Skip to main content
SpringerLink
Log in

Directional rock mass rating (DRMR) for anisotropic rock mass characterization

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

Rock mass classification systems are used to categorize and estimate the role of the most significant parameters influencing rock mass behavior to represent an equivalent continuum. Generally, in these methods, the impact of the related parameters is considered uniform in all directions. Hence, these systems describe the rock mass as an isotropic medium. In some cases, in particular, for layered strata and systematically fractured rocks, the assumption of isotropic behavior may not provide realistic results. Hence, in this paper, to characterize the rock mass anisotropy, a directional rock mass rating (DRMR) has been proposed based on the well-known rock mass rating (RMR). So, DRMR provides a three-dimensional rock mass rating, quantitatively. By means of statistical distribution of DRMR, a classification for the degree of anisotropy of rock mass has been proposed. Furthermore, a criterion to identify the prominent rock mass, isotropic/transversely isotropic/anisotropic situation, is presented. Then the stereonet has been used to demonstrate an all-round graphical representation of DRMR. This with DRMR provides an illustrative insight into the actual rock mass condition and can assist to select the appropriate method for further analysis. Also, the method can be used as a basis to develop practical solutions for many rock engineering issues, such as characterizing the mechanical parameters of rock mass as an anisotropic equivalent continuum, selective directional rock mass improvement, and proper selection of rock tunnel and rock cavern alignments. Finally, the results of some practical applications of the method, based on field data, are presented.

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

Similar content being viewed by others

Abbreviations

A:

Constant (Donath, 1961 equation)

AI :

Anisotropy index based on DRMR

AI m :

Anisotropy index of average DRMR

B:

Constant (Tziallas et al. 2013 equation)

CR k :

Condition Rating of kth discontinuity

CR k i :

Condition Rating of kth discontinuity along i-direction

D:

Constant (Donath, 1961 equation)

Dip :

Dip angle of discontinuity set

Dip ip :

Dip angle of isotropic plane of intact rock

DipDir :

Dip direction of discontinuity set

DipDir ip :

Dip direction of isotropic plane of intact rock

DR1:

Directional Rating of uniaxial compressive strength

DR2:

Directional Rating of fracture frequency

DR3:

Directional Rating of discontinuities conditions

DR4:

Directional Rating of groundwater conditions

DRMR:

Directional Rock Mass Rating

DRMR ave :

Average value of DRMR

DRMR max :

Maximum value of DRMR

DRMR min :

Minimum value of DRMR

GSI:

Geological Strength Index

P wl :

Percentage of soft layers thickness in heterogeneous rock strata

R c :

Anisotropy index of intact rock

R cm :

Anisotropy index of rock mass

RMR:

Rock Mass Rating

RQD:

Rock Quality Designation

RQD i :

Rock Quality Designation along i-direction

\( {\overline{S}}_i \) :

Average spacing of discontinuities along i-direction

UCS i :

UCS of anisotropic intact rock along i-direction

X, Y, Z :

Global Cartesian axes

a :

Constant (Hoek-Brown failure criterion)

c i :

Cohesion of intact rock

c j :

Cohesion of discontinuities

i :

Arbitrary direction to calculate DRMR

k :

Discontinuity number (k = 1 to n)

n :

Number of discontinuity sets

s :

Constant (Hoek-Brown failure criterion)

\( {\overline{s}}^k \) :

Average spacing of kth discontinuity set

u ip :

Unit normal vector of isotropic plane of intact rock

\( {u}_X^{ip} \), \( {u}_Y^{ip} \), \( {u}_Z^{ip} \) :

Components of uip in global Cartesian coordinates

u k :

Unit normal vector of kth discontinuity

\( {u}_X^k \), \( {u}_Y^k \), \( {u}_Z^k \) :

Components of uk in global Cartesian coordinates

v :

Unit vector of arbitrary direction i

v X ,, v Y, v Z :

Components of v in global Cartesian coordinates

v x , v y , v z :

Components of v in local Cartesian coordinates

x, y, z :

Local Cartesian axes

β :

