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The heterogeneous nature of bleeding in cement pastes
Cement and Concrete Research 95 (2017) 108–116
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The heterogeneous nature of bleeding in cement pastes Nadia Massoussi, Emmanuel Keita, Nicolas Roussel ⁎ IFSTTAR, Laboratoire Navier, Université Paris Est, France
a r t i c l e
i n f o
Article history: Received 8 November 2016 Received in revised form 10 February 2017 Accepted 23 February 2017 Available online xxxx
a b s t r a c t We focus in this paper on the bleeding of cement pastes. Our experimental results suggest that bleeding cannot be simply considered as the consolidation of a soft porous material but is of an obvious heterogeneous nature. It indeed leads to the formation of preferential water extraction channels. We measure here the existence of an induction period. This period could, if fully understood and extended, be of major interest from an industrial point of view. It is followed by an accelerating period, during which the apparent permeability of the paste increases due to the formation and percolation of the water extraction channels. The water is then extracted at a constant rate until gravity is not able to further consolidate the zones located between the channels. Only this later regime had been observed and discussed until now in literature. © 2017 Published by Elsevier Ltd.
1. Introduction In recent years, the understanding of the rheological behavior of homogeneous cementitious materials has made significant progress. However, concrete or mortar stability (i.e. the ability of the mixture to stay homogeneous) and the physical phenomena at the origin of this stability (or the lack of stability) are still poorly understood. Concrete or mortar stability can be divided into two major features: the stability of the coarse aggregates or sand particles suspended in the cement matrix (which can reverse into so-called segregation), and the stability of the cement grains suspended in water (which can reverse into so-called bleeding). Although there exist some first-order analysis of aggregates stability [1,2], bleeding is still treated empirically. Moreover, methods allowing for its proper measurement were only recently developed [3, 4]. The most complete state of the art dealing with bleeding is gathered in the thesis of Josserand [5]. The main conclusion from this work is that bleeding of cementitious materials can be seen as a porous mediumconsolidation-like process. We focus in this paper on this specific gravity-induced phase separation process and its kinetics at the scale of cement paste and mortars. Our experimental results on these simpler systems suggest that bleeding of cementitious materials cannot be simply considered as the homogeneous consolidation of a porous material. It is of an obvious heterogeneous nature leading to the formation of preferential water extraction channels within the paste. These can be visually spotted as sometimes observed in literature or in practice. They can also be of a
⁎ Corresponding author. E-mail address: [email protected] (N. Roussel).
http://dx.doi.org/10.1016/j.cemconres.2017.02.012 0008-8846/© 2017 Published by Elsevier Ltd.
length scale of the order of a few times the average diameter of the cement grains and therefore non visible to the human eye. As a consequence, the kinetics of bleeding can be divided into several regimes. First, there exists an induction period displaying a low water extraction velocity. This regime could, if fully understood, be of major interest from an industrial point of view. It is followed by an accelerating period, during which the apparent permeability of the paste increases due to the formation and percolation of the above water extraction channels. Then, there exists an extraction period, during which the water extraction velocity is more or less constant. Finally, a consolidation decelerating regime leads eventually to a situation, in which gravity is not able to further compact the constitutive cement grains. Only the two latters had been discussed until now in literature.
2. Materials and protocol 2.1. Materials A CEM I type cement of specific density 3.14 is used in this study. Its specific surface measured using a Blaine apparatus is 3390 cm2/g. Its maximum solid packing fraction is estimated to be around 59% [6] and its chemical composition is given in Table 1. Pastes with water-to-cement ratio of 0.5 or 0.6 were mixed for 3 min using a Turbo test Rayneri VMI mixer at 840 rpm. Mortars were prepared by first preparing cement pastes at a 0.5 water-to-cement ratio and then mixing manually 50% volume fraction of a natural rounded sand of size 0/4 mm that had been previously washed and dried. It can be noted that beginning of setting for these mixtures was roughly estimated to be around 6 h.
N. Massoussi et al. / Cement and Concrete Research 95 (2017) 108–116 Table 1 Cement chemical composition. SiO2
Al2O3
Fe2O3
CaO
Mgo
Na2O
K2O
SO3
Cl
CAO
21.04%
3.34%
4.14%
65.43%
0.83%
0.22%
0.35%
2.31%
0.02%
0.69%
2.2. Rheometric measurements The rheology measurements were carried out using a C-VOR Bohlin® stress-controlled rheometer equipped with a Vane geometry [7]. The Vane geometry was a four-bladed paddle with a diameter of 25 mm, the outer cup diameter was 50 mm and its depth was 60 mm. Within 1 min after the end of the mixing phase, the cup of the rheometer was filled. The samples were not pre-sheared in order to avoid any potential sand particle migration in the case of mortars [2,8] but care was taken to keep the mixing and placing (i.e. the flow history) identical for all samples. After a 1 min resting time (or 120 min resting time), the initial yield stress (or the yield stress after 2 h of rest) was measured by rotating the Vane geometry at 0.05 s−1. The obtained results are shown in Fig. 1. The yield stresses (i.e. the stress peak before flow onset) for the pastes and mortars with W/C = 0.5 are gathered in Table 2. It can be seen that the yield stress of the mortar is one order of magnitude higher than the yield stress of the paste due to the amplifying role of the rigid sand inclusions [9]. The structuration of the paste occurs at a rate of Athix = 1.3 × 10−2 Pa/s [10]. It occurs at a rate one order of magnitude higher for the mortar (i.e. 1.2 × 10−1 Pa/s). The structuration characteristic time (i.e. the time needed to double the initial yield stress of the mixture) for these two systems containing the same cement at the same W/C ratio is therefore similar and around 300 s [10,11]. This result is in agreement with the influence of inclusions on the thixotropy of cementitious materials [9]. It results from the fact that structural build-up kinetics finds its origin at the level of the constitutive paste and is simply amplified by the presence of rigid sand inclusions [9].
2.3. Bleeding experiments Just after mixing, mixtures were poured into transparent test tubes of diameters 1.4, 2.2, 3.7, 4.8, 7.7, and 16 cm. The total time needed to fill the tube did not exceed 1 min. After filling, the tube was sealed with a plastic film to prevent any water evaporation. Progressive water extraction from the sample was then recorded using numerical image acquisition. A grey level threshold was then applied to the pictures allowing for the automated detection of the boundary between the consolidating sample and the upper extracted water layer. The acquisition period of the extracted water layer thickness was 1 s through the first hour and then 1 min for the following 3 h. It can be noted that,
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Table 2 Yield stresses of the pastes and mortars with W/C = 0.5. Mortars are prepared with 50% volume fraction of sand. Yield stress Cement paste after mixing (W/C = 0.5) Cement paste after 2 h (W/C = 0.5) Mortar after mixing – 50% volume fraction of sand (W/C = 0.5) Mortar after 2 h – 50% volume fraction of sand (W/C = 0.5)
3 Pa 100 Pa 40 Pa 900 Pa
at the end of the test, there were still 2 h left before the initiation of setting. It can moreover be noted that the above image acquisition protocol can only be applied on pure cement paste. Indeed, in such systems, small particles in the system are flocculated with the coarsest cement grains (see discussion further). As a consequence, the extracted water layer is devoided from any suspended fine particles. It is therefore clear and allows for a distinction between the upper water layer and the consolidating paste or mortar. However, we noted that, when high range water reducing type admixtures were added to our system (results not shown here), the extracted water became opaque. This suggests the presence of suspended fine particles in the bleeding water [12]). The boundary between the extracted water layer and the consolidated paste becomes then difficult to detect as observed in [12]. 2.4. Micro-tomography imaging Tests were performed on the XR-μCT laboratory scanner available at Laboratoire Navier (Ultratom from RX-Solution). The tube voltage and tube current were set as 150 kV and 179 μA, respectively. Scan time was around 30 min. 3D images were reconstructed with a voxel size of 54 × 54 × 54 μm by means of the X-Act software provided by the manufacturer of the CT device. In particular, projections were shifted in the vertical direction before reconstruction to take into account the overall settlement of the sample. The total sampled volume size was 1529 × 1529 × 1253 voxels. 3. Experimental results 3.1. Consolidation regime In Fig. 2, we follow the progress of bleeding by measuring the thickness of the extracted water layer as a function of time for three different initial sample heights in a cylinder of diameter 77 mm. It can be noted that the initial water layer thickness in Fig. 2 is the one that already existed at the end of the pouring phase. We suggest that this finds its origin in the shear induced phase separation induced by the pouring and
Fig. 1. Flow onset of pastes and mortars after mixing and after 2 h of rest as function of applied strain. Water to cement ratio is 0.5 and mortars are prepared with 50% volume fraction of sand.
