Concrete compressive strength prediction method based on combined action of fatigue load and sulfate
By dividing the concrete section into deteriorated, reinforced, and intact zones, and using a time-varying diffusion model in the form of a power function and fatigue damage parameter correction, a compressive strength prediction model suitable for the combined action of fatigue load and sulfate was established. This solved the prediction error problem of existing models in composite environments and achieved highly accurate durability design.
Patent Information
- Application Number
- CN202511653369.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-12
- Publication Date
- 2026-02-24
AI Technical Summary
Existing concrete compressive strength prediction models cannot accurately reflect the synergistic effect of fatigue load and sulfate attack. In particular, they cannot quantify the impact of fatigue damage on sulfate transport in composite environments, resulting in large prediction errors and failing to meet durability design requirements.
The concrete section is divided into a deteriorated zone, a reinforced zone, and a intact zone. The compressive strength of each zone is clearly defined. A compressive strength prediction model suitable for the combined action of fatigue load and sulfate is established by using a time-varying diffusion model in the form of a power function and fatigue damage parameter correction.
It accurately reflects the performance gradient characteristics inside concrete, improves prediction accuracy and engineering applicability, with a maximum relative error within 8.2%, and provides a reliable durability design tool.
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Figure SMS_63
Abstract
Description
Technical Field
[0001] This invention relates to the field of concrete compressive strength analysis technology, specifically to a method for predicting concrete compressive strength based on the combined effects of fatigue load and sulfate. Background Technology
[0002] During their service life, concrete structures often face the combined effects of environmental erosion and mechanical loads. Particularly in saline soil areas, coastal regions, and areas with sulfate-containing groundwater, sulfate erosion is one of the main environmental factors leading to concrete performance degradation and shortened structural lifespan. Sulfate ions penetrate the concrete interior, reacting chemically with cementitious products to generate expansive products. Initially, this process may slightly increase material density by filling pores, but later it triggers internal stress, leading to cracking, spalling, and strength loss. On the other hand, concrete structures such as bridges, roads, and offshore platforms are subjected to long-term cyclic loads from vehicles, wind, and waves—i.e., fatigue loads. While fatigue loads do not immediately cause structural failure, they accumulate damage within the concrete, forming a microcrack network that significantly alters its performance.
[0003] Currently, research on the performance degradation of concrete under single-factor influence is quite in-depth, and several predictive models exist. For example, regarding sulfate attack, some studies have attempted to describe the ion transport process based on Fick's diffusion law. However, this law assumes that the diffusion process is driven solely by the concentration gradient and that the material medium is homogeneous and stable, which is not entirely applicable to sulfate ions undergoing complex chemical reactions in concrete. The chemical reactions during sulfate attack continuously alter the pore structure of concrete, causing its diffusion properties to change over time. This nonlinear behavior cannot be accurately described by the classical Fick diffusion law. Furthermore, existing sulfate attack models mostly focus on the chemical degradation itself, lacking a physical-mechanical model that can accurately quantify the evolution of macroscopic mechanical properties such as compressive strength, given the spatial non-homogeneity of the coexistence of reinforcing and deteriorating zones within the concrete during the attack process.
[0004] An even more severe challenge arises from multi-field coupling. Fatigue loading and sulfate attack do not act independently but rather produce a significant synergistic effect. Microcracks generated by fatigue loading provide a rapid pathway for sulfate ion intrusion, accelerating the attack process; conversely, the material softening and microstructural damage caused by sulfate attack reduce the fatigue resistance of concrete. This "1+1>2" superposition effect renders prediction models established under single-factor conditions completely ineffective in actual combined environments. There is an urgent need in this field for a compressive strength prediction model that can couple the damage caused by fatigue loading with the time-varying process of sulfate attack. However, due to the complexity of the interaction mechanism, how to quantify the impact of fatigue damage on key parameters of sulfate transport, and on this basis, construct a unified and accurate compressive strength prediction model that can reflect both the spatial non-uniformity of attack and adapt to the fatigue damage state, has become a key technical bottleneck restricting the durability design and life prediction of concrete structures. Summary of the Invention
[0005] The purpose of this invention is to provide a method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate. By dividing the concrete section into a deteriorated zone, a reinforced zone, and a intact zone, and clearly defining the compressive strength of each zone, this method can accurately reflect the performance gradient characteristics formed inside the concrete during sulfate attack. It overcomes the shortcomings of existing models in describing the non-uniformity of attack, and provides a structural basis for establishing a compressive strength prediction model with clear physical meaning.
