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Probability distribution of convection zone depth of chloride in concrete in a marine tidal environment
Construction and Building Materials 140 (2017) 485–495
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Probability distribution of convection zone depth of chloride in concrete in a marine tidal environment Yan-hong Gao, Jun-zhi Zhang ⇑, Shan Zhang, Yu-rong Zhang College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou 310014, PR China
h i g h l i g h t s Convection depth of chloride with different W/C ratios, admixtures and exposure time was researched. Convection depths of chloride were appeared in all tested concretes. Mean value of convection zone depth of chloride is in a range from 4 mm to 6 mm. Convection zone depth of chloride follows a Gumbel distribution.
a r t i c l e
i n f o
Article history: Received 2 December 2016 Received in revised form 8 February 2017 Accepted 24 February 2017
Keywords: Concrete Chloride Convection zone depth Probability distribution Marine tidal environment
a b s t r a c t Based on a field experiment of concrete exposed to a marine tidal environment and according to measured chloride ingress data, diffusion coefficients of chloride ion in concrete after different exposure time are fitted by Fick-second law. Concrete with different types of admixture are tested in this paper, with water-cement ratios of 0.40, 0.45, 0.50, 0.55 and 0.60, respectively. Based on 270 group chloride ingress curves of test concrete, the convection zone depth of chloride and peak value of chloride concentration in concrete are acquired. According to chloride ingress curves of concrete with different water-cement ratio under the same exposure time, the probability distribution forms of convection zone depth of chloride are investigated by statistical test using the log-normal distribution, the normal distribution and the maximum value distribution, respectively. The statistical results show that the mean value of convection zone depths of chloride is in a range from 4 mm to 6 mmin this paper, disregarding the difference in exposure time, water-cement ratio and with or without the admixture in the specimens. The majority of convection zone depths of chloride in different exposure time and water-cement ratios, as well as the admixture, follow a Gumbel distribution, and the convection zone depth of chloride in total 270 specimens follows a Gumbel distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm. The exposure time, water-cement ratio and different admixture have negligible effect on the mean value and the probabilistic characteristic of convection zone depth of chloride, however, different admixture and lower water-cement ratio can significantly reduce the diffusion coefficients and peak values of chloride concentration in concrete. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The penetration of chloride ions through concrete cover to steel reinforcement resulting in the corrosion of reinforcing steel is a major problem of structures, particularly those exposed to marine environments [1,2]. The existing studies on chloride-induced reinforcing steel corrosion have showed that the penetration of chloride ions in concrete is a complex process, depending on many factors, including not only the concrete material itself but also ⇑ Corresponding author. E-mail address: [email protected] (J.-z. Zhang). http://dx.doi.org/10.1016/j.conbuildmat.2017.02.134 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
the environmental condition where the concrete is exposed to and the loading condition where the concrete structure is subjected to [3–5]. Most of these factors are the random variables. For instance, in some studies, the chloride diffusion coefficient, the chloride concentration calculated on the surface of reinforcing steel bar, the thickness of concrete cover, the threshold chloride concentration, and the convection zone depth of chloride ions in concrete cover were all modeled as the random variables [6–8]. Many concrete structures exposed to marine environment may be subjected to dry-wet cycles, in which moisture transport can also take place in part of the concrete cover. In this case, the transport of chloride ions involves not only the diffusion but also the
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convection. The region which involves both diffusion and convection of chloride ions is often called the convection zone. The convection zone is normally a thin layer from the exposure surface to the location where the chloride concentration has a peak value. The thickness of the convection zone is usually defined to be the convection zone depth [9]. Under wet-dry cycles in natural tidal environment, the convection zone depth is considered as a key variable, which can affect the prediction of chloride concentration in concrete cover, particularly when Fick’s second law is used to calculate the chloride concentration [10,11]. In order to determine the convection zone depth in concrete cover, different artificial simulation environments and field tests have been carried out. It was reported that the depth of washout or convection zone is approximately 7 mm for Portland cement mixture, 14–15 mm for fly ash mixture [12], and 14 mm for marine concretes [13]. Other ranges from 20 mm to 30 mm [14], and from 5 mm to 15 mm were also suggested in literature [15]. In addition, it was found that the depth of convection zone increases with the cracking width [8,16], and thus it is likely that the depth of convection zone will increase with the concrete service life. The mean value of the convection zone depth was found quite different in various concretes exposed to different environments, varying from 5 mm to 20 mm [10,13,17–19]. According to the analysis of 127 chloride ingress curves obtained from concrete under a marine environment, the convection zone depth was found to follow a Beta distribution with l = 8.9 mm, r = 63%, a = 0 and b = 50, in regard of the chloride source and water-cement ratio [20]. Note that, the results described above on the chloride convection zone depth are mostly based on the measured data obtained by using the deterministic model. Even if there was probabilistic research on convection zone depth of chloride, they were all based on the mean value. And the research on the randomness of convection zone depth of chloride is few. In reality, however, there is strong randomness in the process of the chloride ingress into concrete, and the relevant influence parameters on RC structures’ service life such as the chloride diffusion coefficient and the initial corrosion time of the steel bars in concrete are random variables. Therefore, from the durability point of view, the lifetime assessment of a deteriorating RC structure should be carried out by using the probabilistic method and considering the uncertainties of materials, structures, and environmental conditions [21–23]. In a dry-wet cycling environment, chloride ingress into concrete can be divided into two typical zones, namely the convection and diffusion zones. Let the convection zone depth Xc, then the typical
distribution profile of free chloride ions in the convection and diffusion zones can be plotted as what is shown in Fig. 1. Note that the Fick’s second law is commonly used to represent the chloride concentration profile in concrete [24]. However, when a convection zone is involved [4,5,25,26], the Fick’s second law can only be applied in the diffusion zone and thus it needs to know the convection zone depth and the corresponding chloride concentration at that point in order to determine the chloride distribution in the diffusion zone. In this paper an experimental study to determine the convection zone depth and the corresponding chloride concentration at that depth was carried out for concretes with different water to cement ratios, exposed to a marine tidal environment up to 600 d. The experimental work was performed at different stages and the influences of exposed time, water to cement ratio, and concrete admixture on the convection zone depth and corresponding chloride concentration at that depth are examined. The statistical distributions of convection zone depth and corresponding chloride concentration at that depth are also discussed. 2. Mix proportion of concrete and test environment 2.1. Raw material and mix proportion of tested concrete All tested concretes presented in this study were prepared using coarse aggregates of the maximum size 40 mm, fine aggregates (sand) of the fineness modulus 2.4, and Qian-Chao complex Portland cement (PC32.5). The water used in the mix as well as for curing is the laboratory tap water. The admixtures used in tested concretes include chopped basalt fiber (BF) with filament diameter 17 20 lm and tensile strength 390 450 MPa, silica fume (SF) with Bertrand specific area 21,000 m2/kg, and stair fly ash (FA) with fineness 4.6% and apparent density of 2240 kg/m3. Table 1 gives the details of the mix proportion of the tested concretes, in which the percentage of admixture represents the weight percentage of the admixture in the binder. 2.2. Specimen casting The preparation of specimens of the tested concrete is in accordance with the Chinese standards of SL352-2006. Two types of specimens were cast. One is the cubic specimens of size 150 150 150 mm, which were used for the compressive strength test. The other is the cylindrical specimens of size /
Fig. 1. Typical distribution of free chlorides in convection and diffusion zones.
