A new approach in determining the load transfer mechanism

University of Wollongong Thesis Collections

University of Wollongong Thesis Collection

University of Wollongong Year

A new approach in determining the load

transfer mechanism in fully grouted bolts

Hossein JalalifarUniversity of Wollongong

Jalalifar, Hossein, A new approach in determining the load transfer mechanism in fullygrouted bolts, PhD thesis, School of Civil, Mining and Environmental Engineering, Universityof Wollongong, 2006. http://ro.uow.edu.au/theses/855

This paper is posted at Research Online.

http://ro.uow.edu.au/theses/855

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This online version of the thesis may have different page formatting and pagination from the paper copy held in the University of Wollongong Library.

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CHAPTER THREE

REVIEW OF SHEAR BEHAVIOUR OF BOLTS AND

MATERIAL PROPERTIES

CHAPTER 3: Review of shear behaviour of bolts and material properties

51

CHAPTER THREE

REVIEW OF SHEAR BEHAVIOUR OF BOLTS AND

MATERIAL PROPERTIES

3.1. INTRODUCTION

Rock bolts are the main elements of support in modern stabilisation techniques for

geotechnical engineering. They generally work as an additional resistance against

shear failure along joints and weakness planes. The internal steel bar within the

system is the main element resisting axial load under suspension and transverse shear

loads caused by beam bending and slip on joints. Axial forces in the bolt consist of a

component perpendicular to the shear joint, which contributes frictional strength, and

another component parallel to the shear joint plane in the shear direction, which

contributes to the dowel effect. When rock bolts are used to support rock slope and

underground excavations they are affected by axial and shear loading during

movement on the blocks (Figure 3.1). Bolt behaviour under load and how the load is

transferred along its length is important. These are discussed in this chapter. This

chapter consists of two main parts. The first part summarises studies undertaken by

various workers on shear behaviour, and the second part describes the laboratory

tests conducted to define the material properties used in the next chapters.

These studies were first initiated by Dulascka (1972), she was then followed by

Bjurstrom (1974), Haas (1976,1981), Azuar (1977,79), Hibin and Motojim (1981),

Egger and Fernands (1983) and Ludvig (1983), Gerard (1983), Dight (1983),


52

Bjornfot & Stephansson (1984), Larsson (1984), Schubert (1984), Lorig (1985),

Yoshinaka et al. (1987) Spang and Egger, (1990), Stillberg (1991), Holmberg

(1991), Egger and Zabuski (1991), Ferrero (1995), Robbert (1995), Pellet and

Boulon (1995), Pellet et al. (1995, 1996), Goris et al. (1996), Grasselli et al (1999),

Grasselli (2005) and Mahony (2005) worked on the mechanical behaviour of rock

bolts.

Figure 3.1. Stability issues in rock mass reinforced by fully grouted bolts

All experimental testing of grouted bolts were performed as a single shear test using

single shear apparatus, which results in difficulties in the shear joint due to non-

equilibrium and non uniform load on the shear joint. None of the works included

applying tensile loads on the bolt but several studies applied confining pressure on

the moving block. Thus a new method is designed in present research to evaluate

bolt bending in a proper manner, which is discussed later.

Tunnel axis

Rock Joint

Bolt

• •

• •

• •

Ground surface


53

3.2. PAST RESEARCH

Dulascka (1972) established the following expression to find the shear force carried

by a bolt, based on an idealised stress distribution at the point of contact. Her theory

was based on the development of a plastic hinge at the point of maximum moment

given by;

(3.1)

where;

T = Shear force carried by bolt

cσ = Uniaxial compressive strength of rock

bD = Bolt diameter

yσ = Yield stress of bolt

β = Angle between bolt and normal to the joint

The crushing strength of the concrete was at least four times greater than the

compressive strength. As shown in Figure 3.2 there is no static equilibrium

condition in both sides of the shear joint, which limits the system.

Bjurstrom (1974) direct shear test on cement grouted bolts in granite blocks was

aimed at evaluating the influence of various factors affecting the shear strength of

rock joints. The bolts had inclinations between 30o-90o with respect to the joint

surface. He found that for angle <40o bolts failed in tension and for angles >40o the

bolts failed in a combination of shear and tension.

]1)sin03.0

(1[2.0 22 −+=

βσσσ

y

cybDT


54

Figure 3.2. Shear test arrangement in (a) and (b) probable load generation (after Dulasck 1972)

Bjurstrom provided an analytical solution based on an equilibrium of forces acting

on the system and expressed that the total shear strength of a bolt reinforced joint

was dependent on the following three parameters:

i) Shear resistance due to reinforcement effect:

)sin(cos ϕββ tagpTb += (3.2)

where;

bT = The reinforcement effect in shear resistance due to bolting

p = Axial load corresponding to the yield strength due to shear displacement

� = Initial angle between bolt and joint direction

(a) (b)


55

� = The friction angle of the joint

ii) Shear resistance due to the dowel effect:

5.02 )(67.0 cybd dT σσ= (3.3)

where;

bd = Bolt diameter

yσ = Bolt yield strength

cσ = Uniaxial compression strength of the rock

iii) Shear resistance due to friction of joint:

jnjf tagAT ϕσ= (3.4)

where;

jA = Joint area

nσ = Normal stress on joint and

jϕ = Joint friction angle

According to Bjurstrom the total contribution from the bolt to the shear strength of

the joint, shown in Figure 3.3, is given as:

5.02 )(67.0)sin(cos cybt DtagpT σσϕββ ++= + jnj tagA ϕσ (3.5)

Bjurstrom’s estimate of the contribution to increase in strength is acceptable at first

glance, however the mode of failure in surrounding materials was neglected, which is

a limitation.


