the effect of not fully grouted rock bolts on the performance of … · 2018. 4. 12. · the effect...

The Effect of Not Fully Grouted Rock Bolts on thePerformance of Rock Mass

H. Xu, Y. C. Zhao, W. K. Bu

Abstract. According to the characteristics of rock bolts in mining engineering, a mechanical model for not fully groutedrock bolt is presented to obtain the expression of shear displacement, the axial force and the shear stress along the anchorsection. On these bases, the effect of the length of anchor section on the performance of rock mass and the effect of the axialforce at the free end of the bolt on the performance of rock mass are analyzed by COMSOL Multiphysics. According to theresults of numerical simulations, there are some conclusions as following: (1) a moderate length of anchor section, such asthe length of 1.0 m~1.4 m, is favorable in mining supporting design, which can make sure grout and rock in coupled stateand reduce the construction cost; (2) the favorable distance between the rock bolts is from 0.9 m to 1.3 m; (3) more rockbolts should be installed if the rock mass has larger deformation, which also can make sure grout and rock in coupled state.Conversely, less rock bolts should be installed if the rock mass has smaller deformation, which also can reduce theconstruction cost.Keywords: not fully grouted, rock bolt, supporting design, coal roadway, mining engineering.

1. Introduction

Rock bolts have been widely used for rock reinforce-ment in underground engineering for a long time, espe-cially in mining engineering in China. In order to improvethe rock bolting effect, it is necessary to have a good under-standing of the effect of rock bolts on the performance ofrock mass.

Since the 1970s, numerous researchers have carriedout field monitoring (Freeman, 1978; Björnfot & Stephans-son, 1984a,b; Sun, 1984; Choquet & Miller, 1988), labora-tory tests (Hawkes & Evans, 1951; Farmer, 1975; Stillborg,1994; Stjern, 1995; Benmokrane et al., 1995; Hyett et al.,1995; Hagan, 2004; Moosavi et al., 2005; Marthin et al.,2011), analytical approaches (Farmer, 1975; Yazici & Kai-ser, 1992; Hyett et al., 1995; Pellet & Egger, 1996; Li &Stillborg, 1999; Cai et al., 2004; Ren et al., 2010; Marthinet al., 2011; Fahimifar & Ranjbarnia, 2011; He et al., 2015)and numerical simulations (Larson & Olofsson, 1984; Ful-ler et al., 1996; Ivanovic & Neilson, 2009; Deb & Das,2010) for a better understanding of the load transfer mecha-nism between the rock bolts and the surrounding rock mass.Some concepts such as “neutral point”, “pick-up length”and “anchor length”, clearly outline the behavior of fullygrouted rock bolts in a deformed rock formation. Undoubt-edly, these studies contribute to a better comprehension ofthe mechanical behavior of fully grouted rock bolts.

Nevertheless, the characteristics of rock bolts in min-ing engineering are not the same as the characteristics offully grouted rock bolts in civil engineering or other under-

ground engineering in China. These differences are in twoaspects: (1) the rock bolts in mining engineering are notfully grouted. A single rock bolt is divided into “anchor sec-tion” and “freedom section” as shown in Fig. 1. Here, theanchor section means the bolt section within grouted layerand the freedom section means the bolt section withoutgrouted layer; (2) the faceplate is installed at the free end ofthe bolt, which can provide effective support to the rockmass and generate an axial force at the free end of rock bolt.These differences must be taken into account in developinganalytical models for not fully grouted rock bolts.

The aim of this paper is to analyze the effect of notfully grouted rock bolts on the performance of rock mass. Amechanical model for not fully grouted rock bolt is pre-sented first, and then the shear displacement, the axial forceand the shear stress along the anchor section are obtained.On these bases, numerical simulations are carried out byCOMSOL Multiphysics for analyzing the effect of thelength of anchor section on the performance of rock massand the effect of the axial force at the free end of the bolt onthe performance of rock mass.

