A super-critical stress model for polymodal faulting of rocks

Abstract

A polymodal faulting phenomenon is further explored here that comprises penecontemporaneous fractures showing finite dispersion of strikes and dips with poles confined in one annular or two arc regions in stereographic projection. The fracture pattern represents three-dimensional strain of rocks with characteristics distinct from previously known bi-, four- or poly-modal faulting, and thus is unable to be interpreted in terms of the corresponding theories such as conjugate faulting, slip on preexisting weak planes and tensile crack interaction, respectively. Here, a super-critical stress model is advanced to decode stress significance of the specific fracture pattern with a particular emphasis on model prediction for orientations of failure surfaces. The model is an extension of the slip model of Reches (1983) that prescribes formation of four sets of faults in orthorhombic symmetry conforming to the Coulomb-Mohr criterion of τ=C+μσ (equivalent to C=F=τ-μσ where C is cohesion of rocks and F is function of shear stress τ, normal stress σ and friction coefficient μ). The mechanic boundary condition means a super-critical stress state (Fmax>C) because stress resolution allows only two sets of planes to coevally have maximum value of F and thus shear fail equally according to Andersonian (1905, 1951) conjugate faulting derivation that corresponds to a critical stress state, i.e., Fmax is just equal to C. This super-critical stress state further means that there are some planes on which F>C certainly on verge of faulting at least possessing a not even lower tendency than those planes on which C=F, and thus polymodal faulting results. The planes with F≥C tend to be areal distribution with arc or annular geometry in stereographic projection of poles. Given the Coulomb-Mohr friction and failure criteria are not fundamentally different, the super-critical model may also apply to initial failure of intact rocks. The new model represents a major reorganization in thinking about shear failure of rocks and fracturing patterns. Several natural examples are provided with fracture patterns fit to the super-critical model proposed here.