Angle between loading direction and isotropic plane/discontinuity

β m :

Angle β at which the UCS of anisotropic rock is minimum

\( {\theta}_i^k \) :

Angle between normal vector of kth discontinuity and i-direction

\( {\theta}_i^{IP} \) :

Angle between normal vector of isotropic plane and i-direction

λ i :

Cumulative linear frequency of discontinuities along i-direction

λk :

linear frequency of kth discontinuity set

\( {\lambda}_i^k \) :

Linear frequency of kthdiscontinuity set along i-direction

ρ :

Trend of arbitrary direction

ρ d :

Trend of pole of discontinuity

ρ ip :

Trend of pole of isotropic plane of intact rock

σ 1f :

Major principal stress at failure

σ 3 :

Confining minor principal stress

σ ci :

Uniaxial compressive strength of intact rock

\( {\sigma}_{ci}^{max} \) :

Maximum uniaxial compressive strength of intact rock

\( {\sigma}_{ci}^{min} \) :

Minimum uniaxial compressive strength of intact rock

σ cm :

Equivalent uniaxial compressive strength of jointed rock mass

\( {\sigma}_{cm}^{max} \) :

Maximum uniaxial compressive strength of rock mass

\( {\sigma}_{cm}^{min} \) :

Minimum uniaxial compressive strength of rock mass

\( {\sigma}_{ci}^h \) :

Equivalent strength of intact rock in heterogeneous medium

\( {\sigma}_{ci}^S \) :

Uniaxial compressive strength of stronger rock layers in heterogeneous medium

σ cβ :

UCS of anisotropic rock at orientation angle β

φ i :

Internal friction angle of intact rock

φ j :

Internal friction angle of discontinuities

ψ :

Plunge of arbitrary direction

ψ d :

Plunge of the pole of discontinuity

ψ ip :

Plunge of pole of isotropic plane of intact rock

ω :

Rotation angle of the local coordinates

References

  • Agricola G (1556) De re metallica. Translated from the first Latin edition of 1556 by H.C. Hoover and L.H. Hoover, 1950. Dover Publications, Inc., New York

    Google Scholar 

  • Ajalloeian R, Lashkaripour GR (2000) Strength anisotropies in mudrocks. Bull Eng Geol Environ 59:195–199. https://doi.org/10.1007/s100640000055

    Article  Google Scholar 

  • Aksoy CO (2008) Review of rock mass rating classification: historical developments, applications, and restrictions. J Min Sci 44:51–63. https://doi.org/10.1007/s10913-008-0005-2

    Article  Google Scholar 

  • Aydan Ö, Ulusay R, Tokashiki N (2014) A new rock mass quality rating system: rock mass quality rating (RMQR) system and its application to the estimation of geomechanical characteristics of rock masses. Rock Mech Rock Eng 47:1255–1276. https://doi.org/10.1007/978-3-319-09060-3_137

    Article  Google Scholar 

  • Barton N, Quadros E (2014) Most rock masses are likely to be anisotropic. In: In: Rock Mechanics for Natural Resources and Infrastructure SBMR 2014 – ISRM Specialized Conference. CBMR/ABMS and ISRM, Goiania

    Google Scholar 

  • Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6:189–236

    Article  Google Scholar 

  • Bieniawski ZT (1973) Engineering classification of jointed rock masses. Civ Eng South Afr 15:343–353. https://doi.org/10.1016/0148-9062(74)92075-0

    Article  Google Scholar 

  • Bieniawski ZT (1976) Rock mass classification in rock engineering. In: Bieniawski ZT (ed) A Symposium on Exploration for Rock Engineering. Cape Town, pp 97–196

  • Bieniawski ZT (1979) The geomechanics classification in rock engineering applications. Proc 4th Int Congr rock Mech 41–48

  • Bieniawski ZT (1989) Engineering rock mass classification: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons, Inc., New York

    Google Scholar 

  • Chen Z (1995) Recent developments in slope stability analysis. In: 8th International Congress of Rock Mechanic. International Society for Rock Mechanics, pp 1041–1048

