The Maximum Effective Moment Criterion (MEMC) and Its Implications in Structural Geology

Abstract

Abstract The Mohr-Coulomb criterion has been widely used to explain formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which is mathematically expressed as Meff = (σ1 — σ3) L · sin 2α sin α)/2, where σ1-σ3 represents the yield strength of the related rock, L is a unit length and α is the angle between σ1 and deformation bands. This criterion demonstrates that the maximum value appears at angles of ±54.7° to σ1 and there is a slight difference in the moment in the range of 55°±10°. The range covers the whole observations available from nature and experiments. Its major implications include: (1) it can be used to determine the stress state when the related deformation features formed; (2) it provides a new approach to determine the Wk of the related ductile shear zone if only the ratio of the vorticity and strain rate remains fixed; (3) It can be used to explain (a) the obtuse angle in the contraction direction of conjugate kink-bands and extensional crenulation cleavages, (b) formation of low-angle normal faults and high-angle reverse faults, (c) lozenge ductile shear zones in basement terranes, (d) some crocodile structures in seismic profiles and (e) detachment folds in foreland basins.