2. Theoretical Analysis

Windsor (1997) proposed the concept that a rein-forcement system comprises four principal components:the rock mass, the reinforcing element, the internal fixtureand the external fixture. For reinforcement with a rock boltin mining engineering, the reinforcing element refers to therock bolt and the external fixture refers to the faceplate and

Soils and Rocks, São Paulo, 39(3): 317-324, September-December, 2016. 317

Hui Xu, PhD. Student, State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics & Civil Engineering, China University of Mining &Technology, Xuzhou, Jiangsu, China and Heze University, Heze, Shandong, China. e-mail: [email protected] Cheng Zhao, Full Professor, Doctoral Supervisor, State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics & Civil Engineering,China University of Mining & Technology, Xuzhou, Jiangsu, China. e-mail: [email protected] Kui Bu, PhD, Associate Professor, Resources and Environment Department, Heze University, Heze, Shandong, China. e-mail: [email protected] on June 3, 2015; Final Acceptance on May 3, 2016; Discussion open until December 30, 2016.

nut. The internal fixture is the grouted layer, which usuallyuses epoxy resin in mining engineering in China. The inter-nal fixture provides a coupling condition at the interface.When grouted bolts are subjected to an axial pull load, fail-ure may occur at the bolt-grout interface, or at the grout-rock interface. However, in this study we concentrate onthe effect of rock bolts on the performance of rock mass,which is based on the hypothesis that there is no failure atthe bolt-grout interface, or at the grout-rock interface. Inother words, the decoupling at the interface is not consid-ered in this paper.

It is well known that the faceplate restrains the defor-mation of the rock mass, and at the same time, there is anaxial force in the rock bolt. For keeping balance, the anchorsection of rock bolt is induced shear stress at the bolt-groutinterface. And then the shear stress at the bolt-grout inter-face transfers into grouted layer, which also induces shearstress at the grout-rock interface. Finally, the shear stresstransfers into rock mass. When the shear stress at thebolt-grout interface and the shear stress at the grout-rock in-terface are both lower than the shear strength, there is noslippage at the bolt-grout interface and the grout-rock inter-face, which is called coupling stage or compatible deforma-tion stage.

The concept of the mechanical model of a single rockbolt and grouted layer is drawn in Fig. 2 and the equilibriumbalance of the infinitesimal element in anchor section isshown in Fig. 3. According to the balance of the infinitesi-mal element of the rock bolt and grouted layer in anchorsection, the equilibrium equation is written as,

N x dx N x D x dx( ) ( ) ( )� � � �� 0 (1)

where, dx is the length of the infinitesimal element; N(x)and N(x+dx) are the axial force at left side and right side ofthe infinitesimal element, respectively; D is the diameter of

the borehole and �(x) is the shear stress at the grout-rock in-terface.

According to Taylor expansion and ignoring high-order remainders, Eq. 1 can be expressed as below,

dN x

dxD x

( )( )� � � . (2)

The geometrical equation of the infinitesimal elementin anchor section is expressed as,

�uN x

D Edx

a

�4

2

( )

�(3)

where, �u is the extension of the infinitesimal element,which can be expressed as Eq. 4; Ea is the composite elasticmodulus of rock bolt and grouted layer, which can be calcu-lated as Eq. 5.

�u u x dx u x� � �( ) ( ) (4)

where, u(x) and u(x+dx) are the axial displacement at leftside and right side of the infinitesimal element, respec-tively.

E ED

A E AD

a g b� ��

�

�

�

��

��

�

�

�

� �2 2

4 4/ (5)

where, Eb and Eg are elastic modulus of rock bolt andgrouted layer, respectively; A is the area of the cross-section of the rock bolt (He & Li, 2006).

Combining Eq. 3 and Eq. 4, and ignoring high-orderremainders, the following equation can be obtained.

� �u xN x

D Ea( )

( )42�

. (6)

After differential and substituting Eq. 2 into Eq. 6, itturns to Eq. 7.

318 Soils and Rocks, São Paulo, 39(3): 317-324, September-December, 2016.

Xu et al.

Figure 1 - A not fully grouted rock bolt in surrounding rock mass.

Figure 2 - Mechanical model of a single rock bolt and grouted layer.

�� u xx

DEa( )

( )40

�. (7)

When the reinforcement system is in coupling stage,the constitutive equation for grouted layer can be expressedas,

�( ) ( )x Ku x� (8)

where, K is shear stiffness.

Substituting Eq. 8 into Eq. 7, it can be written as,

�� u xKu x

DEa( )

( )40. (9)

The solution for Eq. 9 can be expressed as,

u x C e C ex x( ) � � �1 2� � (10)

where, � �4K

DEa.