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Y.-h. Gao et al. / Construction and Building Materials 140 (2017) 485–495 Table 1 Mix proportion of experimental concrete in the natural tidal zone (kg/m3). Specimen No.
w/b
Cement
Aggregate
Sand
BF Wt/Percent
SF Wt/Percent
FA Wt/Percent
A1 A2 A3 A4 A5 A6 A7 A8 A9
0.40 0.45 0.50 0.55 0.60 0.50 0.50 0.50 0.50
475 422 380 346 317 380 361 304 304
1174 1204 1229 1249 1269 1229 1229 1229 1229
552 567 578 589 597 578 578 578 578
0 0 0 0 0 1.03/(0.062%) 0 0 0
0 0 0 0 0 0 19/(5%) 0 19/(5%)
0 0 0 0 0 0 0 76/(20%) 57/(15%)
Table 2 Compressive strengths of test concrete (MPa). Specimen
Admixtures
Compressive strength
A1 A2 A3 A4 A5 A6 A7 A8 A9
— — — — — BF, 0.062% SF, 5% FA, 20% SF/FA, 5%/15%
32.5 27.2 23.9 20.6 17.1 24.6 25.5 15.8 19.7
100 50 mm, which were used for chloride ingress test. The former were tested after the cubic specimens were cured for 28 days in a standard laboratory curing condition as specified in the standard test SL352-2006 of China (temperature 20 °C ± 5 °C, relative humidity 95%). Table 2 shows the corresponding compressive strength test results. The lowest compressive strength was found in specimen A8 (15.8 MPa); whereas the highest compressive strength was found in specimen A1 (32.5 MPa), the results of which seem to be consistent with what reported in literature [25,26]. For the chloride ingress test, there were 30 (5 6) specimens for each mix type, in which 5 represents the repeated tests, and 6 represents at six different exposure times (60, 120, 240, 360, 480 and 600 days). Before the cylindrical specimens were transported to the site, they were cured for 28 days in a standard laboratory curing condition as specified in the standard test SL352-2006 of China (temperature 20 °C ± 5 °C, relative humidity 95%). In order to simulate the one-dimension ingress, all other surfaces (except for one circular surface) in the specimens were sealed
Fig. 3. Photo of site exposure tests.
using epoxy resin, so that the chloride ions can only transport along the longitudinal direction of the cylinder. 2.3. Exposure environment and testing methods The chloride ingress test was carried out in the natural tidal zone in a marine environment of Zhoushan city, Zhejiang province, China. According to the field investigation and hydrometeorological information, the mean annual temperature of this district is about 20 °C, the seawater immersion time is 4 5 h
Chloride ingress surface
Cl-
Initial coating (Epoxy resin) 50 mm Dike High tide level
100 mm Initial concrete cylinder specimens
Rise and fall of sea water Low tide level
1.2 m Test bar cage of specimens
Fig. 2. Ingress side of specimens in field site test.
Sea level
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The free chloride ion concentration (% wt.conc.)
488
1.200
A1 A2
1.000
A3 A4
0.800
A5 0.600
0.400
0.200
0.000 0
2
4
6
8
10
12
14
16
18
20
Distance from the surface (mm)
The free chloride ion concentratio (% wt.conc.)
Fig. 4. Distribution profile of chloride concentrations in test concrete after exposure 480 d under the marine tidal environment (different w/c ratios).
1.200
A3 A6
1.000
A7 A8
0.800
A9
0.600
0.400
0.200
0.000 0
2
4
6
8
10
12
14
16
18
20
Distance from the surface (mm) Fig. 5. Distribution profile of chloride concentrations in test concrete with the different admixtures after exposure 480 d under the marine tidal environment (w/c ratio 0.50).
Fig. 6. Convection zone depths of w/c ratio 0.50 concrete A3.
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Fig. 7. Convection zone depths of w/c ratio 0.50 BF concrete A6.
Fig. 8. Convection zone depths of w/c ratio 0.50 SF concrete A7.
Fig. 9. Convection zone depths of w/c ratio 0.50 FA concrete A8.
per day, and the time ratio of dry-to-wet in a cycle is about 5:1. The chemical analysis of the seawater in that area indicated that the mean annual content of free chloride ions in the seawater is approximately 13 g/L which is equivalent to the concentration of 13/35 mol/L. The tidal exposure was placed at about 1.2 m above the sea level, so that the concrete specimens were in contact with sea water for about 5 h in a day followed by the dry condition (air), as seen in Fig. 2.
All specimens were placed in a custom-made reinforcing cage and fixed at the testingsite. Fig. 3 shows a snap-shot photo of the site where specimens were placed. 2.4. Measured procedure of free chloride concentration The specimens were taken to the laboratory from the site after they reached the expected exposure time, and grinded into powder
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Fig. 10. Convection zone depths of w/c ratio 0.50 SF/FA concrete A9.
Fig. 11. Peak value of chloride concentrations in w/c ratio 0.50 concrete A3 with the different exposure time.
Fig. 12. Peak value of chloride concentrations in w/c ratio 0.50 concrete A6 with the different exposure time.
starting from the exposed surface into the inside of the specimen with 2 mm interval by using a concrete grinding miller. The pow-
der sample at each depth having a mass of approximately 6 8 g was selected to measure the content of chloride ions. The powder
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Y.-h. Gao et al. / Construction and Building Materials 140 (2017) 485–495 Table 3 Best-fit diffusion coefficients Da for different w/c ratio concrete. Best-fit values (1012 m2/s)
Specimen
A1 A2 A3 A4 A5
60 d
120 d
240 d
360 d
480 d
600 d
2.746 2.874 3.073 3.502 3.894
1.721 1.805 2.035 2.686 3.181
1.562 1.578 1.873 2.057 2.490
1.077 1.240 1.353 1.923 2.180
0.973 1.064 1.152 1.639 2.041
0.838 0.928 1.004 1.434 1.783
Calculated value of A3 Calculated value of A6
Diffusion coefficient (×10
m/s 2)
4.000
Calculated value of A7 Calculated value of A8 3.000
Calculated value of A9 Fitted curve of A3 Fitted curve of A6 Fitted curve of A7
2.000
Fitted curve of A8 Fitted curve of A9
1.000
0.000 0
120
240
360
480
600
Exposure time (d) Fig. 13. Time dependent variation in chloride diffusion coefficient of different admixture concrete with w/c ratio 0.50.
