a geo-engineering classification for rocks and rock masses

International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–101

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doi:10.1016/S136

A geo-engineering classification for rocks and rock masses

T. Ramamurthy*

AngRon Geotech Pvt. Ltd., A-13, Naraina Industrial Area Phase-II, New Delhi l10028, India

Accepted 19 May 2003

Abstract

In this article, an attempt is made to assess the reliability of predicting the uniaxial compressive strength and the corresponding

modulus of a rock mass by current approaches. These two basic engineering properties, when estimated from rock mass rating

(RMR), Q and geological strength index (GSI), indicate hardly any change in the modulus ratio with the change in the quality of the

rock mass from very good to very poor. However, the modulus ratio obtained from the relations involving the joint factor, Jf ;indicate a definite decrease in the modulus ratio with a decrease in the quality of the rock mass. The strength and modulus in the

unconfined and confined states, the modulus ratio and failure strain in the unconfined case were linked to Jf in earlier publications

based on a large experimental database. Some of these relations were adopted to verify the response of jointed test specimens, the

response of the rock mass during excavations for mining and civil underground chambers, in establishing ground reaction curves

including the extent of the broken zone, and the bearing capacity of shallow foundations.

The joint factor is now linked to RMR, Q and GSI. The prediction of compressive strength and modulus of the rock mass appears

to be more suitable. For classifying the rock, based on these properties, the Deere and Miller engineering classification, applicable to

intact rocks, has been suitably modified and adopted. The results of different modes of failure of jointed specimens establish

definite trends of changes in the modulus ratio originating from the intact rock value on the modified Deere and Miller plot.

A geo-engineering classification is evolved by considering strength, modulus, quantifiable weathering index and lithological

aspects of the rock.

r 2003 Elsevier Ltd. All rights reserved.

1. Introduction

Rocks have been classified on the basis of their origin,mineralogical composition, void index, fracture/jointintensity, joint inclination, flow rate of water, velocity ofpropagation of shock wave, weathering, colour or grainsize. When rocks and rock masses are classified forgeotechnical purposes, they need to be classified on thebasis of strength and/or modulus to give an indication oftheir stability and/or deformability. A rock classificationhas to provide a common basis to communicate, toidentify a rock mass within one of the groups havingwell-defined characteristics, and also to provide basicinput data for engineering design. For effective andsuccessful usage of a classification system, it has to besimple, easy to understand, remember and apply.

Only the significant and intrinsic parameters of therock should be considered which will influence the

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ss: [email protected] (T. Ramamurthy).

see front matter r 2003 Elsevier Ltd. All rights reserved.

5-1609(03)00078-9

engineering behaviour most, and each parameter mustrepresent itself exclusively. The parameters should beeasily measurable and be linked in such a way that thequality of the rock mass is reflected in terms of itsstrength and modulus. It is imperative, while classifyinga rock mass and to understand the mass response, toobtain an indication of the extent of reduction which hastaken place in the strength and modulus of intact rock.This is desirable because field tests are time consuming,costly and often adequate in terms of estimating realisticdesign parameters.

Presently, there are four approaches available toestimate the uniaxial compressive strength and corre-sponding modulus, namely: rock mass rating (RMR), Q;Jf and geological strength index (GSI). Each of theapproaches gives different values and each one can betested for its reliability by considering the modulus ratio.The approach of Jf is based on many experimental dataand suggests a continuous decrease of modulus ratiowith the decrease of rock quality—unlike otherapproaches. It also enables one to estimate the

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Nomenclature

cj cohesion intercept on sliding jointE deformation modulusEt tangent modulus at 50% of failure stressGSI geological strength indexJa rating for joint alterationJf joint factorJn joint frequency, i.e. number of joints/mJr rating for joint surface strengthJRC joint roughness coefficientJs rating for joint setsJw rating for water softening, inflow and pressureMr modulus ratiom material parameter as per Hoek and Brownn inclination factor to account for the joint

orientation

Q rock mass qualityQc rock mass quality normalized by sci=100RMR rock mass ratingRQD rock quality designationr strength factor on sliding jointSRF rating for faulting, strength/stress ratio,

squeezing and swellings material parameter as per Hoek and Brownef axial failure straing density of rock mass (g/cm3)fj friction angle on sliding jointtj shear strength on sliding jointsc unconfined compressive strengthsnj normal stress on sliding jointNote: Subscripts i and j added to E; Mr; m; s; ef and

sc refer to the intact rock and jointed rockmass, respectively.

T. Ramamurthy / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–10190

strength and modulus under any required confiningpressure.

A rock, either intact or jointed, should be classified inits simplest state of existence, i.e., in the unconfinedcondition. The influence of in situ stress (i.e. confiningstress) and other environmental factors (such as seepagepressure, etc.) should be considered appropriately in theanalysis for assessing the stability of the rock mass, e.g.in terms of effective stress, as is the practice in saturatedsoils.

2. Classification of intact rocks

For engineering usage, attempts were made to classifyintact rocks based on an individual property, such asuniaxial compressive strength, modulus and point loadstrength index, notably by Coates [1], Deere and Miller[2], Stapledon [3], Franklin et al. [4], Hansagi [5] and theISRM [6,7]. Such simplified classification systems haveserved to understand the upper bound response of therocks.

The classification proposed by Deere and Miller [2]for intact rocks is based on the combined influence ofthe uniaxial compressive strength (sci) and tangentmodulus (Et) at 50% of the failure stress (subscript irefers to the intact rock). This approach has been wellrecognized as a realistic and useful engineering classifi-cation which takes into account more than onemeasurable property at a time. Based on these proper-ties, they categorised rocks into a number of classes,assigning a two lettered combination: the first letterrefers to the compressive strength range; and the secondletter refers to the modulus ratio, i.e., the Et=sci range.Each intact rock type has its specific zone in the regionof sci and Et: The limits of the various classes of intact

rocks are well defined. When intact rocks are classified,the effect of seepage pressure or confining pressure is notconsidered.

