A method for quantitatively evaluating self-healing performance of self-healing concrete

Abstract

The present application relates to a kind of self-healing concrete damage healing performance quantitative evaluation method, comprising: establishing diffusion equation;Solve space-time concentration distribution;Damage-healing constitutive model is constructed;Obtain the evolution law expression of healing variable h with time and space;Obtain the expression of concrete constitutive relationship, to realize the quantitative evaluation of self-healing concrete damage-healing performance.The present application accurately describes the dynamic process of healing product generation under multi-ion environment, can more truly simulate the self-healing behavior of concrete under actual service conditions;Introduce isotropic scalar damage variable d, intuitively represent the degradation of the mechanical properties of concrete;Realize the quantitative mapping from chemical product to mechanical property recovery, provide a theoretical basis for the mechanical property evaluation of self-healing concrete;With the advantages of short analysis period, low cost, wide applicability, can provide early warning information for the safety of engineering structure and take effective safeguard measures.

Description

Technical Field

[0001] This invention relates to the field of self-healing concrete technology, and in particular to a quantitative evaluation method for the damage healing performance of self-healing concrete. Background Technology

[0002] Concrete is a key material in many civilian and military buildings, including tunnels, bridges, airport runways, and even nuclear power plants and command posts. However, under the influence of environmental erosion, load-bearing effects, and material aging, concrete structures commonly develop cracks. These cracks significantly reduce the impermeability of concrete, providing pathways for the intrusion of harmful ions (such as chloride ions), thereby accelerating the softening of the cement matrix and the corrosion of internal reinforcing steel. This problem not only impairs the durability and normal function of the structure but also poses a serious threat to its long-term safety, and may even lead to safety accidents.

[0003] Traditional manual repair methods not only require interrupting the use of the structure but also struggle to repair hidden cracks in their early stages. Existing research indicates that the self-healing mechanism mainly involves the continued hydration of incompletely hydrated cement particles and the reaction of calcium hydroxide with carbon dioxide or carbonate ions to form calcium carbonate precipitates that fill the cracks. In recent years, scholars have attempted to quantitatively describe the self-healing behavior through theoretical modeling and numerical methods. The theory based on continuum damage mechanics (CDM) has been widely applied to the mechanical modeling of self-healing concrete, and some studies have also proposed multi-field coupling models based on chemical-diffusion processes.

[0004] However, existing research largely focuses on the calcium carbonate precipitation mechanism, with less consideration given to the role of sulfate ions in sulfate environments. When concrete is in a high-sulfate environment (such as saline soil, marine engineering, or sulfate groundwater), sulfate ions inevitably penetrate the material's interior, reacting with calcium ions to form precipitates such as calcium sulfate. This process may play a crucial role in crack sealing and permeability barrier function, but current research is mainly limited to experimental observation, lacking systematic theoretical modeling. Furthermore, existing models lack a direct physical connection between microscopic chemical reactions and macroscopic mechanical property recovery, relying somewhat on empirical rules, thus limiting prediction accuracy. Traditional experimental analysis methods (such as loading experiments and SEM observations) are time-consuming and costly, making it difficult to quickly meet the needs of real-time prediction of concrete healing performance in engineering practice, and unable to provide effective support for timely safety warnings of engineering structures. Therefore, how to achieve efficient and convenient theoretical analysis is an urgent problem to be solved. Summary of the Invention

[0005] To address the problems in existing technologies, such as the difficulty in simultaneously considering the chemical precipitation process and the evolution of mechanical properties in a multi-ion environment, and the lack of a theoretical model that can quantitatively describe the entire damage / healing process of self-healing concrete, the present invention aims to provide a quantitative evaluation method for the damage healing performance of self-healing concrete by constructing a damage-healing constitutive model using the Mazars damage model, which can more realistically simulate the self-healing behavior of concrete under actual service conditions.

[0006] To achieve the above objectives, the present invention employs the following technical solution: a quantitative evaluation method for the damage healing performance of self-healing concrete, the method comprising the following sequential steps:

[0007] (1) Based on Fick's second law, establish the carbonate ion With sulfate ions Diffusion equation in concrete;

[0008] (2) Establish the reaction rate equation through the chemical reaction kinetic equation, couple the reaction rate equation with the diffusion equation, establish the concentration change rate equation of calcium carbonate and calcium sulfate, and then solve the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates.

