Microstructure evolution of leached cement paste: Simulation and experiments

Construction and Building Materials 231 (2020) 117155

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Microstructure evolution of leached cement paste: Simulation and experiments Bofu Chen a, Bin Tian b, Xiaochun Lu b,⇑, Bobo Xiong b a b

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, Jiangsu Province 210098, China College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443000, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


A reactive transport model is

developed to simulate changes in microstructure of leached cementitious composites.
The transport properties of each pore size were quantified to predict the pore size evolution of each pore.
The model is successfully applied to predict the pore size distribution of leached cementitious composites.
The connected pores caused by the increasing threshold pore size accelerate the growth of threshold pore size.

a r t i c l e

i n f o

Article history: Received 9 July 2019 Received in revised form 11 September 2019 Accepted 4 October 2019

Keywords: Cementitious composites Decalcification Porosity Pore size

a b s t r a c t In this paper, a reactive transport model is developed to simulate changes in the microstructure of leached cementitious composites. The model simultaneously takes into account the relation between the real microscopic pore size and macroscopic porosity via MIP and nitrogen adsorption, and the coupling between pore size and the transport properties. Quantitative validation of the model is achieved by comparison of simulation and leaching experiments, and the results show good agreement in terms of both the microscopic pore size distribution and the macroscopic porosity. In addition, SEM analysis and simulations indicates that decalcification may leads to a connection of the adjacent pores, and the increase in the critical pore size is much smaller than the threshold pore size. Some adjacent pores may be connected due to the growing threshold pore size, and the new connected pores will accelerate the growth of the threshold pore size. Besides, leaching induces additional peak on differential pore size distribution curve. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding author at: College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443000, China. E-mail address: [email protected] (X. Lu). https://doi.org/10.1016/j.conbuildmat.2019.117155 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

Calcium leaching, as one of the significant degradation processes, is of concern for the structures used for nuclear waste disposal systems, dams, bridges and water tanks. Cementitious composites in contact with water exhibit calcium concentration

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B. Chen et al. / Construction and Building Materials 231 (2020) 117155

gradients that lead to calcium dissolution and diffusion. Due to the change in chemical balances in cement paste, calcium continues leaching, and leads to an inducing progressive decalcification of cement paste. In general, calcium leaching is a complicated physical and chemical process. Long-term leaching causes modification of the microstructure in cement paste and leads to an increase in porosity, which affects the mechanical properties (compressive strength, tensile strength and shear strength) [1–4] of cementbased materials. The physical and chemical mechanism in the leaching process has attracted attention since the early 20th century. In 1988, the existence of a chemical equilibrium in the leaching process was first proved by Berner, and he noted that the amount of calcium leached was directly related to the calcium concentration in the pore solution [5]. In 1992, Adenot proposed that the local chemical equilibrium between solid and liquid phases is the key for modelling leaching [6], and a degradation front within cement paste in contact water with was characterised. [7]. Faucon proved that calcium was more crucial to determine the local equilibrium than other chemical elements in cement paste [8], and calcium concentration was the main factor in equilibrium. Then, he expounded the physical and chemical mechanism of leaching and found that leaching involves calcium dissolution and diffusion [9]. All these above theories provide possibilities for modelling the leaching process. Fick’s Law has been applied to model the leaching of calcium [10], and its use has been further validated [11]. Although the models [6,9,11–14] proposed previously can adequately predict the amount of calcium leached and the degraded depth at the macro-level, they neglect the modification of the microstructure. Modification of the microstructure has been previously confirmed as an important factor in mechanical and transport properties of cement-based materials [15–18]. With the development of measuring techniques, non-homogeneity of microstructural damage in cement paste [19] was proven via leaching experiments, and Nguyen revealed the relation between mechanical property degradation and microstructural damage [20]. Since quantifying microstructural damage is difficult, porosity has usually been used to describe the modification of the microstructure, and Bernard [4] revealed that local microstructural damage leads to nonhomogeneity of the porosity. A series of studies have been conducted on modification of the microstructure during the leaching process [21–25]. Due to the slow kinetics of natural leaching, accelerated experimental approaches were used in these studies. Although the acceleration factor [21] and the effect of acceleration [22,23] were given for the experiments, the conclusions may be not suitable for deionised water leaching due to some uncertainties (such as kind, temperature sensitivity and chemical attack of accelerator). Moreover, porosity was used as a general description of microstructure [22– 25] in these studies, and the pore size distribution was neglected. Segura made a great contribution to the pore size distribution evolution of leached cement mortar [26] via MIP (mercury intrusion porosimetry), and the pore size of leached cement paste was studied via X-ray nanotomography [27]. Then, modification of the microstructure was confirmed via SEM (scanning electron microscopy), and the results indicated that modification of the pore size was the major factor leading to overall changes in porosity [28]. In 2018, a 3D lattice Boltzmann method based on CEMHYD3D and HYMSOTRUC cement hydration models was proposed to simulate changes in pore size [29]. However, the predicted data were not verified experimentally, and the data were easily impacted by the representation of portlandite in the two hydration models. In summary, the focus of leaching in recent years has transitioned from the degraded depth, the amount of calcium leached and porosity to modification of the microstructure. However, porosity cannot represent the microstructure entirely, thus further research

is needed to reveal the modification of the pore size form cement leaching mechanism. This research primarily focuses on the evolution of inhomogeneous microstructural damage and pore size modification in the leaching process. In this paper, the pore size distribution is fitted in the Weibull form to bridge the relation between microscopic pore size and macroscopic porosity. Based on this relation, a simplified 3D calcium reactive diffusion model is established to simulate the microstructure evolution of cement paste during the leaching process. The model can capture changes in different pore sizes and modification of the pore size distribution in leached zones. The model also takes into account the effects of microstructural damage on the chemical and diffusion kinetics process of calcium leaching. Then, a leaching experiment on cement paste was carried out to verify the model. Besides, SEM and simulation were used to identify the microscopic pore structure evolution in leached cement. 2. Modelling The proposed model is a 3D reactive transport model which aims at simulating changes in the microstructure of leached cement paste in contact with water. This model is based on mass conservation of calcium in liquid–solid system and Fick’s law. The model takes into account the relation between the microscopic pore size distribution and macroscopic porosity evolutions, and the coupling between pore size and the transport properties. The outline of the model is show in Fig. 1. 2.1. Mass conservation and porosity evolution According to conservation of mass and Fick’s law, a simplified representation of the leaching process [11] was given:

