The deformation of porous sandstones; are Byerlee friction and the critical state line equivalent?

Certain rock properties that depend on intergranular fracture and frictional sliding appear to be independent of rock type. This relationship is true for the rock-on-rock frictional sliding coefficient. The generalization has been widely applied to geomechanical modelling of upper crustal strength. Porous sandstones can be relatively weak and poorly cohesive, hence susceptible to deformation involving grain fragmentation and pore collapse. The critical state theory is commonly applied to describe such behaviour. Previous work showed that the yield surface is substantially independent of rock type when mean stress and differential stress are normalized by the grain crushing pressure, implying that the critical state line is rock type-independent and equivalent to the frictional sliding criterion. We test these hypotheses using previously published data for a range of porous sandstones augmented by new experimental results on Hollington and Berea sandstones deformed to large strains to define the critical state line over a wide range of pressures for each rock type. Results confirm the rock type-independence of the critical state line and show that it is nearly equivalent to frictional sliding. These relationships point to a simple procedure for estimating approximately the mechanical properties of sandstones based only on petrographic characteristics.