Scale Dependence of Waviness and Unevenness of Natural Rock Joints through Fractal Analysis

Yingchun Li,Hongwei Yang,Shengyue Sun

doi:10.1155/2020/8818815

Yingchun Li, Hongwei Yang + Show 1 more

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https://doi.org/10.1155/2020/8818815

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Abstract

The scale dependence of surface roughness is critical in characterising the hydromechanical properties of field-scale rock joints but is still not well understood, particularly when different orders of roughness are considered. We experimentally reveal the scale dependence of two-order roughness, i.e., waviness and unevenness through fractal parameters using the triangular prism surface area method (TPM). The surfaces of three natural joints of granite with the same dimension of 1000 mm×1000 mm are digitised using a 3D laser scanner at three different measurement resolutions. Waviness and unevenness are quantitatively separated by considering the area variation of joint surface as grid size changes. The corresponding fractal dimensions of waviness and unevenness in sampling window sizes ranging from 100 mm×100 mm to 1000 mm×1000 mm at an interval of 100 mm×100 mm are determined. We find that both the fractal dimensions of waviness and unevenness vary as the window size increases. No obvious stationarity threshold has been found for the three rock joint samples, indicating the surface roughness of natural rock joints should be quantified at the scale of the rock mass in the field.

Highlights

Rock masses contain a large body of joints
The fractal dimension of unevenness rises continuously to a peak value as the sampling window size increases to 400 mm × 400 mm, followed by an overall decrease as the sampling window size is increased to the maximum value of 1000 mm × 1000 mm
The fractal dimensions of unevenness of rock joint samples S2 and S3 in this study (Figures 7(b) and 7(c)) appear unchanged when the window size exceeds 400 mm × 400 mm: the surface of merely one rock joint was studied by Fardin et al [23], based on which affirmative conclusions cannot be drawn without examining the fractal features of several more large-scale rock joints with varying surface roughness

Summary

Introduction

Rock masses contain a large body of joints. The mechanical and hydraulic behaviours of rock joints highly affect the hydromechanical properties of rock masses. Accurate description of joint roughness at the relevant scale is crucial for predicting the hydromechanical coupling of the rock mass. Waviness and unevenness represent large-scale undulations observed in the field and small-scale roughness sampled in the laboratory, respectively [2, 3]. The surface of a laboratory-sized rock joint exhibits two-order asperities, i.e., first-order waviness and second-order unevenness [4,5,6,7,8]. Waviness with comparatively larger wavelength and amplitude primarily contributes to dilation, whereas unevenness of a smaller asperity size is sheared and damaged, providing shear resistance to the shear movement. Numerous empirical and statistical approaches have been proposed to quantify the roughness of rock joints [10,11,12,13,14,15], they have rarely taken into account the two-order roughness of a joint surface that plays distinct roles in the mechanical and hydraulic behaviours of rock joints [7, 16, 17]

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