Performance Degradation Law and Model Construction of Hydraulic Concrete Under Freeze-Thaw Cycles: A Comprehensive Review

Abstract

Hydraulic concrete structures in cold regions often suffer from the combined action of freeze-thaw (FT) cycles and external loads, indicating that these structures often depend on the combined effects of two or more factors. In recent years, researchers around the world have made considerable efforts and explorations to solve this challenge, achieving fruitful research results. This article provides a comprehensive literature review on performance degradation law and model construction of hydraulic concrete under FT cycles. Firstly, the theory and characterization method of FT damage for concrete are introduced. Given the inherent deficiencies of traditional detection methodologies and the constraints imposed by extant computed tomography (CT) technology, there is an urgent need to develop a high-precision segmentation technique for concrete. By capitalizing on the resultant microstructure, a more accurate predictive model can be established. Thereafter, an in-depth discussion is conducted on the damage mechanism of hydraulic structures when subjected to freeze-thaw (FT) cycles in conjunction with external loading scenarios, namely fracture, direct tension, triaxial stress, and hydraulic wear. As the combined effects of different factors cause more serious damage to hydraulic structures than a single factor, the evolution law is more complex. Although researchers have attempted to reveal the deterioration mechanism of multi-factor interaction by means of numerical methods, there are still many fundamental issues that require further exploration and more in-depth research due to the limitations of constitutive models. Finally, the existing research results are summarized, and novel insights are proposed for future research directions. This study promptly identifies the gaps that urgently need to be filled, especially the insufficient understanding of the complex stress state of hydraulic concrete structures and the inadequate research on the performance deterioration law under multi-factor combined action. This investigation aims to determine the future research focus in relation to hydraulic concrete in cold regions that could advance the revelation of the deterioration mechanism caused by multi-factor interaction. By providing a detailed overview of the current hydraulic concrete structures in terms of the combined action of FT cycles and external loads, highlighting the research limitations, and suggesting future research directions, this review seeks to contribute to the safe operation of hydraulic concrete structures in cold regions.

1. Introduction

Hydraulic concrete is a quasi-brittle porous substance that is susceptible to various wet and cold conditions, with FT cycles being the most common factor exerting an impact in cold areas. FT damage occurs when the pore water within concrete freezes and transforms into ice, leading to volume expansion and subsequently inducing pore pressure [1,2,3]. When FT damage occurs repeatedly, it causes internal cracks to spread, the surface to exfoliate, and mechanical properties to deteriorate, and ultimately leads to the failure of hydraulic construction [4,5], which threatens its normal service. In addition to suffering from FT damage, hydraulic concrete structures in cold regions are often subjected to external loads during service, such as fracture [6], direct tension [7], triaxial stress [8], and hydraulic wear [9]. Therefore, the normal service of hydraulic construction often depends on the combined effects of two or more factors. However, due to the combined effects of different factors, the damage to hydraulic concrete structures is more severe than that of a single factor, resulting in a more complex damage evolution law of FT cycles and external loads. This makes it very difficult to reveal the degradation mechanism of multi-factor interaction.

For large hydraulic concrete structures, there may be more or less primary cracks inside during the construction process. Moreover, these concrete structures often serve in complex environments, resulting in the progressive growth of these primary cracks over service time, severely reducing the normal service factor of hydraulic structure, and potentially causing serious fracture failures [10]. Moreover, the FT cycles experienced in the early stage will exacerbate the later fracture behavior. Hence, this establishes a greater need to probe into the fracture principle, development, and evolution law of cracks inside hydraulic structure after FT damage. Significantly, from the perspective of structural mechanics, tensile strength plays a preponderant role in dictating the cracking manifestation of concrete structures [11] and the safe operation of hydraulic structures during service. Moreover, when hydraulic structures are exposed to FT environments, even with timely reinforcement and repairs, their capacity to withstand cyclic tensile loading will experience significant attenuation. As a heterogeneous material, the stress-strain curve of hydraulic concrete under cyclic tensile loading often exhibits significant nonlinear characteristics, and FT cycles can significantly alter this nonlinear behavior.

In addition to being subjected to flexural load and tensile load, some key parts of hydraulic concrete structures are often in a complex triaxial condition during service, and are subjected to the cyclic loading due to the vibration caused by overflow and units, cyclic changes in water level and temperature, and seismic loads [12]. Therefore, the study of the mechanical reaction of structures when subjected to cyclic triaxial stress has moved to the forefront of stability analysis within hydraulic engineering. Comprehending this aspect is pivotal for safeguarding the long-term, stable, and reliable operation of hydraulic facilities.

In addition, hydraulic concrete structures are also susceptible to erosion from various natural conditions. Erosion damage seriously endangers the normal service of structures, and hydraulic wear is a key factor. As a multiphase composite material system, the nonlinear characteristics exhibited by the macroscopic behavior of hydraulic concrete reflect the complexity of microscopic structures. Numerous surface flaws will aggravate wear, and a complex wear principle will emerge as a result [13]. Moreover, in cold-region rivers, hydraulic structures are invariably situated within a compound environment, entailing freeze-thaw and wear. FT damage can cause an increase in microcracks in the concrete and surface matrix detachment, which speeds up wear at a particular level, resulting in a much more substantial reduction in the durability of structures than single-factor action.

The internal damage evolution law of structures subjected to the coupled effect of FT and external loads (fracture, direct tensile, triaxial stress, and hydraulic wear) is complex, accompanied by the development of internal pores/microcracks and the attenuation of macroscopic mechanical properties. The damage accumulation rate is faster than that of a single factor, and the damage evolution law and failure process are significantly different from those of a single factor. Therefore, it is necessary to review and summarize the current research on the performance degradation law and model construction of structures under FT cycles, so as to identify gaps that need to be filled in the existing research, and provide references for the durability design of hydraulic concrete structures and the property evaluation of structures subjected to the coupled effect of various factors. This review consists of five parts, and the knowledge architecture is shown in Figure 1.

This study identifies critical knowledge gaps at present, especially the insufficient understanding of the complex stress state of hydraulic structures and the inadequate research on the performance deterioration law under multi-factor combined action. This investigation aims to determine the future research focus in relation to hydraulic concrete in cold regions that can advance the revelation of the deterioration mechanism caused by multi-factor interaction. By providing a detailed overview of the complex problems currently faced by hydraulic concrete, this review seeks to highlight the research limitations and propose future research directions, contributing to the safe operation of hydraulic structures in cold regions.

