# Fluid Permeability of Ground Steel Slag-Blended Composites Evaluated by Pore Structure

Authors: Jin Yang; Jian Jiang; Ying Su; Xingyang He; Yingbin Wang; Shun Chen; Hongbo Tan; Sang-Keun Oh
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

The resource utilization of steel slag has attracted wide attention. In the present work, the pore structure of cement paste with and without ground basic oxygen furnace slag (BOFS) up to 180 days was investigated by mercury intrusion porosimetry. Permeability was evaluated from the tested pore structure. Results indicate that the porosity, critical pore radius, pore-throat radius, and permeability are increased with the BOFS content and levels off after 28 days. Lower gel porosity and higher coarse capillary porosity were observed in BOFS-blended composites. The calculated permeability (around 0.30–7.49 × 10−19 m2) based on the pore structure agrees well with the range of reported experimental measurements. Well-correlated linear and power-law relationship was noticed between permeability and porosity and characteristic pore radius, respectively.


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## Body

## 1. Introduction

Steel slag is the by-product discharged from the steelmaking process in a conversion furnace. It accounts for approximately 15–20% by mass of the steel output [1, 2]. It was reported that the annual discharge of steel slag was about 170–250 million tons worldwide [3]. Nearly 80 million tons of steel slag is discharged every year in China [4], with a relatively low comprehensive utilization rate of 30%. The accumulated steel slag not only occupies land but also pollutes the environment. Thus, the resource utilization of steel slag is of great significance.The steel slag mainly includes basic oxygen furnace (BOF) slag, electric arc furnace (EAF) slag, and ladle furnace (LF) slag. In Europe, BOF slag and EAF slag accounted for 46% and 38% of the total steel slag, respectively [3]. In China, the major type of steel slag is also BOF slag and accounts for 70% of the total value. BOF slag is formed in a basic oxygen furnace during the conversion of hot metal from the blast furnace into steel [3]. Nowadays, steel slag has been used as pozzolanic material in cement and concrete [5–8], aggregate or filler in asphalt concrete [9, 10], road base materials [11, 12], and so on.Steel slag, with a chemical composition of SiO2, CaO, Fe2O3, FeO, Al2O3, MgO, MnO, and P2O5, has potential pozzolanic reactivity. Usage of steel slag as supplementary cementitious to replace cement has been proved to be an efficient way. However, special attention should be made about the soundness of steel slag in cement-based materials, due to the late expansion of calcium oxide and magnesium oxide. In recent years, with the improvement of steel slag treatment technology (such as heat treatment and carbonization), the negative effect of free CaO and MgO can be efficiently controlled. Presently, steel slag as supplementary materials used in cement-based materials has been extensively investigated on the hydration characteristics [2, 7, 13], mechanical strength [6, 7, 14, 15], and durability [6, 8, 14]. However, a full study on the pore structure of cement paste with steel slag is still limited. It has been accepted that one of the most important benefits of supplementary materials, for example, steel slag, is the pore structure modification for cement-based materials.It is well known that pore structure has a direct impact on the performance, for example, permeability of cement-based materials. In addition to some external methods (e.g., hydrophobic modification [16]), increasing the complexity of the pore structure can also reduce the permeability of cement-based materials. The understanding for permeability, from the view point of critical pore radius [17, 18], porosity [18, 19], pore connectivity [19], water saturation [20, 21], and tortuosity [22], has caused widespread interest among researchers. The intrinsic permeability is usually measured with water and gas. However, the challenge of measurement with water is that it seems not easy to force a liquid flow through the paste [21]. And the prior drying of gas permeability measurement may take more than one year to get a well-defined saturation [21]. As a result, methods for permeability including equations based on pore structure parameters [17, 18, 23], lattice Boltzmann model [21], numerical approaches [20, 24], beam bending [25], and noncontact impedance measurement [26] have also been investigated. In present, permeability of ordinary Portland cement paste and cement-based materials with fly ash, silica fume, metakaolin, and rice husk ash has been studied extensively. However, limited results can be found on the permeability of cement paste with steel slag [6, 8], especially from the perspective of pore structure. It has been reported that permeability to chloride was increased by steel slag, thus having a negative effect on the durability of cement-based materials [6]. However, the mechanism of the influence of steel slag on permeability needs to be further investigated, for example, from the perspective of pore structure. At the same time, it has been known that steel slag has relative low content of reactive glassy phases. The phase composition of steel slag is somewhat different from other supplementary materials, like fly ash, rice husk ash [27], and ground blast furnace slag, which have relatively high glassy phases and are beneficial for the further pozzolanic reaction and microstructure densification. The long-term benefits for pore structure from pozzolanic reaction of steel slag may be strong enough. Thus, it is very important to study systematically the influence of steel slag on the pore structure and understand the permeability of steel slag blended composites from the viewpoint of pore structure.In this study, fluid permeability of cement paste with and without steel slag was investigated based on the pore structure parameters. Four replacement levels of steel slag were adopted as 10%, 20%, 30%, and 40%, with water to binder ratio of 0.44. The curing period is up to 6 months. The pore structure modification of steel slag on the cement paste was studied with mercury intrusion porosimetry. Experimental results on pore size distribution, pore volume fraction, characteristic pore radius, porosity, and the relationships between pore structure and permeability and compressive strength were discussed.


## 2. Materials and Methods

### 2.1. Materials

A Portland cement CEM I 52.5 N, according to EN 197-1, was used in this study. Its specific density and specific surface are 3.10 g/cm3 and 350 m2/kg, respectively. The steel slag is a ground basic oxygen furnace slag (BOFS) obtained from the Wuhan Iron and Steel Corporation, Wuhan. Its specific density and specific surface are 3.34 g/cm3 and 340 m2/kg, respectively. The chemical compositions of both cement and BOFS obtained by the X-ray fluorescence (XRF) spectrometry are shown in Table 1. The phase composition and particle size distribution of BOFS are shown in Figure 1. The main oxide compositions of BOFS are CaO, FeO, Fe2O3, and SiO2. The amount of free lime, namely, f-CaO, satisfies the requirement (≤3% m%) of the Chinese National Standard GB/T 20491 “Steel slag powder used for cement and concrete.” The f-CaO is mainly derived from the lime that is put into the steelmaking process for the purpose of slagging. The basicity coefficient of BOFS, namely, ω(CaO)/(ω(SiO2) + ω(P2O5)), is 3.73, meeting the requirement (≥1.8) of GB/T 20491. The high basicity coefficient would be beneficial for the reactivity of steel slag [28]. According to Shi and Day [29], the main mineral phases of steel slag in present study (basicity coefficient ≥2.4) contain C3S, C2S, C4AF, C2F, and RO (CaO-FeO-MnO-MgO solid solution) phases, and the reactivity belongs to a high level. However, the steel slag is still regarded as a weak Portland clinker due to its low C3S content.Table 1
Chemical composition and physical properties of cement and BOF slag.
Sample
Chemical composition (%)
Specific density (g/cm3)
Specific surface (m2/kg)
SiO2
Al2O3
Fe2O3FeO
CaO
MgO
SO3
P2O5
MnO
f-CaO
CEM
21.06
6.04
3.63
63.98
2.67
2.25
—
—
—
3.10
350
BOFS
11.22
0.94
22.45
43.13
6.63
—
0.33
0.73
1.86
3.34
340Figure 1
XRD pattern and particle size distribution of BOFS.
(a)
(b)


