Rock joints behavior under cyclic direct shear tests

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1 Rok joints behavior under yli diret shear tests F.Homand-Etienne, F. Lefevre, T.Belem, M.Souley Laboratoire Environnement Géoméanique & Ouvrages, Eole Nationale Supérieure de Géologie, B.P. 4, Vandoeuvre-lès-Nany, F-545, Frane To ite this paper : Homand-Etienne F., Lefêvre F., Belem T., Souley M. (999). Rok joints behavior under yli diret shear tests. Pro. 37th U.S. Rok Mehanis Symp., June 6-9, 999, Vail, Colorado, Balkema : Rotterdam, pp ABSTRACT: Cyli diret shear tests were arried out on undulated artifiial joints of mortar, aording to onstant normal stress (CNS) and onstant normal stiffness (CNK) loading onditions. The morphomehanial behavior was analyzed in order to better understand the yli behavior of these joints. One parameter was defined to quantify the degradation of the sheared joints. Two models were then proposed to predit the degradation of the anisotropi joints aording to the loading onditions (CNS or CNK) and the shearing mode (monotonous or yli). The degradation model for the CNK ondition was generalized for both loading onditions and this model is in agreement with the undulated joints test results. INTRODUCTION The mehanial properties of rok masses are strongly dependent on the presene of disontinuities or joints. These disontinuities affet the stability of rok engineering strutures (tunnels, mines, underground storages, open pits). The reponse of a rough joint to shear loading depends on its surfae properties as well as the boundary onditions that are applied by surrounding rok mass. These boundary onditions an exist in a variety of forms and between onstant normal stress (CNS), in the ase of slope stability problems near the surfae, to variable or onstant normal stiffness (CNK) in the viinity of underground exavations. Most of studies on the anisotropi joints shear behaviour showed that degradation seemed to be ontrolled more by surfae undulations than by the distribution of the asperities on this surfae. These observations an be interpreted while being based on the onept of primary and seondary asperities (Jing et al., 993; Kana et al., 996). The seondary asperities are defined by the distribution of the surfae points, while the primary asperities are defined by the surfae geometry (undulations). These primary asperities determine and ontrol the loation of the possible ontat areas (thus of degradation) of the joint walls during shearing. The degradation of the joint walls an be approahed in term of diret quantifiation of wear, evolution of roughness or evolution of the dilatany angle (Plesha 987; Hutson and Dowding 99; Benjelloun et al., 99; Jing et al., 993). To our knowledge, exept the ratio of the degraded asperities area, defined by Ladanyi and Arhambault (969), there does not exist in the literature a parameter of diret quantifiation of wear or degradation of the joint walls during shearing. In this paper, we study the influene of the yles of diret shear on the degradation of an undulated artifiial joint of mortar. These tests were arried out aording to CNS and CNK onditions under various levels of normal stress and normal stiffness. The wear of the sheared joints is diretly quantified by the degree of degradation, D w, defined on the basis of the estimation of the atual surfae areas before and after shear tests (Belem et al. 997). Based on our experimental results, a model of degradation predition during shearing was proposed. The model parameters are related to the joint roughness (angularity and anisotropy). 2 EXPERIMENTAL PROCEDURES 2. Material The seleted joint surfae geometry is an artifiial regularly undulated surfae (primary asperities) with amplitude of 2 mm and a period of 25 mm. The investigated samples are made from moulds of 45 x 5 mm 2 dimension by asting with mortar. The 399