[0009] (3) Based on the Mazars damage model, the damage variable d is defined, and the healing variable h is introduced to modify the damage variable d, so as to construct a damage-healing constitutive model that can describe the mechanical properties of self-healing concrete.

[0010] (4) Substitute the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates, as well as the damage variable d, into the calculation formula of the healing variable h to obtain the evolution law expression of the healing variable h with time and space; then substitute the evolution law expression of the healing variable h with time and space into the damage-healing constitutive model to obtain the expression of the concrete constitutive relationship, thereby realizing the quantitative evaluation of the damage-healing performance of self-healing concrete.

[0011] Step (1) specifically refers to: quantification , Diffusion behavior in concrete microcracks: Measured or reference data on the variation of anion concentration with diffusion time and displacement were obtained, and Fick's second law was used to mathematically characterize the diffusion and transport process of ions in concrete microcracks and pore structures, establishing diffusion equations for the evolution of the concentration field with time and space.

[0012] (1);

[0013] (2);

[0014] In the formula, Represents the concentration of a substance; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively. and These represent the concentrations of carbonate and sulfate ions, respectively.

[0015] Step (2) specifically refers to the following: The chemical reaction kinetic equation is:

[0016] ;

[0017] In the formula, R represents the rate, K is the reaction rate constant, and A represents the reactants. or The concentration of B represents the reactant. The concentration;

[0018] The reaction rate equation is derived from the chemical reaction kinetics equation:

[0019] (3);

[0020] In the formula, It represents the rate of change of a substance's concentration over time. This indicates the rate of change in calcium ion concentration; and These are the reaction rate constants for carbonate ions and sulfate ions, respectively. It is a step function;

[0021] Step function Represented as:

[0022] ;

[0023] In the formula, Represents the concentration of calcium ions; when hour, ;when hour, ;

[0024] From precipitate , The chemical reaction expression is obtained. , The generation rate expression:

[0025] (4);

[0026] (5);

[0027] In the formula, and These represent the rate of change in the concentrations of calcium carbonate and calcium sulfate, respectively.

[0028] Coupled with the diffusion equation and the reaction rate equation, we obtain the equations for the rate of change of concentration of calcium carbonate and calcium sulfate:

[0029] (6);

[0030] (7);

[0031] in, and The Laplace operators representing the concentrations of carbonate and sulfate ions, respectively; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively.

[0032] Solve the diffusion equation and equations (3) to (7) to obtain the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates.

[0033] Step (3) specifically refers to: calculating stress using the Mazars damage model. :

[0034] ;

[0035] in, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively.

[0036] Based on the statistical characteristics of concrete material damage, the Weiber distribution is used to define the value of the damage variable d:

[0037] ;

[0038] in, Peak strain; These are material constants;

[0039] The formula for the healing variable h of self-healing concrete is:

[0040] ;

[0041] in, This indicates the volume of damage inside the self-healing concrete. This represents the volume of the healing deposits after damage to self-healing concrete; healing variable. The value range is [0,1];

[0042] After introducing the healing variable h, a damage-healing constitutive model is constructed:

[0043] .

[0044] Step (4) specifically refers to representing the volume of damage inside the self-healing concrete by using the volume filled by the chemical reaction precipitate. Size:

[0045] ;

[0046] In the formula, It is the volume of the concrete sample;

[0047] The volume of the solid healing product precipitate is used to represent the volume of the healing precipitate after damage to self-healing concrete. :

[0048] (8);

[0049] (9);

[0050] (10);

[0051] in, and These represent the volumes of the precipitates of calcium carbonate and calcium sulfate, respectively. and These represent the molar masses of calcium carbonate and calcium sulfate, respectively. and Let represent the densities of calcium carbonate and calcium sulfate, respectively. Substituting equations (9) and (10) into equation (8), we obtain the expression for the evolution of h over time and space:

[0052] ;

[0053] Considering both damage and two precipitation-healing processes simultaneously, the expression for the constitutive relation of concrete is derived as follows:

[0054] ;

[0055] In the formula, This is the preload coefficient. , All are shape factors; For stress, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively.

