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Effect of porosity on thermal expansion coefficient of cement pastes and mortars
Construction and Building Materials 28 (2012) 468–475
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Effect of porosity on thermal expansion coefficient of cement pastes and mortars Qiang Zeng a,b, Kefei Li a,⇑, Teddy Fen-Chong b, Patrick Dangla b a b
Civil Engineering Department, Tsinghua University, Beijing 100084, PR China Université Paris-Est, Laboratoire Navier, Ecole des Ponts ParisTech, LCPC, UMR CNRS, Champs-sur-Marne 77420, France
a r t i c l e
i n f o
Article history: Received 1 June 2011 Received in revised form 28 August 2011 Accepted 2 September 2011 Available online 15 November 2011 Keywords: Thermal expansion coefficient Cement paste Mortar Porosity Air void
a b s t r a c t The thermal expansion coefficient (TEC) is studied for air-entrained cement pastes and mortars with different porosity. The results show that the porosity has significant effect on the thermal deformation and TEC decreases with porosity. The relation between TEC and porosity observes a power law, ad = a0(1 /)C, and the exponents C for pastes/mortars are respectively 2.66/2.38 in terms of total porosity, and 3.74/2.69 in terms of air void content. The gravimetry and MIP measurements on the porosity and pore size distribution (PSD) indicate that the entrained air voids have not significant influence on the capillary porosity, but change the PSD curves measured by MIP. Three characteristic pore ranges are identified on these PSD curves and air voids are found to interfere with the mercury intrusion process above the scale of 50 nm. Thermal gravity analysis shows that the composition of hydration products and cement hydration degree for both pastes and mortars are almost the same. The decreased TEC with air-entrainment can probably be attributed to the existence of dense shell structures around the air voids. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The thermal expansion coefficient (TEC) is one of important thermo-mechanical properties for cement-based materials. It scales the thermal strain of material and the induced thermal stress if the thermal deformation is restraint. Thus, the common practice of concrete technology is to keep the material TEC as low as possible. Furthermore, the TEC of cement paste is of particular interest since it is a fundamental parameter to determine the internal stress among the different phases in cement-based materials and to predict correctly the possible damage induced by the mismatch of thermal dilatation of each phase [1]. Available experimental results show that the typical values for TEC of hardened cement paste are about 15–20 106/°C [2]. These values are larger than TEC of aggregates, varying from 5 to 12 106/°C depending on the mineral composition [3]. Cement pastes are typical porous materials with total porosity of 20–40% [4], and the pore water is proved to have a significant influence on the material TEC due to the facts that liquid water has a larger TEC than the solid skeleton of material and that the pore water can accumulate stress during thermal process [5,6]. Under saturated and undrained conditions, the thermal pressurization coefficient, defined as the pore pressure increase per unit temperature rise, of oil well cement paste was estimated to be about 0.6 MPa/°C [7]. The thermal dilatation behavior of liquids confined in small pores has been investigated recently [8,9] and quite important ⇑ Corresponding author. E-mail address: [email protected] (K. Li). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.09.010
pore pressure was observed by temperature rising [6,7]. Meanwhile, numerous experimental results indicate that, under drained condition, the TEC of saturated samples of cement pastes have almost the same TEC as dried samples [10], and the TEC appears a maximum value at humidity of 65% [11]. Adopting the microstructure model of hydrates by Powers [12], Bazant [13] developed a hydrothermal model for cement paste TEC, decomposing the total thermal dilatation into pure thermal dilation of skeleton, thermal shrinkage (swelling) and hydrothermic dilation of paste. This model was further calibrated by other authors for different moisture conditions [10,14]. Compared to the detailed research on the role of pore water, little attention has been paid to the influence of material porosity on TEC. For most ceramics, it is reported that the TEC is independent of porosity [15]. However, the porosity of ceramics is controlled, in industry, to fabricate the low TEC materials. For instance, the cordierite ceramics were sintered with porosity about 40% to obtain a TEC as low as 0.4 106/°C [16]. For cement-based materials, Shui et al. [17] showed that the TEC decreased with the increase of material porosity and explained that this decrease was due to the pores accommodating a part of the internal thermal expansion of solid skeleton. This argument was further supported by other experimental observations [18]. However, based on the poromechanics analysis, Ghabezloo obtained the opposite conclusion [19]. Thus, more research is needed to understand the mechanism of porosity’s impact on TEC. To this aim, the TEC of cement pastes and mortars with different porosities are investigated in this paper. The temperature range of TEC measurement is 35 to 15 °C, an usual range for atmospheric exposure of engineering cement-based materials. The
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mercury intrusion porosimetry (MIP) and the thermal gravity analysis (TGA) were performed to characterize the pore structure and hydration products respectively. On the basis of the measurements, the role of porosity on TEC is discussed in depth.
Table 1 Chemical composition and physical properties of cement.
2. Theoretical basis Several available models for TEC of porous media are recalled here to provide a theoretical basis for interpreting the experimental data later in this paper. For sintered porous metals, the TEC relates intimately to the porosity [20] through a power law,
ad ¼ as q1=3 ¼ as ð1 /Þ1=3
ð1Þ
where ad is the TEC of porous material, as is the TEC of solid skeleton, q is the relative density between porous material and its solid skeleton. From this law, the increase of porosity leads to the decrease of material TEC. A general composite model expresses the material TEC as the volume average of skeleton TEC and pore phase TEC [21],
ad ¼ as ð1 /Þ þ ap /
ð2Þ
where ap is the TEC of pore (filling) phase. As the pores are totally dried the pore filling phase is air, and the thermal dilatations of air phase and solid skeleton are no more compatible thus this expression is no longer valid. Ghabezloo [19] gave a poroelastic description of thermal deformation of porous material and derived the differential of TEC with respect to porosity as,
1 @ ad 1 1/ 1 @K d ¼ 2 Ks @/ @T Kd Kd
ð3Þ
where Kd is the drained bulk modulus of porous material, and Ks the unjacked bulk modulus or the bulk modulus of solid matrix. The detailed derivation of equations is given in Appendix A, see also [22]. The experimental results by Odelson et al. [23] show that the undrained bulk modulus decreases with temperature, i.e. @Kd/@T < 0. The term 1=K 2d ½ð1 /Þ=K d 1=K s 1 is negative too since the term 1 / > Kd/Ks holds for most cement-based materials, e.g. Ghabezloo measured Kd/Ks = 0.414 and 1 / = 0.74 for oil-well cement pastes [7]. Accordingly, it is stated that the TEC of cement-based materials, in drained condition, increases with porosity [19]. It is to note that if the drained bulk modulus Kd is regarded as independent on temperature, i.e. @Kd/@T = 0, then Eq. (3) depicts a simple fact that,
@ ad ¼0: @/
ad ¼ ad ð/ ¼ 0Þ ¼ as
ð4Þ
Chemical composition/physical properties
Cement
Silica (Si2) Alumina (Al2O3) Iron oxide (Fe2O3) Calcium oxide (CaO) Magnesium oxide (MgO) Sulfur trioxide (SO3) Sodium oxide (Na2O (eq)) Free calcium oxide (CaO (f)) Chloride (Cl) Loss on ignition (LOI) Density (g/ml) Specific area (m2/kg)
22.93 4.29 2.89 66.23 1.92 0.35 0.70 0.64 0.006 1.70 3.12 343
modulus of sands is 2.5. Air entrainment agent (AEA) was added, in four dosages, into the cement paste and mortar mixtures to create different porosities in hardened samples. Note P (M)-i the paste (mortar) sample with i = 0, 1, 2, 3, 4 standing for the dosage, AEA mass versus cement mass, of 30, 60, 90 and 120 lg/g respectively. After mixing cement pastes and mortars were cast into cylinder tubes of 10 mm diameter and the hardened specimens were demoulded from the tubes at 3 d, then immersed into saturate lime-water. The samples with curing age of 300 d were taken out from limewater and weighted as M0. The samples were then oven-dried at 50 °C to constant weight Md. This temperature is regarded as capable to avoid the possible drying damage in samples [26]. The normalized weight loss in drying process of pastes and mortars were present in Fig. 1. The weight for all samples reached nearly constant after drying of 60 h. For each material, the dried samples were divided into three groups. The first group were kept in desiccator for the thermal dilation measurement, and the second dried group of samples were vacuum-saturated with water. The outlet gas pressure was controlled to under 0.1 atm, and the vacuum-saturation last 48 h to guarantee the saturation of the air voids as well. The vacuum-saturated samples were weighted as Ms. The last group of dried samples were then ground into small particles to perform helium pycnometry (HP), mercury intrusion porosimetry (MIP) and thermal gravity analysis (TGA). 3.3. Porosity and air void content
In fact, Khalili et al. [24] provide the proof of this relation from a boundary value problem in classic poromechanics with the matrix drained modulus independent on temperature.
