Scale Dependency, Heterogeneity and Anisotropy of Surface Roughness of Rock Fractures

It is known that surface roughness of mkfiachrres is scale-dependent and their roughness features changes with respect to the fracture location. Therefore, for proper characterization, accurate determination of surface mughness of rock joints at large-.scale is essential. In this research work a systematic invmtigation is carried out to understand the scale dependency, heterogeneity and anisotropy of the sugace roughness of rmk joints. A large silicon tubber replica, I000 mm XI OOO mm in size, was made in-situ fiom a very large natural rock joint surface and its morphology was digitized at laboratory using a power@ 3-0 laser scanner. The froctal parameters, i.e. fractal dimension D and amplitude parameter A, describing .wrface roughness of the replica were calculated on the basis of the Roughness-Lengh Method (RLM). To inwstigate the scale-dependency of .sut$ace mughness of rock join&, 10 sampling windows ranging in size fmm 100 mrn XI 00 mm to 1 OOO mm x 1000 mm were selected fmm the central part of the replica and their fractal pammeters were calculated The resulh show that both D and A are scale-dependent and their values decrease with increasing size of the sampling windows. However, this .scale-dependency is limited to a cerhin size, defured as the stationarity threshold, and for sampling windows larger than the shtionarity thmshold, the atimated pammeter.~r emain almost constanl It is concluded that for surfce roughness to be accurately characterized on a laboratory scale or in the jield, samples need to be equal to or larger than the stationarity limit. mis inwstigation was extended to evaluate the heterogeneity and anisotropy of roughness of the replica. In this caseI both D and A of sampling windows systematically selected fmm direrent para of the replica and in direrent directions were calculated and compared. The rmults showed that these parameters are diyerent and change with respect to location and direction of sampling windows. By repeating the same ana&.sis for inctvased window .suesI the degree of hetemgeneity significantly decreases and reache stationarity aJer a certain size defined as stationarity threshold while the degree of anisotmpy slightly changes and reaches stationarity. Therdore, the surface roughness of the natural joint and replica can be characterized as isotropic-heterogeneous-.scale-dependent.