Unraveling the Stray Current-Induced Interfacial Transition Zone (ITZ) Effect on Sulfate Corrosion in Concrete

Yong-Qing Chen; Lin-Ya Liu; Da-Wei Huang; Qing-Song Feng; Ren-Peng Chen; Xin Kang

doi:10.1016/j.eng.2024.08.001

Engineering ›› 2024, Vol. 41 ›› Issue (10) :135 -158. DOI: 10.1016/j.eng.2024.08.001

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Unraveling the Stray Current-Induced Interfacial Transition Zone (ITZ) Effect on Sulfate Corrosion in Concrete

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Abstract

The rail transit in sulfate-rich areas faces the combined effects of stray current and salt corrosion; however, the sulfate ion transport and concrete degradation mechanisms under such conditions are still unclear. To address this issue, novel sulfate transport and mesoscale splitting tests were designed, with a focus on considering the differences between the interfacial transition zone (ITZ) and cement matrix. Under the influence of stray current, the ITZ played a pivotal role in regulating the transport and mechanical failure processes of sulfate attack, while the tortuous and blocking effects of aggregates almost disappeared. This phenomenon was termed the “stray current-induced ITZ effect.” The experimental data revealed that the difference in sulfate ion transport attributed to the ITZ ranged from 1.90 to 2.31 times, while the difference in splitting strength ranged from 1.56 to 1.64 times. Through the real-time synchronization of splitting experiments and microsecond-responsive particle image velocimetry (PIV) technology, the mechanical properties were exposed to the consequences of the stray current-induced ITZ effect. The number of splitting cracks in the concrete increased, rather than along the central axis, which was significantly different from the conditions without stray current and the ideal Brazilian disk test. Furthermore, a sulfate ion mass transfer model that incorporates reactivity and electrodiffusion was meticulously constructed. The embedded finite element calculation exhibited excellent agreement with the experimental results, indicating its reliability and accuracy. Additionally, the stress field was determined utilizing analytical methods, and the mechanism underlying crack propagation was successfully obtained. Compared to the cement matrix, a stray current led to more sulfates, more microstructure degradation, and greater increases in thickness and porosity in the ITZ, which was considered to be the essence of the stray current-induced ITZ effect.

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Interfacial transition zone (ITZ) effect / Stray current / Sulfate attack / Transport mechanism / Splitting test / Microstructure

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Yong-Qing Chen, Lin-Ya Liu, Da-Wei Huang, Qing-Song Feng, Ren-Peng Chen, Xin Kang. Unraveling the Stray Current-Induced Interfacial Transition Zone (ITZ) Effect on Sulfate Corrosion in Concrete. Engineering, 2024, 41(10): 135-158 DOI:10.1016/j.eng.2024.08.001

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1. Introduction

Rail transit in sulfate-rich areas faces the combined effects of stray current and salt corrosion [1], [2], [3], [4]. From the perspective of stray current, the vast majority of rail transit uses direct current traction, and the running track is generally used as a negative return line. When the insulation between the track and tunnel segments decreases, stray currents are generated. A stray current will significantly change the transport of ions [5], [6]. On one hand, stray current accelerates the decomposition of hydration products in concrete, leading to severe microstructure degradation [5], [6], and on the other hand, charged ions are affected by electric forces under the action of potential differences [5], [6], [7], [8], [9]. From the perspective of sulfate corrosion, the mechanism of sulfate corrosion is related to the service environment [10], [11], [12], [13]. The severity of sulfate corrosion depends on the exposure conditions [10], [14], [15]. Hydrates containing alumina such as C₃A∙C_S∙H₁₈ and C₃A∙CH∙H₁₈ will be converted into high-sulfate forms (ettringite, C₃A∙3C_S∙H₃₂), which will cause expansion and deterioration in the presence of portlandite [16], [17], [18] (cement chemistry notations are used: C is CaO, A is A1₂O₃, S is SiO₂, C_S is CaSO₄, and H is H₂O). In addition, the crystallization of gypsum caused by cation exchange reactions can also lead to expansion and damage [19], [20], [21], [22]. Sulfate corrosion causes a decrease in the pH of concrete, and the corrosion products exhibit noncementation properties [23], [24]. Moreover, the reaction products have a much larger volume than the initial reactants, resulting in expansion cracking [16], [17], [18].

The degradation of concrete induced by the synergistic action of stray current and sulfate attack has garnered increasing research interest in recent years [25], [26], [27], [28]. Stray current accelerates the internal transfer of external sulfates to cement-based materials, increases the sulfate concentration and the content of corrosion products, and accelerates the deterioration of cement-based materials [25]. Stray current also increases the number of effective collisions between ions, thereby promoting the chemical reaction process of sulfate corrosion, leading to a significant increase in the production of ettringite [26]. In addition, when the stray current exceeds a certain value, the impact of electromigration and electrochemical reactions is more significant than the concentration gradient on the sulfate ion transport process, which will lead to the transformation of sulfate corrosion from “diffusion control” to “reaction control,” and its mechanical degradation is also controlled by reactivity [27], [28]. However, most of the above studies overlooked the multiphase and heterogeneous characteristics of concrete. The concrete can be composed of aggregates, a cement matrix, and an interfacial transition zone (ITZ). The ITZ has a gradient distribution of porosity due to the “wall effect,” and it is easy to form directional deposits of tabular calcium hydroxide crystals. Therefore, the ITZ is characterized by a higher porosity and higher calcium hydroxide content than the cement matrix [29], [30]. Based on our previous studies [5], [6], [7], [9], the ion migration induced by stray current is very sensitive to the microstructure represented by pores, and stray current preferentially promotes the decomposition of calcium hydroxide. Therefore, simplifying the concrete in subway tunnel segments into a single homogeneous material will cause serious errors. The need to separate the ITZ from the cement matrix has also been confirmed by other researchers [31], [32], [33]. For example, Zheng et al. [31] performed a sulfate ion transport experiment involving dry-wet cycles and reported that the ion transport depth in the ITZ was 2 mm deeper than that in the cement matrix and that the sulfate ion concentration in the ITZ was greater than that in the cement matrix. The sulfate wet-dry cycle test conducted by Tu et al. [32] also confirmed that the ITZ is more prone to cracking. Furthermore, through numerical simulations, He et al. [33] demonstrated that the ITZ seriously affects ion transport. However, a comprehensive literature review indicates that understanding the influence of the ITZ on the corrosion of sulfate ions induced by stray currents is still lacking. However, there is sufficient evidence from our studies [5], [6], [7], [9] on chloride ion transport induced by stray currents and from other researchers [31], [32], [33] on sulfate transport in wet-dry cycles that shows that disregarding the uniqueness of the ITZ is an obstacle to accurately evaluating ion corrosion.

In summary, it is crucial to consider the influence of the ITZ in service environments where stray currents coexist with sulfates. There are at least three urgent issues that need to be addressed: ① What is the impact of the ITZ on sulfate ion transport? ② What role does the ITZ play in strength degradation? ③ What are the essence and mechanisms of the influence of the ITZ on transport performance and strength performance? Here, a series of innovative sulfate ion transfer experiments and mechanical tests were conducted to accurately determine the impact of the ITZ. The “stray current-induced ITZ effect” was discovered and defined. Furthermore, a sulfate ion mass transfer model coupled with reactivity and electrodiffusion was constructed, and the results of the embedded finite element calculations were consistent with the experimental results. The impact of the stray current-induced ITZ effect on the mechanical properties was revealed through real-time synchronization of splitting experiments and particle image velocimetry (PIV) technology. Finally, a series of in situ micro/nanoscale experiments were conducted to explore the formation mechanisms of this material. The stray current-induced ITZ effect significantly changed the transport of sulfate ions and the load-bearing characteristics of the corroded concrete. Given the extensive operation and construction of rail transit in sulfate areas around the world, current research provides a crucial basis for its service maintenance and durability design.

2. Materials and methods

2.1. Sample preparation

The same ordinary Portland cement was used as the cementitious material in all the samples, and the main components are shown in Table 1. ITZs with different characteristics were indirectly obtained through aggregates with the same total volume and different particle sizes. The same water-cement ratio was maintained, and the same proportion of high-performance polycarboxylic acid water reducer was added to ensure that the microstructure of the cement matrix was consistent. The specimen preparation process is shown in Fig. 1. Sand and gravel were used as aggregates, featuring particle sizes that spanned from 1.25 to 5.00 mm, 1.25 to 10.00 mm, and 5.00 to 10.00 mm, designated S1, S2, and S3, respectively. Notably, all these aggregates exhibited continuous grading (Fig. 1(a)). To avoid the influence of bleeding, aggregates larger than 10 mm were not used. The fineness modulus of the sand was 2.79. The aggregates were added under saturated and surface-dry conditions, and the weight of water brought by the aggregates was removed when calculating the water-cement ratio of the concrete. The mixed proportions of the mixtures are shown in Table 2. The thickness of the specimens used for the mass transfer performance test was 20 mm, and the thickness of the specimens used for the splitting strength test was 50 mm. All specimens had a diameter of 100 mm (Fig. 1(b)). The distribution diagram of the aggregates in the concrete specimens is shown in Fig. 1(c). The water-cement ratio of the mixture was 0.34. After sieving and washing, the aggregates were weighed and prepared. The mixture was mixed evenly using the same procedure as we used previously [5], [6]. After mixing, standard curing was carried out for 28 days. All test specimens were subjected to vacuum saturation before corrosion testing.