@ ½/ðSCa Þ  C Ca ðSCa Þ @SCa ¼ DivfDe ðSCa Þ  Grad½C Ca ðSCa Þg  @t @t

ð1Þ

where / is the porosity of cement paste, C Ca is the concentration of calcium in the pore solution, t is time; De is the effective diffusion coefficient of calcium in the pore solution, and SCa is the calcium concentration in the solid phase. The left-hand side of Eq. (1) represents the changes in calcium in the pore solution. The first terms on the right-hand side represent the diffusion of calcium in the liquid phase, and the second terms represent the dissolution of calcium in the solid phase. The relation between De and porosity at a temperature of 20 °C (Fig. 2) has been confirmed via experiments on ordinary Portland cement with different water cement ratios and porosities [30]. Considering that De cannot exceed the free diffusion coefficient of calcium in pure water (2.2  10–9 m2/s), the empirical formula was given by extrapolation fitting:

De ¼ eð9:95/29:08Þ ; / 2 ð0; 0:6Þ

ð2Þ

Since porosity is directly affected by water cement ratio, the relations between porosity and other parameters were given based on experiments with a series of water cement ratio [11,20] (Fig. 3). As an embryonic model of porosity during leaching progression, Eq. (1) takes into account the dissolution and diffusion of calcium and provides a comprehensive explanation of leaching. Calcium in the solid phase was considered with the piecewise curve in Fig. 3b. However, the porosity was considered as an average using the relation shown in Fig. 3a, and the non-homogeneity of microstructural damage could not be taken into account. Thus, the effect of inhomogeneous microstructural damage on the calcium concentration in the liquid phase should be reconsidered.

B. Chen et al. / Construction and Building Materials 231 (2020) 117155

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Fig. 1. Overall scheme of leaching simulation.

will peel off from the pore wall. Due to the local proportionality of dissolution, the leaching process can be divided into n steps, and the affected section in the leaching process can also be considered a circle (Fig. 4). At the macro-level, the dissolved solid phase in the n-th leaching step can be expressed as ð/n  /n1 Þdxdydz. Based on the mass conservation of calcium in Fig. 4, we have Eq. (3) for the n-th leaching step:

@ð/n  C Can Þ @ ð/n1  C Can1 Þ dxdydz  dxdydz @t @t @ ð/n  /n1 Þ ¼  SCa dxdydz þ DJ n @t

ð3Þ

where /n is the local porosity in the n-th leaching step, /n1 is the local porosity in the (n-1)-th leaching step, similarly C Can and C Can1 are the calcium concentrations in the pore solution in the leaching process, SCa is the calcium concentration in the solid phase, t is time, and DJn is the diffused calcium in the n-th leaching step. Based on Fick’s law, we have:

DJn ¼ Jinflown  Joutflown ¼ Div½De  GradðC Ca Þdxdydz Fig. 2. Relation between De and porosity [30].

At the micro-level, changes in the microscopic pore structure mainly manifest in the modification of the original pore size and lead to a total increase in porosity [28]. To analyse changes in the microstructure, we assume that the pores are evenly distributed and connected. Then, we can select a microscopic element containing one pore channel and consider the cross section of the pore channel as a circle (Fig. 4). With continuing degradation of the gelling property in the solid phase, the stability of the local microstructure with the remaining insoluble ingredients cannot be maintained [31–33]. The effects of the insoluble ingredients on the local equilibrium have been previously proven to be negligible [8]. Therefore, if the calcium around the pore wall is exhausted during the leaching process, the insoluble ingredients

ð4Þ

where Jinflown is the inflow calcium and Joutflown is the outflow calcium for the n-th leaching step. In Eq. (3), the left-hand side represents the changes in calcium in the liquid phase. The first term on the right-hand side corresponds to the calcium in the dissolved solid phase, which enters into the liquid phase, and the second term accounts for the transportation of calcium in the liquid phase. Eq. (3) can be numerically written in the form:

@ð/n  C Can Þ @ ð/0  C Ca0 Þ dxdydz  dxdydz @t @t n X @ ð/n  /0 Þ  SCa dxdydz þ DJ j ¼ @t j¼0

ð5Þ

In Eq. (5), /0 is the initial porosity, and C Ca0 is the initial calcium concentration in the pore solution./0 can be measured experimentally or determined by the following equation [33]:

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Fig. 3. Relations of the main parameters: (a) relation between the porosity and calcium concentration in the solid phase, (b) relation between the calcium concentrations in the pore solution and the solid phase [11,20].

Fig. 4. Microscopic pore structure in the leaching process.

/0 ¼

w=c  0:17a w=c þ 0:32

ð6Þ

where w=c is the water cement ratio, a is the degree of hydration. Because no calcium exists in the pore solution in the initial state, this value can be considered zero, and we have: n X @ ð/n  C Can Þ @ ð/n  /0 Þ DJ j dxdydz ¼  SCa dxdydz þ @t @t j¼0

ð7Þ

In Eq. (7), porosity is a function of the calcium concentration and the diffusion properties of calcium. With Eq. (2) and Eq. (7), the coupling between porosity and the diffusion properties can be properly taken into account. 2.2. Pore size evolution In the complex solid–liquid leaching system, the continuous decalcification caused by calcium diffusion leads to changes in the microstructure of pores. Conversely, the microstructure of pores controls the dissolution reaction area in the solid phase and the diffusion properties in the liquid phase, consequently controlling the degradation evolution. Thus, the microstructure in cement paste is a significant factor in the calcium leaching. In addition to porosity, the pore size distribution is another important

characteristic of the microstructure in cement paste. To model pore size evolution, the initial pore size distribution of cement paste is key factor. The pore structure of cement-based materials is generally measured by MIP (mercury intrusion porosimetry) or nitrogen adsorption, and the pore size distribution can be captured using the volume of intruded mercury at different pressures based on the Kelvin equation [34]. Based on the significant amount of experimental data for the w=c from 0.3 to 0.5 [35], the relation between cumulative porosity and pore size is similar to the cumulative function of the Weibull distribution.

