Experimental analysis of frost resistance and failure models in engineered cementitious composites with the integration of Yellow River sand

: This study investigates the potential use of Yellow River sand (YRS) sourced from the lower reaches of the Yellow River in China as a sustainable and cost-e ﬀ ective substitute for quartz sand in engineered cementitious composites (ECCs). This region accumulates around 400 million tons of sand annually. The study evaluates the impact of di ﬀ erent YRS replacement percentages (0, 25, 50, 75, and 100%) on mechanical and microstructure properties under freeze-thaw conditions, focusing on assessing the ECC durability during cooling cycles. The results show that YRS exhibits a smaller normal distribution of particle sizes compared to that of quartz sand and a 5.77 times greater speci ﬁ c surface area, a ﬀ ecting the ECC particle size distribution. After 300 cooling cycles, the R25 group maintains 97.5% of the initial mass and 79.4% of ﬂ exural strength, indicating superior durability. The R25 group also demonstrates a minimal decrease of 11.5% in equivalent bending strength, reaching a level of 104.4% compared to R0. The R25 group ’ s porosity is 30.80%, with an average pore size of 20.47 mm, showing 1.3% and 6.7% decreases compared to the R0 group. Additionally, this study establishes a failure progression equation using the Weibull probability distribution model, with calculated values closely aligning with measured values. Overall, this study recommends using YRS as a sustainable ECC material.