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Fig. 2. Thickness of the extracted water layer for cement pastes as a function of time for three different initial sample heights in linear scale. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
filling process [2]. As shown in this figure, in the first 4000 s (around 1 h), bleeding occurs similarly no matter the initial height of the sample. The average fluid extraction velocity in this regime is almost constant and of the order of 10−6 m/s. However, on longer time scales, bleeding rate decreases and the final amount of extracted water becomes proportional to the initial height of material. This suggests that the final compaction state is the same for all samples as shown in Fig. 3, in which we plot the computed final solid volume fraction in the sample as a function of the initial filling height. The uncertainty of the measurement was estimated by carrying out six times the same test for a filling height of 40 cm and by computing the relative standard deviation on the measured final amount of bleeding water. These first results are in agreement with the view of bleeding as a homogeneous consolidation process of a deformable porous media as described in [5]. Indeed, in theory, if we consider that we are facing an homogeneous consolidation of a deformable porous media, we expect from Darcy's Law that the amount of water that has left the sample after a time t shall be proportional to Δρ.g.K.t/μ0 where μ0 is the viscosity of the interstitial fluid, Δρ is the density difference between the particles and the
Fig. 3. Final solid volume fraction of the tested cement paste as function of the initial filing height. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
liquid, K is the permeability of the fresh paste. As a consequence, initially, we expect the bleeding rate to be the same for all samples no matter the initial height as shown in Fig. 2. However, on longer time scales, we expect a decrease in permeability with time because of the consolidation process and the associated increase in solid fraction [13]. Bleeding shall stop when local gravity forces induced by the density difference between cement and water are compensated by the particle interactions, which increase with the local solid volume fraction. If we neglect, as a first step, any contribution of the stress at the wall (see discussion further), this equilibrium shall be local. The same equilibrium shall be reached anywhere in the sample when bleeding stops and final consolidation is reached. We moreover expect that the final solid fraction of the paste, assuming that it is reached before setting, shall be the same for all samples as shown in Fig. 3. The final amount of water that has left the sample is then proportional to the initial height of material tested. The above results confirm, similarly to other authors, that bleeding display, through these regimes, the features of a homogeneous soil-consolidation-like process. We now plot in Fig. 4 the final paste solid volume fraction measured after 4 h for tests carried out on cement pastes and mortars for various tube diameters at a W/C ratio of 0.5. It can be noted that, in the case of mortars, we do not expect any change in the volume of the sand particles through the bleeding process. We therefore compute from the amount of water extracted from the mortar the final solid volume fraction of the constitutive paste located between the sand grains. We see in Fig. 4 that, for large tube diameters, the final paste volume fraction is almost the same in both mortar and pastes. This suggests that the final compaction state of the paste itself is not affected by the presence of sand grains. However, when the tube diameter decreases, the final paste volume fraction reached at the end of the test decreases. This suggests that bleeding becomes affected by the presence of the interface between the material and the tube wall. This effect is stronger in the case of the mortars. In the case of the 1.4 cm diameter tube, the filling of the tube was difficult and required a slight vibration. No bleeding was however measured and the final paste solid volume fraction stayed equal to the initial solid volume fraction. We moreover noted, through all our experiments, the apparently random creation of water extraction channels at the surface of our samples as shown in Figs. 5 and 6. These channels formed mainly during the first 1000 s of the test. Through that step, cement particles were visually observed to be extracted from the sample through these channels at a
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Fig. 4. Final solid volume fraction of the constitutive paste for different tube diameters for mortars and pastes. Water-to-cement ratio is 0.5. Volume fraction of sand is 50% for the mortars. The dotted line is the initial paste volume fraction.
velocity obviously far higher than the average 10−6 m/s water extraction velocity estimated from Fig. 2. This suggests that the local water velocity in these channels was far higher than the average water extraction velocity. Cement particles accumulation at the surface resulted, in some cases, in the formation of the specific shapes shown in Fig. 5. As illustrated in Fig. 6, the number of these channels strongly and randomly varied between two identical tests although the measured final amount of extracted water was the same. Our micro-tomography images show the presence of these channels inside the bulk of the samples as shown in Fig. 7, in which we show the same slice of material at the center of a tube of diameter 77 mm, 30 min and 2.5 h after pouring. Due to beam hardening effects on cylindrical samples, density appears lower close to the walls of the sample. Fig. 7(right) shows however the presence of vertical channels within the paste. Their diameter is of the order of a couple millimeters.
water extraction rate. This regime was not visible using a linear time scale as in Fig. 2. This regime can be associated to a low capacity of the system to extract water. In the following, we will call this regime the induction period of bleeding. It can be reminded here that the initial water layer thickness measured in this regime is the one that already existed at the end of the pouring phase. This induction period, as shown in Fig. 8, is followed by an acceleration period during which the water extraction rate increases and ultimately reaches the two regimes discussed above. Considering once again Darcy's law, this observation suggests that the apparent permeability of the sample in the acceleration regime following the induction period is higher than the initial permeability of the sample after pouring. In most of the tests, as described above, it is during that period that extracting water channels are formed and detected visually at the surface of the sample.
3.2. Paradox at short time scales 4. Discussion and analysis We now plot in Fig. 8 the results of Fig. 2 in a log scale of time, in which the focus is given to short time scales. We see in Fig. 8 that, below 1000 s (i.e. around 15 min), there exists a regime of very low
Fig. 5. Water extraction channels visible at the upper surface of the sample. Initial sample height is 40 cm. Tube diameter is 77 mm. Water to cement ratio is 0.6.
4.1. Stability and stress at the wall By writing the force equilibrium on a layer of material in a cylinder, we know that a stress at the wall τ = ρgR/2 where ρ is the density of the material and R is the radius of the cylinder shall prevent the material from flowing. Considering the dimension of the tubes and the fact that the free surface is not a meniscus, we expect surface tension effects to be neglectable compared to gravity stresses. If the material yield stress is higher than ρgR/2, it means that it is not possible to fill the cylinder under the effect of gravity alone. To fill the tube, some additional energy such as the one brought through vibration would be needed [14]. In a cementitious material, there exists a difference in density Δρ between the interacting cement particles and the fluid. A similar force equilibrium as above suggests that a stress at the wall higher than τ = ΔρgR/2 shall prevent the separation of the solid and liquid phases. The stress induced in the percolated skeleton of interacting grains by the difference in density can then indeed be transferred to the vertical wall preventing the material from bleeding. It can be noted that a similar dimensional scaling would be obtained on a section of the same material between two parallel walls (i.e. a formwork).