[0056] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: First, the present invention establishes a diffusion equation for carbonate and sulfate ions by introducing Fick's second law, and constructs an ion diffusion-chemical reaction coupled field by combining it with its chemical reaction kinetic equation. This accurately describes the dynamic process of healing product formation under multi-ion conditions, overcoming the shortcomings of traditional models in not considering complex chemical environments, and can more realistically simulate the self-healing behavior of concrete under actual service conditions. Second, the present invention constructs a damage-healing constitutive model by using the Mazars damage model and introduces an isotropic scalar damage variable d, which intuitively characterizes the degradation of the mechanical properties of concrete. Furthermore, by defining the healing variable h and linking the volume of precipitate with the volume of damage, a damage-healing constitutive relationship considering the self-healing effect was established, realizing a quantitative mapping from chemical products to the restoration of mechanical properties, and providing a theoretical basis for the mechanical property evaluation of self-healing concrete. Thirdly, by coupling the diffusion equation and the reaction rate equation and adopting an efficient numerical solution strategy, this invention can quickly predict the repair effect and mechanical property evolution of self-healing concrete under different conditions. Compared with empirical methods that rely on a large number of experiments, this invention has the advantages of short analysis cycle, low cost, and wide applicability, and can provide early warning information and take effective safeguard measures for the safety of engineering structures. Attached Figure Description

[0057] Figure 1 This diagram illustrates the relationship between time, healing variables, and displacement when the degree of pre-compression damage remains constant.

[0058] Figure 2 This diagram illustrates the relationship between the carbonate diffusion coefficient, healing variable, and displacement while keeping time and damage level constant.

[0059] Figure 3 This diagram illustrates the relationship between the sulfate diffusion coefficient, healing variable, and displacement while keeping time and damage level constant.

[0060] Figure 4 This diagram illustrates the relationship between the carbonate reaction rate constant, the healing variable, and the displacement, while keeping time and damage level constant.

[0061] Figure 5 This diagram illustrates the relationship between the sulfate reaction rate constant, healing variable, and displacement, while keeping time and damage level constant.

[0062] Figure 6 This diagram illustrates the relationship between time, stress, and strain while keeping the reactant diffusion coefficient, reaction rate constant, and damage level constant constant.

[0063] Figure 7This diagram illustrates the relationship between damage degree, stress, and strain while keeping the reactant diffusion coefficient, reaction rate constant, and time constant.

[0064] Figure 8 This is a flowchart of the method of the present invention. Detailed Implementation

[0065] like Figure 8 As shown, a quantitative evaluation method for the damage healing performance of self-healing concrete is provided, comprising the following sequential steps:

[0066] (1) Based on Fick's second law, establish the carbonate ion With sulfate ions Diffusion equation in concrete;

[0067] (2) Establish the reaction rate equation through the chemical reaction kinetic equation, couple the reaction rate equation with the diffusion equation, establish the concentration change rate equation of calcium carbonate and calcium sulfate, and then solve the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates.

[0068] (3) Based on the Mazars damage model, the damage variable d is defined, and the healing variable h is introduced to modify the damage variable d, so as to construct a damage-healing constitutive model that can describe the mechanical properties of self-healing concrete.

[0069] (4) Substitute the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates, as well as the damage variable d, into the calculation formula of the healing variable h to obtain the evolution law expression of the healing variable h with time and space; then substitute the evolution law expression of the healing variable h with time and space into the damage-healing constitutive model to obtain the expression of the concrete constitutive relationship, thereby realizing the quantitative evaluation of the damage-healing performance of self-healing concrete.

[0070] Step (1) specifically refers to: quantification , Diffusion behavior in concrete microcracks: Measured or reference data on the variation of anion concentration with diffusion time and displacement were obtained, and Fick's second law was used to mathematically characterize the diffusion and transport process of ions in concrete microcracks and pore structures, establishing diffusion equations for the evolution of the concentration field with time and space.

[0071] (1);

[0072] (2);

[0073] In the formula, Represents the concentration of a substance; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively. and These represent the concentrations of carbonate and sulfate ions, respectively.

[0074] Step (2) specifically refers to the following: The chemical reaction kinetic equation is:

[0075] ;

[0076] In the formula, R represents the rate, K is the reaction rate constant, and A represents the reactants. or The concentration of B represents the reactant. The concentration;

[0077] The reaction rate equation is derived from the chemical reaction kinetics equation:

[0078] (3);

[0079] In the formula, It represents the rate of change of a substance's concentration over time. This indicates the rate of change in calcium ion concentration; and These are the reaction rate constants for carbonate ions and sulfate ions, respectively. It is a step function;

[0080] Step function Represented as:

[0081] ;

[0082] In the formula, Represents the concentration of calcium ions; when hour, ;when hour, ;

[0083] From precipitate , The chemical reaction expression is obtained. , The generation rate expression:

[0084] (4);

[0085] (5);

[0086] In the formula, and These represent the rate of change in the concentrations of calcium carbonate and calcium sulfate, respectively.