  a  Dp /c ¼ /0 exp  b

ð8Þ

where /c is the cumulative porosity, Dp is the pore diameter in nm,

a is the shape parameter, and b is the scale parameter. The parameters a and b vary with w/c and can be determined by experimental data. The comparison between fitted and experimental data [35] for 28 days (Fig. 5) has been shown to be in good agreement. Then, the porosity with different pore sizes for the initial state can be given by derivate Dp :

    a    a Dp a1 Dp dDp /w0 Dp ¼ /0 exp  b b b

ð9Þ

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According to the spatial geometry relation in Fig. 4, we have the iterative equation of the diameter of an arbitrary pore:

Dpn

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D/n ½Dpðn1Þ  ¼ Dpðn1Þ 1 þ /wðn1Þ ½Dpðn1Þ 

ð12Þ

where Dpðn1Þ is the pore diameter of the ðn  1Þ-th leaching step. With the determined pore diameter Dpn and its corresponding   porosity /n Dpn , we can determine the pore size distribution func  tion /wn Dp of the n-th leaching step. Since the pore size distribution of the initial step is determined with Eq. (9), we can obtain the pore size distribution of an arbitrary leaching step with the iterative Eqs. (11) and (12). 2.3. Chemical and diffusion kinetics

Fig. 5. Comparison between the fitted and experimental data from [35].

Due to the decisive roles of capillary pores in porosity [28] and diffusivity properties [36] in the leached zone, pore sizes ranging from several nanometres to tens of micrometres are taken into account in the model. The De of different pore sizes can be given by substituting Eq. (9) into Eq. (2). Similarly, the pore size evolution of an arbitrary pore can be calculated if we apply Eq. (7) at the micro-level (Fig. 6). For the n-th leaching step, the increase in porosity /n  /n1 is a cumulative value of porosity increases in all pore sizes. Due to the slow kinetics of leaching in pure water, the calcium concentrations of both the solid and liquid phases are in a quasi-steady state in a given instant. Thus, based on Eq. (7), the porosity increase in different   pore sizes (D/n Dp ) mainly depends linearly on the De of different   pore sizes (Fig. 6). Thus, D/n Dp can be divided from the total /n  /n1 by the De of different pore sizes.





D/n Dp ¼ ð/n  /n1 Þ

h  i De /wðn1Þ Dp De ð/n1 Þ

ð10Þ

  where /wðn1Þ Dp is the pore size distribution function of the ðn  1Þ-th leaching step. In addition, we have the porosity of arbitrary pore diameter Dpn of the n-th leaching step.

  /n Dpn ¼ /wðn1Þ ½Dpðn1Þ  þ D/n ½Dpðn1Þ 

ð11Þ

To solve Eq. (7), one of the two unknowns (porosity /n or the calcium concentration in the pore solution C Can ) must be determined. Because the porosity is an implicit function, the only approach to solving Eq. (7) is to identify the calcium concentration in the pore solution. Because the dissolution reaction is much faster than the diffusion process [11], the instantaneous dissolution reaction is determined by the diffusion process. Thus, the changes in calcium in the pore solution caused by chemical kinetics and diffusion kinetics are similar, and the calcium concentration distribution (Fig. 7) in the leached zone is an error function multiplied by a factor. Due to the infinite distance caused by the error function, the calcium concentration distribution from equilibrium concentration (Ceq ¼ 21mol=m3) [5,11] to zero is a piecewise function. In addition, during leaching under the conditions of a natural environment or without renewed water, the calcium concentration in outside water may not always be zero and should be considered. Therefore, we extend the equation to an arbitrary dissolutiondiffusion process from the C eq to a low calcium concentration C CaL in outside water.

C Ca ðl; t Þ ¼

8
CaL

  þ k C eq  C CaL erf

:



2

 l pffiffiffiffiffiffiffiffiffi ffi 0  l < ld Deð/Þt

ð13Þ

C eq ld  l

where l is the distance from the surface to the inner core, ld is the degraded depth, and k is the concentration boundary factor.

"

!#1 ld k ¼ erf pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Deð/Þt

ð14Þ

To solve ld , the Rankine-Hugoniot condition at the interface between the sound zone and the leached zone is determined based on the flux balance of calcium in the complex solid–liquid system.

Fig. 6. Pore size evolution in leaching process.

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poral dimensions. We let Dt be the time for each step of the leaching process, and then we have the growth rate of ld for time t ¼ nDt.

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Deð/n Þ v ðnDtÞ ¼ g nDt

ð18Þ

Since the growth rate of ld is a complex function of the effective diffusion coefficient and time, the real ld is approached with the incremental method.

ld ðtÞ ¼ Fig. 7. The calcium concentration in a porous medium.

@C Ca @l /Deð/Þ ¼ ð1  /ÞSCa @t @l

ð15Þ

ð16Þ

We should note that the porosity / and calcium concentration SCa at the interface are the initial values and can be measured. Since solving g directly is difficult, here, we let the left-hand side of Eq. (16) equal s, and we have s 2 ð0; 0:0063Þ based on the relation in Fig. 3a. Then, the relation in Eq. (16) is treated by numerical approximation (Fig. 8).

