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Article

Chloride Transport Modeling of Binary Mineral Admixture High-Performance Concrete Under Sustained Compressive Stress

by
Wenqi Ma
1,
Xiaokang Cheng
2,*,
Jie Nie
2,
Xiang Li
1,
Jia Zeng
3 and
Ziling Sun
1
1
School of Civil Engineering, Changde Vocational Technical College, Changde 415000, China
2
College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang 414006, China
3
Guangdong Province Expressway Co., Ltd., Guangzhou 510630, China
*
Author to whom correspondence should be addressed.
Buildings 2026, 16(5), 985; https://doi.org/10.3390/buildings16050985 (registering DOI)
Submission received: 23 January 2026 / Revised: 18 February 2026 / Accepted: 27 February 2026 / Published: 3 March 2026
(This article belongs to the Section Building Materials, and Repair & Renovation)
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Abstract

The objective of this study was to experimentally quantify and analytically model chloride ion transport in high-performance concrete incorporating single and binary mineral admixtures under sustained compressive loading, thereby improving durability prediction for load-bearing concrete exposed to chloride environments. A series of accelerated chloride transport experiments was conducted on high-performance concrete subjected to sustained compressive loading. The surface strain evolution of concrete was investigated under different compressive stress ratios and admixture dosages. The effects of the admixture dosage and sustained compressive stress ratio on chloride distribution were analyzed. A chloride diffusion coefficient model that incorporated sustained compressive loading and composite mineral admixtures was established, and its validity was verified. The influences of key parameters on chloride transport in binary-blended high-performance concrete were further discussed. The results showed that the strain of ordinary concrete specimens was the largest, followed by that of high-performance concrete with a single admixture of fly ash or silica fume, and the strain of high-performance concrete with double admixtures of fly ash and silica fume was the smallest. The chloride concentration in concrete first decreased and then increased with the increase in compressive stress level. The largest change amplitude was observed in ordinary concrete, and the smallest was in high-performance concrete with double admixtures of fly ash and silica fume. An increase in the time decay coefficient caused the chloride concentration in binary-blended high-performance concrete to decrease first and then increase. When the fly ash content was kept constant, the chloride concentration gradually decreased with increasing silica fume content. When the silica fume content reached 17%, the chloride concentration at a diffusion depth of 11 mm approached zero.

1. Introduction

Chloride ions exhibit high corrosive properties, capable of damaging the passivation film of reinforcing steel, leading to their presence in concrete structures located near marine environments [1,2,3,4,5,6]. Among these, high-performance concrete has gained widespread application in coastal concrete structures due to its excellent resistance to chloride ion penetration, which results from the incorporation of additives. Under extensive laboratory testing and field-scale engineering observations, it has been demonstrated that high-performance concrete structures subjected simultaneously to sustained/mechanical loading and chloride exposure exhibit more severe corrosion deterioration than comparable members exposed to chlorides alone [7,8,9,10,11]. Chloride ion penetration into concrete occurs through various pathways, with diffusion being the most common mechanism [12]. Accordingly, a systematic investigation into the mechanisms governing chloride ion migration in high-performance concrete when subjected to mechanical loading is required.
In recent years, researchers have conducted extensive studies on chloride ion transport behavior in high-performance concrete under load. Zhou et al. [11] performed chloride diffusion tests for fly ash concrete under sustained uniaxial compression and revealed a stress-level-dependent trend, yet the investigation excluded silica fume and did not cover binary FA–SF (fly ash and silica fume mixtures). Zhang et al. [13] reported that high-performance concrete may show higher sensitivity of apparent diffusion to microcrack development under uniaxial compression, but this study did not present a coupling parameterization of the stress ratio connecting high-performance concrete with a binary mineral admixture. Zhang et al. [14] found that an increase in the silica fume content initially reduced and then increased the chloride ion diffusion coefficient in concrete. Wongkeo et al. [15] evaluated self-compacting concrete containing high levels of fly ash and silica fume, but the work did not incorporate sustained compressive loading, and the reported durability indices were not directly linked to stress-dependent chloride concentration profiles required for durability prediction of load-bearing members. In summary, existing studies have primarily focused on the effects of a single admixture or considered the contents of fly ash and silica fume, without simultaneously accounting for the influence of external loads. Consequently, it has become essential to conduct an in-depth assessment of chloride ion transport characteristics in concrete containing composite admixtures when subjected to external mechanical loading.
A modeling framework for the chloride diffusion coefficient in high-performance concrete provides an effective basis for forecasting and interpreting chloride ion transport processes within the material [16,17]. Li et al. [18] formulated a diffusion coefficient model considering external loads for concrete with fly ash and slag, but silica fume was not included, and the model validation did not emphasize chloride concentration profiles under sustained compression for binary FA–SF high-performance concrete systems. Tang et al. [19] proposed a diffusion model for concrete containing fly ash and silica fume. However, the model did not include sustained compressive loading. It also did not quantify how compressive stress changes chloride concentration profiles, which is essential for durability prediction of marine members under long-term service loads. Although the chloride diffusion coefficient models established in the aforementioned studies considered the effects of a single admixture and sustained loads or the effects of composite admixtures, the established models did not simultaneously account for the combined influences of sustained loads and composite admixtures. Therefore, it is necessary to develop a chloride diffusion coefficient model that incorporates both sustained loads and composite admixtures.
Developing a chloride diffusion coefficient model that accounts for sustained compressive loading and blended mineral admixtures is a prerequisite for rationally evaluating the durability behavior of coastal concrete pier columns. A series of accelerated chloride transport experiments was conducted on high-performance concrete subjected to sustained compressive loading. The surface strain evolution of concrete was then examined under different compressive stress ratios and admixture dosages. The effects of the admixture dosage and sustained compressive stress ratio on chloride distribution were analyzed. A chloride diffusion coefficient model that incorporated sustained compressive loading and composite mineral admixtures was established, and its validity was verified. The influences of key parameters on chloride transport in binary-blended high-performance concrete were further discussed.