3. Response of jointed rocks

It is well recognized that the engineering behaviour ofa rock mass is controlled by more than one factor, andthe influence of each of these factors differs greatly. Anyattempt to classify rock based on a single parameter, likejoint frequency, will not be satisfactory. A descriptiverock mass classification proposed by Terzaghi [8] hasbeen useful for tunnels and for a particular type ofconstruction technique, but it could not be extended forfoundations and slopes. However, Terzaghi’s classifica-tion paved the way for recognizing a number of factorssuch as joint spacing, joint orientation, the nature ofjoint surface and nature of joint filling influencing therock mass behaviour. Two of the most commonly usednumerically expressed rock mass classifications, theRMR system by Bieniawski [9] and the Q system byBarton et al. [10] consider some of these factors withvarying emphases, in addition to other parameters.These classification systems have been developed basi-cally for the stability of the tunnels and offer aprocedure for choosing tunnel supports depending uponthe quality of the rock mass. The modulus of the rockmass is not included in these classifications for the widerapplication to rock foundations and slopes.

Bieniawski’s RMR classification has six parameters tobe considered, namely: uniaxial compressive strength(sci) of the intact rock, joint spacing, rock qualitydesignation (RQD), condition of the joints, water flow/pressure and the inclination of the discontinuities. Inthese parameters, the combined effect of RQD and joint

ARTICLE IN PRESST. Ramamurthy / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–101 91

spacing is obviously reflected by considering the jointfrequency (Jn), the condition of the joints is reflected inthe sliding friction angle on the discontinuities and theinfluence of the orientation of joints is not consideredstrictly on the basis of the anisotropic response of therock mass.

Even in the case of the initial Q-system [10], sixparameters are considered, namely: RQD, joint set (Js;Barton uses Jn), joint roughness (Jr), seepage and itspressure (Jw), joint alteration (Ja) and stress reductionfactor (SRF). In this system, RQD and joint sets couldbe covered in the joint frequency, joint roughness andjoint alteration in the sliding friction angle along thesliding joint, with the joint water effect and the stressreduction factor forming part of the design considera-tion. The Q-system did not include the influence of theuniaxial compressive strength of the intact rock nor theorientation of the critical or any other joint in the mass,earlier to 2002. Recently, Barton [11] introduced theinfluence of compressive strength of the intact rock intothe earlier Q-system as indicated in the later part of thisarticle. The values of Ja and Jr are to be considered nowfor the least favourable joint set. The orientation of thejoint has significant influence on the strength andmodulus of the mass. Therefore, the consideration ofthe inclination of a sliding joint, joint frequency and thestrength along the sliding joint in terms of friction angleare the most important factors to be considered whichinfluence the strength and modulus of the rock mass.The weakness introduced into an intact rock is the resultof their combined influence.

Hypothetical stress–strain curves for three differentrocks are shown in Fig. 1. Curves OA, OB and OCrepresent three stress–strain curves with failure occur-ring at A, B and C, respectively. Curves OA and OBhave same modulus but different strengths and strains at

Fig. 1. Hypothetical stress–strain curves.

failure. Whereas the curves OA and OC have the samestrength but different moduli and failure strains. Soneither strength nor modulus alone could be chosen torepresent the overall quality of a rock. Therefore,strength and modulus in combination provide a betterunderstanding of the rock response.

3.1. Strength and modulus from RMR

Bieniawski [9,12,13] suggested shear strength para-meters, cj and fj; for a jointed rock mass (cj refers to thecohesion intercept and fj refers to the friction angle; thesubscript j refers to jointed rock/rock mass) for fivelevels of the overall rock mass ratings of RMR,reflecting the range of the quality of the rock. Thesevalues of shear strength parameters are used to calculatethe uniaxial compressive strength (scj) of the mass as perthe Mohr–Coulomb criterion, below equation and isreferred to as scjl in Table 1,

scj ¼ 2cj cos fj=ð1 � sin fjÞ: ð1Þ

Kalamaras and Bieniawski [14] suggested the follow-ing relation linking the compressive strength of a rockmass (referred as scj2) with that of the intact rockthrough RMR, based on the studies of Carter et al. [15],as

scj2=sci ¼ exp½ðRMR � 100Þ=24�; ð2Þ

where the subscript i refers to the intact rock.For values of sci ¼ 100 MPa and for various values of

RMR, the compressive strengths of the rock mass (scj2)are determined from Eq. (2). A considerable differencein the values of scj1 and scj2 is shown in Table 1.

Surprisingly the ratios of scj2=sci match well with thevalues calculated based on the joint factor, Jf [16–18].The values of Jf vary from zero for an intact rock toover 500 for a highly jointed rock. By considering Jf ¼500 as a limiting value for practical purposes, one maywrite,

Jf=5 ¼ 100 � RMR or RMR ¼ 100 � ðJf=5Þ; ð3Þ

since Jf ¼ 0; when the value of RMR=100 for an intactrock.

Inserting Eq. (3) in the following equation, as perRamamurthy [18],

scj=sci ¼ exp½�0:008Jf �; ð4Þ

one obtains

scj=sci ¼ exp½ðRMR � 100Þ=25�; ð5Þ

which is not very different from Eq. (2).Since scj is linked to sci through RMR from Eq. (2)

and verified with Eq. (4), it is now possible to link RMRand Q with Jf to obtain scj and modulus, Ej; for a rockmass.