[0006] To achieve the above objectives, the present invention proposes the following technical solution:
[0007] A method for predicting the compressive strength of concrete under the combined effects of fatigue load and sulfate includes the following steps:
[0008] S1. Divide the cross section of the concrete used to make the cube component into a deteriorated zone, a reinforced zone, and a intact zone from the outside to the inside.
[0009] Definition: The third compressive strength of the deteriorated zone is zero; the second compressive strength of the reinforced zone is related to the initial compressive strength of the concrete through a reinforcement factor greater than 1; the first compressive strength of the intact zone is equal to the initial compressive strength of the concrete.
[0010] S2. Based on the sulfate corrosion process, determine the cross-sectional areas of the deteriorated area, the reinforced area, and the intact area, and calculate the third ultimate bearing capacity of the deteriorated area, the second ultimate bearing capacity of the reinforced area, and the first ultimate bearing capacity of the intact area in combination with the third compressive strength, the second compressive strength, and the first compressive strength, respectively.
[0011] The overall ultimate bearing capacity of the concrete is obtained by summing the first ultimate bearing capacity, the second ultimate bearing capacity, and the third ultimate bearing capacity.
[0012] S3. Based on the overall ultimate bearing capacity of the concrete and combined with the overall cross-sectional area of the concrete, construct a first compressive strength prediction model for the concrete subjected only to sulfate erosion.
[0013] The parameters of the first compressive strength prediction model include at least the depth of the reinforcement zone;
[0014] S4. Construct a time-varying diffusion depth model of sulfate ions in the concrete as a function of time: ;
[0015] In the above formula, d represents the diffusion depth of sulfate ions, which is equivalent to the depth of the enhancement region; k p The first parameter is α, which reflects the combined influence of the initial permeability of concrete and the external corrosive environment; the second parameter is t, which reflects the kinetic influence of chemical reactions on diffusion behavior during sulfate attack; and t represents the diffusion time of the sulfate ions within the concrete.
[0016] S5. Obtain at least one fatigue damage parameter of the concrete after it has undergone fatigue loading, and correct the first parameter and the second parameter of the time-varying diffusion depth model based on the fatigue damage parameter to reflect the accelerating effect of fatigue loading on the sulfate erosion rate.
[0017] S6. Based on the modified time-varying diffusion depth model, the first compressive strength prediction model is coupled to obtain the second compressive strength prediction model of the concrete under the combined action of fatigue load and sulfate attack.
[0018] As a preferred embodiment of the present invention, the relationship between the second compressive strength of the reinforced zone and the initial compressive strength of the concrete is as follows: ;
[0019] in, The second compressive strength of the reinforced region; The enhancement coefficient is greater than 1; The initial compressive strength is given.
[0020] As a preferred embodiment of the present invention, step S2, which involves calculating the third ultimate bearing capacity of the deteriorated zone, the second ultimate bearing capacity of the reinforced zone, and the first ultimate bearing capacity of the intact zone based on the sulfate corrosion process, specifically includes the following steps:
[0021] S201. Based on the sulfate erosion process, calculate the cross-sectional areas of the deteriorated zone, the enhanced zone, and the intact zone, respectively;
[0022] S202. According to Newton's second law:
[0023] The third ultimate bearing capacity is calculated based on the cross-sectional area of the deteriorated zone and the third compressive strength.
[0024] The second ultimate bearing capacity is calculated based on the cross-sectional area of the reinforced region and the second compressive strength.
[0025] The first ultimate bearing capacity is calculated based on the cross-sectional area of the intact region and the first compressive strength.
[0026] Since the third compressive strength is zero, the third ultimate bearing capacity is zero and is not included in the calculation of the overall ultimate bearing capacity of the concrete.
