Simulation method for FRP-constrained coal gangue concrete cracking analysis in sulfate erosion environment

Through microstructure modeling and multi-scale simulation, the impact of sulfate erosion on concrete is dynamically evaluated, and the inhibitory effect of FRP layer on coal gangue concrete cracking is evaluated in combination with finite element analysis, which solves the problem of FRP in the existing technology to evaluate the effect of concrete cracking inhibition, achieving higher simulation accuracy and structural design guidance.

CN119827386AActive Publication Date: 2025-04-15CHINA UNIV OF MINING & TECH +1
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Patent Information

Application Number
CN202411933905.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-26
Publication Date
2025-04-15
Estimated Expiration
2044-12-26

AI Technical Summary

Technical Problem

In the sulfate erosion environment, it is difficult for the prior art to effectively evaluate the inhibitory effect of FRP on coal gangue concrete cracking, and the existing methods are insufficient in scalability, making it difficult to adapt to different types of concrete and erosion conditions.

Method used

By obtaining the same concrete samples as the gangue concrete to be evaluated, microstructure images are prepared, microstructure models are generated, and sulfate concentration fields are introduced into the model to dynamically evaluate the impact of sulfate erosion on the properties of concrete. Combined with finite element analysis, a concrete structure model and bond contact model were established to evaluate the inhibitory effect of the FRP layer on concrete cracking.

Benefits of technology

It is achieved to accurately predict changes in concrete mechanical properties in the sulfate erosion environment, improve simulation accuracy, and effectively evaluate the inhibitory effect of FRP layer on concrete cracking through constraint evaluation index, providing guidance on structural design optimization and material selection.

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Abstract

The invention provides a simulation method for FRP-constrained coal gangue concrete cracking analysis in a sulfate erosion environment, and relates to the technical field of material scientificity, the microstructure of coal gangue concrete is obtained through a scanning electron microscope, solid and pore parts are separated out through image processing, and a microscopic model is generated. Then, determining the influence of sulfate erosion on the elastic modulus and Poisson's ratio of concrete, establishing a concrete and FRP constraint model in combination with finite element software, and generating the stress of the model in the sulfate erosion environment based on the strain generated by inputting a mechanical load to the model and the change of the elastic modulus in the sulfate erosion environment; and on the basis, calculating a stress intensity factor and a crack limiting factor of the FRP layer, and generating a constraint evaluation factor to evaluate the inhibition effect of the FRP on concrete cracking.
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Description

Technical Field

[0001] The invention relates to the technical field of material science, and in particular to a simulation method for crack analysis of FRP-constrained gangue concrete in a sulfate attack environment. Background Art

[0002] Gangue concrete is widely used in engineering construction as an environmentally friendly building material. However, in a sulfate attack environment, gangue concrete is susceptible to chemical corrosion, resulting in a decrease in its structural performance and an increased risk of cracking. This corrosion phenomenon not only affects the durability of concrete, but may also lead to structural failure, seriously affecting the safety and service life of buildings. Traditional concrete protection measures are often unable to effectively deal with the complex problems caused by sulfate attack, so a solution that can enhance the concrete's resistance to sulfate attack is needed. In recent years, fiber reinforced plastics (FRP) 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 the cracking of gangue concrete in a sulfate attack environment remains a technical problem.

[0003] In the prior art, publication number CN118133627 discloses a simulation method and system for cracking analysis of concrete under sulfate attack, which establishes a mesoscopic concrete model according to a real concrete structure; obtains the mechanical and chemical parameters of each component of the real concrete and assigns them to the mesoscopic concrete model; applies boundary conditions to the mesoscopic concrete model according to the actual working environment of the concrete to simulate the actual sulfate attack cracking process of the concrete; divides the mesoscopic concrete model into grids and sets a solution error; constructs a chemical transmission force phase field coupling model under sulfate attack, and uses the coupling model to solve the cracking process of concrete under sulfate attack based on the grid division and the solution error in combination with the assigned parameters and the applied boundary conditions.