ARTICLE IN PRESS

Table 1

Estimation and comparison of scj values as per Hoek and Brown [27], Bieniawski [13] and Kalamaras and Bieniawski [14] for sci ¼ l00MPa

RMR ðscjÞHB (MPa) scj1 (MPa) scj2 (MPa) ðscjÞHB=scj1 ðscjÞHB=scj2 Ej (GPa) Ej=scj2 Ej=ðscjÞHB

100 100.0 3.5a 100 29.0 1.0 177.80 1778 1778

80 33.0 1.97 43.5 16.8 0.76 56.20 1292 1703

60 10.8 1.18 18.9 9.2 0.57 17.80 942 1648

40 3.6 0.64 8.2 5.6 0.44 5.60 682 1556

20 1.18 0.26 3.56 4.5 0.33 1.78 500 1508

0 0.39 — 1.15 — 0.34 0.56 361 1436

aValues by extrapolation. ðscjÞHB as per Eq. (15) for undisturbed rock mass; scj1 as per cj and fj values from Bieniawski [13]; scj2 as per Kalamaras

and Bieniawski [14]; Ej from Serafim and Pereira [23].


Barton [19] recommends

RMR ¼ 15 log Q þ 50; ð6Þ

instead of the commonly adopted average relation,Bieniawski [20], namely

RMR ¼ 9 loge Q þ 44: ð7Þ

In fact Eq. (6) represents a flatter oblique line betweenthe limits, Bieniawski [21],

RMR ¼ 9 loge Q þ 62 ð8Þ

and

RMR ¼ 9 loge Q þ 26: ð9Þ

Replacing RMR by Jf , as per Eq. (3), Eq. (6) gives

Jf ¼ 250ð1 � 0:3 log QÞ: ð10Þ

Now Eq. (4) in terms of Q will be given by

scj=sci ¼ exp½0:6 log Q � 2�: ð11Þ

Similarly, the following relations are obtained for Ej/Ei by inserting the corresponding values of RMR and Q

in place of Jf as per Ramamurthy [18] as follows:

Ej=Ei ¼ exp½�0:0115Jf � ð12Þ

as

Ej=Ei ¼ exp½ðRMR � 100Þ=17:4� ð13Þ

and

Ej=Ei ¼ exp½0:8625 log Q � 2:875�: ð14Þ

It may be noted that the relations in Eqs. (12)–(14) arefor the tangent modulus at 50% of the failure stress. Formost practical purposes in the case of undisturbed rockmasses, the initial tangent modulus, the secant modulusup to 50% of the failure stress and the tangent modulusmay be taken as having similar values. The secantmodulus is to be treated as the deformation modulus.It is clear from the above relations that one couldaccept Jf ; RMR and Q to define the weakness in arock mass and establish definite linkages between scj andsci and also Ej and Ei: Referring to Table 1, inaddition to the uniaxial compressive strengths fromBieniawski [13] and from Kalamaras and Bieniawski[14], it also provides ðscjÞHB as per Hoek and Brown [22]

using the relation,

scj=sci ¼ Osj; sj ¼ exp½ðRMR � 100Þ=9�; ð15Þ

for an undisturbed rock mass. It is observed that the cj

and foj values recommended by Bieniawski from [9,13]

appear to be rather on the lower side, resulting in quitelow values of scj1: In fact, for RMR=80, scj1 is just1.97 MPa, placing the rock mass in a very weakcategory, and, for RMRo 60, the rock mass will havescj1 less than 1 MPa and is to be treated as a soil.

The ratios of ðscjÞHB=scj1 are quite high, i.e. forRMR=80, the ratio is about 17 and at RMR=20, it ismore than 5. On the contrary, the values of scj2 fromKalamaras and Bieniawski are higher than those givenby Hoek and Brown criterion [22]. For RMR=80, scj2 isabout 30% more and, at RMR=20, about 300%.Similar comparisons for disturbed rock masses willshow still larger differences. Table 1 also shows theestimated values of Ej Serafim and Pereira [23] asfollows:

Ej ¼ 10ðRMR�10Þ=40 ðGPaÞ: ð16Þ

From this table, the modulus ratio Ej=scj2 is 1778 forRMR=100 and continuously decreases with decrease ofRMR and achieves a value of 361 for RMR=0. If oneuses Ej=scjl; very high values of modulus ratio will result.When ðscjÞHB is adopted to see the variation in thevalues of modulus ratio, only a marginal decrease isnoticed, i.e. from 1703 to 1508 for RMR varying from80 to 20. From these approaches, the modulus ratiosappear to be high, not only at RMR=80, but also atRMR=20, particularly with ðscjÞHB and scj1:

3.2. Strength and modulus from GSI

Hoek [24], Hoek et al. [25] and Hoek and Brown [26]advocate the adoption of the GSI to estimate thematerial parameters, mj and sj; of the Hoek–Brownfailure criterion to predict strength under any desiredconfining pressure. GSI considers modifications to theRMR and Q systems mainly to estimate the compressivestrength of a rock mass. From the RMR ratings ofBieniawski [20], referred to as (RMR)76, GSI considers

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able 2

rediction of scj; Ej and Mrj for sci ¼ 100MPa; data from Hoek [24]

SI s Os scj (MPa) Ej (GPa) Mrj ¼ Ej=scj

5 0.190 0.436 43.6 75 1720

5 0.062 0.249 24.9 40 1606

5 0.021 0.145 14.5 24 1655

2 0.015 0.122 12.2 20 1639

0 0.012 0.110 11.0 18 1636

0 0.004 0.063 6.3 10 1587

8 0.003 0.055 5.5 9 1636

0 0.0013 0.036 3.6a 6 1875

8 0.001 0.032 3.2 5 1563

4 0.0004 0.020 2.0 3 1500

verage 1642

aEstimated from Eq. (21).

