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

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 A_θ*) 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 (D_tp), 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 (i_d) unique for the applied normal load. This clearly proves the validity of Grasselli's (2001) “threshold apparent dip angle” concept.