Compression Damage Precursors of Silane-Protected Concrete Under Sulfate Erosion Based on Acoustic Emission Characterization

Abstract

Concrete materials exposed to sulfate-rich geological environments are prone to structural durability degradation due to chemical erosion. Silane-based protective materials can enhance the durability of concrete structures under harsh environmental conditions. This study investigates the evolution of acoustic emission (AE) precursor characteristics in silane-protected, sulfate-eroded concrete specimens during uniaxial compression failure. Unlike existing research focused primarily on protective material properties, this work establishes a novel framework linking “silane treatment–AE parameters–failure precursor identification”, thereby bridging the research gap in damage evolution analysis of sulfate-eroded concrete under silane protection. Uniaxial compressive strength tests and AE monitoring were conducted on both silane-protected and unprotected sulfate-eroded concrete specimens. A diagnostic system integrating dynamic analysis of the acoustic emission b-value, mutation detection of energy concentration index ρ, and multifractal detrended fluctuation analysis (MF-DFA) was developed. The results demonstrate that silane-protected specimens exhibited a distinct b-value escalation followed by an abrupt decline prior to peak load, whereas unprotected specimens showed disordered fluctuations. The mutation point of energy concentration ρ for silane-protected specimens occurred at 0.83 σc, representing a 9.2% threshold elevation compared to 0.76 σc for unprotected specimens, confirming delayed damage accumulation in protected specimens. MF-DFA revealed narrowing spectrum width ($∆\alpha$) in unprotected specimens, indicating reduced heterogeneity in AE signals, while protected specimens maintained significant multifractal divergence. $∆f\left(\alpha \right)$ peak localization revealed that weak AE signals dominated during early loading stages in both groups, with crack evolution primarily involving sliding and friction. During the mid-late elastic phase, crack propagation became the predominant failure mode. Experimental evidence confirms the engineering significance of silane protection in extending service life of concrete structures in sulfate environments. The proposed multi-parameter AE diagnostic methodology provides quantitative criteria for the safety monitoring of protected concrete structures in sulfate-rich conditions.

1. Introduction

Concrete is recognized as a high-quality material in global infrastructure projects due to its excellent mechanical properties and cost-effectiveness [1,2,3]. However, when concrete structures are subjected to harsh environments, such as those containing sulfate and chloride ions, they become vulnerable to the infiltration of harmful agents. These agents can penetrate the concrete, exacerbating performance degradation and significantly impacting the service life of concrete infrastructures [4,5,6]. Developed countries invest substantial resources annually in the maintenance and rehabilitation of aging national infrastructure [7]. The operational service life of infrastructures in harsh environments rich in sulfate and chloride ions can be dramatically reduced from 100 years to about 40 years, and in extreme conditions, even to as low as about 10 years [8].

Western and southwestern China are characterized by numerous salt lakes and karst landscapes, with soils and water bodies abundant in sulfate ions. Many local reports indicate that the degradation and destabilization of concrete infrastructure in these regions are primarily due to sulfate erosion [9,10]. Sulfate ions are widely recognized as a common source of corrosion in soil, groundwater, rivers, and other environments [11,12,13]. The degradation of concrete properties due to sulfate exposure can generally be classified into three categories: chemical erosion, physical erosion, and combined chemical–physical erosion [14,15,16,17]. Numerous studies have shown that sulfate ions present in pore water can react with cement or hydration products to form calcite or gypsum, establishing chemical erosion as a primary cause of concrete deterioration in sulfate environments [18,19]. However, some investigations indicate that the crystallization of sulfates can lead to physical damage in concrete by inducing internal volume expansion and crack formation [20,21]. Additionally, during the chemical erosion process, sodium sulfate (Na₂SO₄) can react with cement or hydration products, expanding threefold in volume and causing severe structural damage to concrete [22,23]. Researchers have proposed various concrete protection strategies to mitigate sulfate attacks, including surface coatings, admixture modifications, and chemical admixture. Among these, silane-based treatments stand out due to their superior permeability, durability, and versatility.

The part of the native pore structure of concrete in contact with moisture tends to be the region where sulfate erosion begins [8]. This susceptibility can be attributed to the porous structure and strong hydrophilicity of concrete, which facilitate moisture penetration into the interior of the material. The infiltration of erosive moisture is a prerequisite for the degradation of concrete structures [24,25,26]. The effective waterproofing of concrete serves to protect the structure from the detrimental effects of sulfate erosion. Numerous researchers have demonstrated the improvement of concrete durability by enhancing hydrophobicity and minimizing water absorption [27,28,29]. Silanes have been employed for about 50 years as protective agents for porous cementitious materials in building applications [30,31]. The application of silane for concrete protection can be broadly categorized into two main types. The first is silane impregnation treatment, which forms a physical barrier by creating a hydrophobic film on the concrete surface. This treatment inhibits capillary water absorption, thus safeguarding the concrete from erosion [32,33,34,35,36,37]. The second application involves the use of silanes as hydrophobic admixtures to modify concrete to enhance its water repellency, thereby reducing water infiltration. However, it is important to note that modified hydrophobic concrete can adversely affect the original hydration reaction of cement, potentially reducing the mechanical strength of the concrete [30,31].

Sulfate erosion of concrete linings leads to material degradation and a decline in bearing capacity, compromising concrete safety [6,23,38,39]. Numerous studies have addressed this issue, focusing on the mechanisms of erosion degradation [40,41], the performance of eroded structures [42,43], and measures for concrete erosion protection [44]. However, the relationship between concrete erosion and protection in sulfate environments is complex [45]. Zhang et al. [46] conducted long-term erosion tests on concrete mixed with sulfate ions. Their findings revealed that specimens with a water source experienced severe erosion damage, while those without water showed little to no change. The deterioration behavior of concrete under sulfate attack was analyzed by Cheng et al. [47]. In recent years, many researchers have employed nondestructive testing (NDT) techniques, such as scanning electron microscopy (SEM), X-ray diffraction (XRD), and computed tomography (CT), to analyze the deterioration characteristics of concrete under sulfate erosion [48,49,50]. Liu et al. [49] utilized X-ray computed tomography (X-CT) and ultrasonic testing to conduct a comprehensive evaluation of the deterioration characteristics of concrete structures following sulfate erosion. Furthermore, Liu et al. [44] examined the protective performance of silane coatings on concrete structures in sulfate environments by integrating ultrasonic velocimetry and CT scanning imaging. While NDT methods, such as SEM, XRD, and nuclear magnetic resonance (NMR), can be effective in assessing the internal structural changes in concrete, it is crucial to acknowledge that concrete structures often endure specific stress states. Consequently, the above methods may not accurately reflect the damage characteristics of sulfate erosion concrete in silane-protected conditions. Additionally, AE monitoring enables the real-time tracking of damage stage transitions and identification of critical damage thresholds. However, ultrasonic testing can only reflect cumulative damage through wave velocity attenuation changes, unable to distinguish between microcrack initiation and propagation stages. SEM analysis observes static crack morphologies post-unloading, unable to reconstruct dynamic damage mechanisms during loading.