was kept for 2 h in a 150 °C oven after sieving with 0.63 mm screen. After then, it was cooled down in indoor temperature to measure the concentration of free chloride ions [27]. 3. Test results and discussion 3.1. Free chloride concentration in concrete Based on the field exposure tests described above, the concentration distribution profile of free chloride ions in each specimen at a given exposure time can be obtained. Figs. 4 and 5 show the typical concentration distribution profiles, in which each concentration plotted represents the average values of the measured concentrations in the five repeated tests. It can be seen from both figures that, the surface concentration is lower than that at an inner point, and there is a clear convection zone in the concentration distribution profile of free chloride ions. This feature is due to the specimens that were subjected to wet-dry cycles [4,12,17]. 3.2. Convection zone depth of chloride in concrete As discussed above, the distance from the exposed surface to the point where the chloride has a highest concentration is called the convection zone depth of chloride in concrete. Note that the concentration of chloride ions in the specimen was measured at every 2 mm. The convection zone depth of chloride directly measured in each specimen was the integral number of 2 mm (i.e. 2, 4, 6 mm and so on). In order to avoid this problem, a curve fitting technique was used, in which a curve is found to best fit the exper-
imentally measured data in which case the peak point of the theoretically fitted curve is not the same as the peak point of the experimentally measured curve. From the theoretically fitted curve one can easily calculate the convection zone depth and the corresponding chloride concentration at that depth. Fig. 6 shows the convection zone depths of chloride at six different exposed times for specimens with w/c ratio 0.50 (A3). Obviously, there is strong randomness in convection zone depth, in which the mean value of the convection zone depth in concrete (A3) is 3.97 mm. Figs. 7–10 show the convection zone depths of chloride at six different exposed times for specimens with different admixtures (A6–A9). Analogously, the mean value of convection zone depths of concrete A6, A7, A8, A9 are 3.76 mm, 3.21 mm, 4.33 mm, 3.68 mm respectively. Moreover, the mean values of convection zone depths of A6 to A9 are all lower than that of A3 except A8. That is, the addition of fly ash (FA) into concrete has little effect on decreasing the convection zone depth of concrete before 600 d. Overall, as seen from Figs. 6 to 10, there is a clear capillarity adsorption in the surface layer of the concrete owing to the natural dry-wet cycling action, which leads to a convection zone near to the exposed surface. The convection zone depth is in a range from 4 mm to 6 mm, disregarding the difference in exposure time, w/c ratio and with or without the admixture in the specimens. Moreover, there is strong randomness in the data obtained from the tests [4,12,25]. 3.3. Peak value of chloride concentration in concrete According to the exposure test and the chloride ingress curves discussed above, the peak values of chloride concentration in
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specimens A3 are plotted in Fig. 11. Note that the peak value is the largest concentration in the ingress curve, in the present study, which represents the mean concentration obtained from five repeated tests (i.e. identical specimens, under the same exposure time and condition, e.g. Figs. 4 and 5). Fig. 11 indicates that the peak value of the chloride concentration in concrete A3 increases with increasing exposure time. Similarly, other concrete specimens of different w/c ratios or the different admixtures can be analyzed. Fig. 12 shows the variation of the peak value of chloride concentrations in concrete A6 of w/ c ratio 0.50 with the exposure time. The results shown in Figs. 11 and 12 for different concretes illustrate that the peak value of chloride concentration generally increases with the increased exposure time, and the increased w/ c ratio. Except for the chopped basalt fiber (BF) concrete A6, other admixtures in concrete can decrease effectively the peak value of chloride concentration if all other conditions remain the same. Moreover, the statistical analysis for all tested concretes (e.g. Figs. 11 and 12) shows that the increase speed of the peak value of chloride concentration slows down obviously after exposure 360 d. The reason for this is mainly due to the decrease of the concentration difference between the environmental chloride concentration in sea water and the inner layer chloride concentration in the concrete. 3.4. Diffusion coefficient of chloride ions in concrete The error function solution to Fick’s second law of diffusion, given in Eq. (1), is commonly used to fit the experimentally obtained chloride concentration profiles in concrete:
x C x;t ¼ C 0 þ ðC s C 0 Þ 1 erf pffiffiffiffiffiffiffiffi 2 Da t
ð1Þ
where C x;t is the chloride concentration at depth x and time t, C s and C 0 are the surface and initial chloride concentrations, respectively, Da is the apparent diffusion coefficient of chloride ions in concrete, and erf is the statistical error function. Note that, Eq. (1) can only be applied to the diffusion zone. For the present study, there exists a convection zone and thus the surface chloride concentration used in Eq. (1) should be the chloride concentration at the peak point and the depth x should be replaced with ðx xc Þ, where xc is the convection zone depth of chloride in concrete. Note that the initial chloride concentration is zero. Thus, the chloride concentration profile in the diffusion zone in the present case can be expressed as follows:
x xc C x;t ¼ C sm 1 erf pffiffiffiffiffiffiffiffi 2 Da t
ð2Þ
where C sm represents the peak value of the free chloride concentration in concrete. According to Eq. (2), for given xc and C sm , one can determine the diffusion coefficient of chloride ions by using the best fit of Eq. (2) with the experimentally obtained chloride concentration profile. Table 3 shows the results obtained for concrete mixes with different w/c ratios at different exposure times. It is worth noting that the values obtained in Table 3 are the average values obtained from five repeated tests. The data in Table 3 show that although there is no consistent change in C sm and xc with time, the value of Da decreases with the time for all of the tested concretes. Moreover, the apparent diffusion coefficient of each tested concrete tends slowly to be a steady value. In general, the diffusion coefficient of chloride ions in concrete rises with the increase of w/c ratio. It is noticed from the present data that, after the exposure 600 d, the chloride diffusion coefficient in the concrete of w/c ratio 0.40 (A1) is only half of
Table 4 Statistical parameters and probability distribution forms of convection zone depths. Specimens
Mean value
A11 A12 A13 A14 A15 A16 A21 A22 A23 A24 A25 A26 A31 A32 A33 A34 A35 A36 A41 A42 A43 A44 A45 A46 A51 A52 A53 A54 A55 A56 A61 A62 A63 A64 A65 A66 A71 A72 A73 A74 A75 A76 A81 A82 A83 A84 A85 A86 A91 A92 A93 A94 A95 A96
3.94 3.96 4.02 4.02 5.68 3.96 3.90 3.98 3.50 4.02 4.96 4.04 3.20 4.18 3.58 3.78 5.00 4.10 4.16 4.52 4.34 4.18 4.98 4.15 3.94 3.48 3.38 3.80 6.50 4.00 2.96 3.50 4.68 3.30 4.12 4.02 2.14 4.00 3.30 2.56 3.98 3.30 3.20 5.10 4.92 3.94 4.16 4.64 2.06 4.30 3.50 4.12 4.10 4.00
lx
Standard deviation
rx
0.090 0.11 0.29 0.11 0.75 0.06 0.07 0.08 1.00 0.18 1.01 0.11 1.01 0.47 0.89 0.84 0.92 0.14 0.48 1.22 0.34 0.22 0.98 0.13 0.13 0.86 1.73 1.62 0.48 0.07 0.90 1.25 2.00 1.10 0.38 0.18 0.11 0.07 1.10 0.87 0.16 1.00 0.96 1.10 1.03 0.90 0.22 0.95 0.15 0.96 1.26 1.36 0.12 0.07
Distribution form Normal Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Log-normal Gumbel Normal Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Log-normal Gumbel Normal Gumbel Gumbel Gumbel Log-normal Gumbel Normal Gumbel Normal Normal Gumbel Log-normal Gumbel Gumbel Gumbel Gumbel Normal Gumbel Gumbel Normal Normal Gumbel Normal Normal Gumbel Normal
Table 5 Statistical parameters and probability distribution forms of convection zone depths with exposure time. Exposure time
Mean value
60 d 120 d 240 d 360 d 480 d 600 d
3.28 4.11 3.92 3.75 4.83 4.02
lx
Standard deviation 0.92 0.89 1.23 0.99 1.00 0.55
rx
Distribution form Gumbel Gumbel Gumbel Gumbel Normal Gumbel
that in the concrete of w/c ratio 0.60 (A5). This demonstrates that the effect of w/c ratio on the chloride diffusion coefficient in concrete is very significant.
