A comparative review in regardsto estimating bearing capacityin jointed rock masses in northeastJordanAli El-Naqa

Abstract There are a number of different methodsused for estimating the bearing capacity in jointedrock masses. In this paper, the geological strengthindex (GSI) introduced by Hoek et al. (1995) wasused to estimate the bearing capacity of the rockmass via rock mass rating (RMR). An empiricalrelationship is proposed to estimate the bearingcapacity of the rock mass using the GSI-dependenttoughness factor (TF). The proposed formula wascorrelated with bearing capacity equations used inthe literature. The regression analyses showedexponential relationships with a high correlationcoefficient.

Resume Il existe de nombreuses methodesdifferentes pour estimer la capacite portante d’unmassif rocheux fracture. Dans cet article, on utilise legeological strength index (GSI) introduit par Hoeket al. (1995) pour evaluer la capacite portante dumassif rocheux en s’appuyant sur le Rock MassRating (RMR). On propose une relation empiriquepour estimer la capacite portante du massif rocheuxa partir de l’indice de tenacite (toughnessfactor—TF) qui depend du GSI. La formuleproposee est mise en relation avec les equations deportance donnees dans la litterature. Les analyses deregression montrent une relation exponentielle avecun fort coefficient de correlation.

Keywords Bearing capacity Æ Jointed rock mass ÆGeological strength index (GSI)

Mots cles Capacite portante Æ Massif rocheux ÆFissures Æ Geological strength index GSI

Introduction

Bearing capacity is an important factor for the design ofdams, roads, bridges and other engineering structures,particularly when large rock masses are the foundationmaterials. The prediction of bearing capacity is based on themechanical behaviour of a rock mass, including the strengthand deformability of both the rock mass and the intact rock.Rock masses are inhomogeneous, discontinuous mediacomposed of rock material and naturally occurring dis-continuities such as joints, fractures and bedding planes.Bearing capacity failures of structures founded on rockmasses are related to joint spacing with respect to foun-dation width, joint orientation, joint condition (open orclosed) and rock type. Figure 1 illustrates typical failuremodes associated with different rock mass conditions,modified from those suggested by Sower (1979) andKulhawy and Goodman (1980). The failure modes can bedescribed for four general rock mass conditions includingintact, jointed, layered and fractured:

1. Intact rock refers to a rock mass with a typical dis-continuity spacing greater than four to five times thewidth of the foundation. Two types of bearing capacityfailure modes are possible depending on the rock type:local shear failure and general wedge failure, associatedwith brittle and ductile rock respectively.

2. Bearing capacity failures in jointed rock masses aredependent on the spacing, orientation and condition ofthe discontinuities. Two types of bearing capacity fail-ure modes are possible for structures founded on rockmasses in which the predominant discontinuities aresteeply dipping and closely spaced as illustrated inFig. 1c, d. Discontinuities that are open (Fig. 1c) offerlittle lateral restraint hence failure is initiated by thecompressive failure of individual rock columns. Tightlyclosed discontinuities (Fig. 1d) on the other hand,provide lateral restraint such that general shear is thelikely mode of failure. In rock masses with steeplydipping joints and a joint spacing greater than thewidth of the foundation (Fig. 1e), failure is likely to beinitiated by splitting, which eventually progresses to thegeneral shear mode. Where the joints are dippingbetween 20 and 70� with respect to the foundationplane, shear failure is again the most likely mode(Fig. 1f), particularly as a discontinuity is likely todefine at least one surface of the potential shear wedge.