Introduction
In the construction industry, concrete stands as the most extensively utilized material.Researchers worldwide have consistently enhanced it to overcome its limitations and align with current building standards [1].Addressing the limitations of conventional concrete, including its low tensile strength, ductility, and toughness, is essential to mitigate issues like corrosion and enhance the overall durability with long structural lifespan [2,3].To address these issues, scholars have investigated alternative materials, such as fiber-reinforced concrete [4][5][6][7][8], polymer-modified concrete [9], fiber composite materials concrete [10][11][12][13][14], and ultrahigh-performance concrete (UHPC) [15][16][17].Although fiberreinforced concrete has addressed various issues, concerns remain about its longevity due to long-term problems, including reduced strength and reduced ductility [18].The construction industry relies on the development of materials and methods to ensure that the structure meets the requirements of modern construction practices.In response to the need to improve the productivity of construction projects, engineered cementitious composites (ECCs) have emerged as a compelling solution.ECC is distinguished by its exceptional ability to be an ultra-flexible, durable, and hardening material, superior to conventional concrete in several aspects.In particular, ECC exhibits an ultimate tensile stress of 3-6%, 310-450 times higher than that of conventional concrete [19][20][21][22].This innovation strategically reduces the incorporation of fine aggregates while eliminating coarse aggregates from the mix, enhancing the multiple cracking capacity and tensile strain hardening properties of concrete [23].With outstanding tensile strength, ingenious crack management, and damage resistance, ECC is proving to be desirable in a wide range of applications such as in formwork [24], pavements [25], bridges [26], structural beam panels [27], and reinforcement of existing structures [28,29].
Although ECC exhibits exceptional mechanical properties and durability, its high cost poses a barrier to its widespread implementation as a building material.The cost of manufacturing and shipping quartz sand is higher than that of river sand (RS), which restricts the widespread use of ECC in real-world engineering applications.To lower construction costs, numerous researchers have created geo-materials that can partially replace quartz sand [30][31][32].In particular, extensive research has been carried out on the use of RS to improve its properties and promote sustainable development [33].Researchers are investigating on incorporating green building materials [34][35][36][37] as substitutes for cement in ECC, with positive outcomes [38][39][40].However, siltation of rivers, especially the Yellow River, remains a serious problem [41,42].Excessive sedimentation creates the risk of flooding and environmental complications.The region accumulates around 400 million tons of mud and sand annually [43,44].Yan et al. [45] used ultrafine sand from the Yellow River; natural RS was used with different material contents of 0, 20, 40, 60, 80, and 100% in UHPC.With a commitment to promoting cost-effective and sustainable construction methods [46][47][48][49], this study suggests the partial or complete replacement of quartz sand with the Yellow River sand (YRS) in ECC formulations.This substitution can have advantages such as cost savings and increased performance in cement-based materials.In addition, it offers a potential solution to the problem of large sediment deposits along the Yellow River.In the cold climate conditions of Henan Province in northern China, concrete structures face challenges related to fundamental mechanical properties and ECC salt freezing resistance capability issues.The grading of salt holds significant importance for ensuring the safety of driving, as it increases the risk of structural collapse and failure [50].While various theories exist regarding freezing issues [51][52][53][54], several recent studies have explored the mechanical and durability properties of ECC and lightweight engineered cementitious composites (LECCs) under challenging environmental conditions.Humur and Çevik [55] studied that adding nanosilica and hybrid fibers significantly improved the compressive strength and durability in lightweight geopolymer composites under heating-cooling cycles, although polypropylene fibers displayed weaknesses in bonding characteristics and resulted in micro-cracks and capillaries.Low temperatures and freeze-thaw cycles led to a decrease in the nominal fracture energy and different damage mechanisms, transforming ECC from ductile to a brittle fracture mode at low temperatures while retaining the ductile behavior even after 100 freeze-thaw cycles [56].Long et al. [57] studied polyethylene ECC (PE-ECC) under ultra-low-temperature freeze-thaw cycles and found significant reductions in flexural static load strength, flexural strength, and bending deflection, with lower toughness and interfacial bonding strength, leading to increased fiber pullout damage.PE-ECC fatigue life followed the two-parameter Weibull distribution, providing equations for fatigue life under different conditions.Azadmanesh et al. [58] studied the effect of freeze-thaw cycles on the mechanical properties of ECC with unoiled polyvinyl alcohol (PVA) fibers, and polymers such as styrene-butadiene rubber and ethylene vinyl acetate improved tensile and flexural properties, preserving mechanical properties and achieving increases in tensile strain and compressive strength.Gou et al. [59] investigated LECC durability under combined sulfate-chloride attack and freeze-thaw cycles, finding accelerated failure and surface damage, with different salt solutions affecting the mass loss and relative dynamic elastic modulus differently, ultimately providing insights into LECC's performance in harsh environments.It is crucial to delve into the impact of factors such as cell size and water saturation [60][61][62][63].This study focuses on Henan Province, using YRS in the Yellow River Diversion Project to replace the natural quartz sand in ECC.The primary objective is to address specific infrastructure challenges in the region, with a particular emphasis on enhancing the durability in the face of freeze-thaw environmental conditions.While previous studies primarily incorporated YRS in UHPC [64,65], this research introduces a novel application of YRS in ECC formulations under freeze-thaw environmental conditions.This study offers potential advantages such as cost savings and improved performance in cementbased materials.Moreover, it addresses the environmental issue of large sediment deposits along the Yellow River by utilizing the sand for construction use.The study provides a novel approach by exploring the use of YRS in ECC under Henan Province's cold climate conditions, where concrete structures face challenges related to fundamental mechanical properties and ECC salt freezing resistance.
The purpose of this study is to assess the durability and strength characteristics of ECC utilizing various YRS replacement percentages after the freeze-thaw cycle.The microstructure properties of ECC-YRS were analyzed in detail by mercury infiltration porosimetry (MIP) and scanning electron microscopy (SEM) tests.In addition, this research proposed a damage evolution equation using the Weibull probability distribution model.The calculated values agree closely with the measured values, showing high accuracy.Overall, this study provides an insight into the potential of YRS as a sustainable and economical option for ECC integration.

