Nonlinear shear behavior of rock joints using a linearized implementation of the Barton–Bandis model

Abstract

Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing, inducing dilation and resulting in nonlinear joint shear strength and shear stress vs. shear displacement behaviors. The Barton–Bandis (BB) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints. The BB model accounts for asperity roughness and strength through the joint roughness coefficient (JRC) and joint wall compressive strength (JCS) parameters. Nevertheless, many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr–Coulomb (M−C) model, which is only appropriate for smooth and non-dilatant joints. This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior. To bridge the BB and the M−C models, this paper aims to provide a linearized implementation of the BB model using a tangential technique to obtain the equivalent M−C parameters that can satisfy the nonlinear shear behavior of rock joints. These equivalent parameters, namely the equivalent peak cohesion, friction angle, and dilation angle, are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing. The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre- and post-peak regions of shear displacement, respectively. Likewise, the pre- and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established. Verifications of the linearized implementation of the BB model show that the shear stress-shear displacement curves, the dilation behavior, and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.

Keywords

• Rock joints
• Joint shear behavior
• Friction and dilation
• Barton–Bandis (B–B) model
• Equivalent Mohr–Coulomb (M–C) parameters