2. Experimental Design

2.1. Materials

Concrete cubes measuring 100 mm × 100 mm × 100 mm were cast for the experimental program. Ordinary Portland cement (CEM I) (South Cement Co., Ltd., Hangzhou, China) with a nominal strength class of 42.5 MPa was adopted as the primary binder, and its major oxide composition together with key physical indices are reported in Table 1.
The mixture proportions adopted in this work are summarized in Table 2. The fly ash used met the requirements for Grade II fly ash (Changsha Xingtie Building Material Technology Co., Ltd., Changsha, China), with a density of 2144 kg/m3. The slag used was S95 slag powder (Hunan Huatianeng Environmental Protection Technology Development Co., Ltd., Changsha, China), with a density of 2910 kg/m3. A polycarboxylate super-plasticizer (SP) (Hunan Zhongyan Building Materials Technology Co., Ltd., Changsha, China) with a water-reducing rate of 20% was added to improve the worka-bility of the concrete. Following casting, all specimens were removed from the molds after 24 h and then subjected to standard curing for 28 days under an environment of 20 °C and 95% relative humidity. After the curing period, three specimens from each batch were selected for compressive strength determination, and the resulting compressive strength values, denoted as fc, are reported in Table 2. For each mix, the variability of compressive strength, slump, and air content is quantified and reported based on replicate measurements/specimens using the mean, standard deviation (SD), and coefficient of variation (COV), thereby characterizing the repeatability and inherent experimental scatter of the experimental results [20,21,22]. In addition, the mean values, SD, COV, air content, and compressive strength for each mixture proportion in this study are presented in Table 3. The mean values, SD, and COV obtained in this study all met the relevant requirements [23,24,25].
Prior to the application of compressive stress levels, all surfaces of the concrete specimens except the upper surface were coated with epoxy resin, as shown in Figure 1.

2.2. Chloride Penetration Experiment

To characterize the strain variation in different regions of the concrete surface under corrosion conditions, strain measurements were conducted along the x-axis and y-axis at two positions (A and B) on the top surface, as shown in Figure 1, based on the study in reference [26]. A load cell (Dongguan Lixian Instrument Scientific Co., Ltd., Dongguan, China) was used to monitor the sustained compressive stress, and spring washers were added at the nut to maintain the applied load. The measurement error was within ±2% of the applied stress. During the 180-day exposure period, the applied stress was checked every day. The deviation from the target stress was kept within ±2%. If the deviation exceeded 2%, the load was adjusted back to the target value. The applied load was adjusted by tightening the nut on the loading rod. These measurements were used to test the changes in normal strain in the x-direction and y-direction under different compressive stress levels, with three stress groups set: 0, 0.3 fc, and 0.5 fc. The specimen identification numbers are provided in Table 4, with three specimens tested for each condition. After loading was completed, the strain at the two measurement points on the upper surface of the concrete specimen under load was tested. The neutral salt-spray exposure was conducted using a 5 wt% NaCl solution, and the solution pH was maintained between 6.5 and 7.2. The chamber temperature was controlled at 20 ± 2 °C, and the target relative humidity was 95% (near-saturated conditions). The spray deposition rate was verified using standard collectors with an effective area of 80 cm2. The target deposition rate was 1–2 mL/(80 cm2·h). Collectors were placed at multiple locations inside the chamber. Deposition was considered uniform when all locations satisfied the target range. In addition, temperature and relative humidity were recorded every 8 h and were cross-checked weekly. The spray deposition rate was checked every 24 h using the 80 cm2 collectors, and the collector positions were rotated among chamber locations to confirm spatial uniformity. The solution pH was measured once per day.
Subsequently, the concrete specimen device under load was subjected to corrosion protection treatment and placed in a salt spray chamber for salt spray exposure. The solution tank contained a 5% NaCl solution, which was sprayed through nozzles to ensure that the upper surface of the concrete specimen under load was covered with chloride salts. The experiment duration was 180 days, as shown in Figure 1.