Received: 26 February 2002 / Accepted: 25 February 2004Published online: 22 June 2004ª Springer-Verlag 2004

A. El-NaqaDepartment of Water Management and Environment,Faculty of Natural Resources and Environment,Hashemite University, 13116 Zarqa, JordanE-mail: elnaqa@hu.edu.jo

DOI 10.1007/s10064-004-0235-8 Bull Eng Geol Env (2004) 63:233–245 233

3. In multi-layered rock masses, when each layer has dif-ferent material properties, the failure modes are morecomplicated. Two scenarios have been discussed by

Sower (1979), both involving a founding layer of rigidrock underlain by a soft highly deformable layer, withbedding planes dipping at less than 20� with respect tothe foundation plane. In the first case (Fig. 1g), a thickrigid layer overlies the soft layer, while in the secondcase (Fig. 1h) the rigid layer is thin. In both cases, failure

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Fig. 1Typical bearing capacity failure modes associated with various rockconditions (Sower 1979)

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is initiated by tensile failure. However, in the first case,tensile failure is caused by flexure of the rigid thicklayer, while in the second case it results from a punchingthrough of the thin rigid upper layer. The limitingthickness of the rigid layer in both cases is controlled bythe consistency of the properties of that layer.

4. A highly fractured rock mass is one which contains twoor more discontinuity sets with typical joint spacingsthat are small with respect to the foundation width(Fig. 1i). It behaves in a manner similar to densecohesionless sands and gravels and hence the mode offailure is likely to be general shear.

In addition to the failure of the foundation rock, aggressivereactions within the rock mineralogy or with ground wateror surface water chemistry can lead to bearing capacityfailure. Examples include: loss of strength with time(typical of some clay shales); reduction of load bearingcapacity caused by chemical reaction between the foun-dation element and the ground water or surface water;rock materials susceptible to solution processes andadditional stresses imposed by swelling minerals. Potentialsecondary causes of failure should be identified during thesite investigation phase of the project in order that theireffects can be minimized.In this paper a simple method to determine the bearingcapacity of jointed rock masses has been used, based on

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Fig. 1(Contd.)

A comparative review in regards to estimating bearing capacity in jointed rock masses in northeast Jordan

the geological strength index (GSI) proposed by Hoeket al. (1995). The index is derived from the rock massrating of Bieniawski (1989) but includes the rock masstoughness-factor (TF) proposed by El-Mannai Enbaya andTarhuni (2000). This new empirical relationship can beused to estimate the bearing capacity of the rock masswith a good degree of accuracy.

Site geology

The study area is located a few kilometres to the north of theZarqa River, 20 km north of Amman City (Fig. 2). Thegeology of the area consists generally of fine-grained hori-zontally bedded, marine sediments of Cretaceous age

(Table 1). Figure 3 provides a geological map of the studyarea, which consists of two main rock formations: theKurnub Sandstone Formation of the Kurnub Group and theNaur Limestone Formation of the Ajlun Group (Bender1974). The Kurnub Sandstone Formation (Lower Creta-ceous) consists predominantly of varicoloured, friable,medium to fine grained, massive to locally thinly beddedsandstones interbedded with siltstones, claystones andshales together with gypsum bands. Figure 4 shows a lith-ological profile of the Kurnub Group. The upper contact isclearly marked by a change from sandstone to nodularlimestone, dolomite and marl containing dark grey or greensilty clays. This formation is highly jointed and has threemajor joint sets oriented NW–SE, NE–SW and NNE–SSW.The Kurnub Sandstone Group is overlain conformably bya thick sequence of carbonate rocks of Cenomanian to

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Fig. 2Location map of the study area

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Fig. 3Geological map of the study area(Bender 1974)

Table 1Geological classification of the rock units in the study area

Epoch Age Group Formation Symbol Thickness (m) Rock type

Upper Cretaceous Holocene Balqa Alluvium Qal 10–40 Soil, sand and gravelMaestrichtain Muwaqqar B3 60–70 Chalk, marl and chalky limestoneCampanian Amman B2 80–120 Chert, limestone with phosphateSantonian Ghudran B1 15–20 Chalk, marl and marly limestoneTuronian Ajlun Wadi Sir A7 90–110 Hard crystalline limestone, dolo

mitic and some chertCenomanian Shueib A5–6 75–100 Light-grey limestone interbedded

with marls and marly limestoneHummar A4 40–60 Hard dense limestone and dolo

mitic limestoneFuheis A3 60–80 Grey and olive green soft marl.

