The dependence of capillary sorptivity and gas permeability on initial water content for unsaturated cement mortars

Cement and Concrete Composites 104 (2019) 103356

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The dependence of capillary sorptivity and gas permeability on initial water content for unsaturated cement mortars

T

Fangzhou Rena,b, Chunsheng Zhoua,b,*, Qiang Zengc, Zhu Dingd, Feng Xingd, Wei Wanga,b a

Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin, 150090, China c College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, China d Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil Engineering, Shenzhen University, Shenzhen, 518060, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Mortar Capillary sorptivity Gas permeability Water saturation

Capillary sorptivity and gas permeability characterizing the penetration ease of water and gas deserve attention in the current attempts to quantify durability performance for cement-based materials. To investigate their dependences on water content, disk specimens of cement mortars are prepared and thoroughly preconditioned. At ambient condition, available models could quantify the measured dependence of gas permeability except capillary sorptivity. Surprisingly, it follows another bilinear law with a transitional saturation degree, beyond which capillary condensation occurs in gel pores at equilibrium. This extraordinary disagreement is ascribed to the dynamic structure of C–S–H gel and thus mortars, which are sensitive to water removal and regain. Physically, it is also responsible to several unexpected anomalous characteristics of water absorption. The unsaturated flow theory is no longer applicable if ignoring its sensitivity to water, which is the key to approach the transport mechanisms of water and other deleterious agents in common unsaturated cement-based materials.

1. Introduction In engineering practice of concrete construction, many physical and chemical processes are mediated by water [1,2], including of course the much concerned deterioration of cement-based material under various environmental actions [3,4]. The durability performance of cementbased material is mostly determined by the coupled penetration of various masses. In essence, the water content enforces fundamental influence on almost all the transport properties of deleterious gases, ions as well as water itself in cement-based material, and thus determines its durability to a great extent [5]. Since the cement-based materials under service are rarely saturated by water, it is important to characterize the dependence of mass transport properties on water content. Among the widely used indicators quantifying the durability potential of cement-based material, the relevent capillary sorptivity and gas permeability are much easy to measure on well-controlled unsaturated material in laboratory and even in field [6]. Therefore, the unsaturated capillary sorptivity and gas permeability quantifying the penetration ease of water and gases deserve much attention in the current attempts to quantitatively predict the durability performance of cement-based material.

*

Capillary sorptivity represents the velocity of water absorption into unsaturated cement-based material under the driving action of capillary pressure [7]. Based on the Richards equation [8] or unsaturated flow theory [9], in the one-dimensional absorption into homogeneous porous medium of uniform water content, the absorbed water volume per unit area is theoretically proportional to the square root of elapsed time [2]. The proportional coefficient is clearly defined as the capillary sorptivity, which is first introduced by Philip in the neighbouring field of soil physics [10]. When it is directly borrowed to quantify cementbased material, although the square root of time law still holds, the strict definition of capillary sorptivity faces several robust challenges due to several unexpected anomalous behaviors of water absorption into cement-based material [11–13]. Moreover, although several models have been established to quantify the dependence of capillary sorptivity on initial water content [10,14–19], they are mostly developed from the function of hydraulic diffusivity in terms of saturation degree, which could be experimentally measured through the Richards equation [20]. Since the hydraulic diffusivity is intimately linked to water permeability, cement-based material having anomalously low water permeability may also have anomalous hydraulic diffusivity [21], possibly making the models of capillary sorptivity initially proposed for

Corresponding author. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China. E-mail address: [email protected] (C. Zhou).

https://doi.org/10.1016/j.cemconcomp.2019.103356 Received 26 February 2019; Received in revised form 19 May 2019; Accepted 24 June 2019 Available online 28 June 2019 0958-9465/ © 2019 Elsevier Ltd. All rights reserved.

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without altering its micro-structure does not exist at all [21,22,35]. Furthermore, it is broadly accepted that drying preconditioning will invariably induce micro-cracking to fragile cement-based material, which will bias the measured capillary sorptivity and gas permeability thereafter. Therefore, comprises have to be made. Precisely, the totally dry state can be practically defined as that having no evaporable water, which could be operationally and quickly achieved by oven-drying at 105 °C until constant weight with good reproducibility. From these considerations, the totally dry state without evaporable water is herein selected as the reference dry state to help define the evaporable water content. Since micro-cracking damage is inevitably incorporated into the micro-structure of cement-based material after oven-drying at elevated temperature, the capillary sorptivity and gas permeability experimentally measured at reference dry state is only nominal, and thus cannot be directly treated as that actual values in accordance with ideal totally dry state without incorporation of micro-cracks. In another aspect, it is also very difficult to achieve complete water saturation for cement-based material [36]. For relatively large samples of very low permeability, the time required for liquid to penetrate throughout them may be surprisingly long and impractical [2]. To simplify this analysis, the frequently adopted vacuum saturation method is employed to achieve water saturation state, at which water content could reach its maximum value under common service condition. As usual, the water saturation degree Θ (−) is therefore operationally defined as,

