Experimental study of elastic properties of different constituents of partially saturated argillite using nano-indentation tests

Engineering Geology 191 (2015) 61–70

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Experimental study of elastic properties of different constituents of partially saturated argillite using nano-indentation tests C. Auvray a,⁎, G. Arnold b, G. Armand c a b c

Université de Lorraine, CNRS, CREGU, GeoRessources Lab., Vandœuvre-lès-Nancy F-54518, France LPMT, Université de Haute Alsace, 68093 Mulhouse, France ANDRA, Direction scientifique, Service mécanique des fluides et des solides, 55290 Bure France

a r t i c l e

i n f o

Article history: Received 22 October 2013 Received in revised form 6 February 2015 Accepted 24 February 2015 Available online 19 March 2015 Keywords: Argillite Nano-indentation Grid indentation technique Instantaneous and deferred unloading modulus Water saturation

a b s t r a c t Callovo-Oxfordian argillite, obtained from the ANDRA underground research laboratory in Meuse/Haute-Marne (France), is characterized as a multiphase material. The argillite is composed of carbonate inclusions (10–50 μm) embedded in an argillaceous matrix (representing expanding clay minerals, such as smectites). The matrix itself is also multiphase, composed of clay aggregates of 1 μm-size carbonate and quartz inclusions. The high sensitivity of the mechanical behaviour of argillite to saturation is an important characteristic of this material as it has been previously demonstrated in macro-scale mechanical experiments performed under varying degrees of humidity. The study presented here consists of grids of nano-indentation tests performed under controlled saturation conditions. The influence of the load hold time before unloading has been studied. Series of indentations were performed without or with load hold, which led to consider instantaneous or deferred unloading moduli respectively. The experimental procedure employed allows the micro-mechanical properties of the different phases (matrix and inclusions) to be determined under controlled hydration and therefore under partially saturated conditions. Several series of measurements were performed at relative humidity levels of 50%, 85%, 90% and 95%, and at a constant temperature of 20 °C. A statistical analysis enabled to discriminate the deferred unloading modulus of the different phases. At 50% humidity, we measured a mean deferred unloading modulus of 16 GPa for the clay matrix (a mean instantaneous unloading modulus of 13 GPa was observed for the clay matrix and moduli higher than 70 GPa were measured for the carbonate macro-inclusions). The mean deferred unloading modulus of the matrix appears to decrease with increasing saturation; at 95% humidity (near-saturation) it is less than 5 GPa. However, it was impossible to verify the instantaneous unloading modulus of the carbonate macro-inclusions at this high-level of saturation. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Callovo-Oxfordian argillites obtained from the ANDRA underground research laboratory in Meuse/Haute-Marne (France) are a multiphase material. The rock is composed of an argillaceous matrix of expanding clays such as smectites, which contains inclusions of carbonate of several tens of microns in size. The matrix itself is also multiphase, composed of sheeted clays containing 1-μm size quartz and carbonate inclusions (Robinet, 2008; Robinet et al., 2012). Preliminary results of micromechanical tests obtained during millimetre-scale indentation experiments on argillite (Magnenet et al., 2011a) highlighted the importance of being able to discriminate between these phases using a grid indentation technique (Constantinides et al., 2006). The high saturation sensitivity of argillite, an important characteristic that mainly results from the presence of expanding clays, has been demonstrated through

⁎ Corresponding author.

http://dx.doi.org/10.1016/j.enggeo.2015.02.010 0013-7952/© 2015 Elsevier B.V. All rights reserved.

