Freezing behavior of cement pastes saturated with NaCl solution

Construction and Building Materials 59 (2014) 99–110

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Freezing behavior of cement pastes saturated with NaCl solution Qiang Zeng a,b, Teddy Fen-Chong b, Kefei Li a,⇑ a b

Civil Engineering Department, Tsinghua University, Beijing 100084, PR China Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, F-77420 Marne-la-Vallée, France

h i g h l i g h t s  Freezing strains of cement pastes saturated with salt solution are measured.  Thermal expansion coefficient of dried samples relates to cement hydrates.  Pore ice content is evaluated from phase change law and pore structure.  Liquid pressure dominates over interfacial energy during pore freezing.  Poroelastic model predicts reasonably well the freezing strains in first cycle.

a r t i c l e

i n f o

Article history: Received 9 December 2013 Received in revised form 19 February 2014 Accepted 21 February 2014 Available online 15 March 2014 Keywords: Freezing Crystallization Pore structure Capillarity Poromechanics

a b s t r a c t This study investigates the freezing behaviors of two cement pastes saturated with water and salt (NaCl) solutions of different concentrations. Special experimental set-up was designed to measure the freezing strains of cylindrical specimens in undrained condition. Using the interfacial curvature properties involved in mercury intrusion under pressure and ice penetration under freezing, the pore ice saturation degree is evaluated through mercury intrusion porosimetry (MIP) data. Experimental results show that both porosity and pore connectivity have impact on the ice saturation degree during freezing. Poromechanical model is established for the freezing strain in the first cooling phase, and the poromechanical simulation agrees reasonably well with the measured strains. The modeling puts in evidence: (1) the freezing strain is induced by pore pressure and thermal contraction of solid matrix, and (2) among the pore pressure contributions the liquid pressure dominates over the interface energy contribution. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Frost damage remains one of durability concerns for cementbased materials in engineering [1]. From laboratory tests and in situ observations, the damage patterns of materials were identified as internal cracking and/or surface scaling [2,3]. The internal cracking tends to decrease the material dynamic modulus and increase the porosity and permeability of materials [4] while the surface scaling, mostly occurring with the presence of solutes, leads to material surface removal with a solute pessimum concentration around 3% [5]. The material damages relate closely to the mechanical effects arising from the liquid/ice phase change in the porous network for internal freezing [6,7] or in the brine layer above the material surface for scaling [8,9]. Through a comprehensive poromechanical modeling framework that takes into account these confined phase change ⇑ Corresponding author. Tel./fax: +86 1062781408. E-mail address: [email protected] (K. Li). http://dx.doi.org/10.1016/j.conbuildmat.2014.02.042 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

processes, Coussy [10,11] linked the internal freezing deformation of a liquid-saturated porous medium to the density change, interface energy, fusion entropy, and thermal dilation discrepancy between pore fluids and solid phases. Furthermore, these identified deformation sources were analyzed in terms of the poromechanical properties of materials, ice formation rates, or applied boundary conditions [12–21]. This model can explain the internal freezing expansion of hardened cement pastes without air entrainment from the positive liquid pressure as ice nucleates in pores [21] as well as the internal freezing contraction of air-entrained samples from the negative liquid pressure as the ice nucleation starts in air voids [11,21–23]. In addition, this contraction decreases the deformation difference between surface brine ice and solid skeleton beneath the ice, thus improving the frost resistance of air-entrained cement-based materials to surface scaling [22]. In these poromechanical-based works on the internal freezing of cement-based porous materials, the mechanical effect of the in-pore solutes has not been taken into account. This is usually also the case for ice content measurement as in [24,25]. However the

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pore solution of cement-based materials is rather concentrated: the solutes (ions) will definitely have impact on the crystallization process of pore solution and herein the generated pressure. Motivated by this need, this study designs an experimental procedure to measure the freezing deformation of cement-based materials saturated by salt solution of different concentrations (NaCl solution at 0%, 1.5%, 3%, 6%, 10% and 15%), and explores the freezing behavior of materials through poromechanical modeling taking into account the pore solution solutes. The paper is organized as follows: the materials (cement pastes) and experimental procedures are introduced in Section 2; the measured deformation of freezing cement pastes are presented in Section 3; the pore solution crystallization processes are quantified in Section 4 with characterized pore structure; the internal freezing behavior of materials is interpreted through poromechanical modeling taking into account the pore solution crystallization in Section 5, and some further discussion is also given on the confrontation between measured deformations and predictions from poromechanical modeling.