### 2.2. Mixture Proportion

According to GB/T 51003, the maximum dosage of steel slag in cement and concrete should not exceed 30%. To further investigate a higher content limitation, the maximum dosage of 40% was chosen in the present work. The pure cement (100% cement) was set as a reference mixture to study the effect of steel slag content. Mixtures with different BOFS replacement levels (0%, 10%, 20%, 30%, and 40% by mass) are shown in Table2. The water to binder ratio (w/b) of all mixtures was fixed at 0.44 to prepare concrete with strength grade of C40 (above 40 MPa). All the mixtures were mixed in a standard 5 L mixer for 2 min with a revolution speed of 62 ± 5 r/min and another 2 min with a revolution speed of 126 ± 10 r/min. All the fresh mixtures were cured with temperature and relative humidity of 20°C and RH > 95%, respectively. The compressive strength was tested according to the Chinese national standard GB/T 17671. The loading rate was kept at 2.4 kN/s. At least three valid specimens were tested in parallel, and the deviation was kept within 5%.Table 2
Mixture proportion of BOFS-blended mixtures.
Sample
Cement (%)
BOF slag (%)
w/b ratio
Ref.
100
0
0.44
BOFS1
90
10
0.44
BOFS2
80
20
0.44
BOFS3
70
30
0.44
BOFS4
60
40
0.44


### 2.3. Mercury Intrusion Porosimetry (MIP)

It is well known that mercury intrusion porosimetry is one of the most commonly used techniques for pore structure characterization [18, 30–34]. Another effective pore structure determination method is nitrogen adsorption and desorption (NAD) which is suitable for pore size smaller than 60–100 nm [35, 36].In present study, an Auto Pore 9420 mercury intrusion porosimetry was used to investigate the incremental and cumulative pore size distribution (PSD) of samples from 3 days up to 180 days. The particle size of sample pieces is around 4–5 mm. The obtained sample pieces were immersed in alcohol to stop further hydration. Before testing, some 2 to 3 g of sample was dried in the oven at 50°C for 24 h. The samples were intruded in a low-pressure porosimeter from initial pressure of 1.03 psi up to 30 psi first and then moved in a high-pressure porosimeter with pressure up to 55000 psi. The corresponding pore diameter is from 3.3 nm to 175μm, according to the Washburn equation (equation (1)). The equilibration time in low- and high-pressure stage is 6 seconds. The surface tension of mercury is 0.458 N/m (485 dynes/cm), and the contact angle between the mercury and the pore surface is 130°. Total porosity was directly obtained from the mercury intrusion result. The porosity in pore range below 10 nm, between 10–100 nm, and above 100 nm for cement pastes with BOFS was calculated based on the cumulative pore size distribution:(1)DP=−4γcosθP,where DP is the pore diameter at pressure P, γ stands for the surface tension of mercury, and θ the contact angle between the mercury and the pore surface.


### 2.4. Determining the Characteristic Pore Radius

Two characteristic pore radii, namely, critical pore radius (Lc) and pore-throat radius, at which hydraulic conductance is maximum (Lmax), were investigated in present study. The example of derivative curves for Lc and Lmax is shown in Figure 2. The critical pore radius, Lc, is related to the smallest pore radius of the subset of largest pore which creates a connected path through the sample [37, 38]. The critical pore radius corresponds to the steepest slope (inflection point) of the cumulative PSD or the peak location of the incremental curve and is the most frequently occurring pore size in interconnected pores [39], thus controlling the transport or permeability property of hardened cement matrix. The critical pore radius is linked with the inflection point of pressure (threshold pressure) at which mercury first spans the permeable solid and percolation begins. It was reported in [37] that critical pore radius is linked to the first peak, i.e., the rightmost peak in Figure 2. Thus, the critical pore radius can be determined by the first peak location to characterize the pore entry size of the pore structure connectivity.Figure 2
Example of typical MIP derivative curves forLc and Lmax determination.
(a)
(b)L
max is the pore-throat diameter at which hydraulic conductance is maximum [40, 41], corresponding to the diameter at the highest point in the (V–Vc) D3–D curve, where V is the cumulative intrusion volume at pressure P and Vc is the cumulative intrusion volume corresponding to Lc (Figure 2).


### 2.5. Calculation for Fluid Permeability and Mechanical Strength

Permeability is an important factor concerning the transport property of fluid through a porous solid. The Katz–Thompson equation provides an important contribution in facilitating the fluid permeability of solid materials from mercury intrusion data. It was proved that the calculated results tracked well with experimental results for cement-based materials [17, 23], especially with a relatively high w/c. The equation is derived from percolation theory, and the derived permeability is in unit of millidarcy and has a fundamental unit of area. The related equations are shown as follows [40–42]:(2)SLmax=VLmaxVtot,where S(Lmax) is the fraction of total porosity filled at Lmax; the definition of Lmax can be seen in Section 2.3 and Figure 2; VLmax is the cumulative intrusion volume at Lmax and Vtot is the total intrusion volume:(3)k=189Lmax2LmaxLcϕSLmax,where k (m2) is the absolute permeability and ϕ is the total porosity.


## 2.1. Materials

A Portland cement CEM I 52.5 N, according to EN 197-1, was used in this study. Its specific density and specific surface are 3.10 g/cm3 and 350 m2/kg, respectively. The steel slag is a ground basic oxygen furnace slag (BOFS) obtained from the Wuhan Iron and Steel Corporation, Wuhan. Its specific density and specific surface are 3.34 g/cm3 and 340 m2/kg, respectively. The chemical compositions of both cement and BOFS obtained by the X-ray fluorescence (XRF) spectrometry are shown in Table 1. The phase composition and particle size distribution of BOFS are shown in Figure 1. The main oxide compositions of BOFS are CaO, FeO, Fe2O3, and SiO2. The amount of free lime, namely, f-CaO, satisfies the requirement (≤3% m%) of the Chinese National Standard GB/T 20491 “Steel slag powder used for cement and concrete.” The f-CaO is mainly derived from the lime that is put into the steelmaking process for the purpose of slagging. The basicity coefficient of BOFS, namely, ω(CaO)/(ω(SiO2) + ω(P2O5)), is 3.73, meeting the requirement (≥1.8) of GB/T 20491. The high basicity coefficient would be beneficial for the reactivity of steel slag [28]. According to Shi and Day [29], the main mineral phases of steel slag in present study (basicity coefficient ≥2.4) contain C3S, C2S, C4AF, C2F, and RO (CaO-FeO-MnO-MgO solid solution) phases, and the reactivity belongs to a high level. However, the steel slag is still regarded as a weak Portland clinker due to its low C3S content.Table 1
Chemical composition and physical properties of cement and BOF slag.
Sample
Chemical composition (%)
Specific density (g/cm3)
Specific surface (m2/kg)
SiO2
Al2O3
Fe2O3FeO
CaO
MgO
SO3
P2O5
MnO
f-CaO
CEM
21.06
6.04
3.63
63.98
2.67
2.25
—
—
—
3.10
350
BOFS
11.22
0.94
22.45
43.13
6.63
—
0.33
0.73
1.86
3.34
340Figure 1
XRD pattern and particle size distribution of BOFS.
(a)
(b)