T. Ramamurthy / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–101 93

the first four terms of RMR: namely, the compressivestrength of intact rock (scj), RQD, spacing and alsoconditions of the discontinuities, assigning 10 points tothe ground water and zero to the joint orientation.Therefore, to obtain GSI values higher than 18, one hasto consider

GSI ¼ ðRMRÞ76: ð17Þ

For values of (RMR)76 o18, the use of Q0 values isrecommended. Alternatively, one could also adoptBieniawski [27], referred to as (RMR)89, by enhancingthe ground water rating to 15 instead of 10 in (RMR)76.Therefore, for (RMR)89>23,

GSI ¼ ðRMRÞ89 � 5: ð18Þ

For (RMR)89 o23, the Q0 value obtained is asfollows:

Q0 ¼ ðRQD=JsÞðJr=JaÞ ð19Þ

and used to arrive at GSI as

GSI ¼ 9 loge Q0 þ 44: ð20Þ

Here, Js; Jr and Ja refer to ratings of the joint setnumber, joint roughness and joint alteration, respec-tively; Barton [10,11] uses Jn and not Js:

On the basis of the GSI, the following equation is tobe adopted to estimate the uniaxial compressive strengthof rock mass for GSI>25 in the case of an undisturbedrock mass,

scj=sci ¼ Osj; sj ¼ exp½ðGSI � 100Þ=9�: ð21Þ

It is clear from the above expressions that, inestimating the compressive strength of a rock mass,the compressive strength of the intact rock has beenconsidered twice for GSI>25: the first time in estimat-ing the value of GSI; and the second time in estimatingthe compressive strength of the rock mass. Forestimating the deformation modulus, Hoek [24] recom-mends the use of Eq. (16) as per Serafim and Pereirausing RMR as per Bieniawski [9,13] and not the GSIsystem.

The values of GSI, sj and Ej are shown in Table 5 byHoek [24] have been adopted in calculating the values ofmodulus ratio, Mrj; in Table 2. The values of Mrj aresurprisingly high, ranging from 1500 to 1875, with anaverage value of 1642. These values of Mrj do notdecrease, continuously with the decrease of GSI values.An important aspect of suggesting the use of GSI is toestimate the strength without water pressure, so thatseepage pressure and confining pressure can be con-sidered in the analysis in terms of effective stress. It isrecognized that the strength, volume change andmodulus are controlled by the effective stress. Therefore,the modulus value may also have to be obtained in thedry state and linked to that of the intact rock.Depending upon the seepage and confining pressures,

T

P

G

8

7

6

6

6

5

4

4

3

3

A

the modulus could be enhanced to account for theeffective stress influence.

3.3. Strength and modulus from Q

Barton [11] suggests modification to Q values byconsidering the influence of uniaxial compressivestrength of the intact rock (sci) in the following form:

Qc ¼ Qsci=100 ð22Þ

and recommends Qc values for estimating the compres-sive strength and modulus of rock mass as

scj ¼ 5gQl=3c ðMPaÞ ð23Þ

and

Ej ¼ 10Ql=3c ðGPaÞ; ð24Þ

where, g is the density of the rock mass in g/cm3 or t/m3.Eq. (23) may be written, say for g ¼ 2:5 g/cm3, as

scj ¼ 2:7ðQsciÞ1=3 ðMPaÞ ð25Þ

suggesting that Q is linked to the compressive strengthof a rock mass through the intact rock strength.However, the modulus of a rock mass is not linked tothe modulus of the intact rock through Q: The range ofvalues of Q or Qc is very wide. Even if the Qc valuesvaried from 0.001 to 1000, the values of ðQcÞ

1=3

considered in the estimation of the compressive strengthand the modulus of rock mass, effectively vary from 0.1to 10 representing a scale of 1–100.

Another important recommendation of Barton [11] isto assess the cohesion intercept and friction angle ofrock mass using the following expressions:

cj ¼ ðRQD=JsÞ ð1=SRFÞ ðsci=100Þ ðMPaÞ ð26Þ

foj ¼ tan�1ðJrJw=JaÞ; ð27Þ

where, Js is joint set number (Barton uses Jn instead),SRF the stress reduction number, Jr the joint roughnessnumber, Jw the for seepage and its pressure and Ja thejoint alteration number.

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Table 5

Proposed joint strength parameter, r; for filled-up joints at residual

stage [17]

Gouge material Friction angle, foj Joint strength, r=tanfo

j

Gravelly sand 45 1.00

Coarse sand 40 0.84

Fine sand 35 0.70

Silty sand 32 0.62

Clayey sand 30 0.58

Clayey silt

Clay—25% 25 0.47

Clay—50% 15 0.27

Clay—75% 10 0.18

Table 3

Values of scj;cj; fj and Ej as per Barton [11] for sci ¼ 100MPa, g ¼ 2:5 g/cm3

Qc scj1 (MPa) cj (MPa) foj (MPa) scj2 (MPa) scj1=scj2 Ej (GPa) Mrj

100 58.0 50 63 412.7 1/7 40 690

10 26.9 10 45 48.3 1/1.8 22 818

1.2 13.3 2.5 26 8.0 1.7 10.7 805

0.04 4.3 0.26 9 0.61 7.0 3.5 814

0.008 1.2 0.01 5 0.022 54 0.9 750

Before grouting

0.45 9.0 1.7 14 4.4 2.05 7.0 778

After grouting

8.3 25 8.3 63 69 1/2.76 20.0 800

scj1 from Barton, Eq. (23).

scj2 from cj and fj values suggested by Barton [11].

