A rigorous multiscale random field approach to generate large scale rough rock surfaces

Estimating the shear strength of large in situ rock discontinuities is non-trivial because of the multiscale nature of roughness and the fact that only a very limited extent of discontinuity morphology is visible along traces. Recently, a novel stochastic method based on random field theory and Monte Carlo semi-analytical estimation of shear strength was proposed. The method was validated at laboratory scale and its application to one large natural surface showed that it has the potential to bypass the scale effect. However, a critical issue was reported by the authors of the study: it was found that the random field approach used could not generate the correct distribution of gradients on the simulated surfaces, which translates into an inaccurate prediction of shear strength. The authors had to manually adjust the input of the model to achieve a satisfactory prediction. This paper presents a new multiscale approach using random field theory, which now allows a rigorous generation of large synthetic 3D surfaces with controlled distribution of asperity heights and gradients from the profile of a 2D fracture trace (as might be visible in a rock face) referred to as a seed trace. Each seed trace is first decomposed into three daughter profiles corresponding to three levels of roughness. The statistics of each daughter profile form the input of the random field model at each scale level, allowing synthetic daughter surfaces to be created at each scale level. The synthetic daughter surfaces are then superimposed to obtain a composite rough surface comprising three levels of roughness. The approach was successfully validated with 25 input seed traces, coming from 5 different natural surfaces. This rigorous multiscale approach is essential to apply the stochastic method that was recently developed to predict the shear strength of large in situ discontinuities.