g¼

0:0006 þ 0:806s0:5446 ; s 2 ð0; 0:0063Þ 0:8496 þ s0:5446

ð19Þ

Similarly, the lt ðt Þ is transformed as:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi If we let lt ¼ 2 Deð/Þt, g ¼ ld =lt and substitute Eqs. (13) and (14) into Eq. (15), we have:

pffiffiffiffi /C eq g perfðgÞ ¼ expðg2 Þ ð1  /ÞSCa

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi Deð/i Þ gDt i¼0 i Dt

Xn

ð17Þ

Then, the factor k in Eq. (14) can be determined with a certain g; however, the degraded depth cannot be simply considered to be pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ld ¼ 2g Deð/Þt due to the varying effective diffusion coefficient in both the spatial and temporal dimensions. In the spatial dimension, the effective diffusion coefficient is an integrated value of the leached zone (Fig. 7); thus, we can use the average porosity / to determine it. Meanwhile, we let /n be the average porosity of the leached zone for the n-th leaching process, and the effective diffu  sion coefficient can be expressed as De /n in the spatial and tem-

lt ðtÞ ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi Deð/i Þ Dt i¼0 iDt

Xn

ð20Þ

In this complex solid–liquid system, due to the chemical kinetics and diffusion kinetics, the porosity in the leached zone changes throughout the leaching process. With the measured initial porosity and calcium concentration in the solid phase, the key parameter g is determined. Since Eq. (7) can be solved with calcium concentration and the calcium concentration in the leached zone is determined by the degraded depth. Then, we substitute the initial porosity /0 into Eqs. (19) and (7) as the iterative initial step, and we can use the degraded depth and the average porosity /1 of the leached zone for the first step of leaching. Similarly, the degraded depth, the average porosity and the calcium concentration distribution for the n-th step of leaching can be calculated via iteration. Two boundary conditions exist in the leaching process: (i) contact with water and (ii) no contact with water. For an infinite volume of water, the calcium concentration in aqueous solutions is considered constant. The calcium concentration in a finite volume of water can be calculated with Eq. (7) and the volume of water. Thus, the concentration at the boundary contact with water can be expressed as:

ðiÞ

8 <

C CaL ¼ C CaW Infinitewater  Pn  DJ 0 i Finitewater Vw

: C CaL ¼ C CaW þ

ð21Þ

where C CaW is the initial calcium concentration in water, DJi is the amount of calcium leached at the boundary, and V w is the volume of water. For the second boundary of no contact with water, no transportation of calcium occurs, and the boundary can be expressed with the diffusion coefficient De :

ðiiÞ De ¼ 0

ð22Þ

Since the initial porosity /0 can be measured experimentally or determined with Eq. (6), and the calcium concentration in the solid phase is determined by chemical analysis, this model allows prediction of the changes in the microstructure, calcium concentration in the pore solution, degraded depth and leached calcium amount. To verify the exactness and suitability of the model, experiments were performed, and the results are compared to numerical results. 3. Experiments and verification 3.1. Experimental description

Fig. 8. Relation between

s and g.

In this paper, a leaching experiment is performed on cylindrical cement paste samples of 150 mm in height and 175 mm in

B. Chen et al. / Construction and Building Materials 231 (2020) 117155

diameter prepared using ordinary Portland cement with a watercement ratio of 0.4. The samples were removed from moulds after 48 h and stored for 90 days at 20 °C and 100% relative humidity. The samples were leached in 50 L of deionised water at 20 °C for 90 days and 180 days. The top and bottom surfaces were treated with an impermeable material to exclude the influence of asymmetrical water pressure. EDTA titration was used to measure the amount of leached calcium that entered deionised water. Phenolphthalein was used to determine the leached zone and the degraded depth due to the different pH levels between the leached zone and the sound zone (pH value in sound zone is higher than 12.5 due to the saturation calcium concentration in pore solution, and phenolphthalein colour is pink) [26]. Then, several samples were cut at different times, and three offset points along the radial direction at half the height of the samples were sampled to measure the spatial distribution of porosity (Fig. 9). Due to the drawbacks (ink-bottle effect, contact angle effect and pore volume compression effect) of MIP [35], deviation is difficult to be overcome for nanometer pores. Thus, MIP and nitrogen adsorption were combined to measure the porosity and pore size distribution. Especially for the vulnerable leached zone, MIP provides reasonable data for pore diameter larger than 60 nm, and nitrogen adsorption gives better data for the smaller pores [28]. Because porosity and the pore size distribution are difficult to measure along the degraded depth at the millimetre level, the measurements are the average values of each measuring point, and the predicted average values were calculated using the same volume principle. Each measuring point include six measurement samples (three for MIP, three for nitrogen adsorption), the measurement samples were cut from the leached zone by a diamond saw. The samples were cubes, in order to measure the entire leached zone, the sizes of samples were determined by the degraded depth. Since dried samples were required for MIP and nitrogen adsorption, the freeze drying method [35] was applied for all the samples to avoid the micro cracks caused by capillary stress generation if drying passes through the liquid state. A Micromeritics AutoPore V9620 was used for MIP tests, and the minimum detectable pore diameter could be 3 nm (410Mpa), the contact angle was chosen 130°, while the surface tension of mercury 0.485 N/m [26]. For nitrogen adsorption, samples were crushed and sieved to collect the small particles (from 300 lm to 600 lm) for measurements with a Beckman Coulter SA(TM) 3100 Surface Area and Pore Size Analyzer. Although the average porosity and pore size distribution of the leached zone were determined by experiments, these average values cannot completely represent the microstructure evolution of

7

the leached zone. Especially with a long leaching time, spatial differences in the microstructure gradually develop with the growth of the leached zone. Since the leached zone was narrow at 180 days, it is difficult to quantify the microstructure along the degraded depth via FE-SEM (field emission scanning electron microscope) analysis. Thus, FE-SEM analysis was used for qualitative description as a supplement of MIP and nitrogen adsorption analyses and proving the assumption that the growth of porosity is caused by pore size increase. The samples (about 1 mm thick, 3 mm long and 3 mm wide) were peeled at the middle part and the surface in the leached zone for FE-SEM. A JEOL JSM 7500F SEM was used to observe the microstructure, and the highest resolution cloud be 1 nm (15 kV). 3.2. Results 3.2.1. Degraded depth Fig. 10 illustrates the degradation fronts of samples evolved from the surface of the sample towards the centre of sample over time, and the average degraded depth is approximately 3.0 mm at 90 days and 4.5 mm at 180 days. Fig. 11 shows the modelling results of the porosity distribution (global and local) and calcium concentration (global and local) in the pore solution at 90 days and 180 days. The leached zone and degraded depth are clearly determined by the distributions of porosity and the calcium concentration in the pore solution. The porosity is higher in the leached zone than that in the sound zone, and the calcium concentration is lower in the leached zone than that in the sound zone. The modelled degraded depth is calculated to be 3.3 mm at 90 days and 5.0 mm at 180 days. Overall, the predicted degraded depths are very close to the experimental results, although they are slightly greater than the experimental results. 3.2.2. Leached calcium The comparison between the amount of calcium leached as provided by experimental results, and modelling, are shown in Fig. 12. The cumulative leached calcium in Fig. 12 increases, and its growth rate decreases over time. Because the amount of calcium diffused per unit of time is positively correlated with the concentration gradient of calcium, this phenomenon is easily explained by the increasing degraded depth and the decreasing concentration difference between the saturation concentration and the concentration in deionised water. The modelling and experimental results are very close to each other, although the predicted data slightly overestimate the experimental data.