TEC evaluation and as reference state for freezing deformation measurement. These specimens were oven-dried at 50  C during 7 d, and this treatment is judged capable to dry completely the capillary pores and partially the gel pores [26]. From the dried specimens, a selected group of specimens were saturated respectively with water and NaCl solutions with mass concentrations of 1.5%, 3%, 6%, 10% and 15% through vacuum saturation procedure for 24 h. The vacuum saturated specimens were then kept in water/NaCl solutions for a period of 7 d to achieve a complete saturation. Afterwards, the specimens were removed from water/NaCl solution to dry the specimen surface, and the surfaces were treated with resin epoxy and encapsulated in a plastic membrane to avoid the moisture loss before freezing tests. Table 1 lists all the specimens for freezing deformation measurement. 2.2. Deformation measurement The specimens were taken out from their plastic encapsulation for freezing tests and their lengths were measured as the initial lengths, e.g. L0i for specimen i. Afterwards, the specimens were installed on the LVDT-stand, specially designed for the freezing deformation tests. Fig. 1 shows the experimental set-up for freezing deformation measurement, including LVDT sensor (Type Macrosensor 750), the invar frame and the installed specimens. This set-up was placed into an environmental chamber (Type Espec PL-2k), in which the temperature control range is 40 to 50  C, and the humidity control range is 20–100%. The deformation measured from LVDT was synchronized with temperature and humidity signals from the environmental chamber and recorded into an external data logger. The freezing strain of specimens is calculated as:

2. Materials and experiments

e¼

2.1. Sample preparation Two cement pastes were prepared with different water to cement ratios, PI (w/ c = 0.5) and PII (w/c = 0.3). The mineral contents of the used cement (Type I cement) were evaluated through Bogue’s procedure as: C2 S (21.38%), C3 S (58.88%), C3 A (6.49%), C4 AF (8.77%), Gypsum (0.75%) and others (3.73%). After mixing, the cement pastes were cast into cylinder tubes of 10 mm diameter and placed in chamber at 20  C. At the age of 1 day (d), the hardened specimens were demoulded and immersed into water for curing. To avoid the leaching of specimens, the ratio of specimens to water was kept roughly at 1:1 in volume or 2:1 in weight. The curing procedure last till the age of 360 d for the specimens. For the subsequent experiments, all PI/PII specimens were dried to constant weight and serves for

Table 1 Specimens for freezing deformation experiments. Material

w/c

Specimen

Treatment

PI

0.5

PI-S0-D PI-S0 PI-S1 PI-S2 PI-S3 PI-S4 PI-S5

Oven-dried to constant weight Saturated with water Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of

1.5% 3.0% 6.0% 10% 15%

PII-S0-D PII-S0 PII-S1 PII-S2 PII-S3 PII-S4 PII-S5

Oven-dried to constant weight Saturated with water Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of Saturated with NaCl solution of

1.5% 3.0% 6.0% 10% 15%

PII

0.3

DL0i  DLLVDT;i L0i

ð1Þ

where DL0i is the measured displacement of specimen i, and DLLVDT;i is the thermal deformation of LVDT sensor used for Specimen i measurement. The displacement DLLVDT is determined by the thermal coefficient of LVDT, bLVDT , evaluated as:

DLLVDT ðT 0 ! TÞ ¼ bLVDT ðT  T 0 Þ

ð2Þ

with T 0 the initial temperature. The thermal coefficients of LVDT sensors were finally calibrated as 0.5541–0.5969 lm/ C with the nominal value of 0.5600 lm= C. The cyclic freeze–thaw scheme is illustrated in Fig. 2. To eliminate initial temperature difference between the specimens and the environmental chamber, temperature was first kept constant at 20  C for 1 h, then decreased with a constant freezing rate to 35  C in 2.75 h. Afterwards, the temperature was kept at 35  C for 1 h, then increased with a constant heating rate to 10  C in 2.25 h and followed by a constant temperature (10  C) period for 0.5 h. From the second (normal) cycle the temperature was cycled between 10  C and 35  C for a period of 6 h, i.e. 2.25 h of freezing, 1 h at 35  C, 2.25 h of heating and 0.5hr at 10  C. Both freezing and heating rates were controlled at 20  C/h after ASTM C-666/672 and RILEM CIF/ CDF test methods. The thermal gradient, between the surface and core of cylinder specimens, under such a rate is estimated as within 1:5  C. Thus a homogeneous phase change can be expected for the specimens during the freeze–thaw cycles. All freezing data were recorded after the temperature equilibrium period, i.e. the beginning point marked in Fig. 2.

3. Freezing deformations 3.1. TEC of dried cement pastes The deformation of dried specimens, PI-S0-D and PII-S0-D, was measured by the experimental set-up in Fig. 1 and the freezing strains were calculated through Eq. (1). Four independent

Fig. 1. Experimental set-up for freezing deformation measurement.

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Fig. 2. Temperature cycling scheme for freezing deformation tests.

