Simulation Method for Cracking Analysis of FRP-Constrained Coal Gangue Concrete under Sulfate Erosion Environment

Abstract

This invention provides a simulation method for analyzing the cracking of FRP-constrained coal gangue concrete under sulfate attack conditions, belonging to the field of materials science and technology. This invention obtains the microstructure of coal gangue concrete using a scanning electron microscope and separates the solid and pore components using image processing to generate a microscopic model. Subsequently, by measuring the effects of sulfate attack on the elastic modulus and Poisson's ratio of concrete, a concrete and FRP-constrained model is established using finite element method (FEM) software. Based on the strain generated by the mechanical load input to the model and the change in elastic modulus under sulfate attack conditions, the stress of the model under sulfate attack conditions is generated. Based on this, the stress intensity factor and the crack limitation factor of the FRP layer are calculated to generate a constraint evaluation factor to assess the inhibitory effect of FRP on concrete cracking.

Description

Technical Field

[0001] This invention relates to the field of materials science and technology, specifically to a simulation method for analyzing the cracking of FRP-confined coal gangue concrete under sulfate erosion conditions. Background Technology

[0002] Coal gangue concrete, as an environmentally friendly building material, is widely used in engineering construction. However, under sulfate attack environments, coal gangue concrete is susceptible to chemical corrosion, leading to a decline in its structural performance and an increased risk of cracking. This corrosion not only affects the durability of concrete but can also lead to structural failure, seriously impacting the safety and service life of buildings. Traditional concrete protection measures are often insufficient to effectively address the complex problems caused by sulfate attack, thus requiring a solution that can enhance concrete's resistance to sulfate attack. In recent years, fiber-reinforced polymer (FRP) composites have become an ideal choice for enhancing the performance of concrete structures due to their excellent mechanical properties and corrosion resistance. However, how to scientifically and rationally evaluate the inhibitory effect of FRP on cracking of coal gangue concrete under sulfate attack environments remains a technical challenge.

[0003] In the prior art, CN118133627 discloses a simulation method and system for analyzing the cracking of concrete under sulfate attack. The method involves establishing a micro-concrete model based on a real concrete structure; obtaining the mechanical and chemical parameters of each component of the real concrete and assigning them to the micro-concrete model; applying boundary conditions to the micro-concrete model according to the actual working environment of the concrete to simulate the actual sulfate attack cracking process; meshing the micro-concrete model and setting the solution error; constructing a chemical transport force phase-field coupling model under sulfate attack; and using the coupled model to solve the cracking process of concrete under sulfate attack based on the mesh, solution error, assigned parameters, and applied boundary conditions.

[0004] The main problems with the above method are: it involves coupling calculations using multiple models, which requires a large number of parameters and is quite complex when building the model. It is suitable for concrete structures under specific types and conditions, but when facing other types of concrete and erosion conditions, it is necessary to rebuild the model, resulting in insufficient scalability of the solution; and when analyzing the cracking problem caused by sulfate, it lacks analysis of reinforcement measures, making it difficult to provide effective decision support.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate erosion environment, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate attack environment, the specific steps of which include:

[0009] Step 1: Obtain a concrete sample identical to the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by scanning electron microscopy, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, acquire microstructure images of the sample, binarize the microstructure images using image processing software to distinguish between solid and pore parts, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated to generate a microstructure model;

[0010] Step 2: Initialize the sulfate concentration field in the microstructure model, and measure the changes in the elastic modulus and Poisson's ratio of concrete based on the changes in sulfate concentration to generate the elastic modulus and Poisson's ratio of concrete under sulfate erosion environment;

[0011] Step 3: Establish a concrete structure model based on finite element software, define boundary conditions, measure the strain generated by the concrete structure model under mechanical load, and generate the stress of the concrete structure model under sulfate attack based on the elastic modulus of concrete under sulfate attack and the strain generated by the concrete structure model under mechanical load.

[0012] Step 4: Obtain the elastic modulus and tensile strength of the FRP material, add an FRP layer in the finite element software, generate a bond contact model that combines the concrete structure and the FRP layer, and input the same mechanical load as the concrete structure model into the bond contact model. Measure the strain generated by the bond contact model under the mechanical load. Based on the elastic modulus of the concrete under sulfate attack and the strain generated by the bond contact model under the mechanical load, generate the total stress of the bond contact model under sulfate attack.

[0013] Step 5: In the concrete structure model, a stress intensity factor is generated based on the total stress of the concrete structure model. In the bond contact model, a crack limiting factor under the influence of the FRP layer is generated by combining the constraint effect of the FRP layer on crack propagation. A constraint evaluation index is generated based on the stress intensity factor and the crack limiting factor. The constraint evaluation index is used to determine the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

[0014] Furthermore, the principle underlying the binarization of microstructure images is as follows:

[0015] The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level is counted. A horizontal grayscale histogram is plotted, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by maximizing the inter-class variance. The grayscale image is then segmented using the optimal segmentation threshold, with solid parts marked as white and pore parts marked as black. The principle behind generating the optimal segmentation threshold is as follows:

[0016] Each threshold in the histogram represents the gray value of a pixel that can be selected for image segmentation. In a grayscale image, the gray value ranges from 0 to 255, and the threshold value is any integer within the range of 0 to 255.

[0017] The principle behind selecting the optimal segmentation threshold using the maximum inter-class variance is as follows:

[0018] g(a) 2 = a ω ′ a (μ a - ′ a ) 2

[0019] Where a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, and ω a μ represents the proportion of the solid portion in the total image when the segmentation threshold is a. a ω represents the grayscale value of the solid portion when the segmentation threshold is 'a'. ′ a μ represents the proportion of the pore portion in the total image when the segmentation threshold is a. ′ a This represents the grayscale value of the pore portion when the segmentation threshold is 'a'.

[0020] When g(a) reaches its maximum value, the corresponding threshold a is the optimal segmentation threshold.

[0021] Furthermore, the principle underlying the generation of stress in the concrete structure model is as follows:

[0022] σ h =1·∈0

[0023] Where, σ h E1 represents the elastic modulus of concrete under sulfate attack, and ∈0 represents the strain generated by mechanical loads in the concrete structure model.

[0024] Furthermore, the principle underlying the generation of the total stress in the bonded contact model is as follows:

[0025] The formula used to determine the stress that generates the FRP layer is:

[0026] σF = F ·∈ F

[0027] Where, σ F E represents the stress in the FRP layer. F Represents the elastic modulus of the FRP layer, ∈ F Indicates the strain of the FRP layer;

[0028] The formula used to generate the total stress in the bonded contact model is:

[0029]

[0030] Where, σ z S represents the total stress in the bonded contact model. F S represents the cross-sectional area of ​​the FRP layer. h Let S represent the cross-sectional area of ​​the concrete structure, and let S represent the total area of ​​the entire cross-section, and S = S0. F + h .

[0031] Furthermore, the principle underlying the generation of the constraint evaluation index is as follows:

[0032] The formula used to generate the stress intensity factor is:

[0033]

[0034] Where K1 represents the stress intensity factor, σ h This represents the stress in the concrete structure model, where 'a' represents the input σ to the concrete structure model. h The length of the resulting crack;

[0035] The formula used to generate the crack limiting factor is:

[0036]

[0037] Where K2 represents the crack limiting factor, E represents the elastic modulus of concrete, and D... h E represents the thickness of the concrete in the bond contact model. F D represents the elastic modulus of the FRP layer. F σ represents the thickness of the FRP layer in the adhesive contact model. max σ represents the maximum stress that the FRP layer can withstand. z This represents the total stress in the bonded contact model;

[0038] The formula used to generate the constraint evaluation index is as follows:

[0039]

[0040] Where P represents the constraint evaluation index;

[0041] When P < 1, it indicates that the FRP layer has a positive inhibitory effect on concrete cracking, and the smaller P is, the more obvious the inhibitory effect.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] This invention introduces a sulfate concentration field into the microstructure model through microstructure modeling and multi-scale simulation, dynamically assessing the impact of sulfate erosion on concrete properties. This helps to accurately predict changes in the mechanical properties of concrete under erosive environments and improves the accuracy of the simulation. Furthermore, by establishing a macroscopic concrete structure model through finite element analysis, and combining the dual effects of chemical erosion and physical loads, it more accurately reflects the true stress state of concrete structures under complex environments.

[0044] This invention also effectively evaluates the practical application value of FRP reinforcement technology in sulfate-eroded environments by combining FRP layers with concrete structures and analyzing the comprehensive performance of their interaction through a bond-contact model. By generating the total stress in the bond-contact model, guidance can be provided for structural design optimization and material selection, ensuring the durability and safety of the structure and ultimately improving the practicality and reliability of the overall solution. Furthermore, the stress intensity factor and crack limitation factor are calculated in both the concrete structure model and the bond-contact model, reflecting the relationship between material properties and reinforcement effects. The generated constraint evaluation index more intuitively reflects the constraint effect of FRP on concrete, helping to guide the implementation of appropriate measures. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0047] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0048] Example:

[0049] Please see Figure 1 The present invention provides a technical solution:

[0050] Step 1: Obtain a concrete sample identical to the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by scanning electron microscopy, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, acquire microstructure images of the sample, binarize the microstructure images using image processing software to distinguish between solid and pore parts, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated to generate a microstructure model;

[0051] In this embodiment, a 5×5×5mm sample is cut from the coal gangue concrete. The sample surface is ground to ensure a smooth and flat surface, and then dried in a drying oven. A layer of conductive material is sprayed onto the dried sample surface to prevent charging during observation. The processed sample is then fixed to a scanning electron microscope using conductive adhesive for observation. The pore size of coal gangue concrete is typically between 1μm and 100μm, and the micro-aggregates are typically around 50nm. Therefore, the resolution range of the scanning electron microscope is 0.01μm to 100μm.

[0052] In this embodiment, the principle underlying the binarization of the microstructure image is as follows:

[0053] The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level is counted. A horizontal grayscale histogram is plotted, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by maximizing the inter-class variance. The grayscale image is then segmented using the optimal segmentation threshold, with solid parts marked as white and pore parts marked as black. The principle behind generating the optimal segmentation threshold is as follows:

[0054] Each threshold in the histogram represents the gray value of a pixel that can be selected for image segmentation. In a grayscale image, the gray value ranges from 0 to 255, and the threshold value is any integer within the range of 0 to 255.

[0055] The principle behind selecting the optimal segmentation threshold using the maximum inter-class variance is as follows:

[0056] g(a) 2 = a ω ′ a (μ a - ′ a ) 2

[0057] Where a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, and ω a μ represents the proportion of the solid portion in the total image when the segmentation threshold is a. a ω represents the grayscale value of the solid portion when the segmentation threshold is 'a'. ′ a μ represents the proportion of the pore portion in the total image when the segmentation threshold is a. ′ a This represents the grayscale value of the pore portion when the segmentation threshold is 'a'.

[0058] When g(a) reaches its maximum value, the corresponding threshold a is the optimal segmentation threshold.

[0059] A microstructure model is established using CONSOL software. The binarized microstructure image is imported into COMSOL, and material properties are assigned to each part of the microstructure image. The parts include aggregates, pores, cement paste, etc. The material properties include Poisson's ratio and elasticity model, thus constituting the microstructure model.

[0060] Step 2: Initialize the sulfate concentration field in the microstructure model, and measure the changes in the elastic modulus and Poisson's ratio of concrete based on the changes in sulfate concentration to generate the elastic modulus and Poisson's ratio of concrete under sulfate erosion environment;

[0061] In this embodiment, an initial sodium sulfate concentration field is defined in the microstructure model to obtain the historical sulfate erosion situation of the coal gangue concrete area to be evaluated. As time goes by, the sulfate concentration tends to a stable value, which is used as the initial sulfate concentration. The diffusion process of sulfate in concrete is simulated. As the sulfate erosion process progresses, the changes in the elastic modulus and Poisson's ratio of the concrete are measured until they finally tend to a stable value. The stable value is used as the elastic modulus and Poisson's ratio of the concrete under sulfate erosion environment.

[0062] Step 3: Establish a concrete structure model based on finite element software, define boundary conditions, measure the strain generated by the concrete structure model under mechanical load, and generate the stress of the concrete structure model under sulfate attack based on the elastic modulus of concrete under sulfate attack and the strain generated by the concrete structure model under mechanical load.

[0063] In this embodiment, the principle underlying the generation of stress in the concrete structure model is as follows:

[0064] σ h =1·∈0

[0065] Where, σ h E1 represents the elastic modulus of concrete under sulfate attack, and ∈0 represents the strain generated by mechanical loads in the concrete structure model.

[0066] The concrete structure model is a macroscopic model, in which the stress is calculated through the stress-strain relationship. The strain generated by the external mechanical load on the concrete structure is measured, and then the stress magnitude is determined. The stress of the concrete structure model under mechanical load is proportional to the elastic modulus of the concrete and proportional to the strain.

[0067] Step 4: Obtain the elastic modulus and tensile strength of the FRP material, add an FRP layer in the finite element software, generate a bond contact model that combines the concrete structure and the FRP layer, and input the same mechanical load as the concrete structure model into the bond contact model. Measure the strain generated by the bond contact model under the mechanical load. Based on the elastic modulus of the concrete under sulfate attack and the strain generated by the bond contact model under the mechanical load, generate the total stress of the bond contact model under sulfate attack.

[0068] In this embodiment, the principle underlying the generation of the total stress in the bonded contact model is as follows:

[0069] The formula used to determine the stress that generates the FRP layer is:

[0070] σ F = F ·∈ F

[0071] Where, σ F E represents the stress in the FRP layer. F Represents the elastic modulus of the FRP layer, ∈ F Indicates the strain of the FRP layer;

[0072] The formula used to generate the total stress in the bonded contact model is:

[0073]

[0074] Where, σz S represents the total stress in the bonded contact model. F S represents the cross-sectional area of ​​the FRP layer. h Let S represent the cross-sectional area of ​​the concrete structure, and let S represent the total area of ​​the entire cross-section, and S = S0. F + h .

[0075] Stress is the ratio of the applied force to the bearing area. In the bonded contact model, the overall applied force is the sum of the internal stresses of the FRP layer and the concrete structure. The bearing area of ​​the FRP layer is the cross-sectional area of ​​the FRP layer, and the bearing area of ​​the concrete structure is the cross-sectional area of ​​the concrete structure. After stacking the FRP layer and the concrete layer, the total bearing area is the sum of the cross-sectional areas of the two.

[0076] Step 5: In the concrete structure model, a stress intensity factor is generated based on the total stress of the concrete structure model. In the bond contact model, a crack limiting factor under the influence of the FRP layer is generated by combining the constraint effect of the FRP layer on crack propagation. A constraint evaluation index is generated based on the stress intensity factor and the crack limiting factor. The constraint evaluation index is used to determine the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

[0077] In this embodiment, the principle underlying the generation of the constraint evaluation index is as follows:

[0078] The formula used to generate the stress intensity factor is:

[0079]

[0080] Where K1 represents the stress intensity factor, σ h This represents the stress in the concrete structure model, where 'a' represents the input σ to the concrete structure model. h The length of the resulting crack;

[0081] The linear elastic fracture mechanics assessment of crack propagation reflects the trend of crack propagation. This indicates the effect of crack length on the stress field. As the crack length increases, the stress concentration effect at the crack tip intensifies, and the crack propagation tendency increases.

[0082] The formula used to generate the crack limiting factor is:

[0083]

[0084] Where K2 represents the crack limiting factor, E represents the elastic modulus of concrete, and D... h E represents the thickness of the concrete in the bond contact model. F D represents the elastic modulus of the FRP layer. F σ represents the thickness of the FRP layer in the adhesive contact model.max σ represents the maximum stress that the FRP layer can withstand. z This represents the total stress in the bonded contact model;

[0085] The crack confinement factor reflects the effect of the FRP layer on inhibiting crack propagation. This reflects the contribution of the concrete structure and FRP layer to the overall structural performance. It reflects the remaining load-bearing capacity of the overall structure under total stress. The maximum stress that the FRP layer can withstand is determined by inputting an axial tensile force into the same FRP layer sample until the sample breaks. The stress value that the sample F withstands at the moment of fracture is the maximum stress that the FRP layer can withstand.

[0086] The formula used to generate the constraint evaluation index is as follows:

[0087]

[0088] Where P represents the constraint evaluation index;

[0089] When P < 1, it indicates that the FRP layer has a positive inhibitory effect on concrete cracking, and the smaller P is, the more obvious the inhibitory effect.

[0090] When P < 1, K1 < K2. At this time, the crack limiting factor has a greater effect on limiting cracks than the stress intensity factor has on crack propagation. That is, the FRP layer has a positive inhibitory effect on concrete cracking. The smaller P is, the larger the crack limiting factor is and the more obvious the inhibitory effect is.

[0091] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0092] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0093] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0094] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A simulation method for analyzing cracking of FRP-constrained coal gangue concrete under sulfate attack environment, characterized in that, The specific steps include: Step 1: Obtain a concrete sample identical to the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by scanning electron microscopy, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, acquire microstructure images of the sample, binarize the microstructure images using image processing software to distinguish between solid and pore parts, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated to generate a microstructure model; Step 2: Initialize the sulfate concentration field in the microstructure model, and measure the changes in the elastic modulus and Poisson's ratio of concrete based on the changes in sulfate concentration to generate the elastic modulus and Poisson's ratio of concrete under sulfate erosion environment; Step 3: Establish a concrete structure model based on finite element software, define boundary conditions, measure the strain generated by the concrete structure model under mechanical load, and generate the stress of the concrete structure model under sulfate attack based on the elastic modulus of concrete under sulfate attack and the strain generated by the concrete structure model under mechanical load. Step 4: Obtain the elastic modulus and tensile strength of the FRP material, add an FRP layer in the finite element software, generate a bond contact model that combines the concrete structure and the FRP layer, and input the same mechanical load as the concrete structure model into the bond contact model. Measure the strain generated by the bond contact model under the mechanical load. Based on the elastic modulus of the concrete under sulfate attack and the strain generated by the bond contact model under the mechanical load, generate the total stress of the bond contact model under sulfate attack. Step 5: In the concrete structure model, a stress intensity factor is generated based on the total stress of the concrete structure model. In the bond contact model, a crack limiting factor under the influence of the FRP layer is generated by combining the constraint effect of the FRP layer on crack propagation. A constraint evaluation index is generated based on the stress intensity factor and the crack limiting factor. The constraint evaluation index is used to determine the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

2. The simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate erosion environment according to claim 1, characterized in that: The principle underlying the binarization of the microstructure image in step 1 is as follows: The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level is counted. A horizontal grayscale histogram is plotted, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by maximizing the inter-class variance. The grayscale image is then segmented using the optimal segmentation threshold, with solid parts marked as white and pore parts marked as black. The principle behind generating the optimal segmentation threshold is as follows: Each threshold in the histogram represents the gray value of a pixel that can be selected for image segmentation. In a grayscale image, the gray value ranges from 0 to 255, and the threshold value is any integer within the range of 0 to 255. The principle behind selecting the optimal segmentation threshold using the maximum inter-class variance is as follows: g(a) 2 =ω a oh' a (m a -m′ a ) 2 Where a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, and ω a μ represents the proportion of the solid portion in the total image when the segmentation threshold is a. a ω′ represents the grayscale value of the solid portion when the segmentation threshold is a. a μ′ represents the proportion of the pore portion in the total image when the segmentation threshold is a. a This represents the grayscale value of the pore portion when the segmentation threshold is 'a'. When g(a) reaches its maximum value, the corresponding threshold a is the optimal segmentation threshold.

3. The simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate erosion environment according to claim 1, characterized in that: The principle underlying the generation of stress in the concrete structure model in step 3 is as follows: s h =E1 ∈0 Where, σ h E1 represents the elastic modulus of concrete under sulfate attack, and ∈0 represents the strain generated by mechanical loads in the concrete structure model.

4. The simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate erosion environment according to claim 3, characterized in that: The principle underlying the generation of the total stress in the bonded contact model in step 4 is as follows: The formula used to determine the stress that generates the FRP layer is: σ F =E F ·∈ F Where, σ F E represents the stress in the FRP layer. F Represents the elastic modulus of the FRP layer, ∈ F Indicates the strain of the FRP layer; The formula used to generate the total stress in the bonded contact model is: Where, σ z S represents the total stress in the bonded contact model. F S represents the cross-sectional area of ​​the FRP layer. h Let S represent the cross-sectional area of ​​the concrete structure, and let S represent the total area of ​​the entire cross-section, and S = S0. F +S h .

5. The simulation method for crack analysis of FRP-constrained coal gangue concrete under sulfate erosion environment according to claim 1, characterized in that: The principle underlying the generation of the constraint evaluation index in step 5 is as follows: The formula used to generate the stress intensity factor is: Where K1 represents the stress intensity factor, σ h This represents the stress in the concrete structure model, where 'a' represents the input σ to the concrete structure model. h The length of the resulting crack; The formula used to generate the crack limiting factor is: Where K2 represents the crack limiting factor, E represents the elastic modulus of concrete, and D... h E represents the thickness of the concrete in the bond contact model. F D represents the elastic modulus of the FRP layer. F σ represents the thickness of the FRP layer in the adhesive contact model. max σ represents the maximum stress that the FRP layer can withstand. z This represents the total stress in the bonded contact model; The formula used to generate the constraint evaluation index is as follows: Where P represents the constraint evaluation index; When P < 1, it indicates that the FRP layer has a positive inhibitory effect on concrete cracking, and the smaller P is, the more obvious the inhibitory effect.

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