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4.5 A:Exposure 60 d B:Exposure 120 d C:Exposure 240 d D:Exposure 360 d E:Exposure 480 d F:Exposure 600 d
4.0 F
Probability density
3.5 3.0
B
2.5 2.0 1.5 D 1.0
A
E
C
0.5 0.0 3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Convection depth /mm Fig. 14. PDF of convection zone depths in w/c ratio 0.40 concrete A1.
Fig. 13 shows the chloride diffusion coefficients, similarly calculated using Eq. (2), obtained for concrete mixes with different admixtures at different exposure times. It can be seen from Fig. 13 that, the concrete with the admixture SF/FA (A9) has the lowest chloride diffusion coefficients, whereas the other three concretes (A6, A7 and A8) performed differently at different exposure times. For example, after 120 days exposure the concrete with the admixture FA (A8) has lower chloride diffusion coefficient than other two concretes (A6 and A7). Such behavior was also investigated by Thomas et al. [28]. This shows that the addition of admixture FA has an effect on diminishing the chloride diffusion coefficient. Interestingly, the variation of diffusion coefficient with the exposure time is found to be much less in the concrete with admixture SF (A7) than all of other concretes. This illustrates that the addition of admixture SF is an effective way to decrease the chloride diffusion coefficient, but the influence of SF is negligible over time.
Table 5 shows an alternative statistical analysis, which is according to the exposure time, while all other differences are ignored. Note that, the statistical data shown in Tables 4 and 5 are obtained based on five and 45 specimens, respectively. If the exposure times are further ignored, that is the statistical analysis is based on all tested 270 specimens, then the convection zone depths of chloride is found to follow a maximum value distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm.
4. Probability distribution of convection zone depths
x 2:705 fðxÞ ¼ exp exp 0:858
4.1. Statistical parameters and probability distribution forms of convection zone depths The statistical analysis of the experimentally obtained results shows that the distribution of the convection zone depths of chloride in concrete is largely to follow Gumbel distribution. Table 4 summaries the corresponding statistical analysis results, in which lx and rx are the statistical mean value and standard deviation of the convection zone depths, respectively, and the second number after the letter ‘‘A” stands for the exposure time (1–6 represents 60, 120, 240, 360, 480 and 600 d). As shown in Table 4, the statistical mean value of convection zone depths of chloride in tested concrete subjected to the marine tidal environment is in a range from 4 mm to 6 mm, regardless of the exposure time, w/c ratio, or the use of different admixtures. According to existing studies, the mean value of the convection zone depths of chloride in tested concrete is very much similar [4,12,28].
4.2. Probability density of convection zone depth Based on the analysis described above, the probability density function (PDF) and value of the convection zone depths can be calculated. For example, the probability density function of the convection zone depth for the tested concretes mixes A31 and A36 can be expressed as follows: A31:
ð3Þ
A36:
x 4:037 fðxÞ ¼ exp exp 0:109
ð4Þ
Analogously, the probability density function of the convection zone depth for other specimens can be calculated. Fig. 14 plots the PDF curves of the convection zone depth of chloride in concretes of w/c ratio 0.40 (A1) at different exposure times. As shown in Fig. 14, the mean value of the convection zone depth of chloride in concrete A1 increased generally with increasing exposure time, except for exposure 600 d. The mean value of the convection zone depths of chloride did not entirely coincide with the trend of increasing exposure time. This may be due to the tidal environmental factors in the tested interval time (480– 600 d).Such phenomenon is also investigated by Sadati et al. [25], and Bhutta et al. [29].
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2.5
Probability density
2.0
A:Exposure 60 d B:Exposure 120 d C:Exposure 240 d D:Exposure 360 d E:Exposure 480 d F:Exposure 600 d
F
1.5
1.0 A 0.5 D 0.0 -4.0
-2.0
E
C B
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Convection depth /mm Fig. 15. PDF of convection zone depths in w/s ratio 0.60 concrete A5.
Fig. 15 shows the similar PDF curves of the convection zone depths of chloride in concrete with w/c ratio 0.60 (A5). Its main feature is very much similar to that shown in Fig. 14. In summary, Tables 4 and 5 and Figs. 4 and 5 illustrate that there is strong randomness in chloride ingress in concrete exposed to natural dry-wet cycling marine environment, and the convection zone depth of chloride should be treated as a random variable when investigating the durability and service life of RC structures in marine environments. According to the discussion described above, the randomness of the convection zone depth of chloride in concrete under the natural marine tidal environment can be well described by using a maximum value distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm. The influence of the exposure time, w/c ratio, and admixtures on the probabilistic model, and corresponding statistical results (e.g. the mean value and standard deviation) of the convection zone depth of chloride seems rather small. The probability distribution of the convection zone depth of chloride in concrete under the marine tidal environmentcan be described by the following density function model:
x 3:99 fðxÞ ¼ exp exp 0:819
ð5Þ
depth of chloride is in a range from 4 mm to 6 mm under the natural tidal environment in this paper, regardless of the exposure time, water-cement ratio and admixture type. (2). The exposure time, water-cement ratio, and admixture type have negligible effect on the probabilistic form of convection zone depth of chloride. However, different admixture and lower w/c ratio can reduce significantly the diffusion coefficients and peak values of chloride concentration in concrete with time during the drying-wetting process. (3). The convection zone depth of chloride in 270 specimens follows a Gumbel distribution with mean value of 3.99 mm and standard deviation of 1.05 mm.