To monitor internal damage and crack propagation in loaded materials in real-time, AE is widely utilized as a nondestructive testing method for assessing the state characteristics of concrete, rock, and other materials under mechanical loading [51,52,53,54]. Numerous researchers have used changes in AE signals as a precursor to structural instability to assess the safety of engineered structures [55,56,57,58]. AE signals are generated by the expansion and propagation of internal cracks during loading, exhibiting nonlinear variation characteristics. As such, fractal theory can effectively describe the distribution characteristics of AE sequences in both time and space and characterize the fracture evolution during material damage. Yang et al. [59] investigated the evolution characteristics and precursor features of AE parameters related to concrete damage using multifractal theory. Additionally, the AE b-value has been demonstrated to characterize the damage characteristics of concrete materials [60]. Most studies have focused on the relationship between the damage and the AE b-value of concrete [61,62,63]. Colombo et al. [64] found that the AE b-value in concrete beams correlates with the extension of microcracks. Furthermore, Yang et al. [60] examined the degradation mechanisms of concrete performance in the presence of pH solutions and wet/dry cycles, investigating the AE precursor characteristics of concrete damage using multifractal theory.

While extensive laboratory experiments and theoretical analyses have been conducted to investigate the damage deterioration mechanisms of concrete structures in sulfate environments, limited attention has been devoted to characterizing AE b-value features and destabilization precursors during mechanical loading. Current research predominantly focuses on the failure processes of conventional concrete, with particularly scarce reports regarding the uniaxial compression AE characteristics and fracture precursors of silane-impregnated concrete subjected to sulfate attack. This study systematically examines the fracture precursors of silane-protected concrete in sulfate erosion environments through multi-method analysis incorporating AE b-value, energy concentration patterns, and multifractal theory.

Using sulfate-exposed concrete as a model system, we comparatively analyzed the mechanical loading responses and damage precursors through AE monitoring for both silane-treated and untreated specimens. Notably, the multifractal characteristics of AE sequences were quantitatively evaluated under different protection conditions. The results establish a technical framework for assessing silane protection efficacy and identifying critical damage precursors in concrete structures. These findings offer practical implications for tunnel lining preservation in sulfate-rich environments while providing methodological references for maintaining structural concrete in other aggressive environments, including chloride-laden and marine conditions.

2. Test Procedure

Silane-based protective materials provide multi-dimensional protection for concrete materials by reducing the surface energy of the substrate and limiting the penetration of harmful substances. To evaluate the effect of silane protection of concrete. Based on the principle of concrete damage, the strength of concrete specimens with and without silane protection after cyclic sulfate erosion was determined using uniaxial compression, and the AE during the test were recorded. The mechanical differences in concrete specimens under different protection conditions were comparatively analyzed. The damage characteristics of the compression process and its causes were also analyzed in depth by combining the AE b-value, energy concentration, and dynamic multifractal characteristics. The flowchart is depicted in Figure 1.

2.1. Sample Preparation

To evaluate the silane protection effect on concrete in sulfate erosion environments, this study simulates the accelerated erosion process of concrete typical of actual engineering conditions by implementing dry and wet cycles. The test specimens were extracted from tunnel lining concrete with a designed strength grade of C50, and the concrete mix design parameters are detailed in

Table 1. Concrete mix design parameters (kg/m³).

Cement	Water	Sand	Crushed Stone	Fly Ash	Expansion Agent	Water-Reducing Agent
410	165	711	1066	61	32.8	4.1

. Specimens were prepared by cutting concrete core samples into cylinders measuring 50 mm in diameter and 100 mm in height.

2.2. Experimental Program

2.2.1. Sulfate Erosion and Protection Programs

To simulate the erosion and deterioration process of tunnel lining concrete protected by silane during its actual service life, the prepared specimens were divided into two groups: Group A (silane-protected) and Group B (unprotected). Group A was treated with BS1701 silane from WACKER, Munich, Germany. Existing studies and engineering applications demonstrate that BS1701 silane, through molecular structure optimization, enhanced chemical corrosion resistance, and long-term protection design, exhibits significant technical advantages in sulfate attack environments. Although associated with higher initial costs, it achieves superior engineering economy through extended maintenance cycles and reduced structural repair requirements. Prior to applying the silane, the concrete surface was thoroughly cleaned to ensure it was dry and free of contaminants, and the initial mass of the specimens was recorded. A fine bristle brush, dipped in liquid silane, was used to evenly coat the surface of the specimens. The specimens were then placed in a cool, ventilated area for 12 h to allow for complete absorption of the silane, ensuring no liquid remained on the surface. The specimens were reweighed to determine the mass increase. This process was repeated until the mass increment reached 9.8 g (corresponding to a coverage rate of 500 g/m² as per site design), thereby achieving the desired silane coating protection.

Sulfate erosion in natural environments is a gradual process, often taking years or even decades before significant damage becomes apparent. Based on the groundwater ion analysis results from the tunnel site area, it is necessary to increase the concentration of the erosive medium in laboratory conditions to accelerate the erosion process. To simulate this, a 10% Na₂SO₄ solution was used to accelerate sulfate erosion of the concrete specimens. This concentration allows for the simulation of long-term erosion effects within a shorter timeframe while preventing excessively high concentrations that could skew the experimental conditions away from real-world scenarios. Group A specimens were treated with silane impregnant, while Group B specimens remained untreated. Three specimens were prepared for each group. The erosion and protection characteristics of the concrete specimens are summarized in

Table 2. Erosion solution composition.

