Numerical modeling of crack propagation process in brittle coal sample containing pre-existing crack under compressive load

In this study, a discrete element method based on linear parallel bond model (LPBM) has been used to investigate the growth path of cracks and the amount of force required to create it. The formation of cracks in this method is due to the breaking of the bond between the particles, which forms macro cracks by joining the microcracks. It was found that the average normal forces for breaking the bond in wing crack are about 11 and 30% in oblique and coplanar cracks by investigate the load on the coal sample containing pre-existing cracks, therefore, the growth of wing tensile cracks in the sample is due to the low value of normal forces. The value of shear force required to overcome the parallel bond of particles in oblique and coplanar cracks is about 7.5 and 3.5 times in wing crack, respectively, in order for crack propagation, it is necessary to break the shear bond between the particles in the oblique and coplanar crack path. The average shear force required to break a bond in the coplanar crack path is about 47% in the oblique crack path, which makes the coplanar crack faster than the oblique crack. The wing crack has the highest value in terms of length compared to other secondary (induced) cracks before the peak point (in stress-strain curve), and this causes the pre-existing cracks in the coal seams to be joined using wing cracks.