soils and rocks unsuitable to cement-based material. Because the fragile pore structure of cement-based material is extremely sensitive to water removal and regain during drying preconditioning and following absorption [21,22], the physical significance of capillary sorptivity and its dependence on water content are still open questions. Although transport of gases (CO2, O2, H2O etc.) are seldom driven by pressure gradient in reality, the measurement of gas permeability is much easier than water permeability, and could be carried out on at least partially dried cement-based material. Many experimental data of unsaturated gas permeability have been reported in literature [19,23–28]. When describing its dependence on water content, the available physical or empirical models originally proposed for soils or rocks [29,30] are usually borrowed to describe cement-based materials, which have definitely distinct pore structural characteristics from them. Importantly, these models are all established on the implied assumption of stationary pore structure, which is not modified by water loss or reentry. However, it is well recognized that the micro-structure of cement-based material is vulnerable to water removal especially at elevated temperature, which is widely adopted in general laboratory experience to accelerate the preconditioning if required. Not only the inevitable micro-cracking, the pore structure of cement-based material is also evolving during the alteration of water content due to the collapse or expansion of C–S–H gel [21,22], which makes its permeability to water and other fluids totally different by several orders of magnitudes. As a consequence, the dependence of unsaturated gas permeability on water content is still far away from current understanding without detailed considerations on the evolution of pore structure. In principle, capillary sorptivity and gas permeability of cementbased material are both physically determined by its current pore structure and water distribution. To quantify their dependence on water content, experimental investigation is carried out herein with attention being paid to the evolving pore structure sensitive to water removal and regain. In Section 2, the available models for both unsaturated capillary sorptivity and gas permeability are summarized from literature. In Section 3, an experimental scheme is thoroughly designed and carried out to obtain representative results, which are then analyzed in Section 4. Further discussion is made in Section 5 with regard to the essential water absorption. Finally, several remarks are briefly concluded in Section 6.

Θ = (Weq − Wdry )/(Wsat − Wdry )

(1)

where W (g) denotes the weight of testing specimen and subscript “eq”, “dry”, “sat” indicates the operational equilibrium, absolutely dry and water saturation state, respectively. To help quantify the dependence of capillary sorptivity S (mm/ min0.5) and gas permeability kg (m2) on water saturation Θ , the relative capillary sorptivity Sr (−) and relative gas permeability k rg (−) are usually introduced and defined as,

S (Θ) = S0 × Sr (Θ), kg (Θ) = kg0 × k rg (Θ)

(2)

where the subscript “0” denotes the ideal totally dry state with absent evaporable water and micro-cracks. The totally dry state for cementbased material is almost impossible to achieve without severe drying at 105 °C. In addition to removing evaporable water, drying at elevated temperature will undoubtedly generate micro-cracks and thus significantly bias the measured gas permeability and capillary sorptivity. As a result, the experimentally measured gas permeability and capillary sorptivity at any reference dry state achieved by drying at elevated temperature cannot be directly regarded as the ideal values kg0 and S0 . As a matter of fact, it is not realistic to measure the ideal capillary sorptivity S0 and ideal gas permeability kg0 of cement-based material at ideal totally dry state due to the unavoidable micro-cracking damage enforced by drying at elevated temperature. Consequently, they will be then treated as unknown variables to be determined.

2. Available models in literature 2.1. Definition of saturation degree As the cement-based materials under service are mostly neither saturated nor totally dried, numerous efforts have been devoted to investigate the dependence of capillary sorptivity and gas permeability on initial water saturation degree. The water content of porous medium determines the pore space available to water absorption and gas permeation, and therefore decides the capillary sorptivity and gas permeability together with its pore structure. Before examining the quantitative dependence of capillary sorptivity and gas permeability on water content, it is essential to strictly define the water content or water saturation degree. Cement-based material is so special that it is ambiguous to define its totally saturated and dry states [2], so is its water content and water saturation degree. As a frequently adopted method, the long-established technique of oven-drying to constant weight at elevated temperature is generally appreciated. In regular experimental investigation of mass transport properties, oven-drying at relatively low temperature such as frequently adopted 60 °C is time-consuming due to its tenacious hold on water and very low permeability. Moreover, ambient drying at low relative humidity like that controlled by blue silica gel is also favored [31]. Besides, although the freeze-drying, vacuum-dry and solvent-exchange methods are also recommended when investigating the microstructure of cement-based material [32–34], an efficient drying method

2.2. Modeling relative capillary sorptivity Theoretically, the capillary sorptivity is intimately correlated to hydraulic diffusivity and water permeability as all these three water transport properties can be implemented to quantify the one-dimensional water absorption process into cement-based material [37,38]. Actually, the available theoretical models of capillary sorptivity are mostly deduced from its relationship with hydraulic diffusivity, which could be experimentally determined [2]. Originally, a simple empirical model was proposed by Philip initially for soil materials as [10,14],

Sr (Θ) =

1−Θ

(3)

The above Philip model Eq. (3) clearly indicates that relative sorptivity does not rely on any other physical features of porous medium but only the water saturation degree Θ . 2

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Θ = [1 − βzh + βzh exp(αzh hc )]−1

Moreover, assuming sharp front for water content profile during one-dimensional absorption and widely observed exponential hydraulic diffusivity D (m2/s) with shape parameter n (−),

D (Θ) = D0exp(nΘ)

the corresponding author C. Zhou has proposed unified models for fluid permeability and relative molecular diffusivity [19,37,38,41], from which the relative gas permeability k rg is yielded as,

(4)

the simplified Brutsaert model is also suggested as [15,17]

Sr (Θ) =

1−

1 k rg (Θ) = ⎧1 − Θ ⎡Θ + (1 − Θ) ⎤ ⎫ exp(−nΘ) ⎥⎬ ⎢ ⎨ β zh ⎣ ⎦⎭ ⎩

2n Θ 2n − 1

(5)

(2n − 2nΘ − 1/ θ0) exp (nθ0) − (n − nΘ − 1/ θ0)exp(nθ0 Θ) (2n − 1/ θ0)exp(nθ0) − n + 1/ θ0 (6)

which additionally accounts the volumetric porosity θ0 (−) but in a more complex expression. Based on the assumed exponential expression Eq. (4) for hydraulic diffusivity and its relationship with capillary sorptivity, another approximate Zhou model for relative capillary sorptivity Sr is also yielded in terms of saturation degree Θ and shape parameter n as [19],

Sr (Θ) = (1 − Θ)

τ (n)exp(nΘ) τ [n (1 − Θ)]

