In these tests, the cements are sulfoaluminate double fast cement of strength 42.5. Fly ash is the first grade low calcium fly ash with the specific surface area of 420 m²/kg. Silica ash has a specific surface area of 2000 m²/kg. Fine quartz sand specification are 100–200 mesh, which came from Anhui Fengyang County Shengli Quartz Sand Factory. High-efficiency polycarboxylic acid water reducing agents were produced by Zhengzhou Xinghui Chemical Raw Material Company, while retarders from Shandong Zhongda New Material Company and dilatants from CNBM Zhongyan Technology Co, as shown in Table 1. PVA fibers were produced at the Shangwanwei raw material plant. The PVA parameters are shown in Table 2.

The PVA-ECC substrate formulation is shown in Table 3. PVA fibers are added in volume fractions of 0%, 0.5%, 1.0%, 1.5%, and 2.0%, corresponding to specimen numbers P0, P0.5, P1, P1.5, P2, as shown in Table 4.

There are two specimen standards for this test, as shown in Figure 1. One is a cube with a size of 100 mm × 100 mm ×100 mm, which is used for uniaxial compression tests and AE tests. There are 3 groups of P0-P2, a total of 15 groups of specimens. The other is a flat cylinder with a diameter of 100 mm and a thickness of 50 mm P0-P2 are 4 groups, a total of 20 groups of specimens. Three groups were used for chloride penetration tests, and one group was used for MIP tests.

Firstly, dry materials such as cement, fly ash, silica ash, quartz sand, expansion agent, etc.,. were put into the mixer for stirring for 1.5 min, and the dry materials were stirred evenly. Subsequently, water was poured into the mixer in batches, and PVA fibers were gradually poured evenly. Water reducing agents were poured according to the wetting degree of materials in mixer. After all the materials were stirred evenly, the mixer was closed, and the stirred cement paste was put out for use.

Pour half of the cement paste into mold, then put it on the vibration table, open the vibration table to discharge air in cement paste, and then pour the other half of the cement paste into mold. Repeat above vibration process to make the cement paste more even. Finally, the cement paste was wrapped with preservative film together with the mold. The purpose was to allow the cement paste to continue hydration heat reaction in curing film, thereby effectively inhibiting the generation of microcracks. These were placed in the standard curing room with indoor temperature of 20°C ± 2°C, humidity of 95%, and curing for 28 days.

After standard curing, the specimens were polished to make the surface smooth and flat. The six surfaces of cube specimens and the upper and lower surfaces of flat cylinders were polished using 20 mesh coarse sandpaper.

AE characteristic parameters can reflect the evolution of internal cracks during the damage process of cementitious, rock and other materials. In this paper, ringing counts and cumulative ringing counts are selected to analyse the AE characteristics. Ringing counts refers to the number of oscillations exceeding threshold, which can reflect the intensity and frequency of AE signals. Compressive damage of the specimen is a continuous development process. The speed and strength of internal crack development can be known by the response of ringing counts (Dong, et al., 1995; Ji, et al., 2000). Uniaxial compression tests were carried out on 5 groups of specimens, and stress-strain curves were obtained. As shown in Figure 3, the compressive strength increased first and then decreased with the increase of PVA content. When volume fraction of PVA was 1%, the compressive strength was 57.49MPa, reaching the maximum value, which was 25.6% higher than that of the reference specimen P0. When volume fraction of PVA was 2%, the compressive strength was 15.2% lower than that of the reference specimen P0, indicating that more fibers would reduce the strength of materials.

Figure 4 shows the stress-time-ringing counts-cumulative ringing counts curves of PVA-ECC specimens. According to the change of stress curve slope, compression damage process can be divided into different stages (Zhou et al., 2020). In this paper, it was divided into densification stage, linear-elastic stage, elastic-plastic stage and destruction stage. Table 5 shows the proportion of load duration and AE ringing counts in each stage.

Stage I: The densification stage is defined as the period from the beginning of loading to 30% of peak stress. At the initial stage of loading, original pores and initial defects in specimen began to be continuously compressed. The stress increased nonlinearly, and the growth rate gradually accelerated. Ringing counts were few and sparse, signal intensity was weak, and there were no obvious cracks propagation. PVA reduced the proportion of bearing time and ringing count in densification stage to varying degrees, which was due to the filling of PVA to reduce internal microcracks of ECC.

