Laboratory Modelling of Shear Modelling of Shear Behaviour of Soft Joints Under Vonstan Normal Stiffness Conditiosn

8/12/2019 Laboratory Modelling of Shear Modelling of Shear Behaviour of Soft Joints Under Vonstan Normal Stiffness Conditiosn

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Laboratory modelling of shear

behaviour of soft joints under constant normal stiffness conditionsB. INDRARATNA, A. HAQUE and N. AZIZ

Department of Civil & Mining Engineering, University of Wollongong, NSW 2522, Australia E-mail: [email protected]

Received 25 June 1997Accepted 28 November 1997

Summary

Shear behaviour of regular sawtooth rock joints produced from casting plaster are investigated underconstant normal stiffness (CNS) conditions. Test results obtained in this investigation are alsocompared with the constant normal load (CNL) tests. It is observed that the peak shear stressobtained under CNL conditions always underestimates the peak shear stress corresponding to theCNS condition. Plots of shear stress against normal stress show that a nonlinear (curved) strengthenvelope is acceptable for soft rock joints subjected to a CNS condition, in compa rison with theline ar or bilinear en velopes often proposed for a CNL condition. Models proposed by Patton (1966)and Barton (1973) have also been considered for the predictions of peak shear stress of soft jointsunder CNS conditions. Although Pattons model is appropriate for low asperity angles, itoverestimates the shear strength in the low to medium normal stress range at higher asperity angles.In contrast, while Bartons model is realistic for the CNL condition, it seems to be inappropriate formodelling the shear behaviour of soft joints under CNS conditions. The effect of inll material onthe shear behaviour of the model joints is also investigated, and it is found that a small thickness of bentonite inll reduces the peak stress signicantly. The peak shear stress almost approached that of the shear strength of inll when the inll thickness to asperity height ratio ( t/a ) reached 1.40. Thispaper also introduces an original, empirical shear strength envelope to account for the change innormal stress and surface degradation during CNS shearing.

Keywords: Joints, laboratory tests, models, shear strength, testing methods.

Introduction

The correct evaluation of shear strength of rock joints plays an important role in the designof excavations in rocks, stability analysis of rock slopes and design of rock-socketed piles.The shear behaviour of planar rock joints can be investigated in the laboratory by using aconventional direct shear apparatus where the normal load is kept constant (CNL) duringthe shearing process. However, for nonplanar discontinuities, shearing results in dilation asone asperity overrides another, and if the surrounding rock mass is unable to deform

sufciently, then an inevitable increase in the normal stress occurs during shearing.Therefore, the CNL condition is unrealistic in circumstances where the normal stress in the

Geotechnical and Geological Engineering , 1998, 16 1744

09603182 1998 Chapman & Hall Ltd


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eld changes considerably during the shearing process. In view of this, the direct shearapparatus was modied to accommodate the change in normal stress with dilation duringshearing, thereby making the mode of shearing occur under constant normal stiffness(CNS).

In the past, shear behaviour of hard concrete and cement mortar joints as well as naturalhard rock joints has been investigated using the CNS technique by Johnston and Lam(1989), Ohnishi and Dharmaratne (1990), Archambault et al . (1990), Skinas et al . (1990)and Habereld and Johnston (1994). I t is well known that under the CNL condition, theshear strength of rock joints decreases signicantly due t o the presence of inll materials(Bertacchi and Zaninetti, 1986; Papaliangas et al ., 1993; de Toledo and de Freitas, 1993).However, only limited studies are found in relation to CNS testing of inlled joints, suchas Cheng et al . (1996) w ho argued that the shear stress against the normal stress responseis purely frictional and is independent of the inll thickness. This study is an attempt tofurther investigate the shear behaviour of soft joints under CNS conditions, with special

reference to the inuence of inll.

Applicability of the constant normal stiffness method

The presence of joints in a rock mass can affect its mechanical behaviour depending on theunderground situation. When dilation of the rock joints during shearing is constrained orpartially constrained, an increase in the normal stress over the shear plane occurs whichsubstantially increases the shear resistance. Figure 1 shows an underground excavationwhere potentially unstable rock blocks are constrained between two parallel dilatant rock

joints. The sliding of such block inevitably increases the normal stress, and also, dilationbecomes signicant if the joint surfaces are rough. The increase in normal stress on theshear plane is equal to k .d v, where k is the stiffness of the surrounding rock mass and d vis the dilation. Tests conducted under constant normal load (CNL) condition yield shearstrengths that are too low for such practical situations (Goodman, 1976).

