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International Journal ofRock Mechanics and Mining Sciences

journal homepage: www.elsevier.com/locate/ijrmms

Improving the Hoek–Brown criterion based on the disturbance factor andgeological strength index quantification

Wenkai Fenga, Shan Dongb,⁎, Qi Wangb, Xiaoyu Yib, Zhigang Liub, Huilin Baib

a State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), Chengdu 610059, Chinab Chengdu University of Technology, Chengdu 610059, China

A R T I C L E I N F O

Keywords:Hoek–Brown criterionDisturbance factorGeological strength index quantificationSurface condition ratingStructure plane condition factorStructure rating

A B S T R A C T

A supplementary quantified approach for the GSI system is proposed by focusing on improving the GSI and therock mass disturbance factor (D). The surface condition rating (SCR), the structure plane condition factor (Jc),the rock mass basic quality index (BQ), and the rock mass structure rating (SR) are used in the proposed method.An improved formula for the disturbance factor (D) using the BQ is established. With this method, the GSI valueis a set of possible numbers within given intervals rather than a constant value. The relationship between the GSIand rock mass D reflects not only the disturbance degree of the rock mass from the wave velocity but also thedifference in the disturbance degree from the strength, which increases the accuracy of the D value. In addition,because of the value of the standard differences among the SCR, Jc, BQ and SR, the GSI region may be con-siderably wider due to quantification factors with larger differences. Thus, the method of measuring the intervalvalue can maximize error reductions, and intermediate interval values are recommended for use.

1. Introduction

The mechanical behavior of cataclastic rocks is poorly understoodbecause of difficulties associated with performing observations andanalyses of these rocks from the surface, collecting samples during fieldinvestigations, preparing specimens and conducting laboratory testing.1

Obtaining reliable estimates of rock mass strength and stiffness arecritical when performing a geotechnical analysis.2 Many parametersaffect the deformability and strength of jointed rock mass; thus, de-veloping a universal law that can be used in practical methods forpredicting rock mass strength is generally impossible. Compared withother methods, in situ tests are relatively accurate and can directlyobtain the mechanical parameters of cataclastic rock. However, thesetests can only be performed when exploration adits are excavated;moreover, the cost of conducting in situ tests is high. For laboratoryexperiments, the experimental results could be significantly influencedby the dimensional effect. Because the mechanical properties of cata-clastic rock can change, test results may not be stable when smallperturbations occur in laboratory tests. Over time, many classificationsystems, such as the RQD system, rock mass rating (RMR) system, Qsystem and geological strength index (GSI) system, have been devel-oped. Among them, the GSI system is used for estimating design para-meters.3 Hoek et al. developed the GSI, which can estimate rock mass

deformability and strength.4 In 2002, Hoek and Brown presented a newmethod of GSI parameter selection and introduced the disturbanceparameter D.5 The method for estimating the GSI proposed by Hoekuses two main parameters: rock mass structure and structure planefeatures. Both parameters rely on a qualitative description and a lack ofconcrete quantization parameters. The accuracy of this method dependsmostly on the engineer's experience and judgment with strong sub-jective factors; thus, the structural parameters of a rock mass are dif-ficult to quickly and accurately determine.6

In this paper, a new method for determining the mechanical para-meters of a rock mass is proposed based on the improved Hoek–Browncriterion. The surface condition rating (SCR), the structure plane con-dition factor (Jc), the rock mass basic quality index (BQ), and the rockmass Structure rating (SR) are used in the new method. An improvedformula for the disturbance factor (D) using the BQ is established. Theparameters obtained from laboratory tests are incorporated into theimproved Hoek–Brown formulas used to calculate the physical andmechanical parameters of cataclastic rock mass in the bedding shearzone. In addition, borehole shear testing was performed in the beddingshear zone in the field, and the testing results are compared with theHoek–Brown criterion and the results of the improved method.

https://doi.org/10.1016/j.ijrmms.2018.06.004Received 16 May 2017; Received in revised form 1 May 2018; Accepted 6 June 2018

⁎ Corresponding author.E-mail addresses: fengwenkai@cdut.edu.cn (W. Feng), dongshan1994@hotmail.com (S. Dong), 965067381@qq.com (Q. Wang), xiaou.geo@qq.com (X. Yi),

396492188@qq.com (Z. Liu), 553884932@qq.com (H. Bai).

