Skip to main content
SpringerLink
Log in

Characterization of Anisotropy of Joint Surface Roughness and Aperture by Variogram Approach Based on Digital Image Processing Technique

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

The mechanical and hydraulic anisotropy of rock joints are strongly dependent on the surface roughness and aperture. To date, accurate quantification of the anisotropic characteristics of joint surfaces remains a key issue. For this purpose, the digital image processing (DIP) technique was used to retrieve the joint surface topography, and a variogram function was used to characterize the anisotropy of the joint surface roughness and estimate the joint aperture. A new index, SR V , related to both the sill and the range of the variogram is proposed to describe the anisotropy of the joint surface roughness, and a new aperture index, b, is derived to quantify the joint aperture. These newly proposed indexes, SR V and b, were validated by characterizing three artificial triangular joint surfaces, then the values of both SR V and b were calculated along 42 directions on an artificial joint surface. The range of SR V was between 0.058622 and 0.331283, while that of b was from 0.270433 to 0.397715 mm. The results show that the newly proposed indexes SR V and b are effective for quantifying the anisotropic roughness and aperture of joint surfaces, respectively. In addition, based on the hypothesis that there exists a smooth upper wall for the artificial joint, a relationship between the indexes SR V and b was obtained based on the data analysis. It indicates that the trends of the indexes SR V and b tend to coincide, although some of their individual values differ. In this respect, the hydraulic aperture of rock joints is related to not only surface roughness but also the distribution of asperities on the surface. In addition, this method can also be used to characterize the roughness of real rock joints when the joint surface is treated by dying with ink before taking digital photos. This study provides a new method for properly quantifying the directional variability of joint surface roughness and estimating the mechanical and hydraulic properties of rock joints based on the DIP technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Abbreviations

A :

Section area of trough (mm2)

a :

Range (mm)

b :

Equivalent hydraulic aperture (mm)

C :

Sill (mm2)

D :

Fractal dimension (dimensionless)

D h :

Hydraulic diameter (mm)

h :

Given sample spacing or lag (mm)

h imax, h imin :

Maximum and minimum grey values of image (dimensionless)

h max, h min :

Maximum and minimum asperity height of joint surface (mm)

JRC:

Joint roughness coefficient (dimensionless)

JRCComb :

Value of JRC obtained by comb method of Barton and Choubey (1977) (dimensionless)

JRCDIP :

Value of JRC obtained by digital image processing method (dimensionless)

JRCsuggested :

Value of JRC estimated by SR V (dimensionless)

k :

Scale coefficient (dimensionless)

L :

Length of joint surface (mm)

L image :

Number of pixels of image along its length (pixels)

N(h):

Total number of data pairs separated by certain spatial lag vector h of joint surface (dimensionless)

P :

Perimeter of trough (mm)

p :

Length of variogram curve (mm)

R p :

Roughness profile index (dimensionless)

S :

Area surrounded by curve of the variogram function (mm2)

SR V :

Index quantifying the joint surface anisotropic behavior (dimensionless)

Z 2 :

First derivative root mean square (dimensionless)

z(x, y):

Height at location (x, y) on joint surface (mm)

θ :

Directional angle (°)

γ(h, θ):

Variogram function

γ *(h, θ):

Experimental variogram function

References

  • Alameda-Hernández P, Jiménez-Perálvarez J, Palenzuela JA, El Hamdouni R, Irigaray C, Cabrerizo MA, Chacón J (2014) Improvement of the JRC calculation using different parameters obtained through a new survey method applied to rock discontinuities. Rock Mech Rock Eng 47(6):2047–2060

    Article  Google Scholar 

  • Aydan ö, Shimizu Y, Kawamoto T (1996) The anisotropy of surface morphology characteristics of rock discontinuities. Rock Mech Rock Eng 29(1):47–59

    Article  Google Scholar 

  • Babanouri N, Nasab SK, Sarafrazi S (2013) A hybrid particle swarm optimization and multi-layer perceptron algorithm for bivariate fractal analysis of rock fractures roughness. Int J Rock Mech Min Sci 60:66–74. doi:10.1016/j.ijrmms.2012.12.028