56

Figure 3.3. Components of shear resistance offered by a bolt (after Bjurstrom, 1974)

Hass (1976) carried out a series of single shear tests on chalk and limestone and

reported that the block split during shearing. The stresses on both sides of the shear

joint were suggested to be different which is not a realistic situation around the shear

joint plane (Figure 3.4a). If the loading were truly symmetrical there would be an

equal probability of either block splitting. To better distribute the shear load, Hass

applied a large bearing plate on the moving block, but it was unsuccessful. Figure

3.4b shows the deformed bar subjected to lateral loading. It reveals a non-uniform

situation along the joint plane. It is clearly understood that the single shear test has

difficulties in equal load distribution in the shear joint. One method of minimising

this problem was to by maintaining high confining pressures in order to reduce the

imbalance in the vicinity of the shear joint plane. Non-uniform stress distribution

across the shear joint plane was also investigated by numerical analysis (Afridi and et


57

al, 2001), thus confirming the existence of a non-equilibrium condition across the

shear joint sides (Figure 3.5).

Figure 3.4. (a) Block splitting in one side of shear joint (b) non equilibrium situation in vicinity of shear joint

Figure 3.5. (a) Finite element mesh and (b) deviatoric of stress distribution across the joint (Afridi and et al. 2001)

a b

Hole diameter

Fracture


58

Azuar (1977) found that for bolt installed perpendicular to the joint, the frictional

effect is negligible. This finding is not consistent with the confining theories, which

attribute part of the increase in strength to a frictional component. Azuar also found;

i. The maximum contribution of a rock bolt to the shear resistance of a joint is

influence by bolt orientation to the joint surface. It ranges from 60 to 80 %

of the ultimate tension load of the bolt is installed perpendicularly, and 90

% for an inclined bolt.

ii. The friction characteristics of the joint do not influence the contribution of

the bolt.

iii. For a given shear displacement, dilatancy increases the resistance of the

bolted joint.

Hibino and Motojima (1981) reported on shear tests on non grouted 2 mm diameter

bolts installed in concrete blocks. They considered bolts placed in 2 mm and 40 mm

borehole for fully bonded and point anchored respectively, and reported that:

i. For a given shear displacement the shear resistance of fully bonded bolts

was significantly higher than point anchored ones.

ii. The shear resistance did not increased by bolt inclination. This is in

contrast with other investigators.

iii. Pre-tension loading the bolt reduced the shear displacement but did not

influence shear resistance. This result is not consistent with the laboratory

and numerical results obtained by this author and discussed later in the

thesis.

Hass (1981) reported on the laboratory tests on limestone with artificially cut joints

reinforced by different types of bolts and different orientations (0o, +45o and -45o) to


59

the shear plane, as shown in Figure 3.6. He suggested that bolts would act more

effectively when they are inclined at an acute angle to the shear surface rather than in

the opposite direction, as they tend to elongate as shearing progresses.

The total shear strength offered by a bolt was given by the summation of the bolt

contribution and frictional strength along the shear surface from stress on the shear

plane. Hass could not apply the bolt pre-tension effect because the device designed

was incapable. With increased shear displacement the bars started to pull into the

rock and consequently bolt resistance was reduced. However for bolts with a bearing

plate, the shear resistance increased around 23%.

Figure 3.6. Arrangement for bolt shear testing (after Hass, 1981)


60

Dight (1982) conducted a theoretical analysis of the grouted bolt performance. Dight

assumed that the bolt contribution to the strength of a sheared joint was a resultant of

tensile force in the bolt and the dowel effect (Figure 3.7). The angle of dilation was

given by the following relationship:

Angle of Dilation = iv

tag =− )(1

δδ

Figure 3.7. General deformation patterns for a dowel in shear

The dowel force was determined by Eq (3.6)

))(1(7.14

22

yuyp t

tp

dt −= πσ (3.6)

where;

Reinforcing bar

Grout


61

up = The bearing capacity of the grout or rock t = Axial bolt load in the position of the plastic moment,

yt = Axial load corresponding to the yield strength

yσ = Yield stress of the steel,

d = Bolt diameter

And at the magnitude of pt , the location of plastic hinge was as follows:

))(1(58.0 2

yu

ypg t

tp

dl −=σ

(3.7)

Dight did not make any predictions on bolt behaviour in elastic conditions, if tension

prevails then the yield strength develops immediately. He considered the Eq (3.8)

for a component of axial load in shear and suggested the bolt contribution would be a

summation of Eqs (3.6) and (3.8).

)(cos(sin itagtt byc ++= ϕθθ (3.8)

where;

θ = The angle between the normal vector to the joint and the bolt, and bϕ is the

basic joint friction angle.

Dight reported:

i. The normal stress acting on the joint plane does not influence shear

resistance which is against the criterion of joint confining effect and results

reported by Saeb and Amadei (1992).


62

ii. Joints with inclined bolts had stiffer behaviour than those perpendicular

ones. The deformed length of the bolt was related to the deformability of

the rock.