2. Theory and Characterization Methods of FT Damage for Concrete

2.1. Theory of FT Damage

In 1949, Powers [14] took the lead in proposing the theory of pressure generated by pore water, which aims to explain the FT process inside concrete and the pores’ positive effect on FT resistance. During the process in which pore water freezes and changes into ice, the volume increases by 9% and the unfrozen pore water is squeezed into the surrounding cement matrix, thereby generating water pressure imposing forces on porous skeleton. If the water pressure generated goes beyond the strength of concrete, it will suffer internal damage, as shown in Figure 2. The magnitude of pressure mainly depends on the permeability of concrete, the freezing rate, and the transporting distance of the pore water that has been squeezed out.

For ordinary concrete that is fully water saturated, any squeezed pore water needs to be transported to the outer boundary of the concrete [15]. However, for air-entraining concrete, there are many larger pores inside that can act as containers to hold the pore water discharged by extrusion. However, it should be noted that the pressure inside the concrete can usually be assumed to be atmospheric pressure due to the reduced restriction of pore walls, meaning that any pore water entering the pore will freeze instantaneously [16,17,18]. Due to the additional pores inside the air-entraining concrete, the distance required to transport the squeezed pore water is reduced, and the resistance generated in this process also decreases accordingly. According to the relationship between pressure and resistance, the pore water pressure also decreases accordingly. Fagerlund [19] used Darcy’s law to describe the advection flux of squeezed pore water and considered the volume of material completely saturated between pores, as shown in Figure 3. The general expression for the maximum pressure generated during the freezing process is derived:

$$p_{\max }^{\mathrm{w}}={\displaystyle \frac{0.09\eta }{k(S_1)f_p}}{\displaystyle \frac{d{v}_i}{dt}}$$

(1)

where k(S₁) is the permeability, which is a function of the current liquid saturation S₁. The permeability decreases as the ice content in the pores increases, because the ice in the pores limits the flux of unfrozen pore water. η and v_i represent the viscosity and pore volume fraction, respectively. f_p is the geometry and distance measurement of the flow path of the pore water inside the concrete.

$$f_p=({\displaystyle \frac{La}{9}}+0.5)L^2$$

(2)

where L is the spacing coefficient of the matrix, and a is the specific surface area of the pore system.

Fagerlund’s research [20] showed that concrete will only suffer FT damage when the material reaches a specific critical saturation level. Hence, the saturation of pores must also be considered when evaluating the spacing coefficient L and specific surface area a [21,22]. In addition, although the volume of the pore system may be large enough to accommodate all the squeezed pore water, some pores may become saturated during the freezing process. As such, the variation of the spacing coefficient L and specific surface area a during the FT process should be considered to more accurately evaluate the water pressure generated inside the concrete during the freezing process.

Drawing inspiration from this theory, a number of investigators [22,23] have engineered more elaborate models and determined that the microstructural details markedly impact the FT performance of concrete. This indicates that it is necessary to understand how the pore system evolves with changes in the average pore size and spacing, in order to predict the mechanical effects of FT cycles on the porous skeleton inside concrete. So far, the theory of pore mechanics has been proven to be the best tool for revealing the FT mechanics of concrete [16,24,25,26].

In 2008, porous stress theory was broadened by Coussy and Monteiro [16], specifically addressing multiple properties of FT phenomena. The findings indicate that the combined action of water pressure and crystallization pressure generates tensile stress exceeding 10 MPa on the porous skeleton inside the concrete. The study also showed that pores generated by the air-entrapping agent are capable of functioning as cryopumps and reservoirs for growing ice, introducing unfrozen water from capillary pores into areas conducive to ice formation. Therefore, the pores induced by the air-entrapping agent mainly play a role in alleviating the tensile stress on the porous skeleton of concrete during FT cycles through the cryopump and reservoir effects, as follows: (1) During the FT cycle of concrete, when the temperature drops below the freezing point, the water in the pores will freeze and expand. The tiny pores introduced by the air-entrapping agent can act as a “cryopump”. When water freezes, some of the unfrozen water will be sucked into these pores. This is because the air within the pores is compressed at low temperatures, generating negative pressure and thus attracting the surrounding moisture. This reduces the content of free water inside the concrete, lowers the hydrostatic pressure and osmotic pressure caused by the expansion of water due to freezing, and thereby alleviates the tensile stress on the porous skeleton. (2) The pores induced by the air-entrapping agent can serve as water storage spaces. When concrete is subjected to FT cycles, the water in the pores undergoes volume changes during the processes of freezing and melting. These pores can accommodate the volume changes of water and play a buffering role, just like a “reservoir”. When water freezes and expands, the pores provide additional space, preventing excessive accumulation of ice pressure within the concrete and reducing the tensile action on the porous skeleton, thereby lowering the tensile stress. Meanwhile, during the melting stage, the pores can store excess water, preventing the migration and accumulation of water within the concrete and reducing the stress caused by water redistribution. In terms of verifying pore mechanics models, Zeng et al. [24] demonstrated that this theory can effectively predict the quantitative relationship between temperature and strain obtained by reference [17] in 1953. In addition, the model developed by Zeng et al. [24] also proved that pore mechanics models can predict deformation in both air-entraining concrete and non-air-entraining concrete. The main achievement of the pore mechanics model is to establish the microstructure characteristics of concrete, such as the pore structure and matrix permeability that control the mechanical response of materials. Reference [25] established a uniform continuum with the spherical void of radius R surrounded by the porous solid of thickness L, as shown in Figure 4a. The porous solid is completely saturated with liquid water at t₀, as shown in Figure 4b. As time goes by and the temperature drops to the critical freezing point, ice crystals begin to form in larger pores, as shown in Figure 4c. Ultimately, some of the water in the cement matrix will freeze into ice, causing unfrozen water to be squeezed into the air voids. The shell thickness L determines the volume of the hydrated cement slurry, and all pore water flows in this direction towards the pores of interest. According to the studies of Powers [27] and Liu [28], the pore spacing coefficient increases with the increase in saturation, which leads to an increase in the tensile strain of the porous skeleton, as shown in Figure 5. As the air voids gradually saturate, the increase in void spacing clearly indicates the destructive effect of prolonged exposure to water on the frost resistance inside concrete. Fully saturated concrete exhibits significant expansion during the freezing process, while unsaturated concrete exhibits significant shrinkage during the freezing process. These research findings indicate the importance of critical saturation in determining the FT performance of concrete.