Fig. 9. Samples and points for porosity measurement.

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Fig. 10. Leached samples at different leaching times.

Fig. 11. Predicted data: (a) porosity, (b) the calcium concentration in the pore solution (mol/m3).

3.2.3. Porosity Fig. 13 shows that at the beginning of the leaching process, the average porosities of point a (Fig. 9) and point b (Fig. 9) have some minor variations and then remain constant. This phenomenon demonstrates that at the beginning of the leaching process, the calcium concentration in the pore solution rapidly reaches saturation due to the chemical kinetics; then, the chemical equilibrium inhi-

bits the dissolution of calcium. The average porosity of point c (Fig. 9) increases rapidly at the beginning of leaching. Then, with the growing degraded depth and the increasing calcium concentration in the deionised water caused by leached calcium, the calcium concentration gradient between the pore solution and outside water decreases. Thus, the porosity growth rate at point c gradually decreases over time. The modelling and experimental results

B. Chen et al. / Construction and Building Materials 231 (2020) 117155

9

3.2.4. Pore size distribution The results for average porosity in Fig. 13 indicate that a few changes occur in the microstructures of point a and point b in the sound zone due to the slow kinetics of leaching. Thus, point c was selected to illustrate the modification of the microstructure in the leached zone. The initial relation between pore size and porosity measured by MIP and nitrogen adsorption was fitted according to Eq. (8), a ¼ 1:2269, b ¼ 35:1042 and R2 ¼ 9:8677. Despite the differences between the experimental and predicted pore size distributions of the leached zone, the data shown in Fig. 14 follow the same trend. These differences are probably caused by the fitted initial pore size distribution and the anisotropic pore structure, but they are negligible with the same trend. The pore size in the leached zone grows due to continuous decalcification of the pore wall, and the growth rate slows similarly to the average porosity growth rate in Fig. 13c. In addition, at the initial stage of the leaching process, the pores in the range of 3–100 nm dominate the porosity, but the range extends to approximately 3–180 nm after 180 days. This phenomenon also illustrates that the increase in pore size leads to the growth of porosity in the leached zone. The differences for pore size bigger than 100 nm may be caused by the connection of adjacent pores. Fig. 12. Comparison between experimental and modelled leached calcium amounts.

presented in Fig. 13 are essentially in agreement and reveal the porosity evolution mechanism of cement paste during leaching procession.

3.2.5. SEM analysis The pore structure of unleached and leached cement is clearly observed Fig. 15 (50000 magnification). In Fig. 15a, the unleached cement solid phase is mainly composed of the fibrous or branched fibrous C-S-H and prismatic C–H with relatively unabridged spatial structure. The pores are relatively small and uniformly distributed,

Fig. 13. Comparison between experimental and modelled average porosities: (a) point a, (b) point b, (c) point c.

Fig. 14. Pore size distribution of the leached zone: (a) unleached, (b) after 90 days, (c) after 180 days.

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Fig. 15. SEM images of leached zone: (a) unleached, (b) middle of leached zone at 90 days, (c) surface of leached zone at 90 days, (d) middle of leached zone at 180 days, (e) surface of leached zone at 180 days.

the maximum pore size is about 100 nm. Fig. 15b shows the pores of the middle leached zone at 90 days are bigger than the pores of unleached zone and the maximum pore size exceeds 100 nm. As it shows in Fig. 14 that the pore size range increases during leaching process, when a pore increases to a certain size, it will inevitably lead to a connection of the adjacent pores. Besides, the cumulative porosity of big pores (bigger than 100 nm) grows gradually in leached zone also illustrate that the number of big pores increases. It is reason to believe that the adjacent pores may be connected due to the increasing pore size and dissolving pore wall. As a qualitative supplement, the pores in Fig. 15b are bigger than in Fig. 15a, the roughness of solid phase increases and the pores (red marker) seems to be connected. The surface of the leached zone at 90 days in Fig. 15c indicate that the solid phase structure becomes incom-

plete, pore size increases, and the maximum pore size reaches about 200 nm. The same as it shows in Fig. 15b, the image of middle leached zone at 180 days (Fig. 15d) shows a connection tendency of the adjacent pores, but the pore size is bigger than 90 days. For the surface of leached zone at 180 days (Fig. 15e), the volume of solid phase decreases and the solid structure becomes fragile. The pores grow disorderly and much bigger than 90 days, the maximum pore size exceeds 200 nm. Overall, SEM image at different times shows the consistent trend of pore evolution as the MIP and nitrogen adsorption analyses and supplements the changes in morphology of leached cement paste. In summary, SEM image of leached zone at different times indicate that pore size along the degraded depth is inhomogeneous and leads to an inhomogeneous porosity distribution. Due to the

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chemical and diffusion kinetics, the solid phase of leached zone becomes rough and incomplete. And the dissolved solid phase around pores (pore wall) leads to an increasing pore size, this phenomenon is consistent with the assumption in Section 2.1. Besides, continuous dissolution of solid phase may leads to a connection of the adjacent pores. By comparison, although the simulated degraded depth, cumulative calcium leached and porosity slightly overestimate the experimental data, these differences are negligible. Though, the simulated pore size distribution may be easily impacted by the fitted initial pore size distribution, the pore size evolution can be effectively described by the similar trends of the experimental and simulated data. Besides, SEM analysis supplements the pore size evolution from pore morphology and proves the assumption that the growth of porosity is caused by pore size increase Overall, the model is reasonable and can predict the degraded depth, the cumulative calcium leached and the microstructure evolution.