Table 2 Freezing strains and TEC of PI-S0-D (PII-S0-D) specimen. Measurement

Temperature range ( C)

Maximum strain (35  C) (lm m1 )

TEC

1st 2nd 3rd 4th

18 20 20 20

586ð936Þ 657ð964Þ 629ð971Þ 634ð991Þ

11.05(17.67) 11.94(17.54) 11.44(17.66) 11.53(18.01)

to to to to

 35  35  35  35

(lm m1  C1 )

measurements were performed to measure the TEC of each dried specimen, and Table 2 provides the maximum freezing strains and the evaluated TEC values. From the measurements, the TEC 6  1 of PI and PII, aI;II C and s , are respectively 11:49  10 6  1 II 17:72  10 C , i.e. as is systematically larger than aIs . This is probably due to the different mineral composition of PI and PII specimens: PII specimen (w/c = 0.3) contains more calcium-silicate hydrates (CSH) and Portlandite (CH) in volume fraction (CSH (PI) = 46.2%, CH (PI) = 13.3% and CSH (PII) = 55.4%, CH (PII) = 15.6% as is estimated in [29]). Relevant literature gives aCSH ¼ 14  106  1 C [30] and aCH ¼ 23:3  106  C1 [31]. Thus, lower CH content in PI specimen tends to decrease the TEC value. This observation is consistent with the micromechanical prediction from Ghabezloo [30]. Moreover, the denser microstructure of PII tends to retain more water in gel pores, which may enlarge the TEC of material, as demonstrated by Scherer and coworkers [32–34]. 3.2. Deformation of saturated specimens Fig. 3(a) and (b) shows the freezing strains of PI specimens (PIS0–PI-S5) in terms of freezing time and freezing temperature respectively. Except PI-S1 (1.5% NaCl) and PI-S5 (15% NaCl), all specimens showed significant expansion as temperature decreases under the water nucleation point. This freezing expansion has been observed in other experimental investigations [35]. Through poromechanical interpretation this freezing expansion is induced by both the pore crystallization pressure and the viscous flow pressure [10]. The PI-S1 specimen showed a slight contraction as the temperature decreases below the ice nucleation point. This ‘‘abnormal’’ contraction would be due to the incomplete saturation of specimen. As some occluded voids or capillary pores are just partially saturated or even empty, they can act as the entrained air voids, i.e. the ice nucleates on the pore wall freely and attracts water (solution) confined in smaller pores in the vicinity. This mechanism is named as the ‘‘cyosuction’’, first proposed by Powers and Helmuth [36] and later explained in more elaborated way by different authors [11,14,10,21,28]. The preference of ice nucleation on the internal surface of air voids has been confirmed by ESEM (Environmental Scanning Electron Microscopy) observation [23]. This contraction just below ice nucleation point was also observed

for PI-S2 (3% NaCl) at the third and fourth F–T cycles, but accompanied with more important expansion as temperature cooled down to 35  C, cf. Fig. 3(b). The PI-S5 specimen showed neither significant expansion nor large residual strain. This is obviously related to the high NaCl concentration (15%) of saturating solution. The high NaCl concentration depresses substantially the nucleation point of pore solution, thus retards the crystallization process of liquid water in solution. Quantitative analysis will be given in Sections 4 and 5. Another important observation on the strain–time and strain–temperature curves is the evolution of maximum freezing strains with F–T cycles. The maximum freezing strains increased with F–T cycles, and only PI-S3 (6% NaCl) specimen showed the maximum freezing strain decreased at the last cycle. All specimens, except for PI-S5, showed important residual strains. This residual strain may indicate the internal cracking occurs due to pore freezing. PII specimens, PII-S0–PII-S5, showed completely different deformation behaviors in Fig. 4. As shown in the figures, all specimens, except for PII-S0, had no observable expansion at subzero temperature, and no significant residual freezing strain either. This contrast with Fig. 3 can only be attributed to the denser microstructure of PII material. Having a lower w/c ratio of 0.3, the paste contains much less capillary pores and the percolation of pores is much more limited [37]. Therefore, compared to the corresponding PI specimens much less ice forms during the same freezing process, see quantitative analysis in Section 4. In addition, the ice nucleation points could not be easily detected for PII specimens from strain–temperature curves because there was no obvious contraction or expansion near nucleation point of liquid water. 3.3. Freezing strain characterization The strain–time curve of PI-S0 is retained as typical curve for analysis in Fig. 5. To help the analysis several strain terms are defined as follows. The strain of thermal shrinkage at 35  C, eth , is defined as the pure thermal contraction of porous medium with its enclosed liquid pore solution without crystallization. It is not a really measured value but used as reference to characterize other freezing strains related to pore crystallization. In Fig. 5, this value is read by prolongating the strain–temperature curve from nucleation point to 35  C. Moreover, this eth is also different from the maximum freezing strain of dried specimens PI (II)-S0-D in Table 2 because the confined pore solution has influence on the thermal deformation of saturated porous media under undrained condition. This issue has been extensively investigated in literature [30,32,33,38,34]. The nucleation strain, enu , is defined as the instantaneous strain at the vicinity of ice nucleation point, reflecting the magnitude of overall pore pressure accumulation as nucleation occurs. Theoretically, this value depends on the pore saturation degree, pore solution concentration and freezing rate. The

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Fig. 3. Freezing deformation for PI specimens (PI-S0–PI-S5) in terms of time (a) and temperature (b).