Table 4

Values of n for different orientation angles, b; for U-shaped anisotropy [17,18]

Joint orientation angle, bo 0 10 20 30 40 50 60 70 80 90

Joint inclination parameter, n 0.82 0.46 0.11 0.05 0.09 0.3 0.46 0.64 0.82 0.95


Using the data provided in Tables 6 and 7 of Barton[11], the values of compressive strength of a rock massare calculated from cj and fj as per the Mohr–Coulombcriterion, Eq. (1), and are referred to as scj2 in Table 3 ofthis article. The data in this table suggests that scj2

values differ significantly from the suggested values, scj1

by Eq. (23). The ratio of scj1=scj2 varies from 1:7 to 54:1, depending upon the values of Qc: This table also givesthe values of Ej as given by Barton [11]. The values ofmodulus ratio, Mrj; are more or less constant and arearound 800; in fact, Eqs. (23) and (24) give this ratio as800 for a value of g ¼ 2:5 g/cm3, irrespective of Qc

varying from 0.001 to 1000, i.e. whether the rock isintact, jointed, isotropic or anisotropic. This is contraryto the experimental results which suggest a definitedecrease in Mrj with the decrease in the quality of a rockmass.

3.4. Strength and modulus from Jf

Based on the extensive experimental results in uniaxialcompression on jointed rocks and rock-like materials[18], the compressive strength of a jointed mass is givenby Eq. (4) and the corresponding modulus by Eq. (12),wherein Jf is a joint factor defined as

Jf ¼ Jn=nr; ð28Þ

where, Jn is the joint frequency, i.e., the number ofjoints/metre, which takes care of RQD and joint setsand joint spacing; n the inclination parameter dependingon the inclination of the plane with respect to the majorprincipal stress, the joint or set which is closer toð452fj=2Þ

o with the vertical will be the most critical one

to experience sliding; r the parameter for joint strength,it takes care of the influence of tight or filled joint,thickness of gouge, roughness, extent of weathering ofjoint walls and cementation along the joint. This factorcould be assessed in terms of an equivalent value offriction angle along the joint as tanfj ¼ tj=snj obtainedfrom shear tests, in which tj is the shear strength alongthe joint under a normal stress, snj: The values of n and r

are given in Tables 4 and 5, respectively. The values inTable 5 are suggested values and to be used in theabsence of shear tests. If the gouge material thickness ina meter depth is more than 5 mm, the equivalent numberof joints can be obtained by dividing its thickness inmillimetres by 5mm. A minimum limit of 5mm isconsidered for gouge to be fully operative without theinterference of the roughness of the joints. The value ofJf reflects the weakness introduced by fractures into theintact rock.

ARTICLE IN PRESS

Table 6

Estimation of scj from Jf for sci ¼ 100MPa; assumed Mri ¼ 500 for an

intact rock

Jf RMR Q scj (MPa) Mrj

0 100 2154 100.00 500

100 80 100 44.90 352

200 60 4.64 20.20 248

300 40 0.215 9.10 175

400 20 0.010 4.10 123

500 0 0.000464 1.80 87

Mrj from Eq. (29), RMR from Eq. (3), Q from Eq. (10).

able 7

trength classification of intact and jointed rocks

lass Description sci;j (MPa)

Very high strength >250

High strength 100–250

Moderate strength 50–100

Medium strength 25–50

Low strength 5–25

Very low strength o 5

able 8

odulus ratio classification of intact and jointed rocks

lass Description Modulus ratio of rock Mri;j

Very high modulus ratio >500

High modulus ratio 200–500

Medium modulus ratio 100–200

Low modulus ratio 50–100

Very low modulus ratio o 50


Now, from Eqs. (4) and (12), the modulus ratio of thejointed mass with respect to that of the intact rock isgiven as

Mrj=Mri ¼ exp½�0:0035Jf �: ð29Þ

Table 6 shows the estimated values of scj and Mrj fordifferent values of Jf varying from 0 to 500, along withthe corresponding values of RMR and Q as per Eqs. (3)and (10); for sci ¼ 100 MPa and Mri ¼ 500 of intactrock, the Mrj values from Eq. (29) rapidly decrease withthe increase of Jf and decrease of RMR and Q values.This table suggests that the relation between Ej and sci

cannot be taken as constant when the rock mass isexperiencing continuous fracturing and undergoingchange in its quality. The compressive strength valuespresented in Table 6 are comparable with those given inTable 1 as per Kalamaras and Bieniawski [14].

4. Classification based on strength and modulus

If the compressive strength and modulus of a rockmass are known, one could classify the rock mass alongthe lines of the approach adopted by Deere and Miller[2]. Even though the original classification due to Deereand Miller was suggested only for intact rocks, it couldbe modified to classify rock masses as well. The mainadvantage of such a classification is that it not onlytakes into account two important engineering propertiesof the rock mass but also gives an assessment of thefailure strain (ef ) which the rock is likely to exhibit inuniaxial compression, when the stress–strain response isHookean. That is,

Modulus ratio; Mrj ¼ Ej=scj ¼ 1=efj: ð30Þ

Most rocks under a uniaxial condition and alsounder low confining stress respond close to linearity.In such cases, one could easily establish a linearstress–strain response of the rock mass or adopt ahyperbolic formulation as suggested by Ramamurthyand Arora [28].

Having obtained scj and Ej for jointed rock, one couldadopt these values for classifying the rock mass usingTables 7 and 8 based on strength, as per the ISRM [7]

T

S

C

A

B

C

D

E

F

T

M

C

A

B

C

D

E

classification for intact rocks, and modulus ratio(Mrj ¼ Ej=scj). These tables are applicable to both intactand jointed rocks. Table 7 is an extended version of theDeere and Miller approach [2] and will cover very lowstrength to very high strength rocks. A modulus ratio of500 would mean a minimum failure strain of 0.2%,whereas a ratio of 50 corresponds to a minimum failurestrain of 2% as per Eq. (30). Very weak rocks and dense/compacted soils often show failure strains of the orderof 2%. Therefore, the modulus ratio of 50 is chosen asthe lower limiting value for rocks as per Ramamurthy[18].