Egger and Fernandez (1983) carried out tests in a high capacity press on samples of

bolted concrete blocks, and found:

i. The optimum angle of bolt inclination with respect to the joint varied from

30o to 60o. However Sharma and Pande (1988) found that the best direction

of reinforcement is normal to the major joint direction.

ii. Perpendicular bolts appeared to have the lowest shear resistance.

iii. Shear displacement at failure was minimal for bolts inclined between 40o

and 50o.

Ludvig (1983) performed tests on swellex bolts, split sets, and two sizes of non –

grouted bars. The bolts were at 45o and 90o to the shear joint. Under shear the tube

bolts were generally weaker than the solid bars. He suggested that the swellex bolt

has approximately the same shear resistance as a solid 14 mm diameter non - grouted

bar.

Schubert (1984) proposed an analytical analysis based on the equilibrium of forces

acting on the deformed system and conducted shear tests on bolted concrete and

limestone blocks. The sketch of the shear device used by Schubert is shown in Figure

3.8. His results lead to the following findings:

i. The deformability of the surrounding rock is important for bolt reaction.

ii. Bolts embedded in harder rock require smaller displacements for attaining a

given resistance than those in softer rock.

iii. Soft steels improve the deformability of the bolted system in soft rock.


63

Yoshinaka et al. (1987) study on the direct shearing of 16 mm diameter bolt

suggested 35o –55o angles against the joint plane as most favourable. In addition, a

perpendicular bolt showed lowest contribution to shearing compared to those at a

low angles (Figure3.9). Moreover, no pre-tension was considered.

Figure 3.8. Shear test machine used by Schubert (after Schubert1984)

Figure 3.9. Relationship between shear stress and shear displacement (after Yoshinaka 1987)

Shea

r Str

ess

(MPa

)

Shear displacement (mm)


64

Spang and Egger (1990) made an extensive series of shear tests on grouted bolts and

used sandstone, concrete, and granite. They found the maximum bolt contribution to

the shear strength of the joint was a function of the ultimate strength of the bolt, Tu.

)45.085.0()](sin01.055.1[14.0207.1 φσβσ tagiTT ccuo +++= − (3.9)

where;

uT = Ultimate strength of the bolt

cσ = The uniaxial compressive strength of the rock,

� = Inclination between the bolt and the shear surface

i = Dilation

d = Dimeter of the bolt

� = Friction angle of the joint and following Eq (3.10 ) was expressed for the

shear deformation of the bolt.

]cos

)70

(1)[2.562.552.15( 125.028.014.0

ββ

σσσ tag

duc

cco −+−= −− (3.10)

But this theory was limited to:

i. Steel bolts grouted with cement,

ii. Borehole diameter approximately twice that of the bolt,

iii. A uniaxial strength of rock between 10-70 MPa,

iv. Deformation formula is not accepted for bolts perpendicular to the joint (�

=90o) and,

v. Bolt not subjected to pre-tension

Egger and Zabuski (1991) carried out a single shear test on small diameter bolts

between 2.5 mm to 5 mm. Tests were made without the normal pressure and no pre-

tension across the joint. Figure 3.10 shows the direct shear test apparatus. Bolts


65

failed under a combination of shear and axial forces. Only low strength steel was

used as the technique was not suitable for high strength steel because the load

distributed on the shear joint was not uniform or in equilibrium.

Figure 3.10. Direct shear test device (after Egger and Zabuski 1991)

Holmberg (1991) theoretically examined the mechanical behaviour of non-tension

grouted rock bolts in elastic and yielding conditions. His analytical model was based

on the equilibrium of forces acting on the deformed system. He expressed three

stages and an ultimate condition of bolt, grout interaction. These stages are shown in

Figure 3.11 and were distinguished as follows:

i Bolt and surrounding medium are in an elastic state,

ii Bolt is in elastic and surrounding medium in a yielding state,

iii Bolt and surrounding medium are yielded,

iv Ultimate condition.


66

Holmberg’s theory disregarded the influence of the grout material. The following

conclusions were drawn:

a: Elastic condition b: Elastic bolt and yielding subgrade

c: Yielding bolt and yielding sub-grade

Figure 3.11. Bolt grout behaviour (after Holmberge 1991)

yl up

y

yuy =

tyT

tT

d: Ultimate condition


67

i. The bolt contribution to the shear resistance of a bolted joint from dowelling

and axial load can be determined as a function of deformation for different

load conditions,

ii. The initial angle of the bolt with respect to the direction of deformation is of

minor importance compared to the maximum resistance of the bolted joint,

iii. The initial angle has a great influence on the maximum deformation of the

bolt,

iv. A bolt inclination of 60o with respect to the direction of deformation reduces

the total deformation by four fold compared to a bolt perpendicular to the

direction of deformation,

v. When a steel bolt crushes into the rock mass and develops a shape similar to a

crank handle its ability to resist larger deformation before failure is increased

significantly,

In a jointed rock mass the shear resistance becomes important where the bolt

intersects the joint. When deformation occurs in the rock mass the grouted rock bolt

will be subjected to loading which generates axial and lateral forces in the bolt

(Figure 3.12). Factors influencing include, bolt and hole diameter, steel quality, bolt

elongation, rock and grout strength.

The angle between the bolt and the joint is very important for the behaviour of the

bolted joint surface, especially in determining the type of failure. If the angle is less

than 35o it seems to be a tension failure, and if the angle is approximately 90o, it is in

shear.