[0027] In a preferred embodiment of the present invention, the cross-sectional area of the intact region is equal to the cross-sectional area of the uncorroded region inside the concrete, which is equal to... ;
[0028] The cross-sectional area of the enhanced region is the cross-sectional area of the annular region between the boundary of the deteriorated region and the boundary of the intact region, equal to... ;
[0029] in, The cross-sectional area of the enhanced region; The cross-sectional area of the intact region; Let be the side length of the concrete cubic member; The depth of the deteriorated zone; To enhance the depth of the region.
[0030] As a preferred embodiment of the present invention, the process of concrete being subjected to sulfate erosion includes two stages:
[0031] First stage: The depth of the deteriorated area is zero, and the depth of the enhanced area is less than a preset width value;
[0032] Second stage: The depth of the deteriorated area is equal to the depth of the enhanced area minus the preset width value;
[0033] Wherein, the preset width value is equal to the width of the enhancement area.
[0034] As a preferred embodiment of the present invention, the fatigue damage parameters include macroscopic mechanical property degradation parameters and / or microstructural damage parameters.
[0035] As a preferred technical solution of the present invention, the macroscopic mechanical property deterioration parameter is the ratio of the residual strength of concrete after fatigue loading.
[0036] The microstructure damage parameters are fatigue damage degrees measured based on electrochemical impedance spectroscopy.
[0037] As can be seen from the above technical solutions, the technical solution of the present invention provides a method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate, which has the following beneficial effects compared with the prior art:
[0038] By dividing the concrete section into deteriorated, reinforced, and intact zones, and clearly defining the compressive strength of each zone, the performance gradient characteristics formed inside the concrete during sulfate attack can be accurately reflected. This overcomes the shortcomings of existing models in describing the non-uniformity of attack, and provides a structural basis for establishing a compressive strength prediction model with clear physical meaning.
[0039] The time-varying diffusion model in the form of a power function breaks through the linear assumption of the classical Fick diffusion law based solely on the concentration gradient. It fully considers the dynamic influence of the chemical reactor pore structure in sulfate erosion, more realistically describes the nonlinear diffusion behavior of sulfate ions in concrete, and improves the accuracy of erosion process prediction.
[0040] By introducing fatigue damage parameters such as macroscopic residual strength ratio and microstructural damage degree, the key parameters in the diffusion model are modified, and the accelerating effect of microcrack network caused by fatigue load on sulfate ion transport is quantified. This accurately captures the strength evolution law under the "fatigue-erosion" coupling effect and solves the technical problem of the complete failure of the single factor model in the actual composite environment.
[0041] By coupling the modified diffusion depth model with the partitioned strength model, a compressive strength model applicable to the combined effects of fatigue load and sulfate was established. This model is not only structurally sound and has clearly defined parameters, but it has also been experimentally verified, showing good agreement between predicted and experimental values, with a maximum relative error within 8.2%. It possesses high accuracy and engineering applicability, providing a reliable tool for the durability design and life prediction of concrete structures in complex environments.
[0042] It should be understood that all combinations of the foregoing concepts and the additional concepts described in more detail below can be considered part of the inventive subject matter of this disclosure, provided that such concepts do not contradict each other. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below in conjunction with the embodiments of this invention. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the described embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art to which this invention pertains.
[0044] The terms "first," "second," and similar words used in the specification and claims of this patent application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, unless the context clearly indicates otherwise, the singular forms of "an," "a," or "the," etc., do not indicate a quantity limitation, but rather indicate the presence of at least one. Terms such as "comprising" or "including" mean that the element or object preceding "comprising" encompasses the features, integrals, steps, operations, elements, and / or components listed following "comprising" or "including," and do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof.
[0045] A predictive model for the compressive strength of concrete subjected to sulfate attack without fatigue loading is constructed.
