An approach of continuous-discontinuous cellular automaton method for modeling rock crack propagation is developed, in which level set method, discontinuous enriched shape function, discontinuous cellular automaton and contact friction theory are combined. Firstly, level set method is employed to track the location of the cracks, which are independent with the grids. Secondly, contact friction theory is applied to construct the contact friction model, and frictional stresses between crack surfaces can be exactly described. Thirdly, discontinuous cellular automaton is constructed, and the whole calculations are located on cells, so no assembled stiffness matrix but only cell stiffness is needed. Besides, contact iterations are done simultaneously with the updating of cellular automaton, and a new mixed iteration method is proposed, in which contact states and areas can be previously obtained, and the efficiency can get much higher. Finally, numerical results are given to illustrate the efficiency of the present method.


Natural rocks in the engineering are often under the compression states, with the defects and nonuniformity, they are often rich in joints and cracks. Failure of brittle hard rocks is a gradual process, which involves microcrack initiation, propagation, and coalescence. Because of the randomness of joints and fractures of the rocks, a failure may be occur from the propagation of the initial cracks and faults under external loading, and the traditional strength theory can not be perfect to explain the rock strength.

Failure of rock is considered to be one of the most important processes, which is related to earthquake, orogeny, plate motion and so forth. And the failure process of rock mass is actually a process from continuity to discontinuity. Numerical studies in dislocation, linear-elastic fracture mechanics (Weertman, 1996) and laboratory experiments (Paterson, 1978) have been reported in past few years, in which the fracturing process of rocks under external loading are studied.

With the remarkable development of computer technology, a lot of numerical methods have been developed as useful tools to simulate failure and general behaviors of brittle rock fractures. Those methods can be divided into two types, one is microscopic method, such as molecular dynamic (MD) (Holland & Marder, 1998); and the other is mesoscopic approaches, such as FEM, BEM, DEM, DDA and meshless method (Tang, 1997; Matsuda et al., 2002; Miao et al., 2010). But the former needs a huge amount of computer resources, and can't widely used in practical engineering.

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