Experimental design 2.1 Raw materials
In this study, Portland cement was used as the primary binder following the established technical standards listed in Table 1.PVA fibers were used as reinforcement and to enhance the tensile strength and ductility of ECC, and the main technical characteristics are detailed in Table 2.The primary technical indicators of Grade II fly ash, which was utilized as a supplementary cementitious material for improving the workability and reducing the hydration heat, are detailed in Table 3.To modify the water content, a superplasticizer composed of polycarboxylate was utilized, resulting in a 26.5% reduction in water content.The thickener HPMC-20 (HPMC = hydroxypropyl methylcellulose) was added to the mixture.Their apparent density range was from 0.24 to 0.80 g/cm, and its viscosity grade was between 10 and 200,000.For fine aggregates, both natural quartz sand and YRS were used.YRS was used as a raw material immediately after it was retrieved and dried from the grit chamber of the Puyang City-based Yellow River Diversion Project. Figure 1 depicts the morphology of the materials; the primary technical indicators and mineral compositions of YRS and quartz sand are shown in Tables 4 and 5, respectively.By combining these materials, the study aimed to achieve freeze-thaw resistance, bending toughness, and overall durability in the ECC.The PVA fibers provided reinforcement, while the superplasticizer and thickener improved the workability and consistency.This approach aimed to maximize the performance of ECC under varying environmental conditions.

Mix ratio and production maintenance
In this process, YRS was used as a replacement for quartz sand, with mass replacement rates of 25, 50, 75, and 100%, resulting in the development of YRS-ECC.The actual mixing ratio is shown in Table 6, where, for example, ECC-R25 means YRS replaces quartz sand at a rate of 25%.This systematic variation of optimization levels allowed a detailed investigation of the instrument performance in different contexts, providing valuable insights into studying  160 mm) was utilized to evaluate the compressive performance and flexural stiffness after freezing.After casting, the samples were demolded and allowed to stand for 2 days at room temperature.After 2 days, specimens were subjected to elevated temperatures ranging from 25 to 45°C at a rate of 12°C/h in a steam curing box.The temperature was maintained at 40°C for a duration of 8 h, after which it was gradually increased to 65°C at a consistent rate.After this process, the temperature was gradually reduced to 45°C for 8 h, with a decrease rate of 12°C/h.Subsequently, the temperature remained constant at 45°C for an additional 8 h.Subsequently, a constant cooling process was initiated, causing the ambient temperature to drop at a rate of 10°C/h until reaching 10°C.This testing regimen ensured that material properties, including freeze-thaw characteristics, compressive strength, and various dynamic elastic modulus measurements, are comprehensively addressed.

Experimental method
Particle size distributions of quartz sand and YRS were determined using a laser particle size analyzer chosen specifically for its ability to accommodate the finer particle size of YRS.The rapid freeze-thaw cycle test was conducted according to Test Methods for Durability Long-term Performance and Long-term Performance of Conventional Concrete (GB/T50083-2009) [66].The specimens were subjected to 300 cycles of freeze-thaw, with measurements of mass and relative dynamic elastic modulus performed every 50 cycles.The evaluation of compressive and flexural strength according to the guidelines outlined in the Cement Mortar Strength Test Method (GB-T 17671-2021).A YAW-3000 microcomputer-controlled apparatus was utilized for compression and bending tests, involving a closed-loop testing procedure for precise load control and measurement accuracy.For the compressive strength test, a YAW-3000 electrohydraulic pressure testing machine was operated at a loading rate of 1.2 MPa/s, ensuring consistent and reliable results [67].Additionally, following the Specifications for High Ductile Concrete (DBJ61/T 1112-2021) [68], the four-point bending test was conducted with an electronic universal testing machine with features of microcomputer-controlled displacement loading (WDW-20).The complete experimental setup is shown in Figure 2.
3 Test analysis and results

YRS particle size analysis
In Figure 3, it is shown that both YRS and quartz sand have approximately normal distributions, with YRS notably Experimental analysis of frost resistance and failure models in ECC-YRS  5 containing a considerably smaller particle size distribution.According to the results, the D 90 value for YRS is 157.346μm, indicating that 90% of cumulative particle size is achieved.This value falls within the midpoint of the range for quartz sand, spanning from D 10 to D 50 , as explained in Table 7. YRS has 5.77 times the specific surface area of quartz sand.These results demonstrate the effectiveness of incorporating ECC to enhance its particle size characteristics.