By the gravimetry method mentioned above, the capillary porosity /m and the air-void content /av, for each material, are obtained through weight measurement:
3. Experiments
/m ¼
ð5aÞ
3.1. Materials
/av
ð5bÞ
A type of Portland cement supplied by Larfage was used in the study. The chemical composition and physical properties of cement are given in Table 1. The mineral contents of cement were analyzed, through Bogue’s procedure, as C2S (21.38%), C3S (58.88%), C3A (6.49%), C4AF (8.77%), Gypsum (0.75%) and others (3.73%). This cement corresponds to CEM I type according to European standard [25].
where qw is the density of pore liquid (qw = 0.997 kg/m3 for water) and qs is the skeleton density which can be measured by helium pycnometry (HP) or mercury intrusion porosimetry (MIP). The analysis results are given in Table 2.
3.2. Sample preparation Cement pastes and mortars were prepared with w/c = 0.5. For mortars, the sand–cement ratio was retained as 2.25 and the
ðM0 Md Þ=qw M d =qs ðMs Md Þ=qw ðM 0 M d Þ=qw ¼ Md =qs
3.4. MIP measurement The MIP measurement is based on the principle that the intrusion volume of mercury into a porous medium depends on the applied pressure. Following the assumption that the pore geometry is cylindrical, the pore diameter (size) d can be expressed in terms of pressure P through Washburn equation,
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(a)
3.5. Thermal gravity analysis Ground powder of samples, about 20 g, was analyzed by thermal gravity analysis (TGA) method to determine the non-evaporable water (Wn) and the calcium hydroxide (CH) content. It is known that 1 g ignited Portland cement, completely hydrated, contains 23–27% non-evaporable water, i.e. Wnc(1) = 0.23 0.27 [28]. The stoichiometry analysis from cement hydration reactions gives Wnc(1) = 0.26. Note that the ignition loss of sand is relative small Rs = 0.003, the Wn for cement in mortar samples is then calculated as,
Wnm ¼ mm n
3:25 Rc 2:25Rs mm ð1 Rc Þ
ð7Þ
with mm n for the measured non-evaporable water from mortar samples, mm the ignited weight of mortar and Rc the ignition loss of cement (see Table 1). For both cement pastes and mortars, the hydration degree of samples is calculated by
(b)
bc;m ¼
Wnc;m Wnc;m ¼ Wnc ð1Þ 0:26
ð8Þ
The calculated hydration degrees of cement pastes and mortars are presented in Table 2. 3.6. TEC measurement
Fig. 1. Normalized sample weight loss for pastes (a) and mortars (b) during ovendrying period at temperature 50 °C.
d¼
4c cos h P
ð6Þ
where c is the surface tension of mercury (0.485 N/m), h is the contact angle between mercury and pore wall and h = 130° is commonly adopted for cement-based materials [27]. The MIP device used in this study is of type Autopore IV 9510 with maximum and minimum applied pressures as 414 MPa and 1.4 kPa, corresponding to a minimum pore size (diameter) of 3 nm and maximum pore size of 890 lm. Dried samples for all materials were subject to MIP measurement and the pore size distribution is analyzed through Eq. (6).
The thermal expansion coefficient of samples was measured with LVDT (Type Macrosensor 750), and the experimental setup is illustrated in Fig. 2. Both the samples and LVDTs were placed in an environmental chamber (Type Espec PL-2k). The temperature range was set as 35 to 15 °C. Compared to the conventional range for TEC measurement, e.g. 20–85 °C [17], this temperature range is more centered on low (negative) temperature and the measurements intend to give TEC for cement-based pastes in conventional atmospheric environments for cold regions. The cooling rate is controlled to 0.33 °C/min. Since the geometry of samples is relative small, the temperature distribution in samples can be assumed uniform under this rate. In addition, the humidity of the environmental chamber during TEC measurement was controlled as 25%. The recordings of temperature and sample deformation were synchronized by a digital data logger. The TEC is calculated from the linear regression of recorded deformation with respect to temperature h,
ad ¼
1 @L @ e ¼ L0 @h @h
ð9Þ
where ad is the TEC of samples in drained condition, L, L0 are respectively the lengths of samples at test temperature h and reference temperature 20 °C, and e is the linear strain of samples e = (L L0)/L0.
Table 2 Physical and chemical properties of cement pastes (mortars). AEA dosage
P0(M0) 0
P1(M1) 1
P2(M2) 2
P3(M3) 3
P4(M4) 4
Bulk density (MIP) (g/ml) Bulk density (Gravimetry) (g/ml) Skeleton density (HP) (g/ml) Skeleton density (MIP) (g/ml) Air void (Nominal) (%) Air void (Gravimetry) (%) Porosity (Gravimetry) (–) Porosity (MIP) (–) Wn content (TGA) (–) CH conetnt (TGA) (–) Hydration degree (–)
1.85(2.06) 1.52(1.99) 2.06(2.35) 2.38(2.48) 0(0) 0(0) 0.26(0.15) 0.22(0.13) 0.24(0.23) 0.18(0.16) 0.90(0.90)
1.78(2.01) 1.57(1.87) 2.12(2.23) 2.36(2.40) 1.5 (1.5) 1.8(1.7) 0.26(0.16) 0.25(0.16) 0.24(0.23) 0.18(0.16) 0.90(0.89)
1.65(1.76) 1.39(1.81) 1.98(2.24) 2.30(2.47) 3.0(3.0) 3.2(3.1) 0.27 (0.15) 0.28 (0.18) 0.26 (0.23) 0.19 (0.16) 0.99(0.90)
1.58(1.70) 1.39(2.00) 2.01(2.18) 2.24(2.47) 4.5(4.5) 4.5(5.5) 0.27(0.13) 0.29(0.19) 0.26(0.24) 0.18(0.14) 0.99(0.92)
1.52(1.67) 1.33(1.76) 1.97(2.20) 2.30(2.48) 6.0(6.0) 6.3(6.1) 0.26(0.15) 0.32(0.22) 0.25(0.24) 0.18(0.19) 0.95(0.92)
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deformation temperature Thermal probe
LVDT
Data Logger
Invar rods
Sample
Invar rods
Upper plate
Computer Base plate
Environmental chamber Fig. 2. Experimental setup for TEC measurements.