2 mortar is a mixture of very fine sand, ement, silia fume and water. The mortar is arefully vibrated in order to get bubblefree samples and after the setting they are ured at 2 C in water during 28 days. 2.2 Shear tests Two series of yli diret shear tests were onduted on several mortar undulated joints aording to the onstant normal stress (CNS) and onstant normal stiffness (CNK) boundary onditions. These tests have been arried out with a new omputer-ontrolled 3D-shear apparatus providing onstant normal load (CNL), onstant normal stress (CNS) and onstant normal stiffness (CNK) shear tests. This shear apparatus run using eletri miromotors. The shear motion is due to two symmetrial and opposite movements of the two shear boxes. The shear and normal loading apaity is 2 kn. Several diret shear tests were arried out under (i) onstant normal stresses ranged between.5 and 6 MPa for CNS ondition, and (ii) onstant normal stiffnesses ranged between. and 3. MPa/mm with different initial normal stresses for CNK ondition. Eah test onsisted of ten yles of forward and reverse shear diretions. All shear tests were performed until a mm shear displaement is ahieved. 2.3 Topography data aquisition In order to quantify the degradation of the sheared joints, topographi measurements were arried out before and after the shear tests with a laser profilometer (Sabbadini et al. 995; Homand- Etienne et al. 995; Belem et al. 997). This equipment allows three-dimensional measurements of the joint wall surfaes. The measurement system uses the laser triangulation priniple between a laser plane and a CCD amera shifted with respet to the laser plane (the laser plane unit and video amera being indeformable). The topographi profile orresponds to the rossing of the laser beam with the sample surfae. The laser profilometer is made up mainly of an optial sensor equipped with a CCD amera of a 5 μm resolution and with a He-Ne laser of 67 nm wavelengths. The design features of the laser beam are: 4 mm length; 5 μm thikness; 5 μm of vertial resolution (z axis); 73 μm of horizontal resolution (x or y axis aording to the sensor position); 5 μm of standard deviation of the error of the white noise due to the mehanial vibration. Before omputing the joint surfae degradation, the row data must be proessed to obtain regularly spaed and detrended data. 3 RESULTS OF CNS SHEAR TESTS 3. Cyli shear behavior Figure shows urves of CNS yli shear tests performed on the undulated joints under normal stresses of and 4 MPa (Figure a and b, respetively). This figure inludes the shear strength (σ t ) and normal displaement (U n ) vs shear displaement (W x ). For the two normal stress levels, the shear strength-shear displaement urves show an inrease of σ t as a funtion of yles while the dilatany (U n ) dereases. This behavior is exatly the opposite of that observed by Hutson and Dowding (99) on undulated artifiial granite joints. The analysis of all the arried out tests leads us to think that the figure a is representative of the response of the undulated joint for tests arried out at σ n < 2 MPa while the figure b is representative of the undulated joint response for tests arried out at σ n 2 MPa. Beyond 5 MPa, surfaes present signifiant degradations due to the failure of the mortar. The observation of sheared surfaes indiates: for σ n 5 MPa, a main effet of morphology (undulations); for σ n > 5 MPa, a main effet of material (mortar). Beause the material is not a natural rok, the dominating effet of morphology on shear behavior has been prioritized. In order to study more preisely the evolution of the shear urves, eah urve was subdivided into 5 parts and results were disussed based on the average values alulated on eah part. Thus, for eah yle the average frition oeffiient μ m (σ t /σ n ) and the average angle of dilatany i m ( ) are alulated in eah part b,, d and e (Figure 2) and for the first part a of the shear urves. Figure 3 shows the variation of average frition angle μ m for eah normal stress level after the yles (top) and 7 (bottom) in the parts b,, d and e. The analysis of all the urves shows that the evolution of μ m at yle (Figure 3, top) is representative of that observed until the sixth yle. 4