2.2. Novel sulfate ion transport experiment

An innovative experimental device for sulfate ion transport was developed (Figs. 2(a) and (b)). The developed experimental device achieved excellent water sealing of upstream and downstream solution tanks through rubber rings (Figs. 2(c) and (d)). The innovative sulfate ion transport experimental device converted the measurement of sulfate ion transport depth and concentration by grinding powders into a measurement of sulfate ion concentration in downstream solutions. Compared with traditional equipment, the titration accuracy of the innovative experimental equipment was 0.01% (±20 μL and 20 mL), and the influence of the aggregates was completely avoided during grinding (the aggregates were considered nontransmissible compared to the cement matrix; therefore, the more aggregates there were when grinding the concrete powders, the poorer the accuracy) (Fig. 2(e)). The traditional method of determining sulfate transport performance is destructive. Its accuracy depends on the position of the ground powders, and the aggregate powders have a dilution effect that leads to the unreliability of the results.

A 10% concentration of sodium sulfate solution was used as the corrosive liquid of the cathode. One reason was that high sulfate ion concentrations are common in northwest China [34], [35]. The other reason was that errors might be caused by an insufficient supply of sulfate ions. As reported in previous studies, a 10% sodium sulfate solution would be fully dissolved, ensuring the accuracy of the experiment [35], [36], [37]. The sodium sulfate solution was replaced every three days to maintain a constant sulfate concentration. After the saturated specimens were installed, the solutions were immediately filled, and electric currents were applied. This time was recorded as the start time of corrosion. Stray current corrosion was simulated through constant voltage loading, and the decrease in insulation degree was simulated through the increase in electric current caused by the entry of ions and the deterioration of concrete under constant voltage conditions. The voltage was set to 0, 5, 10, or 15 V. The different tests were named VaSb, where a represents the applied voltage (a = 0, 5, 10, or 15, respectively) and b represents the sample number (b = 1, 2, or 3, depending on aggregate grading). The concentration of sulfate ions in the anode solution tank was checked every 12 hours until sulfate ions were detected and the sampling frequency was reduced. Lead ions were used as indicator electrodes to determine the concentration of sulfate ions by potentiometric titration. The measurement process was as follows: First, the test solution in a 20 mL downstream solution tank was accurately aspirated, then 80 mL of anhydrous ethanol and 80 mL of distilled water were added, and the pH was adjusted to 4-6. It was further mixed thoroughly in the instrument and finally titrated with lead nitrate standard solution. It is worth noting that anhydrous ethanol was added during the experimental process to reduce the solubility of lead sulfate, resulting in a significant increase at the endpoint of potentiometric titration. The total amount of sulfate ions transmitted was calculated by multiplying the concentration of sulfate ions by the volume of the anode solution tank.

2.3. Observation of splitting based on PIV technology

The tensile strength of the deteriorated concrete composite materials was much lower than the compressive strength. Therefore, the failure of concrete structures was mainly caused by tensile failure. The splitting tensile test is considered the most effective method for determining the tensile strength of brittle materials and is usually superior to direct tensile tests and fracture modulus tests [38]. After 28 days of coupled corrosion caused by stray current-induced sulfate attack (Fig. 3(a)), the specimens were subjected to a splitting test to measure their tensile deterioration. Monotonic displacement loading was uniformly applied at a constant loading rate of 7.5 × 10⁻⁶ m·s⁻¹. To study the full-field deformation and localized failure characteristics of concrete, it was necessary to measure the strain data on its surface. The use of traditional strain gauges was susceptible to the influence of specimen deformation and lacked the ability to provide full field strain information. Therefore, PIV technology was utilized to capture deformation field information using optical imaging principles. The microsecond-level response revealed the deformation and cracking characteristics of the aggregates, ITZ, and cement matrix. It is noninvasive and has a high resolution, avoids interference with the specimen, and can also achieve transient measurement of the full deformation field. To use PIV technology, the first step was to create a speckle system on the tested samples. The preparation method for the speckle system is briefly described as follows: ① The white paint spray was maintained at an angle of 45° and a distance of 20-30 cm, and the surfaces of the samples were sprayed in an orderly manner to fully cover the base color (priming paint). ② The black paint tank was shaken to make it even. A distance of 20-30 cm was maintained at a 45° angle, and then the specimens were slowly and uniformly sprayed over the surfaces (with speckle paint), forming uniform black and white speckles as tracer points (Fig. 3(b)).

The PIV system produced by Correlated Solutions, Inc. in the United States was adopted, and it included the following four parts: an image acquisition system charge-coupled device camera, a lighting system, a computer with related data processing software, and a synchronizer (Fig. 3 (c)). The black and white speckle system produced by PIV technology has excellent tracking performance in deformation fields. High-frequency camera photographic technology (162 Hz) and image processing technology VIC-2D (a fully integrated solution that utilizes optimized correlation algorithms to provide non-contact, full-field, two-dimensional displacement, and strain data for mechanical testing on planar specimens) were utilized to achieve highly accurate deformation field calculations on the surfaces of the samples (in-plane displacement accuracy: 0.00001 × FOV (field of view); strain accuracy: ∼10 με (microstrain, which is a strain of one part per million)). A high-speed camera with a time sampling frequency of 36 000 Hz was used to record the crack evolutionary characteristics during the splitting process. The laser generator and image acquisition system were connected to the computer by a synchronizer, and the sampling frequency was adjusted to synchronize the high-frequency camera with the light source pulse, thereby accurately obtaining the tracer particle images. Therefore, the origin of the failure of concrete specimens under sulfate attack induced by stray currents was revealed, and experimental evidence was provided to support the construction of mesoscopic models of splitting and fracture toughness of deteriorated concrete specimens.

2.4. In situ microstructure evolutionary measurement and analysis methods

The thickness of the ITZ is very small, which makes it difficult to separate from the cement matrix. Therefore, it is almost impossible to obtain the ITZ powder required by the quantitative X-ray diffraction (QXRD) and thermogravimetry/derivative thermogravimetry (TG/DTG) quantitative methods. In situ microscopic observation and quantitative techniques were used. The backscattered electron (BSE) mode of the FEI Quanta 650 FEG (a high-performance scanning electron microscope; FEI Corporation, USA) was used to observe the microstructures of the deteriorated ITZ and cement matrix corroded by stray current and sulfate ions. The acceleration voltage range was 200 V-30 kV, and the maximum beam current was 200 nA. The grayscale image obtained using this mode was combined with ImageJ software to quantitatively analyze the distribution of corrosion products and porosity. The experimental procedure for scanning electron microscopy (SEM) observation was as follows: Low-magnification observation was used to determine the overall deterioration morphology, and the distribution of elements such as S and Ca was further obtained, which could provide information on the migration mechanisms of sulfate ions. Furthermore, high-magnification observations were used to determine the characteristic morphology of the surrounding area of specific aggregates. Line scanning was utilized to determine the evolution of elements from the ITZ to the cement matrix. In image analysis, considering the nonuniformity of the microstructure of concrete materials, hundreds of regions were counted to obtain reliable porosity and product evolutionary data.

Notably, SEM also has its own drawbacks: the amplification factor is not sufficiently high and can only be observed at the micrometer scale, which cannot be used to observe nanoscale morphology and obtain nanomechanical properties. In addition, SEM observations can only reveal two-dimensional morphology and lack the ability to characterize three-dimensional morphology. To investigate the mechanisms of crack propagation in corroded concrete at the nanoscale, atomic force microscope (AFM) technology was employed for a detailed analysis of specific regions. The primary focus of this analysis was to examine the microstructural differences between the ITZ and the cement matrix. In this experiment, a Park XE7 (PARK Co., Ltd., the Republic of Korea) atomic force microscope was utilized, which boasts an error of less than 0.02 nm. An Olympus microcantilever beam (OMCL-AC55TS-B3, (Olympus Corporation, Japan) with an elastic coefficient of k = 85 N∙m⁻¹ and a resonance frequency of f = 1600 kHz was selected. The tapping mode of imaging was adopted, and the properties of the corroded concrete were studied at the atomic scale, with high-resolution, three-dimensional imaging of the surfaces and no damage to the samples.

The grayscale image of the backscatter mode of SEM can obtain relevant information such as porosity and can derive certain product information through the elemental energy spectrum. The tapping mode of AFM can capture local nanoscale information. However, the above two methods were not sufficient for accurately determining the thickness of the ITZ, nor could they characterize the mechanical strength indicators of the ITZ and cement matrix simultaneously. Hardness is an important mechanical performance indicator that reflects the ability of solid materials to resist local deformation. Therefore, the Vickers hardness was further adopted to characterize the thickness and local mechanical properties of the ITZ in corroded concrete. An HX-1000T (Shanghai SUNNY HENGPING Scientific Instrument Co., Ltd., China) digital intelligent microhardness tester was used, with a load of 50 g and a duration of 10 seconds. After unloading, a square pyramid indentation was pressed on the surfaces of the samples. The length of the two diagonals was measured, and the average value d was used to calculate the indentation area (A). The ratio of the load to the indentation area was calculated, which was the Vickers hardness (HV;kgf∙mm⁻², 1 kgf = 9.80665 N). The indentation area is shown in Eq. (1) [39].

