Geostatistical algorithm for evaluation of primary and secondary roughness

Joint roughness is combination of primary and secondary roughness. Ordinarily primary roughness is a geostatistical part of a joint surface that has a periodic nature but secondary roughness or unevenness is a statistical part of that which have a random nature. Using roughness generating algorithms is a useful method for evaluation of joint roughness. In this paper after determining geostatistical parameters of the joint profile, were presented two roughness generating algorithms using Mount-Carlo method for evaluation of primary (GJRGAP) and secondary (GJRGAS) roughness. These based on geostatistical parameters (range and sill) and statistical parameters (standard deviation of asperities height, SDH, and standard deviation of asperities angle, SDA) for generation two-dimensional joint roughness profiles. In this study different geostatistical regions were defined depending on the range and SDH. As SDH increases, the height of the generated asperities increases and asperities become sharper and at a specific range (a specific curve) relation between SDH and SDA is linear. As the range in GJRGAP becomes larger (the base of the asperities) the shape of asperities becomes flatter. The results illustrate that joint profiles have larger SDA with increase of SDH and decrease of range. Consequencely increase of SDA leads to joint roughness parameters such Z2, Z3 and Rp increases. The results showed that secondary roughness or unevenness has a great influence on roughness values. In general, it can be concluded that the shape and size of asperities are appropriate parameters to approach the field scale from the laboratory scale.