International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

Available online 15 June 20181365-1609/ © 2018 Elsevier Ltd. All rights reserved.

T

2. Improvement and application of the Hoek–Brown criterion

2.1. Hoek–Brown criterion

The Hoek-Brown criterion was originally developed to estimate therock mass strength for a jointed rock mass based on estimates ofblockiness and the surface condition of discontinuities.7 The Hoek–-Brown rock criterion is based on the Griffith criterion of brittleness,which is a nonlinear empirical relationship for the limiting principalstress of rock failure.5 The Hoek–Brown rock criterion is expressed asfollows:

⎜ ⎟= + ⎛⎝

+ ⎞⎠

σ σ σ m σσ

1c ic

1 33

0.5

(1)

where σ1 and σ3 are the major and minor effective principal stresses atfailure, respectively, σc is the uniaxial compressive strength of the intactrock material, and mi is an empirical parameter.

The Hoek–Brown rock criterion is mainly intended for use on rockblocks with high cohesion and integrity; this criterion is not applicableto loose jointed rock masses. The modified Hoek–Brown criterion hasbeen improved by Hoek et al. to expand its applicability. The additionalempirical parameters of mb and a, which are related to the rock prop-erties, were proposed and the parameter of s, which represents thefracturing degree of the rock mass ranging from 0 to 1, was included tomake the Hoek–Brown rock criterion suitable for use in rock masses.8,9

⎜ ⎟= + ⎛⎝

+ ⎞⎠

σ σ σ m σσ

sc bc

a

1 33

(2)

Undisturbed rock mass:

= ⎛⎝

− ⎞⎠

m RMR mexp 10028b i (3)

= ⎛⎝

− ⎞⎠

s RMRexp 1009 (4)

=a 0.5 (5)

Disturbed rock:

= ⎛⎝

− ⎞⎠

m RMR mexp 10014b i (6)

= ⎛⎝

− ⎞⎠

s RMRexp 1006 (7)

=a 0.5 (8)

The Hoek-Brown criterion5 is used to determine a yield surface forintact rock based on laboratory test results. Additionally, a new GSIparameter selection method introducing D is presented, which is afactor that depends on the degree of disturbance to which the rock masshas been subjected by blast damage and stress relaxation.

= ⎛⎝

−−

⎞⎠

m GSID

mexp 10028 14b i (9)

= ⎛⎝

−−

⎞⎠

s GSID

exp 1009 3 (10)

= + −− −a e e12

16

( )GSI/15 20/3(11)

Parameters mb, s, and a all depend on the GSI, which ranges from 5(for a highly cataclastic, poor rock mass) to 100 (for an intact rockmass). The parameter mi is the Hoek–Brown constant for intact rock,and its value (1.0–35.0) reflects the hardness of the rock mass. Thevalue of D ranges from 0 (for an undisturbed rock mass) to 1 (for adisturbed rock mass)

When < < ′σ σ σt max3 3 , the formula for the rock mass shear-strengthparameters C and φ can be obtained using Eqs. (12) and (13)5:

′ = ⎡⎣⎢

+ ′+ + + + ′

⎤⎦⎥

−

−φam s m σ

a a am s m σsin

6 ( )2(1 )(2 ) 6 ( )

b b na

b b na

31

31 (12)

′ =+ + − ′ + ′

+ + + + ′ + +

−

−c

σ a s a m σ s m σa a am s m σ a a

[(1 2 ) (1 ) ]( )(1 )(2 ) 1 (6 ( ) )/(1 )(2 )

ci b n b na

b b na

3 31

31 (13)

=′

σσ

σnci

33 max

(14)

Hoek et al. suggest determining the maximum confining level for aslope and deep tunnels using the following equations5:

⎜ ⎟

′′

= ⎛⎝

′ ⎞⎠

−σσ

σγH

0.72cm

cm3 max0.91

(15)

⎜ ⎟

′′

= ⎛⎝

′ ⎞⎠

−σσ

σγH

0.47cm

cm3 max0.94

(16)

where γ is the bulk density of the rock mass, h is the slope height or theembedded depth of a tunnel, and σcm is the compressive strength of therock mass.