(1)

A = \frac{d^{2}}{2 \sin θ}

Thus, the Vickers hardness was calculated via Eq. (2) [39]:

(2)

H V = \frac{P}{A} = \frac{2 P \sin θ}{d^{2}} = \frac{1.8544 P}{d^{2}}

where

P

is the load, N; d is the diagonal length, μm; and θ is the contact angle between the indenter and the material surface, θ = 136°.

The randomness of the porosity, surface smoothness, particle distribution of the aggregates, and unhydrated clinker particle distribution in the ITZ results in a certain degree of dispersion in the microhardness. Therefore, the test points for the distribution of the Vickers hardness should be arranged around the same aggregate to reduce the differences caused by the dispersion of the microhardness of different aggregates. In the present study, a box plot was used to process the data to avoid artificially determining the width of the ITZ, and the standard microhardness values of the mortar matrix were determined using lower quartiles of the box plot.

The advanced detection methods mentioned above all require drying of the samples, which are prepared using an organic solvent replacement method that can preserve the nanoscale microstructure to the greatest extent possible. The sample preparation procedure was as follows: The samples were immersed in 99.5% isopropanol for 2 weeks and then placed in a 2.5 × 10⁻² mbar (1 mbar = 100 Pa) vacuum chamber for three days. A semiautomatic polishing program was used to prepare samples after resin inlay for instrument indentation, AFM, SEM imaging, and X-ray spectroscopy. The samples were roughly ground with 600, 400, and 200-grit SiC papers in sequence, and finally, the ground and cleaned samples were polished on an alumina grinding FibrMet (Lake Bluff, USA) disc with abrasive sizes of 9, 3, and 1 μm to obtain flat and smooth surfaces.

3. Stray current-induced effect of the ITZ on sulfate ion transport

The sulfate transport results are shown in Fig. 4. The migration front of sulfate ions gradually approached the downstream anode solution tank as the corrosion time increased. Finally, the entire specimen was penetrated, and the binding ability of the cement slurry to sulfate ions (including chemical binding and physical adsorption) was saturated. The breakthrough time t₀ is the time when sulfate ions begin to leave the specimen and enter the downstream reservoir, which is a complex function of the concrete transport properties and sulfate reactivity (Section 5). As shown in Fig. 4, when there was no stray current, sulfate ions were not detected in the downstream solution after continuous corrosion for 28 days. When there was a stray current, the increased sulfate mass showed two-stage or three-stage distribution patterns (Figs. 4(b)-(d)). The division of each stage was mainly determined based on the slope of the experimental curves, and different stages reflected the rate of increase in sulfate ions in the downstream solution tank. Samples V5S1, V10S1, and V15S1 were selected as examples to illustrate the division methods of each stage (Figs. 4(b)-(d)). In general, the transport rate of sulfate ions in the third stage was the highest, followed by that in the first stage, and that in the second stage was the slowest. The larger the aggregate size was, the earlier the sulfate ions in the cathode solution tank were detected, and the shorter the duration of the second stage. The experimental results not only demonstrated excellent upstream and downstream solution isolation but also indicated that diffusion based on a concentration gradient was not sufficient to breakdown the sample within 28 days. The experimental results demonstrated the necessity of using concrete specimens with smaller thicknesses, especially for analyzing the role of the ITZ.

The transport of sulfate ions did not exhibit a first-order functional line similar to the steady-state transport of chloride ions described in NT Build 443 [40] or ASTM C1556−11a [41]. Chemical reactions or adsorption binding with the cement matrix first occurred when sulfate ions entered the concrete, and only the remaining free ions could continue to be transported forward, which was a nonstationary process. During the nonstationary transport process, the concentration of sulfate ions varied with both depth and time. Once the sulfate ions penetrated the entire depth of the specimens and their reactivity with the cement matrix began to diminish, leading to a relatively stable concentration distribution within the specimens over time, a quasisteady state sulfate ion entry condition was achieved (the three-stage distribution of sulfate mass increase in the anode solution tank, rather than a first-order function curve, is referred to as the quasisteady state of sulfate ion transport induced by stray current). During the experiment, the corrosion conditions were standardized to remain consistent, with the sole variance being the aggregate size. Therefore, it can be inferred that the ITZ played an important role in the transport of sulfate ions induced by stray currents. Under varying stray current conditions, the discrepancy in the quantity of sulfate ions transported due to the ITZs ranged from 1.90 to 2.31 times (V5S1 and V5S3 in Fig. 4(b), V10S1 and V10S3 in Fig. 4(c), and V15S1 and V15S3 in Fig. 4(d)).

4. Stray current-induced effect of the ITZ on concrete splitting failure under sulfate attack

4.1. Failure patterns

The advanced experimental system designed in the current research (Fig. 2) was used to complete the designed corrosion program. Furthermore, the PIV system was utilized to collect local displacement vector maps corresponding to the splitting tests (Fig. 5). The focus of the tensile strength experiment was to capture the local deformation of deteriorated concrete specimens corroded by stray current coupled with sulfate based on the sensitivity of PIV to displacement and time, which provided an experimental basis and validation for constructing a mesoscopic model (obtained by tracking the speckle displacement, which was much smaller than the size of the aggregates). Fig. 5 shows that when there was no stray current, the local deformation decreased, and the concrete exhibited good uniformity. The effective strain in the transverse direction was lower than that of the specimens under stray current conditions. Under the condition of no stray current, there was one main tensile crack in the middle of the splitting failure mode, but the details were slightly different. For the V0S1 sample, the cracks appeared straighter than those in the V0S2 and V0S3 samples (Fig. 5(a)). However, V0S2 and V0S3 exhibited more twists and turns, and even exposed aggregates were observed in V0S3 at 2000 ms (Figs. 5(b) and (c)). With increasing stray current, the splitting behaviors of the corroded concrete significantly changed. During the splitting process, more local deformation occurred, and more closed contours of the stress field were observed. Due to the incompressibility of the aggregates, it could be inferred that the location with greater deformation occurred in the ITZ. A common rule was that more fine aggregates formed more closed strain field contours because the number of fine aggregates was greater than the same volume (mass) of aggregates (Figs. 5(d)-(j)).

The tensile cracks in the samples with more fine aggregates were more severe (see the first vertical column of the samples in Fig. 6), while the coarser aggregates made the cracks more curved (see the morphology of the failure specimens in Fig. 6). Furthermore, when there was no stray current, the highest transverse strain was in the central axis. With increasing stray current, the number of tensile cracks tended to increase. The cracks formed simultaneously along multiple ITZs, which was also confirmed by experimental and theoretical research in Section 6. In the splitting test, first, the difference in the position of the ITZ was the key factor leading to crack formation. ITZs at different positions exhibited different deformation and stress distribution characteristics during the loading process. The sample S1 had smaller aggregates than the samples S2 and S3, which led to a more uniform ITZ. These degraded ITZs were prone to cracking at the axis of maximum tensile stress and forming connections. The ITZs of larger aggregates deviated from the central axis, causing their cracks to deviate from the central axis and exhibit twists and turns (see S2 and S3 in Fig. 6). Second, the physical and mechanical properties of the ITZ had a significant impact on the formation and propagation of cracks. The ITZ was the weaker area between the aggregates and cement matrix, and its strength and toughness were lower than those of the other parts. In the splitting test, the ITZ became the starting point and propagation path of the cracks. Due to the differences in the properties of the ITZ at different positions, such as a thicker ITZ and greater porosity in concrete with larger aggregates, initial cracks were more likely to form, which led to cracks appearing at different positions within the ITZ, resulting in the formation of multiple cracks. The degree of degradation of the ITZ in the experiment was mainly controlled by the stray currents, which led to larger stray currents forming more weakened ITZs and more cracks (see the comparison of the horizontal subgraphs in Fig. 6).