mechanical tests on macroscopic samples under varying degrees of humidity (Escoffier, 2002; Hoxha et al., 2007; Hu et al., 2014). In order to better apprehend the mechanical behaviour of the different constituents, we have designed a study in which several series of nano-indentation tests were conducted on partially saturated samples. The area of the contact surface in our experiments is on the order of a few square microns, allowing the different phases to be discriminated at a much finer scale than it has previously been possible. The experiments were performed using a nano-indentation system that is placed within a climatic chamber. This procedure therefore allows nanoindentation tests to be performed under variable saturation levels (Auvray et al., 2013). In the present study, series of measurements were performed at a constant temperature of 20 °C at 50%, 85%, 90% and 95% humidity. The data obtained in this nanometric study can be compared with the elastic properties of different argillite constituents estimated at millimetre-scale in an earlier study (Magnenet et al., 2011a) to establish reference values for the elastic properties of the different constituents. In the future, they could be integrated into multiscale behaviour models

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and lead to important improvements in our understanding of the mechanical and micro-mechanical behaviour of rocks.

Table 1 Indentation tester specifications. Load range Load resolution Maximum depth Depth resolution Maximum load rate XY stage XY resolution

2. Experimental procedures The experimental procedure that was used in this study was developed by the GeoRessources Laboratory (Nancy, France) and is presented in Auvray et al., 2013. The nano-indentation test-bench is installed in a climatic chamber (Vötsch Industrietechnik GmbH) and consists of two modules, one containing the nano-indenter (CSM-Instruments) and the other containing an optical microscope that allows the surface of the sample to be viewed (Fig. 1). The sample is moved between the two modules by means of a motorised stage, which allows indentation tests to be undertaken in grids. The nano-indentation test grid is defined by programming the offset between two measurements, as well as the number of columns and rows. All tests are conducted within a millimetre-scale area. The technical specifications of the nanoindentation tester are provided in Table 1. The surfaces of the sample must be perfectly flat and smooth as well as parallel to the support stage axes the distance between the support stage plane and the indented surface must not vary more than 5 μm. Though these requirements are systematic when preparing samples for indentation tests, they are especially important for performing nano-indentation experiments (Vandamme, 2008; Miller et al., 2008). To achieve this high degree of surface smoothness, the samples underwent five stages of lapping/abrasion during which progressively finer abrasives were applied: F80, F220, F360, F800 and F1200 (corresponding to mean grit-sizes of 185 μm, 58 μm, 23 μm, 6.5 μm and 3.0 μm, respectively). The indentation procedure consisted of pressing an indenter into the surface of a sample by applying an increasing normal load. Once the indenter reached a defined depth hL1, a partial unloading was applied (down to hU1) and followed by a second loading up to the maximum depth hL2. Then the indenter was removed with a controlled rate until total unloading. This procedure was performed in a repetitive manner at different points on the sample surface at a constant interval along both the x- and y-axes. The load was directly applied by an electromagnet assembly to a vertical rod, the end of which houses a standard Berkovich diamond indenter (Fig. 2). Displacement of the rod was measured by a capacitive detector and the rod was supported by two guide

0.1–500 mN 0.04 μN 200 μm 0.04 nm 10 N/min 120 × 20 mm 0.25 μm

springs (Randall et al., 1997). The system has load and displacement resolutions of 0.04 μN and b 0.04 nm respectively. In order to determine the elastic modulus of the different constituents we used the model of Oliver and Pharr (1992) calculated by CSMInstruments Indentation software. This model allows Young's modulus (Eit) of the indented zone to be derived from load–displacement curves (Fig. 3) using the expression of the reduced modulus Er: Er ¼

pffiffiffi S π qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2β Ap ðhc Þ

ð1Þ

where S is the elastic unloading stiffness, defined as the tangent of the unloading curve, and β is a correction factor related to the geometry of the indenter. Ap(hc) is the projected contact area of the indentation as a function of contact depth, hc, which is obtained from: hc ¼ hmax −ε

Fmax S

ð2Þ

where Fmax is the load value before unloading and ε is a coefficient that depends on the indenter geometry. The value of Young's modulus of the indented material is obtained from expression (3) where Ei and νi are the elastic modulus and Poisson's ratio of the indenter, and νit is the Poisson's ratio of the indentation zone (set at 0.30 for the whole sample).

1 1−ν2it 1−ν2i ¼ þ Er Eit Ei

Fig. 1. Nano-indentation tester installed in climatic chamber.