Acknowledgements The authors would like to gratefully acknowledge the financial supports of the Natural Science Foundation of Zhejiang Province, China (grant nos.: LY17E090007, LY13E090008) and the National Natural Science Foundation of China (grant nos.: 50879079 and 51279181). References
5. Conclusions A field concrete experiment was conducted in this paper, with different water-cement ratios and admixtures, under a natural marine tidal zone for the longest exposure time 600 d. Based on the measured free chloride concentration and the convection zone depth of chloride in test concrete, 270 chloride ingress curves were acquired, and then the coefficients of chloride and the probability distribution forms of convection zone depth of chloride in concrete were analyzed. The following conclusions were drawn. (1). Under a natural marine tidal environment, there is an obvious change of temperature and humidity. Due to the capillary adsorption, chloride ion will migrate back and forth at the surface of concrete. The mean value of convection zone
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Probability distribution of convection zone depth of chloride in concrete in a marine tidal environment Yan-hong Gao, Jun-zhi Zhang ⇑, Shan Zhang, Yu-rong Zhang College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou 310014, PR China
h i g h l i g h t s Convection depth of chloride with different W/C ratios, admixtures and exposure time was researched. Convection depths of chloride were appeared in all tested concretes. Mean value of convection zone depth of chloride is in a range from 4 mm to 6 mm. Convection zone depth of chloride follows a Gumbel distribution.
a r t i c l e
i n f o
Article history: Received 2 December 2016 Received in revised form 8 February 2017 Accepted 24 February 2017
Keywords: Concrete Chloride Convection zone depth Probability distribution Marine tidal environment
a b s t r a c t Based on a field experiment of concrete exposed to a marine tidal environment and according to measured chloride ingress data, diffusion coefficients of chloride ion in concrete after different exposure time are fitted by Fick-second law. Concrete with different types of admixture are tested in this paper, with water-cement ratios of 0.40, 0.45, 0.50, 0.55 and 0.60, respectively. Based on 270 group chloride ingress curves of test concrete, the convection zone depth of chloride and peak value of chloride concentration in concrete are acquired. According to chloride ingress curves of concrete with different water-cement ratio under the same exposure time, the probability distribution forms of convection zone depth of chloride are investigated by statistical test using the log-normal distribution, the normal distribution and the maximum value distribution, respectively. The statistical results show that the mean value of convection zone depths of chloride is in a range from 4 mm to 6 mmin this paper, disregarding the difference in exposure time, water-cement ratio and with or without the admixture in the specimens. The majority of convection zone depths of chloride in different exposure time and water-cement ratios, as well as the admixture, follow a Gumbel distribution, and the convection zone depth of chloride in total 270 specimens follows a Gumbel distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm. The exposure time, water-cement ratio and different admixture have negligible effect on the mean value and the probabilistic characteristic of convection zone depth of chloride, however, different admixture and lower water-cement ratio can significantly reduce the diffusion coefficients and peak values of chloride concentration in concrete. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The penetration of chloride ions through concrete cover to steel reinforcement resulting in the corrosion of reinforcing steel is a major problem of structures, particularly those exposed to marine environments [1,2]. The existing studies on chloride-induced reinforcing steel corrosion have showed that the penetration of chloride ions in concrete is a complex process, depending on many factors, including not only the concrete material itself but also ⇑ Corresponding author. E-mail address: [email protected] (J.-z. Zhang). http://dx.doi.org/10.1016/j.conbuildmat.2017.02.134 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
the environmental condition where the concrete is exposed to and the loading condition where the concrete structure is subjected to [3–5]. Most of these factors are the random variables. For instance, in some studies, the chloride diffusion coefficient, the chloride concentration calculated on the surface of reinforcing steel bar, the thickness of concrete cover, the threshold chloride concentration, and the convection zone depth of chloride ions in concrete cover were all modeled as the random variables [6–8]. Many concrete structures exposed to marine environment may be subjected to dry-wet cycles, in which moisture transport can also take place in part of the concrete cover. In this case, the transport of chloride ions involves not only the diffusion but also the
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convection. The region which involves both diffusion and convection of chloride ions is often called the convection zone. The convection zone is normally a thin layer from the exposure surface to the location where the chloride concentration has a peak value. The thickness of the convection zone is usually defined to be the convection zone depth [9]. Under wet-dry cycles in natural tidal environment, the convection zone depth is considered as a key variable, which can affect the prediction of chloride concentration in concrete cover, particularly when Fick’s second law is used to calculate the chloride concentration [10,11]. In order to determine the convection zone depth in concrete cover, different artificial simulation environments and field tests have been carried out. It was reported that the depth of washout or convection zone is approximately 7 mm for Portland cement mixture, 14–15 mm for fly ash mixture [12], and 14 mm for marine concretes [13]. Other ranges from 20 mm to 30 mm [14], and from 5 mm to 15 mm were also suggested in literature [15]. In addition, it was found that the depth of convection zone increases with the cracking width [8,16], and thus it is likely that the depth of convection zone will increase with the concrete service life. The mean value of the convection zone depth was found quite different in various concretes exposed to different environments, varying from 5 mm to 20 mm [10,13,17–19]. According to the analysis of 127 chloride ingress curves obtained from concrete under a marine environment, the convection zone depth was found to follow a Beta distribution with l = 8.9 mm, r = 63%, a = 0 and b = 50, in regard of the chloride source and water-cement ratio [20]. Note that, the results described above on the chloride convection zone depth are mostly based on the measured data obtained by using the deterministic model. Even if there was probabilistic research on convection zone depth of chloride, they were all based on the mean value. And the research on the randomness of convection zone depth of chloride is few. In reality, however, there is strong randomness in the process of the chloride ingress into concrete, and the relevant influence parameters on RC structures’ service life such as the chloride diffusion coefficient and the initial corrosion time of the steel bars in concrete are random variables. Therefore, from the durability point of view, the lifetime assessment of a deteriorating RC structure should be carried out by using the probabilistic method and considering the uncertainties of materials, structures, and environmental conditions [21–23]. In a dry-wet cycling environment, chloride ingress into concrete can be divided into two typical zones, namely the convection and diffusion zones. Let the convection zone depth Xc, then the typical
distribution profile of free chloride ions in the convection and diffusion zones can be plotted as what is shown in Fig. 1. Note that the Fick’s second law is commonly used to represent the chloride concentration profile in concrete [24]. However, when a convection zone is involved [4,5,25,26], the Fick’s second law can only be applied in the diffusion zone and thus it needs to know the convection zone depth and the corresponding chloride concentration at that point in order to determine the chloride distribution in the diffusion zone. In this paper an experimental study to determine the convection zone depth and the corresponding chloride concentration at that depth was carried out for concretes with different water to cement ratios, exposed to a marine tidal environment up to 600 d. The experimental work was performed at different stages and the influences of exposed time, water to cement ratio, and concrete admixture on the convection zone depth and corresponding chloride concentration at that depth are examined. The statistical distributions of convection zone depth and corresponding chloride concentration at that depth are also discussed. 2. Mix proportion of concrete and test environment 2.1. Raw material and mix proportion of tested concrete All tested concretes presented in this study were prepared using coarse aggregates of the maximum size 40 mm, fine aggregates (sand) of the fineness modulus 2.4, and Qian-Chao complex Portland cement (PC32.5). The water used in the mix as well as for curing is the laboratory tap water. The admixtures used in tested concretes include chopped basalt fiber (BF) with filament diameter 17 20 lm and tensile strength 390 450 MPa, silica fume (SF) with Bertrand specific area 21,000 m2/kg, and stair fly ash (FA) with fineness 4.6% and apparent density of 2240 kg/m3. Table 1 gives the details of the mix proportion of the tested concretes, in which the percentage of admixture represents the weight percentage of the admixture in the binder. 2.2. Specimen casting The preparation of specimens of the tested concrete is in accordance with the Chinese standards of SL352-2006. Two types of specimens were cast. One is the cubic specimens of size 150 150 150 mm, which were used for the compressive strength test. The other is the cylindrical specimens of size /
Fig. 1. Typical distribution of free chlorides in convection and diffusion zones.