When < <σ σ0 1/4 c3 , the compressive strength of the rock mass σcmcan be expressed as follows:

′ = + − − ++ +

−σ σ m s a m s m s

a a( 4 ( 8 ))( /4 )

2(1 )(2 )cm cib b b

a 1

(17)

From the above analyses, the key to determining the mechanicalparameters of a rock mass is to determine the quantified values of GSIand D.5

2.2. Improved method for calculating the geological strength index

2.2.1. Quantitative analysis of rock mass structureBased on the rock mass structure and structure plane feature, we

propose solutions to the issues discussed above. We combine the rockmass structure plane surface grade SCR, Jc, BQ, and SR to determine thevalue of the quantization parameter. The GSI value is presented as a setof possible numbers in certain intervals rather than a constant value.

Quantification of the structure plane characteristics: The rock massstructure plane surface grade SCR includes three factors: the infillingrating Rf, the weathering rating Rw, and the roughness rating Rr. Thevalue of Rf, Rw and y are shown in Table 1. The formulae for SCR and Jcare as follows:

= + +SCR R R Rf w r (18)

Table 1SCR value table of the structural surface condition rating.12

Infilling rating (Rf) Thickness Value Weathering rating (Rw) Value Roughness rating (Rr) Value SCR

None / 6 Unweathered 6 Very rough 6 Rf + Rw + Rr

Hard < 5mm 4 Slightly weathered 5 Rough 5Hard > 5mm 2 Moderately weathered 3 Slightly rough 3Soft < 5mm 2 Highly weathered 1 Smooth 1Soft > 5mm 0 Decomposed 0 Slickenside 0

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

97

=J J JJcw s

a (19)

where Jw represents the rating for the waviness of the rock massstructure (ranging from 1 to 10), which can be expressed by a/d, wherea is the roughness between the peaks and valleys of the structure plane,and d is the maximum value of structure plane roughness; Js is thesmoothness rating (ranging from 1 to 20); and Ja is the joint alterationfactor rating.10,11 The values of Jw, Js and Ja are shown in Tables 2–4.

Quantification of the rock-mass structure: In this paper, the rockmass BQ and SR are introduced. The parameter BQ is defined as follows:

= + +BQ R K100 3 250c v (20)

⎜ ⎟= ⎛⎝

⎞⎠

Kvvvmp

rp

2

(21)

where Kv is the rock mass integrity index (ranging from 0 to 1), vmp isthe wave velocity of the rock mass, vrp is the wave velocity of the rockblock, and Rc is the uniaxial saturated compressive strength. When

> +R K90 30c v , then = +R K90 30c v ; when > +K R0.04 0.4v c , then= +K R0.04 0.4v c .The parameter SR13 can be expressed using the volumetric joint

count (Jv).

= − +SR J17.5 ln 79.8v (22)

The formula for Jv14 is as follows:

∑= +=

JS

NA

15v

i

n

i

r

1 (23)

where Si is the average distance between i groups, Nr is a randomnumber of joints in a particular area of joints, and A is the statisticalarea.

From the analysis above, a new standard is established using therock mass structure and structure plane parameters (Fig. 1). In the newmethod, the following values should be determined in order: SCR, BQ,SR and Jc. The value range in which the four parameters intersect is theGSI value. This paper is the first to combine the structural plane and therock mass strength to improve the GSI because the rock mass strength isclosely related to the structure plane. In the BQ method, the rock massstrength is primarily determined from the saturated uniaxial compres-sive strength. The rock physical mechanical parameters, including themineral composition, lithology, structural characteristics, particle sizeand shape, weathering degree, microstructure surface, etc., are the keyelements that influence the compressive strength. In general, a rockmass that is mainly composed of quartz and feldspar has betterweathering resistance than one composed of calcite, and calcite hasbetter weathering resistance compared with clay minerals, and thecompressive strength also increases. The sample of uniaxial compres-sive strength is cylindrical with no structure plane, although microcracks are observed in the sample. Additionally, a certain relationshipwith the structural plane is observed in more fractured rock massescorrespond to a smaller compressive strength of the rock mass. When

Table 2Terms used to describe large-scale waviness.13

Waviness terms Undulation Rating for waviness Jw

Interlocking (large scale) 3Stepped 2.5Large undulation > 3% 2Small moderate undulation 0.3–3% 1.5Planar < 0.3% 1

