Multi-Factor Coupling Model of Concrete Chloride-Ion Diffusion Coefficient in a Salt Lake

Immersion in salt-lake solution was adopted to periodically test the concrete chloride-ion diffusion coefficient. The regression analysis was also completed. Also investigated was the time-dependent law of concrete chloride-ion diffusion coefficient with time. The influence of chloride-ion concentration in solution, water-tocement ratio, and corrosion time on the largeness and accumulation rate of the concrete chloride-ion diffusion coefficient was also analyzed. Test results show that the concrete chloride-ion diffusion coefficient gradually decreased with increasing time and increased with increasing chloride-ion concentration in a salt lake . Taking into account the influence of factors such as water–binder ratio, chloride-ion concentration, and time-varying characteristics, a multi-factor calculation model for the concrete chloride-ion diffusion coefficient was established. Combining the prediction results and the measured data reported in this paper, the effectiveness and applicability of the established concrete chloride-ion diffusion coefficient calculation model were compared and verified, and the durability design and service life of a concrete structure under cool chlorine were compared. The results of analysis provide important boundary conditions.

chloride-ion diffusion coefficient is an important parameter in predicting the service life of concrete structures. Many scholars [7][8][9][10][11] have established the concrete chloride-ion diffusion coefficient of the prediction model for marine environments, the model parameters are mainly sometimes become model [7,8] , water-to-binder ratio [9][10][11], the time-varying model, etc. However, neither the concentration of chloride ions in an environment influencing the chloride-ion diffusion coefficient of concrete has been reported nor has a model been set up to determine the concrete chloride-ion diffusion coefficient of chloride-ion concentration in a salt environment.
Furthermore, a multi-factor model of determining the chloride-ion diffusion coefficient of concrete in a salt-lake environment has not been published, to the best of our knowledge, in the literature. In view of this, analyses of actual salt-lake brine immersion test data from the Qinghai, Inner Mongolia, Xinjiang, and Tibet regions have been carried out,, and the concentration of chloride-ion solution, water-to-cement ratio, and the influence of the exposure time of surface chloride-ion concentration discussed. A salt-lake environment was built using experimental data from a concrete chloride-ion diffusion coefficient calculation model using multiple factors. An experiment comparing empirical model calculation values with measured data was conducted and the results compared with the corrected values, thus verifying the effectiveness and applicability of the model.

2
Test design

Test plan
A simulated salt-lake-brine immersion test was carried out to study the concentration of chlorine-ion solution, water-to-cement ratio of surface chloride-ion concentration, and the influence of exposure time. The concrete test was divided into two test groups as shown in Table 1. The tests used a mix of conch cement, p.o. 42. 5 cement, medium-grade natural river sand, stone produced in Nanchang Anyi with a (5-16)-mm continuous gradation of gravel, tap water, and carboxylic acid as a superplasticizer, with a water-reduction rate of >20%. The differences in proportion between the concrete in the two test groups are shown in Table 1. The chemical compositions of the salt solution are shown in Table 2.

Test steps
The test steps are as follows: 1) The sizes of all concrete block specimens were 100 mm×100 mm×100 mm and were cured, on average, for 28 d. After removing the specimens from molds, specimens designated Group 1 were soaked in Xinjiang, Inner Mongolia, Qinghai, and Tibet experimental salt solutions, while designated Group 2 specimens were soaked in a Qinghai salt-lake experimental solution. The exposure times were t=28, 56, 90, 270, and 520 d.
As described in the literature [12,13] , the three-dimensional was derived based on Fick's second law applied to the chloride-ion-diffusion theory model: 2) The specimens were removed after different exposure times and powder was collected from the two sides of the specimen by drilling. The drilling equipment comprised a small drill with a drill diameter of 6 mm; the drilling position is shown in Fig. 2. In the figure, labels I-IV show the four powder collection points. The distances from a collection point to the two sides of the specimen are d1=20 mm and d2=20 mm. Eight holes were drilled on each test piece. The sampling depths were selected as 0-5, 5-10, 10-15, 15-20, and 20-25 mm, and the powder collected from each concrete sample weighed approximately 5 g. A sieve with a pore size of 0.15 mm was used to remove coarse particles. 3) The concrete chloride-ion content determination method used for different exposure times can be found in [14] .

Relationship between chloride-ion diffusion coefficient and solution concentration
As shown in Fig. 3(a), the chloride-ion diffusion coefficient of concrete in each group increases with increasing chloride-ion concentration in the salt-lake solution. In addition, the growth rate is faster when the chloride-ion concentration is less than 10.8%, and then gradually slows down and gradually increases until it reaches a stable state. In the same salt-lake solution, the longer the corrosion time, the smaller the chloride ion diffusion coefficient of the concrete. The linear function, power function, exponential function, polynomials, and other functions of MatLab software (MathWorks, USA) were used to perform regression analysis on the data plotted in Fig. 2. Considering the boundary value (i.e., the chloride-ion diffusion coefficient when the corrosion time is zero is also zero), the results show that the chloride-ion diffusion coefficient on the concrete surface has a significant power-function relationship with the chloride-ion concentration in the saltlake solution for exposure times of 28 and 56 d, The correlation coefficients R for exposure times of 28, 56, 90, 270 and 520 d are 0.953, 0.951, 0.942, 0.958, and 0.961, respectively. Therefore, the relationship between the chloride diffusion coefficient of the concrete surface and the chloride-ion concentration in the solution can be expressed by an exponential equation: where α and β are the fitting parameters as shown in Table 3. Dt is the chloride-ion diffusion coefficient and CCl is the chloride-ion concentration in salt-lake solution in percent.

