Research Paper Prediction of fracture trajectory in anisotropic rocks using modified maximum tangential stress criterion Ehsan Mohtarami a,⇑ , Alireza Baghbanan a , Hamid Hashemolhosseini b a Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran b Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran article info Article history: Received 22 February 2017 Received in revised form 25 July 2017 Accepted 28 July 2017 Keywords: Stress intensity factor Anisotropic rock Crack trajectory T-stress Hollow Center Cracked Disc (HCCD) Anisotropic Maximum Tangential Stress (AMTS) abstract A new criterion to predict crack propagation trajectory in anisotropic rocks with incorporating the con- cept of T-stress in formulating stress field near the crack tip was developed. The developed criterion along with enrichment functions and interaction integral in the extended finite element method (XFEM) frame- work made a sophisticated tool in modeling fracturing process in anisotropic media. Numerical results indicated that stress intensity factors considerably depend on orientation of anisotropy axes and ratio of the elastic modulus. The proposed formulation for anisotropic media provides a more accurate predic- tion of crack propagation trajectory compared with conventional methods, especially in mixed mode conditions. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction There are many deficits such as cracks, joints and fractures in rock structures. Consequently, when a rock is subjected to mechanical loading considering different environmental factors, it probably fails and new cracks possibly extend from the tips of preexisting discontinuities. Evaluating the stress intensity factor and predicting the crack propagation trajectory are highly impor- tant in different fields of rock engineering works such as hydraulic fracturing, underground excavation, rock mass stability analysis, hydrocarbon reservoirs, and blasting operations [1–6]. Further- more, predicting the crack propagation path provides valuable information on optimizing stone blocks (in building-stone quar- ries), the stability of rock structures and their post-destruction vol- ume (in rock slopes), and the efficient analysis of hydraulic fracturing in hydrocarbon and geothermal reservoirs. In reality, cracked structures and rock masses are often subjected to complex loading conditions, and their failures mostly occur due to the simultaneous contribution of several loads. Thus, the fracture of cracked components and structures may grow along non-straight paths, and not necessarily in the direction of the initial crack [7]. Therefore, investigating the crack initiation angle and the crack propagation path under mixed loading mode are the favorite sub- jects for researchers in the field of rock mechanics. Several theoret- ical models [8–13] and experimental techniques [14–18] have been developed to investigate the mixed mode crack growth (the combination of opening and shearing modes) in rocks. However, the theoretical models are limited to simple geometries, loads and uncomplicated behavior of materials. An anisotropic rock has different elastic moduli, strengths, Poisson’s ratios and permeabil- ity properties in different directions. The anisotropic case is much more complex than the isotropic case. Many previous studies are based on the isotropic and continuous assumption, simply for necessity and/or convenience of obtaining closed form solutions [19]. In practice, however, engineers must deal with discontinuous anisotropic rocks. One method to overcome these weaknesses is to use numerical modeling techniques. Today, numerical methods are used as an efficient tool for problem-solving in complex conditions. One such efficient numerical method used to model crack initiation and propagation is the Extended Finite Element Method (XFEM). Its basic concept is to enrich the local solution by applying a partition of unity framework to a standard Finite Element Method [20]. The fracturing process is modeled on the basis of the enrichment of polynomial approximation space, adding new functions to the approximation space, and thereby increasing the degrees of free- dom of nodes. For example, by employing the discontinuous Heav- iside function, crack surfaces can be modeled without considering them as geometric boundaries. In addition, the singularity of stress http://dx.doi.org/10.1016/j.compgeo.2017.07.025 0266-352X/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: e.mohtarami@mi.iut.ac.ir (E. Mohtarami). Computers and Geotechnics 92 (2017) 108–120 Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo