ABSTRACT:

This paper examines the relationship between roughness estimates and the resolution of the surface measurements on which they are based. To do so, several fracture replicas are digitized with a stereotopometric camera at three different resolutions. Subsequently, the variations in the calculated 3D roughness parameters are analyzed. By direct shear testing the replicas with a range of normal stresses, the failure envelope defined by the laboratory results can be compared to the strength envelopes predicted according to empirical shear criteria. In doing so, an empirical relationship between resolution and roughness can be established to correct the predicted shear strength. The development of such an expression permits consistent and accurate shear strength estimates to be obtained. With further verification, the proposed correction will allow different practitioners to obtain consistent shear strength estimates using 3D surface measurements from different equipment with varying resolution.

1 INTRODUCTION

Recent research has yielded promising new3Dparameters to better characterize surface roughness of rock discontinuities using high resolution 3D surface measurements (Tatone & Grasselli 2009a). Nevertheless, the influence of varying measurement resolution on roughness estimates has yet to be considered in detail. As outlined by several researchers, measurement resolution (or point spacing) can have a significant impact on the parameterization of discontinuity roughness (e.g. Hong et al. 2008, Tatone & Grasselli 2009b). Thus, to facilitate comparison of 3D roughness parameters derived from 3D data with different resolutions, it is essential that the resolution of the system being used be known and disclosed. Moreover, to avoid misleading estimates of discontinuity shear strength via empirical strength criteria, the relationship between roughness estimates and the resolution of measurement on which they are based must be understood. At present there are no suggested methods or guidelines to determine what resolution (nominal point spacing) should be used to measure discontinuity roughness.

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