Crack interaction and fracturing of geomaterials with multiscale cracks

Abstract

Geomaterials contain numerous cracks whose interaction affects the macroscopic mechanical properties of the materials significantly. We propose a mechanical model of cracks of 3 scale levels to investigate the pattern of crack propagation and possible failure modes produced. For modelling crack interaction between different scale levels, we model the unloading domain of influence of a single crack as the sphere with the diameter being the crack size drawn around the crack center. When the tip of a lower scale crack propagates into the influence domain of a crack of a higher scale level, the propagating crack of a lower scale will be unloaded and never grow from this tip. Propagation and coalescence of cracks of different scale levels for different initial crack concentration result in different patterns of cracks propagation and failure. For relatively lower initial crack concentrations, the interaction of cracks of the first scale level dominates, producing failure due to the coalescence of cracks of the first scale level. With the increase of the initial crack concentration, the coalescence of cracks of the third scale level dominates leading to failure at a higher initial concentration. With the further increase of the initial crack concentration, the failure is produced by the coalescence of cracks of the second scale level. At even higher initial crack concentrations the failure is again produced by the coalescence of cracks of the first scale level. The dynamic strength decreases with the increase in the initial crack concentration. • A model of interaction, growth and coalescence of self-similar cracks of 3 scale levels is proposed. • The unloading effect of higher scale level cracks on the propagation of lower scale level cracks is considered. • Degradation of the effective deformation modulus is considered in solving crack-tip equations of motion. • The discreteness of crack propagation at the accelerating stage of loading is discovered. • At certain intervals of the initial crack concentration cracks of the lowest scale level will coalesce first.