Ferrero (1995) proposed a shear strength model for reinforced rock joints based on

the numerical and laboratory studies of large shear blocks. He suggested that the

overall strength of the reinforced joint could be attributed to a combination of the


68

dowel and the incremental axial force due to bar deformation. Figure 3.13 shows the

shear test apparatus which tends to suffer from an out of balance load on the shear

joint plane.

Figure 3.12. A grouted rock bolt subjected to lateral force

Ferrero’s analytical model was applicable to bolts installed perpendicular to the joint

surface in stratified bedding planes. As shown in Figure 3.14, the proposed analytical

model was expressed by

F = ϕαααα tagQtQt rr )cossin(sincos −−− (3.11)

where;

ϕ = Joint friction angle

rt = Load induced in the bolt

Q = Force due to dowel effect

α = Angle between the joint and the dowel axis and

F = Global reinforced joint resistance.


69

According to his experimental and modelling evidence, Ferrero suggested failure

could possible occur in one of the following ways, depending on the prevalent type

of stress:

i. Failure due to the combination of the axial and shear force acting at the

bolt-joint intersection.

ii. Failure due to the axial force following the formation of hinge points.

Figure 3.13. Ferrero’s shear test machine

Figure 3.14. Resistance mechanism of a reinforced rock joint (after Ferrero 1995)


70

The first yielding mechanism is likely to occur with stiffer and stronger rock at the

bolt, joint plane intersection under a combination of shear and normal forces.

As shown in Figure 3.15, the bolt is loaded by the axial and frictional forces that

develop between the bolt and surrounding grout.

The following equations were developed to describe the relationship between the bar

tension at the point of maximum moment and bolt, joint intersection respectively.

0

20

2 yx

Dpt bur = (3.12)

5.12

0

20

0

20 )

41(

2 x

yy

xDpt bur += (3.13)

The second failure mechanism occurs when the maximum computed bending

moment in A exceeds the maximum yielding moment of the bolt. Usually this kind

of failure occurs in weak and less stiff rocks.

Figure 3.15. Forces acting on the failure mechanism (after Ferrero 1995)


71

The yielding conditions propagate from the plastic hinges up to the joint intersection,

which causes tensile stress to affect the bolt. However, Ferrero stated that pre-tension

does not influence maximum resistance of the system. This appeared to be in contrast

with both the experimental and numerical studies undertaken in this current thesis,

which is discussed later in Chapters 5 and 7.

Pellet and Egger (1995) analytical model for the contribution of bolts to the shear

strength of a rock joint, took into account the interaction between the axial and the

shear forces mobilised in the bolt, and large plastic displacements of the bolt during

loading. A description of bolt behaviour must be divided in two sections. The first

concerns the elastic range (from the beginning of the loading process) and the second

deals with the plastic range (from the yield to the failure of the bolt). The shape of

the stressed bolt and the failure envelope for both elastic and plastic deformations are

shown in Figure 3.16 and Figure 3.17 respectively. They used the Tresca criterion as

a failure criterion for the bolt.

a)

(a)


72

b)

Figure 3.16. Force components and deformation of a bolt, a) in elastic zone, and b) in plastic zone (after Pellet and Eager 1995)

a)

b)

Figure 3.17. Evolution of shear and axial forces in a bolt, a) in elastic zone, and b) in plastic zone (after Pellet and Egger, 1995)

Relationship between axial and shear forces in elastic conditions

Axial and shear forces at the yield limit

Yield limit

Failure criterion

Axial and shear forces at failure


73

The shear forces at the end of both the elastic limit and plastic region are obtained

from Eq 3.14 and Eq 3.15 respectively.

)4

(5.0 oeelb

buoe ND

DpQ −=σπ

(3.14)

22

2

)(1618 ecb

ofec

bof

D

NDQ

σπσπ

−= (3.15)

where;

oeQ = Shear force acting at point O at the yield stress of the bolt

oeN = Axial force acting at shear plane at the yield stress of the bolt

elσ = Yield stress of the bolt

bD = Dimeter of the bolt

ofQ = Shear force acting at shear plane at failure of the bolt

ofN = Axial force acting at shear plane at failure of the bolt

ecσ = Failure stress of the bolt

The displacement of the bolt in elastic and plastic stages were expressed by the

following equations:

βπ sin

8192344

4

ub

oeoe

pDE

bQU = (3.16)

)sin(

sin

opu

opoeof p

QU

ωβω∆−

∆= (3.17)

Where opω∆ = )sin)(1(cossinarccos[ 2222 βββf

e

f

e

ll

ll

−± (3.18)


74

where:

el = Distance between bolt extremity (point O) and the location of the maximum

bending moment (point A)

fl = The length of the part O-A at failure

Pellet and Eagers’ evaluations showed that bolt inclination has a significant influence

on maximum joint displacement. The greatest displacement is reached when the bolt

is normal to the joint. As the angle between bolt and joint decreased, displacement

drops rapidly (Figure 3.18).

Figure 3.18. Joint displacement as a function of angle � for different UCS value (after Pellet 1994)

Pellet’s theory is valid for the inclined bolts less than 90o and is not properly

acceptable for bolts sharply perpendicular to the joints.

