Y-Geo: New Combined Finite-Discrete Element Numerical Code for Geomechanical Applications O. K. Mahabadi 1 ; A. Lisjak 2 ; A. Munjiza 3 ; and G. Grasselli 4 Abstract: The purpose of this paper is to present Y-Geo, a new numerical code for geomechanical applications based on the combined finite- discrete element method (FDEM). FDEM is an innovative numerical technique that combines the advantages of continuum-based modeling approaches and discrete element methods to overcome the inability of these methods to capture progressive damage and failure processes in rock. In particular, FDEM offers the ability to explicitly model the transition from continuum to discontinuous behavior by fracture and frag- mentation processes. Several algorithmic developments have been implemented in Y-Geo to specifically address a broad range of rock mechan- ics problems. These features include (1) a quasi-static friction law, (2) the Mohr-Coulomb failure criterion, (3) a rock joint shear strength criterion, (4) a dissipative impact model, (5) an in situ stress initialization routine, (6) a material mapping function (for an exact representation of heterogeneous models), and (7) a tool to incorporate material heterogeneity and transverse isotropy. Application of Y-Geo is illustrated with two case studies that span the capabilities of the code, ranging from laboratory tests to complex engineering-scale problems. DOI: 10.1061/ (ASCE)GM.1943-5622.0000216. © 2012 American Society of Civil Engineers. CE Database subject headings: Finite element method; Discrete elements; Rock mechanics; Shear strength; Damage; Failures. Author keywords: Combined finite/discrete element method; FEM/DEM; Rock mechanics; Shear strength; Heterogeneity; Rock fall; FDEM. Introduction Geomaterials including rock are discontinuous by nature at many scales of observation. At the microscale (submillimeter), rocks consist of different mineral grains, microcracks, pores, or other material flaws. At the engineering scale (tens to hundreds of meters), rocks may be characterized by weak features such as bedding planes, schistosity, and foliation. Finally, at the regional scale, geo- logy can be highly variable, containing different rock types with existing fracture networks and faults as a result of tectonic loading. Considering the discontinuous nature of rock, there is a set of rock engineering problems that aim to maximize the formation of new dis- continuities. Examples of these problems include block caving and blasting. In block caving mining, a realistic estimation of failure initia- tion, subsequent fragmentation, and flow of ore through drawpoints are crucial to the economical success of the operations. The con- sequences of rock blasting, including fracturing of the rock and fragment size distributions, should be predicted during the design of mining operations. In contrast, another set of rock mechanics problems aims to limit failure of rock and the formation of discontinuities. Examples of this set include stability assessment of open pit and natural slopes, dams, and the stability of underground openings [i.e., formation of ex- cavation damaged zone (EDZ), spalling, structurally controlled instability]. In these cases, the existing rock fabric and dis- continuities should be considered as part of the stability assessment. Modeling techniques have been used to investigate these problems. The most commonly used techniques are continuum approaches, including finite-difference methods (FDM), finite- element methods (FEM), and boundary-element methods (BEM). These methods have been successfully applied to the assessment of global behavior of rock masses and the analysis of stress and deformation. However, explicit representation of fractures and fracture growth is not straightforward in these methods, mainly because of their continuum assumptions. For instance, in FDM, these assumptions require the functions to be continuous across neighboring cells or grid points. For FEM, the continuum assump- tions permit the elements to undergo only small strains. Therefore, even when fracturing is allowed, for instance, through Goodman joint elements (Goodman et al. 1968), large-scale opening, sliding, or complete detachment of elements is not possible. Also, a large number of fractures may cause the FEM stiffness matrix to be ill- conditioned. Fracture analysis using BEM has also been limited to isolated, noninteracting cracks (Jing 2003; Shen et al. 2011). Fur- thermore, BEM is restricted in handling material heterogeneity and nonlinearity (i.e., plasticity). The limitations of continuum approaches motivated the de- velopment of discrete element methods (DEMs) (Cundall 1971; Cundall and Strack 1979; Lemos et al. 1985; Mustoe et al. 1989; Williams and Mustoe 1993; Shi and Goodman 1988; Potyondy and Cundall 2004). Although continuum models are based on consti- tutive laws, DEMs are based on interaction laws. Also, unlike continuum techniques, the contact patterns of the DEM system can continuously change as the system deforms. Many DEM techniques 1 Research Associate, Geomechanics Research Group, Lassonde Insti- tute, Civil Engineering Dept., Univ. of Toronto, Toronto, ON, Canada M5S 1A4. 2 Ph.D. Student, Geomechanics Research Group, Lassonde Institute, Civil Engineering Dept., Univ. of Toronto, Toronto, ON, Canada M5S 1A4. 3 Professor, Dept. of Engineering, Queen Mary Univ. of London, London E1 4NS, U.K. 4 Assistant Professor, Geomechanics Research Group, Lassonde Insti- tute, Civil Engineering Dept., Univ. of Toronto, Toronto, ON, Canada M5S 1A4 (corresponding author). E-mail: giovanni.grasselli@utoronto.ca Note. This manuscript was submitted on April 26, 2011; approved on March 7, 2012; published online on March 12, 2012. Discussion period open until May 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the International Journal of Geomechanics, Vol. 12, No. 6, December 1, 2012. ©ASCE, ISSN 1532-3641/2012/6- 676e688/$25.00. 676 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / NOVEMBER/DECEMBER 2012 Int. J. Geomech. 2012.12:676-688. Downloaded from ascelibrary.org by TORONTO UNIVERSITY OF on 07/02/13. Copyright ASCE. For personal use only; all rights reserved.