4.2. Load-displacement results

Splitting tests were conducted on specimens subjected to sulfate corrosion with three different aggregate distributions (ITZ distributions) under four different stray current conditions. The vertical load and displacement data were recorded, and the load-displacement curves of the different concrete specimens were plotted, as shown in Fig. 7. The load-displacement curves of the corroded concrete could be divided into four stages: ① compaction stage, ② elastic stage, ③ crack propagation stage, and ④ postpeak residual stage. As the vertical force increased, the ITZs perpendicular to the loading direction were compressed, and the initial existing pores and cracks in the ITZs gradually closed. Therefore, the vertical loading exhibited a nonlinear increase with displacement. After the ITZ could not be further compressed, the elastic stage occurred, where the vertical pressure and vertical displacement exhibited a linear relationship. As the loading process continued, new cracks appeared in the specimens. This stage is called the microcrack propagation stage. In this stage, the vertical load growth rate decreased, and the slopes of the load-displacement curves decreased. When the vertical load reached the ultimate strength of the concrete, the specimens were split (Fig. 5, Fig. 6), the storage stress in the concrete was instantly released, and the concrete entered the postpeak residual stage. The most special aspect of sulfate corrosion induced by stray current was that under the induction of stray current, in which the ITZ became a fast transport channel for sulfate ions. Therefore, the location with the fastest degradation rate occurred in the ITZ, and the strength limit was first reached at the ITZ position. The higher the stray current was, the greater the degradation of the ITZ compared to that of the cement matrix. Therefore, when subjected to a constant voltage of 15 V during the stray current corrosion, multiple ITZs near the center of the samples reached the limit state, and more crack development could be seen after cracking (Fig. 5, Fig. 6). The different concrete samples were mainly affected by stray currents. When the stray currents were the same, different ITZ distributions were the reason for the differences in the load-displacement curves of the different specimens (Fig. 7). The larger the aggregate was, the lower its bearing capacity. The initial ITZ formed by the coarser aggregates and cement matrix was thicker, and the rate of sulfate ion transfer was faster, further leading to more intense chemical reactions and widening of the difference in porosity and strength between the ITZ and cement matrix (Section 7). Under varying stray current conditions, the discrepancy in the splitting strength of concrete subjected to sulfate attack, attributed to the ITZ, reached a significant difference of 1.56-1.64 times (V5S1 and V5S3 in Fig. 7(b), V10S1 and V10S3 in Fig. 7(c), and V15S1 and V15S3 in Fig. 7(d)).

5. Diffusion-migration-reaction model and the influencing mechanism of the ITZ

5.1. Governing equations

Compared to an environment without an electric field, the transport speed of sulfate ions in an environment with an electric field was much faster (Fig. 4). When the insulation performance of the subways decreased, the stray current leakage became increasingly severe. Therefore, the migration of external

S O_{4}^{2 -}

was accelerated through the combined effects of free diffusion and electromigration. Fig. 8(a) shows a schematic diagram of diffusion, migration, and electrochemical reactions during the experimental process. Fig. 8(a) also shows a schematic diagram of the transport of sulfate ions in the concrete ITZ. To establish a sulfate ion transport model that distinguishes between the ITZ, aggregate, and cement matrix, an ideal spherical aggregate replacement model for equivalent aggregate volume and equivalent ITZ volume was established (Fig. 8(b)). After being invaded by sulfate ions, cement-based materials undergo a series of chemical reactions with Ca(OH)₂, C₃A, and other hydration products, which are influenced by the transport rate. The reaction process causes volume changes, and the rate of volume change caused by chemical reactions between different components and sulfate is also different. Therefore, changes in the transmission process not only affect the concentration distribution of

S O_{4}^{2 -}

in cement-based materials but also affect the chemical reactivity of sulfate attack. Given the significant differences in the hydration products between the ITZ and cement matrix, it was crucial to construct a sulfate ion reactive mass transfer model that considers the ITZ and cement matrix separately. The governing equation for sulfate ion transport is shown in Eq. (3) [42].

(3)

\frac{\partial C_{T}}{\partial t} = D (\frac{\partial^{2} C}{\partial x^{2}} + z \frac{F}{RT} \times \frac{\partial C}{\partial x} \times \frac{\partial ψ}{\partial x})

where

C_{T}

is the total concentration of sulfate; t is the transmission time (the transmission time of

S O_{4}^{2 -}

is consistent with the corrosion time of

S O_{4}^{2 -}

); C is the concentration of free

S O_{4}^{2 -}

; x is the transmission distance of free

S O_{4}^{2 -}

; D is the effective diffusion coefficient; T is absolute temperature; z is the charge number; F and R are Faraday constant and gas constant, respectively; and

ψ

is the gradient of the total electric intensity potential.

5.2. Reactions of sulfate ions during transport

According to previous studies [21], [43], [44], after external sulfate ions enter cement-based materials, they first undergo a chemical reaction with the cement hydration product CH to generate gypsum. More gypsum is generated in the ITZ due to the presence of more CH, which was confirmed by the SEM– energy dispersive spectroscopy (EDS) and AFM analyses in Section 7. As the external sulfate ions persistently penetrated the concrete, the quantity of gypsum produced steadily increased. Some researchers [45], [46] have proposed that the continuous accumulation of gypsum crystals gives rise to internal stress within the material, and more CH reactants lead to an increase in gypsum products. However, others have contended that the volumetric variations resulting from the gypsum formation process could be offset by the presence of capillary pores and the space vacated by CH [47], [48]. In subsequent SEM–EDS and AFM analyses (7.1 Fragile microstructure and sulfur enrichment in the ITZ, 7.2 Nanomechanical properties of the ITZ), within a very small ITZ thickness, the concentration of ettringite was much greater than that in the cement matrix. In addition, concentrated micro/nanocracks were directly observed in the ITZ, while fewer cracks were observed in the cement matrix. Therefore, regardless of whether the generation of gypsum caused cracks, the higher content of ettringite in the ITZ area under the action of stray current indicated that the stray current promoted the chemical reaction of gypsum and provided more reactants for the generation of ettringite (Eqs. (4), (5), (6), (7), (8)).

(4)

S O_{4}^{2 -} + C a^{2 +} + 2 H \to C \bar{S} H_{2} (g y p s u m)

(5)

C_{3} A + 3 C \bar{S} H_{2} + 26 H \to C_{6} A {\bar{S}}_{3} H_{32} (e t t r i n g i t e)

(6)

C_{4} A H_{13} + 3 C \bar{S} H_{2} + 14 H \to C_{6} A {\bar{S}}_{3} H_{32} (e t t r i n g i t e) + C H

(7)

C_{4} A \bar{S} H_{12} + 2 C {\bar{S} H}_{2} + 16 H \to C_{6} A {\bar{S}}_{3} H_{32} (e t t r i n g i t e)

(8)

C_{3} A H_{6} + 3 C \bar{S} H_{2} + 20 H \to C_{6} A {\bar{S}}_{3} H_{32} (e t t r i n g i t e)

Similar to previous studies [49], [50], [51], the formation of ettringite is expressed using a unified expression:

(9)

C A + q C \bar{S} H_{2} \to C_{6} A {\bar{S}}_{3} H_{32}

where

C A = γ_{1} C_{4} A \bar{S} H_{12} + γ_{2} C_{4} A H_{13} + γ_{3} C_{3} A H_{6} + γ_{4} C_{3} A, q = 2 γ_{1} + 3 γ_{2} + 3 γ_{3} + 3 γ_{4}

γ_{i}

represents the proportion coefficient of each aluminum phase component, and

C A_{i}

represents the molar concentration of each aluminate phase. When there are no experimental conditions for measuring the aluminum phases,

q

is assumed to be 8/3.

Assuming that the formation of ettringite is a second-order chemical reaction, as described in Eqs. (4), (5), (6), (7), (8), (9), the sulfate ion depletion rate, gypsum formation rate, and calcium aluminate consumption rate can be obtained based on chemical reaction kinetics (Eqs. (10), (11), (12)) [52]:

(10)

\frac{\partial C_{S O_{4}^{2 -}}}{\partial t} = - k_{1} C_{S O_{4}^{2 -}} C_{{C a}^{2 +}}

(11)

\frac{\partial C_{gpy}}{\partial t} = k_{1} C_{S O_{4}^{2 -}} C_{C_{{C a}^{2 +}}} - k_{2} C_{gpy} C_{CA}

(12)

\frac{\partial C_{CA}}{\partial t} = - k_{2} \frac{C_{gpy} C_{CA}}{q}

where k₁ and k₂ are the chemical reaction rate constants of Eqs. (4), (5), (6), (7), (8), (9);

C_{{C a}^{2 +}}

C_{S O_{4}^{2 -}}

C_{gpy}

, and

C_{C A}

are the concentrations of

C a^{2+}

S O_{4}^{2 -}

, secondary gypsum, and equivalent lumped CA, respectively (Eq. (9)), mol∙m⁻³; and t is the corrosion time (the transmission time of

S O_{4}^{2 -}

is consistent with the corrosion time of

S O_{4}^{2 -}

), d.

5.3. The volume expansion of ettringite (AFt)

One important reason for sulfate corrosion was the volume expansion of the products. On one hand, gypsum was a prereaction for producing ettringite, and on the other hand, the elastic modulus of gypsum was much smaller. Therefore, the volume expansion of the current study mainly considered the volume change caused by ettringite, and the equation for the volume change rate is as follows:

(13)

V_{r} = \frac{V_{r e a c t i o n p r o d u c t s} - V_{r e a c t a n t s}}{V_{r e a c t a n t s}} = \frac{m_{v C_{6} A {\bar{S}}_{3} H_{32}}}{m_{v C A} + γ_{i} m_{v C \bar{S} H_{2}}} - 1

where

V_{r}

represents the volume change rate caused by the chemical reaction process;

V_{reaction products}

represents the total volume of the product, cm⁻³;

V_{reactants}

represents the total volume of reactants, cm⁻³;

m_{v}

represents the unit molar volume, cm³∙mol⁻¹:

m_{v}

m / ρ

(

m

is the unit molar mass, g∙mol⁻¹;

ρ

is the density, g∙cm⁻³). The volume expansion rate of various chemical reactions in sulfate corrosion has been thoroughly and systematically studied, and the volume expansion rate used is shown in Table 3 [53], [54].