Robert (1995) reported shear tests on smooth bars and cone bolts by his double shear

apparatus. He found that failure only happened in one of the joint intersections. His

results showed a non-symmetric situation on both sides of the shear joint, which is


75

likely due to the generation of imbalance in three blocks and is contradicted with

results from DSS in this research (see experimental results in Chapter 5).

Goris et al (1996) carried out a direct shear tests on 69 MPa concrete blocks with in

joint surface area of 0.078 m2 (Figure 3.19). A 15.24 mm diameter cable bolt (258

kN yield strength) was placed perpendicularly into a 25.9 mm diameter hole. It was

found that yield occurred at 220 kN with 4 mm of displacement, which is higher than

the double shear test carried out on the same type of cable bolt. It appears that the

single shear test has a higher shear resistance than the double shear test. This is due

to an unequal distribution of load on the shear joint and concentration of load

through the blocks in front of the bolt, which pushes them together (zone A) resulting

in a higher shear resistance which is not an actual bolt contribution. Another

limitation of the test set up was the maximum shear displacement available being

limited to 46 mm, which prevented the cable from failing.

Figure 3.19. Shear block test assembly (after Goris and et al. 1996)

A


76

3.3. PRE-TENSION EFFECT IN FULLY GROUTED BOLTS

A bolt under tension compresses the rock, which prevents bed separation and

frictional forces developing between the layers, but this does not mean that more

tension creates better stability (Peng 1992). When a bolt is pre-tension loaded it

would influence the shear strength of the joint with forces acting both perpendicular

and parallel to the sheared joint by inducing confining pressure. A general rule for

determining maximum pre-tension is that it should not exceed 60% of the bolt yield

strength or 60% of the anchorage capacity.

Nearly all the tests that were conducted by various authors related to bolt behaviour

under shear were accomplished without pre-tension loading. However, in field

studies and numerical simulations, pre-tension loading was applied and it was

unanimously agreed that it increases reinforcement and improves stability, Lang et

al. 1979, Maleki 1992, Peng and Guo 1992, Jafari and Vutukuri 1994, 1998, Stankus

and Guo 1997, Unrug and Thompson 2002, Zhang and Peng 2002, and Hebblewhite

2005. However, numerical studies placed limitations on bolt, grout, rock contact

interfaces. In addition no experimental tests were conducted to apply pre-tension in

fully encapsulated high strength bolts, especially an evaluation of bolt profile on

shear resistance under various levels of pre-tension loading. In this current research

whole assumptions and limitations from both laboratory and numerical design were

carefully removed. Pre-tension loading was conducted in 0, 5, 10, 20, 50, and 80 kN

loads in laboratory and numerical simulations. In the numerical chapter a new design

of bolt model and contact interfaces is discussed. As discussed above, there are pros

and cons in each method used so far. A brief review of the methods is shown in

Table 3.1.


77

Author Base of the method Advantages Disadvantages

Dulascka (1972)

Development of plastic hinge after max. Moment

Prediction of shear force by bolt

Non static equilibrium condition in shear joint

Bjurstrom (1973)

Equilibrium forces acting on the system

Estimation of shear resistance: due to dowel, reinforcement and friction effect,

Mode of failure in surrounding materials was neglected

Hass (1976)

Single shear test Test were performed on real rocks

Non-uniform stress distribution along the shear joint

Azuar (1977)

Single shear test Different bolt angles were considered

Influence of friction effect could not properly considered

Hibino (1981)

Single shear test Pre-tension was applied

Pre-tension and bolt’s inclination could not considered properly

Hass (1981)

Single shear test Real rocks with different bolt angles were considered

Pre-tension was not applied

Dight (1982)

Theoretical analysis The prediction of dowel effect and hinge point was considered

Neglecting the bolt behaviour in elastic range, poor effect of normal stress on joint

Egger and Fernandz (1983)

Single shear test Different bolt angles was applied

Pre-tension was not applied

Ludvige (1983)

Single shear test Different bolt angles was applied

No fully grouted bolt was tested

Schubert (1984)

Equilibrium forces acting on the deformed system

Real rocks was tested

Pre-tension was not considered

Yashinaka (1987)

Direct shear test Different bolt angles was considered

Pre-tension could not apply

Spang and Egger (1990)

Single shear test Real rocks was tested, max bolt contribution and displacement was predicted

Limited in: grout types, annulus thickness, rock strength and pre-tension

Egger and Zabuski (1991)

Single shear test Prediction of bolt failure at a combination of axial and shear

No joint confinement and bolt pre-tension was considered

Table 3.1. A brief comparison of the used methods in bolt shear behaviour


78

Author Base of the method Advantages Disadvantages Holmberge (1991)

The equilibrium of forces acting on the deformed bar

Bolt behaviour was analysed in both elastic and plastic stages

The effect of grout was disregarded

Ferrero (1995)

Single shear test The plastic stage of the system was considered

In-capability of the method to show the effect of pre-tension

Pellet and Egger (1995)

Theoretical analysis Both elastic and plastic stages was analysed

The effect of grout material was neglected

Goris et al. (1996)

Single shear test Perpendicular bolts was analysed

Non-equilibrium load distribution on the shear joint, Max. Displacement was up to 46 mm

Grasselli (2005)

Double shear test Symmetric situation around the shear joint

Bolt pre-tension was not considered

Mahoni, et al. (2005)

Single shear test Lengthy bolt-grout-concrete anchorage

-

Aziz et al (2005)

Double shear test

Symmetric situation around the shear joint, pretension effect, bolt profile, any grout, bolt & hole diameter

The size of the shear box is small for large bolt diameters and strong steel bolts

3.4. MECHANICAL PROPERTIES OF REINFORCING

MATERIALS

In this part the strength properties of bolts, resin, and concrete are studied. All the

tests were carried out in the laboratory under controlled conditions. Parameters

examined include uniaxial compression strength, shear strength, and modulus of

deformations. These parameters are pertinent to the overall study of the load transfer

mechanism of bolts, resin, and concrete interactions.

