Int J Fract (2016) 199:71–87 DOI 10.1007/s10704-016-0095-9 ORIGINAL PAPER Time-dependent crack propagation in a poroelastic medium using a fully coupled hydromechanical displacement discontinuity method Abolfazl Abdollahipour · Mohammad Fatehi Marji · Alireza Yarahmadi Bafghi · Javad Gholamnejad Received: 23 August 2015 / Accepted: 10 February 2016 / Published online: 22 February 2016 © Springer Science+Business Media Dordrecht 2016 Abstract Many problems in subsurface rocks which are naturally filled with saturated cracks and pores (with one or more fluid phases) are better understood in a poroelastic framework. Displacement discontinu- ity method (DDM) is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic prob- lems. The paper derives fundamental solutions of a poroelastic DDM. Then introduces a numerical for- mulation and implementation for the poroelastic DDM in a code named constant element poroelastic DDM (CEP-DDM). The accuracy and validity of the pro- posed solution and the newly developed code is verified by an analytical solution at short-time and long-time. Numerical results showed good agreement with ana- lytical results at short time (undrained response) and long time (t = 8000 s) (drained response). A crack propagation scheme for crack propagation problems is introduced and demonstrated in an example which enables the code to follow crack propagation in time and space. Keywords Fundamental solutions · Poroelasticity · DDM · Crack propagation · Rock fracture mechanics A. Abdollahipour (B ) · M. F. Marji · A. Y. Bafghi · J. Gholamnejad Faculty of Mining and Metallurgical Engineering, Yazd University, P.O. Box 89195-741, Yazd, Iran e-mail: ab.abdollahipour@gmail.com 1 Introduction The boundary element methods have been extensively used in the field of linear elastic fracture mechanics (LEFM). The Dual boundary element method (DBEM) incorporating two pairs of independent boundary inte- gral equations is used extensively in the analyses of crack propagation process and fatigue (Portela et al. 1992; Fedelinski et al. 1993; Koegl and Gaul 2001; Dirgantara and Aliabadi 2001; Cisilino and Aliabadi 2004; Benedetti et al. 2008; Thanh Tu and Popov 2008; Romlay et al. 2010; Yun and Ang 2010; Kamali Yazdi et al. 2011). Natarajan et al. proposed an XFEM method for SIF computation (Natarajan et al. 2010) and Simp- son and Trevelyan developed an enriched BEM and dual BEM to accurately compute the SIFs(Simpson and Trevelyan 2011). The displacement discontinuity (DD) method (DDM) which is an indirect boundary element method is especially efficient for LEFM problems. It is based on a solution which expresses the stresses and displacements at a point due to a constant DD over a line segment in an elastic body (Crouch 1976). Con- stant DD elements are simple to use and are widely uti- lized in analyzing elastic engineering problems (Kim and Pereira 1997; Shou and Napier 1999; Fatehi Marji et al. 2011; Behnia et al. 2012; Haeri et al. 2013a, b). However, the DDM in its original form (Crouch and Starfield 1983) and its higher order extensions (Fatehi Marji 1997, 2014, 2015) are limited to elastic prob- lems. Fractures are the main flow channels in subsur- face rocks. Change in the fluid pressure induces matrix 123