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Fig. 6. Water extraction channels at the upper surface of samples for 2 tests in identical conditions at the end of the test (contrast artificially enhanced). Initial sample height is 40 cm. Tube diameter is 77 mm. Water-to-cement ratio is 0.6. 27 channels are visible (i.e. larger than 100 μm) on left figure whereas 125 channels are visible on right figure.
This suggests that, according to the yield stress of the material poured in the mold, we can expect three regimes. In the first regime in Fig. 9, the material is fluid enough to fill the mold. It can however potentially bleed, as the stress at the wall, i.e. the yield stress, is not high enough to cover for the difference in density between the components. In this regime, yield stress is neglectable in front of ΔρgR/2. The material shall then consolidate as in a semi-infinite geometry (i.e. the presence of walls and interfaces can be neglected). Bleeding becomes an intrinsic material feature, which does not depend on the geometry of the mold. In this asymptotic case, it was shown that the conditions, under which a cement suspension is stable, result from the competition between particle colloidal interactions and gravity [6]. In the second regime in Fig. 9, the shear stress at the wall does not prevent the filling of the mold but is high enough to prevent bleeding from occurring. As a consequence, in this regime, an intrinsically nonstable material could be stabilized by the presence of the surrounding interfaces. In the third regime in Fig. 9, the shear stress at the wall could prevent bleeding from occurring as above but this shear stress shall also prevent the filling of the mold under the sole effect of gravity. External or internal vibration, by bringing to the system an additional energy, could however allow for a proper filling. This would result in a material, the stability of which would be ensured by the surrounding interfaces.
Several additional comments can be extrapolated from the above regimes. First, as illustrated in Fig. 9, it is only in the case of concrete, the density of which is higher than the density difference between the cement particles and water, that the second regime can exist. For pastes and mortar, this second regime shall not exist. More generally, it can be kept in mind that the extent of the second regime is expected to be small. It shall be, for instance, between 1000 Pa and 1250 Pa yield stress for a concrete in a 20 cm diameter column. Staying in this regime in practice shall therefore prove complex. The most common cases of interface-induced stability should therefore be found in the third high yield stress regime. It can then be concluded that casting a material that would be stabilized by the shear stress at the wall interface would need, in general, that the material is cast using vibration. Second, for most fluid cement pastes in a cylinder like the ones studied in this paper or in the case of self compacting concrete in a form, we can expect to be in the first regime and that the stress at the wall shall be neglected. An exception could be found when the stress at the wall increases through either thixotropy [15,16,17] or through the consolidation process itself [4]. It would then reach ΔρgR/2 and bleeding shall then stop as the material enters the second regime in Fig. 9. If this transition is reached through consolidation, it can however be expected that the level of bleeding needed to do so would be extremely detrimental to
Fig. 7. Micro-tomography imaging of paste samples 30 min (left image) and 2.5 h (right image) after pouring. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
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Fig. 8. Thickness of the extracted water layer as a function of time for three different initial sample heights in log scale. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
the final structural element. We can conclude that such a case should not exist in practice but keep in mind that thixotropic properties could play a role on bleeding reduction for sufficiently slender elements. The above frame allows for the analysis of the results obtained in Fig. 4. The yield stresses of the cement paste and of the mortar are given in Table 2 after 2 h of rest. These values allow for the estimation of the critical tube diameter, below which the stress at the wall shall prevent bleeding. This diameter would be around 2 cm for the cement paste and around 15 cm for the mortar. We see in Fig. 4 that, indeed, above these values, the measured bleeding at the end of the test does not depend on the testing tube diameter. Below these values, our results suggest that a part of the difference in density between cement grains and water is transferred to the tube wall through the stress at the wall interface. In the rest of this paper, we will only focus on results obtained when the tube interface has no effect on bleeding (i.e. sufficiently large tubes).
4.2. Induction period and reorganization of the system It was shown in [6] that colloidal forces and gravity forces competition dictate the occurrence of bleeding in a cement paste. As soon as bleeding occurs and water flows in such a porous medium, a drag force moreover applies on the cement grains. This drag force increases
with water extraction velocity. It can be noted that all three above forces have different dependencies on particle size. The inter-particle colloidal forces can be estimated as being of the order of A0a∗/12H2, where a∗ is the radius of curvature of the “contact” points (i.e. the typical roughness of the grain surface), H is the surface to surface separation distance at “contact” points and A0 is the non-retarded Hamaker constant [18,19]. The Hamaker constant value for C3S is of the order of 1.6 10−20 J [18]. Assuming spherical particles, the gravity force is ΔρgπD3/6 whereas the Stokes drag force can be estimated as 3πμ0DVloc where μ0 is the viscosity of the interstitial fluid and Vloc is the local fluid velocity in the porosity of the paste. We first consider here a homogeneous paste at short time scales. In such an homogeneous medium, the macroscopic water extraction velocity V should follow Darcy's law and write V = ΔρgK/μ0, where μ0 is the viscosity of the interstitial fluid, Δρ is the density difference between the particles and the liquid and K is the permeability. We note here d the typical size of the porosity, through which water is extracted, while D is the average diameter of the cement grains. We consider for a typical cement paste that D is of the order of 10 μm while, when the paste is homogeneous, d shall be, for this kind of dense suspensions, one order of magnitude lower and therefore of the order of 1 μm. The number of pores per surface unit is of the order of D− 2. The permeability of this (initially) homogeneous paste can be
Fig. 9. Filling and bleeding in a column as a function of yield stress. The three regimes from left to right.
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estimated using the Kozeny-Carman relation (K= (1− ϕ)3d2/45ϕ2 with ϕ the solid volume fraction). It is of the order of 10−14 m2 for the 0.6 water-to-cement ratio studied here. This value correlates well with the recent permeability measurements carried out in [20] on fresh cement pastes. It can be noted that the values from [20] were obtained using filtration equipment, in which water and particles all move in the same direction. The conditions under which preferential water extraction channels can form are therefore not fulfilled (see discussion below). Under the natural gravity pressure gradient due to the difference in density between the particle and the liquid, water velocity in the sample shall then be of order Δρ.g.K/μ0, namely lower than the 10− 6 m/s value from Fig. 2. As a consequence, the layer of extracted water above the sample after 104 s (around 3 h) shall be lower than 50 μm. It however reaches 10 mm in Fig. 2. When water flows through this homogeneous porous system at short time scales, flow occurs in the pores. The local velocity Vloc shall relate to the macroscopic water extraction velocity V through Vloc =VD2/ d2 and be therefore two orders of magnitude higher. We now plot in Fig. 10 the magnitudes of the viscous drag force, the colloidal attractive force and the gravity force as a function of cement particle size. From this figure, we can identify three regimes. In regime 1, for fine particles, colloidal forces dominate. As a consequence, we can expect these grains to be flocculated to larger grains. In regime 3, for coarse cement grains, gravity forces dominate. This suggests that the drag force is not able to move these particles upwards and we can expect them to settle through the bleeding process. Finally, in regime 2, for medium size grains with a diameter of order 10 μm, all three forces magnitudes are equivalent. It can be noted that these grains dominate from a volume fraction point of view the size distribution. For these particles, it can be expected that the upward drag force induced by water flow could be at the origin of a rearrangement of the particles. We suggest therefore that, although water flow is extremely slow in the induction stage of bleeding, it is sufficient to induce a progressive local reorganization of the system. This reorganization leads to the formation of the preferred water extraction channels shown in Figs. 5, 6 and 7. We can additionally extrapolate from the above that addition of plasticizers shall reduce the magnitude of attractive colloidal forces. This could allow for the displacement of the smallest particles. For
instance, covering the surface of the grains with a polymer could increase the inter-particle surface-to-surface separating distance by a factor 5 [6]. Keeping in mind that inter-particle forces scale with H−2 [6,18, 19], the average attractive colloidal force could therefore decrease by a factor 25 as illustrated in Fig. 10. As a consequence, drag force would dominate for particles as small as several hundreds of nanometers. This would explain why the extracted water above the sample turns from a transparent layer to an opaque one when high range water reducing type admixtures were added to our system (see Section 2.3). This feature was also reported in [12]. It can finally be noted that, for low water to cement ratio, the permeability of the initially homogeneous system and the initial local water velocity could be low enough for the drag force to be dominated by either the colloidal forces or the gravity for the entire range of cement particle sizes. We would then expect then that less preferential water extraction channels are formed and that bleeding rate does not go through an acceleration phase. This is indeed what we measured on samples prepared with a water-to-cement ratio of 0.5, for which the final amount of extracted water was extremely low but also for which channels could not be visually spotted (results not showed here). As the permeability of such materials shall be lower than the 10− 14 m2 value estimated above, the water extraction velocity shall be lower than 10 − 7 m/s. The water layer thickness above a one-meter high column of pure paste shall therefore not exceed 1 mm. This therefore suggests that any measurable bleeding shall find its origin in the formation of preferential water extraction channels. As soon as water extraction channels do form, flow localizes preferentially in these and it becomes debatable to consider the system as a homogenous porous medium described using a permeability value. The local velocity Vloc relates then to the macroscopic water extraction velocity V through Vloc =V/Nd2c where N is the number of channels per surface unit and dc is the average channel diameter. We now consider that, after a transition period at the end of which the forming channels have reached the surface and reached their average final diameter, we are facing a system in which all water is extracted through these channels. As shown in Fig. 8, the water extraction rate in this regime is constant. This happens before the consolidation of the
Fig. 10. Competition between colloidal force, drag force and gravity force as a function of the size of cement grains.