Based on Tables 7 and 8, a rock whether intact orjointed could be classified and represented by twoletters, e.g. ‘BC’ meaning the rock has high compressivestrength in the range of 100–250 MPa with a mediummodulus ratio between 100 and 200. This classification isthus based on the engineering parameters of rock in anunconfined state. Some of the results of intact rocks arepresented in Fig. 2. In Fig. 3, the location of the intactspecimen is shown at ‘‘I’’ on the sci;j and Ei;j plot. Whenthe experimental data of scj and Ej of the jointedspecimens of the same material as that of the intactspecimen are plotted, all the points fall along an inclinedline originating at ‘‘I’’ and cutting across the constantboundaries of modulus ratio. This behaviour alsosuggests that, as fracturing continues, the locationsrepresented by scj and Ej follow a definite trend. Thegradient of this line for the jointed mass has been foundto be 1.60 on the log–log plot starting from the position‘‘I’’ of the intact specimen, i.e. (log E2�log E1)/(log sc2–log sc1). This value of 1.6 has been found to be anaverage gradient for four modes of failure: namely,splitting, shearing, sliding and rotation of the elementsin a block specimen, as per Singh et al. [29]. Each blockspecimen had an average of more than 260 elementalcubes. More details are available in Singh et al. [30]. The

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Fig. 2. Classification for intact rocks after modification to Deere and

Miller [2] approach; B=Basalt, D=Dolomite, G=Granite, L=Lime-

stone, M=Marble, Scf=Schist flat foliations, SCS=Schist steep

foliations, Sh=Shale, SS=Sandstone.

Fig. 3. Influence of jointing on classification of rocks for four modes

of failure.

Fig. 4. Influence of jointing on classification of rocks due to splitting

mode of failure.

Fig. 5. Influence of jointing on classification of rocks due to shearing

mode of failure.


gradient for other modes of failure in block specimensare: (i) for shearing of material or splitting—1.8, (ii) forsliding along joint—1.5, and (iii) for rotation ofblocks—1.4, Singh et al. [29], refer Figs. 4–7. Whenthe modes of failure are identified, based on the joint

system [30], the above values may be adopted. In theabsence of information on the modes of failure expectedin the rock mass, one may adopt a value of 1.60 as anaverage gradient to be followed by the mass asfracturing progresses.

From the above, it follows that, whenever the valuesof scj and Ej are suggested for any rock mass, theseshould fall as far as possible closer to the gradients

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Fig. 6. Influence of jointing on classification of rocks due to rotational

mode of failure.

Fig. 7. Influence of jointing on classification of rocks due to sliding

mode of failure.

Fig. 8. Influence of jointing on classification of weathered rocks.


suggested above based on the experimental work. Thiswill enable a check on the values to be adopted in theanalysis/design. In the case of weathered rocks, likequartzite, granite and basalt, this gradient was about 1.4from the data of Gupta [31] and Gupta and Rao [32].These three rocks have gone through different stages ofweathering: namely, unweathered (i.e., fresh), slightly,

moderately, highly and completely weathered. Testswere carried out on five levels of weathering of quartziteand four levels of weathering of both granite and basalt.The values of compressive strength and modulus fromtests on these rocks at these levels of weathering arepresented together in Fig. 8.

On the basis of the foregoing, the following gradientsare suggested to establish the scj and Ej relation for theengineering classification when the jointed mass isexperiencing different modes of failure,

(i)
Shearing of rock material or splitting 1.8 (ii) All modes, i.e. no mode is identified 1.6 (iii) Sliding along a weak plane 1.5 (iv) Rotation of blocks or weathered mass 1.4
5. Classification based on strength and failure strain

As suggested by Eq. (30), the modulus ratio is theinverse of the failure strain when the stress–strain curveis linear. Therefore, another way of classifying a rockcould be by using failure compressive strength andfailure axial strain. When Mrj is estimated for a jointedrock, the failure strain could also be estimated assumingthe rock to be responding linearly under a uniaxialcondition. Table 9 suggests the likely minimum failurestrain levels covering both intact and jointed rocks.Using Tables 7 and 9, one could classify the rock, whichwas classified earlier as ‘BC’ on the basis of compressivestrength and modulus, now as ‘BC’, meaning that the

ARTICLE IN PRESST. Ramamurthy / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–10198

rock has a compressive strength in the range of 100–250 MPa and is likely to fail under a minimum axialstrain in the range of 0.5–1.0%. The first letter refers tothe strength and the second smaller letter to thetheoretical minimum failure strain. Further, the ratioof the failure strain of the intact rock to that of thejointed rock is given by

efi=efj ¼ Mrj=Mri ¼ expð�3:50 10�3Jf Þ: ð31Þ

For better prediction of efj; the relation obtained fromthe experimental data between failure strain andmodulus ratio of the jointed rocks may be adopted asper Ramamurthy [18] as follows:

efj ¼ 50ðMrjÞ�0:75 ð%Þ: ð32Þ

The above suggested engineering classifications arebased on the measured/estimated engineering para-meters of rock namely, sci; scj; Ei; Ej; Jn; n; r; and alsofailure strains, and can be applied to both intact andjointed rocks. However, in practice one may prefer toadopt strength and modulus directly for classifying arock. The minimum failure strain in the axial directioncan easily be calculated for any analysis.

