Abstract
Diffusion coefficient from chloride migration test is currently used; however this cannot provide a conventional solution like total chloride contents since it depicts only ion migration velocity in electrical field. This paper proposes a simple analysis technique for chloride behavior using apparent diffusion coefficient from neural network algorithm with time-dependent diffusion phenomena. For this work, thirty mix proportions of high performance concrete are prepared and their diffusion coefficients are obtained after long term-NaCl submerged test. Considering time-dependent diffusion coefficient based on Fick’s 2nd Law and NNA (neural network algorithm), analysis technique for chloride penetration is proposed. The applicability of the proposed technique is verified through the results from accelerated test, long term submerged test, and field investigation results.
1. Introduction
Chloride ions induced into concrete cause a severe corrosion in embedded steel and the durability degradation propagates to structural safety problem [1]. In the earlier researches on deterioration of chloride attack, studies based on field investigations and apparent diffusion have been performed [2–4]. Recently, micromodels based on mass conservation law and behaviors in early aged concrete like porosity, hydration, and saturation have been proposed [5–7]. Furthermore various phenomena like enlarged diffusion and permeation due to cracks and cold joint are considered for quantitative modeling on chloride penetration [8, 9].
Apparent diffusion coefficient based on Fick’s 2nd law is conventionally utilized for evaluating chloride behavior, however migration test and the related techniques are frequently utilized for measuring a resistance to chloride penetration [10, 11] since apparent diffusion coefficient experimentally obtained needs considerably long period. Chloride diffusion coefficients from migration tests indicate ion velocity in electrical field so that they cannot be directly employed to Fick’ 2nd law. For evaluation of chloride behavior using diffusion coefficient from migration test, complicated analysis frame is required [12, 13]. For evaluation of total chloride content, special relationship between free and bound chloride ion, so called isotherm, should be considered in the analysis frame [6, 14, 15]. Apparent diffusion coefficient can provide direct solution-chloride content based on Fick’s 2nd Law to engineers, and this technique has been widely applied for its simple formulation and several familiar-powerful programs like Life 365 [3, 16]. Additionally several engineering advantages like easy employing time effect on diffusion behavior [16] and random variables for stochastic approach [8] are found through treating apparent diffusion coefficient.
NNA (neural network algorithm) is one of the optimization techniques and this has been widely utilized for determination of mix proportions and strength evaluation in concrete research field [17–20]. For analysis of chloride behavior and carbonation, NNA technique is recently adopted [21, 22] but the related analysis technique needs such complicated micromodels and major assumptions that it is not widely used for engineers.
In this paper, apparent diffusion coefficients, which can provide a direct solution (chloride content), are obtained from chloride-submerged condition for 6 months. Major mix components are selected as neurons and training for learning is carried out for optimum apparent diffusion coefficients. The simulated diffusion coefficients are verified with test results. A simple and deterministic analysis technique for chloride behavior is proposed considering time-dependent diffusion characteristics and the apparent diffusion coefficient from NNA. In this paper, diffusion coefficients from various HPC (high performance concrete) mix proportions, NNA application for reasonable selection of diffusion coefficients, and simple technique for chloride penetration prediction are dealt with. In Figure 1, flow chart for the work is shown.
2. Outline of NNA
It is reported that NNA was started by McCulloch and Pitt [23]. A neuron as a unit with process of stimulus and reaction is modeled in the system. The training for learning a data set is conducted with connection strength, transfer function, and biases. The errors between calculated and expected results are reduced with increasing epochs. The training for learning is completed when the error decreases to a target convergence level. In this paper, a back-propagation algorithm is adopted for the neural network. Figure 2 shows an outline of simple neural network architecture [22, 24].
(a) Simple neural network architecture
(b) Activation function
In this network, each element of input is connected to each neuron input through the weight matrix. Neurons () and activated values () in the hidden layer are formulated as (1) and (2). Activated value, can be written as (3). Consider where is input vector, is weight or connection strength, is transfer function, and is bias. In the back-propagation, error () is calculated through (4) considering target value (). Consider For minimizing the error, connection strength () is modified backward form neurons in output layer like where and are gradients of the total error, and is the learning rate.
After the modification of connection strength, NNA repeats the process of calculation and modification until the error decreases within the target convergence.
For the data set, each input should have boundary limits from 0.0 to 1.0. Through data process like (6), each value satisfies the boundary limit. Consider where is input value for training, is actual input data, and and are maximum and minimum values of input data. After calculation, the output value with a range of 0.0~1.0 is obtained and it should be converted to actual value using (6).