ð3Þ

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63

magnet coil

S

N

S

capacitive detector

springs

sapphire reference ring

diamond indenter

Fig. 2. Schematics of the measurement head of the CSM Instruments nano-indentation tester.

3. Experimental test campaigns 3.1. Testing parameters It has been shown (Constantinides et al., 2006; Constantinides and Ulm, 2007) that the statistical processing of nano-indentation tests is only relevant if the typical size of the inclusions (d) is much larger than the typical penetration depth (h) (Fig. 4). If d ≪ h, the material can be considered homogeneous (see Fig. 2 in Constantinides and Ulm (2007)) whereas when d ≫ h, the mechanical behaviour of the individual constituents becomes important. For the argillite, the choice of the indentation depth was particularly problematic because of the wide range of inclusion sizes and the limited number of specimens available. Two characteristic inclusion sizes could be identified under optical

microscopy, the smallest of which was approximately 1 μm in size. In contrast to Abou-Chakra Guery et al. (2008), we were able to distinguish between these 1 μm inclusions and the larger, 10 to 50-μm-size, inclusions of quartz and calcite that are usually referred to. In a previous work (Magnenet et al., 2011a), the following condition was established for similar specimens: 1 μmbhb10 μm:

ð4Þ

However, in the present study, a third phase composed of microinclusions aggregates of a few microns in size could also be observed in the specimens (Fig. 6b). In order to try to assess the behaviour of these aggregates, preliminary tests enabled us to choose to work with a maximal penetration depth around 1 μm.

a initial surface

residual surface profile (after unloading)

indenter

hr

hmax

hs

hc

deformed surface profile (loading)

F

b load

unload

S = dF/dh h

hmax Fig. 3. (a) Diagram of the indentation zone detailing the different indentation parameters: hc = contact depth; hs = surface displacement at the contact perimeter; hr = residual depth after loading; hmax = total indentation displacement.(b) Typical load–displacement curve used for calculation of the elastic unloading modulus: F = load; h = penetration depth; S = elastic unloading stiffness.

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0

100µm

second series of measurements enabled the calculation of a deferred unloading modulus for each loading–unloading cycle. In these series the maximum indentation depth reached in some cases values above 2 μm because of creep during the load hold. A third series was performed in the same conditions as previously with different load hold times at 50% humidity (Table 2).

micro-inclusion macro-inclusion

4. Results and interpretation

Fig. 4. Comparison of typical lengths. The triangles represent the imprints of the indent tip and the small, medium and large circles represent inclusions embedded in the matrix (Magnenet et al., 2011a).

Table 2 Number of tests performed for each level of humidity (0 s: load time = 0 s; 90s: load time = 90 s; Hr = hygrometry). Relative humidity Series no. 1 instantaneous tests (0 s) Series no. 2 deferred behaviour tests (90 s)

Series no. 3 instantaneous and deferred behaviour tests (Hr = 50%)

50% 1517

85% 1587

90% 1618

95% 1547

1401

1596

1554

1496

50% t=0s

50% t = 90 s

50% t = 180 s

50% t = 360 s

1517

1401

1600

1600

A histogram of the modulus values was calculated for each series of indentations performed at given degree of humidity and load hold time. A first statistical analysis has been performed as proposed in Constantinides et al. (2006). The cumulative distribution function Φexp was fitted by the superposition of three normal distributions Φk (with k = 1,2,3) of mean values μk, standard deviation σk and volume fraction ƒk. 1 i Φk ¼ pffiffiffiffiffiffi f k 2π

Z

xi −μ k σk

−∞

2

−t2

e

dt ¼

xi−μ k 1 f 1 þ er f 2 k σ kpffiffi2

The test programme consisted of two series of measurements for each of the four levels of humidity (50%, 85%, 90% and 95%). The number of tests performed for each level of humidity is detailed in Table 2. All tests were performed on pre-saturated material. The following parameters were applied for all series of indentation tests: • • • • •

Loading and unloading velocity: 30.00 mN/min. First loading maximal depth (hL1): 0.85 μm. First unloading minimal depth (hU1): 0.75 μm. Second loading maximal depth (hL2): 1.1 μm. Grid spacing: 100 μm.