5.4. Calcium leaching

Calcium leaching mainly manifests in two parts: portlandite and C-S-H. According to previous research [55], calcium leaching can be calculated via a three-stage function as follows:

(14)

C_{Ca}^{s} (x, t) = \{\begin{matrix} \begin{matrix} [\frac{- 2}{x_{1}^{3}} C_{C a^{2+}}^{3} (x, t) + \frac{3}{x_{1}^{2}} C_{C a^{2+}}^{2} (x, t)] \{C_{CSH0} {[\frac{C_{C a^{2+}} (x, t)}{C_{satu}}]}^{1/3}\}, 0 \leq C_{C a^{2+}} (x, t) \leq x_{1} \end{matrix} \\ \begin{matrix} C_{CSH0} {[\frac{C_{{Ca}^{2+}} (x, t)}{C_{satu}}]}^{1/3}, \end{matrix} x_{1} < C_{C a^{2+}} (x, t) \leq x_{2} \\ \begin{matrix} C_{CSH0} {[\frac{C_{C a^{2+}} (x, t)}{C_{satu}}]}^{1/3} + \frac{C_{CH0}}{{(C_{satu} - x_{2})}^{3}} {[C_{C a^{2+}} (x, t) - x_{2}]}^{3}, \end{matrix} x_{2} < C_{C a^{2+}} (x, t) \end{matrix}

where

C_{Ca}^{s} (x, t)

and

C_{C a^{2+}} (x, t)

are the calcium concentrations in the solid phase and the pore solution, mol∙m⁻³, respectively;

C_{satu}

is the saturated

C a^{2+}

concentration, mol∙m⁻³;

x_{1}

is the

C a^{2+}

concentration in the liquid phase when the C-S-H gel begins to transform into SiO₂ gel, mol∙m⁻³;

x_{2}

is the

C a^{2+}

concentration in the liquid phase when Ca(OH)₂ is completely dissolved, mol∙m⁻³; and

C_{CSH0}

and

C_{CH0}

are the initial concentrations of Ca in the solid phase of the C-S-H gel and CH, mol∙m⁻³, respectively.

5.5. Analytical calculation of model parameters

The porosity of the ITZ was significantly greater than that of the cement matrix, along with a notable enrichment of CH. Furthermore, the transport of sulfate ions was also heavily influenced by the pore structure [56], [57]. Distinct from other inert porous media, the principal hydration products of cement underwent chemical reactions with sulfate ions, leading to volumetric expansion. This expansion was directly associated with the filling of pores, as evidenced by the reduced rate of sulfate transport in the downstream solution (Fig. 4). With the expansion of ettringite and secondary gypsum, the tensile limit between concrete pores was broken, and cracks were generated, further leading to an increase in porosity [58]. Therefore, the accelerated migration of sulfate ions was observed (see Fig. 4 for the third stage, which shows an accelerated increase in sulfate mass). The analytical solutions for the volume and porosity of the ITZ were obtained in subsequent sections, as once the volume and porosity of the ITZ and cement matrix were analytically calculated, the diffusion coefficients of the ITZ and cement matrix (

D_{eff}^{0}

) were calculated as [51], [59]:

(15)

D_{eff}^{0} = D_{b} \frac{6 D_{b} (V_{a} + V_{I}) (1 - V_{a}) +2 V_{I} (D_{I} - D_{b}) (1+2 V_{a} + 2 V_{I})}{3 D_{b} (2+ V_{a}) (V_{a} + V_{I}) +2 V_{I} (1 - V_{a} - V_{I}) (D_{I} - D_{b})}

where

V_{a}

and

V_{I}

are the volume fractions of the aggregate and ITZ, respectively; and

D_{b}

and

D_{I}

are the diffusion coefficients of the cement matrix and ITZ, respectively. It can be described as follows [56]:

(16)

D_{i} = D_{0} φ_{i} β = D_{0} \frac{2 φ_{i}}{3 - φ_{i}}

where

D_{0}

is the diffusion coefficient of ions in water,

φ_{i}

is the porosity of the cement matrix and ITZ,

i

(

i

=1, 2, 3..) represents samples under different working conditions, and

β

is the tortuosity. The ITZ volume fraction in concrete can be obtained using the Monte Carlo method [60], [61]:

(17)

V_{I} = (1 - V_{a}) - (1 - V_{a}) \exp [- (t_{1} h + t_{2} h^{2} + t_{3} h^{3})]

where

h

is the thickness of the ITZ (this value was determined by the Vickers hardness in Section 7), and

t_{1}

t_{2}

, and

t_{3}

are defined in terms of the volume fraction

V_{a}

, mean diameter

〈 D 〉

, mean surface area

〈 S 〉

, and mean volume

〈 V 〉

of the spherical aggregate particles (the method of equivalent polygonal aggregate to spherical aggregate is shown in Fig. 8(b)) [62].

(18)

t_{1} = \frac{V_{a}}{(1 - V_{a}) 〈 V 〉} 〈 S 〉

(19)

t_{2} = \frac{2 π V_{a} 〈 D 〉}{(1 - V_{a}) 〈 V 〉} + \frac{V_{a} {〈 S 〉}^{2}}{2 {(1 - V_{a})}^{2} {〈 V 〉}^{2}}

(20)

t_{3} = \frac{4 π V_{a}}{3 (1 - V_{a}) 〈 V 〉} + \frac{2 π {V_{a}}^{2} 〈 D 〉 〈 S 〉}{3 {(1 - V_{a})}^{2} {〈 V 〉}^{2}}

The filling of pores caused by chemical reactions (φ) was considered as follows [51]:

(21)

φ =max [φ_{0} + {(\frac{Δ V}{V})}_{leach} - {(\frac{Δ V}{V})}_{AFt}, 0]

where

φ_{0}

is the initial porosity, which can be calculated through the water–cement ratio [63], [64] or experimentation;

Δ V

is the volume change;

V

is the origin volume. In the present study, the porosities of the ITZ and matrix were determined through concentric expansion and overflow criteria [65], [66] (Section 7).

(22)

{(\frac{Δ V}{V})}_{leach} = [C_{Ca}^{s} (x, t) - C_{Ca0}^{s}] V_{CH}

where

V_{CH}

is the molar volume of Ca(OH)₂ and

C_{Ca0}^{s}

is the initial amount of calcium in the solid phase before leaching [55].

The expansion of ettringite led to an increase in strain, and calcium leaching led to a weaker local strain resistance. When the combined effects of these two factors surpassed the local threshold strain, microcracks emerged, leading to altered ion transport, as previously investigated [67], [68]. The diffusion coefficient (

D_{e}

) is given as follows:

(23)

D_{e} = \frac{D_{0}}{τ} (1 + \frac{32}{9} C_{d}), C_{d c} \leq C_{d} \leq C_{d e c}

(24)

D_{e} = \frac{D_{0}}{τ} [(1 + \frac{32}{9} C_{d}) + \frac{{(C_{d} - C_{d c})}^{2}}{C_{d e c} - C_{d}}]

where

τ

is the pore tortuosity (to be included in the finite element model for calculation, the calculation method for tortuosity is

τ = φ^{- 1/2}

C_{d}

is the density of the nucleated cracks [67], [68],

C_{d c}

is the infiltration front, and

C_{d e c}

is the fracture front. The cracking of local materials when they reach the limit state will be discussed in subsequent studies.

5.6. Validation and prediction of the diffusion-migration-reaction model

The aggregates were deemed completely inert, preventing the migration of sulfate ions through them. The ITZ and cement matrix were treated as parallel components, yet accounting for their distinct boundary conditions. Based on the governing equation and considering the reactivity of sulfate ions, the diffusion–migration–reaction model was established as follows:

(25)

\{\begin{matrix} \frac{\partial C_{S O_{4}^{2 -}}}{\partial t} = D_{i} (\frac{\partial^{2} C_{S O_{4}^{2 -}}}{\partial x^{2}} + z \frac{F}{RT} \times \frac{\partial C_{S O_{4}^{2 -}}}{\partial x} \times \frac{\partial φ_{i}}{\partial x}) - k_{1} C_{C A} C_{S O_{4}^{2 -}} \\ \frac{d C_{C A}}{d t} = - \frac{k_{1} C_{C A} C_{S O_{4}^{2 -}}}{q}, \frac{d C_{S O_{4}^{2 -}}}{d t} = k_{1} C_{C A} C_{S O_{4}^{2 -}} \end{matrix}

The current experiment involved one-dimensional transmission, and the boundary conditions and initial conditions were as follows:

(26)

\{\begin{matrix} t = 0, 0 < x < L, C_{S O_{4}^{2 -}} = 0, C_{C A} = C_{C A 0} \\ t > 0, x = 0, C_{S O_{4}^{2 -}} = C_{S O_{4}^{2 -}}, C_{C A} = 0 \begin{matrix}  \end{matrix} \\ t = 0, ψ = 0; t > 0, ψ = ψ_{0} \end{matrix}

A range of random aggregate models, each with distinct aggregate gradations in line with experimental observations, were constructed. The analytical equations that encompassed diffusion, migration, and reaction processes were incorporated, taking into account the specific characteristics of the ITZ and cement matrix. Based on the initial and boundary conditions mentioned above, the finite element method was used to solve the partial differential equation [23], and the model parameter inputs are shown in Table 4 [55], [57], [68], [69], [70], [71]. The ITZ was constructed based on limited-scale solid elements between the matrix and aggregate. Based on the above studies, the dependent variable evolutionary relationship of each physical field was established, and the transient mode was adopted. The problem of sulfate ion transport induced by stray current could be seen as a coupled analysis of multiple physical fields, such as electric field-chemical field-diffusion motion. Therefore, a mass transfer analysis method was constructed to consider the significant differences in chemical reactions between the ITZ and cement matrix during sulfate ion transport, and the established model was solved using the finite element method. The concentration and distribution of sulfate ions in different random aggregate models over different time periods were obtained, as shown in Fig. 9.