Fig. 4. Measured and fitted TEC values for air-entrained cement pastes (a) and mortars (b) in terms of total porosity under drained condition.
Fig. 3. Measured thermal deformations of air-entrained cement pastes (a) and mortars (b).
4. Results 4.1. Thermal expansion coefficient The measured thermal strains are presented in Fig. 3a and b for cement pastes and mortars. It can be seen in Fig. 3 that as the air void content decreases from 6.0% (AEA dosage 4) to zero the strains at 35 °C of cement pastes decrease from 450 lm/m to 600 lm/m and strains of mortars decrease from 360 lm/m to 520 lm/m. Note that for cement pastes and mortars, the largest
thermal contractions happen for samples with AEA dosage of 1.5%, i.e. 680 lm/m and 520 lm/m for pastes and mortars respectively. The TEC for each sample was obtained by means of linear regression e h. For each porosity (material pores /m plus entrained air content /av), four samples were measured and the TEC is plotted in terms of porosity in Fig. 4, giving both average and dispersion of TEC values for cement pastes and mortars. Obviously, the TEC decreases with the augmentation of total porosity for both cement pastes and mortars. In Fig. 4, Eq. (1) is used to fit the TEC value in terms of total porosity as well. It can be seen that Eq. (1) cannot capture the TEC in terms of porosity for cement pastes and mortars. A better fitting relation for samples in this study is proposed as,
(
ad ¼
ac ð1 /Þ2:66 ; ac ¼ 26:98 106 = C for cement pastes ac ð1 /Þ2:38 ; ac ¼ 14:71 106 = C for mortars ð10Þ
where ac is the regressed TEC value for / = 0. For pastes, the value of ac is similar to the TEC of Portlandite, i.e. 23.3 106/°C. For mortars, the value of ac is much smaller than that of pastes, due to the existence of quartz sands with TEC about 12 106/°C. The TEC values are also regressed with respect to entrained air content /av as,
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Fig. 5. Measured and fitted TEC values for air-entrained cement pastes (a) and mortars (b) in terms of air voids content under drained condition.
(
ad ¼
3:74
6
ac ð1 /av Þ ; ac ¼ 12:05 10 = C for cement pastes ac ð1 /av Þ2:69 ; ac ¼ 9:99 106 = C for mortars ð11Þ
In Fig. 5a and b are shown the measured and fitted TEC for samples in terms of air void content. From the figures, it is confirmed that TEC is related to porosity, or entrained air content, through a power law, with different exponents for pastes and mortars. 4.2. Pore structure The capillary porosity and air void content measured by gravimetry for all samples are presented in Table 2. The capillary porosity is measured by the gravimetry during the drying procedure described in Section 3.3 and calculated through Eq. (5a). It can be shown that the capillary porosity of pastes is rather constant, around 26%, and that of mortars varies within 13–16%. These values are rather independent of the air voids content and this observation indicates that the air void system introduced by AEA does not interfere with the capillary pore system. The pore size distribution (PSD) of pastes and mortars, measured by MIP, is illustrated in Fig. 6a and b. Significant difference can be observed between the PSD of air-entrained samples and that of the non-entrained samples. The total intruded pore volume increases with the AEA content, from 0.12 ml/g to 0.20 ml/g for pastes and from 0.061 ml/g to 0.128 ml/g for mortars. Evidently,
Fig. 6. Pore size distribution measured by MIP for pastes (a) and mortars (b) with different air void contents.
the air voids introduced by AEA do have influence on the mercury intrusion process. Three characteristic pore ranges are identified and intrusion volume for each range is illustrated in Fig. 7. The detailed influence of air voids on the MIP measurement for each pore range is described as follows. Range of d P 5 lm. Compared to non-entrained samples, the intruded volume increases slightly for pastes but substantially for mortars, cf. Fig. 7. For pastes, this slight increase can be attributed to the mechanical damage of surface air voids of samples by mercury pressure. For mortars, the important increase of intrusion volume is due to the percolation of mercury into air voids through two neighbored interfacial transition zones (ITZ) between aggregates and cement paste, noting that ITZ contains more/larger capillary pores [29]. The mechanism is shown in Fig. 8a. Range of 50 nm 6 d < 5 lm. It is observed from Fig. 7 that during this range both paste and mortar samples have important increase of intrusion volume. This observation can be explained by the mercury percolation into air voids through the capillary pores (or microcracks) in hardened cement pastes, cf. Fig. 8b. Note that SEM image analysis of ‘‘ink-bottle’’ shape pores in cement pastes shows that the ‘‘neck’’ size is about two magnitudes smaller than the ‘‘bottle’’ size [30]. Range of 3 nm 6 d < 50 nm. During this range no significant different intrusion volumes are observed for samples with different entrained air void contents. According to the C–S–H model proposed by Jennings and coworkers [31], on this scale we are
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Fig. 8. Influence of entrained air voids on three characteristic pore size ranges.
Fig. 7. The intruded pore volume at different pore size ranges for paste (a) and mortar (b).
approaching the inter-granular space (10 nm) between C–S–H bundles and the internal space (3 nm) in a C–S–H bundle. In fact, this observation indicates the entrained air voids interfere very little with the pore structure at the scale near C–S–H structures, cf. Fig. 8c. 4.3. Thermal gravity analysis The TGA results for pastes and mortars are presented in Fig. 9. It can be seen that these thermal gravity curves are quite similar. The measured Wn and CH are evaluated from these TGA results and presented in Table 2. The Wn values for hydrated cement in pastes and mortars are about 23–25% and the CH values for hydrated cement in pastes and mortars are 14–19%. The hydration extent of cement, calculated by Eq. (8), attains about 90% for all samples at age of 300 d and no systematic difference of hydration extents is observed between pastes and mortars. This confirms that AEA dosage, with entrained air voids, has no influence on the cement hydration kinetics. 5. Discussion According to classic thermo-elasticity [32], the TEC of a porous medium with homogeneous matrix is independent on its porosity and equal to the TEC of matrix. Ghabezloo et al. [7] derived the TEC of cement-based porous materials under drained and undrained
conditions for pore water, and predicted a material TEC increasing with porosity for undrained condition. However, our TEC measurements on both pastes and mortars specimens in this study do not support these statements. Several causes can be responsible for this discrepancy. Firstly, different porosity in this study is created by entrained air contents and the matrix of pastes and mortars is not homogeneous between the air void surface and bulk paste. Relevant investigations show that, once air voids is entrained by AEA in cement paste, a surface shell of about 1 lm thickness is formed with very dense microstructure [33]. Through EDXA examination, it was also revealed that the C/S ratio in this shell was equal to 1.1, compared to C/S = 1.5 in bulk paste [33]. Although no direct evidence is available to quantify the thermal deformation behavior of this shell, it is believed that this shell, together with the discontinuity created between this shell and the bulk paste, would have an direct impact on the TEC of entrained pastes and mortars. It is interesting to note that, in the works of Shui et al. [17], smaller TEC was measured for fly-ash pastes and at the surface of fly-ash particles (void shell) similar C–S–H product with low C/S ratio was also observed [34]. Secondly, the samples in this study were dried under temperature controlled to 50 °C but it is not sure that all pores are totally dried. In our TGA analysis, the mass loss during 50 °C and 150 °C was recorded as 7.2–11.4% for pastes and 5.6–8.7% for mortars, cf. Fig. 9. This mass loss is mainly the evaporated water. The existence of this quantity of water in pastes and mortars can have effect on the TEC measurement by the possible water flow in pore structure [12]. At last, the thermo-deformation of solid skeleton of pastes and mortars can more or less derive from the ideal
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Fig. 9. Thermal gravimetric analysis results for pastes (a) and mortars (b) with different air void contents.