As another example, Figure 2 s hows a rock socketed pile where the interface betweenthe concrete and the socket is considered to be rough. When this pile is loaded vertically,the side shear resistance develops as a function of the variable normal stress associatedwith the dilation of the rough joint surface. The deformation mechanism and the simplied2-D models are given in Figs 2b, 2c and 2d.

In general, the CNL condition is only realistic for shearing of planar interfaces where

the normal stress applied to the shear plane remains relatively constant such as i n the ca seof rock slope stability problems. However, for situations as illustrated in Figs 1 and 2, t hedevelopment of shear resistance is a function of constant normal stiffness (CNS), and theuse of CNL test results for such cases leads to underestimated shear strengths.

Laboratory investigation

In order to study the shear behaviour of soft rock joints under a constant normal stiffness(CNS) condition, tests were conducted on gypsum plaster joints of identical surfaceproles. A view of the test apparatus developed at the Uni versity of Wollongong, whichcan perform both CNS and CNL testing, is given i n Fig. 3. T he plaster joint (in two halves)was cast within the twin-box assembly, where the bottom box can move only in the

18 Indraratna et al.


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horizontal direction, while the top box can move only in the vertical direction duringshearing. The sizes of the joint specimens that can be cast inside the top and bottom boxesare 250 75 150 mm and 250 75 100 mm, respectively. The apparatus has normaland shear load capacities of 180 kN and 120 kN, respectively. In the current study, shearloads were applied through a horizontal strain controlled device, and a strain rate of

Fig. 1. Joint behaviour at the top of an excavation

Modelling the shear behaviour of soft joints 19


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0.50 mm/min was used for all tests. Changes in normal and shear stress during shearingwere recorded through digital strain meters tted on the axial and horizontal load cells. Anassembly of springs of known stiffness ( k 8.5 kN/mm) was used to simulate the constantnormal stiffness of the rock mass surrounding the joint, as shown in Fig. 3.

Fig. 2. Idealized displacement behaviour of pile socketed in rock (after Johnston & Lam,1989)



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Model material

Gypsum plaster (CaSO 4.H2O hemihydrate, 98%) can be used to make idealized soft rock joints, mainly because this material is universally available and is inexpensive. It can bemoulded into any shape when mixed with water, and the long-term strength is independentof time once the chemical hydration is completed. The initial setting time of plaster isabout 25 minutes when mixed with 60% water by weight. The basic properties of themodel material were determined by performing many tests on 50 mm diameter specimens

Fig. 3. The constant normal stiffness (CNS) shear testing apparatus



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after a curing period of two weeks at an oven-controlled temperature of 50C. The curedplaster showed a consistent uniaxial compressive strength ( c) of 11 to 13 MPa and aYoungs modulus ( E ) of 1.9 to 2.3 GPa. It is found to be suitable for simulating thebehaviour of jointed soft rocks such as coal, friable limestone, clay shale and mudstone. Acomprehensive evaluation of the gypsum plaster rock based on dimensionless strengthfactors is given elsewhere by Indraratna (1990).

Commercial bentonite was used as an inll material between joint interfaces. Directshear tests were conducted on this inll material, and the results showed that its behaviouris similar to a compacted earthll with a peak frictional angle of 34 and a residual valueof 32. In a separate study, Phien-wej et al . (1990) veried that bentonite is representativeof an array of prototype inll materials in relation to the shear strength.

Specimen preparation

The top and bottom moulds were detached from the shear apparatus for casting thespecimens inside it. Plaster was initially mixed with water in the ratio of 5:3 by weight.Subsequently, the bottom mould together with the collar at bottom was lled with themixture and left for at least an hour to ensure adequate hardening before casting the upperspecimen. The bottom of the collar was shaped according to the desired surface prole,and in this study, triangular asperities with an angle of incli nation (i ) of 9.5 (Type I),18.5 (Type II) and 26.5 (Type III) were tested as shown in Fig. 4. A lthough triangularasperities may not ideally represent the more irregular or wavy type of joint proles in theeld, they still provide a simplied basis for comparing the CNL behaviour with CNS.