Tensile damage and shear damage mainly occur during the compression damage process of PVA-ECC. The RA-AF value in AE parameters can characterize tensile cracks and shear cracks. RA is the ratio of rise time to amplitude, and AF is the ratio of ringing count to duration. The study found that (Reboul, et al., 2020) AE signal waveform change gradient under tensile damage is large and signal frequency is high, and the performance is higher AF value and lower RA value; on the contrary, AE signals under shear damage show lower AF values and higher RA values. However, there is no accurate standard for the evaluation of RA and AF values, and the slope method with k as diagonal is commonly used. This method considers that crack above the slash is a tensile crack, and crack below the slash is a shear crack, as shown in Figure 5.

Since the RA-AF threshold of ECC is usually difficult to unify, it is difficult to accurately classify the crack types only by slope method. In recent years, scholars have introduced Gaussian Mixture Model (GMM) to cluster RA-AF values. Based on the probability model, GMM classifies data by probability distribution, and calculates m single Gaussian models under different weight coefficients, and uses the Expectation-Maximization (EM) algorithm to fit m mixed Gaussian distributions. The expression of single Gaussian model is shown in Equation 3 (Luo, et al., 2024; Shi, et al., 2024): N i x → | u → , ∑ i = exp − 1 2 x → − u → T ∑ i − 1 x → − u → 2 π D 2 ∑ i 1 2 (3) where u → = the average vector of D × 1 ; ∑ i = the covariance matrix of D × D .

The GMM expression is calculated by weighting single Gaussian model, as shown in Equation 4: p x i = ∑ i = 1 m α i N x | u i , ∑ i (4) where m = the number of models; α i = the weight of mixed model; N x | u i , ∑ i = the i th single Gaussian model density function.

The crack propagation types of PVA-ECC under uniaxial compression are classified by GMM model. Figure 6 describes the distribution of RA-AF and the proportion of tensile cracks and shear cracks under five PVA contents. It can be seen from (a) that ECC without PVA were dominated by tensile damage during the damage process, and tensile cracks account for 70%. The addition of PVA changed the propagation mode of internal cracks in ECC. The proportion of shear cracks in PVA-ECC under uniaxial compression exceeded 50%, and the proportion of shear cracks increased first and then decreased with the increase of PVA contents. When PVA content was 1%, the proportion of shear cracks was the largest, reaching 62.57%.

The compression of ECC first led to tensile stress, which caused micro-cracks to form in the interior. As shown in Table 6, in densification stages, linear-elasticity stages, and elastic-plastic stages, the number of cracks was small, and the internal cracks were mostly caused by tensile damage. When stress reached the maximum value, the number of cracks increased sharply after the specimen was destroyed, which was consistent with AE event signal activity. In destruction stage, the proportion of shear cracks increased, which was due to the bridging effect of PVA, so that the bite force at crack propagation increased, and internal shear stress of the specimen increased. After shear stress bears part of stress, the degree of crack tensile cracking decreased. The damage mode transited from tensile damage to shear damage. The specimen was not split by a single vertical crack, but formed a multi-directional irregular shear crack, which inhibited the formation of interconnecting cracks and the release of deformation energy. PVA changed internal compression damage mechanism of specimen and improved tensile, shear and fracture toughness of ECC.

Chlorine penetration tests were carried out on ECC with different fiber content. Three tests were carried out on the same batch of specimens to take the average value to obtain the chloride diffusion coefficient of the material as shown in Table 7 and Figure 7. The chloride diffusion coefficients show firstly decrease and then increase with increasing PVA fiber content. When PVA fiber content is 1%, the chloride diffusion coefficient is the smallest, which decreases by 44.2% compared with the baseline specimen P0, and the specimen has the best impermeability performance.