## 2.2. Mixture Proportion

According to GB/T 51003, the maximum dosage of steel slag in cement and concrete should not exceed 30%. To further investigate a higher content limitation, the maximum dosage of 40% was chosen in the present work. The pure cement (100% cement) was set as a reference mixture to study the effect of steel slag content. Mixtures with different BOFS replacement levels (0%, 10%, 20%, 30%, and 40% by mass) are shown in Table2. The water to binder ratio (w/b) of all mixtures was fixed at 0.44 to prepare concrete with strength grade of C40 (above 40 MPa). All the mixtures were mixed in a standard 5 L mixer for 2 min with a revolution speed of 62 ± 5 r/min and another 2 min with a revolution speed of 126 ± 10 r/min. All the fresh mixtures were cured with temperature and relative humidity of 20°C and RH > 95%, respectively. The compressive strength was tested according to the Chinese national standard GB/T 17671. The loading rate was kept at 2.4 kN/s. At least three valid specimens were tested in parallel, and the deviation was kept within 5%.Table 2
Mixture proportion of BOFS-blended mixtures.
Sample
Cement (%)
BOF slag (%)
w/b ratio
Ref.
100
0
0.44
BOFS1
90
10
0.44
BOFS2
80
20
0.44
BOFS3
70
30
0.44
BOFS4
60
40
0.44


## 2.3. Mercury Intrusion Porosimetry (MIP)

It is well known that mercury intrusion porosimetry is one of the most commonly used techniques for pore structure characterization [18, 30–34]. Another effective pore structure determination method is nitrogen adsorption and desorption (NAD) which is suitable for pore size smaller than 60–100 nm [35, 36].In present study, an Auto Pore 9420 mercury intrusion porosimetry was used to investigate the incremental and cumulative pore size distribution (PSD) of samples from 3 days up to 180 days. The particle size of sample pieces is around 4–5 mm. The obtained sample pieces were immersed in alcohol to stop further hydration. Before testing, some 2 to 3 g of sample was dried in the oven at 50°C for 24 h. The samples were intruded in a low-pressure porosimeter from initial pressure of 1.03 psi up to 30 psi first and then moved in a high-pressure porosimeter with pressure up to 55000 psi. The corresponding pore diameter is from 3.3 nm to 175μm, according to the Washburn equation (equation (1)). The equilibration time in low- and high-pressure stage is 6 seconds. The surface tension of mercury is 0.458 N/m (485 dynes/cm), and the contact angle between the mercury and the pore surface is 130°. Total porosity was directly obtained from the mercury intrusion result. The porosity in pore range below 10 nm, between 10–100 nm, and above 100 nm for cement pastes with BOFS was calculated based on the cumulative pore size distribution:(1)DP=−4γcosθP,where DP is the pore diameter at pressure P, γ stands for the surface tension of mercury, and θ the contact angle between the mercury and the pore surface.


## 2.4. Determining the Characteristic Pore Radius

Two characteristic pore radii, namely, critical pore radius (Lc) and pore-throat radius, at which hydraulic conductance is maximum (Lmax), were investigated in present study. The example of derivative curves for Lc and Lmax is shown in Figure 2. The critical pore radius, Lc, is related to the smallest pore radius of the subset of largest pore which creates a connected path through the sample [37, 38]. The critical pore radius corresponds to the steepest slope (inflection point) of the cumulative PSD or the peak location of the incremental curve and is the most frequently occurring pore size in interconnected pores [39], thus controlling the transport or permeability property of hardened cement matrix. The critical pore radius is linked with the inflection point of pressure (threshold pressure) at which mercury first spans the permeable solid and percolation begins. It was reported in [37] that critical pore radius is linked to the first peak, i.e., the rightmost peak in Figure 2. Thus, the critical pore radius can be determined by the first peak location to characterize the pore entry size of the pore structure connectivity.Figure 2
Example of typical MIP derivative curves forLc and Lmax determination.
(a)
(b)L
max is the pore-throat diameter at which hydraulic conductance is maximum [40, 41], corresponding to the diameter at the highest point in the (V–Vc) D3–D curve, where V is the cumulative intrusion volume at pressure P and Vc is the cumulative intrusion volume corresponding to Lc (Figure 2).


## 2.5. Calculation for Fluid Permeability and Mechanical Strength

Permeability is an important factor concerning the transport property of fluid through a porous solid. The Katz–Thompson equation provides an important contribution in facilitating the fluid permeability of solid materials from mercury intrusion data. It was proved that the calculated results tracked well with experimental results for cement-based materials [17, 23], especially with a relatively high w/c. The equation is derived from percolation theory, and the derived permeability is in unit of millidarcy and has a fundamental unit of area. The related equations are shown as follows [40–42]:(2)SLmax=VLmaxVtot,where S(Lmax) is the fraction of total porosity filled at Lmax; the definition of Lmax can be seen in Section 2.3 and Figure 2; VLmax is the cumulative intrusion volume at Lmax and Vtot is the total intrusion volume:(3)k=189Lmax2LmaxLcϕSLmax,where k (m2) is the absolute permeability and ϕ is the total porosity.