After one joint prole was cast in this manner, the top mould was then placed over thebottom mould and lled with the plaster mixture, and the whole assembly wassubsequently cured for another hour at room temperature to complete initial setting. A thinpolythene paper was inserted between the two moulds separating the two fully mated jointsurfaces. During specimen preparation, mild vibration was applied to the mouldsexternally to eliminate any entrapped air. Once initial hardening had taken place, themoulds were stripped and the specimens were cured at 50C inside an oven for two weeks.Before testing, the specimens were allowed to cool down to the room temperature.

Inll joints were prepared by lling the specially designed collar which was externallytted to the top of the bottom specimen. The collar has the same geometric prole requiredfor the joint surface, and it can be adjusted to give any predetermined thickness. Theextended portion was then lled with bentonite having a moisture content of 8.5 ( 1)%.The surface of the inll was levelled carefully and inserted inside the shear box. Once thelower joint surface was prepared, the top half of the joint specimen was placed over it tocomplete the joint assembly.

Test results and discussions

Type I joints: Sawtooth interface with inclination (i) of 9.5

Tests were conducted on many specimens of identical regular sawtooth proles in the largeshear apparatus under constant normal stiffness ( k 8.5 kN/mm), as well as under



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constant normal load (CNL) conditions. The same initial normal stresses ( no 0.16, 0.30,0.56, 1.10, 1.63 and 2.43 MPa) were used in all tests to compare the results of CNS withCNL condition. It is found that CNL tests always underestimate the peak shear stress, andalso at higher normal stresses, they indicate a more pronounced strain-softening behaviour(Fig. 5). T herefore, in practice, the CNS test results will yield more economical design in

jointed rock masses. Skinas et al . (1990) also reported similar observations based on sandbarytescement joints, which, however, are more representative of harder rock types ratherthan soft joints.

The variation of normal stresses was recorded through a digital strain meter as shearingwas progressed. For various initial normal stresses ( no), tests were conduct ed to derive therelationship between the normal stress and the horizontal displacemen t (Fig. 5). T henormal stress generally increases when the asperities on the top half of the joint overridethose on the bottom half, until the peak to peak contact is made to give the maximumdilation. The subsequent downwar d movem ent indicates a gradually decreasing normalstress as shown in the lower part of Fig. 5. H owever, at considerably higher normal stresslevels ( no 2.43 MPa), this trend is not observed because of the shearing of asperities.The dilation of the joint in relation to vertical moveme nt was me asured together with thecorresponding horizontal displacement at a given no (Fig. 6) f or both CNL and CNSconditions under the known normal stiffness of k 8.5 kN/mm. It is observed that theCNL condition always overestimates the dilation of joints, thereby underestimating the

Fig. 4. Interface proles of Type I, II and III joints



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Fig. 5. Variation of shear stress and normal stress with horizontal displacement for Type I joints(i 9.5)



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actual peak shear stress corresponding to the eld conditions. The gradient (linear) of thedilation-normal stress lines (Fig. 6, right-hand side) is representative of the normalstiffness applied to the joint specimens. It is observed that at elevated no values, asexpected, the measured dilation becomes smaller.

The variations of shear stress against normal stress for selected tests under both CN Sand CNL conditions subjected to the same no values are plotted together in Fig. 7 f orcomparison. It is observed that the bilinear CNL peak stress envelope represents an upperbound for all tests, whereas the linear peak stress envelope is more suitable for the CNScondition, with regard to the initial normal stress range between 0.16 and 2.43 MPa. Asobserved in Fig. 7, t he pre-peak stress path of a CNS test tends to follow the strengthenvelope before the maximum shear stress is approached. In other words, the pre-peak behaviour of one CNS test is often adequate to give a good indication of the gradient of the failure envelope, especially under low normal stress levels. In contrast, for theconventional CNL approach, several tests are required to be conducted under differentnormal stress levels to obtain the complete shear strength envelop e. Similar observationshave also been reported by Ohnishi and Dharmaratne (1990) f or cementsand jointssimulating hard rock surfaces.