Among the pore structure parameters, porosity, total pore volume and most probable aperture are important parameters affecting the macroscopic properties of concrete (Li, et al., 2024). Figure 8A depicts the pore size distribution curves. Most probable aperture is the pore size with the highest probability of occurrence, which corresponds to the peak of distribution density in pore size distribution curve. From (a), it is clear that P1 has the smallest most probable aperture. Figure 8B depicts the cumulative porosity curves, where P1 porosity is the smallest at 23.68%. Table 8 shows the measured values of porosity, total pore volume, and most probable aperture for five groups of specimens in MIP tests. It can be seen that porosity, total pore volume and most probable aperture of PVA-ECC show a pattern of firstly decreasing and then increasing with increasing PVA content. The pore structure is optimal at 1% PVA fiber content, suggesting that a moderate amount of PVA fibers improves pore structure and increases compactness, reducing initial defects. However, excessive PVA fibers are difficult to disperse, forming groups that negatively affect fluidity, adhesion, and polymerization, increasing internal porosity and microscopic defects, thus adversely affecting pore size distribution and compressive strength.

The pore sizes are categorized into four ranges: gel pores (<100 nm), transition pores (100–1,000 nm), capillary pores (1,000–10000 nm), and macropores (>10,000 nm) (Zhao Y. C. et al., 2023). The percentage of different pore size ranges in total pore volume is shown in Figure 9.

Gel pores are harmless or less harmful pores, which are mainly formed by cement hydration reaction and gas produced by water evaporation during mixing. Transition pores, capillary pores and macropores are harmful pores. Transition pores are generated by the gap between cement particles. Capillary pores are the voids left by cementitious particles that are not filled by hydration products. Macropores are mainly cracks caused by uneven distribution of aggregates in materials. Harmful pores affect the mechanical properties and durability of ECC. It was found that PVA mainly affected the number of gel pores and capillary pores. Appropriate amount of PVA increased the number of gel pores and decreased the number of capillary pores. Excessive fibers led to poor dispersion of the material, resulting in uneven distribution between aggregates, which made the number of capillary pores and macropores increase.

Fractal theory effectively analyzes the pore size distribution of materials, characterizing the pore structure (Winslow, 1985; Xuan, et al., 2018). Menger sponge model and thermodynamic-based fractal model were used to calculate the fractal dimension. The Menger sponge model assumes a square unit cell with side length R, which is divided equally into n small cubes with r. The contents were obtained by the residual relative volume formula (Wei, et al., 2007), as shown in Equations 5-7: V = 1 − P = r / R 3 − D (5) lg 1 − P = 3 − D lg r / R (6) D = 3 − lg 1 − P lg r / R (7) where D = fractal dimension; p = material porosity, which is the cumulative percentage of mercury that entering material at a given pressure value in mercury compression experiments; r = corresponding pore size at pressure value; R = maximum pore size. R/R responds to the pore size distribution of material. A larger fractal dimension D indicates a more complex pore space and better pore structure of material.

Zhang and Li (1995) proposed thermodynamic fractal model based on the principle of energy conservation, which suggests that the work done by external environment on mercury in MIP test is equal to the increase in surface energy of the mercury that enters pores. Its expression is Equation 8: ∫ 0 V P d V = − ∫ 0 δ σ ⁡ cos ⁡ σ d S (8) where p = the pressure applied when pressing mercury. V = the amount of mercury pressed in specimen. S = the pore surface area.

Pore specific surface area, pore size and mercury intake are correlated by fractal analysis, and after quantitative analysis, the relationship is expressed as shown in Equation 9: ∑ i = 1 n P i Δ V i = C ′ r n 2 − D V n D / 3 (9) where P i = Pressure at i th pressurization, (Pa); Δ V i = Mercury feed at the i th pressing of mercury, (m³); r n = Pore size at n th pressing of mercury, (m); V n = Cumulative mercury feed at stage n , (m³); C ′ = Constant factor; D = Fractal dimensions based on thermodynamic relations.

We demand W n = ∑ i = 1 n P i Δ V i , Q n = V n 1 / 3 / r n , logarithmic conversion is performed to obtain Equation 10: lg W n / r n 2 = D ⁡ lg ⁡ Q n + lg ⁡ C ′ (10)

The five groups fractal dimensions of specimens were calculated based on two fractal models, and the relationship curves for P0 were fitted. As shown in Figure 10, the fractal curves based on thermodynamic relationship present a high degree of linear correlation, and the correlation coefficients R ² are all greater than 0.999, indicating that this model can more accurately reflect the fractal characteristics of pore size distribution of PVA-ECC. Fractal dimensions increased and then decreased with the increase of PVA contents. The larger fractal dimension is, the more complex internal structure of pores is, and the more reasonable pore size distribution is.

