Shape factor of irregular internal cracks in rock-like materials

The initiation, propagation and coalescence of internal cracks will lead to the failure of rock mass. To study the fracture characteristics of the internal cracks in brittle rock mass, the validity and reliability of a cylinder FEM numerical model containing a horizontal circular crack with 1/4-point singular elements are verified by the similar material simulation tests. Then, to analyze the effects of the size and curvature on the fracture characteristics of internal cracks, the relative-size-ratio (n) and relative-curvature-radius-ratio (t) of crack are defined to describe the geometrical feature of the internal cracks. Furthermore, the influences of n and t on the shape factors of crack (Y) are examined by the numerical model with circular and elliptical internal horizontal cracks. In addition, based on the above research results, a simple formula is proposed to calculate the shape factor of arbitrary convex-curve-type internal horizontal crack. Moreover, the comparisons of the calculated results and the numerical simulations of circular, elliptical and irregular crack show that all the deviations are within 2%. Meanwhile, SIF of the irregular crack in this research approaches its maximum at positions of 60° and 300° from X-axis positive direction approximately, where the crack will develop firstly. The results can be applied to the estimation of SIF value of internal cracks in laboratory tests or practical engineering.