    Google Scholar 

  • Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10(1–2):1–54

    Article  Google Scholar 

  • Belem T, Homand-Etienne F, Souley M (2000) Quantitative parameters for rock joint surface roughness. Rock Mech Rock Eng 33(4):217–242

    Article  Google Scholar 

  • Crandall D, Bromhal G, Karpyn ZT (2010) Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures. Int J Rock Mech Min Sci 47(5):784–796

    Article  Google Scholar 

  • Develi K, Babadagli T (1998) Quantification of natural fracture surfaces using fractal geometry. Math Geol 30(8):971–998

    Article  Google Scholar 

  • Du SG, Hu YJ, Hu XF (2009) Measurement of joint roughness coefficient by using profilograph and roughness ruler. J Earth Sci 20(5):890–896

    Article  Google Scholar 

  • Ertunç G, Tercan AE, Hindistan MA, Ünver B, Ünal S, Atalay F, Kıllıoğlu SY (2013) Geostatistical estimation of coal quality variables by using covariance matching constrained Kriging. Int J Coal Geol 112(1):14–25

    Article  Google Scholar 

  • Fardin N, Feng Q, Stephansson O (2004) Application of a new in situ 3D laser scanner to study the scale effect on the rock joint surface roughness. Int J Rock Mech Min Sci 41(2):329–335

    Article  Google Scholar 

  • Feng Q, Fardin N, Jing L, Stephansson O (2003) A new method for in situ non-contact roughness measurement of large rock fracture rock surfaces. Rock Mech Rock Eng 36(1):3–25

    Article  Google Scholar 

  • Grasselli G (2006) Manuel Rocha medal recipient shear strength of rock joints based on quantified surface description. Rock Mech Rock Eng 39(4):295–314

    Article  Google Scholar 

  • Grasselli G, Egger P (2003) Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters. Int J Rock Mech Min Sci 40(1):25–40

    Article  Google Scholar 

  • Hakami E, Larsson E (1996) Aperture measurements and flow experiments on a single natural fracture. Int J Rock Mech Min Sci Geomech Abstr 33(4):395–404

    Article  Google Scholar 

  • Kasmaee S, Gholamnejad J, Yarahmadi A, Mojtahedzadeh H (2010) Reserve estimation of the high phosphorous stockpile at the Choghart iron mine of Iran using geostatistical modeling. Min Sci Technol 20(6):855–860

    Google Scholar 

  • Koyama T, Li B, Jiang Y, Jing L (2009) Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas. Comput Geotech 36(1–2):291–303

    Article  Google Scholar 

  • Kulatilake PHSW, Shou G, Huang TH, Morgan RM (1995) New peak shear strength criteria for anisotropic rock joints. Int J Rock Mech Min Sci Geomech Abstr 32(7):673–697

    Article  Google Scholar 

  • Kulatilake PHSW, Um J, Pan G (1997) Requirements for accurate estimation of fractal parameters for self-affine roughness profiles using the line scaling method. Rock Mech Rock Eng 30(4):181–206

    Article  Google Scholar 

  • Kulatilake PHSW, Balasingam P, Park J, Morgan R (2006) Natural rock joint roughness quantification through fractal techniques. Geotech Geol Eng 24(5):1181–1202

    Article  Google Scholar 

  • Kulatilake PHSW, Park J, Balasingam P, Morgan R (2008) Quantification of aperture and relations between aperture, normal stress and fluid flow for natural single rock fractures. Geotech Geol Eng 26(3):269–281

    Article  Google Scholar 

  • Lee DH (2013) 3-Dimensional profile distortion measured by stylus type surface profilometer. Measurement 46(1):803–814

    Article  Google Scholar 

  • Maerz NH, Franklin JA, Bennett CP (1990) Joint roughness measurement using shadow profilometry. Int J Rock Mech Min Sci Geomech Abstr 27(5):329–343

    Article  Google Scholar 

  • Mah J, Samson C, McKinnon SD, Thibodeau D (2013) 3D laser imaging for surface roughness analysis. Int J Rock Mech Min Sci 58:111–117

