- Email: [email protected]
An effective transport model of sulfate attack in concrete
Construction and Building Materials 216 (2019) 365–378
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An effective transport model of sulfate attack in concrete Hongguang Min, Lili Sui, Feng Xing, Hao Tian, Yingwu Zhou ⇑ Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil Engineering, Shenzhen University, 3688 Nanhai Avenue, Shenzhen 518060, PR China
h i g h l i g h t s New model captures sulfate ions distributions at different sulfate attack ages. A study of effective diffusivity and its effect on sulfate transport model is presented. An effective transport model of sulfate attack in concrete is presented.
a r t i c l e
i n f o
Article history: Received 12 December 2018 Received in revised form 12 April 2019 Accepted 25 April 2019 Available online 9 May 2019 Keywords: Concrete Sulfate attack Sulfate ions distribution Effective diffusivity Sulfate transport model
a b s t r a c t This paper presents both an experimental and theoretical investigation of the consumed and accumulated rates of sulfate ions in concrete. The authors analyze the effects of sulfate solution concentration and the water-cement ratio on the sulfate ions distribution. Based on the diffusion theory, a sulfate transport model for concrete was established considering the effect of surface sulfate concentration. On this basis, an effective transport model of sulfate attack is presented, which relies on effective diffusivity. This model can be applied to predict the sulfate ions distribution; moreover, its predicted values are in good agreement with the experimental ones. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction When concrete structures are in a sulfate environment, external sulfate ions will enter the concrete, which generates a diffusion of sulfate ions in concrete, better known as an external sulfate attack [1,2]. Two causes of this attack are: 1) sulfate ions diffuse from a high concentration to a low concentration in concrete pores and 2) sulfate ions react with the hydration products of cement [3]. Being different from the sulfuric acid corrosion for concrete [4], the concrete sulfate attack is caused by the cracking and spalling of concrete due to the expansion of the sulfate attack products, resulting in a concrete strength loss [5–7]. Sulfate ions from outside environment will attach the concrete through two patterns: diffusion and chemical reaction [3]. Many theoretical analyses and numerical simulations have been published on the relationship between the distribution of sulfate ions or sulfate attack products as well as the effects of expansion stress and strain on concrete [8–14]. However, it is still difficult to quantify the sulfate attack product and its interaction in concrete [15].
⇑ Corresponding author. E-mail addresses: [email protected] (F. Xing), [email protected] (Y. Zhou). https://doi.org/10.1016/j.conbuildmat.2019.04.218 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
This paper considers the close relationship between the consumption of sulfate ions and the concentration of sulfate ions in concrete, which have revealed a variance in the concentration of sulfate ions with time in concrete [9]. Notably, the effective diffusivity of sulfate ions in concrete is an important parameter when determining the distribution of sulfate ions in concrete. Previous study shows that the water-cement ratio has significant effects on the porosity of concrete [16], which in turn affects the transport process of sulfate ions in concrete. In fact, the transport characteristics of sulfate ions in concrete can determine their distribution. These sulfate ions can also reflect the distribution pattern of concrete sulfate attack products, which is the underlying reason for this study on the distribution characteristics of expansion stress in concrete. The lower the water-cement ratio is, the higher the concrete density and the more difficult it becomes for external sulfate ions to penetrate the concrete [17,18]. The low water-cement ratio also explains the slow rate in gypsum and ettringite formations. So, the effect of the water-cement ratio on the diffusion of sulfate ions is very significant. The existing models often fail to analyze the diffusion and consumption processes of sulfate ions in concrete and do not always consider the change of surface sulfate concentration [19–21]. Significantly, the transport process of sulfate ions in concrete is time-dependent [22]; moreover, the
366
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
surface sulfate concentration is not equal to sulfate solution concentration. Instead, this surface sulfate concentration is dependent on the water-cement ratio and sulfate solution concentration. Therefore, the establishment of effective transport model of sulfate attack in concrete is essential, which can help protect concrete sulfate attack. In this research by controlling the sulfate solution concentration and water-cement ratio, the distribution of sulfate ions in concrete was investigated through the following sulfate attack test for concrete. First, the transport process of sulfate ions in concrete was clarified under different conditions of sulfate attack. The diffusion theory made the sulfate transport model possible considering the surface sulfate concentration, the effective diffusivity as well as the first-order chemical reaction rate. And all conclusions were verified by experiments. Finally, the time-dependent regularities of effective diffusivity and surface sulfate concentration were obtained with different water-cement ratios and sulfate solution concentrations. At the same time, the authors also did a thorough study on the effective diffusivity of concrete subjected to sulfate attack. 2. Experimental program 2.1. Specimen design and preparation Three groups of 100 mm 100 mm 100 mm concrete specimens were cast, and the water-cement ratio was 0.57 for 21 specimens, 0.40 for seven specimens and 0.29 for seven specimens, respectively, which were used to study the effect of the watercement ratio on sulfate attack for concrete. The maximum particle size of granite stones was 31.5 mm, which was used as the coarse aggregate. The fine aggregate was medium grade sand with good gradation and tap water as well as Portland cement #425 for casting concrete. The chemical composition of Portland cement #425 and the mix proportions of the concrete specimens are given in Tables 1 and 2, respectively. All prism specimens were placed in a curing room for 28 days where the temperature and relative humidity were 20 ± 2 °C and 95%, respectively.
Fig. 1. Sulfate attack test for concrete: (a) concrete specimen covered with paraffin, and (b) test layout.
2.3. Determination method of sulfate ions content This paper aims to test the sulfate transport from the surface to the inside concrete. Then, the distributions of sulfate ions at different depths in concrete were determined using core samples and slices of concrete specimens as shown in Fig. 2(a) with attack ages of 30 d, 60 d, 90 d, 120 d, 180 d, 240 d, and 300 d. The sampling depths were 1 mm, 3.5 mm, 6.5 mm, 10.5 mm, 15.5 mm, 20.5 mm, and 25.5 mm, in that order, and the corresponding slice thicknesses were 2 mm, 3 mm, 3 mm, 5 mm, 5 mm, 5 mm, and 5 mm, respectively. In the test, a precision cutting machine was used to cut the concrete slices. The thickness of the cutting blade was 0.4 mm, and the error was only about 0.1 mm as shown in Fig. 2(b). The concrete slices were first naturally dried and then mashed in a stainless steel mortar as shown in Fig. 3(a), afterwards, the larger particles, i.e., the coarse aggregates were picked out using a tweezer, and the rest were then ground repeatedly until all the particles could pass through a sieve with a diameter of 0.08 mm, as shown in Fig. 3(b) and (c).
2.2. Sulfate attack test for concrete To reflect the one-dimensional sulfate attack, two lateral surfaces of concrete specimens were tested, and the other four surfaces, including the pouring surface, were sealed with paraffin, as shown in Fig. 1(a). The solution concentrations of sodium sulfate were 1%, 5%, and 10%, respectively. To keep the solution concentration stable, the pool was covered with a plastic film to prevent volatilization during the test, as shown in Fig. 1(b), and the solution was replaced every two weeks. Afterwards, a sulfate attack test for concrete was carried out in a constant temperature room at 28 °C.
Fig. 2. Making concrete slices: (a) concrete core samples, and (b) precision cutting machine.
Table 1 Chemical composition of cement. Chemical composition
SiO2
Al2O3
Fe2O3
CaO
MgO
K2O
Na2O
SO3
f-CaO
Loss of ignition
Content (%)
21.10
5.21
4.18
65.65
1.07
0.58
0.13
1. 02
0.94
0.43
Table 2 Mix proportions of concrete specimen. Water-cement ratio
Cement (kgm3)
Water (kgm3)
Sand ratio (%)
Fine aggregate (kgm3)
Coarse aggregate (kgm3)
Water reducer (% by weight of cement)
0.57 0.40 0.29
195 195 167
342 488 577
36 30 28
670 515 482
1193 1200 1241
0 0 2.2
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
367
Fig. 3. Preparation of concrete powder: (a) mashing concrete slices in a stainless steel mortar, (b) preparing the concrete powder, and (c) sealing the concrete powder.
The sulfate ions content in each layer of the three core samples’ concrete powder was determined by chemical analysis based on ASTM C114-15 [23]. First, the weighed concrete powder was dissolved using hydrochloric acid; then, barium chloride was added to the solution to obtain barium sulfate precipitation. The detailed measurement process is shown in Fig. 4. The average value of the three measurements was taken as the sulfate ions content of the layer; however, the measured data was invalid when the maximum and minimum values all exceeded 10% of the median value. The percentage of sulfate ions content in concrete expressed in sulfur trioxide (SO3) can thus be calculated as [23]:
C SO3 ¼
0:343 ðmt mc Þ 100% mp
ð1Þ
where C SO3 is the percentage of sulfur trioxide content (%); 0.343 is the conversion coefficient of the relative molecular mass between barium sulfate (BaSO4) and sulfur trioxide; mp is the mass of concrete powder (kg), as shown in Fig. 4(a); mc is the mass of crucible (kg), and mt is the total mass of barium sulfate and crucible (kg), as shown in Fig. 4(g).
The challenge of quantifying the sulfate ion taking part in the chemical reaction was met by considering the sulfate attack product of ettringite. When ettringite is dissolved, it often releases sulfate ions into the solution as shown in Fig. 4(d). When this happens, Eq. (1) can be used to measure the part of sulfate ions that chemically react with concrete. To confirm whether the ettringite was dissolved and released as sulfate ions, a subsequent additional test was designed and conducted. 2.4. Additional tests to confirm the dissolution of ettringite Two samples (A and B) with different attack ages were selected for the additional test. An environmental scanning electron microscope (ESEM) test was first used to confirm the existence of ettringite in these samples as shown in Fig. 5. The two samples were ground into two concrete powders and each powder was then equally divided into four parts so as to increase the test sample. Two parts of each concrete powder were dissolved in hydrochloric acid. Filter residues left on the filter paper were identified as A-1, A-2, B-1 and B-2 for samples A and B, respectively. Each sample was poured through a filter to the fill line of their individual cru-
Fig. 4. Measurement processes of sulfate ions content in concrete: (a) weighing the concrete powder, (b) dissolving the concrete powder using hydrochloric acid, (c) filtering using qualitative filter paper, (d) adding the barium chloride, (e) barium sulfate precipitation, (f) filtering using quantitative filter paper, (g) high temperature burning, (h) barium sulfate crystal, (i) cooling to room temperature, and (j) weighing barium sulfate.
368
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Ettringite
Ettringite
(a)
(b)
Fig. 5. SEM images of concrete slices at different sulfate attack stages: (a) concrete slice A and (b) concrete slice B.
Fig. 6. Filter residue: (a) before drying, and (b) after drying.
cible and dried in a constant temperature box at 40 °C for 48 h, as shown in Fig. 6. The alternation of the ettringite in the concrete powder after dissolution was tested by X-ray diffraction (XRD). For comparison, the other two parts of concrete powders A and B without hydrochloric acid treatment were also put into the constant temperature box as control groups and tested by XRD. The results are shown in Figs. 7 and 8 where the chemical compositions of the two filtered residues and two untreated concrete powders (the control group of concrete powder) of samples A and B were all analyzed by XRD. 3. Test results and discussions 3.1. Results of additional tests Fig. 5 gives the test result of ESEM and shows that several acicular ettringite crystals were observed. Figs. 7 and 8 give the test result of XRD and show that the amount of ettringite hardly changed after dissolved in hydrochloric acid, indicating that hydrochloric acid cannot dissolve the ettringite. However, calcium silicate hydrate (C-S-H), gypsum and calcium hydroxide (Ca(OH)2) were dissolved by hydrochloric acid as they cannot be detected in the filter residue. Moreover, because silica dioxide is the main component of sand, the diffraction peak is obvious. Consequently, it was confirmed that only acid-soluble sulfate ions were measured in the test.