Marly limestone and limestoneNaur limestone A1–2 150–220 Limestone interbedded with a

thick sequence of marl andmarly limestone

Lower Cretaceous Albian-Aptian Kurnub sandstone K 300 Massive white and varicolouredsandstone with layers of reddishsilt and shale

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238 Bull Eng Geol Env (2004) 63:233–245

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Tournian age (Upper Cretaceous) referred to as the AjlunGroup. The main outcrop is the Naur Limestone Forma-tion, which is composed predominantly of highly jointedwell-bedded limestone, dolomitic limestone, medium tothin beds of nodular and fossiliferous limestone and marlylimestone intercalated with thick layers of marls (Fig. 5).This formation is intersected at least by three joint setstrending NNW–SSE, NNE–SSW and NW–SE.

Theoretical background

There are a number of techniques available for estimatingthe bearing capacity of rock foundations including ana-lytical methods, traditional bearing capacity equations andfield load tests. Two terms are important in bearingcapacity analyses: the ultimate bearing capacity—definedas the average load per unit area required to producefailure by rupture of a supporting soil or rock mass—andthe allowable bearing—defined as the maximum pressurewhich can be permitted on a foundation soil (rock mass)with an adequate safety against rupture of the soil/rockmass or movement of the foundation of such magnitudethat the structure is impaired.

Methods for computing bearingcapacity

Analytical methodThe ultimate bearing capacity may be estimated from anumber of analytical methods; the more convenientinclude the finite element and limit equilibrium methods.A number of bearing capacity equations reported in theliterature provide explicit solutions for the ultimate bear-ing capacity. The equations represent either empirical orsemi-empirical approximations of the ultimate bearingcapacity and are dependent on the mode of potentialfailure as well as, to some extent, material properties. Inthis respect, selection of an appropriate equation mustanticipate the likely mode of potential failure.The ultimate bearing capacity for the general shear modeof failure can be estimated from the traditional Buisman-Terzaghi (Terzaghi 1943) bearing capacity expression asdefined by Eq. 1. This equation is valid for long contin-uous foundations with length to width ratios in excess often

qult ¼ cNc þ 0:5cBN þ cDNq ð1Þwhere qult=the ultimate bearing capacity; c=effective unitweight (i.e. submerged unit weight if below water table) ofthe rock mass; B=width of foundation; D=depth of foun-dation below ground surface; c=the cohesion intercepts forthe rock mass.The terms Nc, Nc, and Nq are bearing

capacity factors given by the following equations or ob-tained as a function of the friction angle:

Nc ¼ 2N/0:5 N/þ 1ð Þ ð2aÞNc ¼ N/0:5 N/ � 1

� �ð2bÞ

Nq ¼ N2/ ð2cÞ

N/ ¼ tan2 45þ /=2ð Þ ð2dÞwhere /=angle of internal friction for the rock mass.Equation 1 is applicable to failure modes in which bothcohesion and frictional shear strength parameters aredeveloped as illustrated in Fig. 1b, d.In cases where theshear failure is likely to develop along planes of disconti-nuity or through highly fractured rock masses such asillustrated in Fig. 1f and i, cohesion cannot be relied uponto provide resistance to failure. In such cases the ultimatebearing capacity can be estimated from the followingequation:

qult ¼ 0:5cBN þ cDNq ð3ÞLocal shear failure represents a special case where failuresurfaces start to develop but do not propagate to thesurface as illustrated in Fig. 1a. In this case, the depth ofembedment contributes little to the total bearing capacity/stability. An expression for the ultimate bearing capacityapplicable to localised shear failure can be written as:

qult ¼ cNc þ 0:5cBNc ð4ÞEquations 1, 3 and 4 are applicable to long continuousfoundations with length to width ratios (L/B) greater thanten. Table 2 provides correction factors for circular andsquare foundations, as well as rectangular foundationswith L/B ratios less than ten. The ultimate bearing capacityis estimated from the appropriate equation by multiplyingthe correction factor by the value of the correspondingbearing capacity factor. Factors for rectangular founda-tions with L/B ratios other than 2 or 5 can be estimated bylinear interpolation.Figure 1c illustrates a case with poorly constrained col-umns of intact rock where the failure mode is similar to anunconfined compression failure. The ultimate bearingcapacity may be estimated from Eq. 5 (Sower 1979):

qult ¼ 2c tan 45þ /=2ð Þ ð5ÞFor widely spaced and vertically oriented discontinuities,failure generally initiates by splitting beneath the foun-dation as illustrated in Fig. 1e. In such cases, Bishnoi(1968) suggested the following solutions for the ultimatebearing capacity:

For circular foundations

qult ¼ JcNcr ð6aÞFor square foundations

q ¼ 0:85JcNcr ð6bÞFor continuous strip foundations with L/B<32

qult ¼ JcNcr= 2:2 0:18þ L=Bð Þ ð6cÞwhere J=correction factor dependent upon the thickness ofthe foundation rock and the width of the foundation.L=length of the foundation.

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Fig. 4Columnar section of the Kurnub Sandstone Formation

b

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Fig. 5Columnar section of the Naur Limestone Formation

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The bearing capacity factor Ncr is given by:

Ncr ¼2N/2

1þ N/cot /ð Þ S=Bð Þ 1� 1

N/

� �� N/ cot /ð Þ

þ 2N/0:5 ð7ÞGraphical solutions for the correction factor (J) and thebearing capacity factor (Ncr) are provided in Fig. 6 andFig. 7 respectively.Goodman (1989) proposed a method to determine thebearing capacity using the triaxial test on highly jointedcore samples. The bearing capacity of foundations on rockcan be obtained to give an appropriate factor of safety (F)using Eqs. 8, 9 and 10:

qf ¼ qu N/ þ 1� �

ð8Þ

N; ¼ tan2 45þ /=2ð Þ ð9ÞBC ¼ qf =F ð10Þwhere qf=ultimate bearing capacity; /= internal frictionangle of rock mass; BC=allowable bearing capacity,qu=unconfined compressive strength.

Empirical methodsDifferent empirical equations have been developed toestimate the bearing capacity in jointed rock masses. Pecket al. (1974) suggested an empirical correlation betweenthe allowable bearing capacity stress and RQD, which has asignificant influence on the bearing capacity of a rock

mass. Bowles (1988) proposed the following formula, alsobased on the RQD:

qult ¼ qr � RQDð Þ2 ð11Þwhere qr=ultimate strength of rock determined by uniaxialcompression test and RQD=rock quality designationobtained from core logging.Hoek and Brown (1980, 1988) suggested a strength crite-rion for a jointed rock mass may be used to determine thebearing capacity with the equation:

r1 ¼ r3 þ mqcr3 þ sq2c

� �0:5 ð12Þwhere r1=major principle effective stress, r3=minorprinciple effective stress, qc=uniaxial compressionstrength of intact rock and, s and m are material constants(determined using the rock mass rating of Bieniawski1989).Subsequently Hoek et al. (1995) suggested a set ofequations to estimate the material constants m and s basedon the GSI. For the undisturbed rock masses with GSI>25:

m ¼ mi exp GSI�10028

� �s ¼ exp GSI�100

9

� �ð13Þ

where mi is the value of m for the intact rock. The value ofthe mi can be obtained from Hoek and Brown (1988). Bell(1992) suggests the bearing capacity of the strip footingcan be estimated using the Hoek-Brown criterion with(r3=S0.5qu) as follows:

qult ¼ S0:5 þ ms0:5 þ s� �0:5

h iqc ð14Þ

where BC=qult/FS and FS=factor of safety (assumed to be 5).