Fig. 10 shows both the theoretical calculations and experimental findings on the migration of sulfate ions in concrete after 28 days of corrosion. Notably, in the absence of stray current, the transmission depth remained relatively unchanged regardless of the type of aggregates used. However, in the presence of stray current, the difference in transmission caused by the aggregates (ITZs) became highly significant. The migration depths of sulfate ions in V0S1, V0S2, and V0S3 were 3−5 mm, which was consistent with the experimental results observed through downstream solution tanks. After 28 days of corrosion, there was no detectable concentration of sulfate ions in these three groups of experiments, as shown in Fig. 4(a). This could be explained by the fact that although the increase in aggregate size increased the thickness of the ITZ, there was also a more significant blocking effect. When there was a stray current, the diffusion depth was significantly affected by the ITZ, especially when the stray current was caused by 5 V of constant voltage corrosion, and the results for different samples (V5S1, V5S2, and V5S3) showed the most significant differences (Fig. 10). After 28 days of corrosion, the sulfate ions all penetrated the experimental samples, but the sulfate ion concentration that was transmitted was significant. This could also be mutually verified with our study, as shown in Fig. 4. The vertical axis represents the increased mass of sulfate ions, and the horizontal axis represents the corrosion time; therefore, its slope is the sulfate ion transfer rate (Fig. 4). At a constant voltage of 10 V (V10S1, V10S2, and V10S3), the larger ITZs formed by larger aggregates also exhibited greater sulfate transport concentrations. Furthermore, this phenomenon could also be experimentally obtained in samples with constant voltage corrosion of 15 V (V15S1, V15S2, and V15S3). Thus, the significant impact of the ITZ on sulfate ion transport was fully verified through novel and ingenious thin concrete specimens, and it was defined as the ITZ effect caused by stray currents. This effect indicates the direction of durability design for reinforced concrete structures with a risk of stray current leakage in areas such as rail transit. The interface between aggregates and the cement matrix plays a controlling role in the transport of sulfate ions induced by stray currents. Therefore, it could be inferred that under stray current conditions, the ion transfer capacity of the ITZ inside the concrete increases more than that inside the cement matrix. This finding is supported by our previous molecular dynamics research [6] and is consistent with the experimental phenomenon of chloride ion transport in deeply buried rail transit [5]. The visual understanding of this phenomenon is similar to “seepage piping”: Stray current searches for the weakest region (surface ITZ), thereby further weakening the porous ITZ, carrying away the ions decomposed from the hydration products, and further connecting the ITZ to form the main channels (Fig. 9, Fig. 11). Sulfate ions also caused cracks through the formation of ettringite (Section 7), and the formation of ettringite could explain the experimental phenomenon shown in Fig. 4, where the quasisteady state process in the downstream solution tank first increased and then decreased with increasing corrosion time.

6. Analytical solution of the stress field and crack propagation mechanism

For the experimental analysis of the ITZ effect induced by stray current on concrete splitting failure under sulfate corrosion, the linear stage and crack propagation stage exhibited a transition from elastic deformation to elastic–plastic deformation (Fig. 7). According to the principle of linear elastic superposition, the stress state of the concrete splitting test (Brazilian splitting disc) could be composed of a pair of symmetrical linear loads P on two infinite half-planes and a uniformly distributed tensile stress

2 P / (π D h)

(where

D

is the diameter and

h

is the thickness) on the circumference of the disc. The result of superposition was that the circumference of the disk was in a free state (satisfying the boundary conditions) (Fig. 12).

The stress component at any point E within the disk was as follows [72], [73], [74], [75]:

(27)

\{\begin{matrix} σ_{y} = \frac{2 P}{π h} \times \frac{\cos θ_{1}}{r_{1}} \sin^{2} θ_{1} + \frac{2 P}{π h} \times \frac{\cos θ_{2}}{r_{2}} \sin^{2} θ_{2} - \frac{2 P}{π D h} \\ σ_{x} = \frac{2 P}{π h} \times \frac{\cos θ_{1}}{r_{1}} \cos^{2} θ_{1} + \frac{2 P}{π h} \times \frac{\cos θ_{2}}{r_{2}} \cos^{2} θ_{2} - \frac{2 P}{π D h} \end{matrix}

(28)

τ_{xy} = \frac{2 P}{π h} \times \frac{\cos θ_{1}}{r_{1}} \sin θ_{1} \cos θ_{1} - \frac{2 P}{π h} \times \frac{\cos θ_{2}}{r_{2}} \sin θ_{2} \cos θ_{2}

where

σ_{x}

is the horizontal stress component,

σ_{y}

is the vertical stress component,

τ_{xy}

is the shear stress,

r_{1}

is the length of EM,

r_{2}

is the length of EN, θ₁ is the angle between EM and the symmetrical load, θ₂ is the angle between EN and the symmetrical load.

To maintain a positive stress value under compression and a negative stress value under tension, it was specified in the above equation that when point E was located on the right side of the central axis, both

θ_{1}

and

θ_{2}

were taken as positive values, and both were taken as negative values on the left side. According to Eq. (27),

r_{1}

r_{2}

cannot be zero. That is, points M and N at the linear load position of the splitting test were both singular points. These three points have the following relationships:

(29)

\{\begin{matrix} r_{2}^{2} = r_{1}^{2} + D^{2} - 2 r_{1} D \cos θ_{1} \\ \cos θ_{2} = \frac{D^{2} + r_{2}^{2} - r_{1}^{2}}{2 r_{2} D} = \frac{D - r_{1} \cos θ_{1}}{r_{2}} \\ \sin θ_{2} = \sqrt{1 - \cos^{2} θ_{2}} = \frac{r_{1} \sin θ_{1}}{r_{2}} \end{matrix}

The above geometric relationship was substituted into Eqs. (27), (28); thus, the whole strain field was obtained:

(30)

\{\begin{matrix} σ_{y} = \frac{2 P}{π h} [\frac{\cos θ_{1}}{r_{1}} \sin^{2} θ_{1} + \frac{(D - r_{1} \cos θ_{1}) r_{1}^{2} \sin^{2} θ_{1}}{{(r_{1}^{2} + D^{2} - 2 D r_{1} \cos θ_{1})}^{2}} - \frac{1}{D}] \\ σ_{x} = \frac{2 P}{π h} [\frac{\cos^{3} θ_{1}}{r_{1}} + \frac{{(D - r_{1} \cos θ_{1})}^{3}}{{(r_{1}^{2} + D^{2} - 2 D r_{1} \cos θ_{1})}^{2}} - \frac{1}{D}] \end{matrix}

(31)

τ_{xy} = \frac{2 P}{π h} [\frac{\sin θ_{1} \cos^{2} θ_{1}}{r_{1}} - \frac{{(D - r_{1} \cos θ_{1})}^{2} r_{1} \sin θ_{1}}{{(r_{1}^{2} + D^{2} - 2 D r_{1} \cos θ_{1})}^{2}}]

The coordinate axis was translated to the center of the disk, and by solving Eqs. (30), (31), the stress on the entire disk was determined as follows:

(32)

\{\begin{matrix} σ_{y} = \frac{2 P}{π h} \{\frac{(x + \frac{D}{2}) y^{2}}{{[{(x + \frac{D}{2})}^{2} + y^{2}]}^{2}} + \frac{(\frac{D}{2} - x) y^{2}}{{[{(x - \frac{D}{2})}^{2} + y^{2}]}^{2}} - \frac{1}{D}\} \\ σ_{x} = \frac{2 P}{π h} \{\frac{{(x + \frac{D}{2})}^{3}}{{[{(x + \frac{D}{2})}^{2} + y^{2}]}^{2}} + \frac{{(\frac{D}{2} - x)}^{3}}{{[{(x - \frac{D}{2})}^{2} + y^{2}]}^{2}} - \frac{1}{D}\} \end{matrix}

