Development of an elasto-plastic constitutive model for intact rocks

• A softening behaviour of sedimentary rocks from peak strength to residual strength is modelled based on Mohr–Coulomb criterion.
• Dilation behaviour of sedimentary rocks is defined in terms of mathematical equation.
• All of the data are extracted from outcomes of triaxial test on three different rocks such as sandstone, silty-sandstone and mudstone.
• Key factors in these proposed equations are cohesion, friction angle and dilation angle.
• The observation of test data shows deduction in cohesion, minor change in friction angle and deduction in dilation angle.

A constitutive model was developed to describe the nonlinear behaviour of intact rocks under static loading. The model includes the pre-peak elastic and the post-peak strain-softening behaviour, as well as dilation. The model employs the shrinking of the failure criteria by progress of plastic deformation, to consider the strain-softening behaviour of rocks. A non-associated plastic potential function based on the dilation angle is employed to formulate the plastic deformation and dilation of rocks. Triaxial laboratory test results are used to derive the model equations. The model employs the assumptions that crack propagation in rocks during post-peak deformation is a cohesion-losing process, during which the frictional angle is constant. The assumptions were verified through careful study of the laboratory test results. In the developed model, the dilation angle is associated with the confining stress, friction angle of rocks and uniaxial compressive strength of rocks. Rocks have peak dilation angle at the point of peak strength and after that, it decreases with progress of plastic deformation, and is close to zero when rocks reach residual strength. The developed model is implemented in a finite difference code. The numerical results are compared with the test results, which show that the model captures the post-peak behaviour of rocks well.