In conclusion, porous skeleton determines concrete’s FT performance, and the changing law of this structure can accurately characterize FT failure. However, the prerequisite is using high-precision detection technology to accurately obtain the pore evolution. Moreover, different FT conditions and types of concrete have different forms of FT damage, and it is necessary to use the obtained pore structure to establish FT models to predict the frost resistance of a certain type of concrete.

2.2. Effect of Air Content on FT Performance

According to FT theory, the FT degree is determined by the moisture condition inside the concrete before each FT cycle. Once the critical saturation condition is attained, concrete is more susceptible to FT damage. The pores entrained in concrete will reduce saturation and delay the moment it reaches the critical saturation condition [29]. Therefore, introducing an appropriate pore system inside the concrete can significantly improve its frost resistance [30].

The relative dynamic elastic modulus (RDEM) is considered to be the most common index for evaluating FT damage of concrete, and many studies have used this index to prove that the frost resistance of air-entraining concrete is generally better than that of non-air-entraining concrete, as shown in Figure 6. Peng et al. [31] studied the effect of air-entraining agents on the frost resistance of concrete with the water-cement proportion being 0.32, and found that the FT performance of air-entraining concrete can reach up to 300 FT cycles. Xu et al. [32] used the critical saturation theory to predict the performance of concrete in FT environments, and concluded that the addition of air-entraining agents can increase the service life of concrete in FT environments by more than 50 times. Du et al. [33] compared and analyzed the residual strains of air-entraining concrete and non-air-entraining concrete. The results indicate that the residual strain significantly decreases when the air content is 4.5% and 6.9%, suggesting that the FT damage of specimens is relatively small in this state. Farooq et al. [34] studied the variations in mechanical properties between air-entraining high-strength concrete and non-air-entraining high-strength concrete under FT conditions. The FT strain development rate of non-air-entraining high-strength concrete is significantly higher than that of air-entraining high-strength concrete, which indicates that the degradation rate of mechanical properties of the former is higher than that of the latter under FT conditions.

The addition of air-entraining agents will change the pores in concrete and increase its porosity, thus significantly enhancing the frost resistance of concrete [42,43,44]. However, the effect of air-entraining agents on the frost resistance of concrete is to change the pore structure inside the concrete. Hence, accurately determining the pore structure inside frozen concrete is essential for revealing the effect of air-entraining agents.

2.3. Characterization of FT Damage Based on CT Technology

As mentioned above, the internal pore structure plays a crucial part in characterizing the FT damage of concrete. Thus, it is necessary to accurately capture this evolution of FT damage on the pore structure in concrete, with the help of high-accuracy detecting techniques [45,46].

X-ray computed tomography (CT), as a non-destructive 3D imaging technology, can capture 2D photos from varying directions for the purpose of rebuilding the 3D object [47]. The application of this technique in cement-based materials is receiving increasing attention for the following reasons: (1) centimeter-sized large specimens can be imaged with a resolution of micrometer; (2) precise quantitative details of particular constituents can be obtained [48,49]. In particular, it is used to depict these variations within microscopic structures resulting from freezing and thawing [50,51,52].

Chen et al. [53] used CT technology to conduct a microscopic analysis of the FT damage process of shotcrete under FT environments, and concluded that the loosening and sliding of cement mortar became increasingly evident with increasing FT cycles, and that the number of pores increased significantly. Luo et al. [54] quantitatively analyzed the microstructural development of materials under FT conditions using CT technology, and studied the three-dimensional microstructural damage characteristics, pore network (porosity, pore size, and distribution), and microcracks. The concrete microstructure, when exposed to FT action, indicates that the interface transition zone (ITZ) is most susceptible to FT damage. In addition, FT action damages not only the interface transition zone but also the cement matrix and aggregates, significantly affecting the internal micropores and microcracks of concrete. The research results have demonstrated that CT technology can determine the microstructure of concrete, reveal the existence of internal pores and cracks at different stages, and more effectively characterize the cumulative damage caused by FT action. Shields et al. [51] used CT technology to determine the location and source (e.g., pores, aggregates, ITZ, or matrix) of cracks inside concrete exposed to FT action, and measured the volume of cracks, as shown in Figure 7. The results indicate that cracks will appear in the concrete under FT action, and these cracks can provide infiltration paths for water, which will aggravate the damage and reduce the service life of the concrete structure. Paswan and Das [55] conducted a visualization study on the changes in the microscopic structure inside concrete during FT process. This research results indicate that the precise quantification of details like the morphology and content of pores and microcracks in concrete are achievable by combining industrial CT imaging technology with post-processing methods.

Promentilla and Sugiyama [56] used CT technology to characterize the development of microscopic structures inside mortar subjected to FT action, including the porosity, pore distribution, and crack width and curvature connecting the pore network. The number of internal microcracks increases gradually with increasing FT cycles, and the pore connectivity also increases, resulting in an increase in crack curvature; these microcracks also exhibit obvious three-dimensional anisotropy. Liu et al. [57] characterized the change law of microscopic structures in shotcrete subjected to FT action, as shown in Figure 8. CT statistical results indicate that the length of the porous framework and pore structure connectedness are important parameters for characterizing the evolution of micro-scale pore structures, and that the porosity of ITZ plays an important role in this evolution. In addition, CT technology also plays an important role in the construction of FT damage models. Based on the internal microstructure of concrete obtained by CT technology, Hain and Wriggers [58] established a thermal and mechanical coupling microscopic model of cement-based materials under FT damage, and obtained an effective correlation between humidity, temperature, and material nonlinear behavior. The research results indicate that the model can accurately describe the FT damage using the analysis results of the microstructure. Atasham et al. [59] used CT scanning and 3D reconstruction technology to explore the degradation mechanism of concrete in FT environments from a microscopic perspective, and established a model for FT action anchored in Weibull distribution. Through a comparative analysis, it can be concluded that the prediction results of the established model are in good agreement with the experimental data, which verifies the feasibility of this model in evaluating the deterioration performance under FT action.