Table 3Terms to describe small-scale smoothness.13

Smoothness terms Description Rating for smoothness Js

Very rough Near vertical steps and ridges occur with an interlocking effect on the joint surface 3Rough Some ridges and side angles are evident; asperities are clearly visible; and discontinuity surface feels very abrasive (rougher

than sandpaper grade 30)2

Slightly rough Asperities on the discontinuity surfaces are distinguishable and can be felt (similar to sandpaper grade 30–300) 1.5Smooth Surface appears and feels smooth to the touch (smoother than sandpaper grade 300) 1Polished Visual evidence of polishing, which is frequently observed in the coating of chlorite and especially talc 0.75Slickensided Polished and striated surface that results from sliding along a fault surface or other movement surface 0.6–1.5

Table 4Rating for the joint alteration factor Ja.13

Term Description Ja

Rock wall contact Clear jointsHealed or “welded” joints (unweathered) Softening, impermeable filling (quartz, epidote, etc.) 0.75Fresh rock walls (unweathered) No coating or filling on joint surface except for staining 1Alteration of joint wall: Slightly to moderatelyweathered

Joint surface exhibits two classes of higher alterationthan the rock

2

Alteration of joint wall: highly weathered Joint surface exhibits two classes of higher alterationthan the rock

4

Coating or thin fillingFilled joints with partial or no contact between the rock

wall surfacesSand, silt, calcite, etc. Coating of frictional material without clay 3Clay, chlorite, talc, etc. Coating of softening and cohesive minerals 4Sand, silt, calcite, etc. Filling of frictional material without clay 4Compacted clay materials “Hard” filling of softening and cohesive materials 6Soft clay materials Medium to low over-consolidation of filling 8Swelling clay materials Filling material exhibits swelling properties 8–12

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

98

the uniaxial compressive strength of the rock blocks is greater, the rockmass is less likely to be cut by weathering; thus, the uniaxial com-pressive strength of rock blocks is closely related to the structure plane.The GSI quantization method proposed in this paper is concise, con-venient, and practical, and it fully reflects the geological strength indexof the rock mass.

2.2.2. Corrected disturbance coefficientIn this paper, a new computational formula for D is derived. The

formula for the deformation modulus Em is as follows5:

=⎧

⎨⎪

⎩⎪

− ≤

− >

−

−

( )( )

Eσ MPa

σ MPa

1 10 ( 100 )

1 10 ( 100 )m

D σ GSIc

D GSIc

2 100

1040

2

1040

c

(24)

For an undisturbed rock mass, the disturbance coefficient D is 0 andthe deformation modulus is Eud. For a disturbed rock mass, the dis-turbance coefficient is D and the deformation modulus is Ed. The re-lationship between Eud and Ed is as follows:

=−

EE D

11 /2

ud

d (25)

From research on graywacke, Read et al.15 proposed an empiricalformula for Em and RMR that is also applicable to cataclastic rockmasses:

= ⎛⎝

⎞⎠

E RMR0.110m

3

(26)

More than 200 sets of BQ and RMR values are analyzed via re-gression analyses based on hydroelectric, highway and other en-gineering fields, and the results indicated that a good linear relationshipoccurs between RMR and BQ, for which the formula is as follows:

= +BQ RMR80.786 6.0943 (27)

Based on the regression equation, further analysis shows that RMRis well correlated with the quantitative grades by BQ. In the IV and Ⅴlevels only, the BQ method might be conservative by approximatelyone-quarter to one-half of a grade based on the formula.16 From thisformula, the formula for D can be derived as follows:

⎜ ⎟⎜ ⎟= ⎛

⎝− ⎛

⎝

−−

⎞⎠

⎞

⎠D BQ

BQ2 1 80.786

80.786d

ud

3

(28)

where BQud is the basic quality index of an undisturbed rock mass, andBQd is the basic quality index of a disturbed rock mass. For an un-disturbed rock mass, BQud = BQd and D =0; when 23 BQd–BQud

=20.923, then D =1, which means that the rock mass is markedlydisturbed.

In this method, relatively stable layers can be identified fromchanges in the compressional wave velocity; undisturbed and disturbedcore samples can be collected from boreholes; and the uniaxial satu-rated compressive strength can be determined from laboratory testing.From these tests, the basic quality indexes BQud and BQd are acquired.