  • Chen C, Pan E, Amadei B (1998) Determination of deformability and tensile strength of anisotropic rock using Brazilian tests. Int J Rock Mech Min Sci 35:43–61

    Article  Google Scholar 

  • CMRI (1987) Geomechanical classification of roof rocks vis-à-vis roof supports- S&T project report. Dhanbad,

  • Deere DU, Hendron AJ, Patton FD, Cording EJ (1967) Design of surface and near-surface construction in rock. 8th US Symp. Rock Mech. (USRMS)-Failure Break. Rock 237–302

  • Donath FA (1961) Experimental study of shear failure in anisotropic rocks. Geol Soc Am Bull 72:985–990. https://doi.org/10.1130/0016-7606(1961)72[985:ESOSFI]2.0.CO;2

    Article  Google Scholar 

  • Donath FA (1964) Strength variation and deformational behavior in anisotropic rock. In: Judd W (ed) State of Stress in the Earth’s Crust. New York, pp 281–298

  • Garagon M, Çan T (2010) Predicting the strength anisotropy in uniaxial compression of some laminated sandstones using multivariate regression analysis. Mater Struct 43(4):509-517

  • Gonzalez de Vallejo LI (1983) A new rock classification system for underground assessment using surface data. In: International Symposium on Engineering Geology and Underground Construction. Lisbon, pp 85–94

  • Gonzalez de Vallejo LI (1985) Tunnelling evaluation using the surface rock mass classification system SRC. In: ISMR Symposyum on the Role of Rock Mechanics in Excavations for Mining and Civil Works. Zacatecas, Mexico, pp 458–466

    Google Scholar 

  • Gonzalez de Vallejo LI (2003) SRC rock mass classification of tunnels under high tectonic stress excavated in weak rocks. Eng Geol 69:273–285. https://doi.org/10.1016/S0013-7952(02)00286-7

    Article  Google Scholar 

  • González NA, Vargas PE, Carol I et al (2016) Comparison of discrete and equivalent continuum approaches to simulate the mechanical behavior of jointed rock masses. In: Wuttke, Bauer, Sánchez (eds) 1st International Conference on Energy Geotechnics. Taylor & Francis Group, London, pp 255–262

    Google Scholar 

  • Heng S, Guo Y, Yang C et al (2015) Experimental and theoretical study of the anisotropic properties of shale. Int J Rock Mech Min Sci 74:58–68. https://doi.org/10.1016/j.ijrmms.2015.01.003

    Article  Google Scholar 

  • Hoek E (1994) Strength of rock and rock masses. ISRM News J 2:4–16

    Google Scholar 

  • Hoek E, Brown ET (1988) The Hoek-Brown failure criterion - a 1988 update. In: 15th Canadian Rock Mechanics Symposium. pp 31–38

  • Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. Balkema, Rotterdam

    Google Scholar 

  • Hoek E, Carranza-torres C, Corkum B (2002) Hoek-brown failure criterion – 2002 edition. In: Proceedings of NARMS-Tac. pp 267–273

  • Hoek E, Marinos PG, Marinos VP (2005) Characterisation and engineering properties of tectonically undisturbed but lithologically varied sedimentary rock masses. Int J Rock Mech Min Sci 42(2):277-285

  • Huan J, He M, Zhang Z, Li N (2019) Parametric study of integrity on the mechanical properties of transversely isotropic rock mass using DEM. Bull Eng Geol Environ 79:2005–2020

    Article  Google Scholar 

  • Hudson J, Harrison J (2000) Engineering rock mechanics: an introduction to the principles, 2nd edn. Elsevier Science Ltd, Oxford

    Google Scholar 

  • IWPCO (2004) Karun IV dam and hydropower plant- report on increasing the length of grouting galleries of left abutment. Tehran

  • IWPCO (2007) Engineering geology report of Rudbar-e-Lorestan dam and hydropower plant. Tehran

  • IWPCO (2010) Khersan III dam and hydropower plant- final report of diversion tunnel. Tehran