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Fig. 11. Extracted water as function of time in log scales. Conceptual diagram showing the five consecutive stages of the bleeding process. 1: induction period. 2: accelerating regime. 3: constant water extraction rate period. 4: consolidation regime. 5: final consolidated state.
zones between the channels slows down and finally prevents any additional water from being extracted. A constant water extraction rate suggests that the size of the channels does not change anymore. Our tests, on a range of sample heights up to 400 mm, have moreover shown that, no matter the number of channels and their size, the final amount of extracted water and the kinetics of water extraction in the constant rate regime are identical. It can be specifically noted that the duration of the induction period is the same no matter the sample height. As the macroscopic water extraction velocity V is similar for all tests no matter the number and sizes of the channel, this suggests therefore that the system can reach the same water extraction steady and final state for any value of Nd2c . This suggests that any configuration of channels would lead to the same value for Nd2c . If the size of these channels or preferred water extraction paths becomes larger than a few 100 μm (low N, high dc), they can then be visually spotted. We however suggest that, even when they cannot be visually spotted (high N, low dc), they do exist within the paste and are at the origin of the water extraction rate increase at the end of the induction period in Fig. 8. No matter the size and the number of channels, the extraction rate and the final bleeding is the same. There exist therefore an infinity of configuration that can be adopted by the system to extract the same amount of water. They will however all lead to the same final consolidation of the sample. An opened question for such a behavior is the origin of these various configurations. We preliminary suggest here that, similarly to crack initiation, water extraction channels initiation locates at some local defects of the system (i.e. the most permeable zones or the most porous zones). The fact that the duration of the induction period does not depend on the sample height suggests that percolation of the forming channels does not occur when they have propagated over a distance of the height of the sample. We suggest here that channels do percolate when they have propagated over a distance of the order of the average distance between local defects. This distance only depends therefore on the material defects distribution and not on the dimension of the samples. This finally suggests that, for instance, air bubbles localization and size distribution shall play a major role. Indeed, in the initially homogeneous samples, air bubbles are, in average, larger than the typical pore size between grains. They constitute therefore the most permeable zones or local defects, into which water flow can initially concentrate.
channels are being initiated through local particle rearrangements at the local defects of the suspension (air bubbles for instance). As particles are being progressively displaced, the channels typical diameter and typical length increase (accelerating regime in Fig. 11) until these channels do percolate. The system then reaches a steady state (constant water extraction rate period in Fig. 11). In this regime, the channels size and number do not change any more and we reach a system, in which the water is extracted through a constant apparent permeability although the system is already highly heterogeneous. It can be expected that the zones located between the channels are then being consolidated while feeding the channels with water. Finally, in the consolidation period (Cf. Fig. 11), the apparent permeability of the system decreases because of the further compaction of the zones located between the preferred extracting channels until gravity is not able to further consolidate the sample and extract any additional water (Final consolidated state in Fig. 11).
5. Global frame
References
From the above results obtained on systems, for which there was no interaction with wall interfaces, we suggest that, during the induction period (Cf. Fig. 11), water flow induces a viscous drag force allowing for the displacement of intermediate size cement particles and for a reorganization of the system. As a result, preferred water extraction
6. Conclusions We focused in this paper on the bleeding phenomenon, its amplitude and its kinetics at the scale of cement paste and mortars. Our experimental results on simple systems suggest that bleeding cannot be simply considered as the consolidation of a soft porous material but is of an obvious heterogeneous nature leading to the formation of preferential water extraction channels within the cement paste. Our results moreover suggest that, without these channels, bleeding shall be neglectable for most cement-based materials. We discussed here the origin of the induction period, of the accelerating period, of the constant water extraction rate period and of the consolidation period. Only the latters had been observed until now in literature.
Acknowledgement The authors would like to acknowledge the financial support of both Soletanche Bachy© and FNTP (Fédération Nationale des Travaux Publics). The authors acknowledge FNTP committee reviewers for their constructive comments to the text. The authors would like to thank Mr Patrick Aimedieu for the technical and scientific support on the microtomography imaging.
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[4] Y. Peng, S. Jacobsen, Influence of water/cement ratio, admixtures and filler on sedimentation and bleeding of cement paste, Cem. Concr. Res. 54 (December 2013) 133–142. [5] L. Josserand, Ressuage des bétons hydrauliques(Thesis Report (in French), LCPC) 2004. [6] A. Perrot, T. Lecompte, H. Khelifi, C. Brumaud, J. Hot, N. Roussel, Yield stress and bleeding of fresh cement pastes, Cem. Concr. Res. 42 (7) (2012) 937–944. [7] Q.D. Nguyen, D.V. Boger, Direct yield stress measurement with the vane method, J. Rheol. 29 (1985) 335–347. [8] H. Hafid, G. Ovarlez, F. Toussaint, P.H. Jezequel, N. Roussel, Assessment of potential concrete and mortar rheometry artifacts using magnetic resonance imaging, Cem. Concr. Res. 71 (2015) 29–35. [9] F. Mahaut, S. Mokeddem, X. Chateau, N. Roussel, G. Ovarlez, Effect of coarse particle volume fraction on the yield stress and thixotropy of cementitious materials, Cem. Concr. Res. 38 (11) (2008) 1276–1285. [10] N. Roussel, A thixotropy model for fresh fluid concretes: theory, validation and applications, Cem. Concr. Res. 36 (10) (2006) 1797–1806. [11] N. Roussel, G. Ovarlez, S. Garrault, C. Brumaud, The origins of thixotropy of fresh cement pastes, Cem. Concr. Res. 42 (1) (2012) 148–157. [12] M. Neubauer, M. Yang, H.M. Jennings, Interparticle potential and sedimentation, behaviour of cement suspensions: effects of admixtures, Adv. Cem. Based Mater. 8 (1998) 17–27.