Groups	Erosion Solution	Type of Protection
Group A	10% Na2SO4 solution	Silane-protected
Group B	10% Na2SO4 solution	Unprotected

.

Tunnel lining structures are subject to groundwater erosion throughout their service life, with some structures experiencing prolonged infiltration or alternating wet and dry conditions. The sulfate dry–wet cycle test, commonly used in existing studies, is one of the most widely employed methods for accelerated erosion [6,42]. Additionally, the frequency of the wet/dry cycles plays a crucial role in influencing the results. By implementing a cycle of 16 h of soaking followed by 8 h of drying, the treatment process can significantly shorten the overall test duration. The specific experimental design is outlined in

Table 3. Parameter design of wet and dry cycles.

Cycle Length	Dry–Wet Ratio	Drying Temperature	Experiment Length
24 h	1:2	60 °C	180 days

.

The dry–wet cycle test consists of alternating soaking and drying phases. In this test, the specimen undergoes a 24 h wet/dry cycle, with the soaking phase lasting 16 h. During the soaking phase, specimens are fully immersed in the erosion solution to simulate concrete erosion. Specimens are placed upright in an erosion solution chamber, ensuring that the distance from the top of the specimen to the liquid surface is no less than 3 cm. The chamber is maintained at a temperature of 20 ± 0.5 °C. The erosion solution is replaced every 30 days. At the end of the immersion period, the specimens are transferred to the drying phase, where the surface liquid is wiped off, and they are placed in a drying chamber at 60 ± 0.5 °C for 6 h. Subsequently, the specimens are cooled in a well-ventilated area for 2 h. The cycling process of the concrete is illustrated in Figure 2.

2.2.2. Mechanical Test Program

To assess the effect of silane protection on the concrete under sulfate erosion from the perspective of AE characteristics, uniaxial compression tests were conducted on the specimens. These tests analyze the mechanical properties of sulfate-eroded concrete with and without silane protection. The specimen loading test is shown in Figure 3. During compressive loading, data on load conditions, specimen strain, and AE signals were recorded synchronously.

The uniaxial loading tests were performed using a universal materials testing machine (INSTRON 1346) from the British company INSTRON (Buckinghamshire, UK). The loading was applied at a constant rate of 0.5 MPa/s, while the strain of the specimen under load was simultaneously measured. The AE probe operated within a resonant frequency range of 20 kHz to 400 kHz, with a sampling frequency of 1 M/s.

2.3. Uniaxial Compressive Test Results

The tests were conducted on specimens from Group A and Group B after 180 erosion cycles. Three specimens from each group were tested to determine the average compressive strength. The results of the tests are presented in

Table 4. Uniaxial compressive strength of specimens.

Groups	Group A	Group B
Average compressive strength (MPa)	62.0 ± 1.9	54.5 ± 1.1
Coefficient of variation (%)	3.1	2.0

.

The uniaxial compressive strength of the silane impregnated specimens was 62 MPa, which is very close to the design strength of C50 concrete. In comparison, the compressive strength of the uncoated silane specimens was 54.5 MPa, which is approximately 15% lower than the silane-protected group. This indicates that the silane impregnation effectively protects the concrete in a sulfate erosion environment, as the material strength of Group A does not exhibit significant deterioration. Conversely, the concrete specimens in Group B, lacking silane protection, showed marked deterioration due to erosion. This can be attributed to the silane impregnation’s ability to reduce the formation of expansive products caused by sulfate attack by hindering the intrusion of sulfate ions. The silane impregnator slowed the expansion of cracks, thereby preventing a significant reduction in compressive strength. On the other hand, concrete specimens without the silane coating were exposed to sulfate attack, allowing sulfate ions to penetrate the concrete, generate expansive products, and create internal stress concentrations that promoted the growth of microcracks. This crack expansion compromised the integrity of the concrete, resulting in a substantial decrease in compressive strength. Thus, silane impregnator coatings provide significant protection to the compressive strength of concrete in sulfate-aggressive environments.

Further analysis of the AE monitoring results during the uniaxial compression tests revealed distinct characteristics for the two groups of specimens. The AE characteristics of specimens are illustrated in Figure 4 and Figure 5.

Figure 4 demonstrates that the AE characteristics during the uniaxial compression damage process are largely similar for both groups. Throughout the compression process, the strains of both groups exhibited a nonlinear (stage I)-linear (stage II)-nonlinear (stage III) characteristic. The pore cracks within the specimens were gradually compacted, resulting in nonlinear characteristics. As loading continued to increase, the strain transitioned to a linear deformation mode. In the later stages of loading, cracks propagated, leading to the destabilization and damage of the specimens. Notably, the nonlinear deformation in Group B specimens, which lacked silane impregnation, was more pronounced at the onset of loading, with strain reaching 0.002 at approximately 10 s. These specimens experienced destabilization and damage with a maximum strain of about 0.007 at around 105 s. In contrast, Group A specimens with silane impregnation displayed relatively smaller deformation, reaching a strain of 0.002 at about 20 s and a maximum strain of 0.006 at approximately 120 s. This difference can be attributed to the protective silane coating on Group A specimens, which reinforced the micropore structure and minimized sulfate erosion. In contrast, Group B specimens, lacking silane protection, experienced further development of microporosity under sulfate erosion, leading to significant deterioration and a marked reduction in their ability to resist deformation. Consequently, Group B specimens were more susceptible to substantial deformation during the loading process.