2.3. Test of Chloride Concentration

After the experiment, the crystal salt on the surface was removed, and the strain of two measuring points on the upper surface of the concrete under load was measured. Concrete specimens with corroded surfaces were sampled following the method described by Kosalla et al. [27]. The free chloride concentration was measured by electrode method. Before sampling, salt crystals on the exposed surface were removed, and the surface was dry-cleaned. Grinding was then performed along the normal direction to the exposed face. A depth increment of 2 mm was used from 0 to 20 mm. A depth increment of 5 mm was used beyond 20 mm. This scheme followed the NT BUILD 443 principles for collecting powder in 2 mm and 5 mm layers [28]. For each depth increment, at least 5 g of powder was collected to allow replicate measurements. The water-soluble chloride concentration was determined in accordance with ASTM C1218/C1218M [29]. Layer thickness and the number of layers were recorded in full. The same sampling scheme was applied to all specimens. This ensured consistent profile fitting and diffusion back-analysis.
To control cross-contamination, excess powder was removed after each layer using a blower and a soft brush. The grinding chamber and collection zone were then wiped with deionized water. Before sampling the next layer, the grinder was run for 2–3 s without collecting powder. The first powder produced in this step was discarded. This procedure reduced the tailing effect from residual material. Blank checks were also performed. The chloride content of blank powder was required to be close to the detection limit. This verified the effectiveness of the cleaning procedure. The timing of powder extraction and the sampling location could affect the measured chloride distribution. Therefore, the sampling location was fixed. For each depth increment, at least 5 g of powder was collected to allow replicate measurements. Layer thickness and the number of layers were recorded in full. This ensured consistent profile fitting and diffusion back-analysis. The collected samples were ground and sieved through a 75 μm sieve to achieve uniformity. For chloride ion extraction, a predetermined mass of powdered sample was mixed with deionized water at a fixed liquid-to-solid ratio (typically 10:1, using 5 g of powder and 50 g of water) and stirred continuously for 30–60 min until complete dissolution [3]. Therefore, the sampling location was fixed. The powder was sealed immediately after collection, and the free chloride concentration of the specimens was measured using an ion-selective electrode method. Powdered concrete samples were extracted with deionized water under the standard-prescribed conditions, cooled, and filtered to obtain a clear filtrate. The filtrate was acidified with nitric acid and titrated with standardized AgNO3 using potentiometric endpoint detection with a chloride ion-selective electrode. The equivalence point was identified from the inflection point of the mV–volume curve (maximum potential change). Blank correction and dilution/aliquot factors were applied to calculate the chloride content for each depth (Figure 2).

3. Analysis of Experimental Results

3.1. Strain Analysis of Loaded Concrete

Figure 3 illustrates strain changes in concrete under different compressive stress ratios. From Figure 3a,b, it was observed that strain values at mid-span measuring points were larger than those at other points. In Figure 3a, the compressive strain at measuring point A was 20% larger on average than that at measuring point B. Additionally, under the same compressive stress level, the compressive strain values of C1-A were 32.4%, 32.6%, and 61.5% larger on average than those of HPC1-A, HPC2-A, and HPC12-A, respectively. The same pattern applied to measuring point B. Similarly, when the compressive stress level increased from 0.3 fc to 0.5 fc, the compressive strains at all measuring points of concrete specimens increased by 30 με to 40 με, with that of C1-A increasing by 40 με. In Figure 3b, changes in compressive strains at the measuring points of concrete specimens were small, indicating that surface erosion of concrete had little effect on strains in the x-direction. In Figure 3c,d, strains in the y-direction at measuring points A and B changed significantly. In Figure 3c, the tensile strain at measuring point A was small at 0.3 fc. When the compressive stress level reached 0.5 fc, the tensile strains at measuring points C1-A, HPC1-A, HPC2-A, and HPC12-A were 120 με, 85 με, 81 με, and 60 με, respectively. Notably, as the compressive stress level increased to 0.5 fc, except for the significant change in tensile strain at HPC12-B, changes in tensile strain at this point for other specimens were small. Chloride corrosion had a significant effect on normal strains in the y-direction. At a compressive stress level of 0.3 fc, the tensile strains at measuring points C1-A, HPC1-A, and HPC2 increased by an average of 4.2 times, 4.5 times, and 4.3 times compared with those in the uncorroded state, as shown in Figure 3d. Furthermore, in both x and y directions, the strain of ordinary concrete specimens was the largest, followed by that of high-performance concrete with the single admixture of fly ash or silica fume, and the strain of high-performance concrete with double admixtures of fly ash and silica fume was the smallest. In summary, in the x-direction, the normal strain at mid-span measuring points was 20% larger than that at other points, and chloride erosion had little effect on compressive strains of measuring points in the x-direction. In the y-direction, the tensile strain at all measuring points increased with the increase in compressive stress. Chloride corrosion had a significant effect on normal strains in the y-direction. In both x and y directions, the strain difference between high-performance concrete with the single admixture of fly ash and that with the single admixture of silica fume was small. In both directions, the strain of ordinary concrete specimens was the largest, followed by that of high-performance concrete with the single admixture of fly ash or silica fume, and the strain of high-performance concrete with double admixtures of fly ash and silica fume was the smallest. When the compressive stress reached a critical level, the lateral strain increased and microcracks formed, leading to a pronounced increase in the apparent Poisson ratio and the onset of volumetric dilatancy, which reflected interfacial transition zone (ITZ) debonding and microcrack propagation. The loading-induced microcracking increased pore connectivity and reduced tortuosity, thereby enhancing the effective chloride diffusion coefficient [30,31].