0.92% with water-cement ratios of 0.57, 0.40 and 0.29, respectively. The distributions of sulfate ions in concrete with different attack ages are shown in Figs. 9 and 10. Figs. 9 and 10 show that the overall trends of sulfate ions distributions in concrete with different solution concentrations and the water-cement ratios are similar, that is, the closer to the concrete surface, the greater the sulfate ions content, and the sulfate ions content in the first layer (1 mm) is significantly higher than that in the second layer (3.5 mm), showing a sudden drop phenomenon. This sudden drop is a result of the sulfate ions in solution reacting with the hydration products in the concrete pores, causing several sulfate ions to be consumed. Moreover, as the surface concrete is attacked by sulfate ions, gypsum and ettringite are formed with a lower solubility. In this case, the sulfate ions penetrate the surface concrete with increased attack age, thereby promoting the development and deposition of expansion products, which will block the ion transport channels and hinder the further transport of sulfate ions into the concrete. Although surface concrete maintains a high concentration of sulfate ions for a long time, the combination of sulfate ions can also reduce the concentration of sulfate ions inside the concrete. The reduction in sulfate ions slows down the penetration speed and decreases the attack depth of the remaining sulfate ions. In concrete, the surface layer of 0.1 mm is the grout layer, which does not contain any aggregate. The next layer is the mortar layer which has a depth of 0.1–5 mm, which is either free of coarse aggregate or contains only a small amount of coarse aggregate; the concrete layer lies 5 mm under the grout and mortar layers [24]. As a result of bleeding, the water-cement ratio and porosity of the surface layer are larger than that of the internal concrete, which also holds true for the mortar layer. After a certain depth, the water-cement ratio and porosity tend to be constant, and the pore connectivity of the grout layer and the mortar layer are higher than that of the concrete layer. Therefore, the diffusivity within 5 mm of the surface concrete is larger than that of the internal concrete. As the distance from the concrete surface increases, the water-cement ratio gradually approaches that of the internal concrete. Also, the introduction of aggregate makes the ion transport path tortuous, which also reduces the diffusion performance of concrete to a certain extent. 3.3. Time-dependent regularity of surface sulfate concentration in concrete
3.2. Distribution of sulfate ions According to Section 2.3, the percentages of initial sulfate ions content in concrete without sulfate attack were 0.76%, 0.81% and
Fig. 11 shows the time-dependent rules of surface sulfate concentration and the concentration at a depth of 1 mm below the concrete surface as well as their differential concentration. Clearly,
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
369
Fig. 7. Measurement results of concrete powder A: (a) concrete powder A-1, (b) filter residue A-1, (c) concrete powder A-2, and (d) filter residue A-2.
the reaction products generated on the concrete surface are not enough to have a significant effect on the micro-structure of concrete at the initial stage of the sulfate attack. Thus, the concentration difference between surface sulfate concentration and that of sulfate at a depth of 1 mm is small. With the continuous generation of reaction products, the concrete becomes denser, which hinders the transport of external sulfate ions into the concrete, so the concentration difference between surface sulfate concentration and that of 1 mm below the surface concrete increases with sulfate attack age. Therefore, the concentration difference between surface sulfate concentration and that of 1 mm below the concrete surface gradually increases with time. Fig. 12 further shows the effects of the concentration of sodium sulfate (Na2SO4) solution and the water-cement ratio on the timedependent rules of surface sulfate concentration. It can be concluded that the larger the sulfate solution concentration and water-cement ratio are, the more obvious the difference in concentration becomes. 4. Effective transport model of sulfate attack in concrete 4.1. Establishment process of the sulfate transport model There are two forms of sulfate ions in concrete: One is the chemically bound sulfate ions by concrete, i.e., the consumed sulfate ions; the other form is made up of free or adsorbed sulfate ions on the pore wall of concrete, i.e., the diffused sulfate ions, which can continue to diffuse to the area with a low sulfate concentration.
Considering the concrete specimen as a semi-infinite body and assuming that the sulfate ions have diffused into concrete in downward direction; then, the total sulfate ions in the microelement [x, x + Dx] (as shown in Fig. 13) in any period [t, t + Dt] according to the law of mass conservation and Fick’s first law [25] can be obtained as: tþ ZDt
m1 ¼
De t tþ ZDt xþ ZDx
¼ De t
x
@C ðx þ Dx; t Þ @C ðx; tÞ A dt De @x @x @ 2 C ðx; t Þ A dx dt @x2
ð2Þ
where m1 is the total sulfate ions in the microelement (kg); thus, C (x, t) and C(x + Dx, t) are the concentrations of diffused sulfate ions at the locations of x and x + Dx at the moment of t (kgm3), respectively; A is the area of the microelement (m2), and De is the effective diffusivity of sulfate ions in concrete (m2s1). Previous research has shown that the concentration of diffused sulfate ions is the most important factor affecting the chemical reaction process; however, the change of calcium aluminate content has little effect [26]. Therefore, according to the first-order dynamics reaction principle, the reaction of gypsum and ettringite formations in concrete attacked by sulfate is considered a firstorder chemical reaction as [27]:
@C cu ðx; t Þ ¼ k C ðx; tÞ @t
ð3Þ
370
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Fig. 8. Measurement results of concrete powder B: (a) concrete powder B-1, (b) filter residue B-1, (c) concrete powder B-2, and (d) filter residue B-2.
3
2 1.5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
2.5
[SO3] %
5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
3 2
1
0.76
0.5
1
0.76
0
0 0
2
4
6
8
10
12
14
16
0
2
4
6
8
10 12 14 16 18 20 22
Depth (mm)
Depth (mm)
(a)
(b)
Fig. 9. Distributions of sulfate ions in concrete (w/c = 0.57) with different concentrations of Na2SO4 solution: (a) the concentration is equal to 1%, and (b) the concentration is equal to 5%.
where Ccu(x, t) is the concentration of consumed sulfate ions at the locations of x at the moment of t (kgm3), and k is the consumed rate of sulfate ions (k = 3 107 s1). Then, the consumed sulfate ions in the microelement can be obtained as:
tþ ZDt
m2 ¼ t
@C cu ðx; t Þ dt @t
xþ ZDx
tþ ZDt
A dx ¼ k x
xþ ZDx
C ðx; t Þ A dx
dt t
x
ð4Þ
371
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
8
4
2
3
2
1
0.81
0.76
0
0
2
0 4
6
0
8 10 12 14 16 18 20 22 24 26
2
4
6
8
10
Depth (mm)
Depth (mm)
(a)
(b)
5
12
14
16
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
6
[SO3] %
5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
3
2
1
0.92
0
0
2
4
6
8
10
12
14
16
Depth (mm)
(c) Fig. 10. Distributions of sulfate ions in concrete (the concentration of Na2SO4 solution is equal to 10%) with different water-cement ratios: (a) 0.57, (b) 0.40, and (c) 0.29.
where m2 is the consumed sulfate ions in the microelement (kg). Then, the increment of diffused sulfate ions in the microelement can be obtained by Eqs. (2) and (4) as: tþ ZDt
m3 ¼ m1 m2 ¼ De
xþ ZDx
dt t
x
@ 2 C ðx; t Þ A dx þ k @x2
C ðx; t Þ A dx dt
ð5Þ
where m3 is the increment of diffused sulfate ions in the microelement (kg). According to the law of mass conservation, the increment of diffused sulfate ions in the microelement in the period [t, t + Dt] can also be expressed by: xþ ZDx
½C ðx; t þ DtÞ C ðx; t Þ A dx x xþ ZDx
tþ ZDt
¼
dt t
x
@C ðx; t Þ A dx @t
Combining Eqs. (5) and (6) yields:
x
xþ ZDx
dt t
x
m3 ¼
t
¼
t
ð6Þ
@ 2 C ðx; tÞ A dx þ k @x2
dt tþ ZDt
tþ ZDt
xþ ZDx
xþ ZDx
tþ ZDt
De
x
@C ðx; t Þ A dx @t
tþ ZDt
xþ ZDx
C ðx; t Þ A dx
dt t
x
ð7Þ
In Eq. (7), oC(x, t)/ot reflects the change rate of diffused sulfate ions, and the current test results show that the change rate of diffused sulfate ions is very slow, that is, the increment of diffused sulfate ions is extremely small in the period [t, t + Dt]. Ikumi et al. [26] revealed that the diffusivity of sulfate ions has little effect on the chemical reaction of a concrete sulfate attack, while the consumed rate of sulfate ions has a significant effect. Also, the reaction rate of hydration products converted to gypsum and ettringite is very fast, so the consumed sulfate ions plays a dominant role in the overall transport process of sulfate ions [28]. The relationship between the consumed rate and the accumulated rate of sulfate ions is analyzed by Eqs. (3) and (6). In the process of calculating the accumulated rate of diffused sulfate ions, the change curves of sulfate ions in concrete at different depths in Figs. 11 and 12 were linearly processed to obtain the average change rate of the sulfate ions in concrete attacked by sulfate for 300 days.
372
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
5
6 Surface concentration ķ
Surface concentration ķ
5
Concentration of 1mm ĸ
4
Concentration of 1mm ĸ
[SO3] %
[SO3] %
Concentration difference ķ-ĸ
3 2
Concentration difference ķ-ĸ
4 3 2
1
1
0
0 0
60
120
180
240
300
0
120
180
Time (day)
(a)
(b)
10
240
300
240
300
5 Surface concentration ķ
Surface concentration ķ
Concentration of 1mm ĸ
8
Concentration of 1mm ĸ
4
Concentration difference ķ-ĸ
Concentration difference ķ-ĸ
[SO3] %
[SO3] %
60
Time (day)
6 4 2
3 2 1
0
0 0
60
120
180
240
300
0
Time (day)
60
120
180
Time (day)
(c)
(d)
5 Surface concentration ķ Concentration of 1mm ĸ
4
[SO3] %
Concentration difference ķ-ĸ
3 2 1 0 0
60
120
180
240
300
Time (day)
(e) Fig. 11. Time-dependent rules of surface sulfate concentration and the concentration at a depth of 1 mm from the surface as well as their differential concentration: (a) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 1%, (b) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 5%, (c) the watercement ratio is 0.57 with a concentration of Na2SO4 solution of 10%, (d) the water-cement ratio is 0.40 with a concentration of Na2SO4 solution of 10%, and (e) the watercement ratio is 0.29 with a concentration of Na2SO4 solution of 10%.