maximum freezing strain, eex , is defined as the absolute strain as cooling temperature reaches 35  C. The strain by pore pressure, epr , for F–T cycles is thus defined as the difference between the thermal shrinkage eth and maximum freezing strain eex , i.e. epr ¼ eex  eth . Actually, the strain epr includes all effects associated with the crystallization process of pore solution. As a F–T cycle is finished specimens generally cannot resume their initial lengths. The residual strain is noted as ere . The low temperature residual strain, eif , is defined as eex in ith F–T cycle minus its value in the precedent cycle. All the strains are illustrated in Fig. 5. Table 3 shows the characteristic strains for PI (II)-S0–PI (II)-S5 extracted from Figs. 3 and 4. The pure thermal strain eth of PII specimens is systematically larger than PI specimens, which can be attributed to the larger TEC of Paste II and the TEC discrepancy between solid paste and pore solution. Significant nucleation strain just below water freezing point, enu , was only observed for PI-S0 (water saturated), PI-S3 (6% NaCl) and PI-S4 (10% NaCl) specimens. The maximum nucleation strain appeared for PI-S3 specimen at the third cycle with enu ¼ 575 lm/m. The maximum freezing strain eex and pore pressure strain epr for PI specimens are significantly larger than Paste II specimens, and maximum values are eex ¼ 1782 lm/m and epr ¼ 2133 lm/m (PI-S3). These values reflect the pore pressure level due to pore crystallization process, thus this observation can only be explained by the more advanced

crystallization extent in PI specimens. The specimens PI-S0–PI-S4 show significant residual strains ere and eif while PI-S5 (15% NaCl) and all PII specimens show no positive residual strains (expansions). The positive residual strains can quantify the material internal cracking (damage) induced by the F–T cycles. These residual strains show that high NaCl concentration (15%NaCl), denser microstucture (w/c = 0.3) help to limit the freezing damage, due to a more limited extent of crystallization. These strains will be quantified in terms of crystallization extent and pore structure in the poromechanical analysis part of this paper, cf. Section 5. 4. Freezing of pore fluid and saturation degree 4.1. Thermodynamic equilibrium between ice and water Under freezing, ice first forms in larger pores then penetrates into smaller pores. This process is controlled by the percolated ‘‘throat’’ size of pores [6,7]. From the chemical equilibrium between bulk pore solution and ice crystal, the difference between ice and liquid solution pressures P c  Pl writes [3,39]:

Pc  Pl ¼





qc  1 ðPl  P0 Þ þ PG þ PA qw

ð3Þ

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Fig. 4. Freezing deformation for PII specimens (PII-S0–PII-S5) in terms of time (a) and temperature (b).

the pores are much less percolated during crystallization and the local liquid pressure in pores can accumulate up to 100 MPa [21]. In this case, the effect of this term is significant. The second term at the right side of Eq. (3) represents the pressure from fusion energy,

    T0 PG ¼ qc S f ðT 0  T Þ þ C f ðT  T 0 Þ þ T ln T

ð4Þ

where S f is the melting entropy of ice at P ¼ 0:1 MPa (atmosphere pressure) and the bulk water freezing/melting temperature T 0 , retained as qc S f ¼ 1:2227 (MPa/ C); C f is the difference of heat capacity between the liquid and solid phases at freezing temperature T(< T 0 ): C f ¼ 2:1 þ 0:00482ðT  T 0 Þ (J g1 K1 ) [41]. The third term at the right side of Eq. (3) stands for the effect of salt,

PA ¼ Fig. 5. Strains defined for a typical freezing strain curve of paste specimens.

qc RT ln aw

ð5Þ

M H2 O 1

The first term at the right side represents the effect of liquid pressure with qc and qw as the ice and liquid water densities. Generally this term is very small as pores are well connected since P l is very near to P0 (often retained as the external atmospheric pressure) [18,40]. However, under freezing in undrained condition

where R is the ideal gas constant 8:314472 (J K1 mol ), MH2 O is the molar mass of water(ice) (kg/mol), and ln aw the water activity in pore solution. The water activity is related to the osmotic coefficient P through [43]:

ln aw ¼ 

mT M H2 O P 1000

ð6Þ

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Table 3 Characteristic freezing strains (106 ) for PI and PII specimens (eth : thermal strain; strain; eif : low temperature residual strain). Specimen

Strain

1st cycle PI

enu : nucleation strain; eex : maximum freezing strain; epr : pore pressure strain; ere : residual