The relation of BQ and D is derived using the intermediate para-meter RMR. BQ is closely related to the uniaxial compressive strengthand integrity parameters of the rock mass, i.e., D is related to the

Fig. 1. Qualification of GIS based on the joint condition and BQ.

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

99

strength and wave velocity. This method reflects the breaking conditionof the rock mass before and after a disturbance; in addition, it can re-flect variations arising from the strength characteristics of different rockmasses or for different degrees of weathering.

3. Examples

3.1. Meishui hydropower station

To verify the validity and feasibility of this method, a broken zone ofdocite is chosen with an approximate width of 55m near the LancangRiver fault belt in Mangkam County of the Tibet Autonomous Region,where many adits were excavated. The 35# adit is randomly selected inthis paper.

In the 35# adit, the joints are moderately weathered and filled withrock fragments, and the adit is slightly rough. The RQD is approxi-mately 43%, and the wave velocity of the rock mass is 4810.1 m/sbefore a disturbance and 4244.3 m/s after a disturbance.

According to the experiments, the elastic modulus is 22 GPa, and thecompressive strengths are 52.5MPa and 46.9MPa before and after adisturbance, respectively. Based on the method, the SCR =10, Jc=1.5, the BQd =349.3, the BQud =398.9, and SR =22.4. Finally, thevalue of D is 0.832, and the GSI ranges from 37 to 44. The cohesive cranges from 1.42 to 1.72, and the friction angle φ is between 31.1 and34.7. The values of D and GSI calculated using the Hoek-Brown cri-terion are 0.9 and 43, respectively. The cohesive c is 2.36, and thefriction angle φ is 41.6.

Large in situ shear tests were performed to compare the resultsdetermined using the method in this paper and the Hoek-Brown cri-terion. The large in situ shear tests resulted in a cohesive c value from1.6 to 1.9 and a friction angle φ between 23 and 30. The results ob-tained using the method in this paper are better correlated with theresults of the large in situ shear tests compared with Hoek-Brown cri-terion.

3.2. Daguangbao landslide

The Daguangbao landslide, with an estimated influenced area of7.3–10 million m2 and a volume of 750–840 million m3, is the largestlandslide induced by the 2008 Wenchuan earthquake. Moreover, thislandslide is the largest known landslide in China and one of the world'slargest landslides. The rock in the bedding shear zone is cataclastic andforms the weak structural plane of the landslide. The sliding surfacecrack and formation mechanism of the Daguangbao landslide can bedivided into a shattered-sliding surface cracked mechanism, skin fric-tion sharp fall mechanism, and locked segment suddenly snipped out-burst mechanism.17–21 In addition, remote sensing research on the

Daguangbao landslide was performed by Yin et al.22,23

Field investigations suggest that the Daguangbao landslide mayhave occurred because of the presence of a cataclastic rock mass. Thus,the mechanical parameters are central to the formation mechanism ofthe cataclastic rock mass in the Daguangbao landslide. Research on themain slippage plane of the crushed rock mass and the relatively intactrock mass on the south side of the landslide had been performed.Because of weathering and erosion of the material, the completestructure plane is restricted and the layout of the rock mass is notconducive to research. Thus, this investigation focused on two sites andtwo aspects of each site: 1#: areas where the rock is comparativelycomplete, and 2#: areas where the rock is cataclastic. At these sites, therock was marked with a 50 cm by 50 cm square for the measurement ofjoint occurrences, roughness, aperture, fill, spacing, trace length, andweathering/erosion.

The lithology of the 1# areas is dolomite of the Sinian-agedDengying Formation, and it is mainly controlled by four joint sets.These joint sets are moderately weathered with few rock fragmentsfilling it; the roughness rating is slightly rough; and the waviness term islarge undulation (Fig. 2). Then, we determined that the Js =1.5, Jw=2, Ja =2, Jc =1.5, and SCR =10.

The lithology of the 2# area is dolomite of the Sinian-agedDengying Formation, and it is mainly controlled by four joint sets.These joint sets are highly weathered with small amounts of rockfragments and clay infilling. The roughness rating is slightly rough; andthe waviness term is planar (Fig. 3). Thus, the Js =2, Jw =1, Ja =4and Jc =0.5, and SCR =8.