The first series of tests were performed without application of a load holding period. A typical loading path is presented in Fig. 5a. The instantaneous unloading modulus was calculated for each loading-unloading cycle using experimentally-derived loading paths (see examples in Fig. 8). In the second series of measurements the load was held for 90 s before each unloading. A typical loading path is shown in Fig. 5b. This

ð5Þ

The number of 3 phases has been chosen arbitrarily. It corresponds to the description of the argillite: (i) a weak phase that can correspond to the argillaceous matrix, (ii) a mean phase where the argillaceous matrix is hardened by the presence of hard micro-inclusions and (iii) a hard phase that corresponds to the larger hard inclusions. The optimization algorithm consisted in the minimization of the cost function ε defined by expression (6):   X3   εðPÞ ¼ Φexp − k¼1 Φk 

3.2. Experimental protocols

!!

ð6Þ

where P is the vector of parameters to be optimized: μk, σk, ƒk with k = 1,2,3 satisfying the constrain ƒ1 + ƒ2 + ƒ3 = 1. It enabled the determination of the mean values and standard deviation of each normal distribution, as well as their volume fractions. Instantaneous unloading modulus frequency distributions were obtained for each level of humidity from the first series of indentation tests (Fig. 9). 50% humidity (Fig. 9a): • Indentation imprints for the argillite matrix are illustrated in Fig. 6 and their corresponding experimental load–displacement curves are presented in Fig. 8. The matrix yielded instantaneous unloading modulus values of between 1 and 40 GPa. The frequency distribution is very wide across this range. A mean modulus value of 13 GPa was derived for 50% of the total number of measurements. • The mean modulus of 5.6 GPa (17% of all measurements) obtained from statistical analysis, appears to represent particular indentation zones which exhibit a higher degree of porosity, or even a total absence of micro-inclusions. • The carbonate macro-inclusions are represented by modulus values greater than 70 GPa, comparable to the value determined for pure

Fig. 5. Load–time curves for: (a) instantaneous unloading tests and (b) deferred unloading tests.

C. Auvray et al. / Engineering Geology 191 (2015) 61–70

a

0

65

b

5µm

0

5µm

Fig. 6. Photographs of indents in argillaceous matrix containing micro-inclusions (b1 μm-size) of calcite and quartz. (a) Matrix with a low proportion of micro-inclusions, E = 5GPa; (b) matrix with a high proportion of micro-inclusions, E = 40GPa. (Hr = 50%, instantaneous unloading test).

carbonate crystal (Ahrens, 1995). A typical indentation mark for this type of inclusion is shown in Fig. 7, and its corresponding experimental load–displacement curve is presented in Fig. 8. • The intermediate modulus values, which represent 33% of the values obtained, correspond to the various micro-inclusions present in the clay matrix. 85% humidity (Fig. 9b): • The argillite matrix is represented by moduli distributed between 1 and 30 GPa, with a mean modulus of 12 GPa obtained for 48.5% of the measurements. • The mean modulus of 8.3 GPa (13% of measurements) seems to represent particular indentation zones that exhibited higher porosity or a near-total absence of micro-inclusions. • Only a few very-high modulus values (equal to or greater than 70 GPa) were measured. • Intermediate modulus values (38.5% of the test points) are widely dispersed. 90% humidity (Fig. 9c): • The matrix is represented by modulus values of between 1 and 30 GPa, with the maximum frequency at 9.7 GPa (50% of measurements). • The mean modulus of 6 GPa (31% of measurements) seems to represent particular zones that exhibited higher porosity or a low proportion of micro-inclusions. • No indentation tests yielded modulus values greater than 30 GPa.