Table 3 gives the average reaction rates of sulfate ions in concrete attacked by sulfate for 300 days. The ratio of the consumed rate to the accumulated rate of sulfate ions under different conditions are all between 90 and 300, so the accumulated rate of sulfate ions can be ignored when compared with the consumed rate. That is,
@C ðx; tÞ k C ðx; t Þ @t
ð8Þ
Substituting Eq. (8) into Eq. (7) yields:
(
a2 C ðx; tÞ ¼ 0 pffiffiffiffiffiffiffiffiffiffiffi a ¼ k=De @ 2 C ðx; t Þ @x2
ð9Þ
where a is the effective coefficient of diffusion (m1). Combined with the initial condition and boundary condition (as shown in Fig. 14), the transport model of diffused sulfate ions in
373
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
8
6 5 4
0.57 (Eq.13) 0.40 (Eq.13) 0.29 (Eq.13) 0.57 0.40 0.29
7 6
[SO3] %
7
[SO3] %
8
1% (Eq.12) 5% (Eq.12) 10% (Eq.12) 1% 5% 10%
3
5 4 3
2
2
1
1 0
0 0
60
120
180
240
0
300
60
120
180
240
300
Time (day)
Time (day)
(a)
(b)
Fig. 12. Effects of the concentration of Na2SO4 solution and the water-cement ratio on the time-dependent rules of surface sulfate concentration: (a) the effect of the concentration of Na2SO4 solution with a water-cement ratio of 0.57, and (b) the effect of the water-cement ratio with a concentration of Na2SO4 solution of 10%.
C
Cs(t) C0 Fig. 13. One dimensional microelement in concrete.
0 concrete at any moment and at any depth can be then expressed as:
(
Cðx; tÞ ¼
C s ðt Þsinh½aðdxÞþC 0 sinhðaxÞ ;x sinhðadÞ
ð10Þ
C0; x P d
where d is the depth of the sulfate attack (m); C0 is the initial sulfate concentration (%), and Cs (t) is the surface sulfate concentration (%). The surface sulfate concentration can be fitted by Eq. (10) at different attack ages. Tables 4–8 give surface sulfate concentration, the effective coefficient of diffusion and other parameters under different conditions of sulfate attack. Combined with Fig. 12, the change law of surface sulfate concentration with time at any sulfate solution concentration can be obtained as:
C s ðt Þ ¼ C 0 þ k n
t
b ð11Þ
t360
where kn is the environmental effect function, which is related to the sulfate solution concentration and water-cement ratio; t360 rep-
d
x
Fig. 14. The boundary condition of the transport model at the moment of t.
resents the attack age of 360 days, and b is the coefficient of accumulated rate of sulfate ions, which is related to the mode of sulfate attack. For the concrete with a water-cement ratio of 0.57, the test data with the solution concentration of 1% in Fig. 12a are fitted by Eq. (11) as:
8 < C ðt Þ ¼ C þ k t 0:7 s 0 1 t 360 ; R2 ¼ 0:99 : 0:56 k1 ¼ 2:032S
ð12Þ
where S is the percentage of sulfate solution concentration and k1 is the effect function of the sulfate solution concentration. In the Na2SO4 solution with a concentration of 10%, surface sulfate concentration of concrete with different water-cement ratios in Fig. 12b can be expressed as:
Table 3 Average change reaction rates of sulfate ions in concrete after 300-day sulfate attack. The concentration of Na2SO4 solution
Water-cement ratio
Depth (mm)
Consumed rate (107 s1)
Accumulated rate (109 s1)
Consumed rate/Accumulated rate
1%
0.57
5%
0.57
10%
0.57
10%
0.40
10%
0.29
3.5 6.5 3.5 6.5 3.5 6.5 3.5 6.5 3.5 6.5
5.043 3.816 9.303 5.154 15.045 8.526 7.674 3.882 6.642 3.936
3.550 1.975 9.031 3.695 16.415 8.032 6.743 1.867 4.992 1.512
142 193 103 139 92 106 114 202 133 260
374
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Table 4 Parameter values of concrete (w/c = 0.57) with 1% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
6.6 1.178 64.79 0.99
9.2 1.411 87.53 0.72
10.0 1.568 91.66 0.99
12.5 1.708 100.37 0.95
12.7 2.053 115.15 0.99
15.0 2.409 121.99 0.97
16.5 2.681 126.24 0.99
Table 5 Parameter values of concrete (w/c = 0.57) with 5% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
10.0 1.511 84.49 0.98
10.5 1.99 104.52 0.97
14.0 2.437 131.91 0.98
15.5 2.893 144.33 0.95
17.0 3.596 140.08 0.95
20.0 4.254 145.02 0.95
20.5 4.807 154.24 0.99
Table 6 Parameter values of concrete (w/c = 0.57) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
10.5 1.915 95.86 0.99
13.0 3.139 151.84 0.96
18.0 3.152 144.93 0.95
20.5 3.857 146.07 0.90
22.5 6.15 154.26 0.97
23.0 6.882 169.71 0.98
25.5 7.67 173.92 0.99
Table 7 Parameter values of concrete (w/c = 0.40) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
6.5 1.319 106.34 0.99
9.5 1.722 125.59 0.95
10.2 2.14 132.6 0.97
10.5 2.694 142.11 0.98
14.0 3.175 166.86 0.98
15.0 3.377 156.69 0.99
16.0 3.830 159.13 0.98
Table 8 Parameter values of concrete (w/c = 0.29) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
5.0 1.335 117.24 0.99
6.5 1.693 127.87 0.99
8.2 1.882 145.46 0.99
9.0 2.121 153.69 0.98
10.5 2.816 150.26 0.90
12.0 3.257 158.80 0.96
14.5 3.758 166.89 0.99
8 < :
C s ðt Þ ¼ C 0 þ k 1 k 2
k2 ¼ 0:13e3:53w=c
t t 360
0:7 ; R2 ¼ 0:94
ð13Þ
8
where k2 is the effect function of the water-cement ratio. So,
6 ð14Þ
The surface sulfate concentration was predicted by Eq. (14), and the predicted values were in good agreement with the test results. The average relative error is 6.94%, as shown in Fig. 15. Hence, the sulfate transport model for concrete related to sulfate solution concentration and the water-cement ratio can be obtained by Eqs. (10) and (14) as:
Cðx; tÞ ¼
8 0:7
> > t < C0 þð2:032S0:56 Þð0:13e3:53w=c Þ t360 sinh½aðdxÞþC 0 sinhðaxÞ > > :
sinhðadÞ
[SO3] %
0:7 t C s ðtÞ ¼ C 0 þ 2:032S0:56 0:13e3:53w=c t 360
1%, 0.57 (Eq.14) 5%, 0.57 (Eq.14) 10%, 0.57 (Eq.14) 10%, 0.40 (Eq.14) 10%, 0.29 (Eq.14) 1%, 0.57 5%, 0.57 10%, 0.57 10%, 0.40 10%, 0.29
7
5 4 3 2 1 0
;x < d
C0; x P d ð15Þ
0
60
120
180
240
300
Time (day) Fig. 15. Comparison of calculated and experimental surface concentrations in concrete.
375
180
180
150
150
120
120
α (m-1)
α (m-1)
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
90
1%
60
0.57
60
5%
30
90
0.40
30
0.29
10% 0
0 30
60
30
90 120 150 180 210 240 270 300
60
90 120 150 180 210 240 270 300
Time (day)
Time (day)
(a)
(b)
Fig. 16. Relationship between the effective coefficient of diffusion for concrete and time: (a) the water-cement ratio is 0.57, and (b) the concentration of Na2SO4 solution is 10%.
With the development of cement hydration and the generation of expansion products of sulfate attack, the concrete structure becomes more compact, which leads to a decrease in the effective diffusivity of sulfate ions De with time [27,29]. However, the constant of the chemical reaction rate k is only related to the temperature and types of reactants [30]. Therefore, the effective coefficient of diffusion a will increase with attack age, as shown in Fig. 16.
In the process of concrete sulfate attack with the same watercement ratio and different solution concentrations, the greater the effective coefficient of diffusion a, the faster the speed of sulfate attack; moreover, the effective coefficient of diffusion a increases with the increasing sulfate solution concentration. However, in the process of a concrete sulfate attack with different water-cement ratios and the same solution concentration, no obvious regularity exists in the effective coefficient of diffusion during the whole process of sulfate attack. The main reason is that the initial effective diffusivities of sulfate ions in concrete with different water-cement ratios are different. This means that different vari-
Table 9 Effective coefficient of diffusion and other parameters under different conditions.
Table 10 Effective diffusivity of sulfate ions and other parameters under different conditions.
4.2. Effective transport model of sulfate attack considering effective diffusivity
The concentration of Na2SO4 solution
Water-cement ratio
t0 (day)
a0
n
R2
The concentration of Na2SO4 solution
Water-cement ratio
t0 (day)
De,0 (1011 m2 s1)
m
R2
1% 5% 10% 10% 10%
0.57 0.57 0.57 0.40 0.29
30 30 30 30 30
64.79 84.49 95.86 106.34 117.24
0.35 0.30 0.29 0.20 0.15
0.97 0.90 0.92 0.88 0.92
1% 5% 10% 10% 10%
0.57 0.57 0.57 0.40 0.29
30 30 30 30 30
7.15 4.20 3.26 2.65 2.18
0.7 0.6 0.6 0.4 0.3
0.97 0.94 0.97 0.96 0.94
1% (Eq.17) 5% (Eq.17) 10% (Eq.17) 1% 5% 10%
De (10-11 m2·s-1)
7 6 5 4 3 2 1
4
0.57 (Eq. 17) 0.40 (Eq. 17) 0.29 (Eq. 17) 0.57 0.40 0.29
3.5
De (10-11 m2·s-1)
8
3 2.5 2 1.5 1 0.5
0
0 30
60
90 120 150 180 210 240 270 300
30
60
90 120 150 180 210 240 270 300
Time (day)
Time (day)
(a)
(b)
Fig. 17. Relationship between the effective diffusivity of sulfate ions in concrete and time: (a) the water-cement ratio is 0.57, and (b) the concentration of Na2SO4 solution is 10%.
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
ables in cement content will also lead to different degrees of hydration in the later hydration stage. The calcium aluminate content also affects the number of expansion products [31,32], which then affects the change of the concrete microstructure. To establish a quantitative relationship between the effective coefficient of diffusion and the attack age, the time-dependent law of the effective coefficient of diffusion can be described as [33]:
3
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
[SO3] %
2.5 2
1.5 1
at ¼ a0
ð16Þ
5
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
0.76
0.5
n t t0
where a0 is the initial effective coefficient of diffusion (m1); at is the effective time-dependent coefficient of diffusion (m1), and n is the growth index. The test data in Fig. 16 were fitted by Eq. (16), and the effective coefficient of diffusion a0 and other corresponding parameters are
[SO3] %
376
3 2 1 0.76
0
0
0
2
4
6
8
10
12
14
16
0
2
4
6
8 10 12 14 16 18 20 22
Depth (mm)
Depth (mm)
(a)
(b) Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
[SO3] %
6
4
5
2
0
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
8
3 2 1 0.81
0.76
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26
0
2
4
Depth (mm)
6
(c)
12
14
16
3 2
5 10%, 180 d [34]
10%, Eq.(18)
4
5%, 180 d [34]
[SO3] %
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
10
(d)
5
1
8
Depth (mm)
3
5%, Eq.(18)
2 1
0.92
0.68
0
0 0
2
4
6
8
10
Depth (mm)
(e)
12
14
16
0
6
12
18
24
30
36
Depth (mm)
(f)
Fig. 18. Comparison of calculated and experimental concentration distributions for concrete in this paper and those in the literature [34]: (a) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 1%, (b) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 5%, (c) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 10%, (d) the water-cement ratio is 0.40 with a concentration of Na2SO4 solution of 10%, (e) the water-cement ratio is 0.29 with a concentration of Na2SO4 solution of 10%, and (f) the water-cement ratio is 0.38 with the concentration of Na2SO4 solution of 5% and 10% [34].