Type II joints: Sawtooth interfaces with inclination (i) of 18.5

Several tests were conducted on Type II joints under the same initial loading conditions asin Type I. The initial normal stress ( no) was varied from 0.05 to 2.43 MPa. As shown inFig. 8, a well dened peak shear stress curve is observed for all the tests, and the maximum

shear stress is attained at a lower horizontal strain as the initial normal stress is increased.The rate of increase in normal stress during shearing seems to be more pronounced underlow initial normal stress. At high initial normal stresses (e.g. no 2.43 MPa), signicantshearing of asperities is associated with an almost constant normal stress in comparisonwith the curves corresponding to lower no values. In fact, this behaviour is similar to theconventional shearing of planar surfaces at constant normal stress.

The effect of initial normal stress and stiffness on joint dilation is also investigated andillustrated in Fig. 9. It is obvious that dilation increases with decreasing initial normalstress. Also as expected, the Type II joints ( i 18.5) cause a greater degree of dilation forthe same no rmal stres s levels, in comparison with the Type I ( i 9.5) joints previously

illustrated in Fig. 6.

Type III joints: Sawtooth interfaces with inclination (i) of 26.5

Tests were conducted on Type III specimens under the same initial normal stresses asapplied for Type I and II joints. As expected, well-dened, peak shear stress curves wereobtained corresponding to small shear displacements. The rate of increase in normal stressis signicant at low initial normal stress, and shearing through asperities occurred atelevated normal stress level s (Fig. 10).

The shear stress and normal stress relationship for Type I, II and III proles are plottedin Fig. 11 f or comparison. It is observed that a nonlinear peak stress envelope is moreapplicable for interface Type II and III, whereas a linear envelope is sufcient for Type I



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Fig. 6. Effect of initial normal stress and stiffness on dilation of type I joints ( i 9.5)


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joints. Benchmark tests were also conducted on planar interfaces at different normalstress levels where an average basic friction angle ( b) of 37.5 was obtained. Thebehaviour of Type II and III joints ( i 18.5 and 26.5) represented by the nonlinearenvelope can be explained as follows. At low normal stresses, the apparent friction angleis signicantly greater than b because of the enhanced shearing resistance offered by theangular asperities. However, at elevated stress levels, increased degradation of asperities isassociated with a reduction of the apparent friction angle, which tends to approach thebasic friction angle for planar surfaces at high stress levels after considerable shearing. Incontrast, Type I joints ( i 9.5) are less frictional due to the smaller angle of asperities,and their behaviour does not indicate a pronounced nonlinear trend. The apparent frictionangle remains relatively constant at around 47. Moreover, as discussed earlier for Type I

joints in Fig. 7, t he CNS stress paths (pre-peak) tend to follow the strength envelope in thecase of Type II and III joints as well, particularly at lowmedium stress levels( n 1.5 MPa).

Fig. 7. Shear stress versus normal stress curves for Type I joints ( i 9.5) under CNL and CNSconditions



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Fig. 8. Variation of shear stress and normal stress with horizontal displacement for Type II joints(i 18.5) under CNS conditions



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Fig. 9. Effect of initial normal stress on dilation of Type II joints ( i 18.5) under CNS conditions


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Fig. 10. Variation of shear stress and normal stress with horizontal displacement for Type III joints(i 26.5) under CNS conditions



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Shear tests on sawtooth (Type I) inll joints

Tests were carried out on bentonite lled joints for various thicknesses ( t 1 to 4 mm)using Type I joint proles under an initial normal stress of 0.16 MPa and 0.30 MPa. Thevariation of shear stress with horizontal displacement are shown in Figs 12a a nd 13a. It isobserved that even a small inll thickness of 1 mm is capable of reducing the peak shearstrength of fresh joints by approximately 50%. As the inll thickness is increased further,the peak shear stress is found to decrease accordingly, ultimately approaching the shearstrength of pure inll at a thickness of 4 mm ( t / a 1.40). The effect of inll thickness onthe joint dilations and normal stress increments was recorded during shearing, and isplotted in Figs 12(b, c) and 13(b, c). I t is observed that as the inll thickness increases, thechange in dilation and normal stress with horizontal displacement becomes gradual. Infact, when the t/a ratio is equal to or greater than unity, the shear behaviour becomessimilar to the tests conducted under the CNL condition. For a t/a ratio of 1.60 (i.e. inll

Fig. 11. Shear stress versus normal stress curves for Type I, II and III joints under CNSconditions



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Fig. 12. Shear behaviour of inlled Type I joint under no 0.16 MPa



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Fig. 13. Shear behaviour of inlled Type I joint under no 0.30 MPa



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thickness of 4 mm), the reduction in normal stress is associated with joint compression(negative dilation) as shown in Figs 12c a nd 13c.