Based on previous research results, it is known that CT technology can capture the microstructural evolution under FT action and extract different types of microstructures according to the needs of researchers, which provides a means to quantificationally characterize the degree of FT. However, most CT studies are based on traditional threshold segmentation methods, which exhibit significant limitations due to inherent segmentation mechanism issues. The primary reason is that threshold segmentation relies on trial-and-error to determine the critical thresholds between pores/cracks and mortar, and between mortar and coarse aggregates, which can result in some microcracks or capillary pores being incorrectly segmented into the mortar phase or aggregate phase category and unable to accurately capture the evolution of microcracks and capillary pores caused by FT damage, making CT technology a bottleneck in revealing the evolution of internal microstructures in concrete.

3. Fracture Characteristics of Concrete Under FT Cycles

Concrete is a kind of heterogeneous material with high compressive strength, but its cracking resistance is poor [60,61]. When external loads are applied to concrete, local stress concentration will occur near defects, which will aggravate the development of damage and ultimately lead to the failure of the entire concrete component [62,63]. Considering its complex microstructure and quasi-brittle characteristics, the strength performance of concrete is insufficient to describe the material behavior. The fracture behavior is helpful to analyze the response of concrete structures to external loads. Applying fracture behavior to analyze mechanical properties provides a reasonable basis for the failure assessment of concrete structures and helps to better understand designing methodologies for structures.

According to the review in Section 2, the expansion that occurs when the pore water inside concrete freezes causes internal tensile stress, which is manifested as unrecoverable tensile strain and microcracks [64,65,66]. Therefore, the FT damage to concrete could be considered as a complex crack propagation procedure, which significantly affects the fracture performance of concrete [67]. Previous studies on the FT damage of concrete mostly focus on strength reduction, mass loss, and ultrasonic characteristic changes [68,69,70]. However, considering the quasi-brittleness of concrete and the fact that most structures are subjected to the coupling effect of multiple factors, it is not enough to reveal FT damage solely from the perspective of strength or mass loss. Some studies have proved that FT damage can be better understood from the perspective of fracture mechanics [71,72,73]. During freeze-thaw cycles, internal microcracks propagate due to the expansive pressure of freezing water. Fracture mechanics can quantitatively analyze the initiation, propagation, and critical conditions of cracks. The ability of concrete to resist FT deterioration can be evaluated through parameters such as fracture energy, toughness, and the crack propagation rate, revealing the damage accumulation process. In addition, the correlation between fracture characteristics and pore structure as well as strength is conducive to optimizing the FT-resistant design of concrete. For instance, fiber toughening can be used to suppress crack propagation and enhance the fracture performance of concrete under FT cycles.

Kosior-Kazberuk [74] pointed out that the fracture energy is a fundamental parameter for characterizing the cracking resistance and fracture toughness of concrete, and studied the effect of FT action on fracture energy. Investigations have indicated that internal damage caused by FT cycles exerts a substantial impact on fracture energy, which is related to changes in the bearing and deformability of concrete. Ma et al. [75] compared the fracture toughness of ordinary concrete, air-entraining concrete, and mineral mixed concrete, and found that fracture toughness significantly decreased with the increase in FT cycles, and the frost resistance of air-entraining concrete and mineral mixed concrete was better than that of ordinary concrete. Dong et al. [76] combined CT technology with a micro-scale bonding model to conduct a quantitative study on the impacts of FT cycles on the microstructure damage and fracture behavior of concrete under three-point flexural load. The analysis shows that the microcracks caused by FT action are the main reason for the degradation in concrete’s fracture performance. Wang and Petrů [77] evaluated the fracture energy release rate of concrete experiencing FT action and found that the fracture energy release rate significantly decreased with increasing FT cycles, and the way in which concrete fails also changed with increasing FT cycles. Zhou and Qiao [78] measured the dynamic elastic modulus and bond fracture energy of shotcrete under different FT cycles according to ASTM C215 and RILEM TC 50-FMC, and found that both test methods can detect material deterioration caused by cumulative FT damage, and the fracture energy characteristics were more sensitive and decay faster than the dynamic elastic modulus, as shown in Figure 9.

Previous studies have shown that fracture parameters are highly sensitive to the microstructural changes in concrete caused by FT damage. Although there is evidence that the fracture mechanics method is suitable for analyzing the degradation process of concrete, there is still no consistent theoretical and experimental research on the changes in concrete fracture parameters during the FT process. To conduct a more effective analysis of fracture behavior and reveal how FT damage affects fracture parameters, it is crucial to utilize state-of-the-art non-destructive technologies like digital image correlation (DIC) and acoustic emission (AE), and to establish appropriate constitutive models for use in the finite element method (FEM) and discrete element method (DEM). The benefits of DIC and AE are as follows: (1) DIC is capable of computing surface strain and determining crack growth and fracture performance [79,80,81]; (2) AE can monitor internal damage and help distinguish types and locations of cracking [82,83,84]. Based on the outstanding advantages of DIC and AE, they can be used to calibrate the mesoscopic parameters of FEM and DEM and verify numerical models. The combination of experiments and simulations (DIC/AE data-driven FEM/DEM parameter optimization) can more accurately quantify the fracture behavior of concrete under the coupling effect of FT and load, and reveal the crack propagation mechanism.

Due to the heterogeneity of concrete, its fracture process is complex, being accompanied by the initiation, propagation, branching, and coalescence of microcracks [85,86,87]. In the past few years, researchers have focused on precisely capturing the fracture characteristic of structures using microscopic models. The aim is to enhance the comprehension of crack growth and the evolution of the fracture mechanism. FEM [88,89] and DEM [90,91] can both be utilized to construct the model for concrete from a mesoscopic perspective. Nevertheless, owing to the disadvantages of constitutive models, it is challenging to precisely predict the large-scale cracking of concrete using FEM [92]. Moreover, DEM, relying on discontinuity, has the capacity to compute crack growth and reproduce the entire fracture process of concrete from microscopic damage to macroscopic cracks, and has therefore been broadly utilized by scholars. Liu and his team [93] delved into the utilization of DEM for simulating crack growth. They contended that the model exhibits a greater capacity to seize this transition process from ductile to brittle failure for flexural concrete beams. By constructing a DEM model, Nitka and Tejchman [94] attained a rather precise representation of the fracture characteristics. They held the view that this model has vast development prospects in the prediction of concrete microscopic and macroscopic fractures. Rucka et al. [95] studied the fracture evolution of concrete and found that the established DEM model has high applicability for monitoring the initiation and propagation of cracks, as shown in Figure 10. Xu et al. [96] used a DEM model to effectively reproduce the fracture behavior of concrete, proving that DEM is an efficient means of exploring concrete fracture.

