Construction method of constitutive model for concrete repair interface considering freeze-thaw effect

Abstract

The application discloses a method for constructing a constitutive model of a concrete repair interface considering the freezing and thawing effect, and steps are as follows: step 1, performing an interface direct shear test on a test piece with a concrete repair interface subjected to different numbers of freezing and thawing cycles, obtaining corresponding shear stress and shear strain of different numbers, and establishing an interface shear stress-strain relationship curve corresponding to different numbers; step 2, extracting three key parameters from each interface shear stress-strain relationship curve obtained in step 1, dividing the three key parameters into a pre-peak stage and a post-peak stage, and extracting two key parameters in the post-peak stage; step 3, constructing five key evolution functions of the freezing and thawing cycle number; and step 4, establishing a constitutive model of the pre-peak stage and a constitutive model of the post-peak stage according to the evolution functions. The constitutive model constructed by the method can reflect the characteristics of the whole interface shear change process.

Description

Technical Field

[0001] This invention belongs to the field of concrete structure repair and interface mechanical analysis technology, specifically involving a method for constructing a constitutive model of the concrete repair interface that takes freeze-thaw action into account. Background Technology

[0002] Concrete structures operating in cold regions are susceptible to repeated freeze-thaw cycles, leading to the formation and gradual expansion of microcracks within the material, thus deteriorating structural performance. When repairing concrete using polyurethane mortar, epoxy mortar, or cement-based materials, the repair interface often becomes a weak point in the structure, and its mechanical properties directly affect the repair effect and the overall structural safety.

[0003] In existing research, constitutive models for repair interfaces mostly use a single function to describe the interface shearing behavior, which makes it difficult to simultaneously reflect the full process characteristics of the interface from initial loading and nonlinear development to post-peak failure. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a constitutive model of a concrete repair interface that takes into account freeze-thaw action, thereby solving the problem that existing constitutive models cannot reflect the full process of interface shear change.

[0005] The technical solution adopted in this invention is a method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action, the steps of which are as follows: Step 1: Conduct interfacial direct shear tests on specimens with concrete repair interfaces that have undergone different numbers of freeze-thaw cycles to obtain the shear stress and shear strain corresponding to different numbers of cycles, and establish the interfacial shear stress-strain relationship curves corresponding to different numbers of cycles. Step 2: Extract three key parameters from each interface shear stress-strain relationship curve obtained in Step 1. Divide the curve into pre-peak stage and post-peak stage based on the three key parameters, and extract two key parameters in the post-peak stage. Step 3: Construct five evolution functions for the number of key iterations and the number of iterations. Step 4: Establish constitutive models for the pre-peak and post-peak stages based on the evolution function.

[0006] The invention is further characterized by: In step 1, the expression for shear stress is: (1) In equation (1), F is the shear load obtained through the interface direct shear test, in N; A is the interface shear area, in mm². Shear stress; The expression for shear strain is: (2) In equation (2), δ is the shear displacement obtained by the interfacial direct shear test, in mm; h is the thickness of the repair layer, in mm; For shear strain.

[0007] The specific process of step 2 is as follows: Step 2.1: Extract the peak shear stress from each interface shear stress-strain curve obtained in Step 1. Peak shear strain Initial shear stiffness data; Step 2.2, using the peak shear stress extracted in Step 2.1 and peak shear strain The corresponding point is used as the boundary point, and the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the pre-peak stage; the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the post-peak stage; Step 2.3: Extract residual shear stress in the post-peak stage. and residual shear strain .

[0008] In step 2.1, the initial shear stiffness The slope of the tangent at the origin of the interface shear stress-strain curve; In step 2.3, residual shear stress The value includes two cases. Case 1: In the post-peak stage, when the shear strain increases while the shear stress change does not exceed ±5%, the interface is determined to have entered the stable slip stage, and all shear stresses in this stable slip stage are taken. The average value is used as Case 2: If the stress drops abruptly after the peak and there is no obvious residual plateau, take the slope of the interface shear stress-shear strain curve in the post-peak stage. When the absolute value of the tangent slope is less than the peak shear stress... 1% and continuous shear strain When the increment exceeds 0.05, all shear stresses within that interval will be affected. The average value is used as ; Residual shear strain The value is: For case 1, the residual shear stress is taken as... The corresponding initial shear strain is used as Regarding scenario 2, residual shear stress The corresponding shear strain is as .

