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An Investigation of Discontinuity Roughness Scale Dependency Using High-Resolution Surface Measurements

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Abstract

The influence of roughness on the hydro-mechanical behavior of rock discontinuities has long been recognized. As a result, several definitions and measures of roughness have been developed. According to the ISRM (Int J Rock Mech Min Sci Geomech Abstr 15(6):319–368, 1978), discontinuity roughness comprises large-scale (waviness) and small-scale (unevenness) components. However, the division between these scales is not clear and most investigations of surface roughness have been restricted to small fracture surfaces (<1 m2). Hence, the large-scale components of roughness are often neglected. Furthermore, these investigations typically define roughness using two-dimensional profiles rather than three-dimensional surfaces, which can lead to biased estimates of roughness. These limitations have led to some contradictory findings regarding roughness scale dependency (scale effects). This paper aims to provide some explanation of these contradictory findings. Through the in situ digitization and analysis of two adjacent large-scale (~2 × 3 m2 and ~2 × 2 m2) migmatitic-gneiss fracture surfaces, the influence of sample size on roughness estimates are investigated. In addition, the influence of measurement resolution on roughness estimates is investigated by digitizing small-scale (100 × 100 mm2) samples from the same fracture with varying resolution. The findings show roughness to increase as a function of the sampling window size, in contrast to what is commonly assumed. That is, the combined waviness and unevenness of a discontinuity relative to its mean plane increases with scale. Compared to the sampling window size, the resolution of surface measurements is shown to have a far greater influence on roughness estimates. This influence of measurement resolution may explain some of the contradictory roughness scale relationships that have been published previously. It is important to note that the observed decrease in shear strength with increasing scale, as observed in many prior studies, is not being questioned; rather, a clarification of the role of roughness in this phenomenon is sought.

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Notes

  1. http://www.gom.com/metrology-systems/system-overview/atos.html.

  2. http://www.gom.com/metrology-systems/system-overview/atos.html.

  3. Since the results for the left and right rectangular and square windows were found to display similar trends, only the results from the right square sampling windows are plotted herein.

  4. The ‘average’ values of θ *max /[C + 1] and θ *max /[C + 1]2D are represent mean of the values calculated at each orientation.

  5. In this particular case, ‘large’ and ‘steep’ refer to steps in the fracture greater than ~50 mm and inclinations steeper than ~75° measured relative to the best-fit plane through the fracture surface.

  6. The ‘average’ values of R P and Z 2 represent the mean of the individual values calculated for each profile.

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Acknowledgments

This work has been supported by the Natural Science and Engineering Research Council of Canada in the form of Discovery Grant No. 341275 and RTI Grant No. 345516 held by G. Grasselli and a Canada Graduate Scholarship held by B.S.A. Tatone. The authors would also like to thank Pulin Mondal for his assistance with the field work required for this study.

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  1. Geomechanics Research Group, Department of Civil Engineering, University of Toronto, 35 St. George St, Toronto, ON, M5S 1A4, Canada

    Bryan S. A. Tatone & Giovanni Grasselli

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  1. Bryan S. A. Tatone
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Correspondence to Giovanni Grasselli.

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Tatone, B.S.A., Grasselli, G. An Investigation of Discontinuity Roughness Scale Dependency Using High-Resolution Surface Measurements. Rock Mech Rock Eng 46, 657–681 (2013). https://doi.org/10.1007/s00603-012-0294-2

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