Although a large number of studies have proved the outstanding advantages of DEM in simulating concrete fracture performance, no researchers have introduced FT damage into a DEM model to simulate how FT impacts the entire fracture process of concrete. Therefore, it is essential to construct the DEM fracture model considering FT indexes in order to precisely characterize the fracture characteristics of concrete under FT action.

4. Tensile Characteristics of Concrete Under FT Cycles

Concrete has a tensile performance that is roughly one-tenth of its compressive performance. Tensile performance, which is of great significance during structural service, predominantly governs concrete cracking [97,98,99]. Furthermore, hydraulic concrete structures in cold zones are likely to be affected by FT, and the tensile strength of concrete is more sensitive to FT degradation than the compressive strength. This is because there are defects such as pores and microcracks inside the concrete. During the FT cycle, the water in the pores freezes and expands, generating tensile stress. Due to the fact that the tensile strength of concrete is much lower than its compressive strength, the tensile stress is more likely to cause microcracks to propagate and connect, thereby leading to damage to concrete structures. It has a relatively high compressive strength and can resist ice expansion pressure to a certain extent. Therefore, compared with compressive strength, tensile strength is more likely to be significantly reduced due to FT cycles, which can have a greater impact on the crack resistance and overall performance of concrete structures. Hence, researchers and field engineers have begun to pay attention to the role of FT damage in influencing tensile performance.

Zhou et al. [97,98] studied the tensile properties and elastic modulus of ultra-high-performance concrete under FT action. The elastic modulus, tensile strength, strain capacity, and energy absorption capacity of ultra-high-performance concrete significantly decrease after long-term FT action, and its tensile stress-strain curve also shows a downward tendency with increasing FT cycles, especially in the strain softening stage, as shown in Figure 11. It is also pointed out that the method based on energy is more sensitive and effective than the method based on elastic modulus in evaluating the cumulative deterioration of structures under FT action. Komar and Boyd [100] conducted tensile and compressive tests on frozen concrete and found that tensile strength is more sensitive to FT degradation than compressive strength. Wang et al. [101] proposed a 2D mesoscale numerical approach for studying the mechanical properties of frozen concrete, including deformation and strength. The simulation results indicate that FT action severely deteriorates the tensile properties of concrete. Jin et al. [99] used a thermo-force sequential coupling simulation method to conclude that a decrease in temperature leads to more aggregates reaching the failure state, which results in more concentrated macroscopic cracks caused by direct tensile stress. In addition to the aforementioned studies, earlier studies have also examined how FT action affects tensile performance. The specific test conditions and research contents are listed in

Table 1. Research review of freeze-thaw on tensile performance of concrete.

Literature	Standard	FT Temperature (°C)	Water-Cement Ratio	Pore Content (%)	Measurement Parameter
Shi [102]	ASTM C666-84	−30~10	0.35	/(Air-entraining)	fc, E, fts, τ, Gs
Hasan [103]	ASTM C666-97	−17.8~4.4	0.50	/(Air-entraining)	RDEM, ft, E, Gs
Shang and Song [104]	GBJ82-85	−15~6	0.50	1.7	RDEM, ∆m, fts, fc, E
Ji et al. [105]	GBJ82-85	−17~8	0.5	1.9	fc, E, fts
Hanjari et al. [69]	RILEM TC 176-IDC	/	0.57	/(Non-air-entraining)	RDEM, fc, E, fts

Note: f_t is the direct tensile strength; f_ts is the splitting tensile strength; f_c is the compressive strength; τ is the shear strength; G_s is the shear modulus; E is the elastic modulus; RDEM is the relative dynamic elastic modulus; and ∆m is the mass loss.

.

According to previous research, the ability of structures to withstand tensile loads can be remarkably weakened by FT action [69,100,101,102,103,104,105], which plays a crucial role in ensuring the normal service of engineering. Owing to testing constraints, just a segment of scholars have investigated the splitting and flexural behaviors of concrete under FT action [69,102,104,105], and research on the characteristics of concrete under the coupling of freeze-thaw and monotonic direct tensile loads is even scarcer [97,98,103]. However, the above research is not sufficient for hydraulic engineering. Given that hydraulic structures commonly experience powerful flood releases and severe seismic events, these factors will cause the hydraulic concrete to endure continuous cyclic loads, thereby decreasing its tensile strength, which in turn leads to cracking, the loss of load-bearing capacity, and ultimate failure [106].

Up until now, no study findings have been reported on hydraulic concrete subjected to the coupling effect of freeze-thaw and cyclic tension. In addition, as a heterogeneous material, the stress-strain curve of hydraulic concrete under cyclic tensile loading often exhibits significant nonlinear characteristics [107], and FT damage can significantly change this nonlinear behavior. Hence, it is urgent to fill the gap in the study of the nonlinear characteristics of hydraulic concrete under the coupling action of freeze-thaw and cyclic tension. This requires the establishment of a multi-factor model to reveal the evolution laws of principal strain, principal crack width, and internal microcrack of hydraulic concrete subjected to different FT cycles under cyclic tensile loads.

5. Triaxial Test and Numerical Simulation of Concrete Under FT Action

According to the mechanism of FT action, it can markedly weaken the mechanical performance of concrete, such as its fracture characteristics (see Section 3) and direct tensile characteristics (see Section 4). However, some key parts of hydraulic concrete structures are often subjected to complex triaxial stresses, in addition to flexural load and tensile load. How does FT damage affect the triaxial properties of concrete? This is mainly reflected in two aspects: microstructure deterioration and macroscopic mechanical property degradation. The FT cycle causes the pore water inside the concrete to undergo repeated phase changes, generating expansion pressure and triggering the propagation of microcracks and the formation of a connected crack network, thereby reducing the density of the material. Under the triaxial stress state, FT damage will significantly weaken the confining pressure effect of concrete: on the one hand, the development of cracks leads to an uneven distribution of internal stress, weakening the reinforcing effect of hydrostatic pressure on strength; on the other hand, the accumulation of damage leads to a simultaneous decrease in peak stress and deformation capacity, especially significantly reducing the lateral deformation capacity. The triaxial characteristics of concrete generally include two types: static triaxial characteristics and dynamic triaxial characteristics. The research progress on the damage evolution of concrete under triaxial loading is summarized and reviewed below.