high humidity levels as the inclusion would presumably sink into the saturated clay matrix without being deformed by the indenter. 2. The modulus of the matrix appears to decrease with increasing humidity (from a mean value of 13 GPa for 50% humidity to between 6.6 and 8.9 GPa for 95% humidity). This diminution of modulus with saturation can be linked to the lamellar structure of expanding clays where the number of water layers is correlated to the degree of saturation. Similar results have previously been obtained in uniaxial compression tests undertaken on standard-size cylindrical samples (38 mm diameter, 76 mm height), in which the elastic modulus was shown to diminish under increasingly saturated conditions (Hoxha et al., 2007; Magnenet et al., 2011b). 3. Modulus values much lower than the mean values of the matrix are probably due to the presence of micropores below the indenter, resulting in an under-estimation of the modulus of the bulk matrix. 4. Values that are significantly higher than the mean values of the matrix are probably due to the proximity of an inclusion (a mass of micro-inclusions or a single macro-inclusion) beneath the indented zone. The deferred unloading modulus frequency distributions for each degree of humidity for the second series of measurements (which included application of a 90-second load holding period) are presented in Fig. 10. At 50% humidity (Fig. 10a): • The matrix yields a wide range of modulus values, from 1 to 40 GPa. A number of peaks are apparent (at 12, 15, 18, 24 and 28 GPa) in the frequency distribution plot. A mean modulus of 16 GPa (from 69% of the total number of measurements) was derived from statistical analysis.

95% humidity (Fig. 9d): • The matrix is represented by modulus values of between 1 and 20 GPa, with two frequency peaks visible at 6.6 and 8.9 GPa. These two peaks represent a total of 88% of the values. • No indentation tests yielded modulus values greater than 30 GPa and the remainder of the values represent no more than 11% of the total number of measurements made. Assuming that the different phases are similarly distributed in the different indented zones, the instantaneous unloading modulus frequency distributions for the four different levels of humidity can be compared and interpreted as follows: 1. The observed tightening of the frequency distribution with increasing humidity is most likely due to the behaviour of the clay matrix. It is difficult, or even impossible, to envisage indentation of an inclusion (be it a mass of micro-inclusions or a single macro-inclusion) at

0

10µm

Fig. 7. Photograph of an indent in a calcite macro-inclusion (approximately 30 μm in size), E = 70 GPa (Hr = 50%, instantaneous unloading tests).

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250 carbonate macro-inclusion E = 70GPa matrix with high proportion of micro-inclusions E = 40GPa matrix with low proportion of micro-inclusions E = 5GPa

200

F (N)

150

100

50

0 0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

h (µm) Fig. 8. Experimental load–displacement curves for the indents shown in Figs. 6 and 7.

• The 7% of measurements that together yield a mean modulus of 4.6 GPa appear to represent the presence of micropores and/or a total absence of micro-inclusions in the indentation zone. • Values typical of carbonate macro-inclusions (~70 GPa) were not recorded in this series of measurements. • The other indentation moduli that can be observed in the frequency distribution graphs (24% of the total number of measurements) correspond to variable proportions of different micro-inclusions present in the clay matrix.

At 85% humidity (Fig. 10b): • The matrix is represented by modulus values of between 5 and 20 GPa, with a peak at 11 GPa (55% of measurements). • Very high modulus values typical of carbonate macro-inclusions (equal to or greater than 70 GPa) were not obtained at this level of humidity. • Almost none of the indentation tests yielded modulus values greater than 30 GPa.

b

13 GPa 50%

Normalized frequency (%)

Normalized frequency (%)

a

d Normalized frequency (%)

Normalized frequency (%)

c

Fig. 9. Experimental instantaneous unloading modulus frequency distributions for tests performed at relative humidity levels (Hr) of: (a) 50% (b) 85%, (c) 90% and (d) 95%. Dashed lines show the three normal distributions with corresponding mean modulus values calculated from statistical processing.

