Keywords

1 Introduction

The project is located in the northeastern part of the Qinghai-Tibet Plateau. The average daily temperature is below 0 ℃, and the lowest temperature reaches −18 ℃. The annual precipitation is 600 mm. There are significant daily temperature differences and high annual evaporation rates, which lead to sodium sulfate corrosion, sulfate corrosion and freeze-thaw damage under the action of various reasons [1, 2]. These factors are the main reasons for the deterioration and shortened service life of concrete structures in the high-altitude saline areas of northwest China [3]. In addition, freeze-thaw cycles cause hydrostatic pressure and seepage pressure from liquid water to enter the concrete, causing expansion pressure and accelerating concrete degradation [4]. The addition of fly ash improves the irregularity and average pore size of concrete pores, thereby improving the freeze-thaw resistance of concrete. But it also reduces the compressive strength of concrete [5]. On the other hand, the addition of slag reduces the porosity of cement store and increases the number of gel pores, thereby improving the frost resistance of concrete. The addition of silica powder fills the pores, reduces the pore size of concrete, and improves its frost resistance [6,7,8]. When combined with silica powder, it has the advantages of abundant output, low transportation costs, and high quality.

This paper studies the effect of silica fume addition on sodium sulfate attack on concrete exposed to freeze-thaw cycles (KSD). Various tests were conducted on concrete samples with different silica fume contents to explore the effects of different sulfate dry-to-wet attack and freeze-thaw cycle time ratios [9]. This study uses gray system theory and establishes a GM (1,1) model to predict the service life of concrete structures under the action of salt freezing. Three key indicators: mass loss rate, relative dynamic elastic modulus, and compressive strength are used as indicators [10]. These findings provide valuable insights into the potential application of silica fume concrete on highways in the Northwest and similar environmental areas.

2 Raw Materials and Test Method

2.1 Material Selection

Table 1. Chemical composition of silica fume%
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At present, scholars have conducted extensive research on the sulfate corrosion resistance of slag powder cement concrete. The results show that the corrosion resistance coefficient of anti-corrosion concrete using anti-sulfate corrosion agents is higher than that of ordinary concrete. These findings provide valuable data and guidance for assessing the durability and predicting the service life of concrete structures exposed to high concentrations of sulfate [10,11,12].

In order to study the durability and service life of silica fume concrete, the experimental materials were designed by comparing the characteristics of concrete resistance to sulfate attack and frost resistance. The test raw materials were chosen for this purpose.

Cement: ordinary P·O 42.5grade cement.

Aggregate: polished gravel, 5–15 mm continuous gradation.

Sand: river sand, fineness modulus is 2.84, medium sand.

Water reducer: polycarboxylates highperformance waterreducing admixture

Airentraining agent: LYYQ airentraining agent.

Silica fume: the main chemical composition is shown in Table 1 and the performance index in Table 2.

Table 2. Silica fume performance table
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2.2 Mixture Ratio

In this study, a total of 120 cube specimens measuring 100 mm × 100 mm × 100 mm and 36 prism specimens measuring 100 mm × 100 mm × 400 mm were used, each group consisted of 3 specimens. Reduce the uncertainty of large data gaps by using multiple specimens to obtain more scientific data. The concrete specimens were prepared in accordance with the’ Standard for Test Methods of Long-Term Performance and Durability of Ordinary Concrete'(GB/T 50082-2009). After 28 days of standard curing, the specimens were subjected to an alternate sulfate sodium erosion-freeze-thaw cycle test. The test procedure is detailed in Table 3.

Table 3. Mix proportion and working performance of concrete
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It was observed during mixing at a water-cement ratio of 0.35 that the addition of water-reducing admixture resulted in a decrease in concrete slump. This effect was more pronounced when the dose was 10% and above, causing some separation and bleeding when the dose reached 15%.