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Y.-h. Gao et al. / Construction and Building Materials 140 (2017) 485–495 Table 1 Mix proportion of experimental concrete in the natural tidal zone (kg/m3). Specimen No.
w/b
Cement
Aggregate
Sand
BF Wt/Percent
SF Wt/Percent
FA Wt/Percent
A1 A2 A3 A4 A5 A6 A7 A8 A9
0.40 0.45 0.50 0.55 0.60 0.50 0.50 0.50 0.50
475 422 380 346 317 380 361 304 304
1174 1204 1229 1249 1269 1229 1229 1229 1229
552 567 578 589 597 578 578 578 578
0 0 0 0 0 1.03/(0.062%) 0 0 0
0 0 0 0 0 0 19/(5%) 0 19/(5%)
0 0 0 0 0 0 0 76/(20%) 57/(15%)
Table 2 Compressive strengths of test concrete (MPa). Specimen
Admixtures
Compressive strength
A1 A2 A3 A4 A5 A6 A7 A8 A9
— — — — — BF, 0.062% SF, 5% FA, 20% SF/FA, 5%/15%
32.5 27.2 23.9 20.6 17.1 24.6 25.5 15.8 19.7
100 50 mm, which were used for chloride ingress test. The former were tested after the cubic specimens were cured for 28 days in a standard laboratory curing condition as specified in the standard test SL352-2006 of China (temperature 20 °C ± 5 °C, relative humidity 95%). Table 2 shows the corresponding compressive strength test results. The lowest compressive strength was found in specimen A8 (15.8 MPa); whereas the highest compressive strength was found in specimen A1 (32.5 MPa), the results of which seem to be consistent with what reported in literature [25,26]. For the chloride ingress test, there were 30 (5 6) specimens for each mix type, in which 5 represents the repeated tests, and 6 represents at six different exposure times (60, 120, 240, 360, 480 and 600 days). Before the cylindrical specimens were transported to the site, they were cured for 28 days in a standard laboratory curing condition as specified in the standard test SL352-2006 of China (temperature 20 °C ± 5 °C, relative humidity 95%). In order to simulate the one-dimension ingress, all other surfaces (except for one circular surface) in the specimens were sealed
Fig. 3. Photo of site exposure tests.
using epoxy resin, so that the chloride ions can only transport along the longitudinal direction of the cylinder. 2.3. Exposure environment and testing methods The chloride ingress test was carried out in the natural tidal zone in a marine environment of Zhoushan city, Zhejiang province, China. According to the field investigation and hydrometeorological information, the mean annual temperature of this district is about 20 °C, the seawater immersion time is 4 5 h
Chloride ingress surface
Cl-
Initial coating (Epoxy resin) 50 mm Dike High tide level
100 mm Initial concrete cylinder specimens
Rise and fall of sea water Low tide level
1.2 m Test bar cage of specimens
Fig. 2. Ingress side of specimens in field site test.
Sea level
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The free chloride ion concentration (% wt.conc.)
488
1.200
A1 A2
1.000
A3 A4
0.800
A5 0.600
0.400
0.200
0.000 0
2
4
6
8
10
12
14
16
18
20
Distance from the surface (mm)
The free chloride ion concentratio (% wt.conc.)
Fig. 4. Distribution profile of chloride concentrations in test concrete after exposure 480 d under the marine tidal environment (different w/c ratios).
1.200
A3 A6
1.000
A7 A8
0.800
A9
0.600
0.400
0.200
0.000 0
2
4
6
8
10
12
14
16
18
20
Distance from the surface (mm) Fig. 5. Distribution profile of chloride concentrations in test concrete with the different admixtures after exposure 480 d under the marine tidal environment (w/c ratio 0.50).
Fig. 6. Convection zone depths of w/c ratio 0.50 concrete A3.
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489
Fig. 7. Convection zone depths of w/c ratio 0.50 BF concrete A6.
Fig. 8. Convection zone depths of w/c ratio 0.50 SF concrete A7.
Fig. 9. Convection zone depths of w/c ratio 0.50 FA concrete A8.
per day, and the time ratio of dry-to-wet in a cycle is about 5:1. The chemical analysis of the seawater in that area indicated that the mean annual content of free chloride ions in the seawater is approximately 13 g/L which is equivalent to the concentration of 13/35 mol/L. The tidal exposure was placed at about 1.2 m above the sea level, so that the concrete specimens were in contact with sea water for about 5 h in a day followed by the dry condition (air), as seen in Fig. 2.
All specimens were placed in a custom-made reinforcing cage and fixed at the testingsite. Fig. 3 shows a snap-shot photo of the site where specimens were placed. 2.4. Measured procedure of free chloride concentration The specimens were taken to the laboratory from the site after they reached the expected exposure time, and grinded into powder
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Fig. 10. Convection zone depths of w/c ratio 0.50 SF/FA concrete A9.
Fig. 11. Peak value of chloride concentrations in w/c ratio 0.50 concrete A3 with the different exposure time.
Fig. 12. Peak value of chloride concentrations in w/c ratio 0.50 concrete A6 with the different exposure time.
starting from the exposed surface into the inside of the specimen with 2 mm interval by using a concrete grinding miller. The pow-
der sample at each depth having a mass of approximately 6 8 g was selected to measure the content of chloride ions. The powder
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Y.-h. Gao et al. / Construction and Building Materials 140 (2017) 485–495 Table 3 Best-fit diffusion coefficients Da for different w/c ratio concrete. Best-fit values (1012 m2/s)
Specimen
A1 A2 A3 A4 A5
60 d
120 d
240 d
360 d
480 d
600 d
2.746 2.874 3.073 3.502 3.894
1.721 1.805 2.035 2.686 3.181
1.562 1.578 1.873 2.057 2.490
1.077 1.240 1.353 1.923 2.180
0.973 1.064 1.152 1.639 2.041
0.838 0.928 1.004 1.434 1.783
Calculated value of A3 Calculated value of A6
Diffusion coefficient (×10
m/s 2)
4.000
Calculated value of A7 Calculated value of A8 3.000
Calculated value of A9 Fitted curve of A3 Fitted curve of A6 Fitted curve of A7
2.000
Fitted curve of A8 Fitted curve of A9
1.000
0.000 0
120
240
360
480
600
Exposure time (d) Fig. 13. Time dependent variation in chloride diffusion coefficient of different admixture concrete with w/c ratio 0.50.
