Computation of direction dependent joint surface parameters through the algorithm of triangular prism surface area method: A theoretical and experimental study

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Grasselli's (2001) methodology on the quantification of the “shear-induced potential contact zones” is fundamentally very strong at properly dealing with the physics of the shear phenomenon. However, the high precision measurement system and the triangulation algorithm he used may not be easily accessible for everyone due to its industrial characteristics. Therefore, a simple technique called “the modified shear-induced potential contact zones” is introduced in the present work. By executing this technique on the surface coordinates of a large number of rock joints digitized through a specially developed mechatronic surface scanning device, “maximum possible and total potential contact areas” (A0 and Aθ*) and “directional surface parameters” (θ*max : maximum apparent dip angle, c2 : shape parameter, θ*max/c2 : change of angularity) are calculated in a specified direction. Ratio A0/c2 is proposed for a new directional roughness parameter. Surface roughness is also characterized by fractal dimension (Dtp), alternatively. Using a specially developed shear box, shear tests are performed in the direction of parameter calculation. Then, by a series of quantitative comparisons between the directional surface parameters and both the fractal dimensions and the shear strengths, the ability of the parameters to relate with the surface roughness and the shear strength is examined. In general, the results are satisfactory for the reliability of the modified technique. The main advantage of the introduced technique is its algorithmic simplicity facilitating direct applicability for basic 2D data sets, [z = f (x, y)], which can be practically acquired via easily accessible and cost-effective surface measurement systems. Additionally, another simple recipe is also introduced predicting contact zones visually prior to shearing. Then, total potential contact areas predicted in the shear direction are visually compared with the actual images of contacts observed in the tests. The best match is obtained when the threshold apparent inclination (θ*cr) is chosen equal to the experimental dilation angle (id) unique for the applied normal load. This clearly proves the validity of Grasselli's (2001) “threshold apparent dip angle” concept.

Original languageEnglish
Pages (from-to)895-911
Number of pages17
JournalInternational Journal of Solids and Structures
Publication statusPublished - 1 Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd


The author is thankful to C. Comlekci and O. G. Develi for their unique contributions in designing and manufacturing the surface scanning device and the direct shear box as well as the software developments, and also to Prof. M. Vardar at ITU and Prof. T. Babadagli at University of Alberta for their valuable advising throughout this study. This work was partly supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) [Project No: YDABÇAG198Y016]. All these supports are gratefully acknowledged.

FundersFunder number
Türkiye Bilimsel ve Teknolojik Araştirma KurumuYDABÇAG198Y016


    • Contact areas
    • Fractal dimension
    • Rock joints
    • Shear tests
    • Surface roughness
    • Surface scanning


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