3.2. Error Analysis of Chloride Concentration

Figure 4 and Figure 5 show the relative errors of the three sets of experimental chloride concentration data under different concrete types and compressive stress levels, respectively. As indicated by Figure 1 and Figure 2, the relative errors of all measurements were below 15%, which satisfied the requirement of the relevant code [29]. This result demonstrated that the mean chloride concentrations were sufficiently reliable for subsequent analysis of chloride transport.

3.3. Effect of Concrete Types

Figure 6 shows the influence of concrete types on chloride ion diffusion in high-performance concrete under compressive stress. According to Figure 4a, the chloride concentration at measuring point C1F0-A was 12.4%, 15.6%, and 34.1% higher than that at measuring points HPC1F0-A, HPC2F0-A, and HPC12F0-A, respectively. In Figure 4b, when the compressive stress level increased to 0.3 fc, the chloride concentration at measuring point C1F0-A was 13.4%, 15.4%, and 33.6% higher than that at measuring points HPC1F0-A, HPC2F0-A, and HPC2F0-A, respectively. The variation pattern of the chloride concentration of each specimen in Figure 4c was similar to that in Figure 4b. In addition, in Figure 4d–f, the variation pattern of chloride concentration at measuring point B of each concrete specimen was relatively similar to that at measuring point A. This indicated that the strain changes at different measuring points of the same cross-section had little effect on the distribution of chloride concentration. In summary, the chloride ion diffusion rate of ordinary concrete specimens was the fastest. The chloride diffusion rate of high-performance concrete specimens with the single admixture of fly ash or silica fume was slower, and the difference in chloride concentration between the two was small. The chloride ion diffusion rate of high-performance concrete specimens with double admixtures of fly ash and silica fume was the slowest. Ordinary concrete had high porosity and coarse connected capillary pores, so chloride ions migrated rapidly under stress gradients and osmotic pressure. It contained less C-S-H gel and more defective AFt crystals, leading to weak chloride adsorption and a higher diffusion coefficient. Adding fly ash or silica fume produced secondary C-S-H that refined pores, blocked channels, and densified the ITZ, increasing diffusion resistance. Using both admixtures worked best, as fly ash filled macropores and silica fume blocked nanoscale pores, forming a dense barrier [32,33].

3.4. Effect of Stress Level

Figure 7 shows the influence of compressive stress levels on chloride ion diffusion in high-performance concrete under compressive stress. According to Figure 5a, when the compressive stress level increased from 0 to 0.3 fc, the chloride concentration at measuring point C1F1-A was 12% lower on average than that at measuring point C1F0-A. When the compressive stress level increased from 0.3 fc to 0.5 fc, the chloride ion concentration at measuring point C1F2-A was 19.7% higher on average than that at measuring point C1F1-A. In Figure 5b, the chloride concentration at measuring point HPC1F1-A was 10.6% lower on average than that at measuring point HPC1F0-A. When the compressive stress level increased from 0.3 fc to 0.5 fc, the chloride concentration at measuring point HPC1F2-A was 16.8% higher on average than that at measuring point HPC1F1-A. The variation pattern of the chloride concentration in Figure 5c was relatively similar to that in Figure 5b. In Figure 5d, the chloride concentration at measuring point HPC12F1-A was 8.5% lower on average than that at measuring point HPC12F0-A, and the chloride concentration at measuring point HPC12F2-A was 14% higher on average than that at measuring point HPC12F1-A. Table 5 reports the absolute changes in chloride concentration at each depth for the high-performance concrete incorporating binary mineral admixtures. Using ΔC01, ΔC12, and ΔC02, the absolute changes in chloride concentration were defined as those between HPC12F1-A and HPC12F0-A, between HPC12F2-A and HPC12F1-A, and between HPC12F2-A and HPC12F0-A, respectively. These definitions are summarized in Table 2. At diffusion depths of 22.5 mm and 27.5 mm, the chloride concentrations in high-performance concrete were relatively low. Therefore, the corresponding absolute changes in chloride concentration were not considered meaningful for interpretation [34,35]. In this study, the 95% expanded uncertainty associated with chloride determination was evaluated following the procedure reported in reference [36] and was expressed as ΔU01, ΔU12, and ΔU02, as summarized in Table 6. The absolute changes in chloride concentration at the investigated diffusion depths were all within the measurement-uncertainty bounds of the adopted chloride test method. The possible reason was that low compressive stress compacted the pore structure and promoted closure of pore throats, thereby reducing pore connectivity. At higher stress levels, the lateral tensile strain increased and induced microcracking; once cracks became connected, they coupled with the pre-existing pore network and reconfigured the transport pathways, forming more continuous channels for chloride ingress [37,38,39,40]. In summary, the chloride concentration in concrete first decreased and then increased with the increase in the compressive stress level. The largest change amplitude was observed in ordinary concrete, and the smallest was in high-performance concrete with double admixtures of fly ash and silica fume.

