The Theory of Critical Distances to Model the Short- to Long-crack Transition in Geological Materials Subjected to Mode I Static Loading

The Theory of Critical Distances postulates that, in cracked materials subjected to static loading, breakage takes place when a distance dependent effective stress exceeds the material tensile strength. Such an effective stress is equal to the stress calculated either at a certain distance from the notch tip (Point Method), averaged over a line (Line Method), over an area (Area Method) or, finally, averaged in a finite volume (Volume Method). The necessary characteristic length is a material property which can directly be determined by combining the material ultimate tensile strength with the plane strain fracture toughness. In the present investigation, by re-analysing a large number of experimental results taken from the literature, it is shown that the Theory of Critical Distances is successful in modelling the transition from the short- to the long-crack regime in geological materials subjected to Mode I static loading.