Shear Behaviour of Jointed Rock: A State of Art

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SHEAR BEHAVIOUR OF JOINTED ROCK: A STATE OF ART

A.K. Shrivastava Lecturer, Department of Civil Engineering, Delhi College of Engineering, Delhi–110 042, India. E-mail: aksrivastava@dce.ac.in K.S. Rao

Professor, Department of Civil Engineering, Indian Institute of Technology, New Delhi, India. E-mail: raoks@civil.iitd.ernet.in

ABSTRACT: The rock joints are mechanical discontinuities of geological origin. The presence of joints, fractures and other plane of weakness reduce the shear strength of rock. Realistic evaluation of the shear strength of rock joints plays an important role in the design of deep underground openings in jointed rocks, stability analysis of rock slopes, rock socketed piles, anchored rock slopes.

Various parameters like, joint roughness, scale, stiffness of the surrounding rock mass, shear rate, condition of the joint i.e. unfilled joint/infilled joint, infill type, infill thickess and drainage condition of the infill material influence the shear behaviour of rock joint. The influence of these parameters on shear strength of jointed rock has been studied by different researchers such as Patton (1966), Barton & Choubey (1977), Indrartna & Haque (1998, 1999), and Weildeniya (2005). Based on their laboratory, analytical and numerical studies various shear strength models have been proposed. In this paper a critical review is attempted to study the influence of these parameter on the shear behavior of jointed rock.

It has been observed that for non planar joint where the dilation of the joint is resisted by surrounding rock mass, CNS is a proper boundary condition to investigate the shear behavior of joint than the CNL boundary condition and CNS boundary condition will result in higher shear strength. The effect of infill material and its thickness is to reduce the shear strength of the rock joint. Shear rate, influences significantly the shear behavior of rock joint. 1. INTRODUCTION

Rock is heterogeneous and quite often discontinuous, i.e. rock masses are typically jointed. These rock joints are the mechanical discontinuities of geological origin. These discontinuities may be in the form of joints, faults, bedding planes or other recurrent planar fractures. In general the engineering properties of rock with discontinuities have quite different properties from those of intact rock, and in many cases, the discontinuities completely dominate the performance of the in situ rock mass. The presence of joints, fractures and other plane of weakness reduce the shear strength.

Most likely mode of failure plays an important role to decide relevant range of stress for testing, joint set or sets which need testing, and method of testing for proper planning of investigations of joint shear strength. The mode of failure is controlled by the orientation of the joints with respect to the loading directions, and spacing of the joint.

Therefore correct evaluation of the shear strength of rock joints plays an important role in the design of deep under- ground openings in jointed rocks, stability analysis of rock slopes and risk assessment of underground waste disposal.

Shear strength of rock joints depends on the following factors: (a) stiffness of the surrounding rock mass (b) shear rate (c) joint roughness (d) size of joint i.e. scale effect (e) joint condition i.e. unfilled joint/infilled joint. A critical

review is attempted in this paper to study the influence of some of this parameter on the shear behavior of jointed rock.

2. REVIEWS ON FACTORS EFFECTING SHEAR BEHAVIOUR OF ROCK JOINT

There are many factors which influence the shear behaviour of the rock joint. The effect of following three parameters has been discussed in this review.

2.1 Stiffness of the Surrounding Rock Mass

The shear behaviour of planar rock joints can be investigated in the laboratory by using a conventional direct shear apparatus where the normal load is kept constant (CNL) during the shearing process. This particular mode of shearing is suitable for situations where the surrounding rock freely allows the joint to shear without restricting the dilation, thereby keeping normal stress constant during shearing process. Shear testing under a Constant Normal Load (CNL) boundary condition is only beneficial for cases such as non-reinforced rock slopes.

However, for no planar discontinuities, shearing results in dilation as one asperity overrides another, and if the surrounding rock mass is unable to deform sufficiently, then an inevitable increase in the normal stress occurs during shearing. Therefore, shearing of rough joints under such

IGC 2009, Guntur, INDIA

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circumstances no longer takes place under Constant Normal Load (CNL), but rather under variable normal load where stiffness of the surrounding rock mass plays an important role in the shear behaviour. This particular mode of shearing is called as shearing under Constant Normal Stiffness (CNS) boundary conditions. For deep underground opening or rock anchor-reinforced slopes or socketed piles shear tests under CNL condition are not appropriate. A more representative behaviour of joints would be achieved if the shear tests were carried out under boundary conditions of Constant Normal Stiffness (CNS).

