Three-Dimensional Geostatistical Analysis of Rock Fracture Roughness and Its Degradation with Shearing

Three-dimensional surface geometry of rock discontinuities and its evolution with shearing are ofgreat importance in understanding the deformability and hydro-mechanical behavior of rock masses.In the present research, surfaces of three natural rock fractures were digitized and studied before andafter the direct shear test. The variography analysis of the surfaces indicated a strong non-linear trendin the data. Therefore, the spatial variability of rock fracture surfaces was decomposed to onedeterministic component characterized by a base polynomial function, and one stochastic componentdescribed by the variogram of residuals. By using an image-processing technique, 343 damaged zoneswith different sizes, shapes, initial roughness characteristics, local stress fields, and asperity strengthvalues were spatially located and clustered. In order to characterize the overall spatial structure of thedegraded zones, the concept of ‘pseudo-zonal variogram’ was introduced. The results showed that thespatial continuity at the damage locations increased due to asperity degradation. The increase in thevariogram range was anisotropic and tended to be higher in the shear direction; thus, the direction ofmaximum continuity rotated towards the shear direction. Finally, the regression-kriging method wasused to reconstruct the morphology of the intact surfaces and degraded areas. The cross-validationerror of interpolation for the damaged zones was found smaller than that obtained for the intactsurface.

Keywords:

Rock fracture roughness , Spatial structure , Variography , Degraded zones , Regressionkriging , Image processing