[0087] Sediment , The chemical reaction expression is:

[0088] ;

[0089] ;

[0090] Coupled with the diffusion equation and the reaction rate equation, we obtain the equations for the rate of change of concentration of calcium carbonate and calcium sulfate:

[0091] (6);

[0092] (7);

[0093] in, and The Laplace operators representing the concentrations of carbonate and sulfate ions, respectively; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively.

[0094] Solve the diffusion equation and equations (3) to (7) to obtain the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates.

[0095] Step (3) specifically refers to: calculating stress using the Mazars damage model. :

[0096] ;

[0097] in, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively.

[0098] Based on the statistical characteristics of concrete material damage, the Weiber distribution is used to define the value of the damage variable d:

[0099] ;

[0100] in, Peak strain; These are material constants;

[0101] The formula for the healing variable h of self-healing concrete is:

[0102] ;

[0103] in, This indicates the volume of damage inside the self-healing concrete. This represents the volume of the healing deposits after damage to self-healing concrete; healing variable. The value range is [0,1];

[0104] After introducing the healing variable h, a damage-healing constitutive model is constructed:

[0105] .

[0106] Step (4) specifically refers to representing the volume of damage inside the self-healing concrete by using the volume filled by the chemical reaction precipitate. Size:

[0107] ;

[0108] In the formula, It is the volume of the concrete sample;

[0109] The volume of the solid healing product precipitate is used to represent the volume of the healing precipitate after damage to self-healing concrete. :

[0110] (8);

[0111] (9);

[0112] (10);

[0113] in, and These represent the volumes of the precipitates of calcium carbonate and calcium sulfate, respectively. and These represent the molar masses of calcium carbonate and calcium sulfate, respectively. and Let represent the densities of calcium carbonate and calcium sulfate, respectively. Substituting equations (9) and (10) into equation (8), we obtain the expression for the evolution of h over time and space:

[0114] ;

[0115] Considering both damage and two precipitation-healing processes simultaneously, the expression for the constitutive relation of concrete is derived as follows:

[0116] ;

[0117] In the formula, This is the preload coefficient. , All are shape factors; For stress, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively.

[0118] like Figure 1 As shown, the self-healing concrete exhibits the best repair effect at a time of 15 days, with the widest range of decrease in the healing variable, indicating that the material's damage healing range is the broadest at this time. The shorter the time, the weaker the healing effect of the self-healing concrete. When the time is 1 day, the healing effect of the self-healing concrete is significantly limited, showing a healing response only within a very small displacement range approaching 0, and quickly approaching 0. The horizontal axis x represents the length of the self-healing concrete.

[0119] like Figure 2 As shown, the two curves have a generally consistent shape, both exhibiting a distribution trend of rapid decay from the crack surface inwards, indicating that the healing products are mainly concentrated in the region near the crack interface. Near the crack surface (x < 0.15 m), the healing variable h corresponding to the case with a larger diffusion coefficient (black solid line) is slightly higher than that corresponding to a smaller diffusion coefficient (red line), indicating that a faster diffusion rate helps carbonate ions enter the material surface more quickly, thereby promoting CaCO3 deposition in a short time. With increasing distance, the difference between the two curves decreases rapidly, almost coinciding at (x > 0.15 m), indicating that the diffusion depth of carbonate ions is limited under these conditions, and the reaction is mainly concentrated in the surface region.

[0120] like Figure 3 As shown, the two curves exhibit similar overall trends, both rapidly decaying near the crack surface (x < 0.021 m), indicating that the healing reaction is mainly concentrated near the crack boundary, with minimal diffusion inwards. With increasing carbonate diffusion coefficient (black line), the curve shifts slightly to the right, and the decay becomes more gradual, suggesting that the diffusion range of carbonate ions expands, allowing them to penetrate deeper into the material and promote calcium carbonate deposition. Conversely, under conditions of a smaller diffusion coefficient (red line), the healing variable h decays faster, indicating that the reaction is more significantly limited by diffusion.

