A simplified theoretical model to predict the shear behaviour of concrete–rock joints with Gaussian irregularities

The inherent randomness in the roughness of concrete–rock joints poses challenges when analysing their shear behaviour. Traditionally, theoretical models simplify these complex geometries by approximating them as regular triangular asperities. This study presents a novel micro-mechanical model developed to simulate the shear behaviour. The model accounts for the complex and random roughness of joint profiles by considering varying asperity heights as Gaussian distribution. Local stress distribution among individual asperities was determined. A failure envelope, mapping joint dilation against asperity height, was obtained, making it possible to identify the critical joint dilation for individual asperities at which individual asperity failure results. The parameter of shear area ratio, which captures the portion of failed asperities relative to all asperities, is introduced, and its semi-analytical solution is derived. In addition, a wedge-shaped planar failure surface is determined based on laboratory observations and equations to estimate post-failure residual resistance are obtained. A series of direct shear tests on rock–concrete joints with a range of geometries was conducted to validate the proposed model, and reasonably close agreement was obtained between predicted and measured performance. An additional case study analysing the results of field tests on a drilled pile socketed in rock was conducted using the proposed method. The results showed good agreement with the measured data, demonstrating the validity and practicality of the proposed approach.