[13] L. Josserand, O. Coussy, F. de Larrard, Bleeding of concrete as an ageing consolidation process, Cem. Concr. Res. 36 (9) (September 2006) 1603–1608. [14] N. Roussel, Rheology of fresh concrete: from measurements to predictions of casting processes, Mater. Struct. 40 (10) (2007) 1001–1012. [15] G. Ovarlez, N. Roussel, A physical model for the prediction of lateral stress exerted by self-compacting concrete on formwork, Mater. Struct. 39 (2) (2006) 269–279. [16] P.H. Billberg, N. Roussel, S. Amziane, M. Beitzel, G. Charitou, B. Freund, J.N. Gardner, G. Grampeix, C.A. Graubner, L. Keller, K.H. Khayat, D. Lange, A.F. Omran, A. Perrot, T. Proske, R. Quattrociocchi, Y. Vanhove, Field validation of models for predicting lateral form pressure exerted by SCC, Cem. Concr. Compos. 54 (2014) 70–79. [17] J.C. Tchamba, S. Amziane, G. Ovarlez, N. Roussel, Lateral stress exerted by fresh cement paste on formwork: laboratory experiments, Cem. Concr. Res. 38 (4) (2008) 459–466. [18] J. Flatt, P. Bowen, Yodel: a yield stress model for suspensions, J. Am. Ceram. Soc. 89 (4) (2006) 1244–1256. [19] N. Roussel, A. Lemaître, R.J. Flatt, P. Coussot, Steady state flow of cement suspensions: a micro-mechanical state of the art, Cem. Concr. Res. 40 (2010) 77–84. [20] V. Picandet, D. Rangeard, A. Perrot, T. Lecompte, Permeability measurement of fresh cement paste, Cem. Concr. Res. 41 (3) (March 2011) 330–338.
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Cement and Concrete Research journal homepage: www.elsevier.com/locate/cemconres
The heterogeneous nature of bleeding in cement pastes Nadia Massoussi, Emmanuel Keita, Nicolas Roussel ⁎ IFSTTAR, Laboratoire Navier, Université Paris Est, France
a r t i c l e
i n f o
Article history: Received 8 November 2016 Received in revised form 10 February 2017 Accepted 23 February 2017 Available online xxxx
a b s t r a c t We focus in this paper on the bleeding of cement pastes. Our experimental results suggest that bleeding cannot be simply considered as the consolidation of a soft porous material but is of an obvious heterogeneous nature. It indeed leads to the formation of preferential water extraction channels. We measure here the existence of an induction period. This period could, if fully understood and extended, be of major interest from an industrial point of view. It is followed by an accelerating period, during which the apparent permeability of the paste increases due to the formation and percolation of the water extraction channels. The water is then extracted at a constant rate until gravity is not able to further consolidate the zones located between the channels. Only this later regime had been observed and discussed until now in literature. © 2017 Published by Elsevier Ltd.
1. Introduction In recent years, the understanding of the rheological behavior of homogeneous cementitious materials has made significant progress. However, concrete or mortar stability (i.e. the ability of the mixture to stay homogeneous) and the physical phenomena at the origin of this stability (or the lack of stability) are still poorly understood. Concrete or mortar stability can be divided into two major features: the stability of the coarse aggregates or sand particles suspended in the cement matrix (which can reverse into so-called segregation), and the stability of the cement grains suspended in water (which can reverse into so-called bleeding). Although there exist some first-order analysis of aggregates stability [1,2], bleeding is still treated empirically. Moreover, methods allowing for its proper measurement were only recently developed [3, 4]. The most complete state of the art dealing with bleeding is gathered in the thesis of Josserand [5]. The main conclusion from this work is that bleeding of cementitious materials can be seen as a porous mediumconsolidation-like process. We focus in this paper on this specific gravity-induced phase separation process and its kinetics at the scale of cement paste and mortars. Our experimental results on these simpler systems suggest that bleeding of cementitious materials cannot be simply considered as the homogeneous consolidation of a porous material. It is of an obvious heterogeneous nature leading to the formation of preferential water extraction channels within the paste. These can be visually spotted as sometimes observed in literature or in practice. They can also be of a
⁎ Corresponding author. E-mail address: [email protected] (N. Roussel).
http://dx.doi.org/10.1016/j.cemconres.2017.02.012 0008-8846/© 2017 Published by Elsevier Ltd.
length scale of the order of a few times the average diameter of the cement grains and therefore non visible to the human eye. As a consequence, the kinetics of bleeding can be divided into several regimes. First, there exists an induction period displaying a low water extraction velocity. This regime could, if fully understood, be of major interest from an industrial point of view. It is followed by an accelerating period, during which the apparent permeability of the paste increases due to the formation and percolation of the above water extraction channels. Then, there exists an extraction period, during which the water extraction velocity is more or less constant. Finally, a consolidation decelerating regime leads eventually to a situation, in which gravity is not able to further compact the constitutive cement grains. Only the two latters had been discussed until now in literature.
2. Materials and protocol 2.1. Materials A CEM I type cement of specific density 3.14 is used in this study. Its specific surface measured using a Blaine apparatus is 3390 cm2/g. Its maximum solid packing fraction is estimated to be around 59% [6] and its chemical composition is given in Table 1. Pastes with water-to-cement ratio of 0.5 or 0.6 were mixed for 3 min using a Turbo test Rayneri VMI mixer at 840 rpm. Mortars were prepared by first preparing cement pastes at a 0.5 water-to-cement ratio and then mixing manually 50% volume fraction of a natural rounded sand of size 0/4 mm that had been previously washed and dried. It can be noted that beginning of setting for these mixtures was roughly estimated to be around 6 h.
N. Massoussi et al. / Cement and Concrete Research 95 (2017) 108–116 Table 1 Cement chemical composition. SiO2
Al2O3
Fe2O3
CaO
Mgo
Na2O
K2O
SO3
Cl
CAO
21.04%
3.34%
4.14%
65.43%
0.83%
0.22%
0.35%
2.31%
0.02%
0.69%
2.2. Rheometric measurements The rheology measurements were carried out using a C-VOR Bohlin® stress-controlled rheometer equipped with a Vane geometry [7]. The Vane geometry was a four-bladed paddle with a diameter of 25 mm, the outer cup diameter was 50 mm and its depth was 60 mm. Within 1 min after the end of the mixing phase, the cup of the rheometer was filled. The samples were not pre-sheared in order to avoid any potential sand particle migration in the case of mortars [2,8] but care was taken to keep the mixing and placing (i.e. the flow history) identical for all samples. After a 1 min resting time (or 120 min resting time), the initial yield stress (or the yield stress after 2 h of rest) was measured by rotating the Vane geometry at 0.05 s−1. The obtained results are shown in Fig. 1. The yield stresses (i.e. the stress peak before flow onset) for the pastes and mortars with W/C = 0.5 are gathered in Table 2. It can be seen that the yield stress of the mortar is one order of magnitude higher than the yield stress of the paste due to the amplifying role of the rigid sand inclusions [9]. The structuration of the paste occurs at a rate of Athix = 1.3 × 10−2 Pa/s [10]. It occurs at a rate one order of magnitude higher for the mortar (i.e. 1.2 × 10−1 Pa/s). The structuration characteristic time (i.e. the time needed to double the initial yield stress of the mixture) for these two systems containing the same cement at the same W/C ratio is therefore similar and around 300 s [10,11]. This result is in agreement with the influence of inclusions on the thixotropy of cementitious materials [9]. It results from the fact that structural build-up kinetics finds its origin at the level of the constitutive paste and is simply amplified by the presence of rigid sand inclusions [9].