3.4.1. Bolt types

Seven different types were tested for tensile strength. Three bolts are the popular

types used widely by the Australian mining industry. Figure 3.20 shows the

Table 3.1. Continued


79

photographs for various bolts and Table 3.2 lists their physical specifications. They

are similar in diameter core size, but have different profile heights and spacings.

Figure 3.21 shows the general profile details of the bolts. Tensile, bending, and shear

strength of the steel bolt are the most important mechanical parameters that influence

its behaviour when loaded axially and in shear.

Figure 3.20. Different Bolt Types used for axial and shear behaviour tests

Figure 3.21. Profiles specification

Rib Spacing Rib Width

Outer Diam. (mm)

Core Diam. (mm)

Rib Height

T1 T2 T4 T5 T6 T3


80

3.4.2. Bolt strength tests

Three kinds of laboratory tests were carried out on different Types of bolts (Table

3.2). They are:

• Tensile strength

• Bending strength

• Direct shear test

Table 3.2. Physical specifications of different bolt types

Bolt

Bolt

Commercial

name

Rib

Spacing

(mm)

Core

diameter

(mm)

Rib

height

(mm)

T1 AX 11.5 21.7 1.0

T2 AXR 12 21.7 1.5

T3 JX 24.0 21.7 1.2

T4 Deformed 9.7 19.6 1.3

T5 All Thread 1.4 10.3 0.6

T6 N12 7.74 11.7 0.8

3.4.2.1. Tensile strength test

A 33 cm bolt length, was cut and tested for tensile strength by pull testing. A

universal Instron tensile testing machine was used to carry out the tensile test. The

tensile test on all re-bar specimens were carried out in accordance with the Australian

Standards for tensile tests No AS 1391. A typical tensile test arrangement is shown in

Figure 3.22. The test specimen was installed between the two large grips of the

testing machine and then loaded in tension. The computer controlled tensile test

loaded the specimen at a constant rate until failure. While the test progressed load


81

and displacement values were monitored by the computer. The load displacement

curves in Figure 3.24 to 3.27 show a typical behaviour of the steel with elastic

behaviour in the beginning of the test and small displacement till yielding point.

Beyond the yield point the bolt will deform without any further increase in the load

until it is strain hardened. Finally the bolt fails when the cross section contracts in the

form of a cap and cone known as (necking).

Figure 3.22. Bolt clamped in Instron Universal Testing Machine

As can be seen from the loading profile of the tested bolt (Figure 3.23) the following

features were deduced;

a) Elastic range

b) Yield point

c) Elasto-plastic range

d) Failure range

The yield strength is an important factor in determining tension, which influences its

performance. It should be noted that although a roof bolt of high yield strength is

desirable, its use in situ should be avoided. When a high strength bolt fails it is most

Bolt

Grips


82

likely to shoot out of the hole so quickly it could severely injure anyone in its path

(Peng 1986). Accordingly, current bolts used in mines are 320 kN. The value of the

yield and ultimate failure loads in all types of bolts are described in Table 3.3.

Table 3.3. Bolt tensile strength

Figure 3.23. Stretching of the bolts after tensile test

Bolt Yield Point (kN)

Tensile Strength

(kN)

Yield stress (MPa)

Ultimate stress (MPa)

T1 260 328 683 862

T2 256 342 673 900

T3 210 358 552 942

T4 163 194 518 617

T5 38 44 365 423

T6 57 67 501 593

Necking/Yielding/Failure

T1 T2 T3 T4 T5 T6


83

Figure 3.24. Load- deflection curve at tensile test in various bolts

Figure 3.25. Load- deflection curve at tensile test of Bolt Type T5 and T6

3.4.2.2. Three point load bending test

For a better understanding of the bending behaviour of the bolts used, several tests

were carried out in 3PLBT (three point load bending test). Figure 3.28 shows the

three point load test set up. Three types of bolts used for axial and double shearing

tests were tested under pure bending by this method. The bending behaviour of Bolt

Figure 3.26. Load- deflection curve at tensile test in cable bolt

Figure 3.27. Load- deflection curve at tensile test of Bolt Type T4

T

T6

T5

T3

0

50

100

150

200

250

300

350

400

0 20 40 60 80

Displacement (mm)

Tens

ile L

oad

(kN

) . T1

T2

0

50

100

150

200

250

300

0 5 10 15

Displacement (mm)

Ten

sile

load

(kN

)

.

0

50

100

150

200

250

0 10 20 30 40 50 60

Displacement (mm)

Ten

sile

load

(kN

)


84

Types T1, T2 and T3 is displayed in Figure 3.29. Bolt Type T1 has the lowest

bending strength while Bolt Types T2 and T3 exhibited higher bending loads

Figure 3.28. Three point load bending test set up

Figure 3.29. Load- displacement behaviour of 3PLBT

3.4.2.3. Direct shear test

The direct shear tests were carried out with a guillotine especially designed with

replaceable bushes to ensure a proper fit and that the bolt will not bend before being

sheared. The shear forces are the resultant of shear stresses distributed over the cross

sectional area and act parallel to the cut surface. Figure 3.30 shows the average shear

load versus shear displacement for Bolt Type T1 and T3 respectively.