The peak shear stress vs normal stress relationships reported by Papaliangas et al .(1993) and Phien-wej et al . (1990) reveal that the friction angle determined by CNL testingdecreases with an increase in inll thickness, and it becomes equal to that of the inll ata certain stage. In contrast, test results reported by Cheng et al . (1996) on i 22.5asperities of concreterock joints under CNS conditions indicate that the apparent frictionangle is independent of the inll thickness. Based on the current study conducted on soft

joints, the variation of shear stress against normal stress for different inll thickness isplotted in Fig. 14. It is observed that the apparent shear strength of the joint decreasesrapidly with a small amount of inll. At a t/a ratio o f 1.40, th e shear strength of the jointbecomes equal to that of the pure inll as shown in Fig. 17.

Shear tests on sawtooth (Type II) inll joints

Five tests were conducted on Type II joints for various inll thicknesses ( t 1.5 to 9 mm)under an initial normal stress of 0.30 MPa. The shear behaviour of all the tests are plottedin Fig. 15 f or comparison with that of the no inll joint. The drop in peak shear stress of the inlled joints becomes insignicant as the inll thickness is increased beyond 7 mm oras t/a exceeds 1.40 (Fig. 15a). T he increase in normal stress is observed until the t/a ratioexceeds 1.0, beyond which a decrease in no rmal stress is noted (Fig. 15b). This isassociated with the joint compressive behaviour (Fig. 15c) suggesting that the inuence of asperities is now negligible.

The shear deformation corresponding to the peak shear stress for various t/a ratios (Fig.15a) show that the horizontal displacement drops signicantly as the t/a ratio of 1.40 isapproached. Therefore, the t/a ratio of 1.40 can be considered as critical for

no 0.30 MPa. A similar type of behaviour was also reported by Phien-wej et al . (1990)for tests carried out under a constant normal load (CNL) condition. However, for CNLtests, the actual t/a ratios were observed to be much higher (exceeding 2), even at smallnormal stresses.

The variation in shear stress with normal stress is plotted in Fig. 16, r epresenting typicalstress paths. It is observed that once the t/a ratio of 1.40 is exceeded, the corresponding

stress path plots to the left (i.e. reduction in both shear and normal stress). If the critical t/aratio is not exceeded, then the stress paths plot to the right indicating an increase in normalstress at all times.

The peak shear stress obtained for Type II inlled joints is plotted against t/a ratiotogether with the no inll joints in Fig. 17. It is observed that the joint strength decreasesby almost 50% due to the addition of a thin layer of inll (say, 1.5 mm). As the inllthickness is increased further, the peak shear stress continues to drop gradually, and aftera certain value of t/a ratio is reached (1.40), further decrease in strength becomes marginal.Figure 17 c learly illustrates that as the t/a ratio increases, the overall joint strengthapproaches that of the pure bentonite inll (or becomes asymptotic). Furthermore, the dropin peak shear stress is much steeper for Type II joints than for Type I joints. This isnaturally because of the higher asperity angle.



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Fig. 14. Stress path plots for inlled Type I joints under CNS conditions



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Fig. 15. Shear behaviour of inlled Type II joint under no 0.30 MPa



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Models for peak shear strength envelope

Patton (1966) conducted a series of tests on regular sawteeth articial joints under constantnormal load conditions (CNL). A bilinear shear strength envelope tted these tests resultsvery well. This envelope can be rewritten in the following forms:

For asperity sliding: p(CNL) n(CNL) tan( b i0) (1)For asperity shearing: p(CNL) c n(CNL) tan( b) (2)

where, CNL constant normal load condition, p peak shear stress, n normal stress,b basic friction angle, c cohesion intercept and i0 initial asperity angle. According

to Patton (1966), t he sliding of asperities takes place under low normal stress, but after acertain magnitude of stress is exceeded, shearing through asperities takes place. Incontrast, other researchers considered simultaneous sliding and shearing to obtain differentstrength envelope s (Barton, 1973; Maksimovic, 1996). It has been observed that the peak shear strength predicted by Pattons model at lowmedium normal stress generallyoverestimates the actual strength.