2nd cycle PII

3rd cycle

4th cycle

PI

PII

PI

PII

PI

PII

S0

eth enu eex epr ere eif

577 306 944 1521 410 –

878 0 672 206 6 –

509 414 1231 1740 313 592

715 0 507 208 10 11

560 425 1305 1865 300 336

710 0 497 213 10 0

547 468 1337 1884 – 332

703 0 497 206 – 10

S1

eth enu eex epr ere eif

746 0 0 746 341 –

1322 0 1157 165 160 –

675 0 183 858 155 388

930 0 819 111 31 63

704 0 72 776 104 44

915 0 809 106 10 21

706 0 55 651 – 23

893 0 820 73 – 21

S2

eth enu eex epr ere eif

829 0 802 1631 408 –

897 0 863 34 2 –

622 0 982 1604 230 437

804 0 708 96 32 10

574 0 787 1461 138 35

785 0 698 87 20 22

639 0 614 1253 – 35

764 0 699 65 – 21

S3

eth enu eex epr ere eif

589 306 1051 1640 466 –

1285 0 1197 88 175 –

390 467 1749 2139 419 1049

937 0 854 83 54 65

371 575 1782 2133 269 460

929 0 865 64 43 65

437 445 1153 1590 – 360

923 0 867 56 – 45

S4

eth enu eex epr ere eif

617 0 700 1317 379 –

1135 0 1074 61 24 –

348 25 1284 1632 199 841

955 0 882 73 10 10

336 98 1356 1692 209 269

968 0 888 80 1 0

338 49 1037 1375 – 110

966 0 883 83 – 10

S5

eth enu eex epr ere eif

892 0 665 217 631 –

1189 0 1128 61 43 –

715 0 513 202 1 61

997 0 869 128 2 0

786 0 490 296 35 24

931 0 871 60 0 0

766 0 405 361 – 120

947 0 860 87 – 11

The osmotic coefficient P characterizes the deviation of a solvent from the ideal behavior. Based on the Gibbs–Duhem equation for an aqueous solution, the osmotic coefficient can be expressed as [43],

P¼1þ

X X 1Z I xi ln ci  xi ln ci dI I 0 i i

ð7Þ 1

where mi is the specific molality of species i (in mol kg ), mT is the P overall molality mT ¼ mi ; xi is the molar fraction defined as P xi ¼ mi =mT ; I is the ionic strength defined as I ¼ i mi zi (mol/kg) and ln ci is the activity coefficient of species i. According to Lin and Lee [43], the activity coefficient ln ci of an individual ion is evaluated as a combination of the individual ionic long-range interaction and short-range solvation effect:

" ln ci ¼

A/ z2i

#  C i z2i Ia 2 1=2 þ þ ln 1 þ Bi I 1=2 Bi T 1 þ Bi I I1=2

ð8Þ

where A/ is the Debye–Hückel constant dependent on temperature, Bi ; C i are species-dependent constants and a ¼ 1:29 [43].

much larger than PII (0.063 ml/g), confirming that PII has denser microstructure. The obtained PSD curves were used to deduce the pore structure for crystallization process. For modeling purpose, this study employs the multi-peak Gauss formula to fit the obtained PSD curves,

" pffiffiffi # N  X 2Ai dv 2 2 pffiffiffiffi exp 2ðlog D  log Di Þ =wi ¼ f0 þ d logðDÞ wi p i

ð9Þ

where D is the pore diameter, f0 ; Ai ; wi and Di are fitting parameters. Using Eq. (9), the PSD curves of PI and PII are fitted and illustrated in Fig. 6. The parameters of multi-peak Gauss fitting are given in Table 4. It can be found that the characteristic pore size for each peak of Paste II is systematically smaller than that of PI. Although the PSD curves are deduced from MIP measurement in which high confining pressure is applied to the cement paste, which is not necessarily the case for ice formation by freezing temperature, both involve the same non-wetting phase invasion process throughout the porous network (thus including the same ‘‘ink-bottle’’ and pore connectivity effects [44]). This allows the estimation of ice saturation degree from MIP-induced PSD curves.

4.2. Pore size distribution 4.3. Saturation degree The pore size distribution (PSD) of PI and PII specimens were characterized by mercury intrusion porosimetry (MIP) method [37]. The intruded specific pore volume v for PI (0.161 ml/g) is

The physical processes of ice penetration under freezing and mercury intrusion under pressure are similar: a non-wetting phase

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(ice or mercury) invades pore structure progressively and a complementary wetting phase (liquid solution or air) retreats correspondingly. The interface between wetting phase and nonwetting phase penetrates from material surface into inner part progressively from larger pores to smaller pores. As a non-wetting phase penetrates into pores, the pressure differences can be calculated through Young–Laplace equation:

Pm  Pg ¼ 

Pc  Pl ¼ 

2cmg cos hmg r

2ccl cos hcl rd

ðMercury intrusionÞ

ðFreezingÞ

ð10aÞ

ð10bÞ

In the equation, Pc and P l are ice crystal (non-wetting phase) and liquid (wetting phase) pressures; P m and Pg are mercury (non-wetting phase) and air (wetting) pressures; ccl and cmg are respectively the ice–liquid and mercury–air surface tensions, hcl and hmg are respectively the ice–liquid and mercury–air contact angles. For the following quantitative analysis, the contact angle hcl is assumed to be 180 and hmg is taken as 130 [45,46]. The MIP measurement provides the intrusion mercury volume v m in terms of mercury pressure Pm , which can be converted to rðv m Þ relation through Eq. (10a), i.e. the integral form of Fig. 6. For freezing process, the P c  Pl can be evaluated from Eq. (3) in terms of pore solution composition and freezing temperature. Through Eq. (10b), the capillary pressure Pc  P l at a certain freezing temperature T can be related to a pore size r. Due to the similarity of mercury intrusion and ice penetration in pores, the corresponding pore volume occupied by ice crystals can be evaluated through the same rðv m Þ relation from MIP measurement (cf. [47]). Using PSD curves from MIP measurement, Fig. 7 gives the evolution of pore ice volume for PI and PII specimens for a