3. Test Program for Apparent Diffusion Coefficient
3.1. Outline of Test Program
In this section, tests for learning and training of NNA are explained. Thirty mix proportions for HPC are prepared. Target slump and air content are mm and %, respectively. Three w/b (water to binder) ratios are set as as 0.37, 0.42, and 0.47. After 28 days of water curing, the specimens were kept in 3.5% of NaCl solution for 6 months. For 1-dimensinal intrusion of chloride ion, sides and bottoms were coated with epoxy except top surface. After 6 months of submerging in NaCl solution, chloride profiles were measured based on AASHTO T 260. Through regression of chloride profile, surface chloride contents and apparent diffusion coefficients are obtained. For binding materials, OPC (ordinary portland cement) was used. GGBFS (ground granulated blast furnace slag), FA (fly ash), and SF (silica fume) were added for mineral admixtures. In Table 1, chemical compositions and physical properties of cement and the used mineral admixtures are listed. The physical properties of aggregates are listed in Table 2. Thirty mix properties which are used for learning and training of NNA are listed in Table 3.
3.2. Test Results
3.2.1. Compressive Strength with Ages
Compressive strength is measured at the age of 7, 28, 91, and 270 days. In Figure 3, the results of compressive strength with different ages are shown. The results show typical strength development, higher strength with lower w/b ratio. The smallest strength at the age 7 days is measured in f30o70 (30% replacement of FA) in Figure 3. Compared with the results in OPC, the strength ratio is only 69.9%, however, in the long term (270 days), concrete with mineral admixtures mostly shows higher strength than OPC concrete. It is reported that the ability of a mineral admixture to react with calcium hydroxide present in the hydrated Portland cement paste and to form additional calcium silicate hydrates can lead to significant reduction in porosity of both the matrix and the transition zone. Consequently, considerable improvement in ultimate strength and water-tightness can be achieved by incorporation of mineral admixtures [25]. Silica fume is very effective to strength development both in the short and in the long term. In the case of 270 days, the highest strength is measured in f10s05 (17.5% increase for OPC result, w/b 0.37), g30s05 (16.7% increase for OPC result, w/b 0.42), and g30s05 (31.0% increase for OPC result, w/b 0.47). In many researches, the effect of silica fume is found to be considerable both to strength and to durability [26, 27].
(a) w/b 0.37 series
(b) w/b 0.42 series
(c) w/b 0.47 series
3.2.2. Apparent Diffusion Coefficient
In Table 4, the results of apparent diffusion coefficient are listed. The maximum and minimum results are measured in o100-47 (7.3 10−12 m2/sec) and g30s05-37 (1.4 10−12 m2/sec), respectively. The lower w/b ratio concrete has, the lower diffusion coefficients are measured. The mix proportions with mineral admixture have lower results than those with only OPC. Since the mix proportions with lower w/b ratio and large amount of binder have more hydrates amount and smaller porosity, penetration of chloride ion is impeded [7, 13, 15]. Concrete with FA can have large amount of hydrates due to pozzolan reaction and this leads low diffusion of chloride ion. In the case of GGBFS, low diffusion coefficients are measured due to the small porosity from latent hydraulic properties and chemical binding of chloride ion [5, 6, 28]. The comparisons of mineral admixture group with OPC series are shown in Figure 4.
(a) OPC and slag mixture series with various w/b ratios
(b) OPC and fly ash series with various w/b ratios
(c) OPC and combined mixture series with various w/b ratios
In order to evaluate the relationship between strength and diffusion coefficient, linear regression analysis is performed and the results are shown in Figure 5 with test results.
The regression results are listed in (7a)~(7d). Consider where denotes the compressive strength (MPa) at days, is measured diffusion coefficient (×1012 m2/sec). It is observed the gradients of (7a), (7b), (7c), and (7d) increase with ages and this shows higher strength is related with lower diffusion coefficient with aging.
3.2.3. NNA Application to Diffusion Coefficient
NNA technique is applied to simulation of diffusion coefficient and the results are compared with those from multiregression analysis. Seven mix components like w/b ratio, unit content of cement, GGBFS, FA, SF, sand, and coarse aggregate are considered as input neurons. Output neuron is fixed as apparent diffusion coefficient. MATLAB program is used for this regression analysis. Back propagation algorithm is adopted and Tan-Sigmoid function is used for transfer function among various functions like linear transfer and log-sigmoid [24]. Training number is set as 2,000 and the error to target convergence is set as 10−12 for learning process. The number of neuron is only 7 so that the simulation is usually completed within 2,000 trials. The decrease in error with increasing epoch is shown in Figure 6.
In Table 5, the result from multiregression analysis is listed. From the analysis, the average of relative error is 19.8%, which is reasonable; however 70.6% of relative error is calculated in the case of g50o50-47.
In Figure 7, the results from multiregression in Table 5 are compared with those from NNA and experiment. The results from NNA show more reasonable prediction with average relative error of 4.1%, which is very close to test results compared with 19.8% of average relative error from multiregression analysis. The comparisons of relative error from each technique are shown in Figure 8.