Substituting Eq. 10 into Eq. 6 and Eq. 8, the expres-sions for N(x) and �(x) can be written as,

N xD E

C e C ea x x( ) ( )� � ��

� �� 2

1 24(11)

� � �( ) ( )x K C e C ex x� � �1 2 . (12)

According to Fig. 2, the boundary conditions are ex-pressed as Eq. 13,

x l N l Pm m� �, ( ) , (13a)

� �( )x Ddx Plm

��0 (13b)

where, lm is the length of anchor section, P is the axial forceat the free end of rock bolt.

Combining Eq. 11-Eq. 13, the expressions for u(x),N(x) and �(x) can be expressed as following:

u xP

D E e ee e

al l

x x

m m( )

( )( )�

��

�

42��

� �� (14)

N xP

e ee e

l l

x x

m m( ) ( )�

��

�

�

� �

� � (15)

��

� � �� ( )

( )( )x

P

D e ee e

l l

x x

m m�

��

�

� . (16)

3. Numerical Simulation ModelThe deformation of rock mass before rock bolts sup-

porting and after rock bolts supporting are shown in Fig. 4.An effective region, such as the red region in Fig. 4, is se-lected as the research object. Here, the range of effective re-gion is wider than the influence range of a single rock bolt.Considering the unloading effect of excavation, the me-chanical model of the effective region is proposed in Fig. 5.The left and right boundaries in Fig. 5 are fixed as the sameas top boundary. The bottom boundary in Fig. 5 is uniformstress boundary, which simulates the unloading of excava-tion. Since the model is axisymmetric, it is sufficient to ana-lyze only half of the model in Fig. 5, which is named simpli-fied model shown in Fig. 6. The boundaries of simplifiedmodel are the same as the boundaries of model in Fig. 5 ex-cept the left boundary. The left boundary of simplifiedmodel is divided into two parts, which are called anchorsection boundary and freedom section boundary, respec-tively. For anchor section boundary, the horizontal dis-


The Effect of Not Fully Grouted Rock Bolts on the Performance of Rock Mass

Figure 3 - Equilibrium element of the rock bolt and grouted layerin anchor section.

Figure 4 - Deformation of rock mass in coal roadway.

Figure 5 - Mechanical model of the effective region.

placement is zero and the vertical displacement is calcu-lated according to Eq. 17; for freedom section boundary,the horizontal displacement is also zero but the vertical dis-placement is obtained according to Eq. 18. Thus, the nu-merical simulation model is built by COMSOL Multi-physics with free mesh, in which the height is 2.4 m and thewidth is 2 m. The boundary conditions of numerical simula-tion model and the coordinate system are shown in Fig. 7.

u yP

D E e ee e

l ya

l l

y y

m

m m( )

( )( )1 2

1

4

0

1 1� ��

�

� � �

�

�

��

(17)

u yP y l

E A

P

D E e ee e

m

b

al l

l l

m m

m m

( )( )

( )( )

22

2

4

��

�

��

�

�

�� l y lm2

(18)

where, lm is the length of anchor section, P is the axial forceat the free end of rock bolt.

4. Analysis on the Influence of Not FullyGrouted Rock Bolt on the Performance ofRock Mass

According to the proposed model, the performance ofrock mass mainly depends on the axial force P at the freeend of rock bolt and the length of anchor section lm. The uni-form load on the bottom boundary in Fig. 6 equals to20�106 Pa and the other basic parameters are listed in Ta-ble 1.

4.1. Influence of the length of anchor section

For researching the effect of the length of anchor sec-tion lm on the performance of rock mass, the axial force P atthe free end of rock bolt should be a constant. Here, the ax-ial force P equals to 80�103 N and the length of anchor sec-tion lm changes from 0 m to 2.2 m in the proposed simula-tion model. The expression lm = 0 m means that there is norock bolt supporting.

The numerical results including vertical displace-ment, vertical stress and vertical strain are shown in Fig. 8.The vertical displacement of bottom boundary in simula-tion model is shown in Fig.9, which means the vertical dis-placement of rock mass at the roof of roadway. When thelength of anchor section increases from 0 m to 0.6 m, thevertical displacement of rock mass at the faceplate de-creases from 67.8�10-3 m to 3.63�10-3 m, which means thatthe vertical displacement of rock mass decreases signifi-cantly if the rock mass is supported by rock bolt. But on theother side, when the length of anchor section increases from1.4 m to 2.2 m, the vertical displacement of rock mass at thefaceplate decreases from 2.02�10-3 m to 1.18�10-3 m, whichmeans that the supporting performance of rock bolt cannotimprove significantly only by increasing the length of an-chor section.

