Application of slightly overlapped circular particles assembly in numerical simulation of rocks with high friction angles A. Fakhimi * Departments of Mineral and Mechanical Engineering, New Mexico Institute of Mining and Technology, Socorro, NM, USA Department of Civil Engineering, Tarbiat Modarres University, Tehran, Iran Received 21 October 2003; accepted 19 March 2004 Available online Abstract Brittle rocks show complex mechanical behavior under loading. A promising approach in simulation of rock deformation is the use of interaction of bonded circular particles through normal and shear springs. Each contact bond can break if the applied force is greater than the bond strength. Although the synthetic material obtained with this approach behaves similar to rocks in many aspects, it shows low friction angle compared to actual values. In this paper, a new technique is introduced to obtain a realistic rock friction angle and failure envelope for the synthetic material. The idea is to allow circular particles to overlap slightly with a double force–displacement contact law. In addition, tensile strength of this synthetic model is briefly examined. All numerical computations were conducted using Continuum Analysis, two-dimensional (CA2) program developed by the author which has the capability to model rock deformation using a hybrid explicit finite difference-distinct element method. D 2004 Elsevier B.V. All rights reserved. Keywords: Failure envelope; Friction angle; Distinct element method; Interaction of rigid circular particles; Fracture of brittle rock 1. Introduction Crack propagation in brittle rocks is of great interest to rock engineers. Two general numerical approaches, a continuum model and a distinct element scheme are usually implemented in simulation of rock damage and deformation. Some of the techniques used in the continuum approach are damage (De Borst, 2002), elasto-plastic (Vermeer and De Borst, 1984) and visco-plastic (Fakhimi and Fairhurst, 1994) methods. The problem with the continuum formula- tion of rock softening, as needed for modeling brittle behavior, is the dependency of the results on the mesh resolution; by reducing the mesh size, the amount of energy dissipated along the induced shear band is reduced which is not consistent with physical obser- vations. To remedy the problem, a non-local contin- uum approach can be adopted in which a weighted average of an invariant of plastic strain, in a region around a point, is considered as the softening param- eter (Bazant, 1976). This approach resolves the prob- 0013-7952/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2004.03.006 * Department of Mineral Engineering, New Mexico Tech., 296 MSEC Building, Leroy Place, Socorro, NM 87801-4796, USA. Tel.: +1-505-835-6577; fax: +1-505-835-5252. E-mail address: hamed@nmt.edu (A. Fakhimi). www.elsevier.com/locate/enggeo Engineering Geology 74 (2004) 129 – 138