[0009] Step 3 involves the following steps: For each key parameter, the number of freeze-thaw cycles is used as the parameter. Perform a non - linear regression analysis with the independent variable to determine the optimal form based on the criterion that the goodness of fit is close to 1, and take the optimal form as the evolution function; The general expression of the evolution function for each key parameter is:

[0010]

[0011]

[0012]

[0013]

[0014] In the formula, , , , , are the parameter values when the number of freeze - thaw cycles is 0 respectively; to are regression functions that satisfy , and their specific forms are determined by fitting the test data.

[0015] In step 4, the expression of the constitutive model in the pre - peak stage is: (3) Where, (4) (5) In formulas (3) - (5), is the peak shear stress after n freeze - thaw cycles; is the peak shear strain after n freeze - thaw cycles; is the initial shear stiffness after n freeze - thaw cycles; x is the ratio of the current shear strain to the peak shear strain, which is a dimensionless strain variable; is the shape parameter, and its value reflects the type of pre - peak behavior of the interface. When m(n) < 1, the curve shows an initial hardening type; when m(n) = 1, it degenerates into an ideal elastic - plastic type; when 1 < m(n) < 3, it shows initial softening characteristics; The expression of the constitutive model in the post - peak stage is: (6) In formula (6), and are the residual shear stress and residual shear strain after cycles of freeze - thaw and after cycles of freeze - thaw respectively.

[0016] Step 4 is followed by step 5, the specific process of which is as follows: Step 5.1, calculate the evolution function obtained through step 3. , , , , These parameters are converted into input parameters for the cohesive force model in the finite element method software. Step 5.2: Set the friction coefficient in the friction model of the finite element method software. Legal contact behavior; Among them, the coefficient of friction The results were obtained by fitting the Mohr-Coulomb criterion through interfacial direct shear tests under different normal pressures. The normal contact behavior adopts a hard contact model; Step 5.3: The cohesive force model after setting parameters in Step 5.1 and the friction model after setting parameters in Step 5.2 are coupled through the post-damage activation friction module in the finite element software so that they can be activated sequentially at different stages. Step 5.4: Model and perform numerical analysis in the finite element software after the processing in step 5.3.

[0017] In step 5.1, the input parameters include tangential stiffness. Damage initiation stress Normal damage initiation stress, damage initiation displacement Completely destroy displacement ; in,

[0018] In the formula, h is the thickness of the repair layer;

[0019] The normal damage initiation stress adopts the maximum stress criterion, and is set to a value of [value missing]. 5% to 15% or determined by normal tensile testing;

[0020] .

[0021] In step 5.3, the activation process at different stages is as follows: Phase 1: When the interface is shifted At that time, only the cohesive force model is activated, when the shape parameter At this time, the nonlinearity in the pre-peak stage is not significant, and the cohesive model still adopts the general linear elasticity assumption. At that time, the cohesive force model adopts user-defined material embedding pre-peak stage constitutive model and post-peak stage constitutive model to achieve accurate nonlinear simulation; Phase Two: When At this time, the cohesive model dominates, and damage evolution degenerates according to the linear displacement softening criterion. At this point, the interfacial shear stress... from Gradually decrease to This corresponds to the constitutive model of the post-peak stage; Phase 3: When the interface shifts When the cohesive model completely fails, the friction model is activated, and the residual shear strength at the interface is determined by the friction coefficient. Together with the normal contact pressure, for pure shear loading conditions, the normal contact pressure is a constant generated by the clamp constraint, and the shear stress... Remaining as residual shear stress .