Compared with no rock bolt supporting, the relativereduction of vertical displacement of rock mass is shown in


Xu et al.

Figure 6 - Simplified model.

Figure 7 - Numerical simulation model.

Table 1 - Basic parameters of rock mass and rock bolt.

Rock mass’s deformation modulus Em 0.5�109 Pa

Poisson’s ratio of rock mass �m 0.30

Density of rock mass �m 2200 kg/m3

Young’s modulus of rock bolt Eb 210�109 Pa

Length of rock bolt l 2.4 m

Diameter of rock bolt Db 24�10-3 m

Diameter of borehole 36�10-3 m

Deformation modulus of grouted layer 15�109 Pa

Grouted layer’s shear stiffness 0.6�109 Pa/m

Fig. 10. The distance from left boundary increases from 0 mto 1.4 m while the relative reduction of vertical displace-ment of rock mass decreases from about 90% to about 10%.If the range in which the relative reduction of vertical dis-placement of rock mass is more than 10% is defined as theinfluence range of a single rock bolt, the corresponding dis-tance from the left boundary is defined as the influence ra-dius of a single rock bolt. The influence radius of a singlerock bolt with different length of anchor section is shown inFig. 11. When the length of anchor section increases from0.2 m to 2.2 m, the influence radius of a single rock bolt in-creases from 1.37 m to 1.49 m, which indicates that increas-ing the length of anchor section will increase the influenceradius of a single rock bolt, however, the influence radius ofa single rock bolt keeps almost constant if it exceeds certainlength.

The shear stress at the grout-rock interface with dif-ferent length of anchor section is also obtained in Fig. 12.

According to the curves in Fig. 12, the shear stress at thegrout-rock interface has not uniform distribution along theaxial direction of rock bolt. Taking lm = 1.8 m for example,the value of shear stress at the end of anchor section is0.28�106 Pa while the value of shear stress at the point be-tween anchor section and freedom section is 0.64�106 Pa,which shows that decoupling behavior occurs more easilyat the point between anchor section and freedom sectionthan at the end of anchor section. On the other hand, whenthe axial force P equals to 80�103 N and the length of an-chor section increases from 0.2 m to 2.2 m, the minimumand the maximum shear stress decreases from 3.52�106 Pato 0.20�106 Pa and from 3.57�106 Pa to 0.61�106 Pa, re-spectively, which means that increasing the length of an-chor section will reduce the value of shear stress at thegrout-rock interface. In other words, increasing the lengthof anchor section can make sure grout and rock in coupledstate.



Figure 9 - Vertical displacement of rock mass at the roof of road-way.

Figure 8 - Numerical results (lm = 1.4 m). (a) Vertical displacement/�10-3 m. (b) Vertical stress/�106 Pa. (c) Vertical strain.

Figure 10 - Relative reduction of vertical displacement of rockmass at the roof of roadway.

4.2. Influence of the axial force at the freeend of rock bolt

For researching the effect of the axial force P at thefree end of rock bolt on the performance of rock mass, thelength of anchor section lm should be a constant. Here, thelength of anchor section lm equals to 1.4 m and the axialforce P at the free end of rock bolt changes from 20�103 Nto 160�103 N in the proposed simulation model.

The vertical displacement of rock mass at the roof ofroadway is shown in Fig. 13. When the axial force at thefree end of rock bolt increases from 20�103 N to 160�103 N,

the vertical displacement of rock mass at the faceplate in-creases from 0.50�10-3 m to 4.03�10-3 m, which indicatesthat increasing the axial force at the free end of rock boltwill increase the vertical displacement of rock mass. How-ever, the vertical displacement of rock mass cannot be sig-nificantly increased. On the other hand, the increasing axialforce at the free end of rock bolt only influences the perfor-mance of rock mass in a small region, in which the distancefrom left boundary is less than 1 m.