5.1. Static Triaxial Characteristics

The triaxial stress state exists in many parts of structures like bridges and dams [12,108,109]. These multi-axial loads are usually generated by boundary constraints, water or soil pressure, and the mechanical performance of concrete is significantly impacted by these factors. Over the past few decades, engineers and scholars have recognized the importance of the triaxial performance of concrete for the safe operation of practical engineering.

Imran [110] and Mahboubi [111] studied the triaxial mechanical response of concrete under different confining pressures. The results indicate that with the increase in confining pressure, the triaxial peak stress, elastic modulus, and deformation capacity of concrete significantly increase. Chen et al. [112,113] investigated the triaxial performance of ordinary concrete under different confining pressures and concluded that its plastic deformation and ultimate strength relied significantly on external confining pressure. Zhou et al. [114] constructed concrete constitutive models under triaxial compression, concluding that high confining pressure slowed crack growth, leading to more stiffness and strength. For the purpose of investigating how confining pressure impacts triaxial strength, Folino and Xargay [115] conducted triaxial tests under different confining pressures and found that the increment in triaxial strength of concrete was not constant, but decreased with increasing confining pressure. Chen et al. [116] studied the influence of confining pressure on the triaxial characteristics of concrete through conventional triaxial tests, and concluded that the damage development rate gradually decreased with increasing confining pressure, and the failure shifted from plastic flow to a bilinear model, manifested as a gradual increase in yield stress and yield strain, as shown in Figure 12 and Figure 13. Furthermore, numerous researchers have triaxial-tested different concrete types like fiber-reinforced concrete [117,118,119] and high-strength concrete [120,121,122], and investigated the impacts of environmental aspects like high temperature [123,124] and chemical corrosion [125,126].

On the basis of relevant experimental studies, researchers have also been exploring the development of constitutive models. The term “constitutive relationship” is a comprehensive term, which can comprise hardening criterion, yield criterion, flow criterion, and failure criterion. Since the renowned Mohr–Coulomb theory was put forward, researchers have constructed and refined many models for specific research objects by incorporating principal shear and normal stresses. The Tresca criterion [127], Drucker-Prager criterion [128], Willam-Warnke criterion [129], von Mises criterion [130], and Ottosen criterion [131], along with their revised formulas, are proposed to advance the modeling of triaxial characteristics of concrete.

Hydraulic concrete in cold regions has already suffered FT damage before bearing the triaxial loads. However, through the literature review, it was found that the constitutive models used by previous researchers are generally based on simple mechanical experiments, overlooking the influence of environmental factors on the triaxial mechanical evolution of concrete. Given that the actual structures in cold zones are subjected to the combined action of freeze-thaw and complex triaxial loads, it is necessary to conduct in-depth research on the evolution of the triaxial mechanical properties of hydraulic concrete under FT conditions.

5.2. Dynamic Triaxial Characteristics

As mentioned above, hydraulic structures commonly exist in complex triaxial stress states during service. At the same time, these concrete structures will also be subjected to different degrees of cyclic loads, such as the vibration caused by overflow and units, cyclic changes in water level and temperature, and seismic loads [12,132,133]. The research on the cyclic triaxial mechanism of concrete can supply guidance for the safety evaluation of structures subjected to dynamic loads. Hence, this research field has become a key focus of structural stability analysis [134,135].

Lokuge et al. [136] established the relationship between axial stress and axial and lateral strains by conducting triaxial cyclic tests on high-strength concrete. When the unloading point occurs in the initial elastic zone, the axial strain decreases faster than the lateral strain, and the Poisson’s ratio decreases. Upon reloading following unloading, the Poisson’s ratio and the lateral and axial strains all revert to their pre-unloading levels. However, when the unloading point occurs in the plastic damage zone, the width of the hysteresis loop, the reduction in stress during each cycle of unloading and reloading (damage), and the slope of the unloading curve (plastic strain) all change with the advance of the unloading point. Lu and Hsu [137] explored the varying trend of tangential Poisson’s ratio in triaxial compression, and concluded that, compared with uniaxial compression, constraints can significantly reduce the tangential Poisson’s ratio. Schmidt et al. [138] concluded that the strain dependence of concrete is more obvious and there is a greater energy dissipation in each cycle at a higher temperature. Zhu et al. [139] suggested that the curing system significantly affects cyclic triaxial characteristics of concrete. With the increase in the curing temperature, the cyclic triaxial failure mode of concrete transitions from shear failure to compression failure, and its peak strength, dynamic elastic modulus, and dilatancy angle all show a decreasing trend, as shown in Figure 14 and Figure 15.

According to previous research results, the cyclic triaxial characteristics are crucial for the normal service of concrete structures in complex environments. Although a large body of literature has conducted research on the cyclic triaxial characteristics of concrete, the study of the cyclic triaxial behavior of frozen concrete is somewhat restricted due to limitations in testing technology. This situation greatly limits the understanding of the mechanical damage evolution of concrete structures in complex environments. Hence, conducting research on the damage evolution and deformation of structures under the coupling effect of freeze-thaw and cyclic triaxial loading not only has theoretical significance but also practical application value.

5.3. Numerical Analysis

Over the past few years, as computer technology has advanced, numerical simulation has emerged as a crucial analytical tool [140,141]. This method can overcome the drawbacks of experiments, reduce resource waste, and enable = real-time monitoring of the crack growth inside concrete under stress, thus receiving significant attention from researchers. As one of these methods, DEM is capable of remedying the drawback of FEM with respect to its failure to simulate large-scale cracking. The finite-discrete element method (FDEM) has not yet completely solved the problem of grid dependence [92,142,143]. Therefore, DEMhas been extensively applied in investigating the triaxial mechanism of concrete.

Arulrajah et al. [144] conducted cyclic triaxial tests on recycled concrete aggregates using DEM, providing a better understanding of their macro-micro mechanical interactions and internal mechanisms. Benniu et al. [145] constructed a DEM model that took the saturation ratio into account, which effectively reproduced the triaxial characteristics of concrete. After introducing the improved constitutive models, such as bond displacement softening [146], bilinear cohesive softening [147], and local elastic hardening [148], DEM shows better potential in simulating the crack initiation and propagation, linear strain, and volumetric strain evolution of concrete under triaxial loads. In addition, DEM has demonstrated strong predictive capabilities in multi-level cyclic loading [149,150], size effects [151], and steam curing [139]. Zhu et al. [139] introduced steam curing indicators into microscopic parameters to establish a DEM model for steam-cured concrete, and verified the outstanding advantages of this model in predicting the triaxial characteristics of steam-cured concrete, as shown in

Table 2. The outstanding capacity of DEM in predicting triaxial characteristics of concrete.