3 σ t (MPa).5 yle σ t (MPa) 5 yle.3. yle yle a) -5 b) U n (mm) 2.5 yle U n (mm) 2.5 yle yle yle Figure. Typial undulated joints CNS shear test urves (a) σ n = MPa and (b) σ n = 4 MPa. σt (MPa) 3 2 part b part part d part e..9 μm Un (mm) partb shear displaement (mm) part part d part e shear displaement (mm) Figure 2. Loation of the studied parts on the shear stress (top) and dilatany (bottom) urves. Indeed, Figure 3 shows that from the part b (just after the peak) the average frition oeffiient dereases gradually in the parts, d and e. In the same way, the evolution of μ m at yle 7 (Figure 3, bottom) is representative of that observed until the tenth yle. This figure espeially highlights a perfet elastoplasti behavior of the joint from yle 7. To support these assertions onerning the behavior of the undulated joint, we also analyzed the dilatany urves in the same way that those of the tangential stress parts b d e μm parts b d e σn=.5 MPa σn= MPa σn=2 MPa σn=3 MPa σn=4 MPa σn=5 MPa Figure 3. Average frition oeffiient σ m for eah part after yle (top) and yle 7 (bottom). Figure 4 presents the evolution of the average dilatany angle, i m, with respet to the yles of shear for the test arried out at σ n = 4 MPa and for eah part. For the first yles ( to 6), figure 4 shows that the average dilatany angle i m dereases in the part b while it inreases slightly in the parts, d and e. 4

4 This observation an be explained by the fat that initially, the slight inrease in the average dilatany angle i m of the parts, d and e is produed by the wear materials due to the surfaes degradation in ontat, whih are distributed along the undulation. Moreover, this degradation implies a signifiant fall in i m in the part b whih is explained by the umulated effet of the wear and the aumulation of the wear materials due to the shear yles i m ( ) part e part d part part b Cyles Figure 4. Variation in the average dilatany angle with yles (σ n = 4 MPa). In the last yles (7 to ), the average dilatany angles i m ( ) are nearly idential for all the studied parts (i m_b i m_ i m_d i m_e ) and orrespond to the residual behavior. The very lose values of the average dilatany angles of all the studied parts mean that undulated morphology was transformed into a surfae almost in saw teeth. Following these observations we onsider that figure 4 is representative of the tests arried out at σ n 2 MPa beause at σ n = MPa we estimate that the undulations have undergone a moderate degradation. The part (Figure 5) is representative of μ m evolution in all the studied parts for the tests at σ n 2 MPa μm σn=5 MPa σn=3 MPa σn=4 MPa σn=2 MPa yles Figure 5. Variation in frition oeffiient yles for CNS shear test in part. Indeed, in the part, the average frition oeffiient inreases globally from one yle to another for all normal stress levels exept σ n = 5 MPa where a slight redution in μ m is observed away from yle 5. The inrease in μ m is assoiated with the inrease in ontat areas. However, from yle 7, μ m inreases very slightly or does not vary any more. This also orresponds to the residual behavior highlighted by the yles. 3.2 Failure riterion Figure 6 shows that the values of peak strength, τ peak, for yle 7 are well fitted by the Mohr- Coulomb riterion with a frition angle, φ peak, of 48 degrees. Assuming that the undulated joints failure riterion is a Mohr-Coulomb riterion, figure 7 illustrates the evolution of the peak and residual frition angles with respet to the yles. τ peak φ peak = σn (MPa) Figure 6. Mohr-Coulomb failure riterion for the yle 7. φ ( ) residual peak Cyles Figure 7. Relationship between Mohr-Coulomb frition angle and yles of shear From yle to yle 6 the peak frition angle φ peak inreases with the number of yles (between 43 and 48 ) as previously suggested by the analysis of the shear and dilatany urves. From the seventh yle, 42