2.3. Bleeding experiments Just after mixing, mixtures were poured into transparent test tubes of diameters 1.4, 2.2, 3.7, 4.8, 7.7, and 16 cm. The total time needed to fill the tube did not exceed 1 min. After filling, the tube was sealed with a plastic film to prevent any water evaporation. Progressive water extraction from the sample was then recorded using numerical image acquisition. A grey level threshold was then applied to the pictures allowing for the automated detection of the boundary between the consolidating sample and the upper extracted water layer. The acquisition period of the extracted water layer thickness was 1 s through the first hour and then 1 min for the following 3 h. It can be noted that,
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Table 2 Yield stresses of the pastes and mortars with W/C = 0.5. Mortars are prepared with 50% volume fraction of sand. Yield stress Cement paste after mixing (W/C = 0.5) Cement paste after 2 h (W/C = 0.5) Mortar after mixing – 50% volume fraction of sand (W/C = 0.5) Mortar after 2 h – 50% volume fraction of sand (W/C = 0.5)
3 Pa 100 Pa 40 Pa 900 Pa
at the end of the test, there were still 2 h left before the initiation of setting. It can moreover be noted that the above image acquisition protocol can only be applied on pure cement paste. Indeed, in such systems, small particles in the system are flocculated with the coarsest cement grains (see discussion further). As a consequence, the extracted water layer is devoided from any suspended fine particles. It is therefore clear and allows for a distinction between the upper water layer and the consolidating paste or mortar. However, we noted that, when high range water reducing type admixtures were added to our system (results not shown here), the extracted water became opaque. This suggests the presence of suspended fine particles in the bleeding water [12]). The boundary between the extracted water layer and the consolidated paste becomes then difficult to detect as observed in [12]. 2.4. Micro-tomography imaging Tests were performed on the XR-μCT laboratory scanner available at Laboratoire Navier (Ultratom from RX-Solution). The tube voltage and tube current were set as 150 kV and 179 μA, respectively. Scan time was around 30 min. 3D images were reconstructed with a voxel size of 54 × 54 × 54 μm by means of the X-Act software provided by the manufacturer of the CT device. In particular, projections were shifted in the vertical direction before reconstruction to take into account the overall settlement of the sample. The total sampled volume size was 1529 × 1529 × 1253 voxels. 3. Experimental results 3.1. Consolidation regime In Fig. 2, we follow the progress of bleeding by measuring the thickness of the extracted water layer as a function of time for three different initial sample heights in a cylinder of diameter 77 mm. It can be noted that the initial water layer thickness in Fig. 2 is the one that already existed at the end of the pouring phase. We suggest that this finds its origin in the shear induced phase separation induced by the pouring and
Fig. 1. Flow onset of pastes and mortars after mixing and after 2 h of rest as function of applied strain. Water to cement ratio is 0.5 and mortars are prepared with 50% volume fraction of sand.
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Fig. 2. Thickness of the extracted water layer for cement pastes as a function of time for three different initial sample heights in linear scale. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
filling process [2]. As shown in this figure, in the first 4000 s (around 1 h), bleeding occurs similarly no matter the initial height of the sample. The average fluid extraction velocity in this regime is almost constant and of the order of 10−6 m/s. However, on longer time scales, bleeding rate decreases and the final amount of extracted water becomes proportional to the initial height of material. This suggests that the final compaction state is the same for all samples as shown in Fig. 3, in which we plot the computed final solid volume fraction in the sample as a function of the initial filling height. The uncertainty of the measurement was estimated by carrying out six times the same test for a filling height of 40 cm and by computing the relative standard deviation on the measured final amount of bleeding water. These first results are in agreement with the view of bleeding as a homogeneous consolidation process of a deformable porous media as described in [5]. Indeed, in theory, if we consider that we are facing an homogeneous consolidation of a deformable porous media, we expect from Darcy's Law that the amount of water that has left the sample after a time t shall be proportional to Δρ.g.K.t/μ0 where μ0 is the viscosity of the interstitial fluid, Δρ is the density difference between the particles and the
Fig. 3. Final solid volume fraction of the tested cement paste as function of the initial filing height. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
liquid, K is the permeability of the fresh paste. As a consequence, initially, we expect the bleeding rate to be the same for all samples no matter the initial height as shown in Fig. 2. However, on longer time scales, we expect a decrease in permeability with time because of the consolidation process and the associated increase in solid fraction [13]. Bleeding shall stop when local gravity forces induced by the density difference between cement and water are compensated by the particle interactions, which increase with the local solid volume fraction. If we neglect, as a first step, any contribution of the stress at the wall (see discussion further), this equilibrium shall be local. The same equilibrium shall be reached anywhere in the sample when bleeding stops and final consolidation is reached. We moreover expect that the final solid fraction of the paste, assuming that it is reached before setting, shall be the same for all samples as shown in Fig. 3. The final amount of water that has left the sample is then proportional to the initial height of material tested. The above results confirm, similarly to other authors, that bleeding display, through these regimes, the features of a homogeneous soil-consolidation-like process. We now plot in Fig. 4 the final paste solid volume fraction measured after 4 h for tests carried out on cement pastes and mortars for various tube diameters at a W/C ratio of 0.5. It can be noted that, in the case of mortars, we do not expect any change in the volume of the sand particles through the bleeding process. We therefore compute from the amount of water extracted from the mortar the final solid volume fraction of the constitutive paste located between the sand grains. We see in Fig. 4 that, for large tube diameters, the final paste volume fraction is almost the same in both mortar and pastes. This suggests that the final compaction state of the paste itself is not affected by the presence of sand grains. However, when the tube diameter decreases, the final paste volume fraction reached at the end of the test decreases. This suggests that bleeding becomes affected by the presence of the interface between the material and the tube wall. This effect is stronger in the case of the mortars. In the case of the 1.4 cm diameter tube, the filling of the tube was difficult and required a slight vibration. No bleeding was however measured and the final paste solid volume fraction stayed equal to the initial solid volume fraction. We moreover noted, through all our experiments, the apparently random creation of water extraction channels at the surface of our samples as shown in Figs. 5 and 6. These channels formed mainly during the first 1000 s of the test. Through that step, cement particles were visually observed to be extracted from the sample through these channels at a
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Fig. 4. Final solid volume fraction of the constitutive paste for different tube diameters for mortars and pastes. Water-to-cement ratio is 0.5. Volume fraction of sand is 50% for the mortars. The dotted line is the initial paste volume fraction.
velocity obviously far higher than the average 10−6 m/s water extraction velocity estimated from Fig. 2. This suggests that the local water velocity in these channels was far higher than the average water extraction velocity. Cement particles accumulation at the surface resulted, in some cases, in the formation of the specific shapes shown in Fig. 5. As illustrated in Fig. 6, the number of these channels strongly and randomly varied between two identical tests although the measured final amount of extracted water was the same. Our micro-tomography images show the presence of these channels inside the bulk of the samples as shown in Fig. 7, in which we show the same slice of material at the center of a tube of diameter 77 mm, 30 min and 2.5 h after pouring. Due to beam hardening effects on cylindrical samples, density appears lower close to the walls of the sample. Fig. 7(right) shows however the presence of vertical channels within the paste. Their diameter is of the order of a couple millimeters.
water extraction rate. This regime was not visible using a linear time scale as in Fig. 2. This regime can be associated to a low capacity of the system to extract water. In the following, we will call this regime the induction period of bleeding. It can be reminded here that the initial water layer thickness measured in this regime is the one that already existed at the end of the pouring phase. This induction period, as shown in Fig. 8, is followed by an acceleration period during which the water extraction rate increases and ultimately reaches the two regimes discussed above. Considering once again Darcy's law, this observation suggests that the apparent permeability of the sample in the acceleration regime following the induction period is higher than the initial permeability of the sample after pouring. In most of the tests, as described above, it is during that period that extracting water channels are formed and detected visually at the surface of the sample.