Curing Temperature	Failure Modes for the Test	Failure Modes for DEM Simulation
40 °C
60 °C
80 °C

.

DEM is particularly effective in predicting the triaxial characteristics of concrete under different conditions such as saturation ratio and cyclic loading for the following reasons. Firstly, DEM can consider the non-uniformity of concrete from a mesoscopic perspective, regarding it as a discrete system composed of aggregates, mortar, and interfaces, etc., and can accurately describe the mechanical behavior and interaction of each component. Secondly, for the variation of the saturation ratio, it can reasonably simulate the influence of water on the mechanical properties of concrete by considering factors such as pore water pressure. Furthermore, under cyclic loading, DEM can track the contact state and energy dissipation between particles, accurately reflect the development process of internal damage in concrete, and thereby effectively predict the triaxial characteristics of concrete under different conditions.

Researchers have established many effective DEM triaxial numerical models, which can precisely simulate triaxial response and failure mode of concrete. However, current research simplifies irregular aggregates into spheres and does not consider the influence of real aggregate shape factors on the triaxial mechanical properties of concrete. Introducing empirical parameters has no practical significance, leading to difficulties in the calibration process. As a result, it becomes imperative to optimize the DEM model through programming. Furthermore, it remains a difficult task to study the triaxial failure mechanism of concrete by incorporating FT damage as an influence indicator for establishing the DEM model.

6. Wear Resistance Characteristics and Prediction Model of Concrete Under FT Cycles

Hydraulic concrete is susceptible to erosion by a variety of natural factors during service, which will gravely endanger the normal service of structures, with wear representing one of the key determinants. Hydraulic wear is the process where the cement matrix and aggregate on the surface of concrete are continuously chipped away due to the impact of water carrying sand. This ranks among the crucial properties of immersed structures [152,153], predominantly occurring in discharge parts of hydraulic structures, including dam overflow surfaces and subsequent discharge sections. As a multiphase composite material system, hydraulic concrete exhibits nonlinear characteristics in its macroscopic behavior, which reflects the complexity of the internal microstructure of concrete. Numerous surface defects will intensify the wear process, presenting a complex wear mechanism, as shown in Figure 16.

There is a certain degree of elastoplastic deformation during the process of water carrying sand to wear concrete. When sand particles impact the concrete surface driven by water flow, elastic deformation occurs first at the contact point with the concrete surface, and then plastic flow begins at the contact center, where the maximum stress occurs. With the consumption of kinetic energy of sand particles, the plastic deformation zone further expands until all the kinetic energy of sand particles is transformed into elastoplastic deformation work of materials [155]. Thereafter, the surface elastic deformation of the concrete will recover, while the plastic deformation will remain, forming impact pits, and the material extruded in the plastic deformation will accumulate at the edges of the pits [156]. Figure 17 presents the hydraulic wear process.

At present, researchers around the world have started to recognize the significance of wear resistance in practical concrete engineering, and have conducted relevant studies on it. Horszczaruk [158,159] established a correlation between wear resistance and mechanical behavior, holding the view that the wear mass loss can be determined using these equations. Mohebi et al. [160] quantitatively analyzed the wear deterioration in terms of the compressive strength and wear depth of concrete. Dandapat and Deb [161] used the aggregation generation algorithm to establish the erosion wear model of structures under sand-bearing water loads. Wang [162] and Lv [163] concluded, through experimental research, that there was a strong linear positive correlation between the compressive strength and wear resistance, as illustrated in Figure 18. This can guide hydraulic engineers to directly use the compressive strength of concrete to evaluate its wear resistance. Omranian and Eftekhar [164] established a relationship model between compressive strength and the wear erosion rate using linear fitting, and concluded that compressive strength was negatively correlated with the wear erosion rate (ER), and the higher the Froude number (Fr), the lower the correlation, as shown in Figure 19. In addition, many researchers have established models for the mechanical parameters and wear indexes of concrete, as shown in

Table 3. Existing empirical models for predicting wear resistance of concrete.

Function Type	Model	Related Parameters	Concrete Type
Linear	$ER=\mathrm{a}{f}_{\mathrm{c}}+\mathrm{b}$	ER: Wear erosion rate; fc: Compressive strength.	Polypropylene and steel fiber-reinforced concrete [164]
	$f_{\mathrm{ab}}=\mathrm{a}{f}_{\mathrm{c}}+\mathrm{b}$	fab: Wear resistance; fc: Compressive strength.	PVA fiber-reinforced concrete [162] Dam concrete mixed with iron tailings aggregates [163]
	$W_{\mathrm{ar}}=\mathrm{a}{f}_{\mathrm{c}}+\mathrm{b}$	War: Wear rate; fc: Compressive strength.	Ordinary concrete [165]
	$D=\mathrm{a}t$	D: Wear depth; t: Wear time.	Ultra-high-performance concrete [166]
Power	$D=\mathrm{a}{f_{\mathrm{c}}}^{\mathrm{b}}$	D: Wear depth; fc: Compressive strength.	High-strength concrete [167]
	$W_{\mathrm{ar}}=\mathrm{a}{v}^{\mathrm{b}}$	War: Wear rate; vb: Flow velocity.	Steel fiber-reinforced hydraulic concrete [168] Rolled dam concrete [169]
Exponential	$M_1=e^{\mathrm{a}{f}_{\mathrm{c}}}$	M1: Mass loss; fc: Compressive strength.	Ultra-high-performance concrete [166]
Logarithmic	$M_1=\mathrm{a}+\mathrm{b}\ln f_{\mathrm{c}}$	M1: Mass loss; fc: Compressive strength.	Polyester fiber fly ash concrete [170]
Polynomial	$M_1={\mathrm{a}}_1+{\mathrm{a}}_2{f}_{\mathrm{f}/\mathrm{t}}+{\mathrm{a}}_3{f_{\mathrm{f}/\mathrm{t}}}^2$	M1: Mass loss; ff/t: Flexural or tensile strength.	Recycled aggregate concrete [171]
	$D={\mathrm{a}}_1+{\mathrm{a}}_2{f}_{\mathrm{c}}+{\mathrm{a}}_3{f_{\mathrm{c}}}^2$	D: Wear depth; fc: Compressive strength.	High-strength hydraulic concrete [158]

. Although there is a quantitative relationship between the mechanical properties and wear resistance of concrete, this is mostly based on empirical prediction models, which are usually only applicable to a certain type of concrete and have no universal applicability. The wear of concrete ultimately boils down to surface roughness problems. How to accurately characterize the surface roughness after different wear times is the key to studying the wear resistance of concrete.

