Discrete Element Modeling of Crack Initiation Stress of Marble Based on Griffith’s Strength Theory

Abstract

Investigating the crack initiation stress of rocks is vital for understanding the gradual damage process of rocks and the evolution law of internal cracks. In this paper, the particle flow code method is used to conduct biaxial compression tests on a marble model with an elliptical crack under different confining pressures. According to the evolution status of microcracks in the rock during compression, four characteristic stresses are defined to reflect the gradual damage process of the marble. Two different methods are used to obtain crack initiation stress of rocks, and the calculation results are compared with those based on Griffith’s strength theory to verify the accuracy of this theory under compressive stress. Based on the numerical simulation results, the evolution law for the strength parameters of marble with the degree of damage is described. According to the proportional relationship between the peak stress and crack initiation stress, a new method for predicting the initiation stress is proposed, whose effectiveness is verified. Overall, the results of this study can serve as a useful guide for solving the important problems of slab cracking and rockburst encountered in underground space engineering.

Simulation of the Griffith's Crack Using Own Method of Predicting the Crack Propagation

“…In fact, in various simulations, depending on the model, the displacements at the crack tip will not be equal to 0, hence the displacements at all points need to be decreased by values obtained at the crack tip. Then the displacements along the radius u r , the displacements perpendicular to the radius u θ, and the resultant displacements u are calculated as in equation (10). In the same way, as in the previous criteria, they are placed on the graph, reduced to a unit radius, according to the assumption in the formula ( 8) that the displacements increase at the rate √r.…”

“…Griffith's crack simulations are also an interesting research topic. In the literature, there are publications by Yin et al [8] or Dewapriya et al [9] where the simulation of symmetrical fracture in graphene was performed with the use of Molecular Dynamic Simulations, or, for example, the work by Wang et al [10], in which the kinked Griffith's crack was analyzed using the Discrete Element Method. The topic of kinked crack has appeared in the literature for a long time [11,12].…”