The AE activity characteristics of the two groups, as depicted in Figure 4, exhibited significant differences. The distribution of AE counts for Group A specimens displayed a triple peak characteristic, occurring at initial loading, near 70 s of loading, and at peak loading. In contrast, Group B specimens exhibited only one AE peak prior to approaching peak load. Throughout the loading process, the cumulative AE counts and cumulative energy for Group A specimens increased rapidly during the nonlinear deformation stage at the beginning of loading, slowed during the linear stage, and then showed significant growth again in the nonlinear stage before peak load. Conversely, the cumulative AE counts and cumulative energy for Group B specimens increased more slowly during both the nonlinear deformation phase at the beginning of loading and the linear phase, with significant growth occurring only in the nonlinear phase before peak load. Overall, the AE activity of Group A specimens was more pronounced than that of Group B specimens throughout the loading cycle. This can be attributed to the protective silane coating on Group A specimens, which mitigated the effects of sulfate erosion on pore fissures, thereby maintaining the integrity of the specimens. In contrast, Group B specimens were more adversely affected by sulfate erosion, leading to the development of numerous pore structures within the specimens. This reduction in overall strength made Group B specimens more prone to cracking during loading, resulting in a higher incidence of active AE in Group A specimens during the early stages of loading compared to Group B specimens. Consequently, the AE phenomena in Group B specimens were more active than those in Group A specimens without erosion, with significant peaks in AE counts and cumulative energy occurring only as loading approached ultimate strength. This indicates that, during the initial loading stage, numerous small energy events occurred.

AE amplitude is a critical parameter that reflects the maximum amplitude in the signal decay waveform, serving as an indicator of the strength of the AE signal and providing preliminary insights into the size of crack scales. This study compares the evolution characteristics of AE amplitude parameters.

As illustrated in Figure 5, the AE amplitude characteristics of the two groups of specimens exhibit significant differences. The distribution of AE amplitudes for Group A specimens, which were treated with a silane impregnation agent, is primarily concentrated in the range of 45 to 70 dB. In contrast, the distribution for Group B specimens, which lacked silane treatment, is mainly concentrated between 45 and 60 dB. Notably, the number of Group A specimens exhibiting AE amplitudes exceeding 70 dB is significantly greater than that of Group B specimens. At the onset of loading, the number of Group A specimens exceeding 70 dB is markedly higher than that of Group B. During this initial loading phase, the AE amplitudes of Group A specimens predominantly range from 45 to 85 dB, with a higher frequency of high-amplitude AE signals. Conversely, the AE amplitudes of Group B specimens are primarily between 45 and 75 dB during this stage, with fewer high-amplitude signals detected. This disparity can be attributed to the protective silane coating on Group A specimens, which enhances their structural integrity and maintains the strength of pore fissures, making them less susceptible to closure. In contrast, Group B specimens, affected by sulfate erosion, exhibit a reduction in overall strength, resulting in pore fissures that are more easily closed during the loading process. Consequently, a greater number of high-amplitude AE signals are observed in Group A specimens in the early stages. The AE amplitudes of Group A specimens primarily range from 45 to 65 dB in the linear stage, while those of Group B specimens range from 45 to 60 dB. The difference in the distribution of AE amplitudes between the two groups during this stage is relatively minor. However, in the nonlinear deformation stage preceding peak load, the AE amplitudes of Group A specimens predominantly range from 45 to 90 dB, whereas those of Group B specimens range from 45 to 80 dB. This observation indicates the emergence of larger-scale cracks within the specimens at this stage. The formation of larger-scale cracks, which connect with earlier ruptures, contributes to the development of a macroscopic damage surface.

3. Calculation of AE b-Value

The AE b-value is a key parameter that describes the energy distribution of AE events and provides insight into the internal crack evolution of concrete. The observed differences in the trend of the AE b-values during the loading process suggest that the silane protection alters the crack evolution behavior of the concrete. The variation can serve as a sensitive indicator for detecting the precursor to cracking in silane-protected concrete.

3.1. AE b-Value Calculation Method

AE amplitude parameters can be utilized to qualitatively assess the evolution of material rupture scales during loading. However, to facilitate a more intuitive analysis of amplitude distribution across various stress-loading intervals, it is essential to introduce a new characteristic parameter analysis based on amplitude. In the context of material deformation and rupture testing, the AE b-value represents the distribution of micro-rupture scales, with its dynamic characteristics reflecting changes in micro-rupture distribution. A larger b-value indicates a predominance of micro-ruptures at smaller scales, while a smaller b-value suggests that larger-scale micro-ruptures occupy a greater proportion. This approach allows for a transition from qualitative to quantitative analysis, enhancing the understanding of material behavior. Moreover, abrupt changes in b-values serve as critical precursors to material damage, typically expressed by the following equation [65,66]:

$$\mathit{lg}N(\ge m)=a-bm$$

(1)

In this equation, N represents the number of events exceeding a particular magnitude m. In this context, $N\ge m$ denotes the number of events exceeding magnitude m, where earthquake magnitude m is replaced by AE amplitude A. Constants a and b characterize this relationship.

The b-value quantifies the distribution slope of AE event quantities across different amplitude levels, with AE amplitudes directly dependent on the evolution of internal pore/crack activities in the specimen. Consequently, the b-value serves as a quantitative indicator of internal crack structure development. It primarily reflects the distribution pattern among event energy levels, with trend significance surpassing numerical significance.

3.2. The b-Value Calculation Results

The variation curves of the AE b-value are presented in Figure 6.

According to Figure 6, significant differences exist in the AE b-value evolution between the two groups of specimens. For Group A (silane-protected) specimens, the b-value first increased, followed by minor fluctuations, and finally decreased. In contrast, the b-value of Group B (unprotected) specimens fluctuated irregularly throughout the loading process.

For Group A specimens, the b-value showed an overall upward trend during the initial loading stage, primarily due to the closure of pores/cracks and initiation of microcracks during the internal stress adjustment phase. In the linear elastic stage, the b-value exhibited slight fluctuations. The silane-protective material on the specimen surface penetrated into the concrete pores and microcracks to form a hydrophobic layer, reducing the ingress of water and sulfate ions. This retarded the generation and propagation of sulfate-induced microcracks. As a result, the internal structure remained relatively intact with fewer microcracks. Therefore, when internal pore/crack changes occurred, high-amplitude acoustic emission events were more likely to generate, leading to b-value fluctuations. When approaching the peak load, the b-value of Group A specimens dropped sharply, indicating an increase in high-amplitude events and the onset of macroscopic failure. This sharp b-value drop point can serve as a precursor indicator for specimen instability.