Barton (1973) i ntroduced a nonlinear strength envelope for nonplanar rock joints for theconstant normal load (CNL) condition as

p

n CNLtan b JRC log 10 c

n(CNL)(3)

Fig. 16. Stress path plots for inlled Type II joints under CNS conditions



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where, b (d n sn), d n peak dilation angle which decreases with an increase innormal stress and sn angle due to shearing of asperities which increases with an increaseof the normal stress as more surface degradation occurs. JRC joint roughness coefcientand c uniaxial compression strength.

The method suggested by Xie and Pariseau (1992) can be used to dene the value of JRC for the Type I, II and III sawteeth proles in the current study, as explainedbelow:

JRC 85.27( D 1)0.57 (4)where

Dlog(4)

log 2 1 cos tan 12h L

In the above, D fractal dimension, h average height of asperity and L average baselength of asperities. Accordingly, JRC values of 4.2, 9.0 and 13.8 were calculated for TypeI, II and III joints, respectively. These values are very close to the simplied methodsuggested by Maksimovic (1996) where the JRC value is considered as half of the initialasperity angle (i.e. io /2).

Fig. 17. Variation of peak shear stress ( peak ) with ( t/a ) ratio for inlled Type I and II joints



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Assuming that at the peak shear strength under the CNS condition, normal stressmomentarily remains constant, Equation 3 (Barton, 1973) can then be employed toestimate the peak shear strength. The shear strength predicted in this m anner for a rangeof normal stresses seems to underestimate the laboratory measurements (Table 1). Seideland Habereld (1995) reported similar conclusions when Bartons model was employed topredict the peak shear strength of hard concreterock joints.

In order to incorporate the effect of asperities on the extent of dilation and surfacedegradation, the behaviour of Typ e I, II and III join ts could be represented by thefollowing equations adopted from Jing et al . (1993) and modied to suit the CNScondition:

Type I: i pi0 1n(CNS)

c

0.19

(5a)

Type II: i pi0 1n(CNS)

c

1.5

(5b)

Type III: i pi0

1 n(CNS)c

3.0

(5c)

Table 1. Experimental and model predicted results of peak shear stress

Experimental results Predicted peak shear stress (MPa)

Asperity type

Initialnormal

stress,no (MPa) n (MPa) peak (MPa)

Barton(1973) Patton(1966) Proposedmodel

0.16 0.53 0.49 0.53 0.57 0.570.30 0.69 0.66 0.64 0.74 0.74

Type I 0.56 0.94 1.01 0.85 1.00 1.00(i 9.5) 1.10 1.50 1.54 1.32 1.61 1.60

1.63 1.83 1.80 1.60 1.97 1.952.43 2.54 2.72 2.24 2.82 2.78

0.05 0.37 0.57 0.46 0.55 0.550.16 0.85 1.30 0.95 1.26 1.18

Type II 0.30 0.92 1.36 1.02 1.36 1.27(i 18.5) 0.56 1.29 1.86 1.36 1.91 1.731.10 1.65 2.25 1.68 2.17 2.16

1.63 1.97 2.44 1.96 2.41 2.522.43 2.57 3.12 2.47 2.87 3.15

0.05 0.61 1.07 0.83 1.13 0.980.16 0.71 1.14 0.98 1.40 1.180.30 1.05 1.61 1.30 2.00 1.59

Type III 0.56 1.13 1.68 1.50 2.41 1.84(i 26.5) 1.10 1.36 2.05 1.83 2.57 2.23

1.63 1.88 2.82 2.16 2.83 2.592.43 2.58 3.35 2.75 3.35 3.16



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where, ip

total dilation angle at peak shear stress under CNS condition, n(CNS) normalstress corresponding to peak shear stress for a given no, c uniaxial compressionstrength, i0 initial angle of asperity.

The increase in normal stress under CNS condition is governed by the amount of dilation of the joints during shearing . In Fig. 18, t he measured dilation ( d v) is divided bythe height of the asperity ( a ) to demonstrate that the normalised ratio ( d v / a ) has a uniquerelationship with the initial normal stress ( no) for a given joint prole. It is veried thatan exponential relationship exists between the ratio, d v / a and no, represented by thefollowing empirical equations:

Joint Prole Type I:d va

0.67 exp( 0.78 no) (6a)

Joint Prole Type II: d va

0.63 exp( 0.97 no) (6b)

Fig. 18. Variation of d v / a with initial normal stress for prole Type I, II and III



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Joint Prole Type III:d va

0.38 exp( 1.02 no) (6c)

The normal stress n(CNS) corresponding to peak shear stress under the constant normalstiffness (CNS) condition can be computed by knowing the associated dilation and normalstiffness of the joints. In order to compare with experimental results, the predicted dilationfor different proles were corrected by the normal compliance of the apparatus which wasdetermined independently.