6. Geo-engineering classification

To have a comprehensive understanding of the rock,its past history, namely the genesis, the predominantrock mineral present and the weathering effect will have

Table 9

Classification of rocks based on failure strain

Class Description Failure strain, efi;j (%)

a Very high failure strain >2

b High failure strain 1–2

c Medium failure strain 0.5–1

d Low failure strain 0.2–0.5

e Very low failure strain o 0.2

Table 10

Weathering grades as per ISRM [7] and Gupta and Rao [33]

Symbol Degree of

weathering (%)

Term Description

W0 0 Fresh No visible sign of ma

W1 o 25 Slightly Discoloration indicat

W2 25–50 Moderately Less than half of the

Fresh or discolored r

corestones

W3 50–75 Highly More than half the ro

discolored rock is pre

W4 >75 Completely Majority of rock mat

original structure of

W5 100 Residual soil All material decompo

to be considered. The weathering process discolors,decomposes and disintegrates the rock and affects thediscontinuities most. It has a decisive influence on thecompressive strength and modulus of rock, either intactor jointed. When these values are found to be low for aparticular rock, it may be due to the weathering inaddition to fracturing. The extent of weathering in arock is usually indicated descriptively in Table 10, ISRM[7]. An extensive study on the influence of weathering ofcrystalline rocks, basalt, granite and quartzite, wascarried out by Gupta and Rao [33]. On the basis of theirfindings and those of other earlier investigations, theyproposed a classification of the degree of weathering interms of Rs indicated in Table 10. The best parameter tomeasure the influence of weathering seems to be theratio of the uniaxial compressive strengths of weatheredto the fresh intact rock specimens,

i:e: Rsð%Þ ¼ ½scðweatheredÞ=scðfreshÞ� 100: ð33Þ

Along with the two lettered classification of rock/rockmass, an indication of the extent of weathering may alsobe indicated by using the appropriate term from Table10, in addition to the generic name and the predominantmineral present, e.g. BC W1 Biotite schist: that is, therock is slightly weathered biotite schist having compres-sive strength between 100 and 250 MPa and mediummodulus ratio ranging between 100 and 200. Such abrief classification will not only reflect the range ofengineering response of the rock but also its geologicalhistory and will be easily understood and interpreted byengineers and geologists.

7. Discussion

The relations for the estimation of uniaxial compres-sive strength and the corresponding modulus from Jf arebased on the experimental results under unconstrainedconditions [18]. Whereas the assessment of these twobasic values of a rock mass, either by RMR, Q or GSI,

R (%)

terial weathering 100–80

es weathering of rock on major discontinuity surfaces 80–50

rock material is decomposed and/or disintegrated to soil.

ock is present either a discontinuous framework or as

50–25

ck is decomposed and /or disintegrated to a soil. Fresh or

sent either as a discontinuous framework or as corestones

25–10

erial is decomposed and /or disintegrated to soil. The

rock mass is still intact

10–1

sed. No trace of rock structure reserved o1

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Table 11

Size effect on modulus ratio [34]

Dia. or side, cm. sci;j (MPa) Ei;j (MPa) Mri;j

NX-size 50.0 50 000 1000

8.0 42.6 40 000 939

23.5 22.23 7500 337

62.0 10.0 2500 250

Values corresponding to NX-size extrapolated from data of other

sizes.


is based on experience and some back analysis. Morerecently, Kalamaras and Bieniawski [14] presented amodified expression to estimate uniaxial compressivestrength of rock mass taking into consideration theexperimental results of Carter et al. [15].

Ideally when field tests are conducted, the test block isto be isolated from the parent mass by careful cuttingand dressing operations in order to assess scj and Ej inthe unconstrained condition. Such a test block shouldhave a slenderness ratio more than one, and preferablytwo. Unfortunately, data from such tests are extremelylimited. Whenever some data are available, it isproposed to indicate the effect of the specimen size,rather than the change in the quality of the rock withinthe test block. As the size increases, the number ofjoints, their inclination, even if the strength along someof the joints remains the same, would affect the responseof the block. If one compares a value reflected by thelarge sized test blocks to that of the intact specimen, thevalues, particularly scj=sci and Ej=Ei; would correspondto a higher order of Jf values or lower values of RMRor Q:

A more recent example is from Natau et al. [34] whosetest results from three sizes of specimens ranging from80 mm to 620 mm were obtained totally in the uncon-fined state. The average results of scj and Ej arepresented in Table 11. From these results, scj of a620 620 1200 mm3 specimen is 0.235 times of thevalues of a 80 mm dia. specimen. By extrapolation, thevalue of compressive strength of NX size, assuming it isto represent an intact rock, this ratio works out to be0.20—which is not very different from the valueestimated for a 80 mm dia. specimen. The sci of theNX size works out to be 50 MPa. Similarly, the ratio ofEj of a 620 mm specimen to Ej of an 80 mm dia.specimen is 1/16; by considering the NX size, this ratiowould be 1/20, again suggesting slightly lower quality ofthe rock in the 80 mm dia. size. These ratios suggest anaverage Jf of 230/m and an average RMR of 55 fromstrength and modulus considerations as per Eqs. (2), (4),(12) and (13). The ratio Mri by considering NX size is1000 and for 80 mm dia. size it is 939. The Mrj for a620 mm size specimen works out to be 250, suggestingconsiderable change in the quality of the rock in thelarger size. These data confirm that the Mrj values

should decrease considerably with the decrease in thequality of the rock and not remain constant or varymarginally.

Earlier investigations of Rocha [35] also suggestedquite low values of Ej=Ei as 1/29 for granite, 1/28 forschist, 1/64 for limestone and 1/108 for quartzite;whereas Bieniawski [36] found the ratio Ej=Ei morethan 0.1 even at RMR=20.

Most of the modulus data is obtained by conductingtests in limited areas in tunnels, in drifts, in boreholesand, even if plate jacking tests are conducted on a levelsurface underground or in open excavation, there isalways some degree of lateral confinement. The mea-sured modulus values tend to be higher particularly forlarger values of Jf or smaller values of RMR or Q: Suchresults need to be corrected for lateral confinement toobtain values corresponding to the unconfined condi-tion. When such data are provided, the designer has thefreedom to choose or modify the strength and modulus,depending upon the in situ stress expected in the field.

