The geometry of echelon fractures in rock: implications from laboratory and numerical experiments

The traces of echelon joints, veins and dikes in rock range from curving to straight. Theoretical analyses using boundary element numerical methods have concluded that straight, open fractures imply a significant remote differential stress whereas curving traces imply a more nearly isotropic stress. We present a series of laboratory experiments which investigate the two-dimensional propagation paths of echelon fractures in PMMA plates as a function of the applied biaxial loading and the initial geometry of a simple fracture array. The experimental results support the theoretical conclusions and verify the accuracy of the numerical method. At the grain scale, rock does not rigorously conform to the assumptions of isotropy, homogeneity and linear elasticity demanded by the numerical method. Nevertheless, results from crack path stability theory suggest that small-scale deviations of a fracture from the ideal path generally do not affect its large-scale behavior. Fracture paths which become kinked or curved by local heterogeneities are found to self-correct to a path governed by competition between the fracture tip and remote stress fields, provided the remote differential stress is non-zero. This enhances our confidence that the numerical method can be used to produce and explain realistic fracture geometries in rock. An unexpected experimental result is the non-perpendicular intersection of fractures grown in the laboratory. Free surface boundary conditions require that the walls of an open fracture be free of shear stress. The principal stresses are therefore aligned with the crack wall, and we might consequently expect an approaching opening mode fracture either to intersect the free surface at a right angle or to turn away and follow an asymptotic, nonintersecting path. Experimental and numerical modeling, however, shows how the near-tip stresses generated by an approaching fracture dominate the local stress field and allow it to propagate along an oblique path very close to intersection with the adjacent free surface.

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