We carry out constant volume simulations of steady-state shear-driven rheology in a simple model of bidisperse soft-core frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We discuss in detail the critical scaling ansatz for the shear-driven jamming transition and carry out a detailed scaling analysis of our resulting data for pressure $p$ and shear stress $\sigma$. Our analysis determines the critical exponent $\beta$ that describes the algebraic divergence of the Bagnold transport coefficients ${lim}_{\dot{\gamma }\to 0}p/{\dot{\gamma }}^2,\sigma /{\dot{\gamma }}^2\sim {({\varphi }_J-\varphi )}^{-\beta }$ as the jamming transition ${\varphi }_J$ is approached from below. For the low strain rates considered in this work, we show that it is still necessary to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data, in which the critical parameters become independent of the size of the window of data used in the analysis. We compare our resulting value $\beta \approx 5.0\pm 0.4$ against previous numerical results and competing theoretical models. Our results confirm that the shear-driven jamming transition in Bagnoldian systems is well described by a critical scaling theory and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.

• Received 12 October 2015
• Revised 15 April 2016

DOI:https://doi.org/10.1103/PhysRevE.93.052902