2.1.1 Shear Behaviour of Joint under CNL Boundary Condition

In the past several researchers have attempted to explain the shear strength of rock discontinuities under CNL boundary conditions. Linear failure criteria provided by Mohr-Coulomb.

t f = ca + s n tan F r (1)

Bilinear failure criterion proposed by Patton (1966), offer a more realistic representation of the shear stress that can be developed along clean (unfilled) discontinuities. These criteria divide a typical curved envelope into two linear segments. The maximum shear strength that can be developed at failure is approximated by the following equations:

At low normal stress, t f = s n tan (F u+ i) (2)

It must be recognized that failure envelopes developed from shear tests on rock are generally curved. However, at high normal stress failure envelopes can be closely approximated by the linear Coulomb equation,

t f = ca+ s n tan F r (3) where, t f = maximum (peak) shear strength at failure, s n = stress normal to the shear plane (discontinuity), ? u = the basic friction angle on smooth planar sliding surface, i = angle of inclination of the first order (major) asperities, ca = the apparent cohesion (shear strength intercept) derived from the asperities, ? r = the residual friction angle of the material comprising the asperities.

Barton & Choubey (1977) proposed empirical non-linear equation for peak shear strength of rough unfilled joints based on the results of direct shear tests performed on a wide variety of model tension fractures. The proposed equation for peak shear strength is as follows, which is sensitive both to variable joint roughness and compressive strength for the rock or joint walls:

t = s n tan [JRC log10 (JCS/s n) + F b] (4) The Joint Roughness Coefficient (JRC) represents a sliding scale of roughness which varies from approx 20 to 0, from roughest to the smoothest end of the roughness. The Joint

wall Compressive Strength (JCS) is equal to the unconfined compressive strength (s c) of the rock if the joint is unweathered, but may reduce to approx (1/4 s c) if the joint walls are weathered. Barton has proposed the equation based on the experimental work at very low normal stress i.e. 0.01 < s n/JCS < 0.3. As it can be seen from the equation that when s n tends to zero, the equation cease to be valid.

Comparing the equation 4 and 2, it is clear that the difference between the equation proposed by Patton and Barton is that asperity angle (i) of the Patton is replaced with a term dependent on normal stress that contains JRC and JCS. JRC may either be obtained by back analysing shear test that have been performed or visual comparison of roughness with ten standard profiles and JCS value can be estimated in the field or in the laboratory using Schmidt Hammer index test.

Several researchers have reported that the visual comparison method of estimating JRC value is subjective and hence unreliable. Research has been carried out to find the proper JRC value with statistical parameter or fractal dimensions. Zhao (1997) modified the Barton’s equation for the mismatched joint

t = s n tan [JRC . JMC log10 (JCS/s n) + F b] (5) Where JMC is joint matching coefficient and it is also obtained by visual inspection that the approximate percentage area in contact with upper and lower wall of joint and its value varies from 0 to 1.

These models available in the literature fail to appropriately determine shear behavior of rock due to limitations of boundary condition. Hence a need to develop the failure criterion for the dilating joint under CNS boundary condition to accurately predict the shear behavior is realised.

2.1.2 Shear Behaviour of Joint under CNS Boundary Condition

Shear Strength of non planar discontinuity increases when tested under CNS boundary condition in comparison to CNL boundary condition, because the dilation of the joint is resisted during the shearing process and this restricted dilation increases the normal load on the joint during the shearing process thereby increasing the peak shear resistance. The normal loading condition in CNS boundary condition can be best represented, by modeling the deformability of the surrounding rock mass with a spring of normal stiffness k = ? s n/? y, where ? s n and ? y are respectively, the change in joint normal stress and displacement restricted during the shearing process. CNS boundary condition does not have any influence on the shear behavior of the planar joint because planar joint does not dilate during the shearing process. At very high normal stress, CNL and CNS boundary condition gives similar shear behavior for non planar rock joint, because under high normal stress the asperity breaks and it behaves like planar joint during the shearing process.

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Test results reported by Indrartna et al. (1998) on modeled soft rock joint with asperity angle i = 9.5° reveals that CNL condition always under estimate the peak shear stress of the joint.

The effect of boundary condition is shown in Figure 1 which is based on the result of shear test performed on the soft model material for rock with asperity 15–30° by the author. In CNL boundary condition pear shear displacement does not changes significantly with the change in normal stress. It was also reported that in CNL boundary condition the peak shear displacement was less than 1% of the length of the specimen but under CNS boundary condition peak shear displacement was higher for the given normal stress.

