Research on quantitative design methods for the durability of reinforced concrete structures in a hot ocean environment

2.1. Raw materials and mix proportion

The concrete strength grades are C30, C40, and C50, corresponding design water-binder ratios of 0.38, 0.36, and 0.31. The cement used is PII42.5 Portland cement produced by Yingde Conch Cement Co., Ltd. The chemical composition of the cement, slag, and fly ash is presented in Table 1. After testing, the indicators meet the product standards. Natural river sand is used as the fine aggregate, while natural gravel with a particle size gradation of 5-25 mm and a maximum particle size of 25mm is used as the coarse aggregate. Laboratory tap water is used as the mixing water. The concrete mix design is shown in Table 2.

2.2. Test methods

The concrete was poured into moulds of Φ100 mm×50 mm. The specimens underwent film curing for 24 hours before moulding and were then removed after an additional 24 hours. Curing occurred in a standard room at 20 °C±2 °C and a relative humidity of 95 %. After 28 days, testing was conducted following GB/T 50082-2009, “Standard Test Method for Long-term Performance and Durability of Ordinary Concrete.” The chloride ion diffusion coefficient of concrete was tested under different temperature conditions (20 ℃, 25 °C, and 30 °C), and the thickness of the concrete protective layer was determined.

Considering the impact of temperature on the chloride diffusion coefficient [12], the calculation equation is as follows:

where $D_0$ and $D$ are the chloride diffusion coefficient at $T_{\mathrm{r}\mathrm{e}\mathrm{f}}=$ 20 °C and $T\text{'}$, respectively; $E_a$ is the apparent activation energy, and it can be taken as 20 kJ/mol in the absence of experimental data; $R$ is the perfect gas constant, 8.31×10^-3kJ/(mol∙K^-1).

Besides examining the impact of temperature on the chloride ion diffusion coefficient, we also need to assess the effects of various factors, including cement composition, curing age, load, and water-cement ratio, on the diffusion coefficient $D$ of chloride ions [12]:

where $\varphi (w/c)$ is the influence coefficient of water-cement ratio on chloride ion diffusion coefficient of concrete. $f\left(\sigma \right)$ is the influence coefficient of load on chloride diffusion coefficient of concrete.

According to JT/T 985-2015, the durability requirements for concrete used in highway bridges and culverts specify that the chloride diffusion coefficient should not fall below the values listed in Table 3. By referencing the chloride ion diffusion coefficient [12] in Table 3, the chloride ion diffusion coefficient at various temperatures can be calculated using Eq. (2). For instance, if the average annual temperature is 22 °C and the maximum temperature in July and August exceeds 35 °C, it becomes essential to account for the effect of temperature on the durability of concrete structures.

The concentration of chloride ions in concrete varies with time and thickness of the concrete. We have established the relationship between the concentration of chloride ions, time, and position. The distribution of chloride ion concentration $C\left(x,t\right)$ can be expressed as:

where $C_0$ is the initial concentration of chloride ion in the concrete, $C_s$ is the chloride ion concentration on exposed surface of concrete, erf is the error function, $\mathrm{e}\mathrm{r}\mathrm{f}z=\frac{2}{\sqrt{\pi }}{\int }_0^z{e}^{-t^2}dt$.

According to the concentration distribution of chloride ion in concrete, the thickness of concrete eroded by chloride ion can be calculated:

When the chloride ion concentration on the surface of the steel bar in the concrete reaches the chloride threshold value, the thickness of the protective layer of the concrete structure can be expressed as:

3.1. The effect of temperature on the diffusion coefficient

The chloride ion diffusion coefficient of concrete with different cementitious materials at different ambient temperatures is shown in Table 4 and Fig. 3. When the water-binder ratio is 0.31, the chloride diffusion coefficient at 20 °C, 25 °C and 30 °C are 1.25×10^-12 m²/s, 1.48×10^-12 m²/s, and 1.52×10^-12 m²/s, respectively. When the water-binder ratio is 0.36, the chloride diffusion coefficient at 20 °C, 25 °C and 30 °C are 1.34×10^-12 m²/s, 1.63×10^-12 m²/s, and 1.84×10^-12 m²/s, respectively. When the water-binder ratio is 0.38, the chloride diffusion coefficient at 20 °C, 25 °C and 30 °C are 1.93×10^-12 m²/s, 2.25×10^-12 m²/s, and 2.7×10^-12 m²/s, respectively. With the increase of temperature, the chloride ion diffusion coefficient increases linearly. The calculated chloride diffusion coefficient is consistent with the experimental results, and the growth slope can be expressed as:

When the apparent activation energy and gas constant of concrete are 20 kJ/mol and 8.314 kJ/(mol∙K^-1) respectively, the growth rate of chloride ion diffusion coefficient of concrete is about 1.028 for every 1 °C increase. For every 5 °C increase, the growth rate of chloride diffusion coefficient of concrete is about 1.15, which can be easily used to calculate the thickness of protective layer of concrete.