thermo-elasticity due to the cracks and defects in skeleton with the presence of entrained air voids [35]. 6. Conclusion 1. In this paper, the linear TEC of cement pastes and mortars with different entrained air void contents are studied under dry and drained conditions. The results show that the porosity has significant effect on TEC and TEC decreases with porosity. For both cement pastes and mortars, the TEC can be expressed in terms of total porosity or entrained air void content through a power law, ad = a0(1 /)C. The exponents C of pastes and mortars are respectively 2.66 and 2.38 for total porosity and 3.74 and 2.69 for air void content. 2. The gravimetry and MIP measurements on the porosity and PSD indicate that the air-void entrainment do not have significant influence on the total capillary porosity, but the PSD curves measured by MIP are significantly influenced by entrained air
voids. Three characteristic ranges of pore size are identified for PSD curves and air voids interfere with the mercury intrusion process above the scale of 50 nm. 3. Thermal gravity analysis shows that the content of hydration products and hydration degree for both pastes and mortars are almost the same. This confirms that the mineral compositions of pastes and mortars are nearly identical for different air void contents. From the available chemistry and microstructure analysis of air voids in cement pastes is confirmed the existence of a dense shell around air voids and rich in low C/S ratio C–S–H. This shell structure, associated with the entrained air voids, may be responsible for the TEC decrease.
Acknowledgement The research is supported by China national major fundamental research Grant (973 Program, No. 2009 CB623106).
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Appendix A. Derivation of Eq. (3) For a porous material, the thermoelasticity relates the total volume V and pore volume V/ to the Terzaghi effective pressure rd, the pore pressure P and the temperature T through [7,6,22],
dV 1 1 ¼ drd þ dP 3ad dT V0 Kd Ks dV / 1 1 ¼ drd þ dP 3a/ dT K/ V /;0 K P
ðA:1aÞ ðA:1bÞ
In the above relations, dV/V0 represents the total volumetric strain, dV//V/,0 is the pore volumetric strain, Kd and Ks are the drained bulk and unjacked moduli, KP and K/ are the moduli linking pore volumetric strain with effective stress and pore pressure, and ad is the linear drained TEC. Employing the Betti’s reciprocal theorem, the moduli adopt the relation //Kp = 1/Kd 1/Ks. Under drained condition and drd = 0, dP = 0, ad can be given by:
ad ¼
1 1 @V 3 V 0 @T P;rd
ðA:2Þ
Actually, Eq. (A.2) is the expression for TEC evaluation from drained tests. The variation of the drained TEC with porosity is then expressed as,
@ ad @ ad @ rd ¼ @/ @ rd @/
ðA:3Þ
Using Eq. (A.1b) and the relation d///0 = (d V//V/,0) (dV/V0), the variation of effective stress with the porosity is then given by,
1 1 @ rd 1 1 1/ 1 ¼ ¼ / KP Kd Kd Ks @/
ðA:4Þ
Combining Eqs. (A.3) and (A.4), one obtains,
1 @ ad 1/ 1 @ ad ¼ Kd Ks @/ @r
ðA:5Þ
From Eq. (A.2), the variation of linear drained TEC with respect to effective pressure rd can be expressed as,
@ ad 1 1 @2V ¼ @ r 3 V 0 @T@ rd
! ¼
1 @1=K d 1 @K d ¼ 3 @T 3K 2d @T
ðA:6Þ
Substituting Eq. (A.6) into Eq. (A.5), one gets,
1 @ ad 1 1/ 1 @K d ¼ 2 Ks @/ @T 3K d K d
ðA:7Þ
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[6] Ghbezloo S. Micromechanics analysis of thermal expansion and thermal pressurization of hardened cement paste. Cem Concr Res 2011. doi:10.1016/ j.cemconres.2011.01.023. [7] Ghabezloo S, Sulem J, Saint-Marc J. The effect of undrained heating on a fluidsaturated hardened cement paste. Cem Concr Res 2009;39:54–64. [8] Xu S, Simmons GC, Scherer GW. Thermal expansion and viscosity of confined liquids. In: Fourkas JT, Levitz P, Urbakh M, Wahl KJ, editors. Dynamics of small confining systems. Mat res soc symp proc, vol. 790. Warrendale: Materials Res Soc; 2004. p. 85–91. [9] Xu S, Scherer GW, Mahadevan TS, Garofalini SH. Thermal expansion of confined water. Langmuir 2009;25(9):5076–83. [10] Sellevold EJ, Bjontegaard O. Coefficient of thermal expansion of cement paste and concrete: mechanisms of moisture interaction. Mater Struct 2006;39:809–15. [11] Helmuth RA. Dimensional changes of hardened Portland cement pastes caused by temperature changes. Proc Highway Res Board 1961;40:315–36. [12] Powers TC. The thermodynamics of volume change and creep. Mater Struct 1968;1(6):487–507. [13] Bazant ZP. Delayed thermal dilatations of cement paste and concrete due to mass transport. Nucl Eng Des 1970;14:308–18. [14] Grasley ZC, Lange DA. Thermal dilation and internal relative humidity of hardened cement paste. Mater Struct 2007;40:311–7. [15] Rice RW. Porosity of ceramics. New York: Marcel Dekker Inc.; 1999. [16] Hirose Y, Doi H, Kamigaito O. Thermal expansion of hot-pressed cordierite glass ceramics. J Mater Sci Lett 1984;3(2):153–5. [17] Shui ZH, Zhang R, Chen W, Xuan D. Effects of mineral admixtures on the thermal expansion properties of hardened cement paste. Constr Build Mater 2010;24(9):1761–7. [18] Qian CX, Zhu CF. Influence of mineral admixture and air-entraining agent on thermal expansion property of cement based materials. J Build Mater 2009;12:310–5. in Chinese. [19] Ghbezloo S. Effect of porosity on the thermal expansion coefficient: a discussion of the paper ’Effects of mineral admixtures on the thermal expansion properties of hardened cement paste by Z.H. Shui, R. Zhang, W. Chen, D. Xuan, Constr Build Mater 24(9) (2010) 1761–1767. Constr Build Mater 2010;24:1796–8. [20] Antonyraj A, Park SJ, German R. Thermal expansion and viscoelastic properties of sintered porous compact. In: Campus JM, German RM, editors. Proceedings of the 2007 international conference on powder metallurgy & particulate materials: Part I, design & modeling of PM materials, components & processes; 2007 May 13–16; Denver, Colorado. Princeton: MPIF; 2007. p. 60–9. [21] Palciauskas VV, Domenico PA. Characterization of drained and undrained response of thermally loaded repository rocks. Water Resour Res 1982;18:281–90. [22] Coussy O. Poromechanics. London: John Wiley& Sons; 2004. [23] Odelson J, Kerr EA, Vichit-Vadakan W. Young’s modulus of cement paste at elevated temperatures. Cem Concr Res 2007;37:258–63. [24] Khalili N, Uchaipichat A, Javadi AA. Skeletal thermal expansion coefficient and thermo-hydro-mechanical constitutive relations for saturated homogeneous porous media. Mech Mater 2010;42:593–8. [25] Comité Européene de Normalisation (CEN). Cement-Part 1: composition, specification, and conformity criteria for common cements. Brussels: EN197-1, CEN; 2000. [26] Aligizaki KK. Pore structure of cement-based materials – testing, interpretation and requirement. New York: Taylor& Francis; 2006. [27] Kaufmann JP, Loser R, Leeman A. Analysis of cement-based materials by multicycle mercury intrusion and nitrogen sorption. J Colloid Interf Sci 2009;336:730–7. [28] Taylor HFW. Cement chemistry. 