C. Auvray et al. / Engineering Geology 191 (2015) 61–70

b

Normalized frequency (%)

Normalized frequency (%)

a

67

d Normalized frequency (%)

Normalized frequency (%)

c

1 < E < 5 GPa 100%

Fig. 10. Experimental deferred unloading modulus frequency distributions for tests performed at relative humidity levels (Hr) of: (a) 50%; (b) 85%; (c) 90%; and (d) 95%. Dashed lines show the three normal distributions with corresponding mean modulus values calculated from statistical processing.

At 90% humidity (Fig. 10c): • The matrix is represented by modulus values of between 2 and 17 GPa that centre on a peak with a mean value of between 5.7 and 7.9 GPa (85% of measurements). • No other modulus values were recorded. At 95% humidity (Fig. 10d): • The matrix is represented by a distribution of moduli between 1 and 5 GPa (100% of measurements). • No other modulus values were recorded. If we once more assume that the different phases are similarly distributed in each indented zone, the deferred unloading modulus frequency distributions determined for the four different humidity levels can be compared and interpreted as follows: 1. The observed tightening of the modulus distribution with increasing humidity is even more significant than in the case of the tests performed without load hold. As previously it is almost impossible to envisage indentation of an inclusion at high humidity levels as the inclusion would sink into the saturated clay matrix. 2. A sharp decrease in the mean modulus of the clay matrix is observed with increasing humidity (from 16 GPa at 50% humidity to less than 5 GPa at 95% humidity). This is most likely due to the increase of the number of water layers in expanding clays with humidity.

3. Values of around 4.6 GPa for 50% humidity are, at this stage, difficult to interpret. However, they may suggest the presence of micropores close to some of the indentation sites. Under creep action, such porosity will enhance the penetration of the indenter, directly leading to underestimation of the modulus. The higher modulus values of ~ 40 GPa for 50% humidity are most likely due to the presence of micro-inclusions in the vicinity of the indenter. In the 85–95% humidity tests, no high modulus values were recorded and only a few low modulus values were determined (at 90 and 95% humidity). 5. Discussion To compare the modulus values obtained in the two series of indentation tests, it is necessary to consider the results for viscous material reported by Feng and Ngan (2002), Feng and Tang (2002) and Ngan et al. (2005). In these studies, stiffness at unloading (Su) was shown to decrease with increasing load holding time (th): •

1 1 h ¼ þ h S Su jP• u j

ð7Þ

where Su is the apparent stiffness, S is the elastic stiffness (used in  Eq. (1)), h h is the penetration speed at the end of the load holding period  and Pu is the unloading rate at the onset of unloading.

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a

Normalized frequency (%)

Normalized frequency (%)

b

c

Normalized frequency (%)

Normalized frequency (%)

d

Fig. 11. Elastic modulus frequency distributions for (a) instantaneous unloading and (b to d) deferred unloading/90 s (b), 180 s (c), 360 s (d).

Consequently, the value obtained from Eq. (3) (Eit) can be an overestimation of the “true” modulus (E) of the material. Moreover, this overestimation will be greater for instantaneous unloading (Eit inst) than for deferred unloading (Eit def). inst NE it de f

NE:

ð8Þ

100

Hr = 50%

90

Hr = 85% Hr = 90%

80

Elastic modulus (GPa)

Eit

The comparison of the results of instantaneous unloading modulus (series 1 in Fig. 9) and deferred unloading modulus (series 2 in Fig. 10) are in good agreement with Eq. (8) for high saturation levels (90% and 95%) where argillite exhibits a more viscous behaviour. The analysis of the results of the two experimental campaigns (instantaneous and deferred unloading nano-indentation tests performed

Hr = 95%

70 60 50 40 30 20 10 0 0

1

2

3

4

5

6

load time (min) Fig. 12. Instantaneous unloading modulus versus loading time (for four series of tests performed under different levels of humidity).