In recent years, non-contact 3D scanning technology has developed rapidly and is considered to be the most reliable, efficient, and accurate surface measurement tool [172]; it is widely used in various fields such as medicine, mechanical engineering, and civil engineering [173,174]. In practical applications, the availability of highly detailed high-precision 3D models allows for the precise study of surface geometric properties, which has facilitated the application of this technology for characterizing the wear damage of concrete. Hasan et al. [175] applied 3D scanning technology to determine the wear morphology and volume loss of concrete. By comparing it in detail with other roughness quantification techniques, Sarker et al. [176] held the view that 3D scanning can capture concrete roughness more effectively. Xiong et al. [177] conducted a quantitative study on the wear resistance characteristics of concrete at different impact angles, and accurately obtained the shape of the impact pit on the concrete surface using 3D scanning, as shown in Figure 20. Although some scholars have begun to apply non-contact 3D scanning technology to the study of concrete wear, most of them only analyze the surface topography of concrete, and few researchers combine 3D scanning and MATLAB 7.0 to deeply analyze the surface topography data, so as to construct a wear prediction model with higher precision for concrete, which plays a vital role in evaluating whether hydraulic structures can function properly under wear conditions.

Moreover, hydraulic structures in northern China are often subject to dual damage from FT and wear [178,179,180,181]. FT action can lead to physical deterioration of concrete [67,182], and such deterioration-induced cumulative damage will bring about scale formation [183,184], cracking, and cement matrix shedding on the concrete surface [185,186]. This will accelerate the wear process and cause greater damage than a single factor. As a result, delving into the deterioration mechanism of hydraulic structures when hydraulic wear and FT action occur together is extremely important for their normal service. Nevertheless, because of experimental difficulty, mechanism complexity, and multi-factor influence, it is challenging to construct a comprehensive prediction model regarding the combined action of the two using traditional analysis methods. A promising approach to solving this problem is projection pursuit regression (PPR), which serves as an exploratory analysis means (EAM) of analyzing complex high-dimensional data [187]. This method associates independent variables with dependent variables through non-parametric and non-hypothetical functions, and projects high-dimensional data onto low-dimensional data to find suitable projections that can mirror the features of high-dimensional data, as shown in Figure 21. Since this method is capable of analyzing multiple factors at the same time, its applications span numerous fields, including hydrology and materials [188,189,190,191]. Projection pursuit regression (PPR) has been demonstrated as an effective means of solving complex issues with multi-factors and multi-indexes, which points out the direction for establishing wear performance prediction models for frozen concrete.

7. Conclusions and Perspectives

This paper reviews the performance degradation law and model construction of hydraulic concrete under FT action. The main findings, based on the literature review, are summarized as follows:

(1) The frost resistance of concrete depends on its pore structure. The evolution of the pore structure under FT cycles can characterize FT damage, but requires high-precision detection techniques. Different FT conditions and concrete types exhibit varied damage patterns, necessitating specific microstructural damage models. However, FT-induced microcracks demonstrate multiscale complexity, challenging conventional detection methods. While CT technology can capture microstructural changes, traditional threshold segmentation fails to accurately distinguish microcracks from capillary pores. Thus, developing more precise three-phase segmentation methods and accurate models is essential to investigate FT effects on pore evolution.

(2) FT damage to concrete is characterized by complex crack propagation that significantly influences its fracture behavior. While existing studies predominantly focus on strength degradation and mass loss, these approaches prove insufficient for analyzing damage mechanisms since concrete structures in cold regions are typically subjected to the combined action of FT cycles and external loads. Although fracture mechanics provides a suitable framework for concrete deterioration analysis, systematic investigations into the evolution of fracture parameters during FT cycles remain scarce. This necessitates the integration of advanced non-destructive testing techniques to develop appropriate constitutive models for numerical simulations. DEM has demonstrated remarkable advantages in simulating concrete fracture, yet no studies have incorporated FT damage into DEM models to simulate its comprehensive effects on the fracture process. Consequently, there is a critical need to develop DEM fracture models that account for FT damage to accurately characterize the fracture behavior of concrete under such conditions.

(3) Research on the direct tensile properties of concrete remains limited due to testing constraints, particularly for monotonic tensile behavior under FT conditions. However, hydraulic concrete structures are frequently subjected to cyclic loads, making studies solely on monotonic tensile properties inadequate. Currently, investigations into the cyclic tensile performance of concrete after FT exposure represent a complete research gap. As a heterogeneous material, concrete exhibits pronounced nonlinearity in its cyclic tensile stress-strain response, a characteristic significantly altered by FT damage. Consequently, there is an urgent need to develop a cyclic tensile model incorporating FT effects to elucidate the strain development, crack propagation, and damage evolution in FT-affected concrete under cyclic loading.

(4) Some key parts of hydraulic structures frequently endure complex triaxial stresses, yet FT effects on triaxial behavior remain unclear. Existing studies, limited by testing techniques, fail to reveal mechanical responses under the coupling effect of FT and triaxial loading, thereby restricting the damage assessment of concrete structures in cold regions. Developing triaxial damage models for FT-affected concrete holds both theoretical and practical significance. While existing DEM triaxial models can reasonably simulate mechanical responses, they suffer from oversimplifications (spherical aggregate assumption) and empirically calibrated parameters lacking clear physical meaning, necessitating programming optimization. The greater challenge lies in incorporating FT damage indicators into mesoscopic parameters to establish triaxial DEM models for investigating failure mechanisms.

(5) In cold-region rivers, hydraulic structures are invariably situated within a compound environment, entailing freeze-thaw and wear. As a result, delving into the deterioration mechanism of hydraulic structures when hydraulic wear and FT action occur together is extremely important for their normal service. Nevertheless, because of experimental difficulty, mechanism complexity, and multi-factor influence, it is challenging to construct a comprehensive prediction model regarding the combined action of the two using traditional analysis methods. PPR has been demonstrated as an effective means for solving complex issues with multi-factors and multi-indexes. This requires the establishment of a wear performance prediction model for frozen concrete based on this theory, and quantitatively studies of how FT action affects the wear resistance of concrete.