[0046] This invention is based on the sulfate attack process of concrete. Using cubic concrete specimens as the research object, the concrete cross-section is divided into three regions from the outside in: the third region, the second region, and the first region. This division method is based on the physicochemical mechanism of sulfate attack, specifically the diffusion and reaction of sulfate ions from the concrete surface, leading to the formation of performance gradient regions within the concrete. The third region is the deterioration zone, located on the outermost layer of the concrete after sulfate attack. The compressive strength of the concrete in this region is denoted as the third compressive strength. The first zone is the intact zone, located in the innermost layer of the concrete. It is a region where sulfate ions have not reached and the concrete has not been subjected to sulfate attack. The compressive strength of the concrete in this zone is recorded as the first compressive strength. The second zone is the reinforcement zone, located between the deteriorated zone and the intact zone. It is a region where the internal compressive strength of the concrete is enhanced. The compressive strength of the concrete in this zone is denoted as the second compressive strength. In this embodiment of the invention, the depth of the reinforced zone can be considered as the diffusion depth of sulfate ions in concrete. This zoning accurately reflects the non-uniformity of concrete during sulfate erosion, providing a structural basis for establishing a predictive model.
[0047] To facilitate the establishment of a predictive model for the compressive strength of concrete subjected to sulfate attack, the embodiments of this invention make the following assumptions:
[0048] First, the sulfate ion content of the concrete itself is negligible; the deterioration and reinforcement zones are entirely formed by the reaction of sulfate ions invading from the outside with the concrete. This assumption simplifies the model, focuses on the impact of external erosion, and is consistent with the actual situation of concrete exposed to sulfate environments in engineering projects.
[0049] Second, during the diffusion of sulfate ions from the concrete surface into its interior, the concrete remains isotropic, and the eroded areas are also isotropic. This assumption ensures the geometric and mechanical symmetry of the model, facilitating the calculation of area and strength using simple geometric relationships.
[0050] Third, in each region of the concrete, the compressive strength of the intact region can be considered as the initial compressive strength of the concrete before it was corroded, i.e., the first compressive strength. The compressive strength is equal to the initial compressive strength; compared to the compressive strength of the intact zone, the deteriorated zone can hardly withstand the load, and its compressive strength is approximately zero, i.e., the third compressive strength. Approximately zero; In the early stages of sulfate attack, the invading sulfate ions react chemically with cementitious products such as calcium hydroxide and other active components to generate expansive products such as ettringite and gypsum. These products precipitate and grow in the pores within the concrete, thus filling and densifying the microstructure of that area. This densification process macroscopically manifests as a phased increase in the compressive strength of that area. Therefore, the secondary compressive strength of the reinforced zone is usually... It must be higher than the first compressive strength of the intact area. This enhancement effect can be achieved through an enhancement coefficient greater than 1. Quantification is performed to ensure that the compressive strength of the reinforced zone and the compressive strength of the intact zone satisfy the following relationship: This is denoted as Formula 1. Since the first compressive strength of the intact zone is equal to the initial compressive strength of the concrete, Formula 1 can also be used to characterize the relationship between the second compressive strength of the reinforced zone and the initial compressive strength of the concrete.
[0051] The enhancement factor of the compressive strength of the reinforced zone The value of depends on the specific mix proportions of the concrete and its corrosive environment. Under typical sulfate conditions, such as the corrosive effect of 5% Na₂SO₄ solution, the increase in compressive strength due to this densification effect is relatively stable and is generally considered to be approximately 1.1. Therefore, in this embodiment of the invention, a reinforcement coefficient is preferred. The value is 1.1.
[0052] Based on the above assumptions and according to Newton's second law, the calculation formula for the compressive ultimate bearing capacity of concrete subjected to sulfate attack in this embodiment of the invention is as follows: This is denoted as Formula 2.
[0053] Formula 2 is based on the well-known law of mechanics: the overall load equals the sum of the products of the stress and area of each region, and is applicable to the calculation of the bearing capacity of non-uniform materials under compression. Here, time t represents the duration of sulfate attack. Since the diffusion and chemical reaction of sulfate ions are time-dependent processes, the cross-sectional areas of the reinforced and intact zones change with time. Therefore, the ultimate compressive bearing capacity of concrete... It is a function of time, reflecting the dynamic impact of the erosion process on concrete performance.
[0054] In formula 2, It is the ultimate compressive load of concrete against sulfate attack. It is the cross-sectional area of the reinforced zone of the concrete subjected to sulfate attack; It is the cross-sectional area of the intact section of concrete subjected to sulfate erosion.