2nd ed. London: Thomas Telford; 1997. [29] Scrivener KL, Crumbie AK, Laugesen P. The interfacial transition zone (ITZ) between cement paste and aggregate in concrete. Interf Sci 2004;12:411–21. [30] Diamond S. Mercury porosimetry: an inappropriate method for the measurement of pore size distributions in cement-based materials. Cem Concr Res 2000;30:1517–25. [31] Tennis PT, Jennings HM. A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes. Cem Concr Res 2000;30:855–63. [32] Mushkelishvili NI. Some basic problems of the mathematical theory of elasticity. The Netherlands: Kluwer Aca; 1963. [33] Ley MT, Chancey R, Juenger MCG, Folliard KJ. The physical and chemical characteristics of the shell of air-entrained bubbles in cement paste. Cem Concr Res 2009;39:417–25. [34] Pieterson HS. Application of TEM to characterize fly ash and slag cements. HERON 1999;44(4):299–310. [35] Cooper HW, Simons G. The effect of cracks on the thermal expansion of rocks. Earth Planet Sci Lett 1977;36(3):404–12.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effect of porosity on thermal expansion coefficient of cement pastes and mortars Qiang Zeng a,b, Kefei Li a,⇑, Teddy Fen-Chong b, Patrick Dangla b a b
Civil Engineering Department, Tsinghua University, Beijing 100084, PR China Université Paris-Est, Laboratoire Navier, Ecole des Ponts ParisTech, LCPC, UMR CNRS, Champs-sur-Marne 77420, France
a r t i c l e
i n f o
Article history: Received 1 June 2011 Received in revised form 28 August 2011 Accepted 2 September 2011 Available online 15 November 2011 Keywords: Thermal expansion coefficient Cement paste Mortar Porosity Air void
a b s t r a c t The thermal expansion coefficient (TEC) is studied for air-entrained cement pastes and mortars with different porosity. The results show that the porosity has significant effect on the thermal deformation and TEC decreases with porosity. The relation between TEC and porosity observes a power law, ad = a0(1 /)C, and the exponents C for pastes/mortars are respectively 2.66/2.38 in terms of total porosity, and 3.74/2.69 in terms of air void content. The gravimetry and MIP measurements on the porosity and pore size distribution (PSD) indicate that the entrained air voids have not significant influence on the capillary porosity, but change the PSD curves measured by MIP. Three characteristic pore ranges are identified on these PSD curves and air voids are found to interfere with the mercury intrusion process above the scale of 50 nm. Thermal gravity analysis shows that the composition of hydration products and cement hydration degree for both pastes and mortars are almost the same. The decreased TEC with air-entrainment can probably be attributed to the existence of dense shell structures around the air voids. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The thermal expansion coefficient (TEC) is one of important thermo-mechanical properties for cement-based materials. It scales the thermal strain of material and the induced thermal stress if the thermal deformation is restraint. Thus, the common practice of concrete technology is to keep the material TEC as low as possible. Furthermore, the TEC of cement paste is of particular interest since it is a fundamental parameter to determine the internal stress among the different phases in cement-based materials and to predict correctly the possible damage induced by the mismatch of thermal dilatation of each phase [1]. Available experimental results show that the typical values for TEC of hardened cement paste are about 15–20 106/°C [2]. These values are larger than TEC of aggregates, varying from 5 to 12 106/°C depending on the mineral composition [3]. Cement pastes are typical porous materials with total porosity of 20–40% [4], and the pore water is proved to have a significant influence on the material TEC due to the facts that liquid water has a larger TEC than the solid skeleton of material and that the pore water can accumulate stress during thermal process [5,6]. Under saturated and undrained conditions, the thermal pressurization coefficient, defined as the pore pressure increase per unit temperature rise, of oil well cement paste was estimated to be about 0.6 MPa/°C [7]. The thermal dilatation behavior of liquids confined in small pores has been investigated recently [8,9] and quite important ⇑ Corresponding author. E-mail address: [email protected] (K. Li). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.09.010
pore pressure was observed by temperature rising [6,7]. Meanwhile, numerous experimental results indicate that, under drained condition, the TEC of saturated samples of cement pastes have almost the same TEC as dried samples [10], and the TEC appears a maximum value at humidity of 65% [11]. Adopting the microstructure model of hydrates by Powers [12], Bazant [13] developed a hydrothermal model for cement paste TEC, decomposing the total thermal dilatation into pure thermal dilation of skeleton, thermal shrinkage (swelling) and hydrothermic dilation of paste. This model was further calibrated by other authors for different moisture conditions [10,14]. Compared to the detailed research on the role of pore water, little attention has been paid to the influence of material porosity on TEC. For most ceramics, it is reported that the TEC is independent of porosity [15]. However, the porosity of ceramics is controlled, in industry, to fabricate the low TEC materials. For instance, the cordierite ceramics were sintered with porosity about 40% to obtain a TEC as low as 0.4 106/°C [16]. For cement-based materials, Shui et al. [17] showed that the TEC decreased with the increase of material porosity and explained that this decrease was due to the pores accommodating a part of the internal thermal expansion of solid skeleton. This argument was further supported by other experimental observations [18]. However, based on the poromechanics analysis, Ghabezloo obtained the opposite conclusion [19]. Thus, more research is needed to understand the mechanism of porosity’s impact on TEC. To this aim, the TEC of cement pastes and mortars with different porosities are investigated in this paper. The temperature range of TEC measurement is 35 to 15 °C, an usual range for atmospheric exposure of engineering cement-based materials. The
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mercury intrusion porosimetry (MIP) and the thermal gravity analysis (TGA) were performed to characterize the pore structure and hydration products respectively. On the basis of the measurements, the role of porosity on TEC is discussed in depth.