3.2. Paradox at short time scales 4. Discussion and analysis We now plot in Fig. 8 the results of Fig. 2 in a log scale of time, in which the focus is given to short time scales. We see in Fig. 8 that, below 1000 s (i.e. around 15 min), there exists a regime of very low
Fig. 5. Water extraction channels visible at the upper surface of the sample. Initial sample height is 40 cm. Tube diameter is 77 mm. Water to cement ratio is 0.6.
4.1. Stability and stress at the wall By writing the force equilibrium on a layer of material in a cylinder, we know that a stress at the wall τ = ρgR/2 where ρ is the density of the material and R is the radius of the cylinder shall prevent the material from flowing. Considering the dimension of the tubes and the fact that the free surface is not a meniscus, we expect surface tension effects to be neglectable compared to gravity stresses. If the material yield stress is higher than ρgR/2, it means that it is not possible to fill the cylinder under the effect of gravity alone. To fill the tube, some additional energy such as the one brought through vibration would be needed [14]. In a cementitious material, there exists a difference in density Δρ between the interacting cement particles and the fluid. A similar force equilibrium as above suggests that a stress at the wall higher than τ = ΔρgR/2 shall prevent the separation of the solid and liquid phases. The stress induced in the percolated skeleton of interacting grains by the difference in density can then indeed be transferred to the vertical wall preventing the material from bleeding. It can be noted that a similar dimensional scaling would be obtained on a section of the same material between two parallel walls (i.e. a formwork).
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Fig. 6. Water extraction channels at the upper surface of samples for 2 tests in identical conditions at the end of the test (contrast artificially enhanced). Initial sample height is 40 cm. Tube diameter is 77 mm. Water-to-cement ratio is 0.6. 27 channels are visible (i.e. larger than 100 μm) on left figure whereas 125 channels are visible on right figure.
This suggests that, according to the yield stress of the material poured in the mold, we can expect three regimes. In the first regime in Fig. 9, the material is fluid enough to fill the mold. It can however potentially bleed, as the stress at the wall, i.e. the yield stress, is not high enough to cover for the difference in density between the components. In this regime, yield stress is neglectable in front of ΔρgR/2. The material shall then consolidate as in a semi-infinite geometry (i.e. the presence of walls and interfaces can be neglected). Bleeding becomes an intrinsic material feature, which does not depend on the geometry of the mold. In this asymptotic case, it was shown that the conditions, under which a cement suspension is stable, result from the competition between particle colloidal interactions and gravity [6]. In the second regime in Fig. 9, the shear stress at the wall does not prevent the filling of the mold but is high enough to prevent bleeding from occurring. As a consequence, in this regime, an intrinsically nonstable material could be stabilized by the presence of the surrounding interfaces. In the third regime in Fig. 9, the shear stress at the wall could prevent bleeding from occurring as above but this shear stress shall also prevent the filling of the mold under the sole effect of gravity. External or internal vibration, by bringing to the system an additional energy, could however allow for a proper filling. This would result in a material, the stability of which would be ensured by the surrounding interfaces.
Several additional comments can be extrapolated from the above regimes. First, as illustrated in Fig. 9, it is only in the case of concrete, the density of which is higher than the density difference between the cement particles and water, that the second regime can exist. For pastes and mortar, this second regime shall not exist. More generally, it can be kept in mind that the extent of the second regime is expected to be small. It shall be, for instance, between 1000 Pa and 1250 Pa yield stress for a concrete in a 20 cm diameter column. Staying in this regime in practice shall therefore prove complex. The most common cases of interface-induced stability should therefore be found in the third high yield stress regime. It can then be concluded that casting a material that would be stabilized by the shear stress at the wall interface would need, in general, that the material is cast using vibration. Second, for most fluid cement pastes in a cylinder like the ones studied in this paper or in the case of self compacting concrete in a form, we can expect to be in the first regime and that the stress at the wall shall be neglected. An exception could be found when the stress at the wall increases through either thixotropy [15,16,17] or through the consolidation process itself [4]. It would then reach ΔρgR/2 and bleeding shall then stop as the material enters the second regime in Fig. 9. If this transition is reached through consolidation, it can however be expected that the level of bleeding needed to do so would be extremely detrimental to
Fig. 7. Micro-tomography imaging of paste samples 30 min (left image) and 2.5 h (right image) after pouring. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
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Fig. 8. Thickness of the extracted water layer as a function of time for three different initial sample heights in log scale. The tube diameter is 77 mm. Water-to-cement ratio is 0.6.
the final structural element. We can conclude that such a case should not exist in practice but keep in mind that thixotropic properties could play a role on bleeding reduction for sufficiently slender elements. The above frame allows for the analysis of the results obtained in Fig. 4. The yield stresses of the cement paste and of the mortar are given in Table 2 after 2 h of rest. These values allow for the estimation of the critical tube diameter, below which the stress at the wall shall prevent bleeding. This diameter would be around 2 cm for the cement paste and around 15 cm for the mortar. We see in Fig. 4 that, indeed, above these values, the measured bleeding at the end of the test does not depend on the testing tube diameter. Below these values, our results suggest that a part of the difference in density between cement grains and water is transferred to the tube wall through the stress at the wall interface. In the rest of this paper, we will only focus on results obtained when the tube interface has no effect on bleeding (i.e. sufficiently large tubes).
4.2. Induction period and reorganization of the system It was shown in [6] that colloidal forces and gravity forces competition dictate the occurrence of bleeding in a cement paste. As soon as bleeding occurs and water flows in such a porous medium, a drag force moreover applies on the cement grains. This drag force increases
with water extraction velocity. It can be noted that all three above forces have different dependencies on particle size. The inter-particle colloidal forces can be estimated as being of the order of A0a∗/12H2, where a∗ is the radius of curvature of the “contact” points (i.e. the typical roughness of the grain surface), H is the surface to surface separation distance at “contact” points and A0 is the non-retarded Hamaker constant [18,19]. The Hamaker constant value for C3S is of the order of 1.6 10−20 J [18]. Assuming spherical particles, the gravity force is ΔρgπD3/6 whereas the Stokes drag force can be estimated as 3πμ0DVloc where μ0 is the viscosity of the interstitial fluid and Vloc is the local fluid velocity in the porosity of the paste. We first consider here a homogeneous paste at short time scales. In such an homogeneous medium, the macroscopic water extraction velocity V should follow Darcy's law and write V = ΔρgK/μ0, where μ0 is the viscosity of the interstitial fluid, Δρ is the density difference between the particles and the liquid and K is the permeability. We note here d the typical size of the porosity, through which water is extracted, while D is the average diameter of the cement grains. We consider for a typical cement paste that D is of the order of 10 μm while, when the paste is homogeneous, d shall be, for this kind of dense suspensions, one order of magnitude lower and therefore of the order of 1 μm. The number of pores per surface unit is of the order of D− 2. The permeability of this (initially) homogeneous paste can be
Fig. 9. Filling and bleeding in a column as a function of yield stress. The three regimes from left to right.