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
shown in Table 9. The results show that Eq. (16) has a high reliability in describing the effective coefficient of diffusion of concrete during sulfate attack. Combined with Eqs. (9) and (16), the relationship between the effective diffusivity of sulfate ions and the effective coefficient of diffusion can be obtained as:
De;t ¼
k
a2t
¼
k
2
a0
2n m t0 t0 ¼ De;0 t t
ð17Þ
where De,t is the effective time-dependent diffusivity of sulfate ions in concrete (m2s1); De,0 is the effective diffusivity of sulfate ions in concrete at the moment t0 (m2s1), and m is the diffusion decay coefficient. Based on Eq. (17), the relationship between the effective diffusivity of sulfate ions in concrete and time can be obtained, as shown in Fig. 17; Table 10 gives the effective diffusivity of sulfate ions in concrete and other parameters with different conditions. It can be seen from Fig. 17 and Table 10 that Eq. (17) has a relatively high fitting accuracy, and the average relative error is 10.73%. Fig. 17 and Table 10 show that the diffusion decay coefficient m is insensitive to the concentration of Na2SO4 solution. Combined with Eqs. (15) and (17), the effective transport model of sulfate attack in concrete can be obtained as:
377
tion concentration and water-cement ratio. The larger the sulfate solution concentration and water-cement ratio are, the larger the difference in concentration is. 2) Based on the diffusion theory, a sulfate transport model was established considering the surface sulfate concentration and the constant of the first-order chemical reaction rate. The model featured in this paper was verified by experiments, which showed that this model has high applicability and prediction accuracy. The effective diffusivities of sulfate ions in concrete were obtained with different attack ages based on the developed model, and a time-dependent model of effective diffusivity was established and verified by experiments. 3) An effective transport model of sulfate attack considering effective diffusivity was presented, which relates to the sulfate solution concentration and the water-cement ratio. The results showed that the model is reliable and meets the general need of those interested in concrete remediation. The extent of this problem was researched and the knowledge of sulfate attack was advanced as well as a new method (model) to calculate that advance. Conflict of interest There is no conflict of interest.
8 0:7 pffiffiffiffiffiffiffiffiffi 0:5m pffiffiffiffiffiffiffiffiffi t 0:5m > 0:56 3:53w=c t t > C þ 2:032S 0:13e sinh k=D ð dx Þ þC sinh k=D x Þð Þ t360 e;0 0 e;0 t0 t0 > 0 ð > <
pffiffiffiffiffiffiffiffiffi t 0:5m C ðx; t Þ ¼ ; x > 0 > > : C0; x P d
ð18Þ
4.3. Verification of the effective transport model of sulfate attack
Acknowledgments
To verify the prediction accuracy of Eq. (18), the calculated values of Eq. (18) were compared with the experimental values in this paper and those in the literature [34], as shown in Fig. 18, and the predicted values were in good agreement with the test results. In this paper, a novel effective transport model of sulfate attack has been verified by experiments. Therefore, the model is reasonable and has high reliability. It can be used to predict the distribution of sulfate ions in concrete at different attack ages and can provide a theoretical basis for the creation of a durability design method of concrete structure and estimate the life cycles of concrete structures under a sulfate environment.
This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 51520105012, 51622808, 51578337, and 51578338) and the China Postdoctoral Science Foundation (2017 M622789).
5. Conclusions In this paper, the consumed and accumulated rates of sulfate ions in concrete as well as the effects of sulfate solution concentration and the water-cement ratio on the sulfate ions distribution were systematically studied. From this research, the conclusions are as follows: 1) Ettringite cannot be dissolved by hydrochloric acid, and thus, the measured sulfate ions are only acid-soluble in the test. The overall trends of sulfate ions distributions are similar in concrete when comparing different sulfate solution concentrations and water-cement ratios. With the increasing sulfate solution concentration and the water-cement ratio, the sulfate ions content and sulfate attack depth in concrete increase accordingly. The surface sulfate concentration is time-dependent and dependent on the sulfate solu-
References [1] R. Ragoug, O.O. Metalssi, F. Barberon, J.M. Torrenti, N. Roussel, L. Divet, et al., Durability of cement pastes exposed to external sulfate attack and leaching: physical and chemical aspects, Cem. Concr. Res. 116 (2019) 134–145. [2] W.V.D.C. Bezerra, G.A. Azeredo, External sulfate attack on compressed stabilized earth blocks, Constr. Build. Mater. 200 (2019) 255–264. [3] K. Sotiriadis, R. Mroz, Simulation of thaumasite sulfate attack on portland cement mixtures using synthesized cement phases, J. Mater. Civ. Eng. 31 (2) (2019) 04018393. [4] H.G. Min, Z.G. Song, Investigation on the sulfuric acid corrosion mechanism for concrete in soaking environment, Adv. Mater. Sci. Eng. 3258123 (2018) 1–10. [5] Y.W. Zhou, H. Tian, L.L. Sui, F. Xing, N.X. Han, Strength deterioration of concrete in sulfate environment: an experimental study and theoretical modeling, Adv. Mater. Sci. Eng. 951209 (2015) 1–13. [6] J. Haufe, A. Vollpracht, Tensile strength of concrete exposed to sulfate attack, Cem. Concr. Res. 116 (2019) 81–88. [7] K. Sotiriadis, E. Nikolopoulou, S. Tsivilis, Sulfate resistance of limestone cement concrete exposed to combined chloride and sulfate environment at low temperature, Cem. Concr. Compos. 34 (8) (2012) 903–910. [8] A.E. Idiart, C.M. López, I. Carol, Chemo-mechanical analysis of concrete cracking and degradation due to external sulfate attack: a meso-scale model, Cem. Concr. Compos. 33 (3) (2011) 411–423. [9] H. Tian, Y.W. Zhou, L.L. Sui, F. Xing, Evolution of the sulfate ion transportdeterioration process in concrete, Anti-Corros. Methods Mater. 63 (3) (2016) 196–204. [10] G.W. Zhao, J.P. Li, F. Han, M. Shi, H.H. Fan, Sulfate-induced degradation of cast-insitu concrete influenced by magnesium, Constr. Build. Mater. 199 (2019) 194–206. [11] X. Ma, O. Çopurog˘lu, E. Schlangen, N.X. Han, F. Xing, Expansion and degradation of cement paste in sodium sulfate solutions, Constr. Build. Mater. 158 (2018) 410–422.
378
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
[12] G.J. Yin, X.B. Zuo, X.H. Sun, Y.J. Tang, Numerical investigation of the external sulfate attack induced expansion response of cement paste by using crystallization pressure, Modell. Simul. Mater. Sci. Eng. 27 (2019) 025006. [13] S. Sarkar, S. Mahadevan, J.C.L. Meeussen, H. van der Sloot, D.S. Kosson, Numerical simulation of cementitious materials degradation under external sulfate attack, Cem. Concr. Compos. 32 (3) (2010) 241–252. [14] B. Bary, Simplified coupled chemo-mechanical modeling of cement pastes behavior subjected to combined leaching and external sulfate attack, Int. J. Numer. Anal. Met. 32 (14) (2008) 1791–1816. [15] I. Oliveira, S.H.P. Cavalaro, A. Aguado, New kinetic model to quantify the internal sulfate attack in concrete, Cem. Concr. Res. 43 (2013) 95–104. [16] W.P. Zhang, H.G. Min, X.L. Gu, Y. Xi, Y.S. Xing, Mesoscale model for thermal conductivity of concrete, Constr. Build. Mater. 98 (2015) 8–16. [17] O.S. BaghabraAl-Amoudi, Sulfate attack and reinforcement corrosion in plain and blended cements exposed to sulfate environments, Build. Environ. 33 (1) (1998) 53–61. [18] O.S.B. Al-Amoudi, Attack on plain and blended cements exposed to aggressive sulfate environments, Cem. Concr. Compos. 24 (3–4) (2002) 305–316. [19] R. Tixier, B. Mobasher, Modeling of damage in cement-based materials subjected to external sulfate attack. I: formulation, J. Mater. Civil Eng. 15 (4) (2003) 305–313. [20] C. Sun, J.K. Chen, J. Zhu, M.H. Zhang, J. Ye, A new diffusion model of sulfate ions in concrete, Constr. Build. Mater. 39 (2013) 39–45. [21] S. Lorente, M. Yssorche-Cubaynes, J. Auger, Sulfate transfer through concrete: migration and diffusion results, Cem. Concr. Compos. 33 (7) (2011) 735–741. [22] Y.W. Zhou, H. Tian, H.Z. Cui, F. Xing, L.L. Sui, Model for sulfate diffusion depth in concrete under complex aggressive environments and its experimental verification, Adv. Mater. Sci. Eng. 693834 (2015) 1–11. [23] ASTM C114-15. Standard test methods for chemical analysis of hydraulic cement. USA: American Society for Testing and Materials; 2015.
[24] P.C. Kreijger, The skin of concrete-composition and properties, Mater. Struct. 17 (4) (1984) 275–283. [25] J.S. Kong, A.N. Ababneh, D.M. Frangopol, Y. Xi, Reliability analysis of chloride penetration in saturated concrete, Probab. Eng. Mech. 17 (3) (2002) 305–315. [26] T. Ikumi, S.H.P. Cavalaro, I. Segura, A. Aguado, Alternative methodology to consider damage and expansions in external sulfate attack modeling, Cem. Concr. Res. 63 (2014) 105–116. [27] P. Gospodinov, R. Kazandjiev, M. Mironova, The effect of sulfate ion diffusion on the structure of cement stone, Cem. Concr. Compos. 18 (6) (1996) 401–407. [28] D. Krajcinovic, M. Basista, K. Mallick, D. Sumarac, Chemo-micromechanics of brittle solids, J. Mech. Phys. Solids 40 (5) (1992) 965–990. [29] P.J. Tumidajski, G.W. Chan, K.E. Philipose, An effective diffusivity for sulfate transport into concrete, Cem. Concr. Res. 25 (6) (1995) 1159–1163. [30] M. Santhanam, M.D. Cohen, J. Olek, Modeling the effects of solution temperature and concentration during sulfate attack on cement mortars, Cem. Concr. Res. 32 (4) (2002) 585–592. [31] F.H. Rasheeduzzafar, A.S. Dakhil, S.S. Al-Gahtani, M.A. Bader Al-Saadoun, Influence of cement composition on the corrosion of reinforcement and sulfate resistance of concrete, ACI Mater. J. 87 (2) (1990) 114–122. [32] C.S. Ouyang, A. Nanni, W.F. Chang, Internal and external sources of sulfate-ions in portland-cement mortar-Two types of chemical attack, Cem. Concr. Res. 18 (5) (1988) 699–709. [33] Z.Q. Jin, W. Sun, Y.S. Zhang, J.Y. Jiang, J.Z. Lai, Interaction between sulfate and chloride solution attack of concretes with and without fly ash, Cem. Concr. Res. 37 (2007) 1223–1232. [34] D.M. Yu, B.W. Guan, R. He, R. Xiong, Z.Z. Liu, Sulfate attack of Portland cement concrete under dynamic flexural loading: a coupling function, Constr. Build. Mater. 115 (2016) 478–485.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An effective transport model of sulfate attack in concrete Hongguang Min, Lili Sui, Feng Xing, Hao Tian, Yingwu Zhou ⇑ Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil Engineering, Shenzhen University, 3688 Nanhai Avenue, Shenzhen 518060, PR China
h i g h l i g h t s New model captures sulfate ions distributions at different sulfate attack ages. A study of effective diffusivity and its effect on sulfate transport model is presented. An effective transport model of sulfate attack in concrete is presented.