Relationship between chloride-ion diffusion coefficient and water-to-cement ratio
As shown in Fig. 3(b), the chloride-ion diffusion coefficient of the concrete surface increases with increasing water-to-cement ratio. When the water-to-cement ratio is the same, the longer the corrosion time, the smaller is the chloride-ion concentration on the concrete surface. The same regression analysis described above was performed on the data plotted in Fig. 3 in MatLab. Considering the boundary value (i.e., the chloride-ion diffusion coefficient when the water-tocement ratio is zero is also zero), the results show that the chloride-ion diffusion coefficient on the concrete surface has a significant exponential function relationship with the water-cement ratio. For exposure times of 28, 56, 90, 270, and 520 d, the correlation coefficients R2 are 0.973, 0.970, 0.965, 0.967, and 0.936, respectively Therefore, the relationship between the chloride-ion concentration on the concrete surface and the water-to-cement ratio can be expressed by the following powerfunction equation that follows the law in [16] : where n and B are fitting parameters with values shown in Table 3, Dt, the concrete chloride-ion diffusion coefficient, and RW/B, the concrete water-to-binder ratio. Many studies [14][15][16][17] have shown that the time-varying model of the concrete chloride-ion diffusion time-varying model o can more reasonably describe the time-varying characteristics of the chloride-ion diffusion coefficient of concrete. Values for concrete chloride-ion diffusion time dependence coefficient m are shown in Table 3. As shown in the table, the time-varying coefficient  Table 3 were fitted using a spreadsheet m was exponentially related to the chloride-ion concentration and water-to-binder ratio in the salt-lake solution. The correlation coefficients were both higher than 0.90, namely, 0.957 and 0.989. The functional relationship is established, as is the relationship between m and the solution's chloride-ion concentration and waterto-binder ratio: where D28 is the chloride-ion diffusion coefficient of the concrete exposed for 28 d, Dt, the chloride-ion diffusion coefficient of concrete, t, the exposure time (in d), and m, the time-varying coefficient: where CCl is the chloride ion concentration (in %) in the salt-lake solution and RW/B is the concrete water-to-binder ratio.

Establishment and verification of the multi-factor model for chloride-ion diffusion coefficient
The Life365 model [17] was applied to calculate the chloride-ion diffusion coefficient and waterto-binder ratio using the following formula: where t is the exposure time (in d) and RW/B is the water-to-binder ratio.

Establishment of the multi-factor model for chloride-ion diffusion coefficient
It is found through the analysis of test results that there is a significant power-function relationship between the chloride-ion diffusion coefficient of the concrete and the chloride-ion concentration and corrosion time of the solution [18,19]. In addition an exponential function relationship with the concrete water-to-binder ratio was found. Based on the comprehensive analysis of experimental data, in this paper we propose the following calculation model to reflect the effects of solution chloride-ion concentration, water-to-binder ratio, and time-varying factors on the diffusion of chloride ions in concrete. Inserting Eqs. (4) and (5) where t is the exposure time (in d), RW/B, the water-to-binder ratio, and CCl, the chloride-ion concentration (in %) in the solution.

Verification of the multi-factor model of chloride-ion diffusion coefficient
Using the test data in this paper, the results of various calculation models for verifying the chloride-ion diffusion coefficient of concrete, including the Life365 model and a multi-factor chloride-ion diffusion coefficient model are shown in Fig. 4. It can be seen from the figure that the a fore-mentioned two models both reflect that the chloride-ion coefficient of concrete decreases with increasing exposure time. In general, the results obtained by multi-factor chloride-ion diffusion coefficient model are closest to the measured values, while the Life365 prediction results deviate significantly from the measured values.
Through further comparison and analysis of the difference between the value predicted by the Life365 model and the model proposed in this paper and the field-measured values, it can be seen from Fig. 4 that the value predicted by the Life365 model increases rapidly with decreasing waterto-binder ratio, while the increase of the value predicted by the proposed model is relatively flat. It can also be seen that when the water-to-binder ratio is greater than 0.35, the values predicted by both the Life365 model and the proposed model are smaller than the measured values. Moreover, the values predicted by the model proposed in this paper are closer to the measured values. When the water-to-binder ratio is 0.35, the values predicted by the Life365 model and the proposed model are consistent with the measured values; when the water-to-binder ratio is less than 0.35, the values predicted by the Life365 model and the proposed model are larger than the measured values, but the values predicted by the model proposed in this paper are closer to the measured values. The reason for these results is that the Life365 model does not consider the effect of solution chloride-ion concentration on the chloride-ion diffusion coefficient of concrete. It can be seen that, when compared with the Life365 model, the proposed model is better adapted to include the effects of the chloride-ion diffusion coefficient of concrete in salt-lake environments.

Conclusions
We draw the following conclusions: 1) When concrete is immersed in salt-lake solution, the chloride-ion diffusion coefficient of the concrete increases with increasing chloride-ion concentration and water-to-cement ratio in the salt-lake solution, and decreases with the delay in the corrosion time. The chloride-ion diffusion coefficient of concrete has a power-function relationship with solution chloride-ion concentration, water-to-binder ratio, and exposure time. The time-dependence coefficient m decreases with increasing chloride-ion solution concentration and water-to-binder ratio.
2) Based on the measured data reported in this paper, a multi-factor coupling calculation model for the chloride-ion diffusion coefficient of concrete is proposed by considering factors like waterto-binder ratio, chloride-ion content, and time-varying characteristics in the solution.
3) Under different water-to-binder ratios and corrosion time conditions, the proposed multifactor coupling calculation model of the concrete chloride-ion diffusion coefficient is more suitable for salt-lake environments than the Life365 model, which is critical to informing the durability design and service life of concrete structures under salt-lake environments. The results of the analysis also provide important boundary condition.

ACKNOWLEDGMENTS
The author thanks Sifeng Liu and Hongfa Yu for valuable discussions on the experimental results.