Fig. 1: Effect of Boundary Condition

on Shear Behavior

2.2 Shear Rate

The rate of shearing is very important for correct evaluation of the shear parameter for the analysis such as shearing at slow rate to study the creep effect in the rock slope or at very high rate for study the condition of blast and earthquake. Crawford et al. (1981) based on the experimental study on the rate dependent shear behaviour of rock joint under CNL boundary condition, concluded that for the hard rock there is significant variation of shear resistance with shear displacement, for intermediate hardness the frictional resistance is independent of shear rate. Softer rock at low normal stresses exhibit increase in shear resistance up to a certain shear rate and after which it remain constant and at high normal stress, the resistance remains constant up to some shearing rate after that it decreases.

Indrartna (2000) reported the results of effect of shear rate on the shear behavior of the soft modeled joint under CNS boundary condition and found that the peak shear stress increases considerably with increase in shear rate, especially at shearing rate of more than 0.5 mm per min. Hence it is important to use proper shearing rate under CNL and CNS boundary for all type of rock.

2.3 Joint Infill

The shear behavior of infilled joint can be distinguished on the basis of the interaction between the joint surfaces. The most obvious effect of a filling material on shear behavior is to separate the discontinuity walls and thereby reduce rock to rock contact. Shear behavior is also influenced by the nature of the filling material and the characteristics of the wall-fill interfaces. The shear behaviour of infilled joints depends on many factors and the following are probably the most important: (a) Mineralogy of the filling material (b) Grading or particle size (c) Over consolidation ratio (for clay filling only) (d) Water content and permeability (e) Wall roughness (f) Thickness of infill (g) Fracturing or crushing of wall rock.

Several investigations have reported that thicker the infill, the lower the joint strength. Filled joint have three thickness ranges, which are, interlocking, interfering and non-interfering. Interlocking when the rock surfaces come in contact, interfering when there is no rock contact but the strength of the joint is greater than that of filler alone and non-interfering when joint behaves as the filler itself. The thickness of infill material does not influence much on shear behavior of planar joint but for rough joints it influences appreciably.

Most research results show that when infill thickness is less than the initial asperity height, infill governs the development of shear plane until rock-to-rock contact occurs. Once, the rock came into contact, shear strength is governed by the asperity angle and the strength of the rock surface. When the infill thickness is greater than the asperity height there will be no interaction between the rock to rock and shear behavior of the joint will be governed by shear behavior of the infill alone. There is a critical ratio of thickness to the asperity (t/a) after which the influence of rock is diminished and shear behavior is controlled by infill alone. The critical t/a ratio reported as 2 by Phein-wej et al. (1990), 1 by De Toledo & De Freitas (1993), 1.6 by Indraratna & Haque (1997). Indraratna et al. (1999) based on shear test on bentonite filled joint under CNS and CNL condition concluded that critical t/a ration obtained by CNS test is significantly smaller than that of CNL test. Kutter & Rautenberg (1979), reported that the strength of clay infill joint increases with the increase of surface roughness whereas sand filled joint is less affected by surface roughness. However the overall shear resistance of the joint was reduced as a result of increasing infill thickness. Various shear strength model has been proposed to predict the shear behavior of infilled joint under CNL and CNS boundary condition.

Welideniya (2005) developed a semi empirical method for predicting the shear strength of infilled joints. Figure 2 shows

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the conceptual development of the shear strength model of infilled joints based on two algebraic functions A and B, the summation of which is assumed to give normalised shear strength (t s/s n) for t/a ratio less than the critical value, (t/a)cr. For rough joint without infill t/a = 0, and the normalised shear strength is equal to tan (F b), as proposed by Patton (1966) for clean joints. Function A is introduced to model to show the decrease in influence of tan (F b + i) term with increasing t/a ratio, while function B gradually increases the affect of term tan(? fill), until (t/a)cr is reached (the a and ß coefficients are greater than unity). At (t/a)cr, function A becomes zero and function B becomes equal to tan (? fill).