[0121] like Figure 4 As shown, the two curves exhibit a consistent overall trend, both rapidly decaying near the crack surface (x < 0.02 m) and approaching zero within a relatively small depth range, indicating that the healing reaction is mainly concentrated in the interface region. Comparing the two curves reveals that the h value under the high reaction rate constant condition (black line) is slightly higher than that under the low reaction rate constant condition (red line), and the curve decays more slowly, indicating that the increased reaction rate accelerates the deposition of calcium carbonate, resulting in a slight increase in the thickness of the healed layer. Conversely, under the low reaction rate condition, insufficient reaction kinetics lead to a reduced rate of calcium ion-carbonate binding, resulting in less healed product formation.

[0122] like Figure 5 As shown, the curves under different reaction rate constants do not differ significantly, with only slight differences near the boundary. The h value near the boundary is slightly higher than that in the inner region, indicating that the reaction mainly occurs in the region near the crack surface, and the effective range of healing is narrower at the same time. As the reaction rate constant decreases, the red line shifts slightly to the left, indicating that at lower reaction rates, the reaction rate between sulfate and calcium ions decreases, the rate of calcium sulfate deposition slows down, resulting in a faster decrease in the healing variable h, and a slight reduction in the healing influence range.

[0123] like Figure 6 As shown, under the condition that the reactant diffusion coefficient, reaction rate constant, and damage degree remain consistent, the stress-strain curve of the material generally shows a gradual upward trend with the extension of curing time, indicating that crack healing products are continuously generated, and the mechanical properties of the material are gradually restored. At t=1 day, the curve peak is the lowest, and the downward segment appears earlier, indicating that the chemical reaction inside the crack has not yet been fully carried out, the amount of self-healing product deposition is limited, and the effect on improving the overall load-bearing capacity of the specimen is weak. When the time is increased to t=7 days, the curve shifts significantly upward, the peak stress increases, and the slope of the downward segment becomes gentler, indicating that the reaction-diffusion process has been significantly advanced in the intermediate stage: the diffusion of carbonate and sulfate ions increases, the generated deposits block the cracks and effectively improve the local stiffness, resulting in a significant enhancement of macroscopic mechanical properties. When the time is further extended to t=15 days, the curve continues to move upward and maintains a similar trend to the 7-day curve, but a certain degree of performance improvement can still be observed, especially in the downward segment, where the material toughness is slightly enhanced. This phenomenon indicates that although the reaction has entered a relatively slow stage, the deposited products continue to be generated, the healed area within the crack further expands, and the material's load-bearing capacity increases accordingly.

[0124] like Figure 7 As shown, when the damage level is 0.6, the self-healing concrete has the best strength recovery effect, with a peak strength of about 36 MPa; when the damage level is 0.8, the strength repair effect of the self-healing concrete is second to that of 0.6, with a peak strength of about 35 MPa; and when the damage level is 1.0, the stress is zero overall, indicating that the self-healing concrete has been damaged and can no longer bear the load.

[0125] In summary, this invention establishes a diffusion equation for carbonate and sulfate ions by introducing Fick's second law, and constructs an ion diffusion-chemical reaction coupled field by combining it with their chemical reaction kinetics equation. This accurately describes the dynamic process of healing product formation under multi-ion conditions, overcoming the shortcomings of traditional models that fail to consider complex chemical environments, and can more realistically simulate the self-healing behavior of concrete under actual service conditions. Furthermore, this invention constructs a damage-healing constitutive model using the Mazars damage model, introducing an isotropic scalar damage variable d to intuitively characterize the degradation of concrete's mechanical properties. By defining the healing variable h and linking the precipitate volume with the damage volume, a damage-healing constitutive relationship considering the self-healing effect is established, realizing a quantitative mapping from chemical products to mechanical property recovery, providing a theoretical basis for the mechanical property evaluation of self-healing concrete. Finally, by coupling the diffusion equation with the reaction rate equation and employing an efficient numerical solution strategy, this invention can quickly predict the repair effect and mechanical property evolution of self-healing concrete under different conditions. Compared to empirical methods relying on numerous experiments, this invention has the advantages of short analysis cycles, low cost, and wide applicability, and can provide early warning information and effective safeguards for the safety of engineering structures.