  • Jaeger JC (1960) Shear failure of anisotropic rocks. Geol Mag 97:65–72

    Article  Google Scholar 

  • Jaeger JC, Cook NG (1979) Fundamentals of rock mechanics. Methuen, London

    Google Scholar 

  • Jakubec J, Laubscher DH (2000) The MRMR rock mass rating classification system in mining practice. In: MassMin 2000. Brisbane, pp 413–421

  • Javadi M, Sharifzadeh M, Shahriar K (2010) A new geometrical model for non-linear fluid flow through rough fractures. J Hydrol 389:18–30. https://doi.org/10.1016/j.jhydrol.2010.05.010

    Article  Google Scholar 

  • Khatik VM, Nandi AK (2018) A generic method for rock mass classification. J Rock Mech Geotech Eng 10:102–116. https://doi.org/10.1016/j.jrmge.2017.09.007

    Article  Google Scholar 

  • KRWA (2016) Kerman water conveyance tunnel- final report of engineering geology. Kerman

  • Laubscher DH (1990) A geomechanics classification system for the rating of rock mass in mine design. J South Afr Inst Min Metall 90:257–273. https://doi.org/10.1016/0148-9062(91)90830-F

    Article  Google Scholar 

  • Lauffer H (1958) Gebirgsklassifizierung für den stollenbau. Geol und Bauwes 24:46–51

    Google Scholar 

  • Lin H, Cao P, Wang Y (2013) Numerical simulation of a layered rock under triaxial compression. Int J Rock Mech Min Sci 60:12–18. https://doi.org/10.1016/j.ijrmms.2012.12.027

    Article  Google Scholar 

  • Lowson AR, Bieniawski ZT (2013) Critical assessment of RMR based tunnel design practices: a practical engineer’s approach. In: Proceedings of the SME: Rapid Excavation & Tunneling Conference. Washington, pp 23–26

  • Maazallahi V, Majdi A (2020) 3D Characterization of uniaxial compressive strength of transversely-isotropic intact rocks. J Min Environ 11:629–641. https://doi.org/10.22044/jme.2020.9039.1791

    Article  Google Scholar 

  • Majdi A, Hassani F (1989) Access tunnel convergence prediction in longwall coal mining. Int J Min Geol Eng 7:283–300. https://doi.org/10.1007/BF00896593

    Article  Google Scholar 

  • Marinos P, Hoek E (2001) Estimating the geotechnical properties of heterogeneous rock masses such as Flysch. Bull Eng Geol Environ 60:85–92

    Article  Google Scholar 

  • Marinos PV (2010) New proposed GSI classification charts for weak and complex rock masses. In: 12th Bulletin of the Geological Society of Greece International Congress. Patras, pp 1248–1258

  • Öge IF (2017) Assessing rock mass permeability using discontinuity properties. Procedia Eng 191:638–645. https://doi.org/10.1016/j.proeng.2017.05.373

    Article  Google Scholar 

  • Pacher F, Rabcewicz L, Golser J (1974) Zum derzeitigen stand der gebirgsklassifizierung im stollen- und tunnelbau. In: 22. Geomechanik-Kolloquium. Salzburg

  • Palmström A (1995) RMi- a rock mass characterization system for rock engineering purposes, PhD Thesis, University of Oslo. University of Oslo

  • Pells PJ, Bieniawski ZT, Hencher SR, Pells SE (2017) Rock quality designation (RQD): time to rest in peace. Can Geotech J 54:825–834. https://doi.org/10.1139/cgj-2016-0012

    Article  Google Scholar 

  • Ramamurthy T (1993) Strength and modulus responses of anisotropic rocks. In: Brown ET (ed) Comprehensive rock engineering. Pergamon press, pp 313–329

  • Ramamurthy T (1996) Stability of rock mass. Indian Geotech J 16:1–73

    Google Scholar 

  • Ritter W (1879) Die statik der tunnelgewölbe. Springer, Berlin

    Google Scholar 

  • Romana M (1985) New adjustment ratings for application of Bieniawski classification to slopes. In: International symposium on the role of rock mechanics. Zacatecas, Mexico, pp 49–53