[0055] Based on Newton's principles of mechanics, a predictive model for the first compressive strength of concrete subjected only to sulfate attack is constructed. The specific calculation model is as follows:
[0056] This is denoted as Formula 3.
[0057] In formula 3, It is the first compressive strength of concrete when subjected only to sulfate attack; This refers to the overall cross-sectional area of the concrete. In this embodiment of the invention, without considering or excluding the possibility of concrete edge / corner spalling, the following is set... =10000mm 2 .
[0058] Substituting Formula 1 into Formula 3, we obtain the following Formula 4:
[0059] .
[0060] In this embodiment of the invention, the depth of the deteriorated zone of the concrete is set as follows: The depth of the enhancement region is The side length of the concrete cube component is Since sulfate attack spreads uniformly inward from the concrete surface, the intact zone is an internal cube with a side length equal to the original side length of the concrete minus twice the depth of the reinforced zone (because the attack occurs from two opposite faces); the reinforced zone is a ring-shaped area between the deteriorated zone and the intact zone. Therefore, the areas of the intact zone and the reinforced zone after sulfate attack on the concrete can be calculated using the following formulas 5 and 6, respectively.
[0061] Formula 5: The formula indicates that the area of the intact region is the cross-sectional area of the inner cube, and its side length is reduced by twice the depth of the reinforcement region.
[0062] Formula 6: This formula indicates that the area of the reinforced region is the difference between the area of the overall cross-sectional area minus the area of the deteriorated region and the area of the intact region, that is, the reinforced region corresponds to... and The annular region between them.
[0063] Substituting formulas 5 and 6 into formula 4, we obtain formula 7 as follows:
[0064] .
[0065] The relationship between the depth of the deteriorated zone and the reinforced zone in concrete changes with the erosion process. In the early stages of erosion, before cracking occurs, the depth of the deteriorated zone is... The depth is 0; in the later stages of erosion, the concrete cracks and deteriorates, at which point the depth of the deteriorated zone increases. Preferably through the depth of the enhancement region With a preset width value The difference is used to characterize this, as shown in Formula 8 below: .
[0066] Under experimental observation, cracks appeared at the leading edge of the reinforced zone in the later stage of erosion. The depth of the deteriorated zone was determined by subtracting a constant width value from the depth of the reinforced zone. Combined with the structural analysis of the concrete cubic component, it can be seen that this constant width value is equal to the width of the reinforced zone, which is the preset width value. The predetermined width value The depth of the reinforced zone can be determined based on the point at which the compressive strength of the concrete begins to decrease. Sure.
[0067] Therefore, based on Formula 8, the compressive strength of concrete subjected only to sulfate attack can be calculated in two parts, namely, the initial stage of attack (…). ) and later stages of erosion ( ).
[0068] In the early stages of erosion, the area of the enhanced zone can be obtained according to Formula 6. The calculation formula is as follows: This is denoted as Formula 9.
[0069] Substituting Formula 9 and Formula 5 into Formula 4 yields the formula for calculating the compressive strength of concrete under sulfate attack in the early stages of erosion. , This is denoted as Formula 10.
[0070] In the later stages of erosion, when the compressive strength of the concrete begins to decline, cracks appear in the concrete, at which point the reinforced zone area... It can be calculated according to the following formula 11: .
[0071] Substituting Formula 11 and Formula 5 into Formula 4 yields the formula for calculating the compressive strength of concrete subjected to sulfate attack in the later stages of erosion. , , denoted as Formula 12.
[0072] Combining formulas 10 and 12, we obtain a predictive model for the overall process of sulfate ion attack on concrete, denoted as formula 13, as follows:
[0073] .
[0074] As can be seen from Formula 13, the compressive strength of concrete varies with the process of sulfate erosion and is a model that changes over time.
[0075] A second compressive strength prediction model for concrete under the combined action of fatigue load and sulfate was constructed.