## 3. Results and Discussions

### 3.1. Pore Size Distribution (PSD)

The incremental pore size distribution of cement composites containing BOFS at 3, 7, 28, and 180 days is shown in Figure3. The first observation is that the peak distribution range is narrowed and gradually shifted to the left from 3 days to 180 days. The pore size range is about 2 μm at 3 days and ultimately narrows to 50 nm at 180 days. Almost no macro voids are found. The decreased pore size range can be explained by the hydrates filling during the hydration of cement and BOFS. At the same time, the composites blended with high BOFS content (30% and 40%) present clearly larger pore size range, namely coarser capillary pore structure, throughout the curing period.Figure 3
Incremental PSD curves of cement pastes with BOFS at different curing ages.
(a)
(b)
(c)
(d)The second observation is the decreased peak number over-time. The peak number of incremental PSD curves can be identified as 5 at 3 days, 4 at 7 days, and 3 at 28 and 180 days. After 28 days, the distribution peaks originally located between 100 nm and 1000 nm corresponding to coarse capillary pore disappearance; and three peaks corresponding to gel pores and fine capillary pores are left. It is also worth noting that the peak of gel pores (below 10 nm) and fine capillary pores (between 10 and 100 nm) becomes sharper and more pronounced. Similar results were also reported in [33], in which two main peaks for gel pores and fine capillary pores were finally identified in fly ash or calcined coal gangue-blended composites.The cumulative pore size distribution of cement composites containing BOFS from 3 days to 180 days are displayed in Figure4. The decreased pore volume with curing age reflects the progress of clinker hydration and further pozzolanic reaction of BOFS. The total mercury intrusion volume of composites blended with BOFS is found always larger than the reference, regardless of the curing age. Besides, the pore volume of blended composites is increased with the BOFS replacement level. The reference paste always shows the lowest pore volume at each curing age. Similar results were also reported in [8] in which cement pastes blended with 10–30% steel slag showed higher pore volume than plain cement paste at 28 days and 360 days. The increased pore volume by BOFS may be explained by the “dilution” effect of the less reactive supplementary cementitious material which leads to an increase of w/c ratio [43] and larger capillary pores. For samples with BOFS content of 30% and 40%, the real w/c ratio can be as high as 0.63 and 0.73, respectively. The resulted higher pore volume by BOFS is similar to some other solid wastes, such as coal fly ash (FA) [31, 35], calcined coal gangue [33], ground granulated blast-furnace slag (GGBS) [44, 45], waste glass powder [46], construction and demolition waste [47], etc. It is also worth noting that some ultrafine wastes, such as silica fume [48] and ground lithium slag [49], can significantly reduce the total pore volume and densify the microstructure even at early ages.Figure 4
Cumulative PSD curves of cement pastes with BOFS at different curing ages.
(a)
(b)
(c)
(d)The absolute porosity in different pore ranges of BOFS blended composites is shown in Figure5. Porosity in three pore ranges, i.e., below 10 nm, between 10–100 nm, and above 100 nm, for BOFS-blended composites from 3 days to 180 days, is investigated to get more insights into the influence of BOFS on the pore volume distribution. Pores below 10 nm, between 10–100 nm, and above 100 nm correspond roughly to gel pores, fine capillary pores, and large capillary pores, respectively. In terms of porosity for pores below 10 nm (Figure 5(a)), the BOFS-blended composites show generally lower gel porosity, which indicates lower C-S-H gel amount. This is different from the fly ash-blended composites [33] in which the gel pore amount is clearly higher than the reference paste. As for the porosity of pores between 10 and 100 nm, it is interesting to find the opposite trends for BOFS-blended composites at early and late ages (Figure 5(b)). At 3 days, the porosity for 10–100 nm decreases with BOFS content; however, from 28 days to 180 days, the porosity increases with BOFS content. This may be understood from the effect of BOFS at early and late ages. For early ages, the “dilution” effect of BOFS can clearly improve the large capillary porosity (Figure 5(c)) as well as the fine capillary pores (10–100 nm). With the continuous pozzolanic reaction and hydrates filling at late ages, the large capillary pores (above 100 nm) are refined gradually into fine capillary pores (10–100 nm), thus contributing to higher fine capillary porosity with larger BOFS content. This can be supported by the clearly decreased coarse capillary pores with curing ages in Figure 5(c). The increased total porosity with BOFS content (Figure 5(d)) is consistent with the result in Figure 4.Figure 5
Absolute porosity in pore range below 10 nm, between 10–100 nm, and above 100 nm for cement pastes with BOFS.
(a)
(b)
(c)
(d)The relative pore volume fraction of BOFS-blended composites is presented in Table3. For pastes at early ages, especially at 3 days, the dominant pore ranges include fine capillary pores (10–100 nm) and large capillary pores (≥100 nm), regardless of either BOFS content. However, from 7 days to 180 days, the gel pores and fine capillary pores dominate. It seems that the gel pores and coarse capillary pores exhibit the most regular overtime change. The proportion of pore volume lying in gel pore range increases dramatically with hydration time, whilst the coarse capillary pore fraction sharply drops after 7 days and stabilizes at a quite low level (less than 5%) after 180 days. According to [50], pore with radius of 100 nm is regarded as threshold, larger than which a more permeable microstructure would be formed. It was also stated by Mehta and Monteiro [51] that a reduction in the large capillary pores (≥100 nm) will reduce the permeability. As shown in Figure 5(c) and Table 3, the clearly higher absolute porosity and relative pore fraction above 100 nm for BOFS blended composites at 3 days and 7 days indicate more permeable structure. However, it seems that the influence of BOFS content on the pores larger than 100 nm at late ages (after 28 days) is not as important as that at early ages (before 7 days).Table 3
Relative pore volume fraction of BOFS-blended composites.
Sample
Pore volume fraction (%)
≤10 nm
10–100 nm
≥100 nm
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
Ref.
20.0
31.4
65.2
64.2
50.5
57.8
30.8
33.0
29.5
10.8
4.0
2.8
BOFS1
20.0
30.4
52.0
52.9
44.0
59.2
42.0
43.4
36.0
10.3
6.0
3.6
BOFS2
19.5
25.8
45.9
52.4
35.5
56.3
48.7
43.8
45.0
17.8
5.4
3.8
BOFS3
17.9
25.3
40.9
45.2
33.5
43.7
53.9
48.6
48.6
31.1
5.2
6.2
BOFS4
16.4
22.6
35.3
41.2
28.5
38.4
58.4
55.4
55.1
39.1
6.3
3.5


### 3.2. Characteristic Pore Radius

The critical pore radius of BOFS-blended composites according to the first peak location of the PSD curve is shown in Figure6 and Table 4. The critical pore radius increases considerably with BOFS content at early ages but drops sharply from 3 days to 28 days, levels off gradually after 28 days, and stabilizes at a low value (10–30 nm). Similarly, the stabilization in critical pore radius is observed after 28 days by Berodier and Scrivener [32] in case of GGBS content of 40% and w/b of 0.4 and after 90 days by Yu and Ye [37] in case of FA content of 30%–50% and w/b of 0.4-0.5. Obviously, the composites blended with 40% BOFS shows the highest critical pore radius throughout the whole curing period. Reference paste presents the lowest critical pore radius than blended composites, especially before 7 days. Similar result is also reported in [32, 33, 37] for FA-blended and GGBS-blended composites.Figure 6
Critical pore radius of cement pastes with BOFS at different curing ages.Table 4
L
c, Lmax, and permeability of BOFS-blended mixtures.
L
c (nm)
L
max (nm)
Permeability (×10−18 m2)
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
Ref.
100
30
10
10
70
25
6.5
6
5.90
0.94
0.04
0.03
BOFS1
200
60
10
15
150
40
7
10
21.30
1.54
0.06
0.07
BOFS2
500
100
30
15
350
70
20
10
105.26
3.90
0.27
0.08
BOFS3
500
100
30
30
350
70
25
25
138.57
5.44
0.75
0.70
BOFS4
700
350
30
30
600
275
20
20
458.16
60.39
0.52
0.42The pore-throat radius corresponding to the maximum hydraulic conductance,Lmax, is present in Figure 7. The overall change of Lmax with curing time and BOFS content in Figure 7 is very similar to the Lc in Figure 6. The relationship between Lc and Lmax can be observed in Figure 8. The high R2 value indicates the good linear correlation between these two characteristic radiuses. The difference is that the Lmax value in Figure 7 is generally lower than the Lc value in Figure 6 with the same curing period and BOFS content. The difference between Lc and Lmax may be understood from the different physical meanings. The Lc is the pore-throat radius corresponding to the threshold pressure at which mercury first spans the solid [41], whilst Lmax is the pore-throat radius corresponding to the maximum hydraulic conductance which happens later. According to equation (3), both Lc and Lmax are the key parameters determining the fluid permeability of porous medium. The higher Lc and Lmax value of BOFS-blended composites than reference paste indicates more permeable structure. This is well consistent with the porosity for pores larger than 100 nm which is regarded as threshold for more permeable microstructure in Figure 5. The permeability and its relationship with characteristic radius will be discussed in the following sections.Figure 7
L
max of cement pastes with BOFS at different curing ages.Figure 8
Linear relationship betweenLc and Lmax.