2.3 Sulfate Sodium Erosion-Freeze-Thaw Cycle Alternating Test

To accelerate the deterioration rate of concrete and facilitate the observation of test silica fume, the method of dry-wet cycle is selected for sulfate attack. Once the specimen reaches the desired curing age, a freeze-thaw cycle test is conducted following the sulfate dry-wet cycle test. In the dry-wet test, the specimen is soaked in a 5%sodium sulfate solution for 16 h. The drying process involves a temperature of 80 ℃ for 6 h, followed by a cooling time of 2 h, completing a cycle of 24 h. The freeze-thaw cycle test includes freezing the specimen for 4 h at a temperature of 18 ± 2 ℃ and then melting it for 2 h at a temperature of 5 ± 2 ℃.This cycle is repeated for a total of 80 days, with 1 sulfate attack and freeze-thaw cycle alternate test(referred to as KSD cycle)performed every 16 days. A total of 5 alternate cycles are conducted, with the lateral fundamental frequency and quality of the concrete specimens determined every 10 days. The compressive strength is measured at intervals of 16 days. The KSD1 test consists of a dry-wet cycle of 4 days followed by a freeze-thaw cycle of 12 days. The KSD2 test involves a dry-wet cycle of 8 days and a freeze-thaw cycle of 8 days. Lastly, the KSD3 test comprises a dry-wet cycle of 12 days followed by a freeze-thaw cycle of 4 days.

3 Test Results and Analysis

3.1 Mass Loss Rate

The mass loss rate of silica fume concrete under three kinds of sulfate sodium erosion freeze-thaw cycle alternating tests is shown in Fig. 1.

Fig. 1.
figure 1

Change of mass loss rate of silica fume concrete under KSD test

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As can be seen from Fig. 1, the trend of silica fume content in silica fume concrete under the KSD test changes from high to low, and then gradually stabilizes. In the KSD1, KSD2 and KSD3 tests, the most significant changes occurred after about 80 freeze-thaw cycles. When the silicon powder content was 5%, the mass loss rates were 1.87%, 1.44% and 1.34% respectively, and then the decline rate gradually Slow down. When the silicon powder content reaches 10%, the mass loss rates are 1.46%, 1.24% and 1.09% respectively, reaching the lowest point during the experiment. Subsequently, as the silicon powder content increased, the mass loss rate increased slightly and stabilized at 1.79%, 1.47% and 1.36% respectively.

Sodium sulfate solution (5%) was used in the three KSD tests to evaluate the mass loss rate of concrete mixed with silica fume at different proportions. The results showed that both percentages had significantly lower mass loss rates compared to concrete without silica fume over 80 days. Compared with concrete without silica fume, the mass loss rate reduction rates of KSD1, KSD2 and KSD3 are 57.7%, 47.5% and 42.3% respectively. Chemical reactions between sulfates and concrete during the early stages of the trial led to the production of slate and gypsum, improving the quality of the concrete. But late in the trial, frost heave cracking and concrete surface cracks resulted, ultimately reducing the quality of the concrete by slowing mortar shedding.

3.2 Relative Dynamic Elastic Modulus

The results of relative dynamic elastic modulus of silica fume concrete under three kinds of sulfate sodium erosion-freeze-thaw cycle alternating tests are shown in Fig. 2.

Fig. 2.
figure 2

Variation of relative dynamic elastic modulus of silica fume concrete under KSD test

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It can be seen from Fig. 2 that as the duration of sulfate dry and wet erosion and freeze-thaw cycles increases, the relative dynamic elastic modulus of concrete decreases slowly. The relative dynamic elastic modulus of silica fume concrete increases first and then decreases. The increase was most significant after 80 freeze-thaw cycles. Subsequently, as the silicon powder content continued to increase, the relative dynamic elastic modulus began to decrease, reaching 84%, 85.9% and 90.3% respectively. The figure clearly shows that when the silicon fume content is 10%, the optimal relative dynamic elastic modulus is achieved. In the early stages of the test, the concrete was not affected by sulfate intrusion, and the chemical reactions of concrete deterioration and sulfate production led to the formation of slabs and gypsum, promoting an increase in the relative dynamic modulus of elasticity. However, during the later stages of the test, the concrete experienced swelling and osmotic pressures due to alternating wet and dry conditions, as well as freeze-thaw cycles. These factors begin to deteriorate the concrete, accelerating the decrease in its relative dynamic modulus of elasticity.