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estimated using the Kozeny-Carman relation (K= (1− ϕ)3d2/45ϕ2 with ϕ the solid volume fraction). It is of the order of 10−14 m2 for the 0.6 water-to-cement ratio studied here. This value correlates well with the recent permeability measurements carried out in [20] on fresh cement pastes. It can be noted that the values from [20] were obtained using filtration equipment, in which water and particles all move in the same direction. The conditions under which preferential water extraction channels can form are therefore not fulfilled (see discussion below). Under the natural gravity pressure gradient due to the difference in density between the particle and the liquid, water velocity in the sample shall then be of order Δρ.g.K/μ0, namely lower than the 10− 6 m/s value from Fig. 2. As a consequence, the layer of extracted water above the sample after 104 s (around 3 h) shall be lower than 50 μm. It however reaches 10 mm in Fig. 2. When water flows through this homogeneous porous system at short time scales, flow occurs in the pores. The local velocity Vloc shall relate to the macroscopic water extraction velocity V through Vloc =VD2/ d2 and be therefore two orders of magnitude higher. We now plot in Fig. 10 the magnitudes of the viscous drag force, the colloidal attractive force and the gravity force as a function of cement particle size. From this figure, we can identify three regimes. In regime 1, for fine particles, colloidal forces dominate. As a consequence, we can expect these grains to be flocculated to larger grains. In regime 3, for coarse cement grains, gravity forces dominate. This suggests that the drag force is not able to move these particles upwards and we can expect them to settle through the bleeding process. Finally, in regime 2, for medium size grains with a diameter of order 10 μm, all three forces magnitudes are equivalent. It can be noted that these grains dominate from a volume fraction point of view the size distribution. For these particles, it can be expected that the upward drag force induced by water flow could be at the origin of a rearrangement of the particles. We suggest therefore that, although water flow is extremely slow in the induction stage of bleeding, it is sufficient to induce a progressive local reorganization of the system. This reorganization leads to the formation of the preferred water extraction channels shown in Figs. 5, 6 and 7. We can additionally extrapolate from the above that addition of plasticizers shall reduce the magnitude of attractive colloidal forces. This could allow for the displacement of the smallest particles. For
instance, covering the surface of the grains with a polymer could increase the inter-particle surface-to-surface separating distance by a factor 5 [6]. Keeping in mind that inter-particle forces scale with H−2 [6,18, 19], the average attractive colloidal force could therefore decrease by a factor 25 as illustrated in Fig. 10. As a consequence, drag force would dominate for particles as small as several hundreds of nanometers. This would explain why the extracted water above the sample turns from a transparent layer to an opaque one when high range water reducing type admixtures were added to our system (see Section 2.3). This feature was also reported in [12]. It can finally be noted that, for low water to cement ratio, the permeability of the initially homogeneous system and the initial local water velocity could be low enough for the drag force to be dominated by either the colloidal forces or the gravity for the entire range of cement particle sizes. We would then expect then that less preferential water extraction channels are formed and that bleeding rate does not go through an acceleration phase. This is indeed what we measured on samples prepared with a water-to-cement ratio of 0.5, for which the final amount of extracted water was extremely low but also for which channels could not be visually spotted (results not showed here). As the permeability of such materials shall be lower than the 10− 14 m2 value estimated above, the water extraction velocity shall be lower than 10 − 7 m/s. The water layer thickness above a one-meter high column of pure paste shall therefore not exceed 1 mm. This therefore suggests that any measurable bleeding shall find its origin in the formation of preferential water extraction channels. As soon as water extraction channels do form, flow localizes preferentially in these and it becomes debatable to consider the system as a homogenous porous medium described using a permeability value. The local velocity Vloc relates then to the macroscopic water extraction velocity V through Vloc =V/Nd2c where N is the number of channels per surface unit and dc is the average channel diameter. We now consider that, after a transition period at the end of which the forming channels have reached the surface and reached their average final diameter, we are facing a system in which all water is extracted through these channels. As shown in Fig. 8, the water extraction rate in this regime is constant. This happens before the consolidation of the
Fig. 10. Competition between colloidal force, drag force and gravity force as a function of the size of cement grains.
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Fig. 11. Extracted water as function of time in log scales. Conceptual diagram showing the five consecutive stages of the bleeding process. 1: induction period. 2: accelerating regime. 3: constant water extraction rate period. 4: consolidation regime. 5: final consolidated state.
zones between the channels slows down and finally prevents any additional water from being extracted. A constant water extraction rate suggests that the size of the channels does not change anymore. Our tests, on a range of sample heights up to 400 mm, have moreover shown that, no matter the number of channels and their size, the final amount of extracted water and the kinetics of water extraction in the constant rate regime are identical. It can be specifically noted that the duration of the induction period is the same no matter the sample height. As the macroscopic water extraction velocity V is similar for all tests no matter the number and sizes of the channel, this suggests therefore that the system can reach the same water extraction steady and final state for any value of Nd2c . This suggests that any configuration of channels would lead to the same value for Nd2c . If the size of these channels or preferred water extraction paths becomes larger than a few 100 μm (low N, high dc), they can then be visually spotted. We however suggest that, even when they cannot be visually spotted (high N, low dc), they do exist within the paste and are at the origin of the water extraction rate increase at the end of the induction period in Fig. 8. No matter the size and the number of channels, the extraction rate and the final bleeding is the same. There exist therefore an infinity of configuration that can be adopted by the system to extract the same amount of water. They will however all lead to the same final consolidation of the sample. An opened question for such a behavior is the origin of these various configurations. We preliminary suggest here that, similarly to crack initiation, water extraction channels initiation locates at some local defects of the system (i.e. the most permeable zones or the most porous zones). The fact that the duration of the induction period does not depend on the sample height suggests that percolation of the forming channels does not occur when they have propagated over a distance of the height of the sample. We suggest here that channels do percolate when they have propagated over a distance of the order of the average distance between local defects. This distance only depends therefore on the material defects distribution and not on the dimension of the samples. This finally suggests that, for instance, air bubbles localization and size distribution shall play a major role. Indeed, in the initially homogeneous samples, air bubbles are, in average, larger than the typical pore size between grains. They constitute therefore the most permeable zones or local defects, into which water flow can initially concentrate.
channels are being initiated through local particle rearrangements at the local defects of the suspension (air bubbles for instance). As particles are being progressively displaced, the channels typical diameter and typical length increase (accelerating regime in Fig. 11) until these channels do percolate. The system then reaches a steady state (constant water extraction rate period in Fig. 11). In this regime, the channels size and number do not change any more and we reach a system, in which the water is extracted through a constant apparent permeability although the system is already highly heterogeneous. It can be expected that the zones located between the channels are then being consolidated while feeding the channels with water. Finally, in the consolidation period (Cf. Fig. 11), the apparent permeability of the system decreases because of the further compaction of the zones located between the preferred extracting channels until gravity is not able to further consolidate the sample and extract any additional water (Final consolidated state in Fig. 11).
5. Global frame
References
From the above results obtained on systems, for which there was no interaction with wall interfaces, we suggest that, during the induction period (Cf. Fig. 11), water flow induces a viscous drag force allowing for the displacement of intermediate size cement particles and for a reorganization of the system. As a result, preferred water extraction
6. Conclusions We focused in this paper on the bleeding phenomenon, its amplitude and its kinetics at the scale of cement paste and mortars. Our experimental results on simple systems suggest that bleeding cannot be simply considered as the consolidation of a soft porous material but is of an obvious heterogeneous nature leading to the formation of preferential water extraction channels within the cement paste. Our results moreover suggest that, without these channels, bleeding shall be neglectable for most cement-based materials. We discussed here the origin of the induction period, of the accelerating period, of the constant water extraction rate period and of the consolidation period. Only the latters had been observed until now in literature.
Acknowledgement The authors would like to acknowledge the financial support of both Soletanche Bachy© and FNTP (Fédération Nationale des Travaux Publics). The authors acknowledge FNTP committee reviewers for their constructive comments to the text. The authors would like to thank Mr Patrick Aimedieu for the technical and scientific support on the microtomography imaging.
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