    Google Scholar 

  • Saeidi O, Rasouli V, Geranmayeh Vaneghi R, Gholami R (2014) A modified failure criterion for transversely isotropic rocks. Geosci Front 5:215–225. https://doi.org/10.1016/j.gsf.2013.05.005

    Article  Google Scholar 

  • Saroglou H, Tsiambaos G (2008) A modified Hoek-Brown failure criterion for anisotropic intact rock. Int J Rock Mech Min Sci 45:223–234. https://doi.org/10.1016/j.ijrmms.2007.05.004

    Article  Google Scholar 

  • Saroglou C, Qi S, Guo S, Wu F (2018) ARMR, a new classification system for the rating of anisotropic rock masses. Bull Eng Geol Environ, vol 78, pp 3611–3626

    Google Scholar 

  • Sen Z, Sadagah BH (2003) Modified rock mass classification system by continuous rating. Eng Geol 67:269–280

    Article  Google Scholar 

  • Senior LA, Goode DJ (1999) Ground-water system, estimation of aquifer hydraulic properties, and effects of pumping on ground-water flow in Triassic sedimentary rocks in and near Lansdale, Pennsylvania, No. 99-422. US Dept. of the Interior, US Geological Survey

  • Sheorey PR (1997) Empirical rock failure criteria. Balkema, Rotterdam

    Google Scholar 

  • Singh B, Goel RK (1999) Rock mass classification: a practical approach in civil engineering. Elsevier, Amsterdam

    Google Scholar 

  • Singh VK, Singh D, Singh TN (2001) Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. International J Rock Mech Min Sci 38(2):269-284

  • STP Consulting Engineers (2018) Report on geology and engineering geology of Kaniguizhan dam site. Tehran,

  • Terzaghi K (1946) Rock defects and loads on tunnel supports. Rock Tunn with steel Support 17–99

  • Tomas R, Delgado J, Seron JB (2007) Modification of slope mass rating (SMR) by continuous functions. Int J Rock Mech Min Sci 44:1062–1069. https://doi.org/10.1016/j.ijrmms.2007.02.004

    Article  Google Scholar 

  • Tziallas GP, Saroglou H, Tsiambaos G (2013) Determination of mechanical properties of flysch using laboratory methods. Eng Geol 166:81–89

  • Venkateswarlu V, Ghose AK, Raju NM (1989) Rock-mass classification for design of roof supports - a statistical evaluation of parameters. Min Sci Technol 8:97–107. https://doi.org/10.1016/S0167-9031(89)90507-0

    Article  Google Scholar 

  • Wickham GE, Tiedemann HR, Skinner EH (1972) Support determinations based on geologic predictions. In: Proc. 1st North American Rapid Excavation & Tunnelling Conference (RETC). pp 43–64

  • Wittke W (2014) Rock mechanics based on an anisotropic jointed rock model (AJRM). Wiley Blackwell, Berlin

    Book  Google Scholar 

  • Wu Q, Kulatilake PHSW (2012) REV and its properties on fracture system and mechanical properties , and an orthotropic constitutive model for a jointed rock mass in a dam site in China. Comput Geotech 43:124–142. https://doi.org/10.1016/j.compgeo.2012.02.010

    Article  Google Scholar 

  • Zhang L (2016) Determination and applications of rock quality designation (RQD). J Rock Mech Geotech Eng 8:389–397. https://doi.org/10.1016/j.jrmge.2015.11.008

    Article  Google Scholar 

  • Zhang L (2017) Engineering properties of rocks, 2nd edn. Elsevier Ltd.

Download references

Author information

Authors and Affiliations

  1. School of Mining Engineering, College of Engineering, University of Tehran, Tehran, 1439957131, Iran

    Vahid Maazallahi & Abbas Majdi

Authors
  1. Vahid Maazallahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abbas Majdi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abbas Majdi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maazallahi, V., Majdi, A. Directional rock mass rating (DRMR) for anisotropic rock mass characterization. Bull Eng Geol Environ 80, 4471–4499 (2021). https://doi.org/10.1007/s10064-021-02143-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-021-02143-3

Keywords

Search

Navigation