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69

50 Hr = 50% 45

Hr = 95%

Elastic modulus (GPa)

40 35 30 25 20 15 10 5 0 0

0,2

0,4

0,6

0,8

1

1,2

penetration during load hold (µm) Fig. 13. Deferred unloading modulus versus penetration during the 90s load hold period (for series of tests performed under 50% and 95% humidity).

under controlled humidity) lead us to put forward the following remarks: i) Regardless of the level of humidity considered, it appeared easier to discriminate between the matrix and the inclusions when a constant hold in loading was applied. We tested this further by performing additional measurements at 50% humidity in which the mechanical loading was held constant for periods of 180 and 360 s (series 3 in Table 2). The observation of the 1st peak (at 4– 6 GPa) is independent of the nature of the phases. This peak becomes increasingly prominent as the load holding period is lengthened (Fig. 11). This suggests that tests with deferred unloading are preferable for discriminating between the elastic modulus of the different constituents in argillites — besides the fact that load hold yields a better approximation of Young's modulus (Eq. (8)). ii) Desaturation of the material facilitates the inclusions to be discriminated more easily. In the case of the instantaneous unloading tests, the modulus is plotted versus the loading time (which is proportional to the maximal load and thus is a rough estimate of the hardness) in Fig. 12. For the series performed at low humidity a variation of the modulus with hardness can be observed whereas in the case of high saturation values of modulus remain low whatever the hardness. In the case of deferred loading tests, deferred unloading modulus is plotted versus the penetration depth during the load holding period (Fig. 13). At low saturation levels, the variation in the deferred unloading modulus is wide. In contrast, when the material is close to saturation, the amount of variability is restricted because macro-inclusions – as well as micro-inclusions – are pushed into the matrix by the indenter tip. Moreover, the penetration increasing with saturation, the reduction is also linked to the increase of the volume tested which appears to be more homogeneous. iii) In this first approach, normal distributions have been considered as it has been done previously in other works (Constantinides and Ulm, 2007). However, in our study, in almost all series a large scatter is observed and the values of modulus extend to more than one decade. Therefore, it would be more relevant to consider log-normal distributions in order to better take into account the small values. Moreover it could even provide a better description of the asymmetric peaks observed in the histograms.

6. Conclusions The results of nano-indentation tests (with instantaneous and deferred unloading) performed under controlled humidity on CallovoOxfordian argillites from the ANDRA underground research laboratory in Meuse/Haute-Marne France, allow us to draw conclusions regarding: i) The influence of water on the deformability of the material. A clear decrease in the instantaneous and deferred unloading modulus has been shown to occur under increasingly saturated conditions. ii) The influence of water on the deformability of the different constituent phases in the material. The elastic-modulus of macroinclusions can only be determined through tests on desaturated (RH = 50%) material since in saturated material, the inclusions themselves will be pressed into the matrix. iii) Typical instantaneous unloading modulus values for different constituents in the material under desaturated (RH = 50%) and neartotal (RH = 95%) saturation conditions. At 50% humidity, we measured a mean deferred unloading modulus of 16 GPa for the clay matrix (a mean instantaneous unloading modulus of 13 GPa was observed for the clay matrix and moduli higher than 70 GPa were measured for the carbonate macro-inclusions). The mean deferred unloading modulus of the matrix appears to decrease with increasing saturation; at 95% humidity (near-saturation) it's less than 5 GPa. However, it's impossible to verify the instantaneous unloading modulus of the carbonate macro-inclusions at this high-level of saturation. Taken together, our results agree with those obtained in nano-indentation tests performed on a mmscale zone presented in Magnenet et al. (2011a). Though some aspects of argillite behaviour still require addressing (for example, additional series of nano-indentation tests could be designed to allow the effects of anisotropy to be taken into account), the future perspectives are numerous and promising. The reference values obtained for the elastic properties of the different constituents can be used to test the robustness of the different mechanical behaviour models currently available. Similarly, they could be incorporated into models that are in development thereby allowing inter-comparisons to be made. Furthermore, these reference values will expand our understanding of the micromechanical properties of rocks, a rapidly developing field of research.

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