4. Chloride Diffusion Coefficient Model Under Compressive Stress

4.1. Establishment of the Chloride Diffusion Coefficient Model

The analytical equation of chloride ion diffusion in saturated concrete is generally expressed by Equation (1).
C ( x , t ) = C s 1 − e r f x ⋅ 2 D a 1 − m t 0 t + t 0 m ⋅ t − 1
where C(x,t) denotes the concentration of free chloride ions at a distance x from the concrete surface at time t; t0 represents the curing period; t is the experimental cycle; m is the time decay coefficient, which is usually taken as 0.65 [41]; and Da refers to the chloride diffusion coefficient of concrete, covering that of ordinary concrete, high-performance concrete with the single addition of fly ash, single addition of silica fume, and binary addition of fly ash and silica fume. To avoid surface crystallized salts inflating the near-surface chloride concentration measured from the outermost powder layers, crystalline salts on the exposed surface were removed before sampling. Powder samples were then collected at successive depth intervals. Chloride concentrations were determined in accordance with the standard method. This procedure reduced the influence of non-uniform chloride deposition on the near-surface chloride distribution. A constant surface chloride concentration was therefore assumed. A similar treatment was also adopted in references [39,40].
It is generally described by Equation (2).
D a = D 1 ⋅ f ( s 1 ,   s 2 ) ⋅ f ( λ )
where D1 represents the apparent chloride diffusion coefficient of ordinary concrete without being subjected to load; f(s1, s2) is the influence coefficient considering the content of admixtures such as fly ash and silica fume, where s1 and s2 are the percentages of fly ash and silica fume respectively; and f(λ) is the influence coefficient taking into account the compressive stress level.
To calculate D1, f(s1, s2), and f(λ), this study is carried out in two steps. The first step involved calculating D1 and f(s1, s2), while the second step focused on calculating f(λ). First, experimental data from C1F0, HPC1F0, HPC2F0, and HPC12F0, as presented in Section 3.2, are substituted into Equation (1) to obtain a set of chloride ion diffusion coefficients for different admixture ratios. These data are then fitted using the MATLAB 2016a toolbox to derive Equation (3).
D a = 6.12 × 10 − 12 ⋅ 1 − 3.95 s 1 − 4.1 s 2 + 3.45 s 1 ⋅ s 2 + 1.45 s 1 2 − 1.23 s 2 2 ,   R 2 ≥ 95 %
The value of D1 in Equation (3) is 6.12 × 10−12 m2/s. The chloride diffusion coefficient, considering the effects of admixtures and sustained loading, is described by Equation (4).
D a = D 1 ⋅ 1 − 3.95 s 1 − 4.1 s 2 + 3.45 s 1 ⋅ s 2 + 1.45 s 1 2 − 1.23 s 2 2 ⋅ f λ
Using all the experimental data from Section 3.2, the chloride diffusion coefficients (Da) are obtained by substituting the data into Equation (1). These values of Da are then substituted into Equation (4) and fitted using the MATLAB toolbox to derive Equation (5).
D a = D 1 ⋅ 1 − 3.95 s 1 − 4.1 s 2 + 3.45 s 1 ⋅ s 2 + 1.45 s 1 2 − 1.23 s 2 2 ⋅ 1 − 2.19 λ + 5.3 λ 2 ,   R 2 ≥ 95 %
Substituting Equation (5) into Equation (1), the predicted chloride concentration of high-performance concrete with single or binary admixtures under compressive stress can be obtained.
Table 7 presents the statistical metrics for Equations (3) and (5), and Figure 8 shows the corresponding residual plots. Table 7 and Figure 8 indicate that the diffusion-coefficient models in Equations (3) and (5) provided good fits to the chloride concentration data.

4.2. Verification of Model

To verify the applicability of the chloride diffusion coefficient model in this study, a comparative analysis was conducted between the experimental values from Zhou et al. [11] and the model values from this study. Based on Zhou et al. [11], the fly ash contents are 0%, 15%, and 30%, and the applied uniaxial compressive stress levels are 0, 0.4, and 0.6, with an experimental period of 60 days. The corresponding comparative analysis is shown in Figure 9.
Based on Figure 9a, it can be seen that, except for the chloride concentration at an erosion depth of 17.5 mm for FA0-C, which deviates significantly from the model value, the experimental chloride concentrations for other cases are in good agreement with the model. Similarly, in Figure 9b, at an erosion depth of 17.5 mm, the chloride ion concentration for FA15-C also shows a noticeable discrepancy with the model value. The likely reason for this is that under high compressive stress, both ordinary concrete and fly ash concrete exhibit increased chloride concentrations due to stress-induced microcracks and increased pore connectivity. Under high pressure, internal damage accumulates, enlarging capillary pores and creating new cracks, which provide additional pathways for chloride transport [42,43]. In conclusion, the model values for chloride concentration match well with the experimental results, demonstrating that the chloride diffusion coefficient model developed in this study, which accounts for the effects of admixtures and sustained loading, is suitable.
The experimental results reported by Tang et al. [19] and Fu et al. [44] were employed to perform a comparative assessment against the model predictions obtained in the present study. In the study by Tang et al. [19], the silica fume contents were 0%, 5%, 10%, and 15%, and the test duration was 60 d, as shown in Figure 5a. According to Figure 10a, it is observed that, except for the chloride concentration at a diffusion depth of 7.5 mm for A-60 and at 12.5 mm for SF-5, which deviated markedly from the predicted values, the experimental chloride concentrations generally exhibited good agreement with the model predictions under the other conditions. In the study by Fu et al. [44], two binary-blended mixtures were investigated: one incorporating 17% fly ash and 3% silica fume, and the other incorporating 14% fly ash and 6% silica fume. The exposure durations were 90 d and 120 d, respectively, and the surface chloride concentration was taken from the experimental measurements according to the test progression, as shown in Figure 10b. The possible reasons were that silica fume refined the pore structure and enhanced chloride-binding capacity, whereas compressive loading induced microcracking and increased the connectivity of capillary pores. Localized crack pathways, ITZ heterogeneity, and saturation gradients could also lead to deviations at individual depths [34,45]. Overall, the proposed chloride diffusion model was applicable for analyzing chloride transport in fly ash–silica fume binary-blended concrete subjected to compressive stress.

