Nonlinear criterion for strength mobilization in brittle failure of rock and its extension to the tunnel scale

Abstract

As underground excavations are getting deeper and field stresses increase, the behavior of intact rock blocks plays an increasingly important role in understanding and estimating the overall rock mass strength. To model the brittle behavior of intact rock blocks, the stress–strain curve is usually idealized considering a linear strength mobilization approach (cohesion-weakening-friction-strengthening, CWFS), however, it is well recognized that rock presents a nonlinear behavior in terms of the confining stress. This study extends the strength mobilization in brittle failure of rock using nonlinear criteria. To determine the model parameters, a standard statistical method that uses the complete laboratory stress–strain curves of the intact rock is employed. Several hypotheses of linear and nonlinear models are statistically compared for different types of rock and confining stress levels. Results demonstrate that the best approach to model the brittle failure of rock is to consider a nonlinear strength envelope, such as the Hoek-Brown criterion assuming a residual uniaxial compressive strength different from zero and a mi parameter that increases, both with simultaneous mobilization. This model helps to recreate high-confining conditions and a more realistic transition between peak and post-peak strength. The obtained parameters are discussed and compared with literature values to verify the validity and to develop guidelines for the estimation of parameters, providing an objective mobilization criterion. Finally, the nonlinear model was applied to a finite element code and extended to a tunnel scale in the brittle rock under high-stress conditions. A reasonable fit between the simulations and the in-situ overbreak measurements was found.

Keywords

• Nonlinear strength
• Strength mobilization
• Brittle failure
• Intact rock
• Scaling