A Bounding Surface Plasticity Model for Intact Rock Exhibiting Size-Dependent Behaviour

A new constitutive model for intact rock is presented recognising that rock strength, stiffness and stress–strain behaviour are affected by the size of the rock being subjected to loading. The model is formulated using bounding surface plasticity theory. It is validated against a new and extensive set of unconfined compression and triaxial compression test results for Gosford sandstone. The samples tested had diameters ranging from 19 to 145 mm and length-to-diameter ratios of 2. The model captures the continuous nonlinear stress–strain behaviour from initial loading, through peak strength to large shear strains, including transition from brittle to ductile behaviour. The size dependency was accounted for through a unified size effect law applied to the unconfined compressive strength—a key model input parameter. The unconfined compressive strength increases with sample size before peaking and then decreasing with further increasing sample size. Inside the constitutive model two hardening laws act simultaneously, each driven by plastic shear strains. The elasticity is stress level dependent. Simple linear loading and bounding surfaces are adopted, defined using the Mohr–Coulomb criterion, along with a non-associated flow rule. The model simulates well the stress–strain behaviour of Gosford sandstone at confining pressures ranging from 0 to 30 MPa for the variety of sample sizes considered.