The scale dependence of rock joint surface roughness

Accurate determination of surface roughness of rock joints at the large-sca le is essential for proper rock mass characterization. Surface roughness of rock joints is commonly characterized using small samples. However, since roughness parameters of rock joints are scale-dependent and their descripto rs change with scale. a systematic investigation has been carried out to un derstand the effect of scale on the surface roughness of rock joints. A sil icon rubber replica. 1000 mm x 1000 mm in size, was Moulded in-situ from a natural rock joint surface and its surface was digitized in the laboratory using a 3-D laser scanner having high accuracy and resolution. The fractal parameters, i.e. the fractal dimension D and amplitude parameter A describi ng surface roughness of the replica, were calculated on the basis of the Ro ughness-Length Method. To investigate the scale-dependency of surface rough ness of rock joints, ten sampling windows ranging in size from 100 mm x 100 mm to 1000 mm x 1000 mm were selected from the central part of the replica and their fractal parameters were calculated. The results show that both D and A are scale-dependent and their values decrease with increasing size o f the sampling windows. This scale-dependency is limited to a certain size, defined as the stationarity threshold. and for sampling windows larger tha n the stationarity threshold, the estimated parameters remain almost consta nt. It is concluded that. for surface roughness to be accurately characteri zed on a laboratory scale or in the field, samples need to be equal to or l arger than the stationarity limit. In this paper we have indicated the meth odology for establishing the value for the stationarity limit for rock join ts. (C) 2001 Elsevier Science Ltd. All rights reserved.