Mass loss rate
Figure 4 illustrates the influence of freeze-thaw cycles on the mass loss rate in YRS-ECC.An improvement is observed in the strength of specimens as the number of freeze cycles increases.This trend is observed within the R0 group; the mass loss rate gradually decreases from 0 to 200 cycles and then experiences a more pronounced decline from 200 to 300 cycles.In contrast, the R25, R50, R75, and R100 groups show a continuous reduction in the mass loss rate from the start to the end of the cycle.This positive effect on particle grading and the gapfilling between quartz sand particles is attributed to the presence of YRS.However, continuous freeze-thaw cycles lead to an increase in microcracks and water absorption in ECC, contributing to a decline in the mass loss rate.The R0 group, with a 1.1% increase in mass, displays the highest growth rate throughout the entire freeze-thaw cycle.In addition, the mass loss rates for YRS-ECC exhibit the following order at different replacement rates: R100 > R50 > R75 > R25 > R0.This trend is a result of YRS impacting particle size distribution via the relative permeability coefficient.As the substitution rate rises, there is a decrease in the relative permeability coefficient, indicating a reduction in material permeability [69].
The variations in YRS-ECC quality during freeze-thaw cycles can be attributed to two main factors.First, damage from frost heaving leads to surface mortar spalling, causing an absolute loss of mass.Second, microscopic cracks develop during the freeze-thaw cycles, gradually becoming saturated with water, thereby enhancing the overall quality of the specimen.The hydrophilic nature of the PVA fiber is essential for establishing a strong bond with cement mortar, preventing freeze-thaw spalling in mortar.The fiber arrangement acts as a bridge in the ECC surface mortar, reducing mass loss by enhancing water absorption.

Relative dynamic modulus of elasticity
Figure 5 depicts the freeze-thaw cycle of YRS-ECC, illustrating both absolute and relative values of its relative dynamic elastic modulus.According to Figure 5(a), a consistent reduction in the dynamic elastic modulus to the initial values is noted among all five specimen groups throughout the freeze-thaw cycle.Notably, R25 exhibits the slowest reduction rate, retaining 97.5% of its initial modulus after 300 cycles, while R75 experiences the highest reduction, reaching 95.5% of its starting value after 300 cycles.Figure 5(b) illustrates how the dynamic elastic modulus reduces to its initial value as the number of freeze-thaw cycles increases.All through the cycle, the YRS-mixed groups consistently outperform the reference group R0 in terms of relative dynamic elastic modulus.R50 and R100 have the largest moduli of elasticity among them, whereas R25 and R75 have the lowest modulus of elasticity, respectively.
According to the "Concrete Structure Durability Design and Construction Guide" [70], and according to existing studies [71], porosity affects a specimen's dynamic elastic modulus.
There are already micro-pores in the concrete, and as the freeze-thaw damage builds up, the number of microcracks inside the specimen grows.The dynamic elastic modulus decreases when thawed water seeps into other cracks and freezes, causing micro-cracks to open and structural material to become loose.Incorporating PVA fibers significantly improves the specimen's cold resistance [72].This is achieved by mitigating concrete degradation through the reduction of early plastic crack development.YRS, with a smaller particle size distribution than quartz sand, improves particle gradation and lowers porosity when incorporated into the mix.It works to alleviate pressure during freezethaw cycles by filling voids [73].This phenomenon becomes more with an increasing number of freeze-thaw cycles, and  Experimental analysis of frost resistance and failure models in ECC-YRS  7 the reference group R0 exhibits a lower relative dynamic elastic modulus compared to the specimens mixed with YRS.

Flexural strength
Figure 6 illustrates the flexural behavior of ECC-YRS throughout freezing cycles.Initially, at cycle 0, the R25 specimens display the highest elasticity within all groups, followed by R100, R50, and the lowest in R75.This trend persists as freezing cycles increase, through R25 reaching 107.64% of the strength of the R0 sample after 300 cycles, while R100 achieves 95.49% compared to the R0 sample's strength.At this point, the strengths of R0, R25, R50, R75, and R100 at 0 freezing cycles are 78.68,80.43, 76.51, 74.78, and 74.5%, respectively.Notably, an optimum performance is observed with the 25% YRS replacement rate in ECC.
The flexural strength of fiber-enhanced cement composites is mainly influenced by the adhesive bonding at the fiber-matrix interface, directly correlating with the material's flexural strength and toughness [74].
YRS plays a crucial role in enhancing the particle gradients and improving the interfacial adhesion due to its small particle size.During the initial cooling phases, YRS significantly impacts the sample's hydration response because of its large surface area.However, with an increasing number of freezing cycles, minor cracks develop in the specimens, leading to a decline in flexural strength.