3.3 Compressive Strength

The compressive strength of silica fume concrete under three kinds of sulfate sodium erosion-freeze-thaw cycle alternate tests is shown in Fig. 3.

Fig. 3.
figure 3

Change of compressive strength of silica fume concrete under KSD test

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It can be seen from Fig. 3 that the compressive strength of concrete increases with the increase of silica fume content, but decreases with the extension of test time. The most obvious changes were observed at 80 freeze-thaw cycles. Compared with 10% and 15% silica fume concrete, the compressive strength of silica fume-free concrete in KSD1, KSD2, and KSD3 increased by 17.7%, 15%, and 10.4% respectively. However, compared with 10% and 15% silica fume concrete, the increases are only 0.7%, 1% and 1.3%. This shows that the compressive strength benefit provided by the silica fume content reaches saturation after 10%. When the silica fume content reaches 10%, the compressive strength benefit is less obvious. The water holding capacity and cohesion of concrete are weakened, and the frost resistance and sulfate corrosion resistance of concrete are reduced.

4 Prediction of Concrete Life Based on Grey Theory

4.1 The Establishment and Error Test of GM(1,1)model

As a new and commonly used prediction model, grey theory is widely applied in civil engineering projects due to its simplicity, few samples, and ability to predict complex factors [13,14,15]. It can be used for various purposes such as high-rise building settlement, slope stability analysis, precast concrete (PC) cost prediction, and geotechnical engineering. The prediction model of grey theory can be classified into five types: GM(1,1)model, GM(0,N)model, GM(1,N)model, grey linear regression model, and grey Markov model application [16]. In this study, the freeze-thaw + sulfate erosion alternating test only considers one dynamic time factor, thus the GM(1,1)model is employed, which refers to the first-order and one-variable grey model.

The modeling process is as follows:

$$ X^{\left( 0 \right)} = \{ x^{(0)} \left( {1} \right),x^{(0)} \left( {2} \right),x^{(0)} \left( {3} \right), \ldots ,x^{(0)} \left( n \right)\} $$
(1)

The time series X(0)of the initial data of the study is accumulated to X(1):

$$ X^{\left( {1} \right)} = \{ x^{({1})} \left( {1} \right),x^{({1})} \left( {2} \right),x^{({1})} \left( {3} \right), \ldots ,x^{({1})} \left( n \right)\} $$
(2)

numerator: \(x^{\left( 1 \right)} k = \sum\limits_{i = 0}^k {x(i)}\)

The whitened differential equation (shadow equation) of GM(1,1)model is:

$$ \overline{\varepsilon } = \frac{1}{n}\sum\limits_{k = 1}^n {\varepsilon (k)} $$
(3)

quorum:

a, u—The undetermined parameter, a reflects the parameter of system development;

u—The grey action quantity mined from the grey system reflects the relationship between data changes.

Applying the least square method, solving Formula (3), we can get:

$$ {\text{A}} = \left( {B^T B} \right)^{1} B^T Y = \left[ {a,u} \right]^T $$
(4)

quorum:

$$ B = \left[ \begin{gathered} \hfill - \frac{1}{2}(x^{\left( 1 \right)} 1 + x^{\left( 1 \right)} 2) 1 \\ \hfill - \frac{1}{2}(x^{\left( 1 \right)} 1 + x^{\left( 1 \right)} 2) 1 \\ \hfill \vdots \vdots \\ \hfill - \frac{1}{2}(x^{\left( 1 \right)} n - 1 + x^{\left( 1 \right)} n) 1 \\ \end{gathered} \right]B = \left[ \begin{gathered} x^{\left( 1 \right)} 2 \\ x^{\left( 1 \right)} 2 \\ \vdots \\ x^{\left( 1 \right)} n \\ \end{gathered} \right] $$
(5)