3. Experimental scheme 3.1. Materials and specimens In order to minimize the variance of measured capillary sorptivity and gas permeability, two mortars of good homogeneity rather than concrete materials are prepared with two white Portland cements but identical W/C= 0.5 and cement to sand ratio of 1:3 by weight. Since the prominent difference between these two mortars is their cement types, they are denoted as M3 and M4 for that mortar using cement of strength grade 32.5 and 42.5, respectively. In fact, mortars M3 and M4 are exactly the same materials in another low-field Nuclear Magnetic Resonance investigations we have carried out on their permeability to various fluids and water vapor adsorption kinetics [21,22]. For more details about these two white cements and mortars, one may refer to Refs. [21,22]. According to the designed mix proportions, raw materials are mixed and casted into prisms of size 100 mm×100 mm×300 mm. After demoulding at 24 h, all prisms are cured under controlled temperature 20±1 °C and RH>95%. At the age of 8 months, a number of cylinders of diameter 50 mm are drilled out from the center of prisms. Neglecting their ends, 13 disks of 25±2 mm thick are cut from the central part of cylinders for each mortar material. After sealing their curved surfaces with epoxy resin and vacuum saturation by water, they are further submitted to a series of preconditioning and experimental tests, as shown in Fig. 1 and clarified later with details.

(7)

where τ is a simple function with a single variable x [19],

τ (x ) = exp( −0. 1153 − 0. 7341x − 0. 0069x 2)

(8)

These above models, suggested from either empirical testing results or the theoretical relationship between capillary sorptivity and exponential hydraulic diffusivity, are then applied to quantify the dependence of capillary sorptivity on initial water saturation degree. 2.3. Modeling relative gas permeability 2.3.1. Genuchten model The available models of gas permeability for unsaturated cementbased material are also borrowed from that initially proposed for soils and other porous mediums [30,39]. Based on only the water retention characteristics continuously described by the Van Genutchen model (VG2) of two fitting parameters α vg (m−1) and βvg (−),

Θ = [1 + (α vg hc ) βvg]−γ with γ = 1 − 1/ βvg

(9)

the relative gas permeability can be analytically yielded through the Mualem's model [30] as,

k rg (Θ) = (1 − Θ)ξ [1 − Θ1/ γ ]2γ

(12)

Above Eq. (12) explicitly gives the relative gas permeability as a function of fitting coefficient βzh and shape parameter n. Since it mainly comes from the Zhou model [38] and Burdine model [29] together, it will be named as ZB model below. Although these above mentioned models for relative capillary sorptivity and gas permeability have been proposed and validated through some experimental results, their successful applications to cement-based materials are still under question since the pore structure characteristics of fragile cement-based material is absolutely different from that of soils and rocks, and is rather sensitive to water removal during drying preconditioning and water absorption [21,22].

The Brutsaert model Eq. (5) takes the shape parameter n of the concerned porous material into consideration, and thus is expected to have better accuracy. Similarly, another approximate solution from the Parlange model is yielded as [18],

Sr (Θ) =

(11)

3.2. Preconditioning and testing procedures

(10)

From the classical definition of capillary sorptivity [10,42], it should be measured on at least partially dried specimen with uniform water content, so is the measurement of gas permeability. How to fabricate these uniformly and partially dried specimens is a key problem in the quantification and verification of the influence of water content on capillary sorptivity and gas permeability, which are rather sensitive to initial water content and its spatial distribution. In order to accelerate the preparation of specimens with uniform water contents, the drying-equilibrating technique rather than natural water vapor sorption method is generally adopted in experimental investigation of their gas permeability [19,24,28,43,44] and capillary sorptivity [45–48] as well. Elevated temperature is sometimes employed to enhance the water removal and redistribution, but may brings microcracking damage to fragile structure of cement-based material. Moreover, the long or short equilibrating time for water redistribution is usually a priori selected. It is hard to ensure uniform distribution of water since the water transport process and thus the equilibrating time

where h c (m) is the capillary pressure head of unsaturated porous material. The tortuosity factor ξ (−) is found to locate in a wide range [−1, 3] with an average value about 0.5 for soils [30], although it has been reported to significantly vary for cement-based materials [24,40]. The coefficient γ (−) enforcing great influence on the modeled relative gas permeability of cement-based material [25] is proposed to be totally different from that for soils of distinct pore structure characteristics [24,27]. Since the relative gas permeability Eq. (10) is derived from the Van Genutchen model Eq. (9) with two parameters and Mualem model, it is denoted as VGM2 model below. 2.3.2. Zhou model Based on the exponential hydraulic diffusivity Eq. (4), the Burdine model quantifying the link between relative permeabilities to water and gas phases [29], as well as the Zhou model suggested to quantify water retention characteristics of cement-based material [38], 3

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Fig. 1. The overall experimental testing plan of capillary sorptivity and gas permeability at various conditions.

specimen. Through these two rounds of measurements, the gas permeability and capillary sorptivity of each specimen are obtained at both partially dried and constant weight states, which are achieved at gentle ambient temperature. In order to quantify the influence of elevated drying temperature on capillary sorptivity and gas permeability, all mortar specimens are further subjected to oven-drying at moderate temperature 60 °C and then severe 105 °C step by step. After reaching constant weight states, their gas permeability and capillary sorptivity are similarly measured twice. Through Eq. (1), the totally dry state achieved at 105 °C also helps determine the evaporable water saturation degree for each specimen after reaching its equilibrium or other constant weight states at various conditions.