to an increase in porosity with chemical dissolution. Thus, a positive correlation exists between the absolute value of DJ and the growth rate of porosity. According to Eq. (4), for an instant, the large calcium concentration gradient and the zero-inflow calcium at the degradation front lead to rapid increases in the absolute value of DJ (Fig. 16b). Then, due to the continuity of the diffusion kinetic, the DJ at the degradation front becomes the inflow calcium close to the degradation front, and a peak close to the degradation front emerges. Thus, the growth rate of porosity increases first and then decreases from the degradation front to the surface (Fig. 16a). As the degraded depth grows over time, the calcium concentration gradient decreases, and the peak of the absolute DJ decreases. Thus, the growth rate of porosity at the degradation front decreases over time. In addition, the evolution of the peak of the absolute DJ obeys the same trend of the degraded depth evolution and is a function of the square root of time.

4. Discussion

4.2. Pore size

Since the boundary in the actual project (nuclear waste disposal systems, dams or bridges) is renewed water or infinite water, the model is applied to a renewed water boundary (the calcium concentration in deionised water is constant at zero). The distributions of the main microstructure parameters along the degraded depth (the positive  direction is from the surface to the centre of the leaching sample in the horizontal plane) are calculated to illustrate the effects of leaching on cement paste in the actual project.

To further clarify the microstructure evolution in the leached zone, the critical pore size and the threshold pore size [37] are selected to describe changes in pore size. The critical pore size represents the pore size of the pores present in the greatest amount and is obtained from the peak of the differential pore size distribution curve [37,38]. The threshold pore size is the diameter where mercury begins to enter and percolate the porous media in an appreciable quantity and can be determined from the first inflection point of the cumulative pore size distribution curve [38]. Since the pore size distribution at each leaching step can be given with Eqs. (11) and (12) via iteration, the critical and threshold pore sizes are simulated (Fig. 17). Since porosity is a comprehensive macro characteristic of the volumes of each pore size, the evolutions of the critical and threshold pore sizes (Fig. 17) follow the same increasing trend of porosity (Fig. 16a). The increase in critical pore size (Fig. 17a) is nonsignificant compared to the increase in threshold pore size (Fig. 17b). However, the huge amount of critical pores is still one of the decisive factors in the microstructure and will be discussed in the following section.

4.1. Porosity The spatial distributions of the porosity obtained numerically (Fig. 16a) illustrate that the microstructural damage close to the surface is greater than that close to the centre. The maximum microstructural damage occurs at the surface of the sample, and the growth rate decreases over time. The porosity in the leached zone ranges from 0.21 to 0.31, and the maximum porosity in the leached zone increases by a factor of 1.47 compared to that in the sound zone. In addition, the growth rate of porosity near the degradation front is higher than the growth rate close to the surface and decreases over time. This phenomenon can be easily explained with the model. As proposed in section 2.2, for an instant, the changes in porosity primarily depend on the De , which depends on the increase in calcium DJ. A negative DJ indicates that the calcium outflow is greater than the calcium inflow, which leads

4.3. Pore structure of the surface According to the simulation in Section 4.2, although the inflow calcium from the inside slows the degradation rate close to the

Fig. 16. The spatial distributions at different times: (a) porosity, (b) increases in the calcium concentration.

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Fig. 17. Typical pore sizes along the degraded depth: (a) critical pore size, (b) threshold pore size.

surface over time, the surface cement paste suffers the worst microstructural damage. Considering the important effect of surface cement paste on durability, the pore structure evolution of the surface is simulated (Fig. 18). The porosity at the surface cement grows rapidly at the beginning, and then the growth rate gradually decreases over time (Fig. 18a). Although the growth

rate slows down due to the decreasing absolute value of DJ at the surface cement (Fig. 16b), the porosity continues to increase due to the chemical and diffusion processes. Fig. 18b and c illustrate that the increases in different pore size volumes and the range of pore size, which dominates the porosity, increase over time. Since the critical pore volume increases, it is worth noting

Fig. 18. Pore structure of the surface cement: (a) porosity, (b) cumulative pore size distribution curve, (c) differential pore size distribution curve.

Fig. 19. Typical pore sizes of the surface cement: (a) critical pore size, (b) threshold pore size.

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that leaching induces additional peak on differential pore size distribution curve. The critical and threshold pore sizes increase rapidly at first, and then the growth rates slow down (Fig. 19). Although the two typical pore sizes (Fig. 19) show the same tendency as the porosity (Fig. 18a), their growth rates are considerably different. The critical pore size after 180 days of leaching increases by a factor of 1.1 compared to the initial state. However, the threshold pore size increases by a factor of 2.2 after 180 days of leaching. Since the total increase in porosity is a result of the increase in pore size, this phenomenon is mainly caused by the amount of pores of different pore sizes. A larger amount of pores corresponds to a smaller increase in pore size. Thus, the pore structure evolution depends heavily on the initial pore size distribution. In addition, if the leaching process is sufficiently long, the increasing threshold pore size may lead to a connection of different pore walls and accelerate surface ageing, which may be the reason that the measured threshold pore size is larger than the simulated pore size in Fig. 14b and c. In summary, the larger absolute value of DJ at the degradation front leads to a rapid increase in porosity (Fig. 16a) and drives the degraded depth evolution. Since the evolution of pore size (Fig. 17) shows the same trend as that of porosity, the evolution of macroscopic porosity can represent the evolution of the microstructure to the same extent. However, the volume of the different pore sizes ultimately determines the evolutions of different pore sizes. Since the surface leaches first, the porosity there remains at a maximum over time, and the increasing threshold pore size may connect the adjacent pores and finally lead to ageing of the surface cement paste. Additionally, the trend of the data (Figs. 16a and 18b) are similar to the data predicted via CEMHYD3D (Figs. 8 and 9 in [29]), but this model can be applied to multiscale and long-term leaching.

