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Shear strain localization into shear bands is associated with velocityweakening instabilities and earthquakes. Here, we simulate steady-stateplane-shear flow of numerical granular material (gouge), confined betweenparallel surfaces. Both constant shear stress and constant strain-rate boundaryconditions are tested and the two types of boundary conditions are found toyield distinct velocity profiles and friction laws. The inertial number, $I$,exerts the largest control on the layers' behavior, but additional dependenciesof friction on normal stress and thickness of the layer are observed underconstant stress boundary condition. We find that shear-band localization, whichis present in the quasistatic regime ($I<10^{-3}$) in rate-controlled shear, isabsent under stress-controlled loading. In the latter case, flow ceases whenmacroscopic friction coefficient approaches the quasistatic friction value. Theinertial regime that occurs at higher inertial numbers ($I>10^{-3}$) isassociated with distributed shear, and friction and porosity that increase withshear rate (rate-strengthening regime). The finding that shear under constantstress boundary condition produces the inertial, distributed shear but neverquasistatic, localized deformation is rationalized based on low fluctuations ofshear forces in granular contacts for stress-controlled loading. By examiningporosity within and outside a shear band, we also provide a mechanical reasonwhy the transition between quasistatic and inertial shear coincides with thetransition between localized and distributed strain.

Strain localization in planar shear of granular media: the role of porosity and boundary conditions