### 3.3. Fluid Permeability

Permeability is the inherent ability of a porous medium to transmit a fluid [41]. The permeability of BOFS-blended composites derived from pore structure is plotted in Figure 9. The first observation is the permeability change over time. All the samples with and without BOFS show a similar decreased permeability with curing period, i.e., sharply dropping before 7 days and gradually leveling off after 28 days. The permeability at 180 days is about 3.01–8.16 × 10−20 m2 for Ref. and lower BOFS content (10–20%) and 4.24–7.04 × 10−19 m2 for higher BOFS content (30–40%). With the hydration process of cement clinker [52] and pozzolanic reaction of BOFS, the internal capillary pore space is physically filled with hydration products, thus resulting in a theoretically decreased pore connectivity and permeability (Figures 9(a)–9(e)).Figure 9
Permeability of cement pastes with BOFS.
(a)
(b)
(c)
(d)
(e)
(f)The second important observation is the increased permeability with increasing BOFS content in Figure9(f). The reference paste without BOFS presents the lowest permeability throughout the whole curing period from 3 days to 180 days. Although the further pozzolanic hydrates of BOFS can achieve a good physical filling, the increased capillary porosity by the “dilution” effect at early stage may not be completely eliminated (Figure 5(d)). The permeability of cement paste with BOFS may be understood to some extent from the perspective of hydration product phase. It has been known that the C-S-H gel is a weakly permeable phase with permeability around 7 × 10−23 m2 [53], far below that of hardened cement paste [21]. Thus, the higher gel porosity (≤10 nm) of cement paste with supplementary cementitious material (for example, GGBS [44, 45] and FA [33]) than reference paste at late ages would be helpful for the permeability resistance. However, it is not the case for BOFS-blended composites. The gel porosity as well pore volume fraction of cement paste with BOFS was found generally lower than the reference paste (Table 3 and Figure 5(a)). Moreover, the increased permeability of cement pastes with BOFS may also be revealed by the increased amount of large capillary pore (above 100 nm) which is considered as a threshold radius (Figure 5(c)) as well as the improved characteristic length in Figures 6 and 7, which will be further discussed in the following sections. The increased permeability with BOFS content is consistent with the FA blended composites before 90 days, as reported by Yu et al. [19]. However, the difference is that cement paste blended with FA was found less permeable than the reference paste after 180 days. It was suggested in [19] that the fully reacted hollow FA particles which act as ink-bottle pores can reduce the connectivity of capillary pores.It was reported in [21] that the permeability of cement-based materials can vary widely from 10−22 to 10−16 m2. The comparison for permeability of cement-based materials including the calculated results in present work and the experimental results in previous references after 28 days is shown in Table 5. A first observation is that the calculated permeability of cement paste with BOFS (around 0.30–7.49 × 10−19 m2) is generally close to the measured values [19, 23, 53–55] in case of similar w/b and curing age, especially for the FA-blended composites (0.12–2 × 10−19 m2) [19]. One can also note that the permeability of mortar and concrete samples is clearly larger than the cement paste by 1–3 orders of magnitude. It may be theoretically expected that the introduction of low-permeability aggregates which are lower than those of cement paste should give lower permeability for mortar and concrete. However, in practice, this does not happen. This is more related to the microdefects which are larger than most capillary pores present in the interfacial transition zone around the aggregate, as stated by Mehta and Monteiro [51]. The observations in Table 5 suggest that the calculated permeability derived from the MIP results in present work agrees well with the range of experimental permeability measurements.Table 5
Permeability for cement-based materials.
Sample
Permeability (10−19 m2)
Method
Source
Paste (w/c = 0.35, water curing, 28 d)
0.89
Measured
[54]
Paste (w/b = 0.4, 0–50% FA, sealed curing, 28 d–180 d)
0.12–1.86
Measured
[19]
Paste (w/c = 0.4–0.6, sealed curing, 28 d)
0.09–18.6
Measured
[55]
Paste (w/b = 0.44, 0–40% BOFS, RH > 95% curing, 28 d–180 d)
0.30–7.49
Calculated
This study
Paste (w/c = 0.45, degree of hydration 67%)
0.95
Measured/calculated
[53]/[24]
Paste (w/c = 0.47, lime water curing, 28 d)
∼7.15
Measured
[23]
Paste (w/b = 0.5, 30% FA, sealed curing, 28 d–180 d)
∼0.8–2
Measured
[19]
Mortar (w/c = 0.55, water curing, 28 d)
85.3
Measured
[56]
Mortar (w/c = 0.38–0.53, water curing, 28 d)
∼100–200
Measured
[57]
Concrete (w/c = 0.4–0.6, RH > 90% curing, 28 d)
0.76–42.2
Measured
[58]
Concrete (w/c = 0.5, water curing, 28 d–120 d)
118.8–149.6
Measured
[59]
Note. The permeability with unit of m/s in some literature is converted to m2, divided by 9.79 × 106 m−1s−1.


### 3.4. Link of Mechanical Strength with Pore Structure

The measured compressive strength of all the samples from 3 days up to 180 days can be seen in Table6. Generally, at early age, especially before 28 days, all the mixtures blended with BOFS showed a decreased compressive strength. And, the higher BOFS content the lower early strength, due to the relatively lower pozzolanic reactivity than cement. This is similar to some other supplementary materials, such as low-calcium fly ash [33, 60]. Figure 10 presents the relationship between compressive strength (in Table 6) and pore structure for BOFS-blended composites. It was found that compressive strength of BOFS blended composites is linearly related to porosity (Figure 10(a)), which means that the compressive strength decreases linearly with the pore amount. This corresponds very well with the findings in the previous work [33] concerning coal fly ash-blended cement-based composites. It was also reported by Röβler and Odler [61] that the strength-porosity relationship can be most accurately expressed with the linear plot. In addition, a power function relationship exists between compressive strength and characteristic pore radius (Lc and Lmax), as shown in Figures 10(b) and 10(c). The compressive strength of BOFS-blended composites reduced with the increase of characteristic pore radius in terms of power function. It was also interesting to find that the compressive strength decreased sharply and then leveled off after the characteristic pore radius is larger than 100 nm. This suggests that the radius of 100 nm may be regarded as threshold for compressive strength. Within the 100 nm range, the reduction in pore size is more conducive to improve the compressive strength of the cement matrix.Table 6
Compressive strength of BOFS-blended mixtures (MPa).
Sample
3 d
7 d
28 d
180 d
Ref.
35.8
45.4
54.4
57.6
BOFS1
33.3
43.2
54.4
63.6
BOFS2
29.6
42.7
50.0
60.0
BOFS3
23.4
38.1
47.1
58.8
BOFS4
18.1
32.1
44.1
57.9Figure 10
Correlation between compressive strength and pore structure.
(a)
(b)
(c)