Once the angle ip

is known, the total friction angle ( ) corresponding to the peak shearstress can be evaluated from ( b i p). The peak shear strength can then be obtained byreplacing io in Equation 1 with the value of i p obtained from Equation 5. Based on thisanalysis, the authors propose the following strength envelope for CNS testing of soft

joints:

p

n CNStan b i0 1

n(CNS)

c(7)

where, n(CNS) ( no k.d v / A) normal stress corresponding to peak shear stress for agiven no under constant normal stiffness condition, k normal stiffness (kN/mm),d v dilation corresponding to peak shear stress (mm), A joint surface area (mm

2) andis a surface property which accounts for the degradation of joints.Equation 7 i s employed to predict the peak shear strength for Type I, II and III proles

for the range ofno

from 0.05 to 2.43 MPa. It is veried that the proposed model predictsthe she ar strength m ore closely, especially in the low to medium stress range, than othermodels (Table 1). The stresses obtained from Equations 1 and 2 (Patton, 1966) andEquation 7 p roposed by the authors are plotted together with the experimental results inFig. 19. It i s evident that the proposed nonlinear equation describes the peak shear strengthenvelope more closely than Pattons bilinear model, for constant normal stiffnessconditions.

Application of the stressdilation relationships

For a given joint stiffness, Equations 5 a nd 6 ca n be used to predict the total dilation angleand the dilation corresponding to peak shear stress for the Type I, II and III proles. Theincremental normal stress ( k.d v / A) for each test is then calculated, and subsequently, theshear strength relationship given by Equation 7 is employed to determine the peak shearstress at the corresponding normal stress. Table 1 s ummarizes the measured and predictedvalues of peak shear stress and the corresponding normal stress for Type I, II and IIIproles, under constant normal stiffness ( k ) of 8.5 kN/mm. Based on this approach , Fig. 19illustrates a comparison between the measured and predicted strength envelopes. Ingeneral, the predicted strength envelopes are in good agreement with the observed results.However, for a wider range of normal stresses (e.g. in the case of hard rock joints), thismodel may not be directly applicable for describing the shear behaviour of joints.



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Conclusions

This investigation veries that the shear behaviour of soft joints under constant normalstiffness (CNS) is different to the conventional shear response observed under constantnormal load (CNL) conditions. In CNL testing, the measured dilation is always greaterthan the CNS testing, hence, CNL data underestimate the peak shear stress of joints. TheCNS experimental results dene a nonlinear shear strength envelope for soft joints incontrast to a bilinear envelope observed for CNL testing. It is of interest to note that priorto attaining the peak shear stress, the stress paths corresponding to CNS tests tend topropagate along the strength envelope, especially at low to medium initial normal stresses( no 1.5 MPa). Pattons (1966) equation overestimates the peak strength for higherasperity angles where joint degradation is inevitable during sliding . Bartons (1973) modelseems to underestimate the shear strength under CNS conditions, although it is adequatefor describing the shear behaviour under CNL conditions. A nonlinear empirical strength

Fig. 19. Experimental and model predicted peak shear stress envelopes for prole Types I, II andIII



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envelope is proposed for soft simulated joints which includes the effect of asperitygeometry and the extent of dilation during shearing.

The shear strength of inll joints is observed to decrease rapidly with an increase ininll thickness. The variation of peak shear stress with inll thickness/asperity height ratio(t/a ) conrms that the peak stress decreases by approximately 50% for t/a 0.40, andbecomes equal to that of the inll for a t/a ratio approaching and exceeding 1.40.

References

Archambault, G., Fortin, M., Gill, D.E., Aubertin, M. and Ladanyi, B. (1990) Experimentalinvestigations for an algorithm simulating the effect of variable normal stiffness ondiscontinuities shear strength, in Proceedings of the International Symposium on Rock Joints ,Leon, Norway, Barton, N. and Stephansson, O. (eds), Balkema, A.A., Rotterdam, pp.1418.

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