(33)

τ_{xy} = \frac{2 P}{π h} \{\frac{{(x + \frac{D}{2})}^{2} y}{{[{(x + \frac{D}{2})}^{2} + y^{2}]}^{2}} - \frac{{(\frac{D}{2} - x)}^{2} y}{{[{(x - \frac{D}{2})}^{2} + y^{2}]}^{2}}\}

According to Eqs. (32), (33), in the case of ideal homogeneity, the tensile stress at the central axis was the highest, and the stress on the central axis is shown in Eq. (34):

(34)

\{\begin{matrix} σ_{x} = \frac{2 P}{π D h} \{\frac{4 D^{2}}{D^{2} - 4 x^{2}} - 1\} \\ \begin{matrix} σ_{y} = - \frac{2 P}{π h D} \\ τ_{xy} = 0 \end{matrix} \end{matrix}

The influence of stray currents on the ITZ suggested that the ITZ not only affected the migration of sulfate ions but also contributed to more severe calcium leaching and crystal damage of ettringite. Consequently, it was reasonable to deduce that the ITZ significantly impacted the mechanical properties of the degraded concrete. To determine the origin of concrete splitting after corrosion, PIV technology was used to directly observe the ITZ. Fig. 13(a) shows that the mechanical analysis system was constructed for the splitting test considering the aggregate and ITZ. Taking V5S1 as an example (Fig. 13(b)), from the appearance of the morphology, direct observation of the first three stages could not distinguish their differences, indicating that the deformation during the compression stage, elastic stage, and crack propagation stage was quite small. With the use of PIV technology (Fig. 5(d)), the strain contour was observed to close around the ITZ. To delve deeper into the mechanisms of ITZ cracking near the central axis and the observed increase in crack count following splitting failure due to stray current, analytical research was primarily conducted on both the elastic stage and the crack propagation (elastic-plastic) stage.

A schematic diagram of the stress at different positions of the ITZ of the aggregate is shown in Fig. 13(c), and its calculation is shown in Eq. (33). According to our previous research [5], there are three mechanisms for cracking, as shown in Fig. 13(c) (I. opening mode, II. tearing mode, and III. sliding mode). Although the initial cracks in the ITZ generally exhibited composite stress mechanisms, for concrete materials, the development of cracks was mainly influenced by the opening mode. Furthermore, whether the cracks continued to develop and the direction of development were mainly controlled by tensile stress. Although the initial pores were inclined, their cracking direction ultimately followed the axis direction (Fig. 5, Fig. 6), and the critical conditions are shown in Eq. (35) [31]. The pore model and crack propagation mechanism near the ITZ are shown in Fig. 13(c).

(35)

G = \frac{2 K_{I}^{2}}{μ (1 + υ^{'})} \underset{δ_{c} \to 0}{l i m} \frac{1}{2 π δ_{c}} \int_{0}^{δ_{c}} \sqrt{\frac{δ_{c} - x}{x}} d x = \frac{2 K_{I}^{2}}{μ (1 + υ^{'})} \underset{δ_{c} \to 0}{l i m} \frac{1}{2 π δ_{c}} \times \frac{π δ_{c}}{2} = \frac{2 K_{I}^{2}}{μ (1 + υ^{'})} = \frac{K_{I}^{2}}{E^{'}}

where

G

is the energy release rate;

μ

is the shear modulus;

K_{I}

is the stress field strength;

υ^{'}

is a function of Poisson’s ratio;

δ_{c}

represents the propagation of cracks, and when

δ_{c} \to 0

, it is the limit state of crack propagation, that is, from the elastic stage to the elastic–plastic stage;

E^{'}

is the elastic modulus. On the crack extension line (

O υ

axis),

θ

= 0,

r

x

When the critical stress field strength was exceeded, cracks propagated, as shown in Eq. (36).

(36)

K \geq K_{C}

where

K

is stress field strength and

K_{C}

is the limit value of the stress field strength that the crack system can withstand.

During the stray current-induced degradation by sulfate ions, ITZ significantly affected ion transport (Section 3). Further research in this section revealed that the ITZ effect induced by stray currents was also reflected in the observed mechanical degradation. In the absence of stray current degradation, there was no significant difference in the load displacement curves of V0S1, V0S2, and V0S3, and the splitting position occurred at the maximum tensile stress position of the specimens, manifested as a cracking line. When there were stray currents, the origin of cracking deteriorated in the ITZs near the maximum tensile stress. Therefore, there were multiple cracking lines.

7. The causes of the ITZ Effect

7.1. Fragile microstructure and sulfur enrichment in the ITZ

Given the challenges associated with effectively isolating the ITZ from the cement matrix, conducting QXRD and TG/DTG tests by grinding powders has become impractical. Instead, following sulfate corrosion induced by stray currents, the appearance morphology and energy spectrum of various elements in proximity to the ITZ were obtained using SEM and EDS. These techniques allowed for the direct observation of elemental differences, as well as disparities in pores and cracks between the ITZ and cement matrix, thereby providing crucial support for sulfate ion transport and splitting failure mechanisms. Taking V5S1 as an example, as shown in Fig. 14, the position of the ITZ was qualitatively determined by the stronger electrochemical decomposition of Ca and the combination of its distance from the aggregates. The area-scanning and line-scanning results from SEM-EDS on Ca and S indicated that the positions with weaker Ca signal peaks exhibited stronger S signals.

The ITZ was the most severely degraded area due to the decomposition of the concrete hydration products triggered by stray currents. This degradation could be attributed to the enrichment of calcium hydroxide crystals caused by the “wall effect.” Additionally, the ITZ served as a faster transport channel for sulfate ions, leading to increased contact between sulfate solutions and pore solutions, which accelerated the rapid and significant degradation of the ITZ location. The significant differences in the ITZ resulted in regular differences in sulfate transfer between the different aggregate concrete samples under the same voltage conditions, which further led to differences in their mechanical properties. It is worth noting that these differences did not exist in the absence of stray currents (Fig. 7, Fig. 10). Further comparative observations of the morphology of the typical ITZ and cement matrix in the V5S1 sample revealed that the ITZ exhibited more severe degradation, and its porous characteristics were directly observed (Fig. 15(a)). Further magnification of the pores between the ITZ and the cement matrix revealed clusters of acicular ettringite (Figs. 15(b) and (c)), while more columnar gypsum was found in the deeper pores of the ITZ (Fig. 15(d)). Needle-shaped ettringite and columnar gypsum were also observed in the pores of the cement matrix (Fig. 15(e)). The sizes of the pores revealed a significantly weakened microstructure of the ITZ compared to that of the cement matrix (Figs. 15(d) and (e)), and the X-ray diffraction (XRD) pattern also confirmed the significant differences (Figs. 15(f) and (g)).

7.2. Nanomechanical properties of the ITZ

AFM was used to precisely identify the pores within the ITZ and cement matrix, and the nanomechanical properties of the pores were quantified through force spectroscopy. During the measurement process, the cantilever carefully approached and “pierced” the samples, subsequently retracting. The deflection and piezoelectric motion of the cantilever were meticulously measured and converted into quantitative assessments of force and probe tip separation, thus yielding mechanical insights about the samples. The elastic modulus, derived from the elastic segments of the stress-strain curves, served as a nanomechanical indicator. The experimental results are shown in Fig. 16, where needle-shaped clusters of ettringite were accurately captured (Figs. 16(a)-(c) and (f)-(h)). However, this needle-shaped ettringite was shorter than when there was no stray current [76], [77], [78], which is also reflected in Fig. 15. Direct image observation also revealed the same patterns; that is, ettringite decomposed under a stray current; therefore, the observed ettringite showed more dispersed characteristics. AFM was also very accurate in its response to the morphology of gypsum, indicating the accuracy of current research on the selection and calibration of AFM probes. Additional testing of the elastic modulus was conducted with nanoscale precision, revealing that AFM could precisely capture the location of pores. This enabled the isolation of mechanical testing for pores within the ITZ and the cement matrix (Figs. 16(d) and (i)). Pores and cracks exhibited smaller elastic moduli due to electrochemical decomposition and sulfate attacks, as shown in the blue areas of Figs. 16(d) and (i). Furthermore, AFM was used to locate different pores in the cement matrix and ITZ, with significant differences in the elastic modulus observed at different locations. A smaller elastic modulus was considered to indicate more severe corrosion, as shown in Figs. 16(e) and (j). The average elastic modulus of the pores in the ITZ was 15.06 GPa, while the average elastic modulus of the pores in the cement matrix was 28.46 GPa. Through statistical analysis of the elastic modulus around the pores, it was found that there was a Gaussian distribution, and the elastic modulus of the pores propagating inside the ITZ was approximately 52.9% of that of the cement matrix (Figs. 16(e) and (j)). The direct AFM evidence explained why the number of splitting cracks increased under the conditions of stray current (Fig. 6) and crack propagation (Fig. 13): The ITZ position generated crack propagation under smaller forces.