For Group B specimens directly exposed to sulfate solution, expansive products (e.g., ettringite and gypsum) formed within the concrete, causing internal stress concentration and microcrack generation. The unprotected specimens had more pores and microcracks, making their internal pore/crack structures more prone to expansion during loading. Consequently, Group B specimens exhibited fewer high-amplitude AE events compared to Group A. As loading continued until cracks connected and coalesced, the b-value fluctuated with a typical multi-peak pattern. Therefore, specimens severely damaged by sulfate attack did not show distinct instability precursor points in their b-value evolution.

Based on fracture mechanics and statistical damage theory, the variation in the b-value is intricately linked to the evolution of internal cracks within concrete, serving as an effective indicator of both damage accumulation and the precursor mechanisms of damage in the material. During the pre-loading phase of the specimen, an increase in the b-value signifies that the formation and propagation of small-scale cracks are predominant, leading to a gradual increase in the internal microcracks present in the concrete. As the specimen approaches its peak load, there is a marked decrease in the b-value, indicating the onset of large-scale crack propagation and signaling a transition into the macro-damage phase. Notably, silane protection appears to mitigate the growth of large-scale cracks, allowing the b-value to remain elevated throughout the loading process before diminishing sharply as the peak load is approached.

4. AE Energy Concentration

The AE energy concentration, denoted as ρ, serves as an indicator of the concentration of AE signal energy and effectively characterizes the localization behavior of cracks within concrete. AE energy concentration is defined as the ratio of cumulative event count $\sum N$ to cumulative energy $\sum E$, represented mathematically as $\rho =\sum N/\sum E$ [67]. An increase in ρ suggests a predominance of low-energy acoustic events, typically associated with crack extension or shear cracking within the specimen. Conversely, a decrease in ρ indicates the generation of fewer high-energy events, which generally occur during the developmental stage of crack linkage and are associated with the emergence of larger cracks within the material. By analyzing the differences in the sudden change points of energy concentration between silane-protected and unprotected specimens, we can further evaluate the impact of silane protection on the energy dynamics of concrete and assess its effectiveness in enhancing crack resistance. Additionally, the mutation points of energy concentration can act as precursors to concrete damage, offering valuable insights for real-time monitoring of engineering structures. This parameter introduces a novel quantitative metric for the safety assessment and lifespan prediction of concrete structures.

The calculated results of the AE energy concentration during the uniaxial compression of specimens subjected to different protection conditions are illustrated in Figure 7.

When comparing the relationships between strain, energy concentration, and crack extension stages under varying protection conditions, it is evident that the AE energy concentration curves of the specimens follow a pattern comprising an initial growth stage, a stable fluctuation stage, and a sudden drop stage as loading stress increases. Notably, these three stages of the ρ curves correspond distinctly with the stages of pore–fracture compaction, crack initiation, stable expansion, and crack instability development as reflected in the specimen strain curves.

The ρ curves for Group B specimens, which lacked a silane impregnation agent, display a significant increase during the early stages of loading. In contrast, the ρ curves for Group A specimens, which were coated with silane protection, show a more gradual increase in this phase, also indicating the occurrence of numerous low-energy events. This phenomenon can be attributed to the direct erosion of Group B specimens by sulfate solution, which leads to the formation of many microcracks in their internal structure, alongside a few unstable and unevenly developed tensile cracks and tensile–shear composite cracks as the material compacts densely. As the load continues to rise, the ρ curve for Group A transitions into a gentle change stage characterized by slight small-amplitude fluctuations. In contrast, the ρ curves for Group B specimens exhibit a general decreasing trend accompanied by more pronounced fluctuations. Wang et al. [68] concluded that the irregular fluctuations observed in the ρ curves can reflect material non-uniformity, indicating active shear cracking during this stage. Moreover, compared to Group B specimens, the crack development in Group A specimens is more stable and uniformly distributed throughout the material. This stability is largely due to the protective silane coating on Group A specimens, which mitigates the impact of sulfate erosion and preserves the integrity of their internal structure. A notable abrupt change occurs between the end of the stable development stage and the onset of the sudden drop stage in the ρ curve. Following this mutation point, a limited number of high-energy events emerge within the specimens, signifying the development of larger-sized cracks. By defining the uniaxial compressive strength of the specimen as σc, it is observed that the mutation point for the silane-protected specimens occurs at 0.83 σc, whereas that for the unprotected specimens is at 0.76 σc. Consequently, it can be inferred that the mutation point in the ρ curve between the stabilization and sudden drop stages can serve as a precursor indicator for damage under compression in concrete specimens. Beyond this mutation point, crack development within the specimen transitions into an unstable phase, with the ρ curve entering the sudden drop stage. This transition is marked by the rapid development and expansion of tensile cracks and mixed tensile–shear cracks, as well as significant shear crack propagation, resulting in a steep decrease in the ρ curve, which signifies the generation of a small number of high-intensity signals within the specimen [69].

In summary, drawing on energy dissipation theory and damage mechanics, the energy concentration degree ρ quantitatively describes the energy redistribution and crack localization behavior of concrete during the loading process, providing a crucial basis for identifying damage precursors. Elevated values of ρ indicate that energy is concentrated in a localized region, suggesting a potential for rapid crack propagation and macroscopic damage to the material. The abrupt change point of the ρ curve (0.83 σc for the silane-protected group and 0.76 σc for the unprotected group) signals a transition in the internal cracks of concrete from decentralized evolution to localized concentration, marking the onset of macroscopic damage. Furthermore, silane protection enhances the cracking resistance of concrete and slows the energy concentration process, thereby shifting the mutation point to a higher stress level.

5. Multifractal Characterization of AE

The AE multifractal characteristic parameter effectively captures the nonlinear complexity and heterogeneity of AE signals, reflecting the diverse nature of crack evolution within concrete. By comparing the variability of AE data from both silane-protected and unprotected specimens and analyzing the influence of silane protection on the complexity of crack evolution, a more comprehensive assessment of the enhancement in crack resistance provided by silane treatment can be achieved. The multifractal characteristic parameters offer a novel perspective for understanding the mechanisms underlying crack evolution in concrete during the loading process.