5. Parameter Sensitivity Analysis

To investigate the effects of different parameters on chloride transport in binary-blended high-performance concrete subjected to compressive stress, HPC12F2-A is taken as an illustrative case. The influences of the time decay coefficient (0.25, 0.45, 0.65, and 0.75), silica fume content (0.05, 0.09, 0.13, and 0.17), and compressive stress level (0, 0.2, 0.5, and 0.7) are examined, as can be seen in Figure 11. The silica fume dosage is investigated because a sensitivity analysis can quantify its governing contribution to the chloride migration coefficient through micro-filling and pozzolanic reactions. These mechanisms densify the pore structure and the interfacial transition zone, which reduces model uncertainty and supports mixture optimization for binary-blended HPC [19,25]. As shown in Figure 11a, increasing the time decay coefficient (m) does not monotonically promote chloride transport. When m is 0.45, the chloride concentrations are lower than those obtained with m = 0.25. When m is increased to 0.65, the chloride concentrations become higher than those for m = 0.45, and they further increase when m reaches 0.75. Overall, increasing m causes the chloride concentration to decrease first and then increase. The possible reason is that when m increases from a low level to a moderate level, the ongoing pozzolanic reaction of fly ash and the micro-filling effect of silica fume act synergistically and reduce pore connectivity. As a result, the effective diffusion pathways gradually contract, and the chloride concentration decreases. However, when m increases further, sustained compressive loading more readily induces microcracking in the interfacial transition zone and other weak regions. It also promotes coupling between cracks and the pre-existing pore network. This process weakens the densification benefits provided by the fly ash and silica fume. It re-establishes more continuous transport pathways and leads to a non-monotonic response. The chloride concentration increases again and continues to rise with increasing m [46,47]. As shown in Figure 11b, when the fly ash content is kept constant, the chloride concentration gradually decreases with increasing silica fume content. When the silica fume content reaches 17%, the chloride concentration at a diffusion depth of 11 mm approaches zero. In Figure 11c, when the compressive stress level increases from 0.5 to 0.7, the chloride concentration increases by an average of 10.5%.

6. Conclusions

A series of accelerated chloride transport experiments were conducted on high-performance concrete subjected to sustained compressive loading. The strain variations on the concrete surface under different compressive stress ratios and admixture proportions were investigated, and the influences of admixture proportions and sustained compressive stress ratios on chloride ion distribution were analyzed. A chloride diffusion coefficient model that accounted for sustained compressive loading and blended mineral admixtures was established and validated. The influences of key parameters on chloride transport in binary-blended high-performance concrete were further discussed. The following main conclusions were drawn:
  • In the longitudinal direction, the normal strain at the midspan gauge was approximately 20% higher than that at the other gauges, and chloride exposure had a negligible influence on the compressive strain measured along the longitudinal direction. In the lateral direction, the tensile strains at all measurement points increased with increasing compressive stress. The strain differences between the high-performance concrete containing fly ash alone and that containing silica fume alone were small in both the longitudinal and lateral directions. In both directions, the normal concrete specimens exhibited the largest strains, followed by the single-admixture high-performance concretes with fly ash or silica fume, whereas the binary-blended high-performance concrete incorporating fly ash and silica fume exhibited the smallest strains.
  • The chloride ion diffusion rate of ordinary concrete specimens was the fastest. The chloride diffusion rate of high-performance concrete specimens with the single admixture of fly ash or silica fume was slower, and the difference in chloride concentration between the two was small. The chloride ion diffusion rate of high-performance concrete specimens with double admixtures of fly ash and silica fume was the slowest. The chloride concentration in concrete first decreased and then increased with the increase in the compressive stress level. The largest change amplitude was observed in ordinary concrete, and the smallest was in high-performance concrete with double admixtures of fly ash and silica fume.
  • An increase in the time decay coefficient caused the chloride concentration in binary-blended high-performance concrete to decrease first and then increase. When the fly ash content was kept constant, the chloride concentration gradually decreased with increasing silica fume content. When the silica fume content reached 17%, the chloride concentration at a diffusion depth of 11 mm approached zero. When the compressive stress level increased from 0.5 to 0.7, the chloride concentration increased by an average of 10.5%.
The limitations of this study are as follows. The salt-spray exposure was idealized. It was limited to one-sided exposure to 5 wt.% NaCl for 180 d under constant temperature and humidity. Drying–wetting cycles and carbonation coupling were not considered. The specimens were 100 mm cubes with a one-dimensional ingress boundary. Size effects and complex field boundary conditions were not covered. The loading regime was limited to sustained uniaxial compression at 0, 0.3 fc, and 0.5 fc. Damage evolution was characterized using surface strain measurements. Direct evidence of internal cracking and microstructural degradation was not obtained. Future work will measure compressive strength at different ages and will develop an evolution model for the stress ratio. The influence of salt-spray deposition on the surface chloride concentration will be considered. SEM, XRD, and MIP will be used to support the microstructural interpretation and to examine relationships among residual strength, damage evolution, and migration parameters. Computer vision methods will be introduced to quantify the surface crack density and crack width during the exposure period. DeepLab v3 [48] will be used for pixel-level semantic segmentation to delineate cracks and to quantify the crack density. EfficientNet [49], such as EfficientNet-B2, will be used as a backbone. It will be integrated with a feature pyramid network for multi-scale segmentation and regression to improve robustness.