[0022] The specific process of step 5.4 is as follows: Step 5.4.1: Create a specimen in the finite element software. The specimen includes a base concrete component and a repair layer component. The specimen geometry is the same as that of the specimen in Step 1. Step 5.4.2: Apply the concrete damage plasticity model (CDP) to both the concrete and the repair layer materials; Step 5.4.3: Define a contact pair between the concrete and the repair layer, and simultaneously activate the cohesion model and the friction model in the contact properties; Step 5.4.4: Discretize the concrete and repair layer using three-dimensional eight-node hexahedral reduced integral elements, and refine the local mesh within a 5 mm thickness area at the repair interface; enlarge the element size in areas far from the interface. Step 5.4.5: Apply triaxial displacement constraint to the bottom of the base concrete and apply displacement control load to the top of the repair layer. The loading direction is parallel to the repair interface, and the loading rate is the same as the test conditions in Step 1. Step 5.4.6: Use the static universal analysis step, enable geometric nonlinearity, and set the initial increment step and minimum increment step to ensure convergence in the damage evolution stage; Step 5.4.7: Extract the reaction force and displacement at the loading end, convert them into shear stress and shear strain using equations (1) and (2), plot the interface shear stress-strain curve, and output the damage variable distribution cloud map to analyze the entire process of interface damage initiation, expansion and evolution.

[0023] The beneficial effects of this invention are: (1) The method of the present invention establishes the pre-peak stage constitutive model and the post-peak stage constitutive model in the form of piecewise functions, which can accurately describe the mechanical behavior of the interface from initial loading to peak value and then to failure. (2) The method of the present invention takes into account the effect of freeze-thaw cycles and establishes the relationship between key parameters and the number of freeze-thaw cycles, which can reflect the evolution law of interface mechanical properties with freeze-thaw cycles. (3) The present invention transforms the constitutive model of the pre-peak stage and the constitutive model and key parameters of the post-peak stage into the cohesive force model and the friction model, which can be directly applied to the finite element numerical calculation to realize the full process simulation of the interface under shear action, and has good engineering application value. Attached Figure Description

[0024] Figure 1 The shear stress-strain curves of the polyurethane mortar-concrete repair interface under different freeze-thaw cycles (0, 50, 100, 150 times) in Example 7 are shown. Figure 2 This is a comparison chart of the shear stress-strain curves from the finite element numerical simulation and physical experiment of zero freeze-thaw cycles in Example 7. Figure 3 This is a comparison chart of shear stress-strain curves from finite element numerical simulation and physical experiment of 50 freeze-thaw cycles in Example 7; Figure 4 This is a comparison chart of shear stress-strain curves from finite element numerical simulation and physical experiment of 100 freeze-thaw cycles in Example 7; Figure 5 This is a comparison chart of the shear stress-strain curves from the finite element numerical simulation and physical experiment of 150 freeze-thaw cycles in Example 7. Detailed Implementation The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0025] Example 1 The present invention provides a method for constructing a constitutive model of a concrete repair interface that considers freeze-thaw action. The steps are as follows: Step 1: Conduct interfacial direct shear tests on specimens with concrete repair interfaces that have undergone different numbers of freeze-thaw cycles. Record the shear load and shear displacement of each specimen. Obtain the shear stress and shear strain corresponding to different cycles based on the shear load and shear displacement, and establish the interfacial shear stress-strain relationship curves corresponding to different cycles. Step 2: Extract three key parameters from each interface shear stress-strain relationship curve obtained in Step 1. Divide the curve into pre-peak stage and post-peak stage based on the three key parameters, and extract two key parameters in the post-peak stage. Five key parameters include: peak shear stress Peak shear strain Initial shear stiffness Residual shear stress Residual shear strain ; Step 3: Construct five evolution functions for the number of key iterations and the number of iterations. Step 4: Since the interface shear stress-strain relationship curves have common characteristics (initial linearity, nonlinear rise, peak value, softening, and residual), constitutive models for the pre-peak stage and post-peak stage are established based on the evolution function.

[0026] Example 2 Based on Example 1, in step 1, the expression for shear stress is: (1) In equation (1), F is the shear load obtained through the interface direct shear test, in N; A is the interface shear area, in mm². Shear stress; The expression for shear strain is: (2) In equation (2), δ is the shear displacement obtained by the interfacial direct shear test, in mm; h is the thickness of the repair layer, in mm; For shear strain.