In order to further study the effect of PVA on pore size distribution, the fractal dimensions of gel pores, transition pores, capillary pores and macropores of five groups of specimens were calculated in Table 9. According to three-dimensional Euclidean space, the fractal dimension D of ECC is between 2 and 3. The transition pores and capillary pores in table have D_S>3. At present, scholars believe that this is due to the presence of ink bottle-shaped pores in cementitious materials (Zeng, et al., 2010; Lee and Jacobsen, 2011). Ink bottle-shaped pores are usually formed by evaporation of water during hardening process of cementitious materials. In MIP test, only when the intrusion pressure is large, mercury will enter the small pore. At this time, the small pore volume is recorded, but it is actually the total volume of large pore and small pore in the ink bottle-shaped pore. According to the data of Table 9, it is speculated that PVA cause ink bottle-shaped pores in specimen.

Figure 11 describes the change of fractal dimension of each pore range under different PVA content. PVA had a great influence on the fractal characteristics of transition pores and capillary pores, and had little influence on the fractal characteristics of gel pores and macropores. This was because the fiber diameter was in range of capillary pore diameter, and the most probable apertures in five groups of specimens were in range of transition pores and capillary pores. Therefore, the fiber had a great influence on the spatial structure distribution of transition pores and capillary pores.

Studies have shown that the fractal dimension of fiber reinforced concrete has a certain correlation with pore structure parameters and mechanical parameters (Li, et al., 2024; Zhao J. et al., 2023). Figure 12 shows the relationship between porosity, total pore volume, most probable aperture of P0, P0.5, P1, P1.5, P2 and their fractal dimension. It can be found that the porosity, total pore volume, and most probable aperture of PVA-ECC have a strong negative correlation with the fractal dimension, and the correlation coefficients R ² are 0.970, 0.981, and 0.863 respectively. The porosity, total pore volume and most probable aperture decrease with the increase of fractal dimension. Fractal dimension can be used to comprehensively characterize pore structure characteristics. The larger fractal dimension leads to the higher complexity of internal pore structure space and the higher ability of pore size occupying the space. This also leads to a smaller most probable aperture, which avoids development of the internal connected pore size to the larger pore size, and reduces the probability and proportion of the larger pore size, while makes the overall porosity and total pore volume lower.

Figure 13 depicts the correlation between fractal dimension and compressive strength. The correlation coefficient R ² is 0.804. Compressive strength has a good positive correlation with fractal dimension, and increases with the increase of fractal dimension. The increase in fractal dimension represents a higher spatial complexity of the pore structure, which indicates an increase in multidirectionality of the initial defects, inhomogeneity and asymmetry of the fracture structure. During initial deformation stage, the internal stresses have not been concentrated due to the randomness of initial defect distribution. During loading process, some of the initial defects and cracks are compacted, while others are “activated” and gradually evolve into connected cracks, resulting in internal stress concentrations. The fractal dimension, representing the spatial complexity of microstructure, is closely related to this “competition” between compact deformation and crack evolution. When fractal dimension is large, it is difficult to form connecting cracks within structure, and stress concentration phenomenon is not easy to occur, while the compressive capacity of specimen is improved to a certain extent.

Figure 14 depicts the correlation between fractal dimension and chloride diffusion coefficient. The correlation coefficient R ² is 0.873. Chloride diffusion coefficient has a good negative correlation with fractal dimension, and decreases with the increase of fractal dimension. With spatial structure becoming complex, the interconnecting pores become less, and the ions is more difficult to flow between pores, so that chloride diffusion coefficient becomes lower, and the impermeability of material is improved.

Fractal dimension indicates that the mechanical strength and impermeability of ECC are closely related to the pore structure characteristics. The fractal dimension can be used to assess or predict the mechanical strength, impermeability and microstructure of PVA-ECC in advance, and to make a comprehensive evaluation of the mechanical properties and durability of material.