a r t i c l e
i n f o
Article history: Received 12 December 2018 Received in revised form 12 April 2019 Accepted 25 April 2019 Available online 9 May 2019 Keywords: Concrete Sulfate attack Sulfate ions distribution Effective diffusivity Sulfate transport model
a b s t r a c t This paper presents both an experimental and theoretical investigation of the consumed and accumulated rates of sulfate ions in concrete. The authors analyze the effects of sulfate solution concentration and the water-cement ratio on the sulfate ions distribution. Based on the diffusion theory, a sulfate transport model for concrete was established considering the effect of surface sulfate concentration. On this basis, an effective transport model of sulfate attack is presented, which relies on effective diffusivity. This model can be applied to predict the sulfate ions distribution; moreover, its predicted values are in good agreement with the experimental ones. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction When concrete structures are in a sulfate environment, external sulfate ions will enter the concrete, which generates a diffusion of sulfate ions in concrete, better known as an external sulfate attack [1,2]. Two causes of this attack are: 1) sulfate ions diffuse from a high concentration to a low concentration in concrete pores and 2) sulfate ions react with the hydration products of cement [3]. Being different from the sulfuric acid corrosion for concrete [4], the concrete sulfate attack is caused by the cracking and spalling of concrete due to the expansion of the sulfate attack products, resulting in a concrete strength loss [5–7]. Sulfate ions from outside environment will attach the concrete through two patterns: diffusion and chemical reaction [3]. Many theoretical analyses and numerical simulations have been published on the relationship between the distribution of sulfate ions or sulfate attack products as well as the effects of expansion stress and strain on concrete [8–14]. However, it is still difficult to quantify the sulfate attack product and its interaction in concrete [15].
⇑ Corresponding author. E-mail addresses: [email protected] (F. Xing), [email protected] (Y. Zhou). https://doi.org/10.1016/j.conbuildmat.2019.04.218 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
This paper considers the close relationship between the consumption of sulfate ions and the concentration of sulfate ions in concrete, which have revealed a variance in the concentration of sulfate ions with time in concrete [9]. Notably, the effective diffusivity of sulfate ions in concrete is an important parameter when determining the distribution of sulfate ions in concrete. Previous study shows that the water-cement ratio has significant effects on the porosity of concrete [16], which in turn affects the transport process of sulfate ions in concrete. In fact, the transport characteristics of sulfate ions in concrete can determine their distribution. These sulfate ions can also reflect the distribution pattern of concrete sulfate attack products, which is the underlying reason for this study on the distribution characteristics of expansion stress in concrete. The lower the water-cement ratio is, the higher the concrete density and the more difficult it becomes for external sulfate ions to penetrate the concrete [17,18]. The low water-cement ratio also explains the slow rate in gypsum and ettringite formations. So, the effect of the water-cement ratio on the diffusion of sulfate ions is very significant. The existing models often fail to analyze the diffusion and consumption processes of sulfate ions in concrete and do not always consider the change of surface sulfate concentration [19–21]. Significantly, the transport process of sulfate ions in concrete is time-dependent [22]; moreover, the
366
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
surface sulfate concentration is not equal to sulfate solution concentration. Instead, this surface sulfate concentration is dependent on the water-cement ratio and sulfate solution concentration. Therefore, the establishment of effective transport model of sulfate attack in concrete is essential, which can help protect concrete sulfate attack. In this research by controlling the sulfate solution concentration and water-cement ratio, the distribution of sulfate ions in concrete was investigated through the following sulfate attack test for concrete. First, the transport process of sulfate ions in concrete was clarified under different conditions of sulfate attack. The diffusion theory made the sulfate transport model possible considering the surface sulfate concentration, the effective diffusivity as well as the first-order chemical reaction rate. And all conclusions were verified by experiments. Finally, the time-dependent regularities of effective diffusivity and surface sulfate concentration were obtained with different water-cement ratios and sulfate solution concentrations. At the same time, the authors also did a thorough study on the effective diffusivity of concrete subjected to sulfate attack. 2. Experimental program 2.1. Specimen design and preparation Three groups of 100 mm 100 mm 100 mm concrete specimens were cast, and the water-cement ratio was 0.57 for 21 specimens, 0.40 for seven specimens and 0.29 for seven specimens, respectively, which were used to study the effect of the watercement ratio on sulfate attack for concrete. The maximum particle size of granite stones was 31.5 mm, which was used as the coarse aggregate. The fine aggregate was medium grade sand with good gradation and tap water as well as Portland cement #425 for casting concrete. The chemical composition of Portland cement #425 and the mix proportions of the concrete specimens are given in Tables 1 and 2, respectively. All prism specimens were placed in a curing room for 28 days where the temperature and relative humidity were 20 ± 2 °C and 95%, respectively.
Fig. 1. Sulfate attack test for concrete: (a) concrete specimen covered with paraffin, and (b) test layout.
2.3. Determination method of sulfate ions content This paper aims to test the sulfate transport from the surface to the inside concrete. Then, the distributions of sulfate ions at different depths in concrete were determined using core samples and slices of concrete specimens as shown in Fig. 2(a) with attack ages of 30 d, 60 d, 90 d, 120 d, 180 d, 240 d, and 300 d. The sampling depths were 1 mm, 3.5 mm, 6.5 mm, 10.5 mm, 15.5 mm, 20.5 mm, and 25.5 mm, in that order, and the corresponding slice thicknesses were 2 mm, 3 mm, 3 mm, 5 mm, 5 mm, 5 mm, and 5 mm, respectively. In the test, a precision cutting machine was used to cut the concrete slices. The thickness of the cutting blade was 0.4 mm, and the error was only about 0.1 mm as shown in Fig. 2(b). The concrete slices were first naturally dried and then mashed in a stainless steel mortar as shown in Fig. 3(a), afterwards, the larger particles, i.e., the coarse aggregates were picked out using a tweezer, and the rest were then ground repeatedly until all the particles could pass through a sieve with a diameter of 0.08 mm, as shown in Fig. 3(b) and (c).
2.2. Sulfate attack test for concrete To reflect the one-dimensional sulfate attack, two lateral surfaces of concrete specimens were tested, and the other four surfaces, including the pouring surface, were sealed with paraffin, as shown in Fig. 1(a). The solution concentrations of sodium sulfate were 1%, 5%, and 10%, respectively. To keep the solution concentration stable, the pool was covered with a plastic film to prevent volatilization during the test, as shown in Fig. 1(b), and the solution was replaced every two weeks. Afterwards, a sulfate attack test for concrete was carried out in a constant temperature room at 28 °C.
Fig. 2. Making concrete slices: (a) concrete core samples, and (b) precision cutting machine.
Table 1 Chemical composition of cement. Chemical composition
SiO2
Al2O3
Fe2O3
CaO
MgO
K2O
Na2O
SO3
f-CaO
Loss of ignition
Content (%)
21.10
5.21
4.18
65.65
1.07
0.58
0.13
1. 02
0.94
0.43
Table 2 Mix proportions of concrete specimen. Water-cement ratio
Cement (kgm3)
Water (kgm3)
Sand ratio (%)
Fine aggregate (kgm3)
Coarse aggregate (kgm3)
Water reducer (% by weight of cement)
0.57 0.40 0.29
195 195 167
342 488 577
36 30 28
670 515 482
1193 1200 1241
0 0 2.2
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
367
Fig. 3. Preparation of concrete powder: (a) mashing concrete slices in a stainless steel mortar, (b) preparing the concrete powder, and (c) sealing the concrete powder.
The sulfate ions content in each layer of the three core samples’ concrete powder was determined by chemical analysis based on ASTM C114-15 [23]. First, the weighed concrete powder was dissolved using hydrochloric acid; then, barium chloride was added to the solution to obtain barium sulfate precipitation. The detailed measurement process is shown in Fig. 4. The average value of the three measurements was taken as the sulfate ions content of the layer; however, the measured data was invalid when the maximum and minimum values all exceeded 10% of the median value. The percentage of sulfate ions content in concrete expressed in sulfur trioxide (SO3) can thus be calculated as [23]:
C SO3 ¼
0:343 ðmt mc Þ 100% mp
ð1Þ
where C SO3 is the percentage of sulfur trioxide content (%); 0.343 is the conversion coefficient of the relative molecular mass between barium sulfate (BaSO4) and sulfur trioxide; mp is the mass of concrete powder (kg), as shown in Fig. 4(a); mc is the mass of crucible (kg), and mt is the total mass of barium sulfate and crucible (kg), as shown in Fig. 4(g).
The challenge of quantifying the sulfate ion taking part in the chemical reaction was met by considering the sulfate attack product of ettringite. When ettringite is dissolved, it often releases sulfate ions into the solution as shown in Fig. 4(d). When this happens, Eq. (1) can be used to measure the part of sulfate ions that chemically react with concrete. To confirm whether the ettringite was dissolved and released as sulfate ions, a subsequent additional test was designed and conducted. 2.4. Additional tests to confirm the dissolution of ettringite Two samples (A and B) with different attack ages were selected for the additional test. An environmental scanning electron microscope (ESEM) test was first used to confirm the existence of ettringite in these samples as shown in Fig. 5. The two samples were ground into two concrete powders and each powder was then equally divided into four parts so as to increase the test sample. Two parts of each concrete powder were dissolved in hydrochloric acid. Filter residues left on the filter paper were identified as A-1, A-2, B-1 and B-2 for samples A and B, respectively. Each sample was poured through a filter to the fill line of their individual cru-
Fig. 4. Measurement processes of sulfate ions content in concrete: (a) weighing the concrete powder, (b) dissolving the concrete powder using hydrochloric acid, (c) filtering using qualitative filter paper, (d) adding the barium chloride, (e) barium sulfate precipitation, (f) filtering using quantitative filter paper, (g) high temperature burning, (h) barium sulfate crystal, (i) cooling to room temperature, and (j) weighing barium sulfate.
368
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Ettringite
Ettringite
(a)
(b)
Fig. 5. SEM images of concrete slices at different sulfate attack stages: (a) concrete slice A and (b) concrete slice B.
Fig. 6. Filter residue: (a) before drying, and (b) after drying.
cible and dried in a constant temperature box at 40 °C for 48 h, as shown in Fig. 6. The alternation of the ettringite in the concrete powder after dissolution was tested by X-ray diffraction (XRD). For comparison, the other two parts of concrete powders A and B without hydrochloric acid treatment were also put into the constant temperature box as control groups and tested by XRD. The results are shown in Figs. 7 and 8 where the chemical compositions of the two filtered residues and two untreated concrete powders (the control group of concrete powder) of samples A and B were all analyzed by XRD. 3. Test results and discussions 3.1. Results of additional tests Fig. 5 gives the test result of ESEM and shows that several acicular ettringite crystals were observed. Figs. 7 and 8 give the test result of XRD and show that the amount of ettringite hardly changed after dissolved in hydrochloric acid, indicating that hydrochloric acid cannot dissolve the ettringite. However, calcium silicate hydrate (C-S-H), gypsum and calcium hydroxide (Ca(OH)2) were dissolved by hydrochloric acid as they cannot be detected in the filter residue. Moreover, because silica dioxide is the main component of sand, the diffraction peak is obvious. Consequently, it was confirmed that only acid-soluble sulfate ions were measured in the test.