[0027] Example 3 Based on Example 2, the specific process of step 2 is as follows: Step 2.1: Extract the peak shear stress from each interface shear stress-strain curve obtained in Step 1. Peak shear strain Initial shear stiffness data; Among them, peak shear stress Take the maximum shear stress value on the interface shear stress-strain relationship curve; Peak shear strain ; Initial shear stiffness The slope of the tangent at the origin of the interface shear stress-strain curve is calculated using the following formula: ; Step 2.2, using the peak shear stress extracted in Step 2.1 and peak shear strain The corresponding point is used as the boundary point, and the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the pre-peak stage; the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the post-peak stage; Step 2.3: Extract residual shear stress in the post-peak stage. and residual shear strain ; Among them, residual shear stress The value can take two cases: Case 1: In the post-peak stage, when the shear strain increases while the shear stress change does not exceed ±5%, the interface is considered to have entered the stable slip stage, and all shear stresses in this stable slip stage are taken. The average value is used as ; Scenario 2: If the stress drops abruptly after the peak and there is no obvious residual plateau, take the slope of the interface shear stress-shear strain curve in the post-peak stage. When the absolute value of the tangent slope is less than the peak shear stress... 1% and continuous shear strain When the increment exceeds 0.05, all shear stresses within that interval will be affected. The average value is used as ; Residual shear strain The value can be: For case 1, take the residual shear stress. The corresponding initial shear strain is used as ; Regarding scenario 2, residual shear stress The corresponding shear strain is as .

[0028] Example 4 Based on Example 3, the specific process of step 3 is as follows: For each key parameter, the number of freeze-thaw cycles is used as the parameter. Perform nonlinear regression analysis on the independent variables to determine the goodness of fit. The optimal form is determined by the criterion of being close to 1, and the optimal form is used as the evolution function; Based on the distribution characteristics of the experimental data, the evolution function of each key parameter can be constructed by selecting power function, exponential function or polynomial function, etc. The general expression for the evolution function of each key parameter is:

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, , , , , These are the parameter values ​​when the number of freeze-thaw cycles is 0; to To meet The regression function, and its specific form is determined by fitting the experimental data.

[0034] Example 5 On the basis of Example 4, in step 4, the constitutive model in the pre-peak stage uses a normalized cubic function to describe the non-linear growth process of shear stress with shear strain, satisfying the following three boundary conditions: (1) When , ; (2) When, And the tangent slope is zero; (3) The tangent slope at the origin is the initial shear stiffness ; To adapt to the curve shape differences of different materials, the shape parameter m(n) is introduced; The expression of the constitutive model in the pre-peak stage is: (3) Where, (4) (5) In formulas (3) to (5), Is the peak shear stress after n freeze-thaw cycles; Is the peak shear strain after n freeze-thaw cycles; Is the initial shear stiffness after n freeze-thaw cycles; x Is the ratio of the current shear strain to the peak shear strain, which is a dimensionless strain variable; Is the shape parameter, and its numerical value reflects the type of pre-peak behavior of the interface. When m(n) < 1, the curve shows an initial hardening type. When m(n) = 1, it degenerates into an ideal elastic-plastic type. When 1 < m(n) < 3, it shows initial softening characteristics; The constitutive model in the post-peak stage uses linear softening to describe the degradation of bearing capacity. It is assumed that from the peak point To the residual point Between, the shear stress decreases linearly with the shear strain; The expression of the constitutive model in the post-peak stage is: (6) In formula (6), And Are respectively the residual shear stress after Freeze-thaw cycles and the residual shear strain after Freeze-thaw cycles.

[0035] Formula (6) is continuous with the constitutive model in the pre-peak stage at . When , the stress drops to . When At this point, the interface enters the full slip phase, and the shear stress remains at [value missing]. constant.