Table 1 Chemical composition and physical properties of cement.
2. Theoretical basis Several available models for TEC of porous media are recalled here to provide a theoretical basis for interpreting the experimental data later in this paper. For sintered porous metals, the TEC relates intimately to the porosity [20] through a power law,
ad ¼ as q1=3 ¼ as ð1 /Þ1=3
ð1Þ
where ad is the TEC of porous material, as is the TEC of solid skeleton, q is the relative density between porous material and its solid skeleton. From this law, the increase of porosity leads to the decrease of material TEC. A general composite model expresses the material TEC as the volume average of skeleton TEC and pore phase TEC [21],
ad ¼ as ð1 /Þ þ ap /
ð2Þ
where ap is the TEC of pore (filling) phase. As the pores are totally dried the pore filling phase is air, and the thermal dilatations of air phase and solid skeleton are no more compatible thus this expression is no longer valid. Ghabezloo [19] gave a poroelastic description of thermal deformation of porous material and derived the differential of TEC with respect to porosity as,
1 @ ad 1 1/ 1 @K d ¼ 2 Ks @/ @T Kd Kd
ð3Þ
where Kd is the drained bulk modulus of porous material, and Ks the unjacked bulk modulus or the bulk modulus of solid matrix. The detailed derivation of equations is given in Appendix A, see also [22]. The experimental results by Odelson et al. [23] show that the undrained bulk modulus decreases with temperature, i.e. @Kd/@T < 0. The term 1=K 2d ½ð1 /Þ=K d 1=K s 1 is negative too since the term 1 / > Kd/Ks holds for most cement-based materials, e.g. Ghabezloo measured Kd/Ks = 0.414 and 1 / = 0.74 for oil-well cement pastes [7]. Accordingly, it is stated that the TEC of cement-based materials, in drained condition, increases with porosity [19]. It is to note that if the drained bulk modulus Kd is regarded as independent on temperature, i.e. @Kd/@T = 0, then Eq. (3) depicts a simple fact that,
@ ad ¼0: @/
ad ¼ ad ð/ ¼ 0Þ ¼ as
ð4Þ
Chemical composition/physical properties
Cement
Silica (Si2) Alumina (Al2O3) Iron oxide (Fe2O3) Calcium oxide (CaO) Magnesium oxide (MgO) Sulfur trioxide (SO3) Sodium oxide (Na2O (eq)) Free calcium oxide (CaO (f)) Chloride (Cl) Loss on ignition (LOI) Density (g/ml) Specific area (m2/kg)
22.93 4.29 2.89 66.23 1.92 0.35 0.70 0.64 0.006 1.70 3.12 343
modulus of sands is 2.5. Air entrainment agent (AEA) was added, in four dosages, into the cement paste and mortar mixtures to create different porosities in hardened samples. Note P (M)-i the paste (mortar) sample with i = 0, 1, 2, 3, 4 standing for the dosage, AEA mass versus cement mass, of 30, 60, 90 and 120 lg/g respectively. After mixing cement pastes and mortars were cast into cylinder tubes of 10 mm diameter and the hardened specimens were demoulded from the tubes at 3 d, then immersed into saturate lime-water. The samples with curing age of 300 d were taken out from limewater and weighted as M0. The samples were then oven-dried at 50 °C to constant weight Md. This temperature is regarded as capable to avoid the possible drying damage in samples [26]. The normalized weight loss in drying process of pastes and mortars were present in Fig. 1. The weight for all samples reached nearly constant after drying of 60 h. For each material, the dried samples were divided into three groups. The first group were kept in desiccator for the thermal dilation measurement, and the second dried group of samples were vacuum-saturated with water. The outlet gas pressure was controlled to under 0.1 atm, and the vacuum-saturation last 48 h to guarantee the saturation of the air voids as well. The vacuum-saturated samples were weighted as Ms. The last group of dried samples were then ground into small particles to perform helium pycnometry (HP), mercury intrusion porosimetry (MIP) and thermal gravity analysis (TGA). 3.3. Porosity and air void content
In fact, Khalili et al. [24] provide the proof of this relation from a boundary value problem in classic poromechanics with the matrix drained modulus independent on temperature.
By the gravimetry method mentioned above, the capillary porosity /m and the air-void content /av, for each material, are obtained through weight measurement:
3. Experiments
/m ¼
ð5aÞ
3.1. Materials
/av
ð5bÞ
A type of Portland cement supplied by Larfage was used in the study. The chemical composition and physical properties of cement are given in Table 1. The mineral contents of cement were analyzed, through Bogue’s procedure, as C2S (21.38%), C3S (58.88%), C3A (6.49%), C4AF (8.77%), Gypsum (0.75%) and others (3.73%). This cement corresponds to CEM I type according to European standard [25].
where qw is the density of pore liquid (qw = 0.997 kg/m3 for water) and qs is the skeleton density which can be measured by helium pycnometry (HP) or mercury intrusion porosimetry (MIP). The analysis results are given in Table 2.
3.2. Sample preparation Cement pastes and mortars were prepared with w/c = 0.5. For mortars, the sand–cement ratio was retained as 2.25 and the
ðM0 Md Þ=qw M d =qs ðMs Md Þ=qw ðM 0 M d Þ=qw ¼ Md =qs
3.4. MIP measurement The MIP measurement is based on the principle that the intrusion volume of mercury into a porous medium depends on the applied pressure. Following the assumption that the pore geometry is cylindrical, the pore diameter (size) d can be expressed in terms of pressure P through Washburn equation,
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(a)
3.5. Thermal gravity analysis Ground powder of samples, about 20 g, was analyzed by thermal gravity analysis (TGA) method to determine the non-evaporable water (Wn) and the calcium hydroxide (CH) content. It is known that 1 g ignited Portland cement, completely hydrated, contains 23–27% non-evaporable water, i.e. Wnc(1) = 0.23 0.27 [28]. The stoichiometry analysis from cement hydration reactions gives Wnc(1) = 0.26. Note that the ignition loss of sand is relative small Rs = 0.003, the Wn for cement in mortar samples is then calculated as,
Wnm ¼ mm n
3:25 Rc 2:25Rs mm ð1 Rc Þ
ð7Þ
with mm n for the measured non-evaporable water from mortar samples, mm the ignited weight of mortar and Rc the ignition loss of cement (see Table 1). For both cement pastes and mortars, the hydration degree of samples is calculated by
(b)
bc;m ¼
Wnc;m Wnc;m ¼ Wnc ð1Þ 0:26
ð8Þ
The calculated hydration degrees of cement pastes and mortars are presented in Table 2. 3.6. TEC measurement
Fig. 1. Normalized sample weight loss for pastes (a) and mortars (b) during ovendrying period at temperature 50 °C.
d¼
4c cos h P
ð6Þ
where c is the surface tension of mercury (0.485 N/m), h is the contact angle between mercury and pore wall and h = 130° is commonly adopted for cement-based materials [27]. The MIP device used in this study is of type Autopore IV 9510 with maximum and minimum applied pressures as 414 MPa and 1.4 kPa, corresponding to a minimum pore size (diameter) of 3 nm and maximum pore size of 890 lm. Dried samples for all materials were subject to MIP measurement and the pore size distribution is analyzed through Eq. (6).