7.3. ITZ thickness and porosity

The concentric expansion method and overflow criterion were deemed effective techniques for determining the porosity of both the ITZ and cement matrix using BSE images. Employing this approach, the initial and deteriorated thicknesses of the ITZ for various aggregate sizes were precisely measured, serving as valuable inputs for establishing the boundary conditions of theoretical analysis (refer to 5 Diffusion–migration–reaction model and the influencing mechanism of the ITZ, 6 Analytical solution of the stress field and crack propagation mechanism). The utilization of BSE images for porosity determination has been shown to be highly accurate, as reported in previous studies [79], [80], [81], [82]. Fig. 17 shows the processes and results of determining the typical ITZ porosity and thickness of V5S1. After obtaining the BSE images, the aggregate boundary was accurately located (accurate edges were determined through the energy spectrum, as shown in Fig. 14). Second, the strips were divided in steps of 2 μm (Fig. 17(a-i)). Subsequently, the differences in grayscale values caused by elastic collisions between BSEs and the sample were used to distinguish between the pores and hydrated phases. The pores exhibited a sudden change in grayscale due to the depression (Fig. 17(a-ii)). Finally, the porosity distribution of the ITZ was obtained (see Fig. 17(a-iii)). On one hand, Fig. 17(a-iii) shows the wall effect: the closer the distance to the aggregate is, the greater the porosity. On the other hand, Fig. 17(a-iii) indicates the existence of a limit for porosity, and the experimental results indicate the presence of some phases that were difficult to decompose due to stray currents, such as the unhydrated cement and calcite phases. This result was also supported by our previous research [31]. It is worth noting that a sufficient number of BSE images were needed to obtain reliable statistical analysis results. According to the statistical pattern in Fig. 17(a-iii), the porosity distribution exhibited a three-stage distribution. The slow change in porosity in the first stage was due to the slower decomposition of phases that were difficult to decompose electrochemically, mainly occurring at the edge of the aggregates. In the second stage, the porosity changed the fastest, mainly due to the decomposition of Portland, while in the third stage, the reason for the slow change in porosity was attributed to the smaller contact area with the environmental solution when the positions were close to the cement matrix. Therefore, the distribution of porosity had both maximum and minimum extreme values and exhibited slow–fast–slow evolutionary patterns, which was consistent with the evolution described by the sigmoid function (Fig. 17(a-iii)). Therefore, the porosity function (

φ (x)

) could ultimately be described using Eq. (37):

(37)

φ (x) = φ_{mor} + Δ φ / [1 + {(x_{a} / x_{0})}^{p}]

where

φ_{mor}

is the porosity of the cement matrix;

Δ φ

represents the difference between

φ_{m a x}

(the maximum porosity of the strip in the ITZ) and

φ_{m o r}

Δ φ = φ_{m a x} - φ_{m o r}

;

p

can be regarded as the porosity reduction coefficient;

x_{0}

represents the abscissa corresponding to the center value of sigmoid function; and

x_{a}

represents the distance from the surface of the aggregate.

The thickness of the ITZ was determined by the Vickers hardness, and this quantitative method has been widely adopted [83], [84], [85], [86], [87]. Although the distribution of elements in SEM–EDS could generally determine the range of the ITZ (Fig. 14), there was not always a clear boundary distinction, which made it difficult to quantitatively distinguish the thickness of the ITZ in the color gradient area. Vickers hardness testing could effectively avoid the influence of subjective judgment. The direction of the Vickers hardness test points gradually shifted from the aggregate to the cement matrix (see Fig. 17 (b-i)), ensuring that at least one point fell inside the aggregate. Spot testing was carried out every 10 μm. For the same aggregate, spot testing was carried out every 120°, and at least three dots of matrix were used for the Vickers hardness test. The aggregate had the highest Vickers hardness. A sharp decrease in the Vickers hardness (Fig. 17(b-ii)) indicated that this position was the ITZ. As the Vickers hardness test progressed toward the cement matrix, the Vickers hardness gradually increased and stabilized. Consistent with previous studies [83], [84], [85], [86], [87], a box plot was drawn using the Vickers hardness data of the cement matrix, and the lower quartile of the box plot was the upper limit value of the ITZ Vickers hardness (Fig. 17(b-iii)). Due to the wall effect, the Vickers hardness of the ITZ was lower than that of the cement matrix. Therefore, the thickness of the ITZ could be accurately calculated and corresponded to different sizes of aggregates. By accumulating the ITZs of different sizes of aggregates, the total volume of the ITZ (

V_{I}

) could be obtained. The thickness of the ITZ and the pore distribution function along the ITZ could determine the ion diffusion coefficient

D_{i}

of the ITZ (Eq. (16)). Figs. 17 (a-iii) and (b-iii) show that stray current-induced sulfate corrosion resulted in a significantly increased ITZ porosity and ITZ thickness (the thickness of the ITZ without degradation is generally reported to be 20–50 μm, and its porosity is generally 20%–30% [29], [65], [79]). The microscopic mechanism of sulfate transport and mechanical property degradation induced by stray current caused the ITZ to deteriorate faster than the cement matrix, resulting in a much larger proportion of sulfate ion transport through the ITZ (Fig. 9, Fig. 10). The harm of crack propagation has been widely proven [88], [89], [90], [91]. This can easily lead to attack by harmful ions such as chloride ions, which in turn leads to the mass loss of steel bars. Ultimately, this seriously affects the durability of infrastructure buildings. It is worth noting that the variability of concrete material properties, such as pore size and chemical composition, has a significant impact on the long-term performance of concrete structures under sulfate attack. This needs to be considered when inputting initial conditions into the model to increase the reliability of structural durability assessment [92].

8. Conclusions

Rail transit systems in sulfate-rich regions encounter the compounded effects of salt and stray current corrosion, yet predicting their durability and lifespan remains challenging due to uncertainties surrounding sulfate ion transportation and concrete degradation mechanisms. To address these complexities, innovative sulfate transportation and mesoscale splitting tests were designed, emphasizing the distinct characteristics of the ITZ and cement matrix. Additionally, a sulfate ion mass transfer model incorporating reactivity and electrodiffusion was developed and integrated into finite element analysis for simulation calculations. Real-time synchronization between splitting experiments and PIV technology enabled the acquisition of mechanical properties. Overall, a comprehensive suite of micro- and nanoscale qualitative and quantitative experiments were conducted to elucidate the underlying mechanisms involved. The following conclusions were obtained:

(1) The stray current-induced ITZ effect was revealed via an innovative sulfate ion transmission test. In the presence of stray current, the ITZ strongly affected the downstream exposure time and transmission rate of sulfate ions. The quasisteady transport of sulfate ions induced by stray current was revealed, which could be attributed to a series of coupled chemical reactions during the transport process. A sulfate ion mass transfer model coupled with reactivity and electrodiffusion was constructed, and the embedded finite element calculation showed good consistency with the experimental results.

(2) Under the action of stray current, the number of splitting cracks in the concrete increased after sulfate attack, rather than along the central axis, which was significantly different from the conditions without stray current and the ideal Brazilian disk test.

(3) Crack propagation starting from the ITZ was captured by PIV technology. The sulfate attack induced by stray current caused the ITZ to move slightly away from the central axis to reach the tensile limit, although only the tensile stress on the central axis was the highest. The crack propagation mode was mainly the opening mode; therefore, the development of multiple cracks was perpendicular to the direction of tensile stress.

(4) The ITZ effect of stray current-induced sulfate attack was attributed to sulfate enrichment, a more degraded microstructure, and the greater thickness and porosity of the ITZ. The weaker mechanical properties of the ITZ also accelerated the rate of sulfate attack, thereby increasing the proportion of sulfate transport through the ITZ and continuously making the ITZ a weak link for stray current-induced sulfate attack.

Acknowledgments

This work was supported by the State Major Program of National Natural Science Foundation of China (52090082), the National Key Research and Development Program of China (2022YFB2602200), and the National Natural Science Foundation of China (52178423 and 52378398).

Compliance with ethics guidelines

Yong-Qing Chen, Lin-Ya Liu, Da-Wei Huang, Qing-Song Feng, Ren-Peng Chen, and Xin Kang declare that they have no conflict of interest or financial conflicts to disclose.

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1. Introduction

2. Materials and methods

2.1. Sample preparation

2.2. Novel sulfate ion transport experiment

2.3. Observation of splitting based on PIV technology

2.4. In situ microstructure evolutionary measurement and analysis methods

3. Stray current-induced effect of the ITZ on sulfate ion transport

4. Stray current-induced effect of the ITZ on concrete splitting failure under sulfate attack

4.1. Failure patterns

4.2. Load-displacement results

5. Diffusion-migration-reaction model and the influencing mechanism of the ITZ

5.1. Governing equations

5.2. Reactions of sulfate ions during transport

5.3. The volume expansion of ettringite (AFt)

5.4. Calcium leaching

5.5. Analytical calculation of model parameters

5.6. Validation and prediction of the diffusion-migration-reaction model

6. Analytical solution of the stress field and crack propagation mechanism

7. The causes of the ITZ Effect

7.1. Fragile microstructure and sulfur enrichment in the ITZ

7.2. Nanomechanical properties of the ITZ

7.3. ITZ thickness and porosity

8. Conclusions

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