Compressive strength
In Figure 7, the impact resistance of YRS-ECC under freezethaw cycles is illustrated.The compressive strength tests  were conducted using a YAW-3000 microcomputer-controlled electro-hydraulic pressure testing machine, operating at a loading rate of 1.2 MPa/s as per ASTM C39 standards.The testing speed was selected to adhere to standard practices, ensuring consistent and reliable results across all specimens.Both compressive and flexural tests were carried out in a controlled laboratory environment with an ambient temperature of approximately 20°C and a relative humidity of around 50%.These conditions were maintained throughout the study to provide consistent testing parameters.As the number of freeze-thaw cycles increases, the compressive strength of the control group R0 decreases.In contrast, the other four YRS-mixed specimen groups show an initial increase in the compressive strength, reaching a peak at 50 cycles, with the R25 group exhibiting the highest strength.The initial increase in strength with YRS content is likely due to the fine particle size and specific surface area of YRS, which allows for improved water absorption and accelerated hydration during freeze-thaw cycles.Consequently, this early enhancement in compressive strength may reflect YRS's beneficial effects on ECC's microstructure.The experimental process is shown in Figure 8.After 300 cycles, the compressive strength of the YRS-mixed groups stabilizes and begins to decline.The compressive strengths of the five groups after 300 cycles, in a descending order, are R25, R50, R0, R75, and R100.The R100 group shows the highest rate of strength loss.The flexural strength follows a similar trend.Compared to specimens not subjected to freeze-thaw cycles, each group experiences reductions of 20.35, 16.47, 19.12, 23.91, and 24.63%, respectively.
These results suggest that a moderate content of 25% can optimize the compressive strength and durability under freeze-thaw cycles.The optimal compressive strength after freeze-thaw cycles is achieved with 25% YRS content.Enhancing the microstructure and matrix of ECC, the fine particle size and specific surface area of YRS improve water absorption and hydration, contributing to enhanced mechanical properties.The fine particle size and specific surface area of YRS improve water absorption and hydration, contributing to enhanced mechanical properties.In contrast, a high YRS content of 100% may have a negative impact on aggregate bonding and overall cohesiveness, leading to reduced performance.This is because excessive YRS may alter the particle distribution and disrupt the matrix integrity, resulting in a decline in mechanical properties.Notably, a 25% YRS ratio proves ideal for maintaining the compressive strength during freeze-thaw cycles.Detection of specimen damage occurs when the rate of compressive strength Experimental analysis of frost resistance and failure models in ECC-YRS  9 loss exceeds 25% [66].After 300 cycles, the R100 group shows the highest loss rate at 23.96%.However, YRS-ECC remains suitable for Henan's climate, proving its effectiveness in freeze-thaw conditions.