The thermal expansion coefficient of samples was measured with LVDT (Type Macrosensor 750), and the experimental setup is illustrated in Fig. 2. Both the samples and LVDTs were placed in an environmental chamber (Type Espec PL-2k). The temperature range was set as 35 to 15 °C. Compared to the conventional range for TEC measurement, e.g. 20–85 °C [17], this temperature range is more centered on low (negative) temperature and the measurements intend to give TEC for cement-based pastes in conventional atmospheric environments for cold regions. The cooling rate is controlled to 0.33 °C/min. Since the geometry of samples is relative small, the temperature distribution in samples can be assumed uniform under this rate. In addition, the humidity of the environmental chamber during TEC measurement was controlled as 25%. The recordings of temperature and sample deformation were synchronized by a digital data logger. The TEC is calculated from the linear regression of recorded deformation with respect to temperature h,
ad ¼
1 @L @ e ¼ L0 @h @h
ð9Þ
where ad is the TEC of samples in drained condition, L, L0 are respectively the lengths of samples at test temperature h and reference temperature 20 °C, and e is the linear strain of samples e = (L L0)/L0.
Table 2 Physical and chemical properties of cement pastes (mortars). AEA dosage
P0(M0) 0
P1(M1) 1
P2(M2) 2
P3(M3) 3
P4(M4) 4
Bulk density (MIP) (g/ml) Bulk density (Gravimetry) (g/ml) Skeleton density (HP) (g/ml) Skeleton density (MIP) (g/ml) Air void (Nominal) (%) Air void (Gravimetry) (%) Porosity (Gravimetry) (–) Porosity (MIP) (–) Wn content (TGA) (–) CH conetnt (TGA) (–) Hydration degree (–)
1.85(2.06) 1.52(1.99) 2.06(2.35) 2.38(2.48) 0(0) 0(0) 0.26(0.15) 0.22(0.13) 0.24(0.23) 0.18(0.16) 0.90(0.90)
1.78(2.01) 1.57(1.87) 2.12(2.23) 2.36(2.40) 1.5 (1.5) 1.8(1.7) 0.26(0.16) 0.25(0.16) 0.24(0.23) 0.18(0.16) 0.90(0.89)
1.65(1.76) 1.39(1.81) 1.98(2.24) 2.30(2.47) 3.0(3.0) 3.2(3.1) 0.27 (0.15) 0.28 (0.18) 0.26 (0.23) 0.19 (0.16) 0.99(0.90)
1.58(1.70) 1.39(2.00) 2.01(2.18) 2.24(2.47) 4.5(4.5) 4.5(5.5) 0.27(0.13) 0.29(0.19) 0.26(0.24) 0.18(0.14) 0.99(0.92)
1.52(1.67) 1.33(1.76) 1.97(2.20) 2.30(2.48) 6.0(6.0) 6.3(6.1) 0.26(0.15) 0.32(0.22) 0.25(0.24) 0.18(0.19) 0.95(0.92)
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deformation temperature Thermal probe
LVDT
Data Logger
Invar rods
Sample
Invar rods
Upper plate
Computer Base plate
Environmental chamber Fig. 2. Experimental setup for TEC measurements.
Fig. 4. Measured and fitted TEC values for air-entrained cement pastes (a) and mortars (b) in terms of total porosity under drained condition.
Fig. 3. Measured thermal deformations of air-entrained cement pastes (a) and mortars (b).
4. Results 4.1. Thermal expansion coefficient The measured thermal strains are presented in Fig. 3a and b for cement pastes and mortars. It can be seen in Fig. 3 that as the air void content decreases from 6.0% (AEA dosage 4) to zero the strains at 35 °C of cement pastes decrease from 450 lm/m to 600 lm/m and strains of mortars decrease from 360 lm/m to 520 lm/m. Note that for cement pastes and mortars, the largest
thermal contractions happen for samples with AEA dosage of 1.5%, i.e. 680 lm/m and 520 lm/m for pastes and mortars respectively. The TEC for each sample was obtained by means of linear regression e h. For each porosity (material pores /m plus entrained air content /av), four samples were measured and the TEC is plotted in terms of porosity in Fig. 4, giving both average and dispersion of TEC values for cement pastes and mortars. Obviously, the TEC decreases with the augmentation of total porosity for both cement pastes and mortars. In Fig. 4, Eq. (1) is used to fit the TEC value in terms of total porosity as well. It can be seen that Eq. (1) cannot capture the TEC in terms of porosity for cement pastes and mortars. A better fitting relation for samples in this study is proposed as,
(
ad ¼
ac ð1 /Þ2:66 ; ac ¼ 26:98 106 = C for cement pastes ac ð1 /Þ2:38 ; ac ¼ 14:71 106 = C for mortars ð10Þ
where ac is the regressed TEC value for / = 0. For pastes, the value of ac is similar to the TEC of Portlandite, i.e. 23.3 106/°C. For mortars, the value of ac is much smaller than that of pastes, due to the existence of quartz sands with TEC about 12 106/°C. The TEC values are also regressed with respect to entrained air content /av as,
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Fig. 5. Measured and fitted TEC values for air-entrained cement pastes (a) and mortars (b) in terms of air voids content under drained condition.
(
ad ¼
3:74
6
ac ð1 /av Þ ; ac ¼ 12:05 10 = C for cement pastes ac ð1 /av Þ2:69 ; ac ¼ 9:99 106 = C for mortars ð11Þ
In Fig. 5a and b are shown the measured and fitted TEC for samples in terms of air void content. From the figures, it is confirmed that TEC is related to porosity, or entrained air content, through a power law, with different exponents for pastes and mortars. 4.2. Pore structure The capillary porosity and air void content measured by gravimetry for all samples are presented in Table 2. The capillary porosity is measured by the gravimetry during the drying procedure described in Section 3.3 and calculated through Eq. (5a). It can be shown that the capillary porosity of pastes is rather constant, around 26%, and that of mortars varies within 13–16%. These values are rather independent of the air voids content and this observation indicates that the air void system introduced by AEA does not interfere with the capillary pore system. The pore size distribution (PSD) of pastes and mortars, measured by MIP, is illustrated in Fig. 6a and b. Significant difference can be observed between the PSD of air-entrained samples and that of the non-entrained samples. The total intruded pore volume increases with the AEA content, from 0.12 ml/g to 0.20 ml/g for pastes and from 0.061 ml/g to 0.128 ml/g for mortars. Evidently,
Fig. 6. Pore size distribution measured by MIP for pastes (a) and mortars (b) with different air void contents.
the air voids introduced by AEA do have influence on the mercury intrusion process. Three characteristic pore ranges are identified and intrusion volume for each range is illustrated in Fig. 7. The detailed influence of air voids on the MIP measurement for each pore range is described as follows. Range of d P 5 lm. Compared to non-entrained samples, the intruded volume increases slightly for pastes but substantially for mortars, cf. Fig. 7. For pastes, this slight increase can be attributed to the mechanical damage of surface air voids of samples by mercury pressure. For mortars, the important increase of intrusion volume is due to the percolation of mercury into air voids through two neighbored interfacial transition zones (ITZ) between aggregates and cement paste, noting that ITZ contains more/larger capillary pores [29]. The mechanism is shown in Fig. 8a. Range of 50 nm 6 d < 5 lm. It is observed from Fig. 7 that during this range both paste and mortar samples have important increase of intrusion volume. This observation can be explained by the mercury percolation into air voids through the capillary pores (or microcracks) in hardened cement pastes, cf. Fig. 8b. Note that SEM image analysis of ‘‘ink-bottle’’ shape pores in cement pastes shows that the ‘‘neck’’ size is about two magnitudes smaller than the ‘‘bottle’’ size [30]. Range of 3 nm 6 d < 50 nm. During this range no significant different intrusion volumes are observed for samples with different entrained air void contents. According to the C–S–H model proposed by Jennings and coworkers [31], on this scale we are
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Fig. 8. Influence of entrained air voids on three characteristic pore size ranges.