5.1. Multifractal Detrended Fluctuation Analysis (MF-DFA) Methodology

Multifractal detrended fluctuation analysis is an extension of the traditional detrended fluctuation analysis (DFA) method, designed to comprehensively capture the dynamic features of nonlinear and non-stationary signals [70,71]. MF-DFA mitigates the effects of non-stationary trends by dividing the sequence into two parts of equal length and fitting them polynomially with least squares. The calculation process of MF-DFA is shown in Figure 8 [72,73,74].

To enhance the subinterval division method of traditional MF-DFA, the sliding window technique is employed.

The multifractal spectrum $f\left(\alpha \right)$ characterizes the fractal intensity and singularity of a time series, as defined by the following equation.

$$\tau \left(q\right)=qh\left(q\right)-1$$

(2)

$$\alpha ={\tau }^{,}\left(q\right)$$

(3)

$$f\left(\alpha \right)=q\alpha -\tau \left(q\right)$$

(4)

The $\tau \left(q\right)$ represents the Renyi index, also known as the scalar function. This distinction is often employed to ascertain whether the sequence possesses multifractal properties. Here, $\alpha$ signifies the singular intensity, and $f\left(\alpha \right)$ denotes the multifractal spectrum.

5.2. Multifractal Characteristics of AE Sequences

The multifractal analysis of AE count sequences during the uniaxial compression of specimens under different protection conditions reveals significant insights. The generalized Hurst exponent $h\left(q\right)$ and the Renyi index $\tau \left(q\right)$ of the AE count sequences are presented in Figure 9, while the corresponding multifractal spectral curves are depicted in Figure 10.

As illustrated in Figure 9, the generalized Hurst index of the AE count sequences across the three stages of uniaxial compression for specimens under different protection conditions demonstrates a nonlinear decreasing trend with respect to q. This observation indicates that the AE sequences for both groups of specimens exhibit multifractal characteristics. In the initial two stages, the AE count sequences for the unprotected group show a concentration in the lower fluctuation range compared to the silane-protected group, suggesting a weaker multifractal nature. Conversely, the specimens in Group A, which are protected by a silane surface, exhibit strong multifractal characteristics during the first two stages, transitioning to weaker multifractal characteristics in the third stage. Analyzing the $h\left(q\right)$ characteristics of the curves with respect to q, it is evident that the AE sequences for both groups of specimens possess good memory and long-range correlation, exhibiting both non-stationarity and stochasticity.

As shown in Figure 9, the Renyi index $\tau \left(q\right)$ of the AE count sequences at the measurement points exhibit good consistency. The middle portions of the curves are up-convex, and all satisfy the overall nonlinear relationship $\tau \left(0\right)=-1$. This further corroborates that the AE count series for specimens under varying protection conditions are characterized by multifractals.

The multifractal spectra of the AE count series for specimens under different protection conditions were analyzed. From Figure 10, it is evident that the multifractal spectral curves across the three stages of uniaxial compression exhibit a single peak convex distribution. The multifractal spectral curves at different stages of compression for specimens under varying protection conditions are generally symmetric, with a relatively stable overall development state. Notably, the multifractal spectral curves of the AE count sequences during the third stage exhibit a pronounced right hook, suggesting that the influence of small fluctuations is slightly dominant.

The $f\left(\alpha \right)$ indicates that the AE sequence possesses a consistent singularity index $\alpha$. The fractal dimension on the subinterval of the sequence is related to the distributional characteristics. A larger value indicates a greater proportion of small fluctuations. The parameter $∆\alpha$ reflects the width of the multifractal spectrum, which in turn indicates the multifractal strength and fluctuation characteristics of the sequence. A larger $∆\alpha$ suggests greater multifractal strength and more complex fluctuations. The calculations for $∆\alpha$ and $∆f\left(\alpha \right)$ are performed as follows.

$$∆\alpha ={\alpha }_{max-}{\alpha }_{min}$$

(5)

$$∆f\left(\alpha \right)=∆f\left({\alpha }_{max}\right)-∆f\left({\alpha }_{min}\right)$$

(6)

The statistical analysis of the multifractal characteristics of the AE series is presented in

Table 5. AE multifractal feature statistics.

	Groups	Stage I		Stage II		Stage III
Index		Group A	Group B	Group A	Group B	Group A	Group B
$∆\alpha$		0.870	0.558	0.797	0.568	0.386	0.731
$∆f\left(\alpha \right)$		−0.317	0.196	−0.079	−0.282	−0.625	−0.537

.

Table 5 shows that the multifractal spectrum width for AE sequences of unprotected concrete is slightly smaller than that of silane-protected concrete in stages I and II, indicating greater multifractal intensity in the AE sequence of silane-protected concrete with more complex fluctuations. In stage III, the unprotected concrete has a larger spectrum width, suggesting more complex fluctuations in its AE sequence. The $∆f\left(\alpha \right)$ ratio of AE sequence size fluctuations reveals that in stages I and III, unprotected concrete exhibits higher $∆f\left(\alpha \right)$, indicating a larger proportion of small fluctuations compared to silane-protected concrete.

This suggests that sulfate erosion compromises the internal structure of unprotected concrete, creating microcracks that expand during loading, leading to more small fluctuations. Conversely, silane-protected concrete remains more intact, with fewer microcracks, resulting in larger fluctuations in the AE sequence. Thus, multifractal characteristics of AE sequences under different protection conditions show clear differences, aligning with actual observations. Overall, the AE multifractal intensity is higher in silane-protected concrete, while unprotected concrete exhibits more small fluctuations, making AE multifractality an effective tool for characterizing damage precursors during uniaxial compression under different protection conditions.

5.3. Dynamic Multifractal Characterization of AE Sequences

Dynamic multifractal spectral features can elucidate differences in AE signals during the uniaxial compression of specimens under various protection conditions. A larger value of $∆\alpha$ indicates more significant differences in the AE data. The parameter $∆f\left(\alpha \right)$ reflects the proportionality of the number of events of different types, where $∆f\left(\alpha \right)>0$ signifies that weak AE signals dominate. Conversely, $∆f\left(\alpha \right)<0$ indicates that strong AE signals are predominant, with crack closure or extension being the main processes. The dynamic multifractal characteristic curves of the corresponding AE sequences for the two groups of specimens are illustrated in Figure 11.

