Estimation of the shear strength of fractured Gosford sandstone based on fractal theory and numerical modelling

The effects of joint roughness on the peak shear strength of fractured rock mass has been extensively investigated. Among these investigations, Barton's JRC-JCS model has been well recognized for its capability to characterize surface geometry. However, shear strength estimation is still a major challenge because of the difficulties involved in accurately calculating the joint roughness coefficient (JRC). Thus, alternative methods such as statistic methods based on fractal theory have been proposed to evaluate the impact of surface morphology on rock joints. Extensive evidences show that, the application of the fractal dimension alone cannot produce a satisfactory estimation of either the JRC or the peak shear strength. Therefore, this paper aims to investigate the peak shear strength of rock joints by adopting the fractal theory and via a numerical simulation. Gosford sandstone taken from Sydney Basin is adopted as the rock materials for both numerical validation and shear strength investigation. Along with numerical simulations on shear strength, a linear function has been proposed to describe the correlations among the root-mean-square of the first derivative of fracture profile (Z(2)), fractal dimension and the standard deviation. The peak shear strength is then accurately interpreted as a function of joint roughness indices: fractal dimension (D), standard deviation (SD) and Z(2). Predictions by the proposed equation are compared with both the numerical simulation results and that reproduced by Barton's equation. Good agreement has been achieved even when the joint roughness coefficients (JRC) is varied which proves that the proposed equation is highly accurate and can be reused in other related applications.