Bending toughness
In this study, the bending hardness evaluation indices vary significantly between specifications [75][76][77].Applying the same bending strength criterion, we assessed the bending toughness index of specimens following guidelines from the literature [68].According to the results in Figure 9, there are three distinct phases that the load-deflection curves of the five sets of test blocks go through when subjected to the freeze-thaw cycle: the elastic phase, the crack propagation phase, and the failure phase.The index of these stages varied among specimen groups, influenced by the freeze-thaw cycle duration and the YRS replacement rate in ECC.Notably, the YRS-mixed R25 group displayed superior bending bearing capacity, exceeding 6,000 N and 6 mm in load-deflection values, respectively, at zero freezethaw cycles.The load-deflection curve encloses the biggest graph area, suggesting that the R25 group has the highest level of toughness.
Comparatively, the R50, R75, and R100 groups displayed bending toughness comparable to R0, with a peak load around 5,000 N, deflection less than 6 mm, and moderately loose curve intervals.After 200 freeze-thaw cycles, a significant reduction in peak load and deflection was observed, highlighting the significant influence of extended freeze-thaw cycles on the load-bearing capacity of materials.The incorporation of YRS enhanced the particle gradation, pore filling, and cohesiveness.However, the complete 100% replacement of YRS caused a reduction in the aggregate bonding force and a decrease in the bending capacity of the specimens.
Figure 10 depicts the rapid decline of the specimen's equivalent bending strength, f eq u , with increasing freezethaw cycles.R25 maintained the best value at zero cycles, with ECC exhibiting the order of bending strengths during freeze-thaw cycles as R25 > R0 > R100 > R50 > R75.After 300 cycles, the R0 and R75 groups experienced 14.6 and 20.2% reductions in equivalent bending strength, while the R25 group had a smaller decline of 11.5%.These reductions represented 105.5 and 124.2% of the corresponding bending strength for the R0 and R75 groups, respectively.The findings highlight the significance of an adequate amount of YRS in preserving the specimen's bending toughness during the freeze-thaw cycle.Notably, the smooth surface of YRS, when increased, diminishes adhesion, resulting in reduced bending strength and disrupting balance in the specimen.It is essential to stress the importance of employing consistent assessment parameters for bending strength across specifications, and our study adopts detailed benchmarks to circumvent the bending strength criterion, relying instead on equivalent flexural strength for evaluation.

Microscopic test analysis
The microstructural characteristics of cementitious materials are closely associated with their macroscopic mechanical properties and durability [78].To explore the relationship between the large-scale mechanical features and the finescale microstructure of YRS-ECC, SEM and MIP tests were conducted.These analyses aimed to examine the pore structure, phase composition, and shape of specimens after exposure to multiple freeze-thaw cycles.In addition, the microscopic-level mechanical properties of YRS-ECC were examined following exposure to freeze-thaw cycles.

SEM test
In this study, we employed a high-resolution cold field-emission scanning electron microscope, for precise imaging and analysis.The microscope operated with an acceleration voltage ranging from 1 to 30 kV, with a magnification range of 100-500,000 and an image resolution of 0.8 nm.ECC specimens, having previously passed a four-point bending test, exhibited increased brittleness after 300 cycles of freezing and thawing.Subsequently, SEM tests were conducted on gold-sprayed samples measuring less than 1cm 3 .Figure 11 depicts the microstructure, highlighting the extensively hydrated YRS-ECC, nearly depleted of Ca (OH)₂ due to the consumption of fly ash from volcanic ash.In the freeze-thaw environment, the breakdown of the interface transition zone (Figure 11(a) and (c)) resulted in 1 μmsized hydration products and cracks.Water infiltration through microscopic cracks, coupled with continuous hydration of Ca (OH)₂ in the interface transition zone, contributed to crack filling.Figure 11(b) reveals the generation of flaky C-S-H gels and needle-like ettringite (AFt), indicating an enhanced cement hydration rate with an appropriately adjusted YRS quantity.The R25 group exhibited a superior bonding force between fibers and the matrix, closely integrated hydration products, an absence of visible pores, and a dense internal structure, supporting its maximum compressive and flexural strength.Conversely, the R100 group, with a higher YRS content, displayed unfilled YRS pores on the matrix surface, as shown in Figure 11(d), numerous 1 μm cracks, AFt production, and pores with reduced cohesion between YRS and fibers, as shown in Figure 11(e), contributing to lower macroscopic mechanical properties.

MIP test
The experiment utilized the AutoPore V 9620, a full-automatic mercury porosimeter from the American Mac Instruments Company.This equipment had a hole range spanning from 3.0 nm to 1,000 μm, a low-pressure range of 0-50 PSIA, a maximum pressure capability of 6000 PSIA,  and a resolution of 0.01 PSIA.After the freeze-thaw cycle, the test specimens were further broken, and samples weighing 1.5-2 g were selected for the MIP test.According to Figure 12, analysis of the MIP results revealed a proportional decrease in porosity and average pore size with an increase in the YRS replacement rate.The reduction reached its minimum at a 25% replacement rate.Specifically, in comparison to the control group R0, the R25 group demonstrated 31.81%porosity and an average pore size of 21.48 mm, representing a decrease of 1.3 and 6.7%, respectively.
In contrast, the R100 group showed a porosity of 37.38% and an average pore size of 31.57mm, indicating a 54.2% increase over R0 and a 53.3% increase over R25.The findings suggest that the addition of YRS in suitable quantities enhances the particle size distribution, decreases the pore size range, and increases the proportion of small pores in the material.The wide specific surface area of YRS enhances cement hydration reactions by filling larger pores.Macroscopic analysis revealed that R25 demonstrated the best mechanical properties after freeze-thaw, reaching its minimum porosity and average pore size at a 25% replacement rate.

