Generation of Roughness Using the Random Midpoint Displacement Method and Its Application to Quantification of Joint Roughness

Abstract

Quantification of roughness plays an important role in modeling strength deformability and fluid flow behaviors of rock joints. A procedure was suggested to simulate joint roughness, and characteristics of the roughness was investigated in this study. Stationary fractional Brownian profiles with known input values of the fractal parameter and other profile properties were generated based on random midpoint displacement method. Also, a procedure to simulate three dimensional roughness surface was suggested using the random midpoint displacement method. Selected statistical roughness parameters were calculated for the generated self-affine profiles to investigate the attribute of roughness. Obtained results show that statistical parameters applied in this study were able to consider correlation structure and amplitude of the profiles. However, effect of data density should be tackled to use statistical parameters for roughness quantification.

Comparison of two fractal interpolation methods

“…The large differences between the two methods are mainly due to the use of different algorithms in the two methods [55,56]. The MD method is a classical application of fractal Brownian motion, and it generates fractal surfaces by randomly changing the elevation displacement of the point [57,58]. With this method, a Gauss random variable leads to the aperiodicity.…”

Development of a New Method for the Quantitative Generation of an Artificial Joint Specimen with Specific Geometric Properties

“…It is known that the roughness of a joint surface generated by the random midpoint displacement method is affected by joint length (L), generation level (GL), asperity amplitude (σ), and the Hurst exponent (H) [22,24]. However, considering the testing environment, such as the size of a specimen and the resolution of a 3D printer, it is reasonable to assume that L and GL are actually determined before the surface generation.…”

“…The generation sequence of a rough joint surface following the random midpoint displacement method: (a) Joint shape when GL = 1, with nine points on the joint surface; (b) Joint shape when GL = 2; (c) Joint shape when GL = 3 (After Seo and Um[22]). …”