### 3.5. Link of Permeability to Porosity and Characteristic Pore Radius

It is well known that the transport property of cement-based material is primarily determined by the pore structure. The relationship between permeability and porosity for BOFS blended composites is shown in Figure11. The permeability of cement paste with and without BOFS is linearly related to the porosity with R2 value of 0.933. As an example, the permeability increases from 3.01 × 10−20 to 4.58 × 10−16 m2 when the porosity increases from 20.81% to 44.95%. It can be generally seen that sample with higher porosity would be more permeable. This is in agreement with the findings in [18, 19, 55, 62]. In addition to porosity, permeability also depends on tortuosity, pore size distribution, characteristic pore radius, pore connectivity [18, 19], etc. In the present work, link of permeability with characteristic pore radius is more interestingly investigated, which will be discussed in the following part.Figure 11
Correlation between permeability and porosity.The relationship between permeability and characteristic pore radius for BOFS-blended composites is displayed in Figure12. It can be seen that the permeability of samples increases with increasing characteristic pore radius. A well-correlated power-law relationship between permeability and characteristic pore radius can be observed with R2 values of 0.991 and 0.997 for Lc and Lmax, respectively. The permeability can be presented by a power-law function of Lc with a best-fitting exponent of 3.72 in Figure 12(a), which is in excellent agreement with the results reported previously by Nyame and Illston [63] (exponent of 3.28) and Halamickova et al. [17] (exponent of 3.35). In addition, the exponent of power-law function between permeability and characteristic length, Lmax, is found as 2.47 in present study (Figure 12(b)), not so different from the reported power value, i.e., 2, in [64].Figure 12
Correlation between characteristic pore radius and permeability.
(a)
(b)It is also worth noting that the permeability corresponding to characteristic radius lower than around 100 nm stays at a relatively low level (Figure12). When the characteristic radius is greater than 100 nm, the permeability shows a significant increase. Thus, the characteristic radius at this value (100 nm) would be the permeability threshold for BOFS-blended composites. This agrees well with the suggestion in [50, 51] in which the radius of 100 nm is regarded as threshold for permeable structure.The minimum capillary permeability of cement paste, according to Powers [65], is around 2.6 × 10−21 to 2.6 × 10−22 m2, below which the capillary pores would be depercolated [55]. The permeability of cement pastes with BOFS reaches minimally 7.53 × 10−20 m2 in Figure 12, which is higher than the threshold value reported by Powers [65]. This indicates that no depercolation of capillary pores occurs in the present work. The result that no depercolation of capillary pores occurred for cement paste with w/c of 0.4 was also reported by Ye [55].


## 3.1. Pore Size Distribution (PSD)

The incremental pore size distribution of cement composites containing BOFS at 3, 7, 28, and 180 days is shown in Figure3. The first observation is that the peak distribution range is narrowed and gradually shifted to the left from 3 days to 180 days. The pore size range is about 2 μm at 3 days and ultimately narrows to 50 nm at 180 days. Almost no macro voids are found. The decreased pore size range can be explained by the hydrates filling during the hydration of cement and BOFS. At the same time, the composites blended with high BOFS content (30% and 40%) present clearly larger pore size range, namely coarser capillary pore structure, throughout the curing period.Figure 3
Incremental PSD curves of cement pastes with BOFS at different curing ages.
(a)
(b)
(c)
(d)The second observation is the decreased peak number over-time. The peak number of incremental PSD curves can be identified as 5 at 3 days, 4 at 7 days, and 3 at 28 and 180 days. After 28 days, the distribution peaks originally located between 100 nm and 1000 nm corresponding to coarse capillary pore disappearance; and three peaks corresponding to gel pores and fine capillary pores are left. It is also worth noting that the peak of gel pores (below 10 nm) and fine capillary pores (between 10 and 100 nm) becomes sharper and more pronounced. Similar results were also reported in [33], in which two main peaks for gel pores and fine capillary pores were finally identified in fly ash or calcined coal gangue-blended composites.The cumulative pore size distribution of cement composites containing BOFS from 3 days to 180 days are displayed in Figure4. The decreased pore volume with curing age reflects the progress of clinker hydration and further pozzolanic reaction of BOFS. The total mercury intrusion volume of composites blended with BOFS is found always larger than the reference, regardless of the curing age. Besides, the pore volume of blended composites is increased with the BOFS replacement level. The reference paste always shows the lowest pore volume at each curing age. Similar results were also reported in [8] in which cement pastes blended with 10–30% steel slag showed higher pore volume than plain cement paste at 28 days and 360 days. The increased pore volume by BOFS may be explained by the “dilution” effect of the less reactive supplementary cementitious material which leads to an increase of w/c ratio [43] and larger capillary pores. For samples with BOFS content of 30% and 40%, the real w/c ratio can be as high as 0.63 and 0.73, respectively. The resulted higher pore volume by BOFS is similar to some other solid wastes, such as coal fly ash (FA) [31, 35], calcined coal gangue [33], ground granulated blast-furnace slag (GGBS) [44, 45], waste glass powder [46], construction and demolition waste [47], etc. It is also worth noting that some ultrafine wastes, such as silica fume [48] and ground lithium slag [49], can significantly reduce the total pore volume and densify the microstructure even at early ages.Figure 4
Cumulative PSD curves of cement pastes with BOFS at different curing ages.
(a)
(b)
(c)
(d)The absolute porosity in different pore ranges of BOFS blended composites is shown in Figure5. Porosity in three pore ranges, i.e., below 10 nm, between 10–100 nm, and above 100 nm, for BOFS-blended composites from 3 days to 180 days, is investigated to get more insights into the influence of BOFS on the pore volume distribution. Pores below 10 nm, between 10–100 nm, and above 100 nm correspond roughly to gel pores, fine capillary pores, and large capillary pores, respectively. In terms of porosity for pores below 10 nm (Figure 5(a)), the BOFS-blended composites show generally lower gel porosity, which indicates lower C-S-H gel amount. This is different from the fly ash-blended composites [33] in which the gel pore amount is clearly higher than the reference paste. As for the porosity of pores between 10 and 100 nm, it is interesting to find the opposite trends for BOFS-blended composites at early and late ages (Figure 5(b)). At 3 days, the porosity for 10–100 nm decreases with BOFS content; however, from 28 days to 180 days, the porosity increases with BOFS content. This may be understood from the effect of BOFS at early and late ages. For early ages, the “dilution” effect of BOFS can clearly improve the large capillary porosity (Figure 5(c)) as well as the fine capillary pores (10–100 nm). With the continuous pozzolanic reaction and hydrates filling at late ages, the large capillary pores (above 100 nm) are refined gradually into fine capillary pores (10–100 nm), thus contributing to higher fine capillary porosity with larger BOFS content. This can be supported by the clearly decreased coarse capillary pores with curing ages in Figure 5(c). The increased total porosity with BOFS content (Figure 5(d)) is consistent with the result in Figure 4.Figure 5
Absolute porosity in pore range below 10 nm, between 10–100 nm, and above 100 nm for cement pastes with BOFS.
(a)
(b)
(c)
(d)The relative pore volume fraction of BOFS-blended composites is presented in Table3. For pastes at early ages, especially at 3 days, the dominant pore ranges include fine capillary pores (10–100 nm) and large capillary pores (≥100 nm), regardless of either BOFS content. However, from 7 days to 180 days, the gel pores and fine capillary pores dominate. It seems that the gel pores and coarse capillary pores exhibit the most regular overtime change. The proportion of pore volume lying in gel pore range increases dramatically with hydration time, whilst the coarse capillary pore fraction sharply drops after 7 days and stabilizes at a quite low level (less than 5%) after 180 days. According to [50], pore with radius of 100 nm is regarded as threshold, larger than which a more permeable microstructure would be formed. It was also stated by Mehta and Monteiro [51] that a reduction in the large capillary pores (≥100 nm) will reduce the permeability. As shown in Figure 5(c) and Table 3, the clearly higher absolute porosity and relative pore fraction above 100 nm for BOFS blended composites at 3 days and 7 days indicate more permeable structure. However, it seems that the influence of BOFS content on the pores larger than 100 nm at late ages (after 28 days) is not as important as that at early ages (before 7 days).Table 3
Relative pore volume fraction of BOFS-blended composites.
Sample
Pore volume fraction (%)
≤10 nm
10–100 nm
≥100 nm
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
Ref.
20.0
31.4
65.2
64.2
50.5
57.8
30.8
33.0
29.5
10.8
4.0
2.8
BOFS1
20.0
30.4
52.0
52.9
44.0
59.2
42.0
43.4
36.0
10.3
6.0
3.6
BOFS2
19.5
25.8
45.9
52.4
35.5
56.3
48.7
43.8
45.0
17.8
5.4
3.8
BOFS3
17.9
25.3
40.9
45.2
33.5
43.7
53.9
48.6
48.6
31.1
5.2
6.2
BOFS4
16.4
22.6
35.3
41.2
28.5
38.4
58.4
55.4
55.1
39.1
6.3
3.5