are closely linked to the transport properties of specific cement-based material and temperature. One has to be cautious to choose the drying temperature and equilibrating time span in preparing specimens of uniform water contents. The self-scaled drying-equilibrating procedure having been proposed by the corresponding author C. Zhou is also applied herein to prepare mortar specimens of various uniform water contents [19]. The equilibrating time for water redistribution in any specimen is judged by the drying of a reference one of the same material at the same condition until reaching constant weight. Room temperature is selected to avoid disfavored micro-cracking damage. Firstly, vacuum-saturated mortar specimens are dried in a desiccator at room temperature (18–32 °C), whose RH≈ 0% is controlled by dehydrated CaCl2. Their weights are monitored at regular intervals. If the weight loss of any specimen is found to decrease by about 10 percents of its total water content at vacuum saturation state, it is then sealed by several plastic films and then adhesive alumina foil to stop water loss and allow redistribution. These procedures are repeated until the last one (reference specimen) reaches constant weight (its change in 7 days is less than 0.01 g). At that time, all those enclosed ones are thought to reach equilibrium with different uniform water contents. This gentle ambient drying and selfscaled equilibrating procedure is carefully designed and performed to prepare partially dried mortar specimens with various uniform water contents as good as possible. Generally, it takes more than 8 months. After preparing partially dried mortar specimens of uniform water contents, gas permeability and capillary sorptivity are measured on each mortar specimen in sequence. When the first-round tests of gas permeability and capillary sorptivity are finished, these two reference specimens in the first round are both sealed to allow newly absorbed water to redistribute. Meanwhile, all the other specimens are again dried in the controlled desiccator of RH≈ 0% until they all reaches constant weight. It takes more than 4 months, which is similar to the costs of water vapor sorption tests [22]. Thereafter, the gas permeability and capillary sorptivity are measured again on each disk

3.3. Gas permeability measurement The measurement of gas permeability is carried out through a Cembureau permeameter [49,50]. Under the intrusion of nitrogen gas at inlet pressure Pi (Pa), the gas flow rate for each specimen is monitored at the downstream until steady flow rate Q (m3/s) is recorded at atmospherical pressure Patm (Pa), from which the apparent gas permeability kapp (m2) can be estimated as,

kapp =

Q 2μg LPatm 2 A Pi2 − Patm

(13)

where A (m ) is the sectional area, L (m) is the thickness, and μg (Pa⋅s) is the dynamic viscosity of nitrogen gas. The apparent gas permeability is repeatedly measured at four inlet pressures (0.2–0.4 MPa). Then the intrinsic gas permeability kg (m2) independent on both the inlet pressure and gas type can be obtained through linear fitting to Ref. [51]. 2

2b ⎞ kapp = kg ⎛1 + P + Patm ⎠ i ⎝ ⎜

⎟

(14)

where b (Pa) is a fitting coefficient. Typical measurements of gas

Fig. 2. Typical fitting of gas permeability and capillary sorptivity for typical specimens of high saturation degrees. 4

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permeability for two specimens of high water saturation degrees are shown in Fig. 2a. When talking about the gas permeability, the intrinsic value kg is always implied without special emphasis.

water is then lost.

3.4. Capillary sorptivity measurement

As mentioned before, the water vapor sorption isotherms for mortars M3 and M4 have been measured and reported in Ref. [22]. Furthermore, their capillary pressure head h c (m) could be deduced from equilibrium relative humidity RH (−) through the Kelvin equation [52],

4.2. Water retention characteristics

Capillary sorptivity is very easy to measure through gravimetric method in common laboratory. Each specimen is weighted by an electronic balance to obtain its initial weight of 0.001 g accuracy, which in turn helps determine its initial water saturation degree. Subsequently, it is put in a water tray with only about 3–5 mm immersed in liquid water. At regular intervals of 15 min in the first 2 h and then 30 min in the later 1 h, disk specimen is moved out and quickly wiped with dry towel to remove the free water on its surface. After recording its wet weight at elapsed time t, it is then reset to the water tray to allow successive absorption of water. Generally, this weighting operation is finished in 30 s to eliminate the possible error brought by the temporary interruption of water absorption. The absorbed water volume per unit area Vw (mm) at time t (min) is further calculated, and then the capillary sorptivity S (mm/min0.5) is easily yielded through linear fitting to Ref. [16],

hc = −

in which c (mm) is a fitting coefficient. In the testing period about 3 h, a robust linear relationship between Vw and t is always observed with high correlation coefficient R2 > 0.99. It also support the good effect of uniform water distribution in mortar specimens prepared through the self-scaled drying-equilibrating procedure. Representative measurements of capillary sorptivity for two specimens of high water saturation degree are shown in Fig. 2b. 4. Experimental results 4.1. Porosity and evaporable water content

4.3. Unsaturated capillary sorptivity

From the weight of each specimen at initial vacuum saturation and following constant weight states achieved through various preconditioning procedures, the volumetric porosity θ0 and water saturation degree Θ for mortar M3 and M4 can be easily calculated, as listed in Table 1. One can see that, mortar M3 of lower strength cement reasonably has higher porosity θ0 . When reaching constant weight states through either ambient drying or 60 °C drying technique, the equilibrium water saturation degree Θ for mortar M3 is lower than M4, which is attributed to its more porous microstructure. It is noted that, when reaching constant weight state through ambient drying technique, although the RH inside the desiccator is controlled to be nearly 0%, a small amount of water still resides in the pore space of mortar specimens. According to the water vapor adsorption and desorption isotherms having been reported in Ref. [22], these very low water contents are already below the monolayer coverage of water molecules on the inner surface of mortars, which is consistent with water saturation degree Θ ≈ 0. 2. However, due to the strong physi-chemical bond of C–S–H gel to water molecule, it is too hard to totally remove the bonded surface water from mortars. If we increase the drying temperature to 60 °C, a little more bonded water will be additionally removed. When the drying temperature reaches 105 °C, all evaporable

