Strain localization due to structural softening during pressure sensitive rate independent yielding

Abstract

AbstractAfter giving a complete analytical solution for the strain softening model associated to Mohr-Coulomb non associated elasto-plastic flow rule (MC-model), the paper demonstrates that this rheology possesses a finite limit load which allows solving for strength drop as a boundary value problem. The MC-model produces a non-dimensional strength drop, which depends on three parameters: the orientation of the shear band versus the least principal stress axis outside the band α0, the peak friction angle φ and the dilatation angle Ψ. The maximum reduction of strength obtained with that strain-softening model is on the order of the confining stress p0. For this weakest regime, the effective friction of the shear band drops from μini = 0.85 at peak to μss = 0.64 at the end of the softening phase. In this model, which considers thick shear bands, the weakest regime is not obtained for an orientation corresponding to the exact Coulomb orientation. Instead, the orientation of the weakest shear zone systematically deviates from the coulomb orientation by an angle, which rises with its internal friction angle. The characteristic shear strain needed to achieve steady state is quantified semi analytically and in the range of parameters valid for Earth, this strain is found to be of the order of 7–8%. These numbers are typical of what is observed in the laboratory, which give us confidence on that MC-model is a good and probably the simplest model to localize strain in numerical codes aimed at modeling the brittle part of the Earth.