5 φ peak is not yles-dependent. In addition, beyond the seventh yle, φ peak and φ residual are quite similar. Consequently, we onsider that φ peak at yle 7 is representative of the frition angles from yles 7 to yle. Figure 8 shows the evolution of peak dilatany angle, i peak, with respet to the yles for.5 < σ n < 5 MPa. The evolution of i peak is diretly related to the number of yles. For a given yle, i peak dereases with the inrease of normal stress. Also for a given normal stress level, i peak dereases with the number of yles. Therefore, for the tests at σ n 2 MPa, the redution of i peak is strong between yles to 7, then weak between yles 7 to i peak ( ) Cyles σn =.5 MPa σn = MPa σn = 2 MPa σn = 3 MPa σn = 4 MPa σn = 5 MPa Figure 8. Variation in peak dilatany angle with yles of shear. By assuming that the undulated joints are dilating (e.g. the undulations play a role in shearing), the failure riterion after one yle of shear has the same form that Patton's riterion (966) τp = σn tan( φμ + i) () where i = initial maximal angle of the undulations, φ μ = basi frition angle. The angle i in Patton's riterion orresponds exatly to the peak dilatany angle. In our ase, the degradation of undulations with the yles indues an inrease in the ontat areas and therefore in the peak shear strength. In order to take into aount the hange of morphology during the yli shearing in the Patton's riterion, we define the angle i with respet to the number of yles (Nb) as: i = θs + k(nb ) for Nb 7 (2) i = 48 for Nb > 7 where k = a material onstant; θ s = the 3D surfae average angle. The angle θ s is defined by: 43 θ s = m m i= α i (3) where α i = angle betwen the normal vetor of the i th elementary surfae and the normal of the mean plane of joint, m = number of onsidered elementary surfaes. For the tested joints : φ μ = 34 and k.5. 4 RESULTS OF CNK SHEAR TESTS Figure 9 shows the shear urves of a test arried out at σ ni = 2 MPa and K n = 2 MPa/mm. The urve shape is typial for all performed CNK tests. For a given yle, σ t inreases ontinuously with the tangential displaement. The frition oeffiient (μ) vs tangential displaement (W x ) urves show that the maximum frition is reahed for tangential displaements of the same order of magnitude as those obtained with the CNS tests. σ t (MPa) yle yle Figure 9. Shear urves of a test at σ ni = 2 MPa and K n = 2 MPa/mm. Moreover, the overall look of these urves is similar to this of the tangential stress (σ t ) vs tangential displaement urves for the CNS tests (peak and stage). But the μ - W x urves do not allow to observe residual frition. We an note an influene of normal stiffness K n on the tangential stiffness K s whih evolves very quikly with σ ni or K n. This means that the ontrol of the effetiveness onstant normal stiffness ats immediately when the first dilatany is reorded. In order to better observe the influene of K n on the joint behavior, we made linear regressions of the average tangential stress σ tm with respet to K n in the first approximation. This average stress was alulated in the range of tangential displaement 2.5 mm < W x < 8.5 mm. An example of linear regression for yle 5 is shown on figure (top panel) and the evolution of their slopes with respet to the yles for different

6 σ ni (bottom panel). On this figure, the test at K n = 3 MPa/mm was not taken into aount beause of the mortar failure. It an be noted on the Figure (bottom panel) that from yle 4, the slopes remain onstant. Other investigations are urrently in progress to overome the analysis of CNK tests σ t (MPa) Kn (MPa/mm) 2 slope s σni=3 MPa σni=2 MPa σni= MPa σni=3 MPa σni=2 MPa σni= MPa 5 Cyles Figure. (top) Values of slope s for CNK tests at yle 5; (bottom) Slope variation vs shear yles. 5 DEGRADATION OF JOINT SURFACES 5. Definition of the degradation degree In order to quantify the degradation of joint between its initial state (prior to shear) and its ultimate state (after shear), Belem et al. (997) have defined the degree of degradation of sheared joint surfaes D w. This degradation parameter is defined from alulation of the atual areas of joint walls whih were estimated from roughness profiling before and after shearing. Aording to these authors, the degree or perentage of degradation