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The critical and threshold pore sizes along the degraded depth follow the same trend as that of porosity. The critical pore size increases by a factor of 1.1 compared to the initial state, and the threshold pore size increases by a factor of 2.2 compared to the initial state. The critical pore size appears to be insignificant compared to the threshold pore size, but due to the large amount of critical pores, the critical pores are still one of the decisive factors in the microstructure.
The maximum values of the critical and threshold pore sizes occur at the surface of the cement paste and leaching induces additional peak on differential pore size distribution curve. Under a renewed water condition, due to continuous leaching, the growing threshold pore size leads to a connection between pores adjacent to the larger pores. Thus, the measured threshold pore size determined via MIP is slightly greater than the simulated threshold pore size.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements This work was financially supported by the National Natural Science Foundation of China (No. 51879145) and the National Natural Science Foundation of China (No. 51509142).

References 5. Conclusions To model changes in the microstructure of cement paste in the leaching process, a model based on the mass balance and chemicaldiffusion kinetics is presented. The leaching of calcium and the coupling between the transport properties and the microscopic pore structure are considered in a continuum sense based on the chemical mechanisms. Since the relation between pore size and porosity is established, the model allows simulation of the porosity, pore size distribution, and critical and threshold pore sizes in cement paste due to leaching. Verification with leaching experiments shows good agreement in terms of the degraded depth, cumulative leached calcium, porosity and pore size distribution. Our analysis leads to following main conclusions:
Based on the experimental MIP and nitrogen adsorption data, the Weibull model is suitable for describing the initial pore size distribution. The fitted pore size distribution function quantifies the relation between pore size and porosity, and the transport property of different pore sizes is also quantified with the relation and Archie’s law.
The growth rate of porosity close to the degradation front is much larger than that close to the surface, but the porosity close to the surface remains maximal in the leached zone. The porosity along the degraded depth ranges from 0.21 to 0.31 after 180 days of leaching compared to that in the sound zone, the maximum porosity increases by a factor of 1.47.
SEM analysis indicate that increases in porosity is mainly cause by the dissolving pore wall and the porosity and pore size along degraded depth are significant inhomogeneous. Besides, the adjacent pores will connected due to the continuous dissolution of pore walls.

[1] M. Jebli, J. Frédéric, P. Céline, et al., Leaching effect on mechanical properties of cement-aggregate interface, Cem. Concr. Compos. 87 (2018) 10–19, https:// doi.org/10.1016/j.cemconcomp.2017.11.018. [2] M. Jebli, F. Jamin, E. Garcia-Diaz, et al., Influence of leaching on the local mechanical properties of an aggregate-cement paste composite, Cem. Concr. Compos. 73 (2016) 241–250, https://doi.org/10.1016/j. cemconcomp.2016.05.001. [3] C. Carde, Raoul François, Effect of the leaching of calcium hydroxide from cement paste on mechanical and physical properties, Cem. Concr. Res. 27 (4) (1997) 539–550, https://doi.org/10.1016/S0008-8846(97)00042-2. [4] F. Bernard, S. Kamali-Bernard, Performance simulation and quantitative analysis of cement-based materials subjected to leaching, Comput. Mater. Sci. 50 (2010) 218–226, https://doi.org/10.1016/j.commatsci.2010.08.002. [5] U.R. Berner, Modelling the incongruent dissolution of hydrated cement minerals, Radiochim. Acta 44–45 (1988) 387–394. [6] F. Adenot, M. Buil, Modelling of the corrosion of the cement paste by deionized water, Cem. Concr. Res. 22 (1992) 489–496, https://doi.org/10.1016/00088846(92)90092-A. [7] F. Adenot, Durabilite du beton: caracterisation et modelisation des processus physiques et chimiques de degradation du ciment PhD Thesis, Université d’Orléans, 1992. [8] P. Faucon, P. Le Bescop, F. Adenot, P. Bonville, J.F. Jacquinot, F. Pineau, B. Felix, Leaching of cement: study of the surface layer, Cem. Concr. Res. 26 (1996) 1707–1715, https://doi.org/10.1016/S0008-8846(96)00157-3. [9] P. Faucon, F. Adenot, J.F. Jacquinot, J.C. Petit, R. Cabrillac, M. Jorda, Long-term behaviour of cement pastes used for nuclear waste disposal: review of physico-chemical mechanisms of water degradation, Cem. Concr. Res. 28 (1998) 847–857, https://doi.org/10.1016/S0008-8846(98)00053-2. [10] M. Buil, A model of the attack of pure water or under saturated lime solution on cement, Astm Spt. 1123 (1991) 227–241. [11] M. Mainguy, C. Tognazzi, J.-M. Torrenti, F. Adenot, Modelling of leaching in pure cement paste and mortar, Cem. Concr. Res. 30 (2000) 83–90, https://doi. org/10.1016/S0008-8846(99)00208-2. [12] J.-M. Torrenti, M. Mainguy, F. Adenot, C. Tognazzi, Modelling of leaching in concrete, in: R. de Borst, N. Bicanic, H. Mang, G. Meschke (Eds.), Computational Modelling of Concrete Structures, Euro-C 1998 Proceedings, Balkema Publishers, Rotterdam, 1998, pp. 531–538. [13] B. Gerard, G. Pijaudier-Cabot, C. Laborderie, Coupled diffusion-damage modelling and the implications on failure due to strain localisation, Int. J. Solids Struct. 35 (1998) 4107–4120, https://doi.org/10.1016/S0020-7683(97) 00304-1.