3.2.1. Uniaxial compression testsUniaxial compression tests were conducted to determine the uni-

axial compressive strength of the disturbed rock. Cylindrical specimenswere used and carefully prepared from intact rock blocks collected fromthe bedding shear zone (Fig. 4). The average specimen size was 50mmin diameter and 100mm in height (Fig. 5). Uniaxial compression testingwas performed on two groups, each with three specimens. The finalaverage results and a typical stress–strain curve are illustrated in Fig. 6.

The material properties obtained from uniaxial testing were as fol-lows: the uniaxial yield stress and peak stress were 39.85 and 60.2MPafor area 1#, respectively, and 31.4 and 43.75MPa for area 2#, re-spectively. The elastic modulus was 79.6MPa for 1# and 39.25MPa for2#. The peak stress of the dolomite in 1# was greater than that of 2#,confirming that the rock mass of 1# was more complete than that of2#.

3.2.2. Point-load testingBecause disturbed rock is broken, intact rock specimens could not

be obtained from either 1# or 2#. Ten point-load tests were performedon the disturbed rock of the two points, and the uniaxial compressive

Fig. 2. Joint field investigation for 1#.

Fig. 3. Joint field investigation for 2#.

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

100

strength of the saturated disturbed rock was calculated from the point-load test results. The following functions are used to convert the pointloading strength to the saturated uniaxial compressive strength.

=R I22.82c s (50) (29)

=I K Is d s(50) (30)

=I PDes 2 (31)

= ⎛⎝

⎞⎠

K De50d

m

(32)

where Is is the point-load strength index without correction, P is thedamage load, De is the distance between loading points, Kd is the cor-rection factor of the size effect, and m is the revised index ranging from0.4 to 0.45. The results of these calculations are summarized in Table 5.The mean value for the uniaxial saturated compressive strength was33.8 MPa for 1# and 25.96MPa for 2#.

3.2.3. Wave velocity testThe wave velocity test of rocks was performed using the intelligent

acoustic wave monitor RSM-SY5, which was invented by the WuhanInstitute of Rock and Soil Mechanics, Chinese Academy of Sciences, totest the wave velocity of rocks in saturated conditions. The averagewave speeds of the 1# and 2# undisturbed rock masses were 3813m/sand 3689m/s, respectively, and the 1# and 2# disturbed rock masseswere 3352.9 m/s and 3102.9 m/s, respectively, based on sonic wavetesting.

3.2.4. Values of the Hoek–Brown parametersUsing the results from the uniaxial compression testing, wave ve-

locity testing, and field investigation described above, the GSI rangewas determined using the method described in this paper. The para-meter values are as follows: the values of BQd, BQud and SR are 347.2,500.6 and 20.3 in 1#, respectively, and 304.1, 474.2 and 15.2 in 2#,respectively.

These parameters were incorporated into Fig. 1 to determine the GSIand BQd, and BQud was incorporated into formula (29) to determine theD. The results from the provided method shows that the D in 1# and 2#are 1.56 and 1.68, respectively. The GSI in 1# and 2# range from 36 to46 and 27 to 38, respectively. In addition, the D results determinedusing the Hoek–Brown criterion in 1# and 2# are both 1. The GSI in 1#and 2# are 45 and 40, respectively.

The lithology on the south side of the landslide is mainly dolomite.The value of mi should be determined via a statistical analysis of theresults of a set of triaxial tests on carefully prepared core samples. Whenlaboratory tests are not possible, an experience table can be used todetermine estimates of σci and mi.5,7 Thus, in this paper, the values of mi

are determined by an experience table, with mi =9 ± 3. The values ofmi, GSI, and D were inserted into formulas (9)–(11) to determine theparameter values of mb, s, and y. For 1#, mb ranges from 0.124 to 0.254,s ranges from 2.33× 10−5 to 1.23× 10−4 and a lies between 0.506and 0.515. For 2#, mb ranges from 0.068 to 0.127, s ranges from7.34×10−6 to 3.22×10−5, and a is between 0.514 and 0.526.