freezing range of 0 to  35  C. Note that the possible eutectic NaCl  2H2 O–ice phase occurring at about 21:3  C is not considered here, due to the available data of the thermodynamic properties of the eutectic NaCl  2H2 O–ice phase. As expected, Paste I specimens contain much more ice volume than Paste II specimens due to larger pore size and higher connectivity of pores of Paste I [37]. Also, higher NaCl concentration decreases the ice volume for a same group of specimens (PI or PII). As the concentration of NaCl solution increases to 15% the equilibrium ice formation temperature is decreased to around 10  C. Fig. 8 illustrates the evolution of pore liquid saturation degree of PI and PII specimens for a freezing range of 0 to  35  C. For PI-S5 specimen (15% NaCl) a temperature of 35  C can only freeze about 40% volume of pore solution while this ice formation extent can be reached by a freezing at 10  C for PI-S0 specimen (water saturated). It is noted that the pore solution is also concentrated from its initial state as water crystallizes from pore solution. Due to very limited ice nucleation extent for PII specimens, the pore ice content achieves only 9.5% (PII-S0) to 7% (PII-S5) for a freezing range of 0 to  35  C. 5. Poromechanical analysis 5.1. Poroelasticity This study considers cement paste saturated with water/solution as a deformable elastic porous medium. Subjected to freezing the pores are progressively invaded by ice crystals (with subscript c) and the amount of liquid pore water/solution (with subscript l) decreases. The relative volumes of the two phases satisfy [10,48]:

/ ¼ /l þ /c ;

/J¼l;c ¼ /0 SJ þ uJ ;

Sl þ Sc ¼ 1

u ¼ /  /0 ; u ¼ ul þ uc

ð11aÞ ð11bÞ

where /0 ; / stand for initial and current porosities, u for the porosity change, and uJ for partial porosity change due to partial pressure PJ . Actually, the term /0 SJ represents the porosity occupied by the phase J during phase transition process, prior to deformation uJ [40]. In this study the freezing strain is measured axially on cylindrical specimens under undrained condition, and the axial strain can be represented by the linearized strain e with the applied stress r ¼ 0. For this particular case, the linearized strain e writes,

1 3

e¼ ¼

  1 2 bl Pl þ bc Pc  b U þ as ðT  T 0 Þ 3K 3

ð12Þ

with  as the trace of strain tensor. The porosity deformation (u ¼ /  /0 ) is given as,

u ¼ b þ

  1 2 1 Pl  U þ ðPc  Pl Þ  3a/ ðT  T 0 Þ N 3 Ncc

ð13Þ

In Eqs. (12) and (13), the liquid pressure P l is an important source for freezing deformation. The liquid pressure is determined through pore mass conservation during crystallization, expressed as,

Pl ¼

   q0l /0 1 2  P GA ðPG þ P A Þ þ P U U  3 bas  a/ ðT  T 0 Þ P ql Sl þ qc Sc 3 ð14Þ

where

 P¼  ¼ Fig. 6. Multi-gauss fitting of PSD curves of (a) PI and (b) PII.

bbc 1 þ Ncc K



 bbc 1 ; þ Ncc K

!



2 qc b 1 ; P GA 1 þ þ ql K N 2

PU ¼

b 1 þ K N

!

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Table 4 Multi-peak Gauss fitting parameters for PSD curves of PI and PII. Material Peak f0

Ai

wi

log Di (Di ) (nm)

Paste I

1 2 3

0.00271 0.00621 0.432 0.102 0.727 0.301 0.647

Paste II

1 2 3

0.00176 0.00250 0.0996 1.055 (11.3) 0.0324 0.329 0.858 (6.9) 0.0199 0.181 0.511 (3.2)

Coefficient R2

5.515 (327340) 0.999 1.190 (15.5) 0.0145 (1.0) 0.999

Fig. 8. Pore liquid saturation degree in terms of freezing temperature for (a) PI and (b) PII specimens.

Fig. 7. Pore ice volume in terms of freezing temperature for (a) PI and (b) PII specimens.

The term U represents the interface energy created from the phase change in pore solution during freezing, and it constitutes another pressure source for freezing strain in Eq. (12). According to the standard poromechanics for saturated media with the assumption that the variations of U with u and T are negligible compared to its variation with Sl , this interface energy can be described as [10],

U¼

Z

where K is the bulk modulus, ks is the bulk modulus of solid matrix, and as the TEC of solid matrix. From Eq. (12) the linear freezing strain is composed of the pore pressure term and thermal term. For pore water freezing, it has been showed that the interface energy term is insignificant compared to liquid pressure, i.e. U  Pl [41]. The poromechanical analysis later in this paper will show that, for pore solution freezing, this interface term remains insignificant compared to Pl and Pcap . In that case, the pore pressure term is dominated by Pl and P cap , and further the pore pressure will be totally determined by Pcap if the liquid pressure P l remains constant, e.g. for well connected pore structure and freezing in drained condition. That explains why porous soft materials show freezing dilatation after nucleation even when the pore fluid is replaced by benzene (which contracts when freezing) [27]. This observation has been explained in pore detailed way by different authors [7,10,14,42].

