Making Coulomb angle-oriented shear bands in numerical tectonic models

- We suggest a way of consistently acquiring the Coulomb angle-oriented shear bands.
- An associated flow rule is the key to initiating a shear band at the Coulomb angle.
- This treatment is effective for different numerical methods and model resolutions.
- Reducing dilation angle can prevent unrealistic expansion of a shear band.
- Reduced dilation angle corresponds to reduced roughness of a natural fault plane.

Localization of shear strain can be induced by strain weakening plasticity in continuum models and is often used to represent faults of various scales. The orientation of the shear bands is thus required to be consistent with those observed from natural faults and with simple theories of brittle failure. Although the Coulomb angle, at which a shear band satisfies the Coulomb failure criterion, is widely used as an assumed fault orientation, the currently available numerical techniques do not always produce shear bands oriented at this angle. We demonstrate that, under an associated plastic flow rule for which dilation and friction angles are equal, the Coulomb angle becomes a unique initial shear band orientation regardless of the numerical methods employed and model resolution. The known problem of overly expanding shear bands in case of a constant dilation angle is preventable if dilation angle is reduced as shear strain along the shear band increases. This treatment corresponds to natural processes reducing roughness of a fault plane.