The height is 220m in 1# and 230m in 2#. The range of σ3max is4.29–4.39MPa in 1# and 4.12–4.28MPa in 2#. As calculated usingformulas (12) and (13), the results from the improved method showthat the deformation moduli in 1# and 2# range from 2.2 to 4.0 and 1.3to 2.5, respectively. The cohesive strength is between 0.54 and 0.78 in1# and between 0.33 and 0.54 in 2#. The internal friction angle rangein 1# and 2# are from 22.1 to 27.8 and 15.4 to 21.3, respectively. Thedeformation modulus values based on the Hoek–Brown criterion in 1#and 2# are 4.9 and 3.3, respectively. The cohesive strength and internalfriction angle based on the Hoek–Brown criterion are 0.74 and 27.3 in1#, respectively, and 0.57 and 22.4 in 2#, respectively.

Fig. 4. Bedding shear zone.

Fig. 5. Broken specimens.

Fig. 6. Stress-strain curve for cataclastic sandone in uniaxial compression test.

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

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4. Comparison of the borehole shear test and Hoek–Browncriterion

4.1. Borehole shear test

A new methodology for determining soil and rock parameters is thephicometer test, which is a borehole shear test directly providing theshear strength in terms of the phicometer friction angle φ and thephicometer cohesion c. To obtain the mechanical parameters of thecataclastic rock mass in areas 1# and 2# of the bedding shear zone, aphicometer shear test for the cataclastic rock mass was used in situ withundisturbed rock. The phicometer shear test has been demonstrated asa useful and powerful tool for soil exploration in terms of determiningthe strength in situ.24–26

A total of eight tests in two groups were performed on areas 1# and2# to determine the shear strength parameters. The rock in the firstgroup (denoted by 1#) was relatively complete. Normal stresses of0.55, 0.85, 1.07, and 1.38MPa were applied to the four boreholes. Theother group (denoted by 2#) was in generally broken rock; for this test,normal stresses of 0.31, 0.48, 0.60, and 0.74MPa were applied to thefour boreholes. When the normal stress was stable, shear stress wasapplied to the rock by lifting the jack until rock failure occurred. Themeasurements from the sensor and the dial gauge were recorded.

4.1.1. Stress–strain curve analysesThe stress–strain curve is nonlinear: when the normal stress is

greater, the curve becomes steeper. In addition, the shear stress in-creases with increasing strain and eventually reaches a maximum valueand the failure of the specimen.

The deformation curve can be conceptually divided into four stages(Figs. 7 and 8). (1) Closure of existing microcracks: in this phase, thedensity of filler increases, the shear deformation is nonlinear, and the

stress–strain curve is concave. (2) Elastic deformation: the rock massalters from a discontinuous medium to a nearly continuous one, thematrix deforms and the material exhibits intact rock behavior char-acterized by constant stiffness. (3) Microfracture development: inelasticdeformation and plastic behavior is observed, in which the curve losesits linearity with a significant increase in strain as microfractures beginto propagate in a stable manner. (4) Fracture coalescence: fracturepropagation, coalescence, and interaction induce degradation of themechanical properties and damage to the rock mass material. Peakstrain was not detected in the borehole shear test; in addition, under thesame normal stress, the shear stress in 1# was larger than that in 2#;thus, the results are consistent with the actual situation.

4.1.2. Shear strength analysisThe maximum shear stress is the strength value of failure. After

analysis and data processing, the experimental results were plotted inFigs. 9 and 10.

At test point 1#, the cohesion is =c 398.7kPa, the internalfriction angle is = °φ 26.3 , and the goodness-of-fit of the linear model is0.95. At test point 2#, cohesion is =c 205.7kPa, the internal frictionangle is = °φ 25.4 , and the goodness-of-fit of the linear model is 0.992.

4.2. Comparison of the results

A marked difference is observed between the values measured in theborehole shear test and those calculated using the Hoek–Brown cri-terion. Several papers have addressed this topic, and to verify the ef-ficiency of our method, the results of several other methods will becompared with results obtained in the method proposed in this paper(Figs. 11 and 12).

Bertuzzi et al.27 expanded the database linking the GSI and the

Table 5Results of point-load testing of disturbed rock in the bedding shear zone.