Then the solution of the time response function is:

$${\mathop{x}\limits^{\frown}}^{(1)} (k + 1) = \left[ {x^{\left( 1 \right)} 1 - \frac{u}{a}} \right]e^{ - ak} + \frac{u}{a} $$
(6)

The fitting value of the initial data is:

$$ {\mathop{x}\limits^{\frown}}^{(0)} (k + 1) = {\mathop{x}\limits^{\frown}}^{(1)} (k + 1) - {\mathop{x}\limits^{\frown}}^{(1)} (k) $$
(7)

Based on the given information, a prediction model for the concrete durability attenuation of silica fume concrete in the freeze-thaw + sulfate dry-wet cycle has been developed.

The residual of the test model is:

$$\varepsilon (k) = x^{(0)} (k) - {\mathop{x}\limits^{\frown}}^{(1)},\quad (k + 1)k = 1,2, \cdots ,n $$
(8)

The mean and variance of the original data sequence are:

$$ \overline{x} = \frac{1}{n}\sum_{k = 1}^n {x^{(0)} (k)} $$
(9)
$$ p = P\left\{ {\left| {\varepsilon (k) - \left. {\overline{\varepsilon }} \right|} \right. < 0.6745S_1 } \right\} $$
(10)

The mean and variance of the data residual are:

$$ \overline{\varepsilon } = \frac{1}{n}\sum_{k = 1}^n {\varepsilon (k)} $$
(11)
$$ S_2^2 = \frac{1}{n}\sum_{k = 1}^n {[\varepsilon (k)} - \overline{\varepsilon }]^2 $$
(12)

Test mean difference ratio C:

$$ C = S_{2} /S_{1} $$
(13)

Small probability error P:

$$ p = P\left\{ {\left| {\varepsilon (k) - \left. {\overline{\varepsilon }} \right|} \right. < 0.6745S_1 } \right\} $$
(14)

According to Table 4, The accuracy of the model can be evaluated based on the mean difference ratio C. It is expected that C should be less than 0.35 and should not exceed 0.65. Another index to assess the model's accuracy is the small error probability p, which should be greater than 0.95 and not less than 0.7. Therefore, based on these two indicators, the model accuracy can be classified into four level.

Table 4. Accuracy grade of grey prediction mode
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According to my country Standard for Test Methods for Long-term Performance and Durability of Ordinary Concrete&quot; (GB/T50082-2009). The quick freezing test is evaluated based on the relative dynamic elastic modulus and mass loss rate, and the sulfate resistance test is evaluated based on the strength corrosion resistance coefficient and mass crrosion resistance coefficient. As can be seen from Figs. 1, 2 and 3, in the sodium sulfate erosion and freeze-thaw cycle alternating test, silica fume concrete was damaged the most, and the corrosion resistance coefficient (Kf) of compressive strength concrete dropped to 75%. Therefore, we use compressive strength as an indicator to predict the service life of silica fume concrete.

4.2 Prediction of Concrete Life Based on Compressive Strength

Based on the GM(1,1)model and the compressive strength data of silica fume concrete obtained from the KSD test, we have developed a prediction model for residual compressive strength. The accuracy grade of this model is presented in Table 5.

Table 5. Qualitybased prediction model and accuracy evaluation
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According to Table 5, the accuracy of predicting the failure behavior of concrete by compressive strength is high. This predictive accuracy can be utilized to forecast the lifespan of silica fume concrete. Figure 4 illustrates the failure time of silica fume concrete predicted by the GM(1,1)model for various dosages and tests.