[0004] The main problems with the above method are: it involves coupling calculations with multiple models, requires many parameters when establishing the model, and is relatively complex. It is suitable for concrete structures of specific types and conditions, but when faced with other types of concrete and erosion conditions, the model needs to be re-established, and the scheme is not extensible enough; and when analyzing the cracking problem caused by sulfate, there is a lack of analysis of reinforcement measures, making it difficult to provide effective decision support.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The object of the present invention is to provide a simulation method for crack analysis of FRP-constrained gangue concrete under sulfate attack environment to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A simulation method for cracking analysis of FRP-confined gangue concrete under sulfate attack environment, the specific steps include:

[0009] Step 1: obtain a concrete sample that is the same as the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by a scanning electron microscope, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, collect a microstructure image of the sample, binarize the microstructure image through image processing software to distinguish the solid part and the pore part, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated, and generate a microstructure model;

[0010] Step 2: Initialize the sulfate concentration field in the microstructure model, determine the changes in the elastic modulus and Poisson's ratio of concrete based on the change in sulfate concentration, and 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 of the concrete structure model under mechanical load, and generate the stress of the concrete structure model under sulfate erosion according to the elastic modulus of concrete under sulfate erosion and the strain of the concrete structure model under mechanical load;

[0012] Step 4: Obtain the elastic modulus and tensile strength of the FRP material, add the FRP layer in the finite element software, generate a bonding contact model combining the concrete structure and the FRP layer, input the same mechanical load as that in the concrete structure model into the bonding contact model, measure the strain generated by the bonding contact model under the mechanical load, and generate the total stress of the bonding contact model under sulfate erosion based on the elastic modulus of the concrete under sulfate erosion environment and the strain generated by the bonding contact model under the mechanical load;

[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, the crack limitation factor under the influence of the FRP layer is generated in combination with the constraint effect of the FRP layer on crack extension. A constraint evaluation index is generated based on the stress intensity factor and the crack limitation factor. The constraint evaluation index is used to judge the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

[0014] Furthermore, the principle for binarizing the microstructure image is as follows:

[0015] The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level in the grayscale image is counted. The grayscale histogram is drawn, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by the maximum inter-class variance. The grayscale image is separated by the optimal segmentation threshold, and the solid part is marked as white and the pore part is marked as black. The principle for generating the optimal segmentation threshold is:

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

[0017] The principle for selecting the best segmentation threshold by maximizing the inter-class variance is:

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

[0019] Among them, a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, ω a Indicates the proportion of the solid part to the total image when the segmentation threshold is a, μ a Indicates the gray value of the solid part when the segmentation threshold is a, ω ′ a It indicates the proportion of the pore part to the total image when the segmentation threshold is a, μ ′ a It represents the gray value of the pore part 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 for generating the stress of the concrete structure model is based on:

[0022] σ h =1·∈0

[0023] Among them, σ h represents the stress of the concrete structure model, E1 represents the elastic modulus of concrete under sulfate attack environment, and ∈0 represents the strain generated by mechanical load in the concrete structure model.

[0024] Furthermore, the total stress of the bonded contact model is generated based on the principle:

[0025] The formula used to generate the stress in the FRP layer is:

[0026] σF = F ∈ F

[0027] Among them, σ F represents the stress in the FRP layer, E F represents the elastic modulus of the FRP layer, ∈ F represents the strain of the FRP layer;

[0028] The total stress for the bonded contact model is generated according to the formula:

[0029]

[0030] Among them, σ z represents the total stress of the bonded contact model, S F represents the cross-sectional area of ​​the FRP layer, S h represents the cross-sectional area of ​​the concrete structure, S represents the total area of ​​the entire cross-sectional area, and S = S F + h .