To investigate the dependence of capillary sorptivity on initial water saturation degree, the gentle self-scaled drying-equilibrating procedure are carefully designed and carried out at ambient condition to prepare mortar specimens of uniform water contents, whose capillary sorptivity and gas permeability can be easily measured together. The experimental capillary sorptivity on mortar specimens of various water contents are shown in Fig. 4a. Due to the impossible task to remove all evaporable water through ambient drying, the actual capillary sorptivity S0 at ideal totally dry state is still unknown, although the nominal capillary sorptivity can be measured on specimens totally dried at 105 °C. To help understand the influence of initial water saturation degree on unsaturated capillary sorptivity, all models summarized in Section 2.2 are also employed to simulate their dependence with a priori assumed shape parameter n and porosity θ0 if needed, as shown in Fig. 4b. Moreover, roughly adopting actual capillary sorptivity S0 = 0.16 mm/ min0.5 and shape parameter n = 6, the unsaturated sorptivity S (Θ) in Eq. (2) with Sr (Θ) predicted from the typical Zhou model Eq. (7) is also shown in Fig. 4a to help analysis these experimental results in comparison to all available models. From Fig. 4, it is very surprised to find that all these models summarized above are obviously incapable to even approximately capture the dependence of capillary sorptivity on water saturation degree over the whole range. In Fig. 4a, the dependence of capillary sorptivity from Zhou model is absolutely and totally different from experimental results. Considering the Zhou model shown in Fig. 4b behaves rather similar to the Philip model and Parlange model, they are also impossible to describe the relationship between capillary sorptivity and initial water saturation. Furthermore, it is easy to judge that the Brutsaert model cannot capture the features of experimental data too. However,

Table 1 Porosity and water saturation at constant weight states after various preconditioning. Mortar

M3 M4

Porosity θ0 (−)

0.229±0.012 0.178±0.002

Evaporable water saturation degree Θ (−) Ambient dry

60 °C dry

105 °C dry

0.115±0.007 0.191±0.015

0.058± 0.003 0.104± 0.005

0 0

(16)

in which R (J/mol/K), T (K) and M (g/mol) is the universe gas constant, absolute temperature and molar mass of water, respectively. The equilibrium water volume fraction w (mL/g) per unit solid mass at various RH s, as reported in the original Fig. 3 in Ref. [22], is herein translated into water saturation degree Θ to give the water vapor sorption isotherms in terms of Θ (RH ) , as shown in Fig. 3a. Thereafter, the water retention characteristics h c (Θ) can be further calculated through Eq. (16) and are shown in Fig. 3b. Since the mortar specimens for capillary sorptivity and gas permeability measurements are prepared from initially water-saturated state through the controlled ambient drying approach, only the desorption isotherms are translated and then nonlinearly fitted through both the VG2 model Eq. (9) and Zhou model Eq. (11). The fitting parameters in Eqs. (9) and (11) are all listed in Table 2. It is noted that the desorption isotherms for both mortars M3 and M4 are selected from the latest ones measured at desorption for 133 days. From Fig. 3b, one can easily see that both the VG2 model Eq. (9) and Zhou model Eq. (11) are of similarly good accuracy to quantify the water retention characteristics of mortars. The obtained coefficients γ, αzh and βzh will be used to simulate the dependence of unsaturated gas permeability on water saturation degree Θ through both the VGM2 model Eq. (10) and ZB model Eq. (12).

(15)

Vw = S t + c

RT ln RH Mw g

5

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Fig. 3. The water vapor desorption isotherms and corresponding water retention curves for mortars M3 and M4.

become negligible and undetectable at Θ > Θcap . The least-square linear fitting gives the Θt and Θcap as 0.501 (0.584) and 0.789 (0.852) for mortar M3 (M4), respectively, as shown in Fig. 4a. The capillary saturation degree Θcap defined from the experimental dependence of capillary sorptivity on initial water saturation degree agrees well with the free water content identified by the low-field nuclear magnetic resonance (NMR) testing [22], and roughly equals to the equilibrium water content at 98% RH. From the multi-exponential fitting to the CPMG relaxation signal from the low-field NMR testing on the vacuum-saturated specimens of the same mortar materials, it was reported in Table 2 of [22] that, the 5th exponentially decayed component for mortar M3 (M4) takes 20.96% (9.55%) of its total water content, which is in good agreement with the free water saturation degree 1 − Θcap = 0. 211 (0.148) defined from the dependence of capillary sorptivity on initial water content, as shown in Fig. 4a. Since the transverse relaxation time T2 (>1.5 s) of the 5th component is rather long, it is definitely free water. The higher Θcap for mortar M3 is obviously attributed its coarser microstructure than mortar M4, which could be seen in their pore size distribution curves already shown in Figs. 1 and 2 of [21]. Besides, Fig. 3a also indicates that the capillary saturation degree is roughly equal to the equilibrium water content at 98% RH. The equilibrium Kelvin diameter of meniscus at 98% RH is a little larger than 100 nm at room temperature, which is of negligible capillarity [53]. In another aspect, the transitional water saturation degree Θt is closely linked to the transitional water allocation between gel pores and interlayer pores. Together with the water vapor desorption isotherms

Table 2 The fitting parameters in VG2 model and Zhou model for mortars M3 and M4. Mortar

VG2 model Eq. (9)

αvg (km M3 M4

1.4481 0.5224

−1

)

Zhou model Eq. (11)

β vg (−)

γ = 1 − 1/ β vg

αzh (km−1)

βzh (−)

1.5566 1.6677

0.3576 0.4004

2.3112E− 5 2.9186E− 5

1.1886E4 6.4272E3

the Brutsaert model gives a threshold of capillary saturation degree Θcap , beyond which the capillary pressure is too low to absorb liquid water through capillarity. It makes good sense since air voids and coarse pores exert little capillary pressure and thus have little ability to absorb liquid water. This feature agrees well with our experimental findings at high water content near saturation. Nevertheless, all available models in literature are invalid in the quantification of the unsaturated capillary sorptivity for mortar specimens prepared under ambient condition. It will be further discussed in Section 5.2 with more details. When looking at the experimental data shown in Fig. 4a, it seems that the capillary sorptivity for mortars M3 and M4 behave in a rather similar bilinear law with respect to water saturation. In addition to the capillary saturation degree Θcap , there is another transitional saturation degree Θt , below which the capillary sorptivity is more sensitive to water saturation degree. In the two ranges of [0, Θt ] and [Θt , Θcap], capillary sorptivity both linearly depends on water saturation degree Θ but with different proportionality. Moreover, their capillary sorptivity