14

B. Chen et al. / Construction and Building Materials 231 (2020) 117155

[14] D. Kuhl, F. Bangert, G. Meschke, Coupled chemo-mechanical deterioration of cementitious materials. Part I: modeling, Int. J. Solids Struct. 41 (2004) 15–40, https://doi.org/10.1016/j.ijsolstr.2003.08.005. [15] D.P.H. Hasselman, Relation between effects of porosity on strength and on Young’s modulus of elasticity of polycrystalline materials, J. Am. Ceram. Soc. 46 (1963) 564–565, https://doi.org/10.1111/j.1151-2916.1963.tb14615.x. [16] W. Wilson, L. Sorelli, A. Tagnit-Hamou, Unveiling micro-chemo-mechanical properties of C–(A)–S–H and other phases in blended-cement pastes, Cem. Concr. Res. 107 (2018) 317–336, https://doi.org/10.1016/j. cemconres.2018.02.010. [17] G. Fabien, J.H. Prévost, H. Bruno, Reactive transport modelling of cement paste leaching in brines, Cem. Concr. Res. 111 (2018) 183–196, https://doi.org/ 10.1016/j.cemconres.2018.05.015. [18] J. Arnold, R. Duddu, K. Brown, et al., Influence of multi-species solute transport on modeling of hydrated Portland cement leaching in strong nitrate solutions, Cem. Concr. Res. 100 (2017) 227–244, https://doi.org/10.1016/j. cemconres.2017.06.002. [19] V.H. Nguyen, H. Colina, J.M. Torrenti, C. Boulay, B. Nedjar, Chemo-mechanical coupling behaviour of leached concrete Part I: experimental results, Nucl. Eng. Design. 237 (2007) 2083–2089, https://doi.org/10.1016/j. nucengdes.2007.02.013. [20] V.H. Nguyen, B. Nedjar, J.M. Torrenti, Chemo-mechanical coupling behaviour of leached concrete: part II: modelling, Nucl. Eng. Design. 237 (2007) 2090– 2097, https://doi.org/10.1016/j.nucengdes.2007.02.012. [21] K. Wan, Y. Li, W. Sun, Experimental and modelling research of the accelerated calcium leaching of cement paste in ammonium nitrate solution, Constr. Build. Mater. 40 (2013) 832–846, https://doi.org/10.1016/ j.conbuildmat.2012.11.066. [22] H. Yang, L. Jiang, Y. Zhang, Q. Pu, Y. Xu, Predicting the calcium leaching behavior of cement pastes in aggressive environments, Constr. Build. Mater. 29 (2012) 88–96, https://doi.org/10.1016/j.conbuildmat.2011.10.031. [23] Y. Yu, Y.X. Zhang, Coupling of chemical kinetics and thermodynamics for simulations of leaching of cement paste in ammonium nitrate solution, Cem. Concr. Res. 95 (2017) 95–107, https://doi.org/10.1016/j. cemconres.2017.02.028. [24] Q.T. Phung, N. Maes, D. Jacques, J. Perko, G. De Schutter, G. Ye, Modelling the evolution of microstructure and transport properties of cement pastes under conditions of accelerated leaching, Constr. Build. Mater. 115 (2016) 179–192, https://doi.org/10.1016/j.conbuildmat.2016.04.049. [25] S.C. Seetharam, R.A. Patel, J. Perko, et al., Quantification of leaching kinetics in OPC mortars via a mesoscale model, Construct. Build. Mater. 180 (2018) 614– 628, https://doi.org/10.1016/j.conbuildmat.2018.05.245. [26] I. Segura, M. Molero, S. Aparicio, et al., Decalcification of cement mortars: Characterisation and modelling, Cem. Concr. Compos. 35 (1) (2013) 136–150, https://doi.org/10.1016/j.cemconcomp.2012.08.015.

[27] N. Bossa, P. Chaurand, V. Jérôme, et al., Micro- and nano-X-ray computedtomography: a step forward in the characterization of the pore network of a leached cement paste, Cem. Concr. Res. 67 (2015) 138–147, https://doi.org/ 10.1016/j.cemconres.2014.08.007. [28] Q.T. Phung, N. Maes, D. Jacques, G. De Schutter, G. Ye, Decalcification of cement paste in NH4NO3 solution: microstructural alterations and its influence on the transport properties. In: J. Bastien, N. Rouleau, M. Fiset, M. Thomassin (Eds.), 10th fib International PhD Symposium in Civil Engineering, Proceedings Presented at the 10th Fib International PhD Symposium in Civil Engineering, pp. 179–187. [29] R.A. Patel, J. Perko, D. Jacques, et al., A three-dimensional lattice Boltzmann method based reactive transport model to simulate changes in cement paste microstructure due to calcium leaching, Construct. Build. Mater. 166 (2018) 158–170, https://doi.org/10.1016/j.conbuildmat.2018.01.114. [30] T.D. Larrard, F. Benboudjema, J.B. Colliat, et al., Concrete calcium leaching at variable temperature: experimental data and numerical model inverse identification, Computat. Mater. Sci. 49 (1) (2010) 35–45, https://doi.org/ 10.1016/j.commatsci.2010.04.017. [31] M. Mainguy, O. Coussy, Propagation fronts during calcium leaching and chloride penetration, J. Eng. Mech. 126 (2000) 250–257. [32] M. Mainguy, F.J. Ulm, F.H. Heukamp, Similarity properties of demineralization and degradation of cracked porous materials, Int. J. Solids Struct. 38 (2001) 7079–7100, https://doi.org/10.1016/S0020-7683(00)00417-0. [33] T.C. Hansen, Physical structure of hardened cement paste. A classical, approach, Mater. Struct. 19 (1986) 423–436, https://doi.org/10.1007/ bf02472146. [34] E.P. Barrett, L.G. Joyner, P.P. Halenda, The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms, J. Am. Chem. Soc. 73 (1) (1951) 373–380, https://doi.org/ 10.1021/ja01145a126. [35] H.Y. Ma, Z.J. Li, Realistic pore structure of Portland cement paste: experimental study and numerical simulation, Comput. Concr. 11 (2013) 317–336, https:// doi.org/10.12989/cac.2013.11.4.317. [36] R.A. Patel, J. Perko, D. Jacques, et al., Effective diffusivity of cement pastes from virtual microstructures: Role of gel porosity and capillary pore percolation, Construct. Build. Mater. 165 (2018) 833–845, https://doi.org/10.1016/ j.conbuildmat.2018.01.010. [37] M.R. Nokken, R.D. Hooton, Using pore parameters to estimate permeability or conductivity of concrete, Mater. Struct. 41 (1) (2008) 1–16, https://doi.org/ 10.1617/s11527-006-9212-y. [38] H. Ma, Mercury intrusion porosimetry in concrete technology: tips in measurement, pore structure parameter acquisition and application, J. Porous Mater. 21 (2) (2014) 207–215, https://doi.org/10.1007/s10934-0139765-4.