This paper uses Smoothed Particle Hydrodynamics (SPH) to analyze failure mechanism by predicting initiation and subsequent propagation of cracks without any special treatment or assumption on the fracturing process. An elasto-plastic damage model is incorporated into the SPH framework to enable non-linear behavior of the material. This constitutive model accounts for the irreversible process caused by plastic strain accumulation and the degradation of material properties due to damage initiation and development. A circular disc loaded diametrically is simulated within the proposed framework. It has been shown that the tensile stress distribution at the central area of the disc agrees well with the theoretical results. In order to study the effect of the loading angle on the failure process, three different central angles of the boundary load are considered in the numerical simulation. In addition to the circular disc, numerical simulations of a ring specimen under diametrically concentrated load are also presented.
Tensile strength of rock is one of the major concern in the study of rock property along with other properties which plays an important role in various geomechanical activities like blasting of rocks, hydraulic fracturing of a borehole, drilling and excavation in mining. Insight into the understanding of the failure process and prediction of failure paths remain a big challenge for a wide range of problems encountered in the field of rock mechanics and rock engineering. Experimental studies indicate that failure processes are generally initiated by the development of microcracks, propagation and interaction of several cracks, defects and inherent flaws. Mechanical properties and failure characteristics of rock materials are sensitive to the loading conditions. For example, the Brazilian test, as an indirect tensile test, is commonly conducted to determine the tensile strength of rock. The failure of the specimen is expected along the loading diameter into two halves, but another failure mode can occur near the loading boundary. Moreover, the tensile strength and failure characteristics can vary significantly with the specimen size and loading conditions.
The prediction of breakage phenomenon and failure mode remains a big challenge in the experimental test. In view of that, many micromechanical models have been proposed. The concept and theories of fracture mechanics have been applied to predict fracture generation and propagation in rock medium (Paterson & Wong 2005). Computational methods are noticeably well suited to investigate the process of rock degradation and failure, such as the lattice based model (Blair & Cook 1998) in which the local element is considered to be failed by tensile cracking if the local tensile stress exceeds the local tensile strength, the local degradation model on FLAC (Fang & Harrison 2002), the synthetic rock mass model based on PFC (Potyondy & Cundall 2004), and the digital image approaches based on the FLAC (Chen et al. 2004), FEM (Ortiz et al. 1987) for localized failure. Tang et al. (2000) analyzed the rock deformation, both pre- and post-failure using finite element code, in which the elastic modulus and strength of the individual elements were assumed to follow the Weibull distribution.