Freeze-thaw damage model of YRS-ECC
Most mechanical damage is caused by internal loosening due to various factors, such as micro-cracks and microcells, which act as weak points initiating resistance to cold temperatures.This phenomenon progresses over time, leading to the degradation of the structure.For dealing with mechanical damage and dynamic modulus, the Weibull growth equation was employed.These equations facilitate quantitative analysis of the correlation between the duration of exposure and the cooling cycle durations in ECC.This analytical approach provides an insight into understanding the complex relationship between the aging of the ECC structure and the degree of deterioration that occurs during the cooling cycle.

Damage variables
The utilization of damage variables and parameters streamlines the characterization of the material degradation index, particularly in the context of mechanical damage in concrete.The presence of concrete defects, indicative of the propagation of cracked components throughout the material, results in the gradual enlargement of damaged areas under increasing compression, causing progressive damage.The nature of the damage field is directly proportional to the freeze-thaw cycling durations.The complex internal composition and structure of the material are reflected in the dynamic elastic modulus variation.The variable D was used as a precise quantitative indicator for tracking the progression of structural weakening within a specific matrix.This integrated approach provides information on material durability and serves as a valuable tool for assessing and solving structural integrity problems: where D = degree of damage, A D = total damage section area, A 0 = initial cross-sectional area, σ = effective stress, σ Figure Experimental analysis of frost resistance and failure models in ECC-YRS  13 true stress, E = elastic modulus, and Ē = dynamic elastic modulus.

Weibull probability distribution model based on freeze-thaw cycles
For the investigation into the freeze-thaw damage of YRS-ECC with varying replacement rates, a Weibull distribution model was employed [79].The inhomogeneity and heterogeneous nature of the concrete caused the damage process due to numerous pores, micro-cracks, and defects.To analyze the damage following freeze-thaw cycles in YRS-ECC with varying substitution rates, a two-parameter Weibull distribution model was utilized for assessment.The probability of material damage and failure is calculated as follows: According to Weibull probability, f (N) is assumed for N freeze-thaw cycles: where η = scale factor and β = Weber shape factor.
Integrating Equation ( 5) in the corresponding function, we obtain: The failure probability is given by Equation (7) as: The trend in P f (N) demonstrates a rising pattern, indicating a direct relationship between the probability of failure and the duration of freeze-thaw cycles.Preceding the cooling cycle (N = 0), P f (N) attains a value of 1.As the duration of the cooling cycle nears the threshold (N) that the ECC can withstand, the observed pattern fades away.At this point, P f (N) is equal to 1, indicating complete material damage with a corresponding damage level of D(N) = 1, with P f (N) and D(N) being equivalent, the probability of failure can be reformulated accordingly.