Proposed methodology

In the present study 56 rock samples were collected fromdifferent carbonate and sandstone rock types along the

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Table 2Correction factors (after Sower 1979)

Foundation shape Cc CcNc correction Nc correction

Circular 1.2 0.70Square 1.25 0.85RectangularL/B=2 1.12 0.9L/B=5 1.05 0.95L/B=10 1.00 1.00

Fig. 6Correction factor for open joints (Bishnoi 1968)

Fig. 7Bearing capacity factor for open joints: S discontinuity spacing; Bbreadth of foundation (Kulhawy and Goodman 1980)

A comparative review in regards to estimating bearing capacity in jointed rock masses in northeast Jordan

Amman-Jerash Highway and their uniaxial compressivestrength values obtained. In addition, joint surveys werecarried out using scan line techniques (Piteau 1973) todetermine the joint characteristics and relevant dataobtained to determine the geological strength index (GSI)as introduced by Hoek et al. (1995). Examples of the jointsurveys are provided in Fig. 8.The GSI can also be estimated based on the 1989 version ofBieniawski’s RMR classification (Bieniawski 1989) as fol-lows:

GSI ¼ RMR89 � 5 ð15ÞThe RMR index proposed by Bieniawski (1973, 1974, 1976,1979, 1989) is the sum of the rates determined for thefollowing rock mass properties: (1) unconfined compres-sive strength of the intact rock; (2) rock quality designa-tion; (3) joint spacing; (4) joint condition; (5) groundwaterconditions and (6) adjustment for joint orientation. Therock quality designation (RQD) values were either deter-mined from boreholes or estimated using the empiricalformulae proposed by Barton et al. (1974) and Priest andHudson (1976).

El-Mannai et al. (2000) introduced the rock mass tough-ness factor (TF), defined as the ratio of the rock massrating (RMR) to the maximum limit of the RMR for atotally intact rock mass (RMR=100). In a similar way,based on GSI a rock mass toughness factor (TF) has beendefined as a ratio of the geological strength index value tothe maximum value of GSI of the intact rock mass.

TF ¼ GSI=100ð Þ ð16Þwhere GSI can be obtained from RMR as mentioned inEq. 15.Hoek (2002) proposed an equation to estimate the uniaxialcompressive strength of the rock mass (rcm) based on theintact rock strength (rci), material constant (mi) and theGSI as follows:

rcm ¼ 0:0034 �m0:8i

� �rci 1:029þ 0:025e�0:1mi

� �� �GSI ð17Þ

The mi values for the jointed sandstone and limestonewere 17 and 12, respectively.The bearing capacity is calculated by multiplying thetoughness factor (TF) by the uniaxial compressive strengthof the rock mass:

BC ¼ TF � rcm ð18Þ

Statistical analysisRegression analysis was used to correlate the bearingcapacity and the geological strength index (GSI) obtainedfrom the rock mass rating (RMR). The estimated bearingcapacity for the jointed limestone and sandstone samplesare summarized in Tables 3 and 4 respectively, and theregression curves obtained between GSI and differentbearing capacity values in Figs. 9 and 10. Table 5 sum-marizes the regression equations obtained betweenthe bearing capacity and GSI. Most of the methodsused to determine the bearing capacity were fitted toexponential regression models that have the highestcorrection coefficients. It was found that the bearingcapacity value estimated using the suggested empiricalformula has a high correlation coefficient and provides agood estimate for bearing capacity compared with theother methods.

Conclusions

The use of the geological strength index (GSI) based on therock mass rating (RMR) provides an acceptable estimateof the bearing capacity of a rock mass; the highest corre-lation coefficient being obtained using the exponentialmodel.The use of rock mass strength parameters provides anacceptable estimate of the bearing capacity for jointed rockmasses. It is advisable to estimate the rock mass strengthfrom the intact rock strength as the direct use of the intactrock strength results in an over-estimate of bearingcapacity.The regression analyses carried out between the GSI andthe bearing capacity indicate that the exponential model

242 Bull Eng Geol Env (2004) 63:233–245

Fig. 8Joint surveys using scanline technique in a Kurnub Sandstone andb Naur Limestone

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Bull Eng Geol Env (2004) 63:233–245 243