Fig. 7. The intruded pore volume at different pore size ranges for paste (a) and mortar (b).
approaching the inter-granular space (10 nm) between C–S–H bundles and the internal space (3 nm) in a C–S–H bundle. In fact, this observation indicates the entrained air voids interfere very little with the pore structure at the scale near C–S–H structures, cf. Fig. 8c. 4.3. Thermal gravity analysis The TGA results for pastes and mortars are presented in Fig. 9. It can be seen that these thermal gravity curves are quite similar. The measured Wn and CH are evaluated from these TGA results and presented in Table 2. The Wn values for hydrated cement in pastes and mortars are about 23–25% and the CH values for hydrated cement in pastes and mortars are 14–19%. The hydration extent of cement, calculated by Eq. (8), attains about 90% for all samples at age of 300 d and no systematic difference of hydration extents is observed between pastes and mortars. This confirms that AEA dosage, with entrained air voids, has no influence on the cement hydration kinetics. 5. Discussion According to classic thermo-elasticity [32], the TEC of a porous medium with homogeneous matrix is independent on its porosity and equal to the TEC of matrix. Ghabezloo et al. [7] derived the TEC of cement-based porous materials under drained and undrained
conditions for pore water, and predicted a material TEC increasing with porosity for undrained condition. However, our TEC measurements on both pastes and mortars specimens in this study do not support these statements. Several causes can be responsible for this discrepancy. Firstly, different porosity in this study is created by entrained air contents and the matrix of pastes and mortars is not homogeneous between the air void surface and bulk paste. Relevant investigations show that, once air voids is entrained by AEA in cement paste, a surface shell of about 1 lm thickness is formed with very dense microstructure [33]. Through EDXA examination, it was also revealed that the C/S ratio in this shell was equal to 1.1, compared to C/S = 1.5 in bulk paste [33]. Although no direct evidence is available to quantify the thermal deformation behavior of this shell, it is believed that this shell, together with the discontinuity created between this shell and the bulk paste, would have an direct impact on the TEC of entrained pastes and mortars. It is interesting to note that, in the works of Shui et al. [17], smaller TEC was measured for fly-ash pastes and at the surface of fly-ash particles (void shell) similar C–S–H product with low C/S ratio was also observed [34]. Secondly, the samples in this study were dried under temperature controlled to 50 °C but it is not sure that all pores are totally dried. In our TGA analysis, the mass loss during 50 °C and 150 °C was recorded as 7.2–11.4% for pastes and 5.6–8.7% for mortars, cf. Fig. 9. This mass loss is mainly the evaporated water. The existence of this quantity of water in pastes and mortars can have effect on the TEC measurement by the possible water flow in pore structure [12]. At last, the thermo-deformation of solid skeleton of pastes and mortars can more or less derive from the ideal
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Fig. 9. Thermal gravimetric analysis results for pastes (a) and mortars (b) with different air void contents.
thermo-elasticity due to the cracks and defects in skeleton with the presence of entrained air voids [35]. 6. Conclusion 1. In this paper, the linear TEC of cement pastes and mortars with different entrained air void contents are studied under dry and drained conditions. The results show that the porosity has significant effect on TEC and TEC decreases with porosity. For both cement pastes and mortars, the TEC can be expressed in terms of total porosity or entrained air void content through a power law, ad = a0(1 /)C. The exponents C of pastes and mortars are respectively 2.66 and 2.38 for total porosity and 3.74 and 2.69 for air void content. 2. The gravimetry and MIP measurements on the porosity and PSD indicate that the air-void entrainment do not have significant influence on the total capillary porosity, but the PSD curves measured by MIP are significantly influenced by entrained air
voids. Three characteristic ranges of pore size are identified for PSD curves and air voids interfere with the mercury intrusion process above the scale of 50 nm. 3. Thermal gravity analysis shows that the content of hydration products and hydration degree for both pastes and mortars are almost the same. This confirms that the mineral compositions of pastes and mortars are nearly identical for different air void contents. From the available chemistry and microstructure analysis of air voids in cement pastes is confirmed the existence of a dense shell around air voids and rich in low C/S ratio C–S–H. This shell structure, associated with the entrained air voids, may be responsible for the TEC decrease.
Acknowledgement The research is supported by China national major fundamental research Grant (973 Program, No. 2009 CB623106).
Q. Zeng et al. / Construction and Building Materials 28 (2012) 468–475
Appendix A. Derivation of Eq. (3) For a porous material, the thermoelasticity relates the total volume V and pore volume V/ to the Terzaghi effective pressure rd, the pore pressure P and the temperature T through [7,6,22],
dV 1 1 ¼ drd þ dP 3ad dT V0 Kd Ks dV / 1 1 ¼ drd þ dP 3a/ dT K/ V /;0 K P
ðA:1aÞ ðA:1bÞ
In the above relations, dV/V0 represents the total volumetric strain, dV//V/,0 is the pore volumetric strain, Kd and Ks are the drained bulk and unjacked moduli, KP and K/ are the moduli linking pore volumetric strain with effective stress and pore pressure, and ad is the linear drained TEC. Employing the Betti’s reciprocal theorem, the moduli adopt the relation //Kp = 1/Kd 1/Ks. Under drained condition and drd = 0, dP = 0, ad can be given by:
ad ¼
1 1 @V 3 V 0 @T P;rd
ðA:2Þ
Actually, Eq. (A.2) is the expression for TEC evaluation from drained tests. The variation of the drained TEC with porosity is then expressed as,
@ ad @ ad @ rd ¼ @/ @ rd @/
ðA:3Þ
Using Eq. (A.1b) and the relation d///0 = (d V//V/,0) (dV/V0), the variation of effective stress with the porosity is then given by,
1 1 @ rd 1 1 1/ 1 ¼ ¼ / KP Kd Kd Ks @/
ðA:4Þ
Combining Eqs. (A.3) and (A.4), one obtains,
1 @ ad 1/ 1 @ ad ¼ Kd Ks @/ @r
ðA:5Þ
From Eq. (A.2), the variation of linear drained TEC with respect to effective pressure rd can be expressed as,
@ ad 1 1 @2V ¼ @ r 3 V 0 @T@ rd
! ¼
1 @1=K d 1 @K d ¼ 3 @T 3K 2d @T
ðA:6Þ
Substituting Eq. (A.6) into Eq. (A.5), one gets,
1 @ ad 1 1/ 1 @K d ¼ 2 Ks @/ @T 3K d K d
ðA:7Þ
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