0.92% with water-cement ratios of 0.57, 0.40 and 0.29, respectively. The distributions of sulfate ions in concrete with different attack ages are shown in Figs. 9 and 10. Figs. 9 and 10 show that the overall trends of sulfate ions distributions in concrete with different solution concentrations and the water-cement ratios are similar, that is, the closer to the concrete surface, the greater the sulfate ions content, and the sulfate ions content in the first layer (1 mm) is significantly higher than that in the second layer (3.5 mm), showing a sudden drop phenomenon. This sudden drop is a result of the sulfate ions in solution reacting with the hydration products in the concrete pores, causing several sulfate ions to be consumed. Moreover, as the surface concrete is attacked by sulfate ions, gypsum and ettringite are formed with a lower solubility. In this case, the sulfate ions penetrate the surface concrete with increased attack age, thereby promoting the development and deposition of expansion products, which will block the ion transport channels and hinder the further transport of sulfate ions into the concrete. Although surface concrete maintains a high concentration of sulfate ions for a long time, the combination of sulfate ions can also reduce the concentration of sulfate ions inside the concrete. The reduction in sulfate ions slows down the penetration speed and decreases the attack depth of the remaining sulfate ions. In concrete, the surface layer of 0.1 mm is the grout layer, which does not contain any aggregate. The next layer is the mortar layer which has a depth of 0.1–5 mm, which is either free of coarse aggregate or contains only a small amount of coarse aggregate; the concrete layer lies 5 mm under the grout and mortar layers [24]. As a result of bleeding, the water-cement ratio and porosity of the surface layer are larger than that of the internal concrete, which also holds true for the mortar layer. After a certain depth, the water-cement ratio and porosity tend to be constant, and the pore connectivity of the grout layer and the mortar layer are higher than that of the concrete layer. Therefore, the diffusivity within 5 mm of the surface concrete is larger than that of the internal concrete. As the distance from the concrete surface increases, the water-cement ratio gradually approaches that of the internal concrete. Also, the introduction of aggregate makes the ion transport path tortuous, which also reduces the diffusion performance of concrete to a certain extent. 3.3. Time-dependent regularity of surface sulfate concentration in concrete
3.2. Distribution of sulfate ions According to Section 2.3, the percentages of initial sulfate ions content in concrete without sulfate attack were 0.76%, 0.81% and
Fig. 11 shows the time-dependent rules of surface sulfate concentration and the concentration at a depth of 1 mm below the concrete surface as well as their differential concentration. Clearly,
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
369
Fig. 7. Measurement results of concrete powder A: (a) concrete powder A-1, (b) filter residue A-1, (c) concrete powder A-2, and (d) filter residue A-2.
the reaction products generated on the concrete surface are not enough to have a significant effect on the micro-structure of concrete at the initial stage of the sulfate attack. Thus, the concentration difference between surface sulfate concentration and that of sulfate at a depth of 1 mm is small. With the continuous generation of reaction products, the concrete becomes denser, which hinders the transport of external sulfate ions into the concrete, so the concentration difference between surface sulfate concentration and that of 1 mm below the surface concrete increases with sulfate attack age. Therefore, the concentration difference between surface sulfate concentration and that of 1 mm below the concrete surface gradually increases with time. Fig. 12 further shows the effects of the concentration of sodium sulfate (Na2SO4) solution and the water-cement ratio on the timedependent rules of surface sulfate concentration. It can be concluded that the larger the sulfate solution concentration and water-cement ratio are, the more obvious the difference in concentration becomes. 4. Effective transport model of sulfate attack in concrete 4.1. Establishment process of the sulfate transport model There are two forms of sulfate ions in concrete: One is the chemically bound sulfate ions by concrete, i.e., the consumed sulfate ions; the other form is made up of free or adsorbed sulfate ions on the pore wall of concrete, i.e., the diffused sulfate ions, which can continue to diffuse to the area with a low sulfate concentration.
Considering the concrete specimen as a semi-infinite body and assuming that the sulfate ions have diffused into concrete in downward direction; then, the total sulfate ions in the microelement [x, x + Dx] (as shown in Fig. 13) in any period [t, t + Dt] according to the law of mass conservation and Fick’s first law [25] can be obtained as: tþ ZDt
m1 ¼
De t tþ ZDt xþ ZDx
¼ De t
x
@C ðx þ Dx; t Þ @C ðx; tÞ A dt De @x @x @ 2 C ðx; t Þ A dx dt @x2
ð2Þ
where m1 is the total sulfate ions in the microelement (kg); thus, C (x, t) and C(x + Dx, t) are the concentrations of diffused sulfate ions at the locations of x and x + Dx at the moment of t (kgm3), respectively; A is the area of the microelement (m2), and De is the effective diffusivity of sulfate ions in concrete (m2s1). Previous research has shown that the concentration of diffused sulfate ions is the most important factor affecting the chemical reaction process; however, the change of calcium aluminate content has little effect [26]. Therefore, according to the first-order dynamics reaction principle, the reaction of gypsum and ettringite formations in concrete attacked by sulfate is considered a firstorder chemical reaction as [27]:
@C cu ðx; t Þ ¼ k C ðx; tÞ @t
ð3Þ
370
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Fig. 8. Measurement results of concrete powder B: (a) concrete powder B-1, (b) filter residue B-1, (c) concrete powder B-2, and (d) filter residue B-2.
3
2 1.5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
2.5
[SO3] %
5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
3 2
1
0.76
0.5
1
0.76
0
0 0
2
4
6
8
10
12
14
16
0
2
4
6
8
10 12 14 16 18 20 22
Depth (mm)
Depth (mm)
(a)
(b)
Fig. 9. Distributions of sulfate ions in concrete (w/c = 0.57) with different concentrations of Na2SO4 solution: (a) the concentration is equal to 1%, and (b) the concentration is equal to 5%.
where Ccu(x, t) is the concentration of consumed sulfate ions at the locations of x at the moment of t (kgm3), and k is the consumed rate of sulfate ions (k = 3 107 s1). Then, the consumed sulfate ions in the microelement can be obtained as:
tþ ZDt
m2 ¼ t
@C cu ðx; t Þ dt @t
xþ ZDx
tþ ZDt
A dx ¼ k x
xþ ZDx
C ðx; t Þ A dx
dt t
x
ð4Þ
371
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
8
4
2
3
2
1
0.81
0.76
0
0
2
0 4
6
0
8 10 12 14 16 18 20 22 24 26
2
4
6
8
10
Depth (mm)
Depth (mm)
(a)
(b)
5
12
14
16
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
6
[SO3] %
5
30 d 60 d 90 d 120 d 180 d 240 d 300 d
3
2
1
0.92
0
0
2
4
6
8
10
12
14
16
Depth (mm)
(c) Fig. 10. Distributions of sulfate ions in concrete (the concentration of Na2SO4 solution is equal to 10%) with different water-cement ratios: (a) 0.57, (b) 0.40, and (c) 0.29.
where m2 is the consumed sulfate ions in the microelement (kg). Then, the increment of diffused sulfate ions in the microelement can be obtained by Eqs. (2) and (4) as: tþ ZDt
m3 ¼ m1 m2 ¼ De
xþ ZDx
dt t
x
@ 2 C ðx; t Þ A dx þ k @x2
C ðx; t Þ A dx dt
ð5Þ
where m3 is the increment of diffused sulfate ions in the microelement (kg). According to the law of mass conservation, the increment of diffused sulfate ions in the microelement in the period [t, t + Dt] can also be expressed by: xþ ZDx
½C ðx; t þ DtÞ C ðx; t Þ A dx x xþ ZDx
tþ ZDt
¼
dt t
x
@C ðx; t Þ A dx @t
Combining Eqs. (5) and (6) yields:
x
xþ ZDx
dt t
x
m3 ¼
t
¼
t
ð6Þ
@ 2 C ðx; tÞ A dx þ k @x2
dt tþ ZDt
tþ ZDt
xþ ZDx
xþ ZDx
tþ ZDt
De
x
@C ðx; t Þ A dx @t
tþ ZDt
xþ ZDx
C ðx; t Þ A dx
dt t
x
ð7Þ
In Eq. (7), oC(x, t)/ot reflects the change rate of diffused sulfate ions, and the current test results show that the change rate of diffused sulfate ions is very slow, that is, the increment of diffused sulfate ions is extremely small in the period [t, t + Dt]. Ikumi et al. [26] revealed that the diffusivity of sulfate ions has little effect on the chemical reaction of a concrete sulfate attack, while the consumed rate of sulfate ions has a significant effect. Also, the reaction rate of hydration products converted to gypsum and ettringite is very fast, so the consumed sulfate ions plays a dominant role in the overall transport process of sulfate ions [28]. The relationship between the consumed rate and the accumulated rate of sulfate ions is analyzed by Eqs. (3) and (6). In the process of calculating the accumulated rate of diffused sulfate ions, the change curves of sulfate ions in concrete at different depths in Figs. 11 and 12 were linearly processed to obtain the average change rate of the sulfate ions in concrete attacked by sulfate for 300 days.
372
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
5
6 Surface concentration ķ
Surface concentration ķ
5
Concentration of 1mm ĸ
4
Concentration of 1mm ĸ
[SO3] %
[SO3] %
Concentration difference ķ-ĸ
3 2
Concentration difference ķ-ĸ
4 3 2
1
1
0
0 0
60
120
180
240
300
0
120
180
Time (day)
(a)
(b)
10
240
300
240
300
5 Surface concentration ķ
Surface concentration ķ
Concentration of 1mm ĸ
8
Concentration of 1mm ĸ
4
Concentration difference ķ-ĸ
Concentration difference ķ-ĸ
[SO3] %
[SO3] %
60
Time (day)
6 4 2
3 2 1
0
0 0
60
120
180
240
300
0
Time (day)
60
120
180
Time (day)
(c)
(d)
5 Surface concentration ķ Concentration of 1mm ĸ
4
[SO3] %
Concentration difference ķ-ĸ
3 2 1 0 0
60
120
180
240
300
Time (day)
(e) Fig. 11. Time-dependent rules of surface sulfate concentration and the concentration at a depth of 1 mm from the surface as well as their differential concentration: (a) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 1%, (b) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 5%, (c) the watercement ratio is 0.57 with a concentration of Na2SO4 solution of 10%, (d) the water-cement ratio is 0.40 with a concentration of Na2SO4 solution of 10%, and (e) the watercement ratio is 0.29 with a concentration of Na2SO4 solution of 10%.
Table 3 gives the average reaction rates of sulfate ions in concrete attacked by sulfate for 300 days. The ratio of the consumed rate to the accumulated rate of sulfate ions under different conditions are all between 90 and 300, so the accumulated rate of sulfate ions can be ignored when compared with the consumed rate. That is,
@C ðx; tÞ k C ðx; t Þ @t
ð8Þ
Substituting Eq. (8) into Eq. (7) yields:
(
a2 C ðx; tÞ ¼ 0 pffiffiffiffiffiffiffiffiffiffiffi a ¼ k=De @ 2 C ðx; t Þ @x2
ð9Þ
where a is the effective coefficient of diffusion (m1). Combined with the initial condition and boundary condition (as shown in Fig. 14), the transport model of diffused sulfate ions in
373
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
8
6 5 4
0.57 (Eq.13) 0.40 (Eq.13) 0.29 (Eq.13) 0.57 0.40 0.29
7 6
[SO3] %
7
[SO3] %
8
1% (Eq.12) 5% (Eq.12) 10% (Eq.12) 1% 5% 10%
3
5 4 3
2
2
1
1 0
0 0
60
120
180
240
0
300
60
120
180
240
300
Time (day)
Time (day)
(a)
(b)
Fig. 12. Effects of the concentration of Na2SO4 solution and the water-cement ratio on the time-dependent rules of surface sulfate concentration: (a) the effect of the concentration of Na2SO4 solution with a water-cement ratio of 0.57, and (b) the effect of the water-cement ratio with a concentration of Na2SO4 solution of 10%.