The axial force at the free end of rock bolt is very im-portant for mining engineering. According to the axialforce at the free end of rock bolt, researchers can optimizethe design of rock bolt supporting. The vertical displace-ment of rock mass at the faceplate with different axial forceis shown in Fig. 14. Obviously, the vertical displacement ofrock mass at the faceplate linearly increases with the in-creasing of axial force at the free end of rock bolt, whichagrees well with the theoretical analysis. Therefore, morerock bolts should be installed if the rock mass has larger de-formation, which also can make sure grout and rock in cou-pled state. Conversely, less rock bolts should be installed ifthe rock mass has smaller deformation, which also can re-duce the construction cost.

The shear stress at the grout-rock interface with dif-ferent axial force is also calculated in Fig. 15. When the ax-ial force at the free end of rock bolt increases from


Xu et al.

Figure 11 - Influence radius of a single rock bolt.

Figure 12 - Shear stress at the grout-rock interface.

Figure 13 - Vertical displacement of rock mass at the roof of road-way.

Figure 14 - Vertical displacement of rock mass at the faceplate.

Figure 15 - Shear stress at the grout-rock interface.

20�103 N to 160�103 N, the minimum and the maximumshear stress increases linearly from 0.103�106 Pa to0.824�106 Pa and from 0.176�106 Pa to 1.41�106 Pa, re-spectively, which also agrees well with the theoretical anal-ysis. It indicates that decoupling behavior can more easilyhappen with bigger axial force. Thus, more rock bolts areinstalled in this case for reducing the axial force of rockbolts and preventing the decoupling behavior.

5. Conclusions

A mechanical model is proposed for not fully groutedrock bolts in rock mass and the effect of not fully groutedrock bolts on the performance of rock mass is discussedbased on a numerical simulation model. It supplies a suffi-cient way to analyze the influence of not fully grouted rockbolts on the performance of rock mass for mining engineer-ing. According to the model, the performance of rock massmainly depends on the length of anchor section and the ax-ial force at the free end of rock bolt, and the following find-ings are obtained.

1) Increasing the length of anchor section will reduce thevertical displacement of rock mass and reduce thevalue of shear stress at the grout-rock interface. How-ever, the influence radius of a single rock bolt keepsalmost constant if the length of anchor section exceedscertain length. Thus, a moderate length of anchor sec-tion, such as the length of 1.0 m~1.4 m, is favorable inmining supporting design, which can make sure groutand rock in coupled state and reduce the constructioncost.

2) For improving the effectiveness of rock bolts supporting,the distance between the rock bolts should be less thanthe influence radius of a single rock bolt. Therefore,the favorable distance between the rock bolts is from0.9 m to 1.3 m, which can explain the phenomenonthat the distance between the rock bolts is about 1.1 min the roadway supporting of mining engineering.

3) The increasing axial force at the free end of rock boltonly influences the performance of rock mass in asmall region, moreover, it will increase the value ofshear stress at the grout-rock interface. Thus, morerock bolts should be installed if the rock mass haslarger deformation, which also can make sure groutand rock in coupled state. Conversely, less rock boltsshould be installed if the rock mass has smaller defor-mation, which also can reduce the construction cost.

Acknowledgments

Financial support for this work, provided by NationalUndergraduate’s Scientific Research Foundation in China(No.201310290009) and the Scientific Research Founda-tion of Heze University (No.XY14KJ01 & No.XYPY02)are gratefully acknowledged.

References

Benmokrane, B.; Chennouf, A. & Mitri, H.S. (1995). Labo-ratory evaluation of cement-based grouts and groutedrock anchors. International Journal of Rock Mechanicsand Mining Sciences & Geomechanics, 32(7):633-642.

Björnfot, F. & Stephansson, O. (1984). Interaction ofgrouted rock bolts and hard rock masses at variableloading in a test drift of the Kiirunavaara Mine, Sweden.Proceedings of the International Symposium on RockBolting, Balkema, Rotterdam, pp. 377-395.

Björnfot, F. & Stephansson, O. (1984). Mechanics groutedrock bolts-field testing in hard rock mining. SwedishRock Engineering Research Foundation.

Cai, Y.; Esaki, T. & Jiang, Y. (2004). An analytical modelto predict axial load in grouted rock bolt for soft rocktunneling. Tunnelling and Underground Space Tech-nology, 19(6):607-618.

Choquet, P. & Miller, F. (1988). Development and fieldtesting of a tension measuring gauge for cable boltsused as ground support. CIM Bulletin, 81(914):53-59.