## 3.2. Characteristic Pore Radius

The critical pore radius of BOFS-blended composites according to the first peak location of the PSD curve is shown in Figure6 and Table 4. The critical pore radius increases considerably with BOFS content at early ages but drops sharply from 3 days to 28 days, levels off gradually after 28 days, and stabilizes at a low value (10–30 nm). Similarly, the stabilization in critical pore radius is observed after 28 days by Berodier and Scrivener [32] in case of GGBS content of 40% and w/b of 0.4 and after 90 days by Yu and Ye [37] in case of FA content of 30%–50% and w/b of 0.4-0.5. Obviously, the composites blended with 40% BOFS shows the highest critical pore radius throughout the whole curing period. Reference paste presents the lowest critical pore radius than blended composites, especially before 7 days. Similar result is also reported in [32, 33, 37] for FA-blended and GGBS-blended composites.Figure 6
Critical pore radius of cement pastes with BOFS at different curing ages.Table 4
L
c, Lmax, and permeability of BOFS-blended mixtures.
L
c (nm)
L
max (nm)
Permeability (×10−18 m2)
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
3 d
7 d
28 d
180 d
Ref.
100
30
10
10
70
25
6.5
6
5.90
0.94
0.04
0.03
BOFS1
200
60
10
15
150
40
7
10
21.30
1.54
0.06
0.07
BOFS2
500
100
30
15
350
70
20
10
105.26
3.90
0.27
0.08
BOFS3
500
100
30
30
350
70
25
25
138.57
5.44
0.75
0.70
BOFS4
700
350
30
30
600
275
20
20
458.16
60.39
0.52
0.42The pore-throat radius corresponding to the maximum hydraulic conductance,Lmax, is present in Figure 7. The overall change of Lmax with curing time and BOFS content in Figure 7 is very similar to the Lc in Figure 6. The relationship between Lc and Lmax can be observed in Figure 8. The high R2 value indicates the good linear correlation between these two characteristic radiuses. The difference is that the Lmax value in Figure 7 is generally lower than the Lc value in Figure 6 with the same curing period and BOFS content. The difference between Lc and Lmax may be understood from the different physical meanings. The Lc is the pore-throat radius corresponding to the threshold pressure at which mercury first spans the solid [41], whilst Lmax is the pore-throat radius corresponding to the maximum hydraulic conductance which happens later. According to equation (3), both Lc and Lmax are the key parameters determining the fluid permeability of porous medium. The higher Lc and Lmax value of BOFS-blended composites than reference paste indicates more permeable structure. This is well consistent with the porosity for pores larger than 100 nm which is regarded as threshold for more permeable microstructure in Figure 5. The permeability and its relationship with characteristic radius will be discussed in the following sections.Figure 7
L
max of cement pastes with BOFS at different curing ages.Figure 8
Linear relationship betweenLc and Lmax.


## 3.3. Fluid Permeability

Permeability is the inherent ability of a porous medium to transmit a fluid [41]. The permeability of BOFS-blended composites derived from pore structure is plotted in Figure 9. The first observation is the permeability change over time. All the samples with and without BOFS show a similar decreased permeability with curing period, i.e., sharply dropping before 7 days and gradually leveling off after 28 days. The permeability at 180 days is about 3.01–8.16 × 10−20 m2 for Ref. and lower BOFS content (10–20%) and 4.24–7.04 × 10−19 m2 for higher BOFS content (30–40%). With the hydration process of cement clinker [52] and pozzolanic reaction of BOFS, the internal capillary pore space is physically filled with hydration products, thus resulting in a theoretically decreased pore connectivity and permeability (Figures 9(a)–9(e)).Figure 9
Permeability of cement pastes with BOFS.
(a)
(b)
(c)
(d)
(e)
(f)The second important observation is the increased permeability with increasing BOFS content in Figure9(f). The reference paste without BOFS presents the lowest permeability throughout the whole curing period from 3 days to 180 days. Although the further pozzolanic hydrates of BOFS can achieve a good physical filling, the increased capillary porosity by the “dilution” effect at early stage may not be completely eliminated (Figure 5(d)). The permeability of cement paste with BOFS may be understood to some extent from the perspective of hydration product phase. It has been known that the C-S-H gel is a weakly permeable phase with permeability around 7 × 10−23 m2 [53], far below that of hardened cement paste [21]. Thus, the higher gel porosity (≤10 nm) of cement paste with supplementary cementitious material (for example, GGBS [44, 45] and FA [33]) than reference paste at late ages would be helpful for the permeability resistance. However, it is not the case for BOFS-blended composites. The gel porosity as well pore volume fraction of cement paste with BOFS was found generally lower than the reference paste (Table 3 and Figure 5(a)). Moreover, the increased permeability of cement pastes with BOFS may also be revealed by the increased amount of large capillary pore (above 100 nm) which is considered as a threshold radius (Figure 5(c)) as well as the improved characteristic length in Figures 6 and 7, which will be further discussed in the following sections. The increased permeability with BOFS content is consistent with the FA blended composites before 90 days, as reported by Yu et al. [19]. However, the difference is that cement paste blended with FA was found less permeable than the reference paste after 180 days. It was suggested in [19] that the fully reacted hollow FA particles which act as ink-bottle pores can reduce the connectivity of capillary pores.It was reported in [21] that the permeability of cement-based materials can vary widely from 10−22 to 10−16 m2. The comparison for permeability of cement-based materials including the calculated results in present work and the experimental results in previous references after 28 days is shown in Table 5. A first observation is that the calculated permeability of cement paste with BOFS (around 0.30–7.49 × 10−19 m2) is generally close to the measured values [19, 23, 53–55] in case of similar w/b and curing age, especially for the FA-blended composites (0.12–2 × 10−19 m2) [19]. One can also note that the permeability of mortar and concrete samples is clearly larger than the cement paste by 1–3 orders of magnitude. It may be theoretically expected that the introduction of low-permeability aggregates which are lower than those of cement paste should give lower permeability for mortar and concrete. However, in practice, this does not happen. This is more related to the microdefects which are larger than most capillary pores present in the interfacial transition zone around the aggregate, as stated by Mehta and Monteiro [51]. The observations in Table 5 suggest that the calculated permeability derived from the MIP results in present work agrees well with the range of experimental permeability measurements.Table 5
Permeability for cement-based materials.
Sample
Permeability (10−19 m2)
Method
Source
Paste (w/c = 0.35, water curing, 28 d)
0.89
Measured
[54]
Paste (w/b = 0.4, 0–50% FA, sealed curing, 28 d–180 d)
0.12–1.86
Measured
[19]
Paste (w/c = 0.4–0.6, sealed curing, 28 d)
0.09–18.6
Measured
[55]
Paste (w/b = 0.44, 0–40% BOFS, RH > 95% curing, 28 d–180 d)
0.30–7.49
Calculated
This study
Paste (w/c = 0.45, degree of hydration 67%)
0.95
Measured/calculated
[53]/[24]
Paste (w/c = 0.47, lime water curing, 28 d)
∼7.15
Measured
[23]
Paste (w/b = 0.5, 30% FA, sealed curing, 28 d–180 d)
∼0.8–2
Measured
[19]
Mortar (w/c = 0.55, water curing, 28 d)
85.3
Measured
[56]
Mortar (w/c = 0.38–0.53, water curing, 28 d)
∼100–200
Measured
[57]
Concrete (w/c = 0.4–0.6, RH > 90% curing, 28 d)
0.76–42.2
Measured
[58]
Concrete (w/c = 0.5, water curing, 28 d–120 d)
118.8–149.6
Measured
[59]
Note. The permeability with unit of m/s in some literature is converted to m2, divided by 9.79 × 106 m−1s−1.