C
Cs(t) C0 Fig. 13. One dimensional microelement in concrete.
0 concrete at any moment and at any depth can be then expressed as:
(
Cðx; tÞ ¼
C s ðt Þsinh½aðdxÞþC 0 sinhðaxÞ ;x sinhðadÞ
ð10Þ
C0; x P d
where d is the depth of the sulfate attack (m); C0 is the initial sulfate concentration (%), and Cs (t) is the surface sulfate concentration (%). The surface sulfate concentration can be fitted by Eq. (10) at different attack ages. Tables 4–8 give surface sulfate concentration, the effective coefficient of diffusion and other parameters under different conditions of sulfate attack. Combined with Fig. 12, the change law of surface sulfate concentration with time at any sulfate solution concentration can be obtained as:
C s ðt Þ ¼ C 0 þ k n
t
b ð11Þ
t360
where kn is the environmental effect function, which is related to the sulfate solution concentration and water-cement ratio; t360 rep-
d
x
Fig. 14. The boundary condition of the transport model at the moment of t.
resents the attack age of 360 days, and b is the coefficient of accumulated rate of sulfate ions, which is related to the mode of sulfate attack. For the concrete with a water-cement ratio of 0.57, the test data with the solution concentration of 1% in Fig. 12a are fitted by Eq. (11) as:
8 < C ðt Þ ¼ C þ k t 0:7 s 0 1 t 360 ; R2 ¼ 0:99 : 0:56 k1 ¼ 2:032S
ð12Þ
where S is the percentage of sulfate solution concentration and k1 is the effect function of the sulfate solution concentration. In the Na2SO4 solution with a concentration of 10%, surface sulfate concentration of concrete with different water-cement ratios in Fig. 12b can be expressed as:
Table 3 Average change reaction rates of sulfate ions in concrete after 300-day sulfate attack. The concentration of Na2SO4 solution
Water-cement ratio
Depth (mm)
Consumed rate (107 s1)
Accumulated rate (109 s1)
Consumed rate/Accumulated rate
1%
0.57
5%
0.57
10%
0.57
10%
0.40
10%
0.29
3.5 6.5 3.5 6.5 3.5 6.5 3.5 6.5 3.5 6.5
5.043 3.816 9.303 5.154 15.045 8.526 7.674 3.882 6.642 3.936
3.550 1.975 9.031 3.695 16.415 8.032 6.743 1.867 4.992 1.512
142 193 103 139 92 106 114 202 133 260
374
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
Table 4 Parameter values of concrete (w/c = 0.57) with 1% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
6.6 1.178 64.79 0.99
9.2 1.411 87.53 0.72
10.0 1.568 91.66 0.99
12.5 1.708 100.37 0.95
12.7 2.053 115.15 0.99
15.0 2.409 121.99 0.97
16.5 2.681 126.24 0.99
Table 5 Parameter values of concrete (w/c = 0.57) with 5% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
10.0 1.511 84.49 0.98
10.5 1.99 104.52 0.97
14.0 2.437 131.91 0.98
15.5 2.893 144.33 0.95
17.0 3.596 140.08 0.95
20.0 4.254 145.02 0.95
20.5 4.807 154.24 0.99
Table 6 Parameter values of concrete (w/c = 0.57) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
10.5 1.915 95.86 0.99
13.0 3.139 151.84 0.96
18.0 3.152 144.93 0.95
20.5 3.857 146.07 0.90
22.5 6.15 154.26 0.97
23.0 6.882 169.71 0.98
25.5 7.67 173.92 0.99
Table 7 Parameter values of concrete (w/c = 0.40) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
6.5 1.319 106.34 0.99
9.5 1.722 125.59 0.95
10.2 2.14 132.6 0.97
10.5 2.694 142.11 0.98
14.0 3.175 166.86 0.98
15.0 3.377 156.69 0.99
16.0 3.830 159.13 0.98
Table 8 Parameter values of concrete (w/c = 0.29) with 10% concentration of Na2SO4 in solution. Time (day)
30
60
90
120
180
240
300
Measured depth d (mm) Surface concentration Cs (%) Effective coefficient a (m1) R2
5.0 1.335 117.24 0.99
6.5 1.693 127.87 0.99
8.2 1.882 145.46 0.99
9.0 2.121 153.69 0.98
10.5 2.816 150.26 0.90
12.0 3.257 158.80 0.96
14.5 3.758 166.89 0.99
8 < :
C s ðt Þ ¼ C 0 þ k 1 k 2
k2 ¼ 0:13e3:53w=c
t t 360
0:7 ; R2 ¼ 0:94
ð13Þ
8
where k2 is the effect function of the water-cement ratio. So,
6 ð14Þ
The surface sulfate concentration was predicted by Eq. (14), and the predicted values were in good agreement with the test results. The average relative error is 6.94%, as shown in Fig. 15. Hence, the sulfate transport model for concrete related to sulfate solution concentration and the water-cement ratio can be obtained by Eqs. (10) and (14) as:
Cðx; tÞ ¼
8 0:7
> > t < C0 þð2:032S0:56 Þð0:13e3:53w=c Þ t360 sinh½aðdxÞþC 0 sinhðaxÞ > > :
sinhðadÞ
[SO3] %
0:7 t C s ðtÞ ¼ C 0 þ 2:032S0:56 0:13e3:53w=c t 360
1%, 0.57 (Eq.14) 5%, 0.57 (Eq.14) 10%, 0.57 (Eq.14) 10%, 0.40 (Eq.14) 10%, 0.29 (Eq.14) 1%, 0.57 5%, 0.57 10%, 0.57 10%, 0.40 10%, 0.29
7
5 4 3 2 1 0
;x < d
C0; x P d ð15Þ
0
60
120
180
240
300
Time (day) Fig. 15. Comparison of calculated and experimental surface concentrations in concrete.
375
180
180
150
150
120
120
α (m-1)
α (m-1)
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
90
1%
60
0.57
60
5%
30
90
0.40
30
0.29
10% 0
0 30
60
30
90 120 150 180 210 240 270 300
60
90 120 150 180 210 240 270 300
Time (day)
Time (day)
(a)
(b)
Fig. 16. Relationship between the effective coefficient of diffusion for concrete and time: (a) the water-cement ratio is 0.57, and (b) the concentration of Na2SO4 solution is 10%.
With the development of cement hydration and the generation of expansion products of sulfate attack, the concrete structure becomes more compact, which leads to a decrease in the effective diffusivity of sulfate ions De with time [27,29]. However, the constant of the chemical reaction rate k is only related to the temperature and types of reactants [30]. Therefore, the effective coefficient of diffusion a will increase with attack age, as shown in Fig. 16.
In the process of concrete sulfate attack with the same watercement ratio and different solution concentrations, the greater the effective coefficient of diffusion a, the faster the speed of sulfate attack; moreover, the effective coefficient of diffusion a increases with the increasing sulfate solution concentration. However, in the process of a concrete sulfate attack with different water-cement ratios and the same solution concentration, no obvious regularity exists in the effective coefficient of diffusion during the whole process of sulfate attack. The main reason is that the initial effective diffusivities of sulfate ions in concrete with different water-cement ratios are different. This means that different vari-
Table 9 Effective coefficient of diffusion and other parameters under different conditions.
Table 10 Effective diffusivity of sulfate ions and other parameters under different conditions.
4.2. Effective transport model of sulfate attack considering effective diffusivity
The concentration of Na2SO4 solution
Water-cement ratio
t0 (day)
a0
n
R2
The concentration of Na2SO4 solution
Water-cement ratio
t0 (day)
De,0 (1011 m2 s1)
m
R2
1% 5% 10% 10% 10%
0.57 0.57 0.57 0.40 0.29
30 30 30 30 30
64.79 84.49 95.86 106.34 117.24
0.35 0.30 0.29 0.20 0.15
0.97 0.90 0.92 0.88 0.92
1% 5% 10% 10% 10%
0.57 0.57 0.57 0.40 0.29
30 30 30 30 30
7.15 4.20 3.26 2.65 2.18
0.7 0.6 0.6 0.4 0.3
0.97 0.94 0.97 0.96 0.94
1% (Eq.17) 5% (Eq.17) 10% (Eq.17) 1% 5% 10%
De (10-11 m2·s-1)
7 6 5 4 3 2 1
4
0.57 (Eq. 17) 0.40 (Eq. 17) 0.29 (Eq. 17) 0.57 0.40 0.29
3.5
De (10-11 m2·s-1)
8
3 2.5 2 1.5 1 0.5
0
0 30
60
90 120 150 180 210 240 270 300
30
60
90 120 150 180 210 240 270 300
Time (day)
Time (day)
(a)
(b)
Fig. 17. Relationship between the effective diffusivity of sulfate ions in concrete and time: (a) the water-cement ratio is 0.57, and (b) the concentration of Na2SO4 solution is 10%.
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
ables in cement content will also lead to different degrees of hydration in the later hydration stage. The calcium aluminate content also affects the number of expansion products [31,32], which then affects the change of the concrete microstructure. To establish a quantitative relationship between the effective coefficient of diffusion and the attack age, the time-dependent law of the effective coefficient of diffusion can be described as [33]:
3
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
[SO3] %
2.5 2
1.5 1
at ¼ a0
ð16Þ
5
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
0.76
0.5
n t t0
where a0 is the initial effective coefficient of diffusion (m1); at is the effective time-dependent coefficient of diffusion (m1), and n is the growth index. The test data in Fig. 16 were fitted by Eq. (16), and the effective coefficient of diffusion a0 and other corresponding parameters are
[SO3] %
376
3 2 1 0.76
0
0
0
2
4
6
8
10
12
14
16
0
2
4
6
8 10 12 14 16 18 20 22
Depth (mm)
Depth (mm)
(a)
(b) Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
[SO3] %
6
4
5
2
0
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
8
3 2 1 0.81
0.76
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26
0
2
4
Depth (mm)
6
(c)
12
14
16
3 2
5 10%, 180 d [34]
10%, Eq.(18)
4
5%, 180 d [34]
[SO3] %
Eq.(18) 30 d 60 d 90 d 120 d 180 d 240 d 300 d
4
[SO3] %
10
(d)
5
1
8
Depth (mm)
3
5%, Eq.(18)
2 1
0.92
0.68
0
0 0
2
4
6
8
10
Depth (mm)
(e)
12
14
16
0
6
12
18
24
30
36
Depth (mm)
(f)
Fig. 18. Comparison of calculated and experimental concentration distributions for concrete in this paper and those in the literature [34]: (a) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 1%, (b) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 5%, (c) the water-cement ratio is 0.57 with a concentration of Na2SO4 solution of 10%, (d) the water-cement ratio is 0.40 with a concentration of Na2SO4 solution of 10%, (e) the water-cement ratio is 0.29 with a concentration of Na2SO4 solution of 10%, and (f) the water-cement ratio is 0.38 with the concentration of Na2SO4 solution of 5% and 10% [34].