for an initially rough surfae is defined as: D w D A (%) = A w t t A A ts n A t A ts = A 2A t s n ; (4) where A = sum of the atual areas of the lower t l u and upper walls prior to shear ( A = A + A ), t t t A = sum of atual areas of the lower and upper t s l u walls after shear ( A = A + A ), A ts ts ts n = nominal area of one joint wall (projetion of joint wall on the mean plane). Considering that the both upper and lower joint walls have initialy the same sizes, then the resulting nominal area A is equal to 2A n, n 5.2 Modeling of degradation Belem (997) developed a model to predit the joints degradation during CNS shearing, depending on the stress level for a given geometry. The model parameters are desribed by the joints morphology (angularity, anisotropy, roughness). This model was improved (Lefêvre 998) in order to take expliitly into aount the CNS and CNK loading onditions, the sample dimensions and the number of shear yles. CNS degradation model For the undulated joints, the basi model was modified and is given by the relation (5): σ n ( βw ) Dw =- - e (5) σ 3 2 ka σ with T Wt n β w = (6) tan θs Ls Ly σ where θ s = 3D average angle, k a = anisotropy oeffiient, σ = uniaxial ompressive strength, T = undulation period, L s = sample length along shear diretion, L y = total displaement for one yle, W t = umulated total displaement, σ n = normal stress. Figure presents the predited urves obtained from the equation (5) for a same mortar but with two different morphologies (Morpho A and B). Morpho A orresponds to the undulated artifiial joint and Morpho B orresponds to the replia of natural shist joint with large undulations. For Morpho A, W t = 4 mm and for Morpho B, W t = 2 mm. For Morpho A2 & B2, W t = 4 mm. The model parameter values are : -Morpho A : T = 25 mm, L s = mm, θ s =.3 -Morpho B : T mm, L s = mm, θ s =.9 Figure shows that the model predition of degradation is more sensitive to the maximum of the 44

7 undulations amplitude (period T) and partiularly to the umulated tangential displaement W t (e.g. yles). The influene of the yles number is well highlighted for Morpho B. Indeed, for this morphology the period T will predetermine the speifi ontats whih will result in high degradations with the yles. Dw (%) Morpho B2 Morpho A2 Morpho A Morpho B 2 σn/ σ Figure. Predited degradation vs normalized normal stress. Figure 2 ompares the alulated values of D w with those predited by the model (equation 5) for the two morphologies (Morpho A and B). Let us reall that for Morpho B, W t = 2 mm and for Morpho A2 and B2, W t = 4 mm. This figure shows that the model rather well predited the degradation of the undulated joint than the degradation of the natural joint replia. Dw (%) Morpho B2 Morpho A2 Morpho B relative tangential displaement of the first part of the yle (L y /4). In addition, the results show that tan(i peak ) deays exponentialy with the yles and tends to tan(θ s ) after shear yles. We thus assume that for eah yle: ΔU n tan(θ s ) ΔW x = tan(θ s ) L y /4 (8) s By ombining equations (7) and (8), equation (6) beomes: 3 2 ka θ T Wt σ K n tan sl ni y β + w = (9) tan θs Ls Ly σ 4 σ The CNK degradation model is then: σ ni βw Dw =- - e () σ and was expressed with regard to σ ni and not to the normal stress estimated from Δσ n, beause the term β w takes into aount the CNK ondition. Dw (%) 8 6 Kn = 3 MPa/mm Kn = 2 MPa/mm 4 Kn = MPa/mm 2 σni/σ Figure 3. Degradation vs initial normal stress σ ni preditive urves for different K n values... σn/ σ.2 Tests-Morpho B Tests-MorphoB2 Tests-Morpho A2 Figure 2. Comparison between model and CNS data. CNK degradation model For the CNK ondition, σ n varies linearly with K n as a funtion of dilatany: Dw (%) σni /σ Kn = MPa/mm Kn = 3 MPa/mm Kn = 2 MPa/mm CNS (Kn = ) σ n = σ ni + Δσ n = σ ni + K n ΔU n (7) Figure 4. Comparison between model and CNK data During one yle of shear, we approximate ΔU n by the produt of peak dilatany rate, tan(i peak ), and the 45 Figure 3 presents the predition urves obtained with the equation () for the artifiial undulated joint with three values of normal stiffness (K n =, 2,