Figure 11 illustrates the differential acoustic emission characteristics of internal damage evolution in concrete under different protective conditions. During the pore/crack compaction stage, the significant reduction in $∆\alpha$ values for the unprotected group was closely related to sulfate-induced microstructural degradation. Gypsum and ettringite crystals formed by sulfate attack generated expansive stresses within pores, leading to extensive microcrack formation. The closure of these microcracks during initial loading released low-energy AE signals, causing abrupt $∆\alpha$ decreases. In contrast, the silane-protected group exhibited a gradual $∆\alpha$ increase, attributed to the hydrophobic film formed via silane hydrolysis–condensation reactions on pore surfaces, which effectively inhibited aggressive ion penetration and reduced microcrack density. This trend likely reflected the progressive closure of incompletely sealed micropores and mechanical interlocking at the silane–matrix interface.

Entering the elastic stage, continuous $∆\alpha$ decline in the unprotected group indicated ongoing structural degradation. Erosion products formed loose layers at the aggregate–paste interface, resulting in a significant reduction in interfacial transition zone (ITZ) strength. As stress approached peak load, interfacial cracks propagated along weakened ITZs, emitting stable low-energy AE signals. The silane-protected group demonstrated delayed $∆\alpha$ reduction due to silane treatment enhancing ITZ densification, forcing crack propagation paths into cement paste matrices and triggering more complex energy release patterns.

During crack propagation, diametrically opposing $∆\alpha$ trends emerged between groups. Persistent Δα decline in unprotected specimens correlated with homogenized AE energy distribution, as interconnected crack networks formed with dominant intergranular fracture and stable energy release. Conversely, abrupt $∆\alpha$ increases in silane-protected specimens signaled crack mode transitions. Beyond critical stress thresholds, localized failures induced sudden brittle fractures releasing high-intensity AE signals. This divergence correlated with fracture toughness differences, as silane treatment improved fracture toughness leading to more abrupt failure processes.

The predominance of negative $∆f\left(\alpha \right)$ values indicated crack closure mechanisms dominated throughout loading. Notably, positive $∆f\left(\alpha \right)$ values observed in the early elastic stage of unprotected specimens corresponded to frictional sliding of erosion product-filled cracks. The significant $∆f\left(\alpha \right)$ reduction in the late elastic stage of silane-protected specimens was associated with high-frequency AE signals generated by concrete fracturing.

Drawing on nonlinear dynamics and fractal theory, multifractal feature parameters quantitatively characterize the multi-scale characteristics of concrete crack evolution, offering fresh insights into the material’s damage mechanisms. These parameters reflect the nonlinear complexity and heterogeneity of AE signals, thereby capturing the diversity and spatial distribution characteristics of crack evolution. This approach reveals the intricate nature of internal crack development within concrete, enhancing our understanding of its damage processes. In summary, dynamic multifractal characteristics reflect changes in AE generation under different protection conditions. For unprotected specimens, sulfate erosion damages the internal structure, causing microfracture formation. As compression continues, these cracks expand, releasing strain energy and reducing AE signal differences. During pore fissure compaction and elastic stages, crack closure and microscopic crack extension limit energy release, resulting in weak AE signals. In contrast, silane-protected specimens maintain a more intact internal structure with fewer microcracks, making strain energy release harder and leading to greater AE signal differences. In the pore–fracture compaction stage, crack closure dominates, while in the elastic stage, crack sliding and friction take precedence. In the yielding phase, significant energy release occurs.

6. Analysis and Discussion

6.1. Analysis of AE Characteristics Calculation Results

In sulfate environments, tunnel lining concrete frequently undergoes significant degradation. Silane-impregnated coatings exhibit proven effectiveness in protecting tunnel concrete from environmental erosion. However, critical damage precursors of silane-coated and uncoated lining structures in erosive conditions remain poorly understood. To address this gap, stress–strain curves of the specimens were correlated with AE b-value and energy concentration ρ to characterize damage precursor information under uniaxial compression. Additionally, multifractal characteristics of the AE sequences were analyzed using the MF-DFA method.

The b-value indirectly reflects the damage state of microcracks within the material’s internal structure. An increase in the AE b-value indicates that the internal structure predominantly develops small microcracks. Conversely, a decrease in the b-value signifies the formation of large-scale cracks within the material, leading to a higher proportion of significant emission events. When the AE b-value fluctuates smoothly within a narrow range, it suggests that no significant changes in AE activity are taking place, and microcrack extension is relatively stable. The jump of the b-value indicates an accelerated rate of microcrack extension within the material, reflecting unstable crack evolution. In the silane protection group, the internal structure remains relatively intact, with fewer microcracks. During the pore–fracture compaction stage, the proportion of small events is larger, resulting in a significant upward trend in the AE b-value. As the loading approaches the peak load, the number of high-amplitude events increases, leading to macro-damage and a sharp decrease in the b-value. In contrast, when the specimens in the unprotected group are subjected to sulfate erosion, numerous microcracks form inside the concrete. As a result, these specimens are more likely to expand internal pore fissures during loading, causing the crack extension changes to be more stable.

An increase in energy concentration ρ is associated with crack extension or shear cracking in the specimens, while a decrease in ρ indicates the presence of larger cracks within the material. When comparing the characteristics of energy concentration under different protective conditions, irregular fluctuations of the ρ curve reflect non-uniform activity within the material, suggesting that the specimens are actively undergoing shear cracking at this stage. Since the specimens in the silane protection group are less affected by sulfate erosion, their internal structures remain relatively intact. Throughout the loading process, crack development in this group is more stable and uniformly distributed. Notably, there is a distinct mutation point between the end of the stable development stage and the onset of a sudden drop in the ρ curve. The mutation point for the silane-protected group occurs at 0.83 σc, while the mutation point for the unprotected group is at 0.76 σc. This mutation point in the ρ curve serves as precursor information for the damage to the specimens. Following this mutation point, the internal crack development of the specimens enters an unstable stage, and the ρ curve reflects this by entering a phase of sudden decline.