Hence for t/a < (t/a)cr in the region of asperity interference,

( )( )tan bA i i k α= φ + − (6)

( )fill 2

tan 1 1/

Bk

β = φ × +

(7)

( ) ( ) ( )fill 2

tan tan 1 1/b

nA B i i k

k

βα τ

= + = φ + − + φ × σ + (8)

where, s n = normal stress ? fill = peak friction angle of the infill K = t/a / (t/a)cr. a and ß = empirical constants

Fig. 2: Shear Strength Model for Infilled Joints Showing the Role of ? fill and ? b (after Welideniya 2005)

3. CONCLUSIONS

The main conclusions from the critical review can be summarized as below: (a) Stiffness of the surrounding rock mass appreciably

influences the shear behavior of the rock joint. Non-planar rock joints tested under CNS boundary condition and planar rock joint tested under CNL boundary condition is more appropriate. Testing of non planar rock joint at low normal stress under CNL boundary condition will always under estimate the shear strength.

(b) There is significant variation of shear resistance with shear displacement rate and its effect is different for different types of rock.

(c) The ratio of infill thickness (t) to asperity height (a) i.e. (t/a) ratio, plays an important role during shearing, irrespective of whether the tests are conducted under CNL or CNS boundary conditions.

Hence there is a need to develop an automated large scale direct shear testing machine to study the shear behavior of the jointed rock under CNL and CNS boundary conditions. The machine must have the capability to study the influence of boundary conditions, shearing rate and infill on the shear behavior of rock joint.

REFERENCES

Barton, N. and Choubey, V. (1977). “The Shear Strength of Rock Joints in Theory and Practice”, Rock Mech. 10, 1–54.

Crawford, A.M. and Curran, J.H. (1981). “The Influence of Shear Velocity on the Frictional Resistance of Rock Discontinuities”, Int. J. RockMech. Min. Sci. and Geomech. Abstr. 18, 505–515.

De Toledo, P.E.C. and De Freitas, M.H. (1993). “Laboratory Testing and Parameters Controlling the Shear Strength of Filled Rock Joints”, Geotechnique, 43, 1–19.

Indraratna, B. and Haque, A. (2000). Shear Behaviour of Rock Joints. Rotterdam: Balkema.

Indraratna, B., Haque, A. and Aziz, N. (1997). “Shear Behaviour of Soft Joints Using Large—Scale Shear Apparatus”, Environmental and Safety Concerns in Underground Constructions, Proc. I st Asian Rock Mech. Symp. (ARMS’9) (eds. Lee, H., Hyungsik, Y. and So-Keul, C.), Balkema (Rotterdam) 515–520.

Indraratna, B., Haque, A. and Aziz, N. (1998). Laboratory “Modelling of Shear Behaviour of Soft Joints Under Constant Normal Stiffness Condition”, Geotechnical and Geological Engineering, Vol. 16, 17–44.

Indraratna, B., Haque, A. and Aziz, N. (1999). “Shear Behaviour of Idealized Joints Under Constant Normal Stiffness”, Geotechnique, Vol. 40, 2, 189–200.

A B

A + B

0 (t/a)critical

t/a ratio

Nor

mal

ised

She

ar S

tren

gth

(ts/s

n)

tanF fill

Non-interfering (t/a) > (t/a)cr

Interferring (t/a) < (t/a)cr

Fully interlocking tan(F b + i)

A = tan (F b + i)(1–k)a

B = ( ) 2

tan 1 1/fill k

β φ × +

where, k = (t/a)/ (t/a)cr

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Kutter, H.K. and Rautenberg, A. (1979). “The Residual Shear Strength of Filled Joints in Rock”, Proc. 4th Int. Congr. Rock Mech., Montreux, Vol. 1, 221–227.

Patton, F.D. (1966). “Multiple Modes of Shear Failure in Rock and Related Materials”, PhD Thesis, University of Illinois, Urbana.

Phien-wej, N., Shrestha, U.B. and Rantucci, G. (1990). “Effect of Infill Thickness on Shear Behaviour of Rock Joints”, in Proc. of the Int. Sym. Norway, pp. 289–94.

Tse, R. and Cruden, D.M. (1979). “Estimating Joint Roughness Coefficients”, Int. J. RockMech. Min. Sci. and Geomech. Abstr, 303–307.

Welideniya, H.S. (2005). “Laboratory Evaluation and Modeling of Shear Strength of Infilled Joints Under Constant Normal Stiffness (CNS) Conditions, PhD Thesis, University of Wollongong, Australia.

Zhao, J. (1997). “Joint Surface Matching and Shear Strength”, Part B: JRC-JMC Shear Strength Criterion. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 34, 179–185.