8 3 MPa/mm) and W t = 4 mm. The model parameters are: T = 25 mm, L s = mm, θ s =.3. Figure 4 ompares the alulated values of D w to those predited by the model (equation ) for various K n. The CNS model is integrated in the diagram (K n = ). The model well predits the degradation of the undulated joint and shows the influene of the normal stiffness. The model suh as it is defined (equations 9-) is the generalized peak strength riterion for both the CNS and CNK loading onditions. Indeed, σ ni & K n orrespond to a CNK ondition and σ ni & K n = orrespond to a CNS path. 6 CONCLUSIONS Many yli diret shear tests were arried out on artifiial undulated joints of mortar. These tests were performed aording to CNS and CNK loading onditions. The morpho-mehanial behavior was analyzed on the shear and dilatany urves for the CNS tests at σ n 2 MPa and the results showed that: for a given yle: based on the shear urves, we observe (i) a lear peak from yle to yle 6 (ii) a perfet elastoplasti behavior from yle 7 to yle ; from the dilatany urves and aording to the parts b,, d and e, we observe that (i) from yle to yle 6: average dilatany angles i m_ = i m_d = i m_e et i m_b i m_de (ii) from yle 7 to yle : i m_b = i m_de and the undulations are pratially transformed into saw teeth. From yle (n-) to yle n: based on the shear urves, we observe (i) from yle to yle 6, the shear strength inreases due to an inrease in the ontat areas, (ii) at yle 7, the residual stress is reahed; from the dilatany urves and aording to the parts, we note (i) from yle to yle 6: i m_b dereases and i m_de slightly inreases in relation to an inrease in the ontat areas (ii) from yle 7 to yle : i m_b = i m_ = i m_d = i m_e. A parameter was defined to quantify the perentage of degradation of sheared joints. Two models were then proposed to predit the degradation of the anisotropi joints aording loading onditions (CNS or CNK) and the shearing mode (monotonous or yli). The degradation model for CNS ondition is then generalized for the two loading onditions; this model well predits the degradation of the undulated joints. REFERENCES Belem T. (997). Morphologie et omportement méanique des disontinuités roheuses. Thèse de Dotorat INPL, Nany, 22p. Belem T., Homand-Etienne F. & Souley M. (997). Fratal analysis of shear joint roughness. Int. J. Rok Meh. & Min. Si., 34:3-4, paper No. 3, p. Benjelloun Z.H., Boulon M. & Billaux D. (99). Experimental and numerial investigation on rok joints. Rok joints, Barton & Stephansson (eds), Balkema, Rotterdam, pp Homand-Etienne F., Belem T., Sabbadini S., Shtuka A. & Royer J.-J. (995). Analysis of the evolution of rok joints morphology with 2D autoorrelation (variomaps). Pro. 7th Int. Conf. on Appl. Stat. & Proba, Paris, Lemaire, Favre & Mebarki (eds), Balkema, Rotterdam, pp Hutson R.W. & Dowding C.H. (99). Joint asperity degradation during yli shear. Int. J. Rok Meh. Min. Si. & Geomeh. Abstr., 27, No. 2, pp Jing L., Nordlund E. & Stephansson O. (993). Study of rok joints under yli loading onditions. Rok Meh. Rok Engng., 26, No. 3, pp Kana D.D., Fox D.J. & Hisiung S.M. (996). Interlok/frition model for dynami shear response in natural jointed rok. Int. J. Rok Meh. Min. Si. & Geomeh. Abstr., 33, No. 4, pp Ladanyi B. & Arhambault G (969). Simulation of the shear behaviour of a jointed rok mass. Pro. tht Symp. on Rok Meh., Berkeley, pp Lefêvre F. (999). Comportement méanique et morphologique des disontinuités en isaillement. Thèse de Dotorat INPL, Nany. (à paraître) Patton F.D. (966). Multiple modes of shear failure in rok. Pro. st. Congr. Int. So. Rok Meh., Lisbon, pp Plesha M.E. (987). Constitutive models for rok disontinuities with dilatany and surfae degradation. Int. J. for Num. & Anal. Meth. in Geom., Vol., pp Sabbadini S., Homand-Etienne F. & Belem T. (995). Fratal and geostatistial analysis of rok joints roughness before and after shear tests. Pro. 2nd Int Conf. on Meh. of Jointed & Faulted Roks, Vienna, Rossmanith (ed), Balkema, Rotterdam, pp