was kept for 2 h in a 150 °C oven after sieving with 0.63 mm screen. After then, it was cooled down in indoor temperature to measure the concentration of free chloride ions [27]. 3. Test results and discussion 3.1. Free chloride concentration in concrete Based on the field exposure tests described above, the concentration distribution profile of free chloride ions in each specimen at a given exposure time can be obtained. Figs. 4 and 5 show the typical concentration distribution profiles, in which each concentration plotted represents the average values of the measured concentrations in the five repeated tests. It can be seen from both figures that, the surface concentration is lower than that at an inner point, and there is a clear convection zone in the concentration distribution profile of free chloride ions. This feature is due to the specimens that were subjected to wet-dry cycles [4,12,17]. 3.2. Convection zone depth of chloride in concrete As discussed above, the distance from the exposed surface to the point where the chloride has a highest concentration is called the convection zone depth of chloride in concrete. Note that the concentration of chloride ions in the specimen was measured at every 2 mm. The convection zone depth of chloride directly measured in each specimen was the integral number of 2 mm (i.e. 2, 4, 6 mm and so on). In order to avoid this problem, a curve fitting technique was used, in which a curve is found to best fit the exper-
imentally measured data in which case the peak point of the theoretically fitted curve is not the same as the peak point of the experimentally measured curve. From the theoretically fitted curve one can easily calculate the convection zone depth and the corresponding chloride concentration at that depth. Fig. 6 shows the convection zone depths of chloride at six different exposed times for specimens with w/c ratio 0.50 (A3). Obviously, there is strong randomness in convection zone depth, in which the mean value of the convection zone depth in concrete (A3) is 3.97 mm. Figs. 7–10 show the convection zone depths of chloride at six different exposed times for specimens with different admixtures (A6–A9). Analogously, the mean value of convection zone depths of concrete A6, A7, A8, A9 are 3.76 mm, 3.21 mm, 4.33 mm, 3.68 mm respectively. Moreover, the mean values of convection zone depths of A6 to A9 are all lower than that of A3 except A8. That is, the addition of fly ash (FA) into concrete has little effect on decreasing the convection zone depth of concrete before 600 d. Overall, as seen from Figs. 6 to 10, there is a clear capillarity adsorption in the surface layer of the concrete owing to the natural dry-wet cycling action, which leads to a convection zone near to the exposed surface. The convection zone depth is in a range from 4 mm to 6 mm, disregarding the difference in exposure time, w/c ratio and with or without the admixture in the specimens. Moreover, there is strong randomness in the data obtained from the tests [4,12,25]. 3.3. Peak value of chloride concentration in concrete According to the exposure test and the chloride ingress curves discussed above, the peak values of chloride concentration in
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specimens A3 are plotted in Fig. 11. Note that the peak value is the largest concentration in the ingress curve, in the present study, which represents the mean concentration obtained from five repeated tests (i.e. identical specimens, under the same exposure time and condition, e.g. Figs. 4 and 5). Fig. 11 indicates that the peak value of the chloride concentration in concrete A3 increases with increasing exposure time. Similarly, other concrete specimens of different w/c ratios or the different admixtures can be analyzed. Fig. 12 shows the variation of the peak value of chloride concentrations in concrete A6 of w/ c ratio 0.50 with the exposure time. The results shown in Figs. 11 and 12 for different concretes illustrate that the peak value of chloride concentration generally increases with the increased exposure time, and the increased w/ c ratio. Except for the chopped basalt fiber (BF) concrete A6, other admixtures in concrete can decrease effectively the peak value of chloride concentration if all other conditions remain the same. Moreover, the statistical analysis for all tested concretes (e.g. Figs. 11 and 12) shows that the increase speed of the peak value of chloride concentration slows down obviously after exposure 360 d. The reason for this is mainly due to the decrease of the concentration difference between the environmental chloride concentration in sea water and the inner layer chloride concentration in the concrete. 3.4. Diffusion coefficient of chloride ions in concrete The error function solution to Fick’s second law of diffusion, given in Eq. (1), is commonly used to fit the experimentally obtained chloride concentration profiles in concrete:
x C x;t ¼ C 0 þ ðC s C 0 Þ 1 erf pffiffiffiffiffiffiffiffi 2 Da t
ð1Þ
where C x;t is the chloride concentration at depth x and time t, C s and C 0 are the surface and initial chloride concentrations, respectively, Da is the apparent diffusion coefficient of chloride ions in concrete, and erf is the statistical error function. Note that, Eq. (1) can only be applied to the diffusion zone. For the present study, there exists a convection zone and thus the surface chloride concentration used in Eq. (1) should be the chloride concentration at the peak point and the depth x should be replaced with ðx xc Þ, where xc is the convection zone depth of chloride in concrete. Note that the initial chloride concentration is zero. Thus, the chloride concentration profile in the diffusion zone in the present case can be expressed as follows:
x xc C x;t ¼ C sm 1 erf pffiffiffiffiffiffiffiffi 2 Da t
ð2Þ
where C sm represents the peak value of the free chloride concentration in concrete. According to Eq. (2), for given xc and C sm , one can determine the diffusion coefficient of chloride ions by using the best fit of Eq. (2) with the experimentally obtained chloride concentration profile. Table 3 shows the results obtained for concrete mixes with different w/c ratios at different exposure times. It is worth noting that the values obtained in Table 3 are the average values obtained from five repeated tests. The data in Table 3 show that although there is no consistent change in C sm and xc with time, the value of Da decreases with the time for all of the tested concretes. Moreover, the apparent diffusion coefficient of each tested concrete tends slowly to be a steady value. In general, the diffusion coefficient of chloride ions in concrete rises with the increase of w/c ratio. It is noticed from the present data that, after the exposure 600 d, the chloride diffusion coefficient in the concrete of w/c ratio 0.40 (A1) is only half of
Table 4 Statistical parameters and probability distribution forms of convection zone depths. Specimens
Mean value
A11 A12 A13 A14 A15 A16 A21 A22 A23 A24 A25 A26 A31 A32 A33 A34 A35 A36 A41 A42 A43 A44 A45 A46 A51 A52 A53 A54 A55 A56 A61 A62 A63 A64 A65 A66 A71 A72 A73 A74 A75 A76 A81 A82 A83 A84 A85 A86 A91 A92 A93 A94 A95 A96
3.94 3.96 4.02 4.02 5.68 3.96 3.90 3.98 3.50 4.02 4.96 4.04 3.20 4.18 3.58 3.78 5.00 4.10 4.16 4.52 4.34 4.18 4.98 4.15 3.94 3.48 3.38 3.80 6.50 4.00 2.96 3.50 4.68 3.30 4.12 4.02 2.14 4.00 3.30 2.56 3.98 3.30 3.20 5.10 4.92 3.94 4.16 4.64 2.06 4.30 3.50 4.12 4.10 4.00
lx
Standard deviation
rx
0.090 0.11 0.29 0.11 0.75 0.06 0.07 0.08 1.00 0.18 1.01 0.11 1.01 0.47 0.89 0.84 0.92 0.14 0.48 1.22 0.34 0.22 0.98 0.13 0.13 0.86 1.73 1.62 0.48 0.07 0.90 1.25 2.00 1.10 0.38 0.18 0.11 0.07 1.10 0.87 0.16 1.00 0.96 1.10 1.03 0.90 0.22 0.95 0.15 0.96 1.26 1.36 0.12 0.07
Distribution form Normal Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Log-normal Gumbel Normal Normal Gumbel Gumbel Gumbel Normal Gumbel Gumbel Log-normal Gumbel Normal Gumbel Gumbel Gumbel Log-normal Gumbel Normal Gumbel Normal Normal Gumbel Log-normal Gumbel Gumbel Gumbel Gumbel Normal Gumbel Gumbel Normal Normal Gumbel Normal Normal Gumbel Normal
Table 5 Statistical parameters and probability distribution forms of convection zone depths with exposure time. Exposure time
Mean value
60 d 120 d 240 d 360 d 480 d 600 d
3.28 4.11 3.92 3.75 4.83 4.02
lx
Standard deviation 0.92 0.89 1.23 0.99 1.00 0.55
rx
Distribution form Gumbel Gumbel Gumbel Gumbel Normal Gumbel
that in the concrete of w/c ratio 0.60 (A5). This demonstrates that the effect of w/c ratio on the chloride diffusion coefficient in concrete is very significant.