(a) OPC and GGBFS series
(b) FA series
(c) Combined series
The chloride profiles based on the diffusion coefficient from NNA are compared with test results which were kept in submerged condition for 6 months in Figure 9. Concrete with lower w/b ratio and larger mineral admixture shows the more reduced chloride penetration. The proposed technique shows reasonable prediction for chloride penetration.
(a) Chloride profile in o100 series
(b) Chloride profile in g30o70 series
(c) Chloride profile in g50o50 series
(d) Chloride profile in f10o90 series
(e) Chloride profile in f20o80 series
(f) Chloride profile in f30o70 series
(g) Chloride profile in f10s05 series
(h) Chloride profile in f20s05 series
(i) Chloride profile in g30s05 series
(j) Chloride profile in g35f15 series
4. Analysis Technique of Chloride Penetration with Time-Dependent Diffusion
4.1. Time-Dependent Diffusion of Chloride Ion
It is reported that chloride diffusion coefficient based on Fick’s 2nd law decreases with time [3, 8]. The governing equation for chloride penetration is listed in (8) and time-dependent diffusion coefficient is listed in (9) [3, 8, 16]. Consider where, and are reference time (28 days) and diffusion coefficient at reference time, is time-dependent diffusion coefficient. is time exponent which is changed with type and amount of mineral admixtures [3, 16], which is defined as where FA and SG denote the replacement ratio of fly ash and slag. For solving (8) with (9), numerical analysis like finite differential method should be employed, however if time term is fixed, averaged diffusion coefficient can be derived as (11a) and (11b) [29]. Consider where is the time after which diffusion coefficient keeps almost constant and it is usually assumed as 30 years.
4.2. Chloride Penetration Analysis Using NNA and Time-Dependent Diffusion Coefficient
The diffusion coefficients from NNA are the results based on the test data which is obtained from 6 months submerged condition, so that they are converted to diffusion coefficient at the reference time (28 days). In Figure 10, analysis technique for chloride behavior using NNA is depicted.
4.3. Comparison with Previous Test Results
In this section, the results from the proposed technique are compared with the previous test results of chloride profiles. In the previous test [28], two types of concrete (FA and OPC) were kept in 3.5% NaCl solution for 46 weeks. Table 6 shows the mix proportions [28].
Conditions for analysis are listed in Table 7 and the analysis results are shown in Figure 11. From Figure 11, it is found that the obtained diffusion coefficient seems to be small but the results from the analysis reasonably agree with the previous chloride profiles.
Another verification is performed using the results from field investigation. In the previous research [28], the chloride profiles were obtained from RC columns after 1 and 10 years in submerged condition. Unfortunately, mix proportions could not be obtained but it was found that it was made up with OPC concrete and w/c (water to cement ratio) was 0.55. Conventional mix proportions are assumed as Table 8 based on the domestic typical mix proportions [30] and analysis conditions are listed in Table 9.
In Figure 12, chloride profiles from field investigation are compared with the results from this study. With elapsed time, chloride profile moves to inside of concrete and the proposed technique is evaluated to reasonably predict the chloride penetration.
This study extends the applicability of NNA which is limitedly utilized for concrete strength and mix proportions to the research on durability. Through learning and training of diffusion coefficient, target value (diffusion coefficient) can be simulated in a given mix proportions. However this technique has still limitation since NNA technique closely depends on data set for training. The data in this paper has limitary material properties like w/b (0.37~0.47) and diffusion coefficient (1.4~7.3 × 10−12 m/sec2) so that it is necessary to extend the range for enhancing application. Various mix proportions with mineral admixtures and variability of surface chloride content will be considered for future study.
5. Conclusions
The conclusions evaluation technique of chloride penetration using apparent diffusion coefficient and neural network algorithm are as follows.(1)Thirty mix proportions for HPC containing GGBFS, FA, and SF are prepared and apparent diffusion coefficients are obtained after 6-month submerged condition of NaCl 3.5%. Seven mix components (w/b, unit content of cement, GGBFS, FA, SF, and fine/coarse aggregate) are selected as neurons and NNA is applied to simulation of diffusion coefficient. The simulated data shows only 4.1% of relative error, which is very accurate compared with the results from multiregression analysis showing 19.8%.(2)Utilizing diffusion coefficient from NNA and time-dependent diffusion, chloride profiles are evaluated. From the comparison with results of long term submerging test and field investigation, the proposed technique is evaluated to reasonably predict the induced chloride profile.(3)The proposed technique is closely dependent on quantitative data set for training and learning. With more extended mix proportions and the related diffusion coefficients, this technique can be modified and more applicable to evaluation of chloride penetration.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This research was supported by Grant (Code 11-Technology Innovation-F04) from Construction Technology Research Program (CTIP) funded by Ministry of Land, Infrastructure, and Transport.