Simulated Rock Profiles for Surface Weathering Estimation

The estimation of rock surface weathering, much like the estimation of shear strength of rock joints, is facilitated by the use of statistical methods on linear profiles. Unfortunately, a number of factors ranging from the size of the sampling interval used to the mathematics of the roughness index chosen can misrepresent the true roughness of a surface. A method is proposed to simulate rock profiles using a combination of generated signals and a Markov process for the purpose of studying and anticipating the effects of many variables on roughness estimates. The large-scale properties of rock are represented as sine waves, sawtooth waves, and a random Markov process and the small-scale properties are simulated with red noise. The generative parameters are varied to produce a corpus of simulated profiles, where sampling and measurement error is also simulated by lightly deflecting measurements with Gaussian-distributed noise. Using the simulated profiles, five different measures for roughness are compared and the results indicate that no one measure alone exhibits sensitivity to all generative parameters. The Fourier transform is applied to compare the frequency content of these simulated profiles to that of real limestone rock, providing some validation that the conclusions drawn from our simulated profiles also extend to profiles from real rock samples.