## 3.4. Link of Mechanical Strength with Pore Structure

The measured compressive strength of all the samples from 3 days up to 180 days can be seen in Table6. Generally, at early age, especially before 28 days, all the mixtures blended with BOFS showed a decreased compressive strength. And, the higher BOFS content the lower early strength, due to the relatively lower pozzolanic reactivity than cement. This is similar to some other supplementary materials, such as low-calcium fly ash [33, 60]. Figure 10 presents the relationship between compressive strength (in Table 6) and pore structure for BOFS-blended composites. It was found that compressive strength of BOFS blended composites is linearly related to porosity (Figure 10(a)), which means that the compressive strength decreases linearly with the pore amount. This corresponds very well with the findings in the previous work [33] concerning coal fly ash-blended cement-based composites. It was also reported by Röβler and Odler [61] that the strength-porosity relationship can be most accurately expressed with the linear plot. In addition, a power function relationship exists between compressive strength and characteristic pore radius (Lc and Lmax), as shown in Figures 10(b) and 10(c). The compressive strength of BOFS-blended composites reduced with the increase of characteristic pore radius in terms of power function. It was also interesting to find that the compressive strength decreased sharply and then leveled off after the characteristic pore radius is larger than 100 nm. This suggests that the radius of 100 nm may be regarded as threshold for compressive strength. Within the 100 nm range, the reduction in pore size is more conducive to improve the compressive strength of the cement matrix.Table 6
Compressive strength of BOFS-blended mixtures (MPa).
Sample
3 d
7 d
28 d
180 d
Ref.
35.8
45.4
54.4
57.6
BOFS1
33.3
43.2
54.4
63.6
BOFS2
29.6
42.7
50.0
60.0
BOFS3
23.4
38.1
47.1
58.8
BOFS4
18.1
32.1
44.1
57.9Figure 10
Correlation between compressive strength and pore structure.
(a)
(b)
(c)


## 3.5. Link of Permeability to Porosity and Characteristic Pore Radius

It is well known that the transport property of cement-based material is primarily determined by the pore structure. The relationship between permeability and porosity for BOFS blended composites is shown in Figure11. The permeability of cement paste with and without BOFS is linearly related to the porosity with R2 value of 0.933. As an example, the permeability increases from 3.01 × 10−20 to 4.58 × 10−16 m2 when the porosity increases from 20.81% to 44.95%. It can be generally seen that sample with higher porosity would be more permeable. This is in agreement with the findings in [18, 19, 55, 62]. In addition to porosity, permeability also depends on tortuosity, pore size distribution, characteristic pore radius, pore connectivity [18, 19], etc. In the present work, link of permeability with characteristic pore radius is more interestingly investigated, which will be discussed in the following part.Figure 11
Correlation between permeability and porosity.The relationship between permeability and characteristic pore radius for BOFS-blended composites is displayed in Figure12. It can be seen that the permeability of samples increases with increasing characteristic pore radius. A well-correlated power-law relationship between permeability and characteristic pore radius can be observed with R2 values of 0.991 and 0.997 for Lc and Lmax, respectively. The permeability can be presented by a power-law function of Lc with a best-fitting exponent of 3.72 in Figure 12(a), which is in excellent agreement with the results reported previously by Nyame and Illston [63] (exponent of 3.28) and Halamickova et al. [17] (exponent of 3.35). In addition, the exponent of power-law function between permeability and characteristic length, Lmax, is found as 2.47 in present study (Figure 12(b)), not so different from the reported power value, i.e., 2, in [64].Figure 12
Correlation between characteristic pore radius and permeability.
(a)
(b)It is also worth noting that the permeability corresponding to characteristic radius lower than around 100 nm stays at a relatively low level (Figure12). When the characteristic radius is greater than 100 nm, the permeability shows a significant increase. Thus, the characteristic radius at this value (100 nm) would be the permeability threshold for BOFS-blended composites. This agrees well with the suggestion in [50, 51] in which the radius of 100 nm is regarded as threshold for permeable structure.The minimum capillary permeability of cement paste, according to Powers [65], is around 2.6 × 10−21 to 2.6 × 10−22 m2, below which the capillary pores would be depercolated [55]. The permeability of cement pastes with BOFS reaches minimally 7.53 × 10−20 m2 in Figure 12, which is higher than the threshold value reported by Powers [65]. This indicates that no depercolation of capillary pores occurs in the present work. The result that no depercolation of capillary pores occurred for cement paste with w/c of 0.4 was also reported by Ye [55].


## 4. Conclusions

(1)
The BOFS-blended composites show generally lower gel porosity and higher coarse capillary porosity (above 100 nm). The coarse capillary pore fraction sharply drops after 7 days and stabilizes at a quite low level (less than 5%) after 180 days.
(2)
Both the critical pore radius and pore-throat radius increase considerably with BOFS content at early ages but drops sharply from 3 days to 28 days. A good linear correlation was observed between these two characteristic radii.
(3)
The compressive strength of BOFS-blended composites decreases linearly with porosity. A power function relationship exists between compressive strength and characteristic pore radius, in which compressive strength decreased sharply when the characteristic pore radius is below 100 nm.
(4)
The permeability is increased with increasing BOFS content, regardless of the curing age. The calculated permeability based on MIP pore parameters is around 0.30–7.49 × 10−19 m2, which agrees well with the range of reported experimental measurements.
(5)
The permeability of BOFS-blended composites was found linearly related to the porosity. A well correlated power-law relationship between permeability and characteristic pore radius was observed. The characteristic radius of 100 nm presented a permeability threshold characteristic, above which the permeability showed a significant increase.
(6)
Future research concerning the relationships between permeability, pore structure connectivity, and complexity may be considered.



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*Source: 6254835-2020-02-10.xml*