Author Contributions

Conceptualization, W.M. and X.L.; methodology, X.C.; software, X.C.; validation, X.L. and J.Z.; formal analysis, W.M. and J.Z.; investigation, X.C. and J.N.; resources, J.N.; data curation, J.N.; writing—original draft preparation, X.C.; writing—review and editing, W.M.; visualization, Z.S.; supervision, J.Z.; project administration, W.M.; funding acquisition, W.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Scientific research project of Hunan Provincial Department of Education, grant number 25B0995.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Conflicts of Interest

Author Jia Zeng is employed by the company Guangdong Province Expressway Co., Ltd., Guangzhou 510630, China. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

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Figure 1. Experimental procedure of chloride ion erosion in concrete.
Figure 1. Experimental procedure of chloride ion erosion in concrete.
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Figure 2. Procedure for testing chloride concentration in concrete.
Figure 2. Procedure for testing chloride concentration in concrete.
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Figure 3. Strain changes at concrete measurement points under different stress ratios. (a) x-direction before the experiment; (b) x-direction after the experiment; (c) y-direction before the experiment; (d) y-direction after the experiment.
Figure 3. Strain changes at concrete measurement points under different stress ratios. (a) x-direction before the experiment; (b) x-direction after the experiment; (c) y-direction before the experiment; (d) y-direction after the experiment.
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Figure 4. Relative error of chloride concentration experimental value under concrete type: (a) λ = 0, measurement point A; (b) λ = 0.3 fc, measurement point A; (c) λ = 0.5 fc, measurement point A; (d) λ = 0, measurement point B; (e) λ = 0.3 fc, measurement point B; (f) λ = 0.5 fc, measurement point B.
Figure 4. Relative error of chloride concentration experimental value under concrete type: (a) λ = 0, measurement point A; (b) λ = 0.3 fc, measurement point A; (c) λ = 0.5 fc, measurement point A; (d) λ = 0, measurement point B; (e) λ = 0.3 fc, measurement point B; (f) λ = 0.5 fc, measurement point B.
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Figure 5. Relative error of chloride concentration experimental value under stress level: (a) C1, measurement point A; (b) HPC1, measurement point A; (c) HPC2, measurement point A; (d) HPC12, measurement point A.
Figure 5. Relative error of chloride concentration experimental value under stress level: (a) C1, measurement point A; (b) HPC1, measurement point A; (c) HPC2, measurement point A; (d) HPC12, measurement point A.
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Figure 6. Effect of concrete types on chloride concentration distribution: (a) λ = 0, measurement point A; (b) λ = 0.3 fc, measurement point A; (c) λ = 0.5 fc, measurement point A; (d) λ = 0, measurement point B; (e) λ = 0.3 fc, measurement point B; (f) λ = 0.5 fc, measurement point B.
Figure 6. Effect of concrete types on chloride concentration distribution: (a) λ = 0, measurement point A; (b) λ = 0.3 fc, measurement point A; (c) λ = 0.5 fc, measurement point A; (d) λ = 0, measurement point B; (e) λ = 0.3 fc, measurement point B; (f) λ = 0.5 fc, measurement point B.
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Figure 7. Effect of stress level on chloride concentration distribution: (a) C1, measurement point A; (b) HPC1, measurement point A; (c) HPC2, measurement point A; (d) HPC12, measurement point A.
Figure 7. Effect of stress level on chloride concentration distribution: (a) C1, measurement point A; (b) HPC1, measurement point A; (c) HPC2, measurement point A; (d) HPC12, measurement point A.
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Figure 8. Residual diagram of correlation equation: (a) Equation (3); (b) Equation (5).
Figure 8. Residual diagram of correlation equation: (a) Equation (3); (b) Equation (5).
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Figure 9. Comparative analysis of experimental value and model value of chloride concentration. (a) FA = 0; (b) FA = 15%; (c) FA = 30%.
Figure 9. Comparative analysis of experimental value and model value of chloride concentration. (a) FA = 0; (b) FA = 15%; (c) FA = 30%.