Position Sample number 1 2 3 4 5 6 7 8 9 10

1# Failing load P/N 3825.2 4526.2 3416.8 2986.2 3469.3 4216.4 4628.3 3715.5 3378.5 4156.4Equivalent diameter De/mm 55.1 51.9 49.6 45.9 52.8 60.2 50.6 53.8 42.9 57.5Point-load strength index Is 1.26 1.68 1.4 1.42 1.24 1.16 1.61 1.28 1.64 1.26Uniaxial saturated compressive strength Rc 29.9 38.9 31.6 31.2 29.1 28.7 41.5 30.2 39.3 30.42

2# Failing load P/N 3215.8 2819.6 3407.5 2914.1 2579.6 3526.8 2903.2 3657.4 3189.4 2966.3Equivalent diameter De/mm 62.3 55.7 48.7 53.9 51.6 55.2 47.3 60.5 52.4 46.2Point-load strength index Is 0.82 0.91 1.43 1 0.96 1.16 1.28 1 1.16 1.4Uniaxial saturated compressive strength Rc 20.7 21.7 32.4 23.6 22.2 27.5 28.9 24.7 27 30.7

Fig. 7. Typical stress-strain curve of 1#.

Fig. 8. Typical stress-strain curve of 2#.

W. Feng et al. International Journal of Rock Mechanics and Mining Sciences 108 (2018) 96–104

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Hoek-Brown Criterion parameters mb, s and a. The improved equationsare as follows:

= ⎛⎝

−−

⎞⎠

m m GSID

exp 10038 24b i (33)

= ⎛⎝

−−

⎞⎠

s GSID

exp 10012 6 (34)

⎜ ⎟= ⎡⎣⎢

⎛⎝

+ ⎛⎝

− − ⎞⎠

⎞⎠

⎤⎦⎥

a GSI1, 12

1.0 exp 1015 (35)

These equations subjectively categorize each of the data sets for theappropriate D value, and three broad categories were used: D =0, D=0–0.8 and D =0.8. Based on the method of Bertuzzi, the cohesivevalue is =c 386.06kPa and the internal friction angle is = °φ 36.8for 1#, and the cohesive value is =c 392.75kPa and the internalfriction angle is = °φ 33.3 for 2#.

Cai et al.3 presented a quantitative approach to assist in the use ofthe GSI system, and it uses the block volume and a joint condition factoras the quantitative characterization factor. According to the method ofCai, the GSI values in 1# and 2# are 50 and 35, respectively. The valuesof cohesion (c) and the internal friction angle φ calculated using thismethod are 254.5 KPa and 31.2° in 1#, respectively, and 238.6 KPa and33 in 2#, respectively.

The shear strength parameters determined using the Hoek–Browncriterion are larger than those obtained from borehole shear testing,and the internal friction angle is smaller than the borehole shear testvalues. Although the internal friction angle phi calculated using theHoek-Brown criterion is a better match than that proposed by thepaper, the cohesion (c) and shear strength better match the results ofthe in situ test than the Hoek-Brown criterion. Additionally, the shearstrength using the improved method in 1# is a better match than thatusing the Bertuzzi and Cai method. In 2#, the shear strength calculatedby Bertuzzi and Cai is well correlated to the results of the boreholeshear test, and the improved method in this paper produced results thatare essentially consistent with the results of Bertuzzi's method.

5. Conclusions

The original GSI system is based on a descriptive approach ren-dering the system somewhat subjective and difficult to use for in-experienced personnel. To assist with the use of the GSI system, asupplementary quantified approach for the GSI system is proposed inthe present study by focusing on improving the GSI and the rock mass

Fig. 9. The fitting curve shear strength of 1#.

Fig. 10. The fitting curve shear strength of 2#.

Fig. 11. Result comparison of 1#.

Fig. 12. Result comparison of 2#.

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D. The relationship between the GSI and the rock mass D not only re-flects the disturbance degree of the rock mass from the wave velocitybut also reflects the difference in the disturbance degree from thestrength, which makes the D value more accurate.

The SCR, Jc, BQ, and SR of the rock mass are considered. With thismethod, the GSI value is a set of possible numbers within given inter-vals rather than a constant value. The proposed method generates fewererrors and is more reasonable than the Hoek–Brown rock-mass strengthcriterion.

Because of the value of the standard differences among the SCR, Jc,BQ and SR, the width of the GSI region may be much larger because ofquantification factors with larger differences. Thus, the method ofmeasuring the interval value can maximize error reductions, and in-termediate interval values are recommended for use.

Acknowledgements

The project was supported by the Sichuan Provincial Youth Scienceand Technology Innovation Team Special Projects of China (Grant no.:2017TD0018).

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