[0076] After constructing a preliminary compressive strength prediction model for concrete under sulfate attack alone, the key aspect of this invention lies in extending this model to a scenario of combined fatigue load and sulfate attack that better reflects actual engineering conditions. The core of this extension is that fatigue load damages the microstructure of concrete, forming a network of microcracks, which significantly alters the diffusion behavior of sulfate ions within the concrete. Therefore, the key parameters characterizing the depth of ion diffusion in the model must be modified to accurately reflect the accelerating effect of fatigue damage on subsequent sulfate attack.
[0077] First, a model relating sulfate ion diffusion depth to time needs to be established. In Fick's law of diffusion, the diffusion depth *d* of ions in concrete is proportional to the square root of the diffusion time *t*, i.e. Where d is the diffusion depth of ions in concrete; k is a proportional parameter related to concrete materials. This law is well applicable to potassium ions, sodium ions and chloride ions, but because sulfate ions react chemically with concrete and change the pore structure inside the concrete, it is not applicable to the calculation of the diffusion depth of sulfate ions in concrete.
[0078] Given the limitations of the classical Fick diffusion law, this embodiment of the invention considers the chemical-physical coupling process of sulfate corrosion and employs a power function form to more flexibly describe the diffusion kinetics of sulfate ions. Specifically, the following formula 14 is used to describe the relationship between the diffusion depth and diffusion time of sulfate ions, i.e. .
[0079] In Formula 14, d is the diffusion depth of sulfate ions; k p Both α and t are proportional parameters related to the concrete mix proportion and the external environment, denoted as the first parameter and the second parameter. The first parameter mainly reflects the proportional coefficient of the initial permeability of the concrete and the corrosiveness of the external sulfate environment. Its value is affected by factors such as the concrete mix proportion, pore structure and concentration of corrosive solution. The second parameter characterizes the kinetic index of the influence of changes in the microstructure of concrete caused by chemical reactions on the ion diffusion behavior during the erosion process, reflecting the non-Fickian diffusion characteristics. t is the diffusion time of sulfate ions in the concrete.
[0080] Table 1 shows the residual strength ratio D of concrete after fatigue. F And fatigue damage degree D obtained based on electrochemical impedance spectroscopy (EIS). R Among them, the residual strength ratio macroscopically characterizes the loss of mechanical properties caused by fatigue loading, while fatigue damage based on EIS quantifies the degree of damage to the internal structure of concrete from the perspective of microscopic electrical properties. The two together define the fatigue damage state of concrete from different dimensions.
[0081] Table 1. Parameter values under different concrete sulfate attack conditions.
[0082]
[0083] The key finding of this invention is that there is a strong correlation between the damage caused by fatigue loading and the diffusion parameters of sulfate attack. Based on the experimental data in Table 1, this invention, through data fitting and mechanism analysis, determines the first parameter k of the fatigued concrete. pf The first parameter k of unfatigue-treated concrete p0 The association is represented according to the following formula 15, i.e.
[0084] Formula 15 in this embodiment of the invention has a clear physical meaning: the greater the fatigue damage, the more developed the microcrack network inside the concrete, providing a faster transport channel for sulfate ions, thus leading to a significant increase in the proportional parameter. Formula 15 quantitatively characterizes the effect of fatigue damage on enhancing the permeability of concrete.
[0085] Substituting Equation 15 into Equation 14, we obtain the diffusion depth d of the unfatigue-treated concrete. s0 Formula, i.e. This is denoted as Formula 16.
[0086] Similarly, fatigue damage also affects the kinetics of the erosion process. The second parameter α of fatigue-treated concrete... fThe second parameter α0 of the unfatigue-treated concrete is characterized by correlation with the following formula 17: .
[0087] Formula 17 is based on the following mechanism: the mechanical property degradation caused by fatigue loading, such as a decrease in residual strength ratio, makes concrete more susceptible to damage under the expansion stress of sulfate erosion products. This, to some extent, alters the kinetics of the erosion process, manifested as a decrease in the time exponent. Formula 17 correlates the loss of macroscopic mechanical properties with erosion kinetic parameters.
[0088] Substituting Formula 17 into Formula 14, we obtain the formula for the diffusion depth of fatigued concrete, i.e. This is denoted as Formula 18.