5.2. Poromechanical results

1

Pcap dSl

ð15Þ

Sl

In isotropic case, the Biot’s tangent modulus (b and bJ ), generalized Biot’s (coupling) modulus (1=N and 1=N IJ ) and the thermal coupling dilatation coefficient (a/ and a/J ) observe [10,49]:

b ¼ bc þ bl ¼ 1 

K ; ks

1 X 1 1 ¼ þ ; N J¼l;c NJJ Ncl

bJ¼c;l ¼ bSJ

1 1 1 þ ¼ ðbJ  /SJ Þ NJJ Ncl ks

a/ ¼ as ðb  /Þ; a/J ¼ as ðbJ  /0 SJ Þ

ð16aÞ ð16bÞ ð16cÞ

The poromechanical model is applied to simulate the freezing strains of PI and PII specimens through Eq. (12). For the pore pressure term, the liquid pressure Pl is evaluated from Eq. (14), the interface energy U from Eq. (15). For the thermal term, the TEC of PI and PII specimens are taken from the measurements in Section 3.1. The relevant parameters required for poromechanical analysis are given in Table 5. Figs. 9 and 10 show the poromechnical simulation of freezing strains for PI and PII specimens together with the measured strains. Fig. 9 gives an acceptable agreement between the measured strains and poromechanical simulation results, except PI-S1 specimen (1.5% NaCl) in Fig. 9b. The important difference in low temperature

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Q. Zeng et al. / Construction and Building Materials 59 (2014) 99–110 Table 5 Poromechanical analysis parameters for PI (PII) specimens. Parameter

Value

Unit

Significance

Reference

/0 K ks

0.26(0.13) 14.6(20.2) 31.8 14.49(17.72)

– GPa GPa

Porosity Bulk modulus of skeleton Bulk modulus of matrix TEC of matrix

– – [50] –

as M H2 O

q0l (S0) q0l (S1) q0l (S2) q0l (S3) q0l (S4) q0l (S5) q0c

106 /K g/mol

18.02 999:7

kg=m3

Molar mass of water Water density (P = 0.1 MPa, T = 293 K)

[51] [52]

1008.2

kg=m3

NaCl solution density (1.5%)

[52]

1018.2

kg=m3

NaCl solution density (3.0%)

[52]

1037.8

kg=m3

NaCl solution density (6.0%)

[52]

1063.0

kg=m3

NaCl solution density (10%)

[52]

1092.6

kg=m3

NaCl solution density (15%)

[52]

917

kg=m3

Ice density (P = 0.1 MPa, T = 293 K)

[53]

Fig. 9. Measured freezing strains and poromechanical simulation for PI specimens: (a) PI-S0 (water-saturated), (b) PI-S1 (1.5% NaCl), (c) PI-S2 (3% NaCl), (d) PI-S3 (6% NaCl), (e) PI-S4 (10% NaCl) and (f) PI-S5 (15% NaCl).

Fig. 10. Measured freezing strains and poromechanical simulation for PII specimens: (a) PII-S0 (water-saturated), (b) PII-S1 (1.5% NaCl), (c) PII-S2 (3% NaCl), (d) PII-S3 (6% NaCl), (e) PII-S4 (10% NaCl) and (f) PII-S5 (15% NaCl).

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Q. Zeng et al. / Construction and Building Materials 59 (2014) 99–110

Fig. 11. Total stain, hydraulic strain, interface strain and thermal strain by poromechanical simulation for PI-S0 (a) and PII-S0 (b) specimens.

range can be partially due to the incomplete initial saturation of the specimen PI-S1 as aforementioned. The significant expansion of PI specimens below ice nucleation is definitely due to the large pore pressure induced by ice formation from pore solution. For PII specimens a reasonable agreement is also observed for measured freezing strains and poromechnical results in Fig. 10. These results imply that the poroelasticity involving the thermodynamics can capture the freezing behavior of cement pastes saturated by water and solutions. Through Eq. (12) four origins for the axial freezing strain below nucleation point T f can be quantified: the hydraulic strain bPl =ð3KÞ, interface strain 2bU=ð9KÞ and thermal strain as ðT  T 0 Þ. For PI(II)-S0 specimens, Fig. 11 gives the total freezing strains in terms of freezing temperature, together with their hydraulic strains, interface strains and thermal strains. From this figure, the relative importance of each strain can be compared. The most important contributions are from the hydraulic and thermal strains. The hydraulic strains show first a contraction then a significant expansion. The contraction of hydraulic strain is due to the temperature dependent density of liquid solution. The thermal strain (contraction) increases linearly with the freezing temperature. While the interface strains contribute much less to the total strain. The liquid pressure P l for all specimens, PI-S0–5 and PII-S0–5, are calculated and presented in Fig. 12. Table 6 presents the minimum liquid pressure, the corresponding freezing temperature and the thermal pressurization coefficient (the pore pressure increase due to a unit temperature increase in undrained conditions [30]) for each specimen. The negative liquid pressure, as aforementioned, is due to the thermal contraction of pore solution and ice crystals. The lowest (negative) liquid pressures attain 5:3 to  20:2 MPa

Fig. 12. Liquid pressure P l from poromechanical simulation for Paste I (a) and Paste II (b) specimens.