Fig. 3The chloride diffusion coefficient at different temperatures

3.2. The effect of water-binder ratio on the diffusion coefficient

In this paper, three water-binder ratios of 0.31, 0.0.36 and 0.38 are studied. Fig. 4 shows the relationship between the diffusion coefficient and the water-binder ratio. Under the given chloride ion concentration and temperature, concrete's chloride ion diffusion coefficient increases with the increase of the water-binder ratio. If the diffusion coefficient is the ordinate, the water-binder ratio is the abscissa. The water-binder ratio significantly affects the concrete with fly ash and stone powder, and the concrete with slag has little influence on the diffusion coefficient. The hydration characteristics of various gelling materials can explain this difference in the analysis below.

3.3. The effect of mineral admixture on the diffusion coefficient

The researchers believe that slag and fly ash can improve the impermeability of concrete. From the test data of this paper, it can be analyzed that slag and fly ash can reduce the chloride ion permeability of concrete, which is a long-term process. In the test, the concrete specimens were only cured for 28 days. The chloride ion erosion test of concrete was carried out, and fly ash, slag and stone powder were not involved in the hydration process. The test data shows that adding 32.9 % fly ash when the water-binder ratio is 0.38 does not significantly differ from the test results at 20 °C for water-binder ratios of 0.36 and 0.38, indicating that the addition of fly ash benefits the resistance to chloride ion penetration of concrete. The water-binder ratio’s ability of resist concrete chloride corrosion is greater than that of mineral admixtures. In Reference [37], the chloride diffusion coefficients of ordinary concrete, 20 % fly ash concrete, 40 % slag concrete and 5 % silica fume concrete were tested according to NT build 443 and NT build 492, respectively. The results show that the addition of fly ash to high water-binder ratio concrete is not conducive to improving impermeability, while the addition of fly ash to low water-binder ratio concrete can improve its impermeability, as shown in table 5. Both 40 % slag and 5 % silica fume can improve the impermeability of concrete. In reference [38], the chloride diffusion coefficient of concrete at 22 °C, 35 °C and 50 °C with a water-binder ratio of 0.4 and silica fume content of 5 % tested. Compared with ordinary concrete, the chloride diffusion coefficient decreased by 52 %, 50 % and 51 %, respectively.

Fig. 4Chloride diffusion coefficient under different water-binder ratio

Based on the results of this study, different types of mineral admixtures and water-binder ratios have different effects on the resistance of concrete to chloride corrosion. Therefore, when the thickness of the concrete protective layer is designed, it is necessary to select the appropriate water-binder ratio and the type and content of mineral admixtures. In addition, good construction technology is also a critical factor in ensuring the crack resistance and durability of concrete.

3.4. Example analysis and calculation

The Gaolangang Bridge of the Huangmaohai Sea Cross-sea Channel Project is situated in a hot marine environment, specifically in a marine chloride environment. The calculation parameters are presented in Table 6. The design service life is 100 years. With a water-binder ratio of 0.31, the chloride ion diffusion coefficient is 1.25×10^-12 m²/s at 20 °C, 1.48×10^-12 m²/s at 25 °C, and 1.52×10^-12 m²/s at 30 °C. The chloride ion diffusion coefficient at 35 °C is calculated to be 1.86×10^-12 m²/s according to Eq. (1). In accordance with the “Code for Durability Design of Concrete Structures in Highway Engineering” (JTG/T3310-2019), the chloride ion concentration and critical chloride ion concentration on the concrete structure’s surface were used to calculate the protective layer thickness of the box girder. The calculated thickness of the protective layer, considering the influence of 25 °C or the maximum temperature of 30 °C, is presented in Table 7 and Fig. 5.

At 20 °C, the chloride ion erosion depth under different environmental action levels is less than the minimum protective layer thickness specified in the ‘Code for Durability of Concrete Structures for Highway Engineering’ (JTG T3310-2019). This suggests that when the box girder reaches its 100-year design service life, chloride ions do not erode the surface of the stressed steel bar, thus preventing steel bar corrosion. At environmental action level III-E, with a maximum temperature of 35 °C, the calculated chloride ion erosion depth is 39.5 cm, which is only 0.5 mm different from the design value of the concrete protective layer thickness of 40 mm. This suggests that the specified minimum protective layer thickness no longer meets the durability design requirements due to temperature effects. Thus, an increase in protective layer thickness or the implementation of additional anti-corrosion measures is required.

Fig. 5Compared with the calculated chloride ion erosion depth and the minimum protective layer thickness in the specification

The design of the protective layer thickness of concrete follows Eq. (5). The environmental action level remains constant, meaning that the chloride ion concentration on the concrete surface equals the critical chloride ion concentration. The chloride ion diffusion coefficient of concrete at a room temperature of 20 °C is already known. Considering the influence of ambient temperature on the chloride ion diffusion coefficient, the growth rate of the chloride ion diffusion coefficient can be calculated by Eq. (6). For every 5 °C increase, the growth rate of the chloride ion diffusion coefficient is 1.15. The protective layer thickness of the concrete structure should be multiplied by a coefficient of 1.07. When the temperature does not increase by 5 °C, the reduction coefficient can be calculated through linear interpolation.