Fig. 4. The dependence of unsaturated capillary sorptivity on water saturation degree. 6

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shown in Fig. 3a, the transitional saturation degree Θt = 0. 501 (0.584) for mortar M3 (M4) roughly equals to its equilibrium water volumetric fraction 0.460 (0.600) at 75% RH, which is also a transitional point from the view of relative water distribution in interlayer pores and gel pores, as clearly indicated by Fig. 8 of [22]. It was reported that, although the water content in interlayer pores continuously increases during water vapor adsorption (see Fig. 7 of [22]), capillary condensation will remarkably occur in gel pores when RH is beyond 75% for mortars M3 and M4 [22]. The Kelvin radius of 3.7 nm in accordance with critical 75% RH agrees well with the equivalent radius 2.82 (2.89) nm for the gel pores of mortar M3 (M4) at initial water saturation state (see Table 2 of [22]). In the case of capillary absorption, it is expected that, when the mortar specimen of water saturation degree Θ > Θt contacts with liquid water, although absorbed liquid water is also redistributed into interlayer pores and makes them expand, its capillary sorptivity is primarily determined by the rate of water absorption into gel pores, inter-hydrates pores and fine capillary pores that are still empty. When regarding to mortar specimen of Θ < Θt , the interlayer pores continuous to collapse along with the decrease of its water content, in turn coarsening its gel pores and inter-hydrates pores that are almost free of water. As a result, the water absorption rate into amplified empty pores gets enhanced by a greater extent. In this sense, the critical equilibrium state at 75% RH brings the transitional dependence of capillary sorptivity at initial water saturation degree Θ = Θt . From these considerations, the transitional water saturation degree Θt is plausibly linked to the critical equilibrium distribution of water in dynamic interlayer pores and gel pores at 75% RH, accounting for the bilinear dependence of capillary sorptivity on water content.

Table 3 The fitting coefficients in the VGM2 and ZB models for unsaturated gas permeability of mortars. Mortar

M3 M4

VGM2 model, Eq. (10)

ZB model, Eq. (12)

kg0 (10−17 m2)

ξ (−)

R2 (−)

kg0 (10−17 m2)

n (−)

R2 (−)

1.6134 1.7883

2.9567 2.2062

0.8991 0.8261

1.8356 2.3152

3.8406 3.3461

0.8984 0.8109

thus treated as undetermined parameter, the experimental data of unsaturated gas pemeability kg for mortars M3 and M4 are both nonlinearly fitted to Eq. (2), in which the relative gas permeability k rg (Θ) is described by either the VGM2 model Eq. (10) or ZB model Eq. (12), as shown in Fig. 5. The regressed actual gas permeability kg0 at ideal Θ = 0 and other fitting coefficients are all listed in Table 3. Through comparing the predicted kg0 with those gas permeability experimentally measured on specimens dried at elevated temperature, the effect of micro-cracking damage induced by drying at elevated temperature could be approximately evaluated. This will be discussed later. From Fig. 5, one can easily see that, both the VGM2 and ZB model could roughly follow the dependence of unsaturated gas permeability on water saturation degree Θ with similar satisfactory accuracy. All unsaturated gas permeability predicted from either VGM2 or ZB model agree well with experimental data, which are measured on mortar M3 (M4) specimens of 0. 141 ≤ Θ ≤ 0. 767 (0. 234 ≤ Θ ≤ 0. 817 ). Within this range, the VGM2 model and ZB model behave rather similarly in predicting the dependence of unsaturated gas permeability on evaporable water content. However, when initial water saturation degree Θ < 0. 14 (0.24) for mortar M3 (M4), the gap between the VGM2 model and ZB model is obvious, and becomes more remarkable when Θ → 0 , as shown in Fig. 5. The ZB model Eq. (12) with shape parameter n > 3 always gives higher gas permeability than the VGM2 model Eq. (10) with tortuosity coefficient ξ < 3. At the ideal totally dry state, the gas permeability kg0 predicted from the ZB model is 13.8% (29.5%) higher than that from the VGM2 model for mortar M3 (M4). From Fig. 3a, the water content Θm ≈ 0. 14 (0.24) for mortar M3 (M4) agrees well with the critical Θm = 0. 14 (0.20) in accordance with monolayer coverage of water molecules at about 25% RH from BET theory [53]. If this monolayer of water is further totally removed, according to the VGM2 model, the gas permeability will significantly increase by 61.3% (78.8%) for M3 (M4), from about 1.0× 10−17 m2 to 1.613× 10−17 (1.788× 10−17 ) m2. This significant increase of gas permeability comes from the noticeable collapse of C–S–H gel after removal of surface water, which will obviously coarsen the pore structure of mortars [21,22].

4.4. Unsaturated gas permeability To avoid the ambiguous influence of elevated temperature on fragile pore structure of cement-based material, the unsaturated gas permeability is measured on specimens with various saturation degrees that are carefully prepared at ambient condition. Since the action of elevated temperature is absent, little micro-cracking damage is incorporated into those mortar specimens, whose gas permeability are only affected by the water saturation degree. The experimental data of their gas permeability kg is shown in Fig. 5 with respect to evaporable water saturation degree Θ . Although gas permeability is recognized to be scattering, it seems that the unsaturated gas permeability for both mortars M3 and M4 obey similar behavior with clear trends. If the actual gas permeability kg0 at ideal totally dry state is unknown and

4.5. Influence of drying temperature Due to the strong water affinity of cement-based material, it is rather tough and time-consuming to totally remove its water content without the action of elevated temperature, which is susceptible to bring micro-cracking damage. Furthermore, it is widely accepted that the almost inevitable cracking damage becomes more severe under more cruel drying condition. Because the gas permeability and capillary sorptivity are both sensitive to micro-cracking damage, the experimental data measured on nominal dry state achieved at elevated temperature are biased and thus denoted as nominal values. Since the nominal gas permeability and capillary sorptvity are generally adopted in laboratory to indicate the transport properties and thus durability performance of cement-based material, it is necessary to understand the influence of drying temperature on them before their applications. With these aims, the nominal gas permeability and capillary sorptivity measured at three constant weight states achieved at different temperatures are averaged on 13 specimens for each mortar and listed in