[0031] Furthermore, the principle for generating the constraint evaluation index is:

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

[0033]

[0034] Where K1 represents the stress intensity factor, σ h represents the stress of the concrete structure model, and a represents the input σ to the concrete structure model h Length of crack produced;

[0035] The formula for generating the crack limiting factor is:

[0036]

[0037] Among them, K2 represents the crack restriction factor, E represents the elastic modulus of concrete, and D h represents the thickness of concrete in the bonded contact model, E F represents the elastic modulus of the FRP layer, D F represents the thickness of the FRP layer in the bonded contact model, σ max represents the maximum stress that the FRP layer can withstand, σ z represents the total stress of the bonded contact model;

[0038] The formula for generating the constraint evaluation index is:

[0039]

[0040] Among them, 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 is.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention introduces sulfate concentration field into the microstructure model through microstructure modeling and multi-scale simulation, dynamically evaluates the influence of sulfate erosion on the properties of concrete, helps to accurately predict the changes in the mechanical properties of concrete under erosion environment, and improves the accuracy of simulation; and establishes a macroscopic concrete structure model through finite element analysis, combining the dual effects of chemical erosion and physical load, more accurately reflects the real stress state of the concrete structure under complex environment.

[0044] The present invention also combines the FRP layer with the concrete structure, analyzes the comprehensive performance of the two under interaction through the bonding contact model, and effectively evaluates the practical application value of FRP reinforcement technology in a sulfate corrosion environment. By generating the total stress of the bonding contact model, it can provide guidance for structural design optimization and material selection, ensure the durability and safety of the structure, and ultimately help improve the practicality and reliability of the overall solution; and calculate the stress intensity factor and crack limitation factor in the concrete structure model and the bonding contact model respectively, reflecting the relationship between material properties and reinforcement effects. By generating a constraint evaluation index, it more intuitively reflects the constraint effect of FRP on concrete, which helps to guide the measures taken. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The figure is a schematic diagram of the method flow of an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0047] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used 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] See also Figure 1 , the present invention provides a technical solution:

[0050] Step 1: obtain a concrete sample that is the same as the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by a scanning electron microscope, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, collect a microstructure image of the sample, binarize the microstructure image through image processing software to distinguish the solid part and the pore part, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated, and generate a microstructure model;

[0051] In this embodiment, a sample of 5×5×5 mm in size is cut from the gangue concrete, the surface of the sample is ground to ensure that the surface is flat and smooth, and the sample is dried in a drying oven. A layer of conductive material is sprayed on the surface of the dried sample to avoid charging during the observation process. The processed sample is fixed to a scanning electron microscope for observation by conductive adhesive. The pore size of the gangue concrete is usually 1 μm to 100 μm, and the micro aggregate is usually 50 nm, so the resolution range of the scanning electron microscope is 0.01 μm to 100 μm.

[0052] In this embodiment, the principle for binarizing the microstructure image is:

[0053] The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level in the grayscale image is counted. The grayscale histogram is drawn, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by the maximum inter-class variance. The grayscale image is separated by the optimal segmentation threshold, and the solid part is marked as white and the pore part is marked as black. The principle for generating the optimal segmentation threshold is:

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

[0055] The principle for selecting the best segmentation threshold by maximizing the inter-class variance is:

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

[0057] Among them, a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, ω a Indicates the proportion of the solid part to the total image when the segmentation threshold is a, μ a Indicates the gray value of the solid part when the segmentation threshold is a, ω ′ a It indicates the proportion of the pore part to the total image when the segmentation threshold is a, μ ′ a It represents the gray value of the pore part 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 based on CONSOL software, and the binarized microstructure image is imported into COMSOL. Material properties are assigned to each part in the microstructure image, including aggregate, pores, cement paste, etc. The material properties include Poisson's ratio and elastic model, which constitute the microstructure model.

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

[0061] In this embodiment, an initialization sodium sulfate concentration field is defined in the microstructure model, and the historical sulfate attack conditions of the coal gangue concrete area to be evaluated are obtained. As time goes by, the sulfate concentration tends to a stable value, and this stable value is used as the initial sulfate concentration. The diffusion process of sulfate in concrete is simulated, and the changes in the elastic modulus and Poisson's ratio of the concrete are measured as the sulfate attack process 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 the sulfate attack environment.