( )
For mathematical calculation, logarithm was applied on both sides of Equation ( 8) to obtain As per Equation ( 10) and the empirical findings, employing X and Y regression enables the determination of parameters for the YRS ECC model with different replacement rates.The resultant calculations are depicted in Figure 13, and Table 8 provides a comprehensive overview of fitting parameters.
In Figure 14, results indicate that the correlation coefficients for R0, R25, R50, R75, and R100 exceed 0.94, and when ECC was replaced with YRS, we obtain a precise correlation of 0.98.
The Weibull probability model shows a close relationship between ECC damage, different YRS replacement rates,   and durations of freezing cycles, demonstrating commendable results in data fitting.The correlation is zero during a freeze-thaw cycle.Equations ( 11) and ( 12) serve as a benchmark for interpreting the evolution of the effect of freezethaw on YRS-ECC.Based on the equation describing the freeze-thaw damage evolution described above, the damage size of ECC can be calculated and also compared with different replacement rates of YRS.The calculated damage level can then be compared with experimental results.Figure 14 illustrates the outcomes of this comparative analysis.
1.067 (15) 6 Conclusions This research aimed to substitute local YRS for quartz sand in ECC production to reduce costs and address flood risks in the lower reaches of the Yellow River, China, promoting sustainable development.The study extensively investigated properties like modulus loss, compressive strength, flexural strength, and flexural stiffness after 300 cooling cycles.Through a systematic analysis of mechanical properties, an equation describing damage evolution was established, recommending the implementation of YRS-ECC in Henan Province, China.The key findings are detailed as follows.
• In general, YRS particle sizes exhibit a smaller normal distribution compared to quartz sand.With a 5.77 times greater specific surface area, YRS significantly affects the particle size distribution of ECC.• After the freeze cycling process, the ECC performance is influenced by the degree of YRS replacement.Throughout 300 freeze-thaw cycles, the sample sizes consistently expanded.The R0 group showed a notable growth rate of 1.1%, while R25 displayed the highest retention of 97.5% of its initial value, indicating superior durability.
• The flexural strength across the five specimen groups exhibited a gradual decline.Notably, R25 consistently demonstrated the highest strength, retaining 79.42% of its original value, while YRS-ECC exhibited the lowest strength at 75% replacement.• The initial reduction in bending toughness was observed consistently among all five specimen groups.It is noteworthy that the R25 group demonstrated the highest peak load, with a minimal decrease of 11.5% in equivalent bending strength, reaching a level of 104.4% compared to the strength exhibited by the R0 group.• Higher moisture levels cause approximately 1 μm cracks in all specimens.The R25 group shows increased internal structure thickness, while the R100 group, with a high YRS content, exhibits a reduced bonding interface due to its smooth surface.contribution to the literature review.MU: Writingreview and contribution to the Discussion section.YC: Methodology, supervision, formal analysis, investigation, resources, writing review and editing, conceptualization and study design, and offered valuable perspectives on the implications of the findings.

Figure 3 :
Figure 3: YRS and quartz sand particle size distributions.(a) Cumulative distribution and (b) differential distribution.

Figure 4 :
Figure 4: Changes in mass for YRS-ECC after repeated freeze-thaw cycles.(a) Change in the mass ratio and (b) total mass loss.Figure 5: YRS-ECC relative dynamic elastic modulus.(a) Relative dynamic elastic modulus and (b) relative dynamic elastic modulus absolute value.

Figure 5 :
Figure 4: Changes in mass for YRS-ECC after repeated freeze-thaw cycles.(a) Change in the mass ratio and (b) total mass loss.Figure 5: YRS-ECC relative dynamic elastic modulus.(a) Relative dynamic elastic modulus and (b) relative dynamic elastic modulus absolute value.

12 :
MIP properties of YRS-ECC (a) pore size distribution and (b) porosity level.

Table 1 :
Primary technical parameters of cement

Table 2 :
Key technical parameters of PVA fibers

Table 3 :
Primary constituents of fly ash Experimental analysis of frost resistance and failure models in ECC-YRS  3 ECC properties and behavior.After the fitting process, prism test blocks measuring (100 × 100 × 400 mm) were used to assess the mass loss and relative dynamic elastic modulus.Simultaneously, a prism test block of dimensions(40 × 40 ×

Table 5 :
Key technical parameters of quartz sand

Table 6 :
ECC mix ratio design for incorporating YRS (kg/m 3 )

Table 8 :
Parameters of the Weibull probability model for YRS-ECC • After freeze-thaw, YRS inclusion leads to a 25% decrease in stiffness and mean cell volume.R25 porosity is 30.80%, with an average pore size of 20.47 mm, showing 1.3 and 6.7% decreases compared to R0. RS significantly impacts structural properties, suggesting controlled integration for optimal ECC operations.•Theoutcomes indicate that the Weibull probability distribution model accurately represents the relationship between the degree of damage and freeze-thaw cycles.The calculated values closely align with the measured values, showing high accuracy.