Fig. 5. The dependence of unsaturated gas permeability kg on water saturation degree Θ. 7

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Table 4 Nominal gas permeability and capillary sorptivity measured at various constant weight states. Mortar

M3 M4

Capillary sorptivity S (mm/min0.5)

Gas permeability kg (× 10−17 m2) Ambient dry

60 °C dry

105 °C dry

Ambient dry

60 °C dry

105 °C dry

1.484± 0.958 1.316± 1.006

2.915±1.220 2.546±2.435

5.715± 1.799 5.518± 0.798

0.117±0.035 0.109±0.032

0.161± 0.042 0.169± 0.033

0.223±0.037 0.236±0.027

one must be also cautious to select the preconditioning method for cement-based material.

Table 4. 4.5.1. Nominal gas permeability Comparing the nominal gas permeability in Table 4 to the predicted actual values in Table 3, one can obviously see that, the gas permeability of mortar M3 (M4) measured at totally dry state is 3.11 (2.38) times of that ideal values kg0 predicted through the ZB models, which gives higher gas permeability than the VGM2 model at Θ = 0 . This remarkable gap must come from the micro-cracking damage induced by the action of high temperature. When drying at moderate temperature 60 °C to constant weight, although Θ = 5. 8% (10.4%) for mortar M3 (M4), the measured nominal gas permeability remains obviously higher than ideal value kg0 predicted from the ZB models by 58.8% (9.9%). Therefore, the influence of elevated temperature on gas permeability is unavoidable even at the widely adopted moderate drying temperature of 60 °C. When comparing the nominal gas permeability of two mortars, it is clearly indicated that, the gas permeability for mortar M4 is always lower than mortar M3 at each constant weight state, but by a rather small extent about 3.6%–14.5%. However, according to the experimental data reported in Table 2 of [21], the water permeability of mortar M3 is about 22 times higher than that of mortar M4. Moreover, if pore water is replaced by isopropanol (IPA), the IPA permeability of mortar M3 is only a little higher than mortar M4 [21]. It seems confusing but plausible since the pore structure of mortars are definitely changed by the water removal due to the collapse of interlayer pores of C–S–H gel [22]. The permeability to either IPA or inert gas for cementbased material is significantly biased by the inevitable alteration of pore structure together with the possible micro-cracking damage after removing pore water especially at elevated temperature. When fluid permeability is applied to indicate the durability performance of cement-based material, one must be cautious to choose the permeating fluid.

5. Discussion 5.1. Invalidity of unsaturated flow theory From the above analysis on the capillary sorptivity measured on unsaturated mortar specimens, it is surprisingly found that none of these available models for unsaturated sorptivity is capable to capture the observed dependence of capillary sorptivity on initial water content. An earlier investigation the corresponding author C. Zhou has carried out on three concretes shows somewhat agreement but fairly rough [19]. Moreover, although good agreements have been reported on several brick materials [15], another experimental investigation on concrete materials of various compositions has revealed apparent disagreement between them [47]. Since these models are strictly derived from the unsaturated flow theory, their disagreement seems pretty unintelligible and implausible. As a matter of fact, the unanticipated failure of these models on cement-based materials is reasonably attributed to its strong sensitivity to water only. It should be kept in mind that, the unsaturated flow theory and theoretical models for capillary sorptivity are originally developed for soils and rocks, whose pore structure are treated to be rigid and unchanged during water removal and regain. However, it is not the case for cement-based material of distinct pore structure sensitive to water. During water vapor adsorption, the adsorbed water molecules will enter the interlayer pores of C–S–H gel with priority, and subsequently makes C–S–H gel expand [22]. During capillary absorption of liquid water, it is thus expected that, the absorbed liquid water will rush into interlayer pores with higher rate than water vapor. This redistribution of absorbed water into interlayer pores has been observed by a single-sided NMR testing [54]. Meanwhile, the expansion of C–S–H gel during capillary absorption will make cement-based material elongate at macroscopic scale, which has been experimentally validated [55]. It is also the physical root responsible to the water permeability of cement-based materials anomalously lower than its permeability to other fluids by several orders of magnitudes [21]. Similarly, the continuous swelling of C–S–H gel will gradually slow down the rate of water absorption, then makes it obviously deviate from the square root of time law, as shown in the reproduced typical deviation in Fig. 6a [12]. Considering the dynamic structure of C–S–H gel and thus cement-based material, it is not surprised to see the disagreement between these available models and experimentally obtained capillary sorptivity at all. As a result, if the strong water sensitivity of C–S–H gel is not taken into account, the unsaturated flow theory is not suitable to quantify the process of capillary absorption into cement-based material any more.

4.5.2. Nominal capillary sorptivity From the experimental data listed in Table 4, it is straightforward to understand the rising of capillary sorptivity with the increase of drying temperature for each mortar, since the water content is reduced and micro-cracking damage is also additionally incorporated. However, when comparing mortars M3 and M4, it is found that their capillary sorptivity are fairly similar at identical constant weight state achieved at 60 °C or 105 °C. Specifically, the averaged capillary sorptivity for mortar M3 of higher water permeability is definitely higher than mortar M4 by 7.3% at ambient dry state. In contrast, when it is tested at constant weight states preconditioned at elevated temperature, the averaged capillary sorptivity for mortar M4 is inversely higher than mortar M3 by about 5%, which may be covered by experimental error. When referring back to Fig. 4a, the capillary sorptivity of mortar M4 does be systematically higher than mortar M3 at any saturation degree Θ . Although mortar M4 has lower permeability to water, IPA as well as inert gas, due to the complicated influence of preconditioning temperature, it is ambiguous to say whose nominal capillary sorptivity is lower. As a consequence, it is tricky to judge the durability performance of cement-based material by only its nominal capillary sorptivity, especially when it is measured on samples having underwent high temperature action. Before testing and applying capillary sorptivity,