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

[0063] In this embodiment, the principle for generating the stress of the concrete structure model is:

[0064] σ h =1·∈0

[0065] Among them, σ h represents the stress of the concrete structure model, E1 represents the elastic modulus of concrete under sulfate attack environment, and ∈0 represents the strain generated by mechanical load 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 caused by the external mechanical load on the force input to the concrete structure is measured to determine the stress magnitude. 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 the FRP layer in the finite element software, generate a bonding contact model that combines the concrete structure and the FRP layer, and input the same mechanical load as that in the concrete structure model into the bonding contact model, measure the strain generated by the bonding contact model under the mechanical load, and generate the total stress of the bonding contact model under sulfate erosion based on the elastic modulus of the concrete under sulfate erosion environment and the strain generated by the bonding contact model under the mechanical load;

[0068] In this embodiment, the principle for generating the total stress of the bonding contact model is:

[0069] The formula used to generate the stress in the FRP layer is:

[0070] σ F = F ∈ F

[0071] Among them, σ F represents the stress in the FRP layer, E F represents the elastic modulus of the FRP layer, ∈ F represents the strain of the FRP layer;

[0072] The total stress for the bonded contact model is generated according to the formula:

[0073]

[0074] Among them, σz represents the total stress of the bonded contact model, S F represents the cross-sectional area of ​​the FRP layer, S h represents the cross-sectional area of ​​the concrete structure, S represents the total area of ​​the entire cross-sectional area, and S = S F + h .

[0075] Stress is the ratio of force to bearing area. In the bonded contact model, the overall 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 the FRP layer and the concrete layer are stacked and combined, 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, the crack limitation factor under the influence of the FRP layer is generated in combination with the constraint effect of the FRP layer on crack extension. A constraint evaluation index is generated based on the stress intensity factor and the crack limitation factor. The constraint evaluation index is used to judge the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

[0077] In this embodiment, the principle for generating the constraint evaluation index is:

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

[0079]

[0080] Where K1 represents the stress intensity factor, σ h represents the stress of the concrete structure model, and a represents the input σ to the concrete structure model h Length of crack produced;

[0081] The crack extension is evaluated based on linear elastic fracture mechanics, reflecting the trend of crack extension. It represents the influence of crack length on the stress field. As the crack length increases, the stress concentration effect at the crack tip increases and the crack expansion tendency increases.

[0082] The formula for generating the crack limiting factor is:

[0083]

[0084] Among them, K2 represents the crack restriction factor, E represents the elastic modulus of concrete, and D h represents the thickness of concrete in the bonded contact model, E F represents the elastic modulus of the FRP layer, D F represents the thickness of the FRP layer in the bonded contact model, σmax represents the maximum stress that the FRP layer can withstand, σ z represents the total stress of the bonded contact model;

[0085] The crack restriction factor reflects the inhibitory effect of the FRP layer on crack extension. It reflects the contribution of the concrete structure and FRP layer to the overall structural performance. It reflects the residual bearing capacity of the whole structure under the total stress. The maximum stress that the FRP layer can withstand is determined by inputting axial tension into the same FRP layer specimen until the specimen breaks. The stress value of the F specimen at the moment of fracture is the maximum stress that the FRP layer can withstand.

[0086] The formula for generating the constraint evaluation index is:

[0087]

[0088] Among them, 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 is.

[0090] When P is less than 1, K1 is less than K2. At this time, the limiting effect of the crack limiting factor on the crack is greater than the effect of the stress intensity factor on the crack extension. 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 and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0092] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods 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 separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0094] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A simulation method for crack analysis of FRP-constrained gangue concrete under sulfate attack environment, characterized in that: The specific steps include: Step 1: obtain a concrete sample that is the same as the coal gangue concrete to be evaluated, prepare the concrete sample into a sample suitable for observation by a scanning electron microscope, set the resolution of the scanning electron microscope to be able to identify pores and solid aggregates in the sample, collect a microstructure image of the sample, binarize the microstructure image through image processing software to distinguish the solid part and the pore part, and obtain the elastic modulus and Poisson's ratio of the coal gangue concrete to be evaluated, and generate a microstructure model; Step 2: Initialize the sulfate concentration field in the microstructure model, determine the changes in the elastic modulus and Poisson's ratio of concrete based on the change in sulfate concentration, and 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 of the concrete structure model under mechanical load, and generate the stress of the concrete structure model under sulfate erosion according to the elastic modulus of concrete under sulfate erosion and the strain of the concrete structure model under mechanical load; Step 4: Obtain the elastic modulus and tensile strength of the FRP material, add the FRP layer in the finite element software, generate a bonding contact model that combines the concrete structure and the FRP layer, and input the same mechanical load as that in the concrete structure model into the bonding contact model, measure the strain generated by the bonding contact model under the mechanical load, and generate the total stress of the bonding contact model under sulfate erosion based on the elastic modulus of the concrete under sulfate erosion environment and the strain generated by the bonding contact model under the mechanical load; 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, the crack limitation factor under the influence of the FRP layer is generated in combination with the constraint effect of the FRP layer on crack extension. A constraint evaluation index is generated based on the stress intensity factor and the crack limitation factor. The constraint evaluation index is used to judge the inhibitory effect of the FRP layer on the cracking of coal gangue concrete.