[0036] Example 6 Based on Example 5, step 5 is included after step 4, and the specific process is as follows: Step 5.1, calculate the evolution function obtained through step 3. , , , , (The parameters in the constitutive models for the pre-peak and post-peak stages constructed in step 4) , , , , The parameters are converted into input parameters for the cohesive force model in the finite element method software (ABAQUS). The cohesive model is used to describe the bonding behavior before the onset of interface damage and the softening process after the onset of damage. The input parameters include tangential stiffness. Damage initiation stress Normal damage initiation stress, damage initiation displacement Completely destroy displacement ; in,

[0037] In the formula, h is the thickness of the repair layer; Tangential stiffness Used to control the slope of the linear response of the interface before damage initiation;

[0038] When the interfacial shear stress reaches the damage initiation stress At that time, damage begins to occur; The normal damage initiation stress adopts the maximum stress criterion, and is set to a value of [value missing]. 5% to 15% or determined by normal tensile testing;

[0039]

[0040] Step 5.2: Set the friction coefficient in the friction model of the finite element method software. Legal contact behavior; The friction model is used to describe the residual shear capacity after the interface is completely destroyed. Its parameters are independent of the number of freeze-thaw cycles and mainly depend on the interface roughness and normal constraint conditions. Among them, the coefficient of friction The results were obtained by fitting the Mohr-Coulomb criterion through interfacial direct shear tests under different normal pressures. If interfacial direct shear tests were not conducted, commonly used values ​​can be used as a reference (0.3~0.6 for concrete-mortar interface). The normal contact behavior adopts a hard contact model, which means that the normal pressure can be transmitted without limit and the interface is allowed to separate under tension; this setting is a standard option in finite element software and does not change with the number of freeze-thaw cycles.

[0041] Step 5.3: To realize the complete mechanical behavior of the pre-peak stage, post-peak stage and residual stages, the cohesive force model after setting parameters in step 5.1 and the friction model after setting parameters in step 5.2 are coupled through the post-damage activation friction module in the finite element software, so as to activate the two models in different stages. The process of activation at different stages is as follows: Phase 1 (before damage initiation): When the interface is displaced At this time, only the cohesive model is activated. The interface behavior is then controlled by the pre-peak constitutive model, exhibiting a nonlinear growth from zero to the peak intensity. It should be noted that the cohesive model in general finite element software uses a linear elasticity assumption, while the pre-peak constitutive model established in step 3 is a cubic nonlinear function. Therefore, the following processing is performed: When shape parameters At this time, the nonlinearity in the pre-peak stage is not significant, and the cohesive model still adopts the general linear elasticity assumption. At that time, the cohesive force model adopts user-defined material embedding pre-peak stage constitutive model and post-peak stage constitutive model to achieve accurate nonlinear simulation; Phase Two (Damage Evolution Period): When At this time, the cohesive model dominates, and damage evolution degenerates according to the linear displacement softening criterion. At this point, the interfacial shear stress... from Gradually decrease to This corresponds to the constitutive model of the post-peak stage; Phase 3 (after complete destruction): When the interface shifts When the cohesive model completely fails, the friction model is activated, and the residual shear strength at the interface is determined by the friction coefficient. Together with the normal contact pressure, for pure shear loading conditions, the normal contact pressure is a constant generated by the clamp constraint, and the shear stress... Remaining as residual shear stress ; Step 5.4: Model and perform numerical analysis in the finite element software after the processing in step 5.3; The specific process is as follows: Step 5.4.1: Create a specimen in the finite element software. The specimen includes a base concrete component and a repair layer component. The specimen geometry is the same as that of the specimen in Step 1. Step 5.4.2: The concrete and repair layer materials are respectively assigned the concrete damage plasticity model (CDP). The material parameters can be determined according to independent material tests or relevant specifications. Step 5.4.3: Define a contact pair between the concrete and the repair layer, and simultaneously activate the cohesion model and the friction model in the contact properties; Step 5.4.4: The concrete and repair layer are discretized using a three-dimensional eight-node hexahedral reduced integral element (C3D8R). To ensure calculation accuracy, the local mesh is refined in the 5 mm thickness area of ​​the repair interface; the element size in the area far from the interface is enlarged (e.g., 10 mm) to take into account the calculation efficiency. Step 5.4.5: Apply triaxial displacement constraint to the bottom of the base concrete and apply displacement control load to the top of the repair layer. The loading direction is parallel to the repair interface, and the loading rate is the same as the test conditions in Step 1. Using displacement control loading can avoid the calculation convergence problem of the constitutive model in the post-peak stage and can obtain the complete interface shear stress-shear strain curve in the post-peak stage. Step 5.4.6: Use the static universal analysis step, enable geometric nonlinearity, and set the initial increment step and minimum increment step to ensure convergence in the damage evolution stage; Step 5.4.7: Extract the reaction force and displacement at the loading end, convert them into shear stress and shear strain using equations (1) and (2), plot the interface shear stress-strain curve, and output the damage variable distribution cloud map to analyze the entire process of interface damage initiation, expansion and evolution.