Table 6 Minimum (negative) liquid pressures and pressurization coefficients for PI and PII specimens. Specimen

S0 S1 S2 S3 S4 S5

Pressure (MPa)

Temperature ( C)

PI

PII

PI

PII

Pressurization coefficient (MPa/ C) PI PII

5.3 6.7 8.1 10.9 14.9 20.2

1.4 2.0 2.4 3.0 4.2 5.8

4.0 3.5 1.5 2.0 6.0 9.7

4.0 3.8 2.0 1.0 5.0 10.0

0.33 0.41 0.44 0.50 0.57 0.68

0.09 0.12 0.13 0.14 0.17 0.19

(PI) and 1:4 to  5:8 MPa (PII) during freezing. The pressurization coefficients vary from 0.33 to 0.68 (PI) and from 0.09 to 0.19 (PII). It is to note the pressurization coefficients of PI specimens are close to literature data (0.6 MPa/ C) for cement paste with the same porosity (/ ¼ 0:26) [30]. As freezing goes on, P l increases significantly, from negative to positive, due to the formation of ice. The more ice forms the higher P l can reach, attaining about 100 MPa for PI-S0 specimen. The NaCl in solution tends to decrease the ice formation. Increasing from zero (S0) to 15%(S5), the NaCl concentration reduces the maximum liquid pressure at 35  C from 100 MPa to 40 MPa (PI) and from 30 MPa to 5 MPa (PII). The different pore structure and the ice saturation degree account for this large contrast on Pl level, cf. Fig. 8. The interface energy U is presented in Fig. 13. The PI specimens have higher values (2.2–7.0 MPa) than the corresponding PII specimens (1.2–2.0 MPa). This is mainly because PI specimens contain more pore ice than PII specimens. The above results confirm again

Q. Zeng et al. / Construction and Building Materials 59 (2014) 99–110

109

pastes. Again, both pore structure and NaCl concentration play important role on the ice saturation degree: from 0.40 for PIS5 to 0.66 for PI-S0 and from 0.07 for PII-S5 to 0.10 for PII-S0 at 35  C. This large contrast in saturation degree of pore ice explains the very different mechanical behaviors of PI and PII specimens. 3. The poromechanical model quantifies the internal freezing strains of saturated cement pastes under undrained condition from pore pressure and thermal contraction of solid matrix. Assuming an elastic behavior to the material solid matrix, the poromechanical simulation results are compared with the experimental observations for the freezing strains during the cooling phase of the first freezing–thawing cycle for PI and PII specimens. Reasonable agreement is found, validating the poroelastic description of freezing strains of saturated cement pastes. The simulation results also put into evidence the relative importance of different strains from pore pressure: the pore liquid pressure and the interface energy. For water/NaCl solution saturated cement pastes, the pore liquid pressure P l (100 MPa) dominates over the interface energy U (1.2– 7.0 MPa). Further simulation of freezing strains after the first cooling phase needs to involve the damage process of solid matrix.

Acknowledgements The authors dedicate this work to the memory of Prof. Olivier Coussy, the initiator of this research. The financial support is from China Major Fundamental Research Grant (973 Program, No. 2009CB623106). Fig. 13. Interface energy U from poromechanical simulation for Paste I (a) and Paste II (b) specimens.

the relative importance of different contributions to the total freezing strain of specimens, i.e. jPl j > jUj. 6. Conclusion 1. This study investigated the freezing behaviors of two cement pastes (PI: w/c = 0.5, PII: w/c = 0.3) saturated with water (S0) and NaCl solution of different concentrations (S1 = 1.5%, S2 = 3%, S3 = 6%, S4 = 10% and S5 = 15%). The freezing strains were measured through a specially designed experimental set-up under undrained condition. The thermal expansion coefficient (TEC) average values of dried specimens are evaluated as aIs ¼ 11:39  106  C1 for PI, and aIIs ¼ 17:72  106  C1 for PII. From the measurement of freezing strains, it is observed that both the NaCl concentration and the pore structure have impact on the freezing strains. The PI specimens, having larger (/0 ¼ 0:26) and more connected porosity, showed clearly the nucleation strains, pore pressure strains as well as residual strains. On the contrary, the PII specimens, having much denser microstructure (/0 ¼ 0:13) and poorly connected pores, showed insignificant freezing strains with respect to the pore crystallization process. 2. The pore ice saturation degree is vital for freezing behaviors of saturated cement pastes. The thermodynamic equilibrium between pore water (solution) and ice is recalled to express the pore capillary pressure during freezing, taking into account the influence of NaCl concentration. Then, by use of the Young– Laplace relation for capillary in-pore mercury intrusion under pressure and ice penetration under freezing, the pore ice saturation degree is evaluated from the MIP measurements on the

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