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
shown in Table 9. The results show that Eq. (16) has a high reliability in describing the effective coefficient of diffusion of concrete during sulfate attack. Combined with Eqs. (9) and (16), the relationship between the effective diffusivity of sulfate ions and the effective coefficient of diffusion can be obtained as:
De;t ¼
k
a2t
¼
k
2
a0
2n m t0 t0 ¼ De;0 t t
ð17Þ
where De,t is the effective time-dependent diffusivity of sulfate ions in concrete (m2s1); De,0 is the effective diffusivity of sulfate ions in concrete at the moment t0 (m2s1), and m is the diffusion decay coefficient. Based on Eq. (17), the relationship between the effective diffusivity of sulfate ions in concrete and time can be obtained, as shown in Fig. 17; Table 10 gives the effective diffusivity of sulfate ions in concrete and other parameters with different conditions. It can be seen from Fig. 17 and Table 10 that Eq. (17) has a relatively high fitting accuracy, and the average relative error is 10.73%. Fig. 17 and Table 10 show that the diffusion decay coefficient m is insensitive to the concentration of Na2SO4 solution. Combined with Eqs. (15) and (17), the effective transport model of sulfate attack in concrete can be obtained as:
377
tion concentration and water-cement ratio. The larger the sulfate solution concentration and water-cement ratio are, the larger the difference in concentration is. 2) Based on the diffusion theory, a sulfate transport model was established considering the surface sulfate concentration and the constant of the first-order chemical reaction rate. The model featured in this paper was verified by experiments, which showed that this model has high applicability and prediction accuracy. The effective diffusivities of sulfate ions in concrete were obtained with different attack ages based on the developed model, and a time-dependent model of effective diffusivity was established and verified by experiments. 3) An effective transport model of sulfate attack considering effective diffusivity was presented, which relates to the sulfate solution concentration and the water-cement ratio. The results showed that the model is reliable and meets the general need of those interested in concrete remediation. The extent of this problem was researched and the knowledge of sulfate attack was advanced as well as a new method (model) to calculate that advance. Conflict of interest There is no conflict of interest.
8 0:7 pffiffiffiffiffiffiffiffiffi 0:5m pffiffiffiffiffiffiffiffiffi t 0:5m > 0:56 3:53w=c t t > C þ 2:032S 0:13e sinh k=D ð dx Þ þC sinh k=D x Þð Þ t360 e;0 0 e;0 t0 t0 > 0 ð > <
pffiffiffiffiffiffiffiffiffi t 0:5m C ðx; t Þ ¼ ; x
ð18Þ
4.3. Verification of the effective transport model of sulfate attack
Acknowledgments
To verify the prediction accuracy of Eq. (18), the calculated values of Eq. (18) were compared with the experimental values in this paper and those in the literature [34], as shown in Fig. 18, and the predicted values were in good agreement with the test results. In this paper, a novel effective transport model of sulfate attack has been verified by experiments. Therefore, the model is reasonable and has high reliability. It can be used to predict the distribution of sulfate ions in concrete at different attack ages and can provide a theoretical basis for the creation of a durability design method of concrete structure and estimate the life cycles of concrete structures under a sulfate environment.
This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 51520105012, 51622808, 51578337, and 51578338) and the China Postdoctoral Science Foundation (2017 M622789).
5. Conclusions In this paper, the consumed and accumulated rates of sulfate ions in concrete as well as the effects of sulfate solution concentration and the water-cement ratio on the sulfate ions distribution were systematically studied. From this research, the conclusions are as follows: 1) Ettringite cannot be dissolved by hydrochloric acid, and thus, the measured sulfate ions are only acid-soluble in the test. The overall trends of sulfate ions distributions are similar in concrete when comparing different sulfate solution concentrations and water-cement ratios. With the increasing sulfate solution concentration and the water-cement ratio, the sulfate ions content and sulfate attack depth in concrete increase accordingly. The surface sulfate concentration is time-dependent and dependent on the sulfate solu-
References [1] R. Ragoug, O.O. Metalssi, F. Barberon, J.M. Torrenti, N. Roussel, L. Divet, et al., Durability of cement pastes exposed to external sulfate attack and leaching: physical and chemical aspects, Cem. Concr. Res. 116 (2019) 134–145. [2] W.V.D.C. Bezerra, G.A. Azeredo, External sulfate attack on compressed stabilized earth blocks, Constr. Build. Mater. 200 (2019) 255–264. [3] K. Sotiriadis, R. Mroz, Simulation of thaumasite sulfate attack on portland cement mixtures using synthesized cement phases, J. Mater. Civ. Eng. 31 (2) (2019) 04018393. [4] H.G. Min, Z.G. Song, Investigation on the sulfuric acid corrosion mechanism for concrete in soaking environment, Adv. Mater. Sci. Eng. 3258123 (2018) 1–10. [5] Y.W. Zhou, H. Tian, L.L. Sui, F. Xing, N.X. Han, Strength deterioration of concrete in sulfate environment: an experimental study and theoretical modeling, Adv. Mater. Sci. Eng. 951209 (2015) 1–13. [6] J. Haufe, A. Vollpracht, Tensile strength of concrete exposed to sulfate attack, Cem. Concr. Res. 116 (2019) 81–88. [7] K. Sotiriadis, E. Nikolopoulou, S. Tsivilis, Sulfate resistance of limestone cement concrete exposed to combined chloride and sulfate environment at low temperature, Cem. Concr. Compos. 34 (8) (2012) 903–910. [8] A.E. Idiart, C.M. López, I. Carol, Chemo-mechanical analysis of concrete cracking and degradation due to external sulfate attack: a meso-scale model, Cem. Concr. Compos. 33 (3) (2011) 411–423. [9] H. Tian, Y.W. Zhou, L.L. Sui, F. Xing, Evolution of the sulfate ion transportdeterioration process in concrete, Anti-Corros. Methods Mater. 63 (3) (2016) 196–204. [10] G.W. Zhao, J.P. Li, F. Han, M. Shi, H.H. Fan, Sulfate-induced degradation of cast-insitu concrete influenced by magnesium, Constr. Build. Mater. 199 (2019) 194–206. [11] X. Ma, O. Çopurog˘lu, E. Schlangen, N.X. Han, F. Xing, Expansion and degradation of cement paste in sodium sulfate solutions, Constr. Build. Mater. 158 (2018) 410–422.
378
H. Min et al. / Construction and Building Materials 216 (2019) 365–378
[12] G.J. Yin, X.B. Zuo, X.H. Sun, Y.J. Tang, Numerical investigation of the external sulfate attack induced expansion response of cement paste by using crystallization pressure, Modell. Simul. Mater. Sci. Eng. 27 (2019) 025006. [13] S. Sarkar, S. Mahadevan, J.C.L. Meeussen, H. van der Sloot, D.S. Kosson, Numerical simulation of cementitious materials degradation under external sulfate attack, Cem. Concr. Compos. 32 (3) (2010) 241–252. [14] B. Bary, Simplified coupled chemo-mechanical modeling of cement pastes behavior subjected to combined leaching and external sulfate attack, Int. J. Numer. Anal. Met. 32 (14) (2008) 1791–1816. [15] I. Oliveira, S.H.P. Cavalaro, A. Aguado, New kinetic model to quantify the internal sulfate attack in concrete, Cem. Concr. Res. 43 (2013) 95–104. [16] W.P. Zhang, H.G. Min, X.L. Gu, Y. Xi, Y.S. Xing, Mesoscale model for thermal conductivity of concrete, Constr. Build. Mater. 98 (2015) 8–16. [17] O.S. BaghabraAl-Amoudi, Sulfate attack and reinforcement corrosion in plain and blended cements exposed to sulfate environments, Build. Environ. 33 (1) (1998) 53–61. [18] O.S.B. Al-Amoudi, Attack on plain and blended cements exposed to aggressive sulfate environments, Cem. Concr. Compos. 24 (3–4) (2002) 305–316. [19] R. Tixier, B. Mobasher, Modeling of damage in cement-based materials subjected to external sulfate attack. I: formulation, J. Mater. Civil Eng. 15 (4) (2003) 305–313. [20] C. Sun, J.K. Chen, J. Zhu, M.H. Zhang, J. Ye, A new diffusion model of sulfate ions in concrete, Constr. Build. Mater. 39 (2013) 39–45. [21] S. Lorente, M. Yssorche-Cubaynes, J. Auger, Sulfate transfer through concrete: migration and diffusion results, Cem. Concr. Compos. 33 (7) (2011) 735–741. [22] Y.W. Zhou, H. Tian, H.Z. Cui, F. Xing, L.L. Sui, Model for sulfate diffusion depth in concrete under complex aggressive environments and its experimental verification, Adv. Mater. Sci. Eng. 693834 (2015) 1–11. [23] ASTM C114-15. Standard test methods for chemical analysis of hydraulic cement. USA: American Society for Testing and Materials; 2015.
[24] P.C. Kreijger, The skin of concrete-composition and properties, Mater. Struct. 17 (4) (1984) 275–283. [25] J.S. Kong, A.N. Ababneh, D.M. Frangopol, Y. Xi, Reliability analysis of chloride penetration in saturated concrete, Probab. Eng. Mech. 17 (3) (2002) 305–315. [26] T. Ikumi, S.H.P. Cavalaro, I. Segura, A. Aguado, Alternative methodology to consider damage and expansions in external sulfate attack modeling, Cem. Concr. Res. 63 (2014) 105–116. [27] P. Gospodinov, R. Kazandjiev, M. Mironova, The effect of sulfate ion diffusion on the structure of cement stone, Cem. Concr. Compos. 18 (6) (1996) 401–407. [28] D. Krajcinovic, M. Basista, K. Mallick, D. Sumarac, Chemo-micromechanics of brittle solids, J. Mech. Phys. Solids 40 (5) (1992) 965–990. [29] P.J. Tumidajski, G.W. Chan, K.E. Philipose, An effective diffusivity for sulfate transport into concrete, Cem. Concr. Res. 25 (6) (1995) 1159–1163. [30] M. Santhanam, M.D. Cohen, J. Olek, Modeling the effects of solution temperature and concentration during sulfate attack on cement mortars, Cem. Concr. Res. 32 (4) (2002) 585–592. [31] F.H. Rasheeduzzafar, A.S. Dakhil, S.S. Al-Gahtani, M.A. Bader Al-Saadoun, Influence of cement composition on the corrosion of reinforcement and sulfate resistance of concrete, ACI Mater. J. 87 (2) (1990) 114–122. [32] C.S. Ouyang, A. Nanni, W.F. Chang, Internal and external sources of sulfate-ions in portland-cement mortar-Two types of chemical attack, Cem. Concr. Res. 18 (5) (1988) 699–709. [33] Z.Q. Jin, W. Sun, Y.S. Zhang, J.Y. Jiang, J.Z. Lai, Interaction between sulfate and chloride solution attack of concretes with and without fly ash, Cem. Concr. Res. 37 (2007) 1223–1232. [34] D.M. Yu, B.W. Guan, R. He, R. Xiong, Z.Z. Liu, Sulfate attack of Portland cement concrete under dynamic flexural loading: a coupling function, Constr. Build. Mater. 115 (2016) 478–485.