    Google Scholar 

  • Murato S, Saito T (1999) The variogram method for a fractal model of a rock joint surface. Geotech Geol Eng 17(3–4):197–210

    Article  Google Scholar 

  • Neves M, Gomes DP (2011) Geostatistics for spatial extremes. A case study of maximum annual rainfall in Portugal. In: 1st International Conference on Spatial Statistics—Mapping Global Change, Enschede, The Netherlands, 23–25 Mar 2011. Procedia Environmental Sciences, pp 246–251

  • Rasouli V, Hosseinian A (2011) Correlations developed for estimation of hydraulic parameters of rough fractures through the simulation of JRC flow channels. Rock Mech Rock Eng 44(4):447–461

    Article  Google Scholar 

  • Roko RO, Daemenj JJK, Myers DE (1997) Variogram characterization of joint surface morphology and asperity deformation during shearing. Int J Rock Mech Min Sci 34(1):71–84

    Article  Google Scholar 

  • Snow DT (1965) A parallel plate model of fractured permeable media. PhD thesis, University of California, Berkeley

  • Srivastava RM (2013) Geostatistics: a toolkit for data analysis, spatial prediction and risk management in the coal industry. Int J Coal Geol 112(1):2–13

    Article  Google Scholar 

  • Sun HQ (1990) Geostatistics and its application. China University of Mining and Technology Press, Xuzhou

    Google Scholar 

  • Tatone BSA, Grasselli G (2010) A new 2D discontinuity roughness parameter and its correlation with JRC. Int J Rock Mech Min Sci 47(8):1391–1400

    Article  Google Scholar 

  • Tatone BSA, Grasselli G (2012) Quantitative measurements of fracture aperture and directional roughness from rock cores. Rock Mech Rock Eng 45(4):619–629

    Article  Google Scholar 

  • Tse R, Cruden DM (1979) Estimating joint roughness coefficients. Int J Rock Mech Min Sci Geomech Abstr 16(5):303–307

    Article  Google Scholar 

  • Wolski M, Podsiadlo P, Stachowiak GW (2010) Applications of the variance orientation transform method to the multi scale characterization of surface roughness and anisotropy. Tribol Int 43(11):2203–2215

    Article  Google Scholar 

  • Xia CC, Tang ZC, Xiao WM, Song YL (2014) New peak shear strength criterion of rock joints based on quantified surface description. Rock Mech Rock Eng 47(2):387–400

    Article  Google Scholar 

  • Xie HP (1995) Fractal description of rock joint. Chin J Geotech Eng 17(1):18–23

    Google Scholar 

  • Yang ZY, Lo SC (1997) An index for describing the anisotropy of joint surfaces. Int J Rock Mech Min Sci 34(6):1031–1044

    Article  Google Scholar 

  • Yang ZY, Di CC, Lo SC (2001a) Two-dimensional Hurst index of joint surfaces. Rock Mech Rock Eng 34(4):323–345

    Article  Google Scholar 

  • Yang ZY, Lo SC, Di CC (2001b) Reassessing the joint roughness coefficient (JRC) estimation using Z 2. Rock Mech Rock Eng 34(3):243–251

    Article  Google Scholar 

Download references

Acknowledgments

This work is funded by the National Science Foundation of China (Grant Nos. 51222401, 51374049, and 51304037), the Key Project of Chinese Ministry of Education (no. 113019A), the Fundamental Research Funds for the Central Universities of China (Grant Nos. N120101001 and N140105001), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110042110035). This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, People’s Republic of China

    S. J. Chen, W. C. Zhu, Q. L. Yu & X. G. Liu

  2. Institute of Mining Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, People’s Republic of China

    S. J. Chen

Authors
  1. S. J. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. C. Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Q. L. Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. X. G. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. C. Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, S.J., Zhu, W.C., Yu, Q.L. et al. Characterization of Anisotropy of Joint Surface Roughness and Aperture by Variogram Approach Based on Digital Image Processing Technique. Rock Mech Rock Eng 49, 855–876 (2016). https://doi.org/10.1007/s00603-015-0795-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-015-0795-x

Keywords

Search

Navigation