[0089] In Formula 18, d sf It is the diffusion depth of sulfate ions in fatigued concrete; D F It is the ratio of the residual strength of concrete after fatigue; D R This is the fatigue damage degree of concrete obtained based on electrochemical impedance spectroscopy. Formula 18 accurately corrects the time-varying diffusion depth of sulfate ions by introducing two measurable fatigue damage indices, thereby quantifying the historical impact of fatigue load into subsequent sulfate attack prediction.
[0090] Finally, by coupling the modified diffusion depth model with the first compressive strength model, a second compressive strength model that can be comprehensively predicted can be obtained. Specifically, substituting Equation 18 into Equation 13 yields the compressive strength prediction model for concrete under the combined effects of fatigue load and sulfate, denoted as Equation 19, as shown below:
[0091] .
[0092] Formula 19 fully describes the evolution of the compressive strength of concrete after undergoing specific fatigue damage and being placed in a sulfate environment, as a function of erosion time. It comprehensively reflects the accelerated erosion caused by fatigue damage, as well as the strength enhancement and deterioration brought about by erosion itself.
[0093] In particular, for concrete that has not undergone fatigue testing, no fatigue damage occurs; therefore, D R =0, D F =1, and its compressive strength under sulfate attack is predicted by the following formula, denoted as Formula 20:
[0094] .
[0095] The validity of Formula 20 verifies the consistency of this model: when fatigue damage is zero, the comprehensive prediction model can seamlessly degenerate into a basic model that only considers sulfate corrosion, proving the rationality and universality of the model architecture.
[0096] For the preparation of the concrete cube component according to the embodiments of the present invention, the preferred composition is as follows:
[0097] By weight: 1209 parts coarse aggregate, 651 parts river sand, 360 parts silicate cement, and 180 parts water.
[0098] The preferred coarse aggregate is natural granite with a particle size of 5mm-20mm. The preferred river sand is medium sand with a particle size less than 4.75mm and a fineness modulus of 2.4. The silicate cement strength grade is 42.5.
[0099] The concrete preparation method of this invention is as follows:
[0100] Weigh each component according to the above weight proportions; add coarse aggregate and river sand to a mixing container such as a single-shaft forced concrete mixer and mix evenly for 25-30 seconds at a mixing speed of 90-140 rpm / min; add 45%-55% water to the mixing container and mix evenly for 25-30 seconds; add slag to the mixing container and mix evenly for 30-40 seconds; add the remaining water to the mixing container and mix evenly for 2-3 minutes; fill the mixture into 100mm×100mm×100mm and 100mm×100mm×400mm molds, compact in three layers during the pouring process, then place the poured molds on a vibrating table to compact for 5-10 seconds, let them stand indoors for 24 hours, then demold, and then move them into a standard curing room with a temperature of 20±2℃ and a relative humidity of 95%±3% for 28 days.
[0101] Conduct normal road vehicle load simulation tests on concrete.
[0102] To simulate the fatigue load of a typical vehicle on a road, a four-point loading method with a sinusoidal wave was used, and the stress level was set to 0.5. The stress ratio was set to 0.1. To reflect the actual fatigue of the road surface, the number of fatigue loading cycles was set to 100,000. The frequency of the loading cycles was 10 Hz.
[0103] Sulfate wet-dry cycle tests were conducted on the concrete after fatigue loading, and compressive strength tests were performed.
[0104] The concrete was soaked in a 5% Na₂SO₄ solution for 15 hours, followed by 1 hour of air drying, then baking at 78-80℃ for 6 hours, and finally air cooling and refrigeration at 25-30℃ for 1 hour. Each wet-dry cycle lasted 24 hours. The number of wet-dry cycles was 150. Mechanical property tests, including compressive strength, were performed on the concrete after a portion of the sulfate wet-dry cycles.
[0105] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.