Table 3.4 shows the results of direct shear tests two types of bolts. The direct shear

test was conducted in an Instron 8033 Servo Controlled 50 tone Compression Testing

Machine.

0

10

20

30

40

50

60

0 10 20 30 40

Displacement (mm)

Load

(K

N)

AXRJABAX

T2 T3 T1


85

Figure 3.30. direct shear test trend in Bolt Types T1 and T3

Table 3.4. Specification of bolts shear test

3.4.3. Resin grout

Epoxy and polyester resins are the most commonly forms of chemicals used in bolt

installation in Australian Mines. The most popular type used is the resin combination

sausage capsule supplied by Minova Australia (formerly known as Fosrock Mining).

Strength tests was carried out on resin, including uniaxial compression tests, double

shear tests, and modulus deformation tests. These tests were carried out on slow

setting (20 minutes) PB1 Mix and Pour resin. A longer setting time was essential for

Bolt type Shear load (kN)

Shear strength (MPa)

Displacement (mm)

T3 236.3 638.12 6.5 T3 237.2 641.3 6 T3 237 640.8 7.3

Average 236.83 640 6.6 T1 237 641 7.2 T1 241.5 653 7 T1 239.8 648.4 6.6

Average 239.43 647.5 6.93

0

50

100

150

200

250

0 2 4 6 8

Shear displacement (mm)

Shea

r Loa

d (k

N)

.

T1T3


86

the strength tests. The diameter of the prepared samples was different for different

tests carried out.

a) Uniaxial Compression Test: A uniaxial compression test is the most common

test performed on rock and other samples, in this case resin. The samples prepared

were 50 mm diameter and the length to diameter tests was 2.5: 1. The samples were

cast in a special plastic mould and tests were accomplished with an Instron machine

of 500 kN capacity. A constant displacement rate of 0.25 mm/min was used to load

the samples to failure. In reality, tested samples break similar to Figure 3.31 and

sometimes the failure cracks are parallel to the axial direction. Figure 3.32 shows the

compression test set up and subsequent tests undertaken. Although simple, care must

be taken when carrying out the test so that errors are minimised and interpretations

are as accurate as possible. The procedure for conducting a UCS test was carried out

in accordance with International Rock Mechanics Standards. Samples were polished

and cut till the height to diameter ratio of 2.5 –3 was achieved. Table 3.5 list the

details of the samples tested and the UCS values obtained. Seven samples were

tested. The average UCS values were 70.8 MPa with SD of +/- 2.55. The UCS

Value obtained was in agreement with the manufacturer’s specified strength of 71

MPa. Figure 3.33 shows the relationship between stress and strain in resin. Figure

3.34 displays the load versus displacement. Some of sample was instrumented with

strain gauges to monitor, axial and lateral deformation of the sample during loading

process.

b) Shear Strength: The shear strength tests were undertaken using double shear

tests with a 50 tonne Avery machine as shown in Figure 3.35. The samples were

prepared by casting in specially prepared moulds 32 mm diameter, which fitted snug

inside the double shear barrel. Four tests were carried out with the average shear


87

strength of 16.2 MPa +/- 1.1 standard deviation. The resin was different from the

sausage type as it had a setting time of 20 minutes, allowing for a proper preparation

of the samples.

Figure 3.31. Typical fracture plane and fracture angle for compression test samples

Table 3.5. Summary of the results obtained from UCS test

Sample Length (mm)

Failure load (KN)

Ucs (MPa)

S1 72.74 146.12 74.42 S3 79.54 142.74 72.7 S4 99 133.5 68 S5 79.5 143 72.7 S6 99 134 68 S7 97.75 136 69 S8 89.8 140 71 SD SD = Standard deviation 70.8 ± 2.5

α

Fracture Plane

Angle of Fracture

Hemispherical Seating

Resin Sample


88

Figure 3.32. Compression test set up

Figure 3.33. Stress strain curve for resin

UCS=73 MPa, E= 10500 MPa Poisson ratio=0.26

0

10

20

30

40

50

60

70

80

-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

strain

Axi

al s

tress

(MPa

)

.

axiallateral

Strain gauge


89

Figure 3.34. Load versus displacement

32mm diameter samples of resin were cast in PVC tube 100mm long for double

shear test. Each sample was placed inside the double shear testing rig and then

loaded by the Avery testing machine until they failed at a standard rate of 2.5 kN per

minute. The double shear test rig is outlined in Figure 3.35. There are two shear

locations to accurately determine the shear properties of the material being tested. A

total of four double shear tests were conducted to accurately determine the peak

shear force of the resin and to ensure consistency of both testing methods and results.

Sample measurements are shown in Table 3.6.

Table 3.6. Double shear test specifications

Sample Diameter

(mm)

Sample area

(mm*2)

Failure load

(kN)

Shear strength

(MPa)

S1 31.95 801.7 25 15.6

S2 31.88 798.2 26.2 16.4

S3 31.95 801.7 28.5 17.7

S4 31.9 800 24.6 15.3

S.D SD = standard deviation 16.2 ± 1.1

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6

Axial displacement (mm)

Com

pres

sive

load

(kN

)

.