The deformation and fracture of materials are directly correlated with changes in AE signals. The varying degrees of damage to the material at different loading stages reflect the dynamic process of AE. In this study, we analyzed the dynamic multifractal characteristics of AE. The $∆\alpha$ of the AE sequence for the unprotected group exhibited a consistent decreasing trend throughout the uniaxial compression loading process. In contrast, the $∆\alpha$ of the silane protection group demonstrated a slow initial increase, followed by a gradual decrease, and ultimately a significant increase. This observation indicates that the variability of AE data for the unprotected group diminishes during continuous loading, while the differences in AE signals for the protected group remain more pronounced. As loading progresses, these internal microcracks continuously expand, releasing strain potential energy. Throughout most of the loading stage, the AE $∆f\left(\alpha \right)$ for both sets of specimens remained below 0. Notably, the AE $∆f\left(\alpha \right)$ peaked in the middle of the elastic phase. Furthermore, the AE $∆f\left(\alpha \right)$ for the unprotected group was greater than 0 during part of the pre-loading period, suggesting that weak AE signals dominated.

6.2. Discussion of Concrete Damage Precursors

A notable correlation exists among the AE b-value, energy concentration ρ, and dynamic multifractal characteristics of concrete under different protective conditions. The silane-protected specimens exhibited relatively intact internal structures with fewer microcracks, showing a significant increasing trend in the AE b-values during the early and middle stages of uniaxial compressive loading. As the loading approached the peak load, the number of high-amplitude events increased, resulting in a sharp decline in the AE b-value. In contrast, the concrete specimens in the unprotected group, which underwent sulfate erosion, developed numerous internal microcracks. This led to a more stable crack extension and fluctuations in the AE b-value during the loading process. During uniaxial compression, the AE of the unprotected group exhibited a continuous decrease throughout the loading process. Conversely, the AE sequences of silane-protected specimens show a slow increase, gradually decreasing to a significant increase trend. This suggests that the variability of AE data for the unprotected group diminishes during continuous loading, while differences in AE signals for the protected group remain more pronounced. The extensive microcracking resulting from sulfate erosion in the unprotected specimens causes continuous expansion of these microcracks, leading to released strain potential energy. Regarding the energy concentration ρ characteristics, the internal structures of the silane-protected specimens remained relatively intact, resulting in more stable and uniformly distributed crack development during loading. Both groups displayed a distinct point of sudden drop in their ρ curves at the end of the stable development stage, with mutation points at 0.83 σc for the silane-protected group and 0.76 σc for the unprotected group. After these mutation points, the internal crack development of the specimens transitioned into an unstable stage, accompanied by a sudden drop in the ρ curve. The findings hold remarkable theoretical implications and practical value for the protection and stability monitoring of concrete in sulfate-rich environments.

The practical application of silane protection in sulfate environments holds significant importance. Research findings indicate that silane impregnation agents effectively enhance the sulfate erosion resistance and compressive strength of concrete, delay crack propagation, and extend the lifespan of structures. In marine engineering, underground construction, and industrial applications, silane protection markedly improves the durability and safety of concrete structures, reduces maintenance costs, and yields substantial economic and social benefits. Future research should focus on further exploring the long-term performance of silane protection, synergistic protective technologies, and the development of new materials to address increasingly complex engineering challenges.

In practical tunneling projects, investigating the crack evolution characteristics of silane-coated protective concrete in sulfate environments through the combined analysis of AE b-values, energy concentration ρ, and dynamic multifractal characteristics could enhance the safety of sulfate-eroded lining concrete during service. However, it should be emphasized that this study focuses solely on the AE b-value, energy concentration ρ, and dynamic multifractal characteristics of lining concrete specimens under uniaxial compression. In real conditions, tunnel linings are subjected to complex forces, and geological and groundwater environments can be complicated and variable. Therefore, further in-depth research is needed to explore the concrete protection and destabilization damage precursors of concrete structures under multifactorial influences. A set of concrete specimens was selected from actual tunneling projects to simulate conditions that may be subjected to sulfate attack. These specimens included samples both with and without silane-based protective coatings, allowing for a comparative analysis of the effects of different protective measures on concrete durability. During the experiments, AE monitoring techniques were employed to track changes in the mechanical properties of the specimens in real time, facilitating the observation of crack evolution and the damage process. Key parameters, including the AE b-value, energy concentration, and multiple fractal characteristics, were monitored and recorded in real time using specialized AE equipment. These data can be utilized to identify cracking precursors in the tunnel lining and compared with actual damage behavior. Leveraging the real-time AE monitoring data, a safety monitoring system was developed to assess the condition of the tunnel lining continuously. The system automatically analyzes the AE characteristics to predict the risk of concrete damage, enabling timely repair or reinforcement measures during tunnel operation.

7. Conclusions

In sulfate-rich environments, concrete infrastructure faces accelerated degradation through sulfate attack, a critical challenge demanding advanced protective solutions. This study establishes an AE-based framework for detecting destabilization precursors in silane-coated concrete under sulfate erosion, yielding three key innovations with practical implications:

(1) The silane coating effectively delays microcrack initiation by reducing sulfate penetration. Silane-protected concrete showed fewer microcracks and a significant increase in the AE b-value during preloading, while unprotected specimens underwent sulfate erosion, forming more microcracks. This quantifiable difference provides a novel criterion for evaluating protective coating efficacy through microcrack suppression capability.

(2) Crack development in silane-protected specimens was more stable, with a distinct mutation point in the energy concentration curve, indicating damage precursors. After mutation points (0.83 σc for silane-protected and 0.76 σc for unprotected), crack development became unstable. This provides a quantifiable criterion for early-warning systems.

(3) Unprotected specimens formed numerous microcracks that expanded during loading, releasing strain potential energy. AE data variability for unprotected specimens diminished, while AE signals for protected specimens showed significant differences. Crack expansion dominated in later stages. This highlights the potential of multifractal analysis for evaluating protective coating performance.

This study provides practical insights into protecting and monitoring concrete in sulfate environments. However, laboratory conditions (fixed sulfate concentration and uniaxial loading) differ significantly from dynamic groundwater environments, potentially altering AE signatures. Due to complex forces, geological conditions, and groundwater variations, accurately determining AE multifractal characteristics, energy concentration, and critical b-values in real-world concrete rupture remains challenging.