Deb, D. & Das, K.C. (2010). Bolt-grout interactions inelastoplastic rock mass using coupled FEM-FDM tech-niques. Advances in Civil Engineering, pp. 1-13.

Fahimifar, A. & Ranjbarnia, M. (2011). Analysis of circu-lar reinforced tunnels by analytical approach. Journal ofStructural Engineering, 1(1):1-5.

Farmer, I.W. (1975). Stress distribution along a resingrouted rock anchor. International Journal of Rock Me-chanics and Mining Sciences & Geomechanics,12(11):347-351.

Freeman, T.J. (1978). The behaviour of fully-bonded rockbolts in the Kielder experimental tunnel. Tunnels andTunnelling International, 10(5):37-40.

Fuller, P.; Hume, B. & Hume, R. (1996). Bolt load simula-tion and its practical application. Proc. 2nd North Ame-rican Rock Mechanics Symposium, Montreal,pp. 187-193.

Hagan, P.C. (2004). Variation in load transfer of a fully en-capsulated rockbolt. Proc. 23rd International Confer-ence on Ground Control in Mining, Morgantown,pp. 33-49.

Hawkes, J.M. & Evans, R.H. (1951). Bond stresses in rein-forced concrete columns and beams. Journal of the In-stitute of Structural Engineers, 24(10):323-327.

He, L.; An, X.M. & Zhao, Z.Y. (2015). Fully grouted rockbolts: An analytical investigation. Rock Mechanics andRock Engineering, 48(3):1181-1196.

He, S.M. & Li, X.P. (2006). Study on mechanism of pre-stressed anchor bolt. Chinese Journal of Rock Mechan-ics and Engineering, 25(9):1876-1880 (In Chinese).

Hyett, A.J.; Bawden, W.F.; Macsporran, G.R. & Moosavi,M. (1995). A constitutive law for bond failure of fully-grouted cable bolts using a modified Hoek cell. Interna-



tional Journal of Rock Mechanics and Mining Sciences& Geomechanics, 32(1):11-36.

Ivanovic, A. & Neilson, R.D. (2009). Modelling of debon-ding along the fixed anchor length. International Jour-nal of Rock Mechanics and Mining Sciences,46(4):699-707.

Larsson, H. & Olofsson, T. (1984). Bolt action in jointedrock. Proc. International Symposium on Rock Bolting,Abisko, pp. 33-46.

Li, C. & Stillborg, B. (1999). Analytical models for rockbolts. International Journal of Rock Mechanics andMining Sciences, 36(8):1013-1029.

Martin, L.B.; Hassen, F.H.; Tijani, M. & Noiret, A. (2011).A new experimental and analytical study of fully grou-ted rockbolts. Proc. 45th US Rock Mechanics/Geo-mechanics Symposium, San Francisco, pp. 11-242.

Moosavi, M.; Jafari, A. & Khosravi, A. (2005). Bond of ce-ment grouted reinforcing bars under constant radialpressure. Cement and Concrete Composites,27(1):103-109.

Pellet, F. & Egger, P. (1996). Analytical model for the me-chanical behaviour of bolted rock joints subjected to

shearing. Rock Mechanics and Rock Engineering,29(2):73-97.

Ren, F.F.; Yang, Z.J.; Chen, J.F. & Chen, W.W. (2010). Ananalytical analysis of the full range behaviour ofgrouted rockbolts based on a tri-linear bond-slip model.Construction and Building Materials, 24(3):361-370.

Stillborg, B. (1994). Professional Users Handbook forRock Bolting. Trans Tech Publications, Germany,268 p.

Stjern, G. (1995). Practical Performance of Rock Bolts.PhD Thesis, Norwegian Institute of Technology Tron-dheim, Norway, 178 p.

Sun X. (1984). Grouted rock bolt used in underground en-gineering in soft surrounding rock or in highly stressedregions. Proc. the International Symposium on RockBolting, Balkema, Rotterdam, pp. 93-101.

Windsor, C.R. (1997). Rock reinforcement systems. Inter-national Journal of Rock Mechanics and Mining Sci-ences, 34(6):919-951.

Yazici, S. & Kaiser, P.K. (1992). Bond strength of groutedcable bolts. International Journal of Rock Mechanicsand Mining Sciences & Geomechanics, 29(3):279-292.


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