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4.5 A:Exposure 60 d B:Exposure 120 d C:Exposure 240 d D:Exposure 360 d E:Exposure 480 d F:Exposure 600 d
4.0 F
Probability density
3.5 3.0
B
2.5 2.0 1.5 D 1.0
A
E
C
0.5 0.0 3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Convection depth /mm Fig. 14. PDF of convection zone depths in w/c ratio 0.40 concrete A1.
Fig. 13 shows the chloride diffusion coefficients, similarly calculated using Eq. (2), obtained for concrete mixes with different admixtures at different exposure times. It can be seen from Fig. 13 that, the concrete with the admixture SF/FA (A9) has the lowest chloride diffusion coefficients, whereas the other three concretes (A6, A7 and A8) performed differently at different exposure times. For example, after 120 days exposure the concrete with the admixture FA (A8) has lower chloride diffusion coefficient than other two concretes (A6 and A7). Such behavior was also investigated by Thomas et al. [28]. This shows that the addition of admixture FA has an effect on diminishing the chloride diffusion coefficient. Interestingly, the variation of diffusion coefficient with the exposure time is found to be much less in the concrete with admixture SF (A7) than all of other concretes. This illustrates that the addition of admixture SF is an effective way to decrease the chloride diffusion coefficient, but the influence of SF is negligible over time.
Table 5 shows an alternative statistical analysis, which is according to the exposure time, while all other differences are ignored. Note that, the statistical data shown in Tables 4 and 5 are obtained based on five and 45 specimens, respectively. If the exposure times are further ignored, that is the statistical analysis is based on all tested 270 specimens, then the convection zone depths of chloride is found to follow a maximum value distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm.
4. Probability distribution of convection zone depths
x 2:705 fðxÞ ¼ exp exp 0:858
4.1. Statistical parameters and probability distribution forms of convection zone depths The statistical analysis of the experimentally obtained results shows that the distribution of the convection zone depths of chloride in concrete is largely to follow Gumbel distribution. Table 4 summaries the corresponding statistical analysis results, in which lx and rx are the statistical mean value and standard deviation of the convection zone depths, respectively, and the second number after the letter ‘‘A” stands for the exposure time (1–6 represents 60, 120, 240, 360, 480 and 600 d). As shown in Table 4, the statistical mean value of convection zone depths of chloride in tested concrete subjected to the marine tidal environment is in a range from 4 mm to 6 mm, regardless of the exposure time, w/c ratio, or the use of different admixtures. According to existing studies, the mean value of the convection zone depths of chloride in tested concrete is very much similar [4,12,28].
4.2. Probability density of convection zone depth Based on the analysis described above, the probability density function (PDF) and value of the convection zone depths can be calculated. For example, the probability density function of the convection zone depth for the tested concretes mixes A31 and A36 can be expressed as follows: A31:
ð3Þ
A36:
x 4:037 fðxÞ ¼ exp exp 0:109
ð4Þ
Analogously, the probability density function of the convection zone depth for other specimens can be calculated. Fig. 14 plots the PDF curves of the convection zone depth of chloride in concretes of w/c ratio 0.40 (A1) at different exposure times. As shown in Fig. 14, the mean value of the convection zone depth of chloride in concrete A1 increased generally with increasing exposure time, except for exposure 600 d. The mean value of the convection zone depths of chloride did not entirely coincide with the trend of increasing exposure time. This may be due to the tidal environmental factors in the tested interval time (480– 600 d).Such phenomenon is also investigated by Sadati et al. [25], and Bhutta et al. [29].
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2.5
Probability density
2.0
A:Exposure 60 d B:Exposure 120 d C:Exposure 240 d D:Exposure 360 d E:Exposure 480 d F:Exposure 600 d
F
1.5
1.0 A 0.5 D 0.0 -4.0
-2.0
E
C B
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Convection depth /mm Fig. 15. PDF of convection zone depths in w/s ratio 0.60 concrete A5.
Fig. 15 shows the similar PDF curves of the convection zone depths of chloride in concrete with w/c ratio 0.60 (A5). Its main feature is very much similar to that shown in Fig. 14. In summary, Tables 4 and 5 and Figs. 4 and 5 illustrate that there is strong randomness in chloride ingress in concrete exposed to natural dry-wet cycling marine environment, and the convection zone depth of chloride should be treated as a random variable when investigating the durability and service life of RC structures in marine environments. According to the discussion described above, the randomness of the convection zone depth of chloride in concrete under the natural marine tidal environment can be well described by using a maximum value distribution with the mean value of 3.99 mm and the standard deviation of 1.05 mm. The influence of the exposure time, w/c ratio, and admixtures on the probabilistic model, and corresponding statistical results (e.g. the mean value and standard deviation) of the convection zone depth of chloride seems rather small. The probability distribution of the convection zone depth of chloride in concrete under the marine tidal environmentcan be described by the following density function model:
x 3:99 fðxÞ ¼ exp exp 0:819
ð5Þ
depth of chloride is in a range from 4 mm to 6 mm under the natural tidal environment in this paper, regardless of the exposure time, water-cement ratio and admixture type. (2). The exposure time, water-cement ratio, and admixture type have negligible effect on the probabilistic form of convection zone depth of chloride. However, different admixture and lower w/c ratio can reduce significantly the diffusion coefficients and peak values of chloride concentration in concrete with time during the drying-wetting process. (3). The convection zone depth of chloride in 270 specimens follows a Gumbel distribution with mean value of 3.99 mm and standard deviation of 1.05 mm.
Acknowledgements The authors would like to gratefully acknowledge the financial supports of the Natural Science Foundation of Zhejiang Province, China (grant nos.: LY17E090007, LY13E090008) and the National Natural Science Foundation of China (grant nos.: 50879079 and 51279181). References
5. Conclusions A field concrete experiment was conducted in this paper, with different water-cement ratios and admixtures, under a natural marine tidal zone for the longest exposure time 600 d. Based on the measured free chloride concentration and the convection zone depth of chloride in test concrete, 270 chloride ingress curves were acquired, and then the coefficients of chloride and the probability distribution forms of convection zone depth of chloride in concrete were analyzed. The following conclusions were drawn. (1). Under a natural marine tidal environment, there is an obvious change of temperature and humidity. Due to the capillary adsorption, chloride ion will migrate back and forth at the surface of concrete. The mean value of convection zone
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