90

a b

Figure 3.35. Double shear test set up (a) shear box set up (b) induced loads

3.4.4. Concrete

3.4.4.1. Uniaxial compressive strength

Four nominal strength 20, 40, 50 and 100 MPa concretes were used in the double

shearing tests. These strengths compare well with the range of rock strength. Some

cylindrical samples from each batch were cast to measure the strength of the

concrete. It was tested in compression to ensure that the required strength had been

obtained. Figure 3.36a & b show the sample during the test and the concrete blocks

after taking out from the water tank.

The modulus of elasticity was calculated from equation which was expressed from

Australia standard AS3600 (1994) and also the typical value of Poisson’s ratio

specified by AS3600 is 0.2.

(3. 19) cmc fE 5.1043.0 ρ=

32 mm

Location of Shear Failure


91

A suitable expression, which applies for concrete excess of 50 MPa, has been

recommended by ACI Committee 363 (1992):

(3. 20)

where;

cE = Modulus of elasticity (MPa)

ρ = Concrete density )/( 3mkg

cmf = Mean value of the concrete compressive strength at the relevant age (MPa)

a b

Figure 3.36. Concrete sample: (a) concrete under the test (b) concrete after 30 days

3.4.4.2. Concrete joint surface properties

In order to estimate the strengthening effect of bolting one has to know the friction

properties of unbolted joints. For this reason a series of direct shear tests was

performed on specimens of broken and intact concrete under a variety of normal

loads. All the samples were tested in direct shear using a direct shear machine, and

some important parameters can obtained such as, peak shear strength, residual shear

69003320 += cmc fE


92

strength, cohesion and angle of internal friction (See Moosavi and Bawden 2003).

The specimen was positioned and then the lower half of the sample was potted in the

shear box ring with the potting compound. After the compound hardened the

appropriate thickness of Plexiglas sheets were placed on top of the lower shear box

to form the shear plane. Whereas the specimen being tested had a weakness plane

(concrete, concrete interface) it was placed in the shear machine such that the joint

plane coincided with the plane of the machine. The friction joint angle can be

estimated by performing repeated shear tests under different normal loads. To

estimate shear resistance of a joint Barton (1966) developed an empirical model

(Brady and Brown 1985). Which can be written as following.

(3.21)

Where, pτ = peak shear stress, nσ = normal stress, JRC = joint roughness coefficient,

JCS = joint compressive strength, and bϕ basic friction angle.

From the data analysis it was found that the joint surface cohesion in both concrete

20 and 40 MPa was zero and the angle of friction was 31 and 38 degree respectively

(Figure 3.37 a and b). As Figure 3.38 shows, once the peak shear strength was

overcome, there was considerable loss of shear resistance. From the laboratory

results the concrete specifications were found as shown in Table 3.7. Also it was

found that the relation between shear stress and normal stress was nearly 0.9 to 1.7

normal stress in 20 and 40 MPa concrete respectively.

��

��

�+= b

nnp

JCSJRCtg ϕ

σστ )(log10


93

a b Figure 3.37. Variation of peak shear stress versus different normal stress in shear joint plane in a: 20 MPa and b: 40 MPa concrete

Table 3.7. Concrete joint properties

Ucs Strength (MPa)

Modulus of Elasticity (MPa)

Poisson ratio Friction angle (o)

20 21000 0.2 31 40 30000 0.2 38 50 30500 0.2 - 100 40100 0.2 -

Figure 3.38. Shear load –versus shear displacement in joint plane in 40 MPa concrete

00.5

11.5

22.5

33.5

44.5

5

0 2 4 6

Normal stress (MPa)

She

ar s

tres

s (M

Pa)

.

0

2

4

6

8

10

12

0 2 4 6

Normal stress (MPa)

She

ar s

tress

(MP

a)

.

0

5

10

15

20

25

0 5 10 15 20 25

displacement (mm)

She

ar lo

ad (k

N)

2.5 kN7.5 kN5 kN


94

3.5. SUMMARY

The following were deduced from the review of bolt reinforcement across the

joint planes;

• Bolt orientation, dowel effect, installation type (full encapsulation versus

point anchor), joint surface friction, bolt material type, medium strength are

important factors for the bolt effectiveness in joint reinforcement

• Bolts installed at inclination to the sheared joint plane contribute to a greater

resistance to shearing than perpendicular bolts.

• The effectiveness of bending and location of the hinge points across the

joint planes is influenced by the pre-tension loads and subsequent

development of axial loads along the bolt.

• There was no reported citing of any study making reference to bolt surface

profile configuration on the load transfer mechanism across the bolt.

• There are no reported results in the case of diversity of resin thickness and

quantitative significance of shear resistance mechanism in different

surrounding rock strengths.

• The effect of pre-tension load on shear behaviour and load transfer

mechanism was not subjected to qualitative analysis.

• All reported shear tests were conducted under single shear test condition,

where there will undoubtedly be asymmetric and a non-uniform distribution

of load across the joint plane.

It is clear that for bolts shearing under symmetrical conditions, the bolt profile

configuration and changes in axial loads require further investigation and to achieve

these aims, extensive laboratory tests were under taken together with numerical


95

simulations and analytical studies which are the subject of research reported in this

thesis

Documents

A new approach in determining the load transfer mechanism