Fig. 4.
figure 4

Failure time diagram of silica fume concrete under KSD test

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The results shown in Fig. 4 indicate that, for the same duration of testing, the longer the damage time of concrete, the higher the ratio of dry-wet erosion of sodium sulfate to freeze-thaw cycle time. This demonstrates that the freeze-thaw damage at 20 ℃ is greater than that caused by a 5%solution of sodium sulfate at 80 ℃. Additionally, the inclusion of silica fume has a positive impact on the service life of concrete, with the best effect observed at a 10%concentration. Compared to concrete without silica fume, the addition of silica fume prolongs the time for KSD1, KSD2, and KSD3 by 112 days, 96 days, and 64 days, respectively. This represents an increase of 124.4%, 85.7%, and 40.0%, respectively. Wu Hairong proposed dividing the freeze-thaw zone into D levels, and the average number of freeze-thaw cycles in the Qinghai Northwest Territories project area is 120 times [17]. Furthermore, the indoor fast freezing method specified in the ‘ordinary concrete long-term performance and durability test method standard’ (GB/T 50082-2009) is equivalent to 10–14 natural environment freeze-thaw cycles. The combination of sodium sulfate dry-wet erosion and freeze-thaw cycles has a synergistic effect, resulting in more accurate predictions of the concrete's lifespan in project areas. The concrete life of the Northwest Territories project is more accurate when considering 10 times the sulfate erosion and freeze-thaw environment. The results can be observed in Fig. 5.

Fig. 5.
figure 5

Presents a service life diagram of silica ash concrete, illustrating the effects of dry and wet erosion as well as freeze-thaw on its durability.

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The cycle time of three types of sodium sulfate salts is difficult to determine in the Northwest Territories area due to variations in precipitation, temperature, and altitude. To predict the service life of concrete, three different ratios of sodium sulfate dry-wet erosion and freeze-thaw cycles have been designed. Figure 5 shows that the increase in sulfate erosion time has a significant impact on the service life of concrete when the number of freeze-thaw cycles in the Qinghai area is determined to be 120 times. The service life of concrete without silica fume is 20 years,18.7 years, and 13.3 years for freeze-thaw and dry-wet erosion ratios of 3:1,1:1, and 1:3, respectively. On the other hand, the service life of silica fume concrete with the optimal durability, at a dosage of 10%, is 48 years,34.7 years, and 18.7 years for the same ratios. These findings can provide valuable insights for predicting the life of silica fume concrete under different sodium sulfate erosion conditions in the Northwest Territories area.

5 Conclusion

In the context of the Garxi project, a sulfate sodium erosion-freeze-thaw cycle alternating test was conducted based on three different sulfate dry-wet erosion and freeze-thaw cycle time ratios. The grey system theory was used to establish the GM(1,1)prediction model for the mechanical properties under this test. The following conclusions were drawn:

  1. (1)

    Under the same test duration, the damage caused by the 20℃ freeze-thaw cycle to concrete is greater than the damage caused by 5%sodium sulfate solution(80℃)dry and wet erosion.

  2. (2)

    In the sodium sulfate-freeze-thaw cycle alternating test, the addition of silica fume can reduce the loss rate of concrete quality, relative dynamic elastic modulus, and compressive strength. The optimal dosage is 10%. However, when the dosage exceeds 10%,the water retention and cohesion of concrete weaken, leading to the hardening of concrete in cement and causing significant defects. This ultimately reduces the frost and sulfate resistance of concrete.

  3. (3)

    In the context of sulfate attack and freeze-thaw cycles, the compressive strength of silica fume concrete is initially compromised. To accurately predict the time at which the concrete gets damaged, the GM(1,1)model is employed based on the compressive strength. This prediction can be utilized to estimate the lifespan of silica fume concrete subjected to the alternating effects of sulfate attack and freeze-thaw cycles.

  4. (4)

    The gray theory model was applied in the preparation of the GM(1,1) model prediction of the mechanical properties of silica fume concrete under the alternating action of sodium sulfate dry and wet erosion and freeze-thaw cycles. The prediction accuracy of the mechanical properties of strength and relative dynamic modulus is high. It can be utilized to predict the failure time of concrete residual compressive strength and relative dynamic elastic modulus in actual projects, but the prediction accuracy of the mass loss rate is poor and it cannot accurately predict the concrete mass failure time.