Table 3Estimation of bearing capacity values in jointed limestone using different methods

Rock type GSI m s rc ri qult Bell method Goodmanmethod

Sowermethod

Suggestedmethod

Strong limestone 63 1.87 0.0164 3.65 25 15.85 3.17 3.63 3.67 3.75Strong limestone 61 1.74 0.0131 4.01 30 17.25 3.45 3.95 4.00 4.05Marly limestone 56 1.45 0.0075 3.78 35 15.80 3.16 3.61 3.81 3.63Marl 49 1.13 0.0035 2.49 30 9.74 1.95 2.25 2.48 2.12Marl-shale 44 0.95 0.002 1.54 22 5.62 1.12 1.34 1.54 1.16Shale 40 0.82 0.0013 1.36 24 5.08 1.02 1.15 1.37 1.00Marly limestone 52 1.26 0.0048 2.59 28 10.44 2.09 2.40 2.59 2.33Nodular marl 48 1.09 0.0031 2.4 30 9.25 1.85 2.16 2.39 2.00Nodular marl 48 1.09 0.0031 2 25 7.71 1.54 1.80 1.98 1.67Marl-shale 46 1.02 0.0025 2.09 28 7.87 1.57 1.85 2.11 1.67Nodular marl 50 1.17 0.0039 2.66 31 10.55 2.11 2.43 2.68 2.31Nodular marl 49 1.13 0.0035 2.65 32 10.39 2.08 2.40 2.67 2.26Nodular marl 49 1.13 0.0035 2.49 30 9.74 1.95 2.25 2.48 2.12Strong limestone 62 1.8 0.0147 6.28 45 27.19 5.44 6.20 6.27 6.40Limestone-marl 57 1.51 0.0084 4.28 40 18.98 3.80 4.10 4.28 4.37Limestone-marl 58 1.56 0.0094 4.7 40 19.91 3.98 4.53 4.69 4.61Limestone-marl 58 1.56 0.0094 4.7 40 19.91 3.98 5.03 5.01 4.61Limestone-marl 58 1.56 0.0094 5.28 45 22.40 4.48 5.09 5.28 5.19Nodular marl 53 1.31 0.0054 2.88 30 11.76 2.35 2.69 2.87 2.64Limestone-marl 59 1.62 0.0105 3.92 32 16.72 3.34 3.80 3.93 3.89Limestone-marl 55 1.4 0.0067 2.6 25 10.76 2.15 2.46 2.59 2.46Limestone-marl 54 1.35 0.006 2.8 28 11.49 2.30 2.63 2.81 2.60Limestone-marl 52 1.26 0.0048 2.22 24 8.95 1.79 2.05 2.21 2.00Limestone-marl 52 1.26 0.0048 2.03 22 8.20 1.64 1.88 2.02 1.83Limestone-marl 50 1.17 0.0039 1.72 20 6.81 1.36 1.57 1.70 1.49Marl-shale 44 0.95 0.002 1.89 27 6.89 1.38 1.65 1.91 1.43Strong limestone 59 1.62 0.015 4.29 37 21.62 4.32 4.16 4.28 4.50Limestone-marl 50 1.26 0.0048 2.96 32 11.93 2.39 2.74 2.97 2.39

Table 4Estimation of bearing capacity values in jointed sandstone using different methods