[0042] Example 7 The specimen used in this embodiment uses polyurethane mortar as the repair material (thickness of 50mm) and ordinary concrete with a strength grade of C40 as the base (thickness of 50mm). The specimen size is 100 mm × 100 mm × 100 mm. The specific implementation process of the present invention is described in detail according to the method described in Example 6.

[0043] Step 1: Conduct interfacial direct shear tests on specimens with concrete repair interfaces subjected to different numbers of freeze-thaw cycles. Obtain the shear stress and shear strain corresponding to different cycles using formulas (1) and (2), and establish the interfacial shear stress-strain relationship curves corresponding to different cycles, as shown in the figure. Figure 1 As shown; The freeze-thaw cycle regime refers to GB / T 50082-2009, with a freezing temperature of -20℃, a thawing temperature of 10℃, a single cycle period of 4 hours, and the number of cycles set to n=0, 50, 100, and 150 times. Step 2: Extract three key parameters from each interface shear stress-strain relationship curve obtained in Step 1. Divide the curve into pre-peak stage and post-peak stage based on the three key parameters, and extract two key parameters in the post-peak stage. The specific process is as follows: Step 2.1: Extract the peak shear stress from each interface shear stress-strain curve obtained in Step 1. Peak shear strain Initial shear stiffness data; Initial shear stiffness The slope of the tangent at the origin of the interface shear stress-strain curve; Step 2.2, using the peak shear stress extracted in Step 2.1 and peak shear strain The corresponding point is used as the boundary point, and the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the pre-peak stage; the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the post-peak stage; Step 2.3: Extract residual shear stress in the post-peak stage. and residual shear strain ; Residual shear stress The value includes two cases. Case 1: In the post-peak stage, when the shear strain increases while the shear stress change does not exceed ±5%, the interface is determined to have entered the stable slip stage, and all shear stresses in this stable slip stage are taken. The average value is used as Case 2: If the stress drops abruptly after the peak and there is no obvious residual plateau, take the slope of the interface shear stress-shear strain curve in the post-peak stage. When the absolute value of the tangent slope is less than the peak shear stress... 1% and continuous shear strain When the increment exceeds 0.05, all shear stresses within that interval will be affected. The average value is used as ; Residual shear strain The value is: For case 1, the residual shear stress is taken as... The corresponding initial shear strain is used as Regarding scenario 2, residual shear stress The corresponding shear strain is as ; The five key parameters extracted are shown in Table 1. Table 1

[0044] Step 3: Construct five evolution functions for the number of key iterations and the number of iterations. The specific process is as follows: For each key parameter, the number of freeze-thaw cycles is used as the parameter. Perform nonlinear regression analysis on the independent variables to determine the goodness of fit. The optimal form is determined by the criterion of being close to 1, and the optimal form is used as the evolution function; The evolution function for each key parameter is expressed as follows:

[0045]

[0046]

[0047]

[0048]

[0049] Step 4: Substitute the data obtained through the evolution function into formulas (3) to (5) to obtain the constitutive model of the pre-peak stage, taking the unfrozen state (n=0) as an example:

[0050] The pre-peak constitutive equations for other freeze-thaw cycles can be obtained in the same way; Substituting the data obtained through the evolution function into formula (6), we obtain the constitutive model of the post-peak stage, taking the unfrozen state as an example:

[0051] The post-peak constitutive equations for other freeze-thaw cycles can be obtained in the same way.