Using the following equation, Ramamurthy [17], theinfluence of confining pressure on Ej can be estimated,

Ej0=Ej3 ¼ 1 � exp½�0:10scj=s03�; ð34Þ

where subscript 0 and 3 refer to s03 ¼ 0 and s3 > 0; s03 isthe effective confining stress.

From Table 6 for RMR=40, scj ¼ 9:1MPa whensci ¼ 100 MPa and say for s03 ¼ 1 MPa, Ej0=Ej3 ¼ 0:597;i.e. the actual unconfined value of Ej will be 0.597 timesthat of the measured value. And for RMR=20, thisratio works out to be 0.34. For values of RMR less than20, this ratio reduces faster. If the confinement is moredue to the in situ stress not being released, this ratiowould be still lower.

This kind of problem will not arise when evaluatingthe scj from field tests, since such tests are conducted oncut block specimens. It would be convenient to estimateeven Ej values from such tests. When these basic values,scj and Ej of a rock mass, are estimated without theinfluence of seepage pressure, it becomes convenient toadopt or enhance them, depending upon the confine-ment, in the effective stress analysis. Any otherengineering property measured in the field and influ-enced by confining pressure may also need to becorrected for confining effect or the magnitude ofconfinement be indicated for realistic analysis anddesign.

Apart from the correlations presented linking RMRand Q to Jf ; one could easily estimate the values of mj

and sj from the values of Jf as follows:For an undisturbed rock mass [22]

mj=mi ¼ exp½ðRMR � 100Þ=28�; ð35Þ

which in terms of Jf will be

mj=mi ¼ exp½�Jf=140� ð36Þ

ARTICLE IN PRESS

Table 12

Estimation of mj=mi and sj from Jf

Jf RMR or GSI mj=mi sj

400 20 0.0574 0.000138

300 40 0.0117 0.00127

200 60 0.240 0.0117

100 80 0.490 0.1080


and for

sj ¼ exp½ðRMR � 100Þ=9� ð37Þ

which in terms of Jf is

sj ¼ exp½�Jf=45�: ð38Þ

The values of mj=mi and sj from Eqs. (36) and (38),are shown in Table 12 for comparison purposes, agreevery closely with the values suggested by Hoek for thecorresponding values of GSI. From the foregoing, itfollows that one may still adopt Bieniawski’s RMR [13]and arrive at the values of mj=mi and sj:

The concept of Jf and the relations developed topredict scj and Ej were applied to interpret the results oflaboratory test specimens:

* to analyse large underground caverns and open mineexcavation by numerical methods;

* to establish ground reaction curves and radii of thebroken zone and also

* to estimate the bearing capacity of surface footings[37–42].

The joint factor, Jf ; is easily and rapidly estimated:two of its three factors come from the geological reportand the third parameter, connected with strength alongthe sliding joint or joint set, could be assessed by fieldshear test at the desired location or arrived at as areasonable value from the many published data. At theresidual state, one could obtain this strength dependingupon the joint condition and its material from Table 5.The values of Jf per metre depth could be estimatedquickly even during the excavation process andscj; Ej; and even efj [18], could be determined toconduct an analysis to choose or alter the supportingsystem.

An other important advantage of using Jf is toestimate the changes in the quality of rock mass byplotting scj and Ej on the modified Deere and Millerchart and classify the rock mass by considering theobserved mode of failure in the field. It is necessary thatthe values of Mrj are lower than that of the intact rockand continuously decrease with the decrease in qualityof the rock mass. Any values of scj and Ej recommendedwill have to stand this test.

8. Conclusions

The objective of the present study has been toexamine the reliability of the prediction of uniaxialcompressive strength and its corresponding modulus bysome of the popular approaches currently in use, toindicate a more reliable approach, and to suggest a Geo-engineering Classification applicable to both intactrocks and rock masses based on these two properties.The following are some of the salient conclusions.

1. The uniaxial compressive strength and modulus ofjointed rocks predicted by RMR, Q and GSI do notsuggest a decrease of modulus ratio with the decreasein the quality of the rock mass.

2. Based on the work of Kalamaras and Bieniawski,linking RMR with sci and scj; correlations betweenthe joint factor, Jf ; and RMR, Q and GSI have beenestablished to predict more reliably the strength andmodulus of rock mass in the unconfined condition.

3. The scj and Ej need to be estimated in uniaxialcompression, without seepage and confining pres-sures, so that their influence can be considered inanalysis and design in terms of the effective stress.

4. The use of joint factor, which enables one to estimatethe strength and modulus in the unconfined state andalso under any desired confining pressure, wasverified in the study of the deformational responseof jointed test specimens, the rock mass aroundunderground excavations, in open excavations, thebearing of surface footings, ground reaction curvesand the extent of broken zone around circularopenings in rock masses.

5. The Deere and Miller engineering classification,originally developed for intact rocks, has been found,after suitable modifications, useful in classifyingjointed rocks as well. The plot of scj and Ej followsa definite trend, starting from the location of intactrock and depending on the mode of failure of therock mass, either by splitting, shearing of rockmaterial, sliding along a joint or by rotation offractured rock elements.

6. An extension of this approach resulted in thesuggestion of a geo-engineering classification applic-able to both intact and jointed rocks, by consideringuniaxial compressive strength, the correspondingmodulus, a measurable engineering weathering indexand genesis of the rock. This will enable a designer toassess the rock mass response in relation to that ofintact rock or soil.

7. There is a greater need to test large jointed specimensin truly unconfined condition, both in the laboratoryand in the field, to estimate compressive strength andmodulus and to link these values to the weaknesscoefficients such as Jf ; RMR, Q or GSI. The modulusvalues are likely to be affected when tests are

ARTICLE IN PRESST. Ramamurthy / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 89–101 101

conducted in boreholes or in limited areas due to thein situ stress not being fully released.

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a geo-engineering classification for rocks and rock masses

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