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Figure 10. Comparative analysis of experimental value and model value of chloride concentration. (a) Tang et al. [19].; (b) Fu et al. [44].
Figure 10. Comparative analysis of experimental value and model value of chloride concentration. (a) Tang et al. [19].; (b) Fu et al. [44].
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Figure 11. Influence of different parameters on chloride ion transport in double-doped high-performance concrete under compressive stress. (a) Time decay coefficient; (b) silica fume content; (c) compressive stress level.
Figure 11. Influence of different parameters on chloride ion transport in double-doped high-performance concrete under compressive stress. (a) Time decay coefficient; (b) silica fume content; (c) compressive stress level.
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Table 1. Chemical compositions and physical properties of cement.
Table 1. Chemical compositions and physical properties of cement.
SiO2Al2O3Fe2O3CaOMgOSO3TiO2K2OLoss on Ignition
Chemical composition (%)21.466.434.5761.251.461.740.220.352.52
Table 2. Mix ratio and related parameters of concrete (kg/m3).
Table 2. Mix ratio and related parameters of concrete (kg/m3).
SpecimenWaterCementFly AshSlagFine AggregateCoarse Aggregatefc (MPa)
C1165460――534.81190.245.6
HPC116543723―534.81190.250.2
HPC2165437―23534.81190.251.7
HPC121654142323534.81190.254.3
Table 3. The value of related parameters.
Table 3. The value of related parameters.
SlumpAir ContentCompressive Strength
Mean (mm)SD (mm)COV (%)Mean (%)SD (%)COV (%)Mean (MPa)SD (MPa)COV (%)
C118012.507.002.000.2311.5045.601.373.00
HPC119013.707.202.100.2511.9050.201.513.01
HPC218513.207.102.000.2412.0051.701.552.96
HPC1220013.706.902.200.2611.8254.301.633.00
Table 4. Experiment specimen number.
Table 4. Experiment specimen number.
Specimen NumberSustained Compressive Load (fc)
C1F0-
C1F10.3
C1F20.5
HPC1F0-
HPC1F10.3
HPC1F20.5
HPC2F0-
HPC2F10.3
HPC2F20.5
HPC12F0-
HPC12F10.3
HPC12F20.5
Table 5. Variation of absolute value of chloride concentration at each depth.
Table 5. Variation of absolute value of chloride concentration at each depth.
Depth (mm)ΔC01 (%)ΔC12 (%)ΔC02 (%)
1−0.0400.0070.004
3−0.0130.0200.011
5−0.0110.0240.009
7−0.0110.0220.011
9−0.0100.0200.010
11−0.0100.0170.007
13−0.0070.0180.010
15−0.0050.0120.007
17−0.0030.0070.003
19−0.0010.0040.002
Table 6. Determination of absolute value change of chloride concentration at different depths.
Table 6. Determination of absolute value change of chloride concentration at different depths.
Depth (mm)ΔU01 (%)StatusΔU12 (%)StatusΔU02 (%)Status
10.003Significant0.003Significant0.003Significant
30.006Significant0.005Significant0.007Significant
50.007Significant0.007Significant0.005Significant
70.004Significant0.010Significant0.005Significant
90.008Significant0.004Significant0.007Significant
110.003Significant0.007Significant0.004Significant
130.006Significant0.004Significant0.009Significant
150.002Significant0.002Significant0.004Significant
170.001Significant0.001Significant0.002Significant
190.001Significant0.001Significant0.002Significant
Table 7. Statistical indicators of Equations (3) and (5).
Table 7. Statistical indicators of Equations (3) and (5).
ModelnkdfR2RMSE(m2/s)NRMSE(%)p_constp_s1p_s2
Equation (3)13231290.9651.28 × 10−133.09<0.001<0.001<0.001
Equation (5)39653910.9731.28 × 10−132.99<0.001<0.001<0.001
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Ma, W.; Cheng, X.; Nie, J.; Li, X.; Zeng, J.; Sun, Z. Chloride Transport Modeling of Binary Mineral Admixture High-Performance Concrete Under Sustained Compressive Stress. Buildings 2026, 16, 985. https://doi.org/10.3390/buildings16050985

AMA Style

Ma W, Cheng X, Nie J, Li X, Zeng J, Sun Z. Chloride Transport Modeling of Binary Mineral Admixture High-Performance Concrete Under Sustained Compressive Stress. Buildings. 2026; 16(5):985. https://doi.org/10.3390/buildings16050985

Chicago/Turabian Style

Ma, Wenqi, Xiaokang Cheng, Jie Nie, Xiang Li, Jia Zeng, and Ziling Sun. 2026. "Chloride Transport Modeling of Binary Mineral Admixture High-Performance Concrete Under Sustained Compressive Stress" Buildings 16, no. 5: 985. https://doi.org/10.3390/buildings16050985

APA Style

Ma, W., Cheng, X., Nie, J., Li, X., Zeng, J., & Sun, Z. (2026). Chloride Transport Modeling of Binary Mineral Admixture High-Performance Concrete Under Sustained Compressive Stress. Buildings, 16(5), 985. https://doi.org/10.3390/buildings16050985

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