracks and joints in rocks has necessitated the consid- eration of jumps in displacement field termed as strong discontinuity especially if the analysis is to approach limit situations close to failure or collapse. Conventional finite element methods have been synonymous with simulation in various solid and fluid mechanics problem. A primary reason for its success has been the remarkable variety of problems that the method D. Deb (&) Department of Mining Engineering, Indian Institute of Technology, Kharagpur 721302, India e-mail: deb@iitkgp.ac.in K. C. Das Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India e-mail: iitiankamal@gmail.com 123 Geotech Geol Eng (2010) 28:643–659 DOI 10.1007/s10706-010-9323-7