The Brittle-Ductile Transition Predicted by a Physics-Based Friction Law

A theory of the brittle-ductile transition (BDT) is shown to be a direct consequence of a recently developed physics-based constitutive law for rock friction (Aharonov & Scholz, 2018, https://doi.org/10.1002/2016JB013829), which assumes exponential creep on contacts. The theory was previously tested against experimental data for sliding at low ambient temperature and stress. Here, theoretical interpretation of experimental data at high temperature and stress shows that at some point the real area of contact reaches a maximum value beyond which it becomes fixed. The constitutive law shows that this marks the onset of the BDT, beyond which sliding changes from frictional to an exponential flow law for low-temperature plasticity. Application to the Earth's crust shows that beyond this point, strength fall linearly with depth until it intersects the power law for bulk flow of the country rock, which marks the lower boundary of the BDT. Modeling, constrained by experimental data for granite, predicts that the BDT starts at a temperature of about 300°C, at a depth of 11–13 km in the continental crust, depending on fault slip rate and temperature gradient. The completion of the BDT is similarly calculated to occur around 475°, at 16–18 km, in agreement with laboratory and field observations. The BDT is thus found to be a region spanning about 175°C with a width of several kilometers. Within the exponential flow region, the structural outcome would be a relatively narrow mylonitized fault zone, which widens into a broader region of shear at the base of the BDT.