[0126] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A quantitative evaluation method for the damage healing performance of self-healing concrete, characterized in that: The method includes the following steps in sequence: (1) Based on Fick's second law, establish the carbonate ion With sulfate ions Diffusion equation in concrete; (2) Establish the reaction rate equation through the chemical reaction kinetic equation, couple the reaction rate equation with the diffusion equation, establish the concentration change rate equation of calcium carbonate and calcium sulfate, and then solve the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates. (3) Based on the Mazars damage model, the damage variable d is defined, and the healing variable h is introduced to modify the damage variable d, so as to construct a damage-healing constitutive model that can describe the mechanical properties of self-healing concrete. (4) Substitute the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates, as well as the damage variable d, into the calculation formula of the healing variable h to obtain the evolution law expression of the healing variable h with time and space; then substitute the evolution law expression of the healing variable h with time and space into the damage-healing constitutive model to obtain the expression of the concrete constitutive relationship, thereby realizing the quantitative evaluation of the damage-healing performance of self-healing concrete.

2. The quantitative evaluation method for the damage healing performance of self-healing concrete according to claim 1, characterized in that: Step (1) specifically refers to: quantification , Diffusion behavior in concrete microcracks: Measured or reference data on the variation of anion concentration with diffusion time and displacement were obtained, and Fick's second law was used to mathematically characterize the diffusion and transport process of ions in concrete microcracks and pore structures, establishing diffusion equations for the evolution of the concentration field with time and space. （1）； （2）； In the formula, Represents the concentration of a substance; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively. and These represent the concentrations of carbonate and sulfate ions, respectively.

3. The quantitative evaluation method for the damage healing performance of self-healing concrete according to claim 1, characterized in that: Step (2) specifically refers to the following: The chemical reaction kinetic equation is: ； In the formula, R represents the rate, K is the reaction rate constant, and A represents the reactants. or The concentration of B represents the reactant. The concentration; The reaction rate equation is derived from the chemical reaction kinetics equation: （3）； In the formula, It represents the rate of change of a substance's concentration over time. This indicates the rate of change in calcium ion concentration; and These are the reaction rate constants for carbonate ions and sulfate ions, respectively. It is a step function; Step function Represented as: ； In the formula, Represents the concentration of calcium ions; when hour, ;when hour, ; From precipitate , The chemical reaction expression is obtained. , The generation rate expression: （4）； （5）； In the formula, and These represent the rate of change in the concentrations of calcium carbonate and calcium sulfate, respectively. Coupled with the diffusion equation and the reaction rate equation, we obtain the equations for the rate of change of concentration of calcium carbonate and calcium sulfate: （6）； （7）； in, and The Laplace operators representing the concentrations of carbonate and sulfate ions, respectively; and These represent the diffusion coefficients of carbonate and sulfate ions in the medium, respectively. Solve the diffusion equation and equations (3) to (7) to obtain the spatiotemporal concentration distribution of carbonate ions, sulfate ions, calcium ions and calcium carbonate and calcium sulfate precipitates.

4. The quantitative evaluation method for the damage healing performance of self-healing concrete according to claim 1, characterized in that: Step (3) specifically refers to: calculating stress using the Mazars damage model. : ； in, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively. Based on the statistical characteristics of concrete material damage, the Weiber distribution is used to define the value of the damage variable d: ； in, Peak strain; These are material constants; The formula for the healing variable h of self-healing concrete is: ； in, This indicates the volume of damage inside the self-healing concrete. This represents the volume of the healing deposits after damage to self-healing concrete; healing variable. The value range is [0,1]; After introducing the healing variable h, a damage-healing constitutive model is constructed: 。 5. The quantitative evaluation method for the damage healing performance of self-healing concrete according to claim 1, characterized in that: Step (4) specifically refers to representing the volume of damage inside the self-healing concrete by using the volume filled by the chemical reaction precipitate. Size: ； In the formula, It is the volume of the concrete sample; The volume of the solid healing product precipitate is used to represent the volume of the healing precipitate after damage to self-healing concrete. : （8）； （9）； （10）； in, and These represent the volumes of the precipitates of calcium carbonate and calcium sulfate, respectively. and These represent the molar masses of calcium carbonate and calcium sulfate, respectively. and Let represent the densities of calcium carbonate and calcium sulfate, respectively. Substituting equations (9) and (10) into equation (8), we obtain the expression for the evolution of h over time and space: ； Considering both damage and two precipitation-healing processes simultaneously, the expression for the constitutive relation of concrete is derived as follows: ； In the formula, This is the preload coefficient. , All are shape factors; For stress, In response, For lossless stiffness; and These represent the undamaged and completely damaged states of the material, respectively.

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