[0052] Step 5: Convert the pre-peak stage constitutive model, post-peak stage constitutive model, and evolution function into input parameters for the cohesion model and friction model in the finite element software (ABAQUS); Specifically: Step 5.1, calculate the evolution function obtained through step 3. , , , , The input parameters are converted into the cohesive force model in the finite element method software. The specific parameter values ​​are shown in Table 2. Table 2

[0053] Step 5.2: Set the friction coefficient in the friction model of the finite element method software. Legal contact behavior; Among them, the coefficient of friction (Calibrated by clamp constraints), normal behavior adopts hard contact; Step 5.3: The cohesive force model after setting parameters in Step 5.1 and the friction model after setting parameters in Step 5.2 are coupled through the post-damage activation friction module in the finite element software, so as to activate them sequentially at different stages. The process of activation at different stages is as follows: Phase 1: When the interface is shifted At that time, only the cohesive force model is activated, when the shape parameter At this time, the nonlinearity in the pre-peak stage is not significant, and the cohesive model still adopts the general linear elasticity assumption. At that time, the cohesive force model adopts user-defined material embedding pre-peak stage constitutive model and post-peak stage constitutive model to achieve accurate nonlinear simulation; Phase Two: When At this time, the cohesive model dominates, and damage evolution degenerates according to the linear displacement softening criterion. At this point, the interfacial shear stress... from Gradually decrease to This corresponds to the constitutive model of the post-peak stage; Phase 3: When the interface shifts When the cohesive model completely fails, the friction model is activated, and the residual shear strength at the interface is determined by the friction coefficient. Together with the normal contact pressure, for pure shear loading conditions, the normal contact pressure is a constant generated by the clamp constraint, and the shear stress... Remaining as residual shear stress ; Step 5.4: Model and perform numerical analysis in the finite element software after the processing in step 5.3; The specific process is as follows: Step 5.4.1: Create a specimen in the finite element software. The specimen includes a base concrete component (100mm×100mm×50mm) and a repair layer component (100mm×100mm×50mm). The specimen geometry is the same as that of the specimen in Step 1. Step 5.4.2: Apply the concrete damage plasticity model (CDP) to both the concrete and the repair layer materials; Step 5.4.3: Define a contact pair between the concrete and the repair layer. In the contact properties, activate both the cohesion model and the friction model. The tangential behavior adopts the penalty function friction model with a friction coefficient of 0.3. The normal behavior adopts hard contact. Input the cohesion model parameters for different freeze-thaw cycles according to Table 2. Step 5.4.4: Discretize the concrete and repair layer using a three-dimensional eight-node hexahedral reduced integral element (C3D8R), and refine the local mesh within a 5 mm thickness area at the repair interface; set the element size to 10 mm in areas far from the interface. Step 5.4.5: Apply triaxial displacement constraint to the bottom of the base concrete and apply displacement control load to the top of the repair layer. The loading direction is parallel to the repair interface, and the loading rate is set to 1 mm / s according to the test conditions. Step 5.4.6: Use the static universal analysis step, enable geometric nonlinearity, and set the initial increment step and minimum increment step to ensure convergence in the damage evolution stage; Step 5.4.7: Extract the reaction force and displacement at the loading end, convert them into shear stress and shear strain using equations (1) and (2), plot the interface shear stress-strain curve, and output the damage variable (SDEG) distribution cloud map to analyze the entire process of interface damage initiation, expansion and evolution.

[0054] To verify the accuracy and effectiveness of the method of this invention, the interface shear stress-shear strain curve obtained in step 5.4.7 was compared with the experimentally measured results curves in step 2 under different freeze-thaw cycles (0, 50, 100, 150 times). The results are as follows: Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown in Table 3, three key parameters—peak shear stress, peak shear strain, and initial shear stiffness—were extracted and compared with the data obtained in step 2.