5.2. Anomalous water absorption In microscopic scale, capillary absorption is a dynamic process of water filling into the empty pore space of at least partially dried mortar specimens, which depends on its current water content and preconditioning history. After preconditioning to a certain water content, the interlayer pores of mortar specimens will obviously collapse and coarsen the gel pores and inter-hydrates pores [21,22]. Thereafter, the 8

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Fig. 6. Two main anomalous characteristics for the water absorption process of cement-based materials.

and thus swelling of C–S–H gel are promoted at higher temperature. This dependence of C–S–H gel expanding rate on temperature is additionally validated from the ending of initial linear phase of water absorption [13], which occurs earlier at higher operating temperature. From these above considerations, several other confusing characteristics of water absorption into cement-based materials are also physically explained by the specific expansion of C–S–H gel during capillary absorption of only water. Considering the complexity of fundamental water transport in cement-based materials of great sensitive pore structure to water removal and regain, the penetration processes of deleterious gases, ions and water itself are still far away from being totally understood. So is the quantitative modeling of the durability performance for common unsaturated cement-based materials under service.

collapsed interlayer pores of C–S–H gel will continuously absorb liquid water and progressively swell during capillary absorption. This partially recoverable contraction of interlayer pores during drying preconditioning and their remarkable expansion during water absorption make the capillary absorption process far more complicated than other porous medium whose pore structure is almost fixed and insensitive to water removal and regain. Based on the unsaturated flow theory, it is strictly yielded that, if the pore structure of porous medium is inert to the absorbed liquid, its capillary absorption will obey the square root of time law [2], from which the capillary sorptivity is defined with clear physical significance. Regarding to porous cement-based material, it is broadly observed that its absorption of many organic liquids complies with this law very well. However, its capillary absorption of water will remarkably deviate sooner or later [12,13], as shown in Fig. 6a. In our opinion, this anomalous deviation is physically brought by the continuous swelling of C–S–H gel in the wetted part of mortar specimen, whose water permeability will progressively decrease by several orders of magnitudes right after contacting with water. Because the absorbed liquid water has to rush through the wetted zone of decreasing water permeability, remarkable deviation from the square root of time law is therefore expected. During water absorption, the progressive expansion of C–S–H gel that gradually changes the pore structure and water transport properties of cement-based material is the hidden physical principle responsible to the extraordinary deviation from the theoretical square root of time law. Although it still holds for a short duration frequently, the physical meaning of capillary sorptivity of water is already obscured for cement-based materials. The water sensitivity of C–S–H gel and thus cement-based material is also the physical root of several other anomalous transport phenomenons. If the liquid absorption is a transport process driven by purely capillarity, the capillary sorptivity will theoretically scale as σ / η (see Fig. 6b), where σ (N/m) and η (Pa⋅s) is the surface tension and dynamic viscosity of the absorbed liquid, respectively [42]. This scaling does hold for the absorption of many organic liquids but except water [55–57]. During capillary absorption of water, the water permeability of the wetted zone of cement-based material is gradually decreasing and retards the rate of subsequent water absorption. As a consequence, it is conceivable to see the experimental data of normalized capillary sorptivity of water beneath those of inert organic liquids, as shown in Fig. 6b. The observable scattering of experimental data of water absorption in Fig. 6b is ascribed to different expanding rates of C–S–H gel of various compositions, which is also dependent on temperature [55]. Thermodynamically, the rate of water entry into the interlayer pores

6. Concluding remarks The capillary sorptivity and gas permeability of two mature cement mortars are carefully measured at various initial water contents and thoroughly investigated with great emphasis on the water sensitivity of C–S–H gel. Several concluding remarks could be made with regard to the quantitative modeling of mass transport and thus durability performance for cement-based materials.

• The dependence of unsaturated gas permeability on water satura-

• •

9

tion degree could be well quantified through both VGM2 and ZB models. If drying at ambient condition, the tortuosity factor in these two models is rather similar but obviously different from that typical values generally determined on specimens preconditioned at elevated temperature, indicating the elusive sensitivity of pore structure to preconditioning temperature. Because of the remarkable collapse of C–S–H gel and coarsening of pore structure during required preconditioning, the gas permeability and capillary sorptivity are both biased especially for drying at elevated temperature. One must be cautious to apply them to indicate the durability performance of cement-based materials. All available models of unsaturated capillary sorptivity in literature are NOT capable to capture its dependence on initial water content, which could be well captured by a bilinear law with characteristic transitional and capillary saturation degrees. This unexpected disagreement between theoretical models and experimental data of capillary sorptivity measured at ambient condition is ascribed to the dynamic structure of C–S–H gel and thus cement-based material, which are definitely rather sensitive to water removal during drying

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•

preconditioning and water regain in capillary absorption. It makes the physical significance of capillary sorptivity of water obscure for cement-based materials. The strong sensitivity of C–S–H gel specific to water is physically responsible to the reported anomalous characteristics of water absorption in cement-based material. If the strong water sensitivity of C–S–H gel is neglected, the unsaturated flow theory is NOT capable to quantify the water transport in cement-based material any more. Importantly, the modeling of durability performance will face great challenges in dealing with the complex transport of water itself and other deleterious agents in common unsaturated cement-based materials.

[23] [24] [25] [26]

[27]

[28]

[29]

Acknowledgment

[30]

The financial supports from the National Natural Science Foundation of China, China (No. 51578194, 51878602) and the Guangdong Provincial Key Laboratory of Durability for Civil Engineering (No. GDDCE 17-5), Shenzhen Durability Center for Civil Engineering, Shenzhen University for the current research work are gratefully acknowledged.

[31]

[32]

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Appendix A. Supplementary data

[34]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.cemconcomp.2019.103356.

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