Rock type GSI m s rc ri qult. Bell method Goodmanmethod

Sowermethod

Suggestedmethod

Friable sanstone-shale 39 1.698 0.0011 0.2 12.5 3.41 0.68 0.21 1.24 0.58Friable sandstone 46 2.18 0.0025 0.39 14.1 5.41 1.08 0.44 0.39 0.97Weak marl-shale 48 2.34 0.0031 0.74 7.3 3.07 0.61 0.85 0.74 0.56Weak marl-shale 48 2.34 0.0031 0.74 7.3 3.07 0.61 0.85 0.74 0.56Sandstone-shale 39 1.698 0.0011 0.65 8.1 2.21 0.44 0.68 0.66 0.38Sandstone-shale 39 1.698 0.0011 0.65 8.1 2.21 0.44 0.68 0.66 0.38Friable sandstone-shale 46 2.18 0.0025 0.87 9.1 3.49 0.70 0.37 0.43 0.63Sandstone-shale 38 1.638 0.001 0.61 9 2.35 0.47 0.63 0.61 0.39Sandstone-shale 46 2.18 0.0025 0.75 7.8 2.99 0.60 0.85 0.73 0.54Sandstone-shale 46 2.18 0.0025 0.75 7.5 2.88 0.58 0.85 0.73 0.52Sandstone-shale 46 2.18 0.0025 0.75 7 2.69 0.54 0.85 0.73 0.48Sandstone-shale 46 2.18 0.0025 0.75 7.2 2.76 0.55 0.85 0.73 0.50Friable sandstone 50 2.515 0.0039 0.8 7.5 3.48 0.70 0.93 0.79 0.64Sandstone-shale 28 1.106 0.0003 0.2 3.2 0.50 0.10 0.19 0.19 0.07Sandstone-shale 26 1.067 0.0003 0.19 3.3 0.51 0.10 0.18 0.19 0.07Sandstone-shale 34 1.42 0.0007 0.23 3.2 0.71 0.14 0.23 0.24 0.11Friable sandstone 51 2.607 0.0043 0.97 8.8 4.26 0.85 1.15 0.98 0.79Friable sandstone-shale 39 1.698 0.0011 0.5 6.8 1.85 0.37 0.53 0.50 0.32Weak marl-shale 44 2.03 0.002 0.77 8.5 2.97 0.59 0.85 0.77 0.52Weak marl-shale 44 2.03 0.002 0.77 8 2.79 0.56 0.85 0.77 0.49Weak marl-shale 44 2.03 0.002 0.68 7.5 2.62 0.52 0.75 0.68 0.46Friable sandstone-shale 34 1.42 0.007 0.43 6 2.63 0.53 0.43 0.44 0.21Friable sandstone-shale 39 1.698 0.0011 0.51 6.4 1.75 0.35 0.54 0.50 0.30Weak marl-shale 44 2.03 0.002 0.63 7 2.45 0.49 0.70 0.64 0.43Weak marl-shale 44 2.03 0.002 0.63 7.5 2.62 0.52 0.70 0.64 0.46Friable sandstone-shale 40 1.76 0.0013 0.57 6 1.74 0.35 0.60 0.58 0.29Weak marl-shale 44 2.03 0.002 0.63 7 2.45 0.49 0.70 0.64 0.43

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244 Bull Eng Geol Env (2004) 63:233–245

Fig. 10Graphical charts of bearingcapacity in jointed Naur Lime-stone using a suggested method,b Bell method, c Goodmanmethod and d Sower method

Fig. 9Graphical charts of bearingcapacity in jointed KurnubSandstone using a suggestedmethod, b Bell method, c Good-man method and d Sowermethod

Table 5Regression equations obtained between bearing capacity values and GSI

Method name Regression equations injointed limestone

Correlationcoefficient (r)

Regression equations injointed sandstone

Correlationcoefficient (r)

Suggested formula BC=0.0483e0.0725 GSI 0.86 BC=0.0068e0.0982 GSI 0.84Bell BC=0.0631e0.0685 GSI 0.83 BC=0.0171e0.0786 GSI 0.73Goodman BC=0.0816e0.0662 GSI 0.82 BC=0.0319e0.0692 GSI 0.67Sower BC=0.1289e0.0589 GSI 0.78 BC=0.0592e0.0543 GSI 0.56

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has the highest correlation coefficient and that thegraphical charts obtained could be used as design chartsfor the same rock types. The use of the GSI to estimate thebearing capacity of the jointed limestone and sandstonesamples was proved to be reliable by the correlationcoefficient of approximately 0.9.

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A comparative review in regards to estimating bearing capacity in jointed rock masses in northeast Jordan