[0055] Table 3

[0056] As shown in Table 3, the relative errors of peak shear stress and initial shear stiffness are both within 5%, and the relative error of peak shear strain is within 10%. The numerical simulation curves and experimental curves show good agreement at all stages. These results fully verify the accuracy and effectiveness of the method of this invention.

Claims

1. A method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action, characterized in that, The steps are as follows: Step 1: Conduct interfacial direct shear tests on specimens with concrete repair interfaces that have undergone different numbers of freeze-thaw cycles to obtain the shear stress and shear strain corresponding to different numbers of cycles, and establish the interfacial shear stress-strain relationship curves corresponding to different numbers of cycles. Step 2: Extract three key parameters from each interface shear stress-strain relationship curve obtained in Step 1. Divide the curve into pre-peak stage and post-peak stage based on the three key parameters, and extract two key parameters in the post-peak stage. Step 3: Construct five evolution functions for the number of key iterations and the number of iterations. Step 4: Establish constitutive models for the pre-peak and post-peak stages based on the evolution function.

2. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 1, characterized in that, In step 1, the expression for shear stress is: （1） In equation (1), F is the shear load obtained through the interface direct shear test, in N; A is the interface shear area, in mm². Shear stress; The expression for shear strain is: （2） In equation (2), δ is the shear displacement obtained by the interfacial direct shear test, in mm; h is the thickness of the repair layer, in mm; For shear strain.

3. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 2, characterized in that, The specific process of step 2 is as follows: Step 2.1: Extract the peak shear stress from each interface shear stress-strain curve obtained in Step 1. Peak shear strain Initial shear stiffness data; Step 2.2, using the peak shear stress extracted in Step 2.1 and peak shear strain The corresponding point is used as the boundary point, and the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the pre-peak stage; the shear strain in the interface shear stress-strain relationship curve is... The portion is divided into the post-peak stage; Step 2.3: Extract residual shear stress in the post-peak stage. and residual shear strain .

4. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 3, characterized in that, In step 2.1, the initial shear stiffness The slope of the tangent at the origin of the interface shear stress-strain curve; In step 2.3, residual shear stress The value includes two cases. Case 1: In the post-peak stage, when the shear strain increases while the shear stress change does not exceed ±5%, the interface is determined to have entered the stable slip stage, and all shear stresses in this stable slip stage are taken. The average value is used as Case 2: If the stress drops abruptly after the peak and there is no obvious residual plateau, take the slope of the interface shear stress-shear strain curve in the post-peak stage. When the absolute value of the tangent slope is less than the peak shear stress... 1% and continuous shear strain When the increment exceeds 0.05, all shear stresses within that interval will be affected. The average value is used as ; Residual shear strain The value is: For case 1, the residual shear stress is taken as... The corresponding initial shear strain is used as Regarding scenario 2, residual shear stress The corresponding shear strain is as .

5. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 4, characterized in that, Step 3 involves the following steps: For each key parameter, the number of freeze-thaw cycles is used as the parameter. Perform nonlinear regression analysis on the independent variables to determine the goodness of fit. The optimal form is determined by the criterion of being close to 1, and the optimal form is used as the evolution function; The general expression for the evolution function of each key parameter is: In the formula, , , , , These are the parameter values ​​when the number of freeze-thaw cycles is 0; to To meet The regression function, in its specific form, is determined by fitting the experimental data.

6. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 5, characterized in that, In step 4, the expression for the constitutive model in the pre-peak stage is: （3） in, （4） （5） In Formulas (3) to (5), is the peak shear stress after n freeze-thaw cycles; is the peak shear strain after n freeze-thaw cycles; is the initial shear stiffness after n freeze-thaw cycles; x is the ratio of the current shear strain to the peak shear strain, which is a dimensionless strain variable; is the shape parameter, and its numerical value reflects the type of pre-peak behavior of the interface. When m(n) < 1, the curve shows an initial hardening type. When m(n) = 1, it degenerates into an ideal elastic-plastic type. When 1 < m(n) < 3, it exhibits initial softening characteristics; The expression for the post-peak constitutive model is: （6） In equation (6), and They are respectively through Residual shear stress after one freeze-thaw cycle and Residual shear strain after one