Claims
1. A method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate, characterized in that, Includes the following steps: S1. Divide the cross section of the concrete used to make the cube component into a deteriorated zone, a reinforced zone, and a intact zone from the outside to the inside. Definition: The third compressive strength of the deteriorated zone is zero; the second compressive strength of the reinforced zone is related to the initial compressive strength of the concrete through a reinforcement factor greater than 1; the first compressive strength of the intact zone is equal to the initial compressive strength of the concrete. S2. Based on the sulfate corrosion process, determine the cross-sectional areas of the deteriorated area, the reinforced area, and the intact area, and calculate the third ultimate bearing capacity of the deteriorated area, the second ultimate bearing capacity of the reinforced area, and the first ultimate bearing capacity of the intact area in combination with the third compressive strength, the second compressive strength, and the first compressive strength, respectively. The overall ultimate bearing capacity of the concrete is obtained by summing the first ultimate bearing capacity, the second ultimate bearing capacity, and the third ultimate bearing capacity. S3. Based on the overall ultimate bearing capacity of the concrete and combined with the overall cross-sectional area of the concrete, construct a first compressive strength prediction model for the concrete subjected only to sulfate erosion. The parameters of the first compressive strength prediction model include at least the depth of the reinforcement zone; S4. Construct a time-varying diffusion depth model of sulfate ions in the concrete as a function of time: ; In the above formula, d represents the diffusion depth of sulfate ions, which is equivalent to the depth of the enhancement region; k p The first parameter is α, which reflects the combined influence of the initial permeability of concrete and the external corrosive environment; the second parameter is t, which reflects the kinetic influence of chemical reactions on diffusion behavior during sulfate attack; and t represents the diffusion time of the sulfate ions within the concrete. S5. Obtain at least one fatigue damage parameter of the concrete after it has undergone fatigue loading, and correct the first parameter and the second parameter of the time-varying diffusion depth model based on the fatigue damage parameter to reflect the accelerating effect of fatigue loading on the sulfate erosion rate. S6. Based on the modified time-varying diffusion depth model, the first compressive strength prediction model is coupled to obtain the second compressive strength prediction model of the concrete under the combined action of fatigue load and sulfate attack.
2. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 1, characterized in that, The relationship between the second compressive strength of the reinforced zone and the initial compressive strength of the concrete is as follows: ; in, The second compressive strength of the reinforced region; The enhancement coefficient is greater than 1; The initial compressive strength is given.
3. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 2, characterized in that, In step S2, the calculation of the third ultimate bearing capacity of the deteriorated zone, the second ultimate bearing capacity of the reinforced zone, and the first ultimate bearing capacity of the intact zone based on the sulfate corrosion process specifically includes the following steps: S201. Based on the sulfate erosion process, calculate the cross-sectional areas of the deteriorated zone, the enhanced zone, and the intact zone, respectively; S202. According to Newton's second law: The third ultimate bearing capacity is calculated based on the cross-sectional area of the deteriorated zone and the third compressive strength. The second ultimate bearing capacity is calculated based on the cross-sectional area of the reinforced region and the second compressive strength. The first ultimate bearing capacity is calculated based on the cross-sectional area of the intact region and the first compressive strength. Since the third compressive strength is zero, the third ultimate bearing capacity is zero and is not included in the calculation of the overall ultimate bearing capacity of the concrete.
4. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 3, characterized in that, The cross-sectional area of the intact zone is equal to the cross-sectional area of the uncorroded area inside the concrete. ; The cross-sectional area of the enhanced region is the cross-sectional area of the annular region between the boundary of the deteriorated region and the boundary of the intact region, equal to... ; in, The cross-sectional area of the enhanced region; The cross-sectional area of the intact region; Let be the side length of the concrete cubic member; The depth of the deteriorated zone; To enhance the depth of the region.
5. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 4, characterized in that, The concrete is subjected to sulfate erosion in two stages: First stage: The depth of the deteriorated area is zero, and the depth of the enhanced area is less than a preset width value; Second stage: The depth of the deteriorated area is equal to the depth of the enhanced area minus the preset width value; Wherein, the preset width value is equal to the width of the enhancement area.
6. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 1, characterized in that, The fatigue damage parameters include macroscopic mechanical property degradation parameters and / or microstructural damage parameters.
7. The method for predicting the compressive strength of concrete based on the combined action of fatigue load and sulfate as described in claim 6, characterized in that, The macroscopic mechanical property degradation parameter is the ratio of the residual strength of concrete after fatigue loading. The microstructure damage parameters are fatigue damage degrees measured based on electrochemical impedance spectroscopy.