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Determination of Joint Roughness Coefficients Using Roughness Parameters

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Abstract

This study used precisely digitized standard roughness profiles to determine roughness parameters such as statistical and 2D discontinuity roughness, and fractal dimensions. Our methods were based on the relationship between the joint roughness coefficient (JRC) values and roughness parameters calculated using power law equations. Statistical and 2D roughness parameters, and fractal dimensions correlated well with JRC values, and had correlation coefficients of over 0.96. However, all of these relationships have a 4th profile (JRC 6–8) that deviates by more than ±5 % from the JRC values given in the standard roughness profiles. This indicates that this profile is statistically different than the others. We suggest that fractal dimensions should be measured within the entire range of the divider, instead of merely measuring values within a suitable range. Normalized intercept values also correlated with the JRC values, similarly to the fractal dimension values discussed above. The root mean square first derivative values, roughness profile indexes, 2D roughness parameter, and fractal dimension values decreased as the sampling interval increased. However, the structure function values increased very rapidly with increasing sampling intervals. This indicates that the roughness parameters are not independent of the sampling interval, and that the different relationships between the JRC values and these roughness parameters are dependent on the sampling interval.

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Abbreviations

a, b, c :

Regression coefficients of power law equation

ACF:

Auto-correlation function

\(A_{{\theta^{*} }}\) :

Potential contact areas

a n :

Normalized intercept yielded by dividing the intercept (log a) by the nominal length of the profile

C :

Dimensionless parameter

CLA:

Centerline average values

D :

Fractal dimension

i ave :

Average roughness angles

JRC:

Joint roughness coefficient

\(L_{{\theta^{*} }}\) :

Normalized length

log a :

Intercept of the Log L(r)−Log r plot

L(r):

Total length of the profile

MSV:

Mean square roughness height

P :

Roughness parameter (Z 2, SF, R p −1, \(\theta_{\text{max}} ^{*} /\left( {C + 1} \right)_{2D}\) and D−1)

r :

Divider value

RMS:

Root mean square roughness height values

R p :

Roughness profile indexes

SD i :

Standard deviation of roughness angle

SF:

Structure function

SI:

Sampling interval

Z 1 :

Mean square first derivative

Z 2 :

Root mean square first derivative values

Z 3 :

Root mean square second derivative

Z 4 :

Percentage excess of distance

\(\theta_{\text{cr}}^{*}\) :

Threshold apparent inclinations

\(\theta_{\text{max}} ^{*}\) :

Maximum apparent inclination

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Acknowledgments

This research was supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (2011-0007281).

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Authors and Affiliations

  1. Department of Geophysics, Kangwon National University, 1 Kangwondaehak-gil, Chuncheon, Gangwon-do, 200-701, Republic of Korea

    Hyun-Sic Jang & Bo-An Jang

  2. Department of Energy Resources Engineering, Chosun University, 309 Pilmun-daero Dong-gu, Gwangju, 501-759, Republic of Korea

    Seong-Seung Kang

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  1. Hyun-Sic Jang
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Correspondence to Bo-An Jang.

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Jang, HS., Kang, SS. & Jang, BA. Determination of Joint Roughness Coefficients Using Roughness Parameters. Rock Mech Rock Eng 47, 2061–2073 (2014). https://doi.org/10.1007/s00603-013-0535-z

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