2. The simulation method for crack analysis of FRP-constrained gangue concrete under sulfate attack environment according to claim 1, characterized in that: The principle for binarizing the microstructure image in step 1 is: The microstructure image is converted into a grayscale image, and the frequency of occurrence of pixels at each grayscale level in the grayscale image is counted. The grayscale histogram is drawn, and the inter-class variance of each threshold in the histogram is calculated. The optimal segmentation threshold is selected by the maximum inter-class variance. The grayscale image is separated by the optimal segmentation threshold, and the solid part is marked as white and the pore part is marked as black. The principle for generating the optimal segmentation threshold is: Each threshold in the histogram represents the grayscale value of a pixel point that can be selected for image segmentation. In a grayscale image, the grayscale value ranges from 0 to 255, and the value of the threshold is all integers in the range of 0 to 255; The principle for selecting the best segmentation threshold by maximizing the inter-class variance is: g(a) 2 =ω a oh' a (m a -m′ a ) 2 Among them, a represents the segmentation threshold, g(a) represents the inter-class variance when the segmentation threshold is a, ω a Indicates the proportion of the solid part to the total image when the segmentation threshold is a, μ a Indicates the gray value of the solid part when the segmentation threshold is a, ω′ a It indicates the proportion of the pore part to the total image when the segmentation threshold is a, μ′ a It represents the gray value of the pore part 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 gangue concrete under sulfate attack environment according to claim 1, characterized in that: The principle for generating the stress of the concrete structure model in step 3 is: s h =E1 ∈0 Among them, σ h represents the stress of the concrete structure model, E1 represents the elastic modulus of concrete under sulfate attack environment, and ∈0 represents the strain generated by mechanical load in the concrete structure model.

4. The simulation method for crack analysis of FRP-constrained gangue concrete under sulfate attack environment according to claim 3, characterized in that: The principle for generating the total stress of the bonding contact model in step 4 is: The formula used to generate the stress in the FRP layer is: σ F =E F ·∈ F Among them, σ F represents the stress in the FRP layer, E F represents the elastic modulus of the FRP layer, ∈ F represents the strain of the FRP layer; The total stress for the bonded contact model is generated according to the formula: Among them, σ z represents the total stress of the bonded contact model, S F represents the cross-sectional area of ​​the FRP layer, S h represents the cross-sectional area of ​​the concrete structure, S represents the total area of ​​the entire cross-sectional area, and S = S F +S h .

5. The method for simulating crack analysis of FRP-constrained gangue concrete in a sulfate attack environment according to claim 1, characterized in that: The principle for generating the constraint evaluation index in step 5 is: The formula used to generate the stress intensity factor is: Where K1 represents the stress intensity factor, σ h represents the stress of the concrete structure model, and a represents the input σ to the concrete structure model h Length of crack produced; The formula for generating the crack limiting factor is: Among them, K2 represents the crack restriction factor, E represents the elastic modulus of concrete, and D h represents the thickness of concrete in the bonded contact model, E F represents the elastic modulus of the FRP layer, D F represents the thickness of the FRP layer in the bonded contact model, σ max represents the maximum stress that the FRP layer can withstand, σ z represents the total stress of the bonded contact model; The formula for generating the constraint evaluation index is: Among them, 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 is.

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