Skip to main content
SpringerLink
Log in

New Peak Shear Strength Criterion of Rock Joints Based on Quantified Surface Description

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

Abstract

The prime objective of this work is to improve our understanding of the shear behavior of rock joints. Attempts are made to relate the peak shear strength of rock joints with its three-dimensional surface morphology parameters. Three groups of tensile joint replicas with different surface morphology are tested with direct shear tests under constant normal load (CNL) conditions. Firstly, the three-dimensional surface characterization of these joints is evaluated by an improved roughness parameter before being tested. Then, a new empirical criterion is proposed for these joints expressed by three-dimensional quantified surface roughness parameters without any averaging variables in such a way that a rational dilatancy angle function is used instead of \({\text{JRC}} \cdot \log_{10} \left( {{{\text{JCS}} \mathord{\left/ {\vphantom {{\text{JCS}} {\sigma_{\text{n}} }}} \right. \kern-\nulldelimiterspace} {\sigma_{\text{n}} }}} \right)\) by satisfying the new peak dilatancy angle boundary conditions under zero and critical-state normal stress (not physical infinite normal stress). The proposed criterion has the capability of estimating the peak shear strength at the laboratory scale and the required roughness parameters can be easily measured. Finally, a comparison among the proposed criterion, Grasselli’s criterion, and Barton’s criterion are made from the perspective of both the rationality of the formula and the prediction accuracy for the three groups of joints. The limitations of Grasselli’s criterion are analyzed in detail. Another 37 experimental data points of fresh rock joints by Grasselli are used to further verify the proposed criterion. Although both the proposed criterion and Grasselli’s criterion have almost equal accuracy of predicting the peak shear strength of rock joints, the proposed criterion is easier and more intuitive from an engineering point of view because of its Mohr–Coulomb type of formulation.

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

Similar content being viewed by others

Abbreviations

A 0 :

Normalized area corresponding to the apparent dip angle \(\theta_{\max }^{*}\) = 0

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

Normalized area corresponding to the apparent dip angle θ *

C :

Roughness parameter characterizing the distribution of apparent dip angles over the joint surface

d n :

Dilatancy angle (°)

d n,0 :

Dilatancy angle at zero normal stress (°)

d n,peak :

Peak dilatancy angle (°)

d n,crit :

Critical dilatancy angle at the critical normal stress (°)

JCS:

Joint wall compressive strength (MPa)

JRC:

Joint roughness coefficient

JRCcal :

Value of JRC obtained by the direct shear test

JRCtilt :

Value of JRC obtained by the tilt test

JRCvisual :

Value of JRC obtained by the visual method

JRC j :

JRC value of the jth profile along the shear direction

Ave:

Average value

SD:

Standard deviation

Max:

Maximum value

Min:

Minimum value

d :

True dip vector

t :

Shear vector

w :

Shear plane

α:

Azimuth (°)

β:

Angle between the schistosity plane and the plane normal to the joint (°)

θ :

Dip angle (°)

θ * :

Apparent dip angle of each triangle along the shear direction (°)

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

Maximum apparent dip angle in the shear direction (°)

φb :

Basic friction angle of the rock joint (°)

δh :

Shear displacement (mm)

δv :

Normal displacement (mm)

τ:

Shear strength (MPa)

τpeak :

Peak shear strength (MPa)

τresidual :

Residual shear strength (MPa)

τpeak,mea :

Measured peak shear strength (MPa)

τpeak,cal :

Calculated peak shear strength by the criterion (MPa)

\(\overline{\sigma }_{\text{ave}}\) :

Average estimation error

σn :

Normal stress (MPa)

σn,crit :

Normal stress at the critical state (MPa)

σt :

Tensile strength (MPa)

i :

Positive integer

m :

Number of samples

References

  • Amadei B, Wibowo J, Sture S et al (1998) Applicability of existing models to predict the behavior of replicas of natural fractures of welded tuff under different boundary conditions. Geotech Geol Eng 16:79–128

    Article  Google Scholar 

  • Asadollahi P, Tonon F (2010) Constitutive model for rock fractures: revisiting Barton’s empirical model. Eng Geol 113:11–32

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bandis SC, Lumsden AC, Barton N (1981) Experimental studies of scale effects on the shear behaviour of rock joints. Int J Rock Mech Sci Geomech Abstr 18:1–21

    Article  Google Scholar 

  • Bandis SC, Lumsden AC, Barton NR (1983) Fundamentals of rock joint deformation. Int J Rock Mech Sci Geomech Abstr 20:249–268

    Article  Google Scholar 

  • Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7:287–332

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Barton N (1982) Modelling rock joint behavior from in situ block tests: implications for nuclear waste repository design. Office of Nuclear Waste Isolation, Columbus, OH, 96 pp, ONWI-308, September 1982

  • Barton N, Bandis SC, Bakhtar K (1985) Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Sci Geomech Abstr 22:121–140

    Article  Google Scholar 

  • Beer AJ, Stead D, Coggan JS (2002) Estimation of the joint roughness coefficient (JRC) by visual comparison. Rock Mech Rock Eng 35:65–74

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Brown SR, Scholz CH (1985) Broad bandwidth study of the topography of natural rock surfaces. J Geophys Res 90:12575–12582

    Article  Google Scholar 

  • Fardin N, Stephansson O, Jing L (2001) The scale dependence of rock joint surface roughness. Int J Rock Mech Min Sci 38:659–669

    Article  Google Scholar 

  • Fardin N (2008) Influence of structural non-stationarity of surface roughness on morphological characterization and mechanical deformation of rock joints. Rock Mech Rock Eng 41:267–297

    Article  Google Scholar 

  • Ghazvinian AH, Taghichian A, Hashemi M et al (2010) The shear behavior of bedding planes of weakness between two different rock types with high strength difference. Rock Mech Rock Eng 43:69–87

    Article  Google Scholar 

  • Ghazvinian AH, Azinfar MJ, Geranmayeh Vaneghi R (2012) Importance of tensile strength on the shear behavior of discontinuities. Rock Mech Rock Eng 45:349–359

    Article  Google Scholar 

  • Grasselli G (2001) Shear strength of rock joints based on quantified surface description. Ph.D. dissertation, Swiss Federal Institute of Technology, Lausanne, Switzerland

  • Grasselli G, Wirth J, Egger P (2002) Quantitative three-dimensional description of a rough surface and parameter evolution with shearing. Int J Rock Mech Min Sci 39:789–800

    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 40:25–40

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Homand F, Belem T, Souley M (2001) Friction and degradation of rock joint surfaces under shear loads. Int J Num Analy Meth Geomech 25:973–999

    Article  Google Scholar 

  • Hong ES, Lee IM, Lee JS (2006) Measurement of rock joint roughness by 3D scanner. Geotech Testing J 29:482–489

    Google Scholar 

  • Hong ES, Lee JS, Lee IM (2008) Underestimation of roughness in rough rock joints. Int J Num Analy Meth Geomech 32:1385–1403

    Article  Google Scholar 

  • Hsiung SM, Ghosh A, Ahola MP et al (1993) Assessment of conventional methodologies for joint roughness coefficient determination. Int J Rock Mech Min Sci Geomech Abstr 30:825–829

    Article  Google Scholar 

  • Huang SL, Oelfke SM, Speck RC (1992) Applicability of fractal characterization and modeling to rock joint profiles. Int J Rock Mech Min Sci Geomech Abstr 29:89–98

    Article  Google Scholar 

  • International Society for Rock Mechanics (ISRM) (1978) Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci Geomech Abstr 15:319–368

    Article  Google Scholar 

  • Jing L (1990) Numerical modelling of jointed rock masses by distinct element method for two- and three-dimensional problems. Ph.D. dissertation, Luleå University of Technology, Luleå, Sweden

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

    Article  Google Scholar 

  • Kulatilake PHSW, Shou G, Huang TH (1995b) Spectral-based peak-shear-strength criterion for rock joints. J Geotech Eng 121:789–796

    Article  Google Scholar 

  • Kulatilake PHSW, Um J, Panda BB et al (1999) Development of new peak shear-strength criterion for anisotropic rock joints. J Eng Mech 125:1010–1017

    Article  Google Scholar 

  • Ladanyi B, Archambault G (1969) Simulation of the shear behavior of a jointed rock mass. In: Proceedings of the 11th US symposium on rock mechanics (USRMS), Berkeley, California, June 1969, pp 105–125

  • Lanaro F (2000) A random field model for surface roughness and aperture of rock fractures. Int J Rock Mech Min Sci 37:1195–1210

    Article  Google Scholar 

  • Lanaro F (2001) Geometry, mechanics and transmissivity of rock fractures. Ph.D. dissertation, Royal Institute of Technology, Stockholm, Sweden

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

    Article  Google Scholar 

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

    Google Scholar 

  • Maksimović M (1992) New description of the shear strength for rock joints. Rock Mech Rock Eng 25:275–284

    Article  Google Scholar 

  • Nasseri MHB, Grasselli G, Mohanty B (2010) Fracture toughness and fracture roughness in anisotropic granitic rocks. Rock Mech Rock Eng 43:403–415

    Article  Google Scholar 

  • Odling NE (1994) Natural fracture profiles, fractal dimension and joint roughness coefficients. Rock Mech Rock Eng 27:135–153

    Article  Google Scholar 

  • Patton FD (1966) Multiple modes of shear failure in rock. In: Proceedings of the 1st congress of the international society of rock mechanics, Lisbon, Portugal, September/October 1966, vol 1, pp 509–513

  • Plesha ME (1987) Constitutive models for rock discontinuities with dilatancy and surface degradation. Int J Numer Anal Methods Geomech 11:345–362

    Article  Google Scholar 

  • Poon CY, Sayles RS, Jones TA (1992) Surface measurement and fractal characterization of naturally fractured rocks. J Phys D Appl Phys 25:1269–1275

    Article  Google Scholar 

  • Power WL, Tullis TE (1991) Euclidean and fractal models for the description of rock surface roughness. J Geophys Res 96:415–424

    Article  Google Scholar 

  • Reeves MJ (1985) Rock surface roughness and frictional strength. Int J Rock Mech Min Sci Geomech Abstr 22:429–442

    Article  Google Scholar 

  • Schneider HJ (1976) The friction and deformation behaviour of rock joints. Rock Mech 8:169–185

    Article  Google Scholar 

  • Son BK, Lee YK, Lee CI (2004) Elasto-plastic simulation of a direct shear test on rough rock joints. Int J Rock Mech Min Sci 41:2A 07

    Google Scholar 

  • Tang ZC, Xia CC, Song YL et al (2012) Discussion about Grasselli’s peak shear strength criterion for rock joints. Chin J Rock Mech Eng 31:356–364 (in Chinese with English abstract)

    Google Scholar 

  • Tatone BSA (2009) Quantitative characterization of natural rock discontinuity roughness in-suit and in the laboratory. Ph.D. dissertation, University of Toronto, Toronto, Canada

  • Tatone BSA, Grasselli G (2009) A method to evaluate the three-dimensional roughness of fracture surfaces in brittle geomaterials. Rev Sci Instrum 80:125110

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tatone BSA, Grasselli G (2012) An investigation of discontinuity roughness scale dependency using high-resolution surface measurements. Rock Mech Rock Eng (in Press)

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

    Article  Google Scholar 

  • Xia CC, Wang W, Ding ZZ (2008) Development of three-dimensional TJXW-3D-typed portable rock surface topography. Chin J Rock Mech Eng 27:1502–1512 (in Chinese with English abstract)

    Google Scholar 

  • Xie HP, Wang JA, Kwaśniewski MA (1999) Multifractal characterization of rock fracture surfaces. Int J Rock Mech Min Sci 36:19–27

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang ZY, Lo SC, Di CC (2001) Reassessing the joint roughness coefficient (JRC) estimation using Z2. Rock Mech Rock Eng 34:243–251

    Article  Google Scholar 

  • Yang ZY, Taghichian A, Huang GD (2011) On the applicability of self-affinity concept in scale of three-dimensional rock joints. Int J Rock Mech Min Sci 48:1173–1187

    Article  Google Scholar 

  • Yu X, Vayssade B (1991) Joint profiles and their roughness parameters. Int J Rock Mech Min Sci Geomech Abstr 28:333–336

    Article  Google Scholar 

  • Zhao J (1997) Joint surface matching and shear strength part B: JRC–JMC shear strength criterion. Int J Rock Mech Min Sci 34:179–185

    Article  Google Scholar 

Download references

Acknowledgments

The work described herein was performed at the Rock Mechanics and Engineering Centre of Tongji University, with financial support from the National Natural Science Foundation of China via grant nos. 51278378 and 40972178. The authors acknowledge the financial support from the Major State Basic Research Development Program of China (973 Program, no. 2011CB013800). The work was also supported by the Program for Changjiang Scholars and Innovative Research Team in University via grant no. IRT1029. The first author thanks Dr. Jie Zhang of Tongji University for the helpful discussions on the work presented and Yan Ping for the language assistance. We appreciate the anonymous reviewers for their valuable comments and suggestions to improving this manuscript.

Author information

Authors and Affiliations

  1. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, People’s Republic of China

    Cai-Chu Xia, Zhi-Cheng Tang & Ying-Long Song

  2. Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, People’s Republic of China

    Cai-Chu Xia, Zhi-Cheng Tang, Wei-Min Xiao & Ying-Long Song

  3. Department of Geotechnical Engineering, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Wei-Min Xiao

Authors
  1. Cai-Chu Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Cheng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei-Min Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ying-Long Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Cheng Tang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, CC., Tang, ZC., Xiao, WM. et al. New Peak Shear Strength Criterion of Rock Joints Based on Quantified Surface Description. Rock Mech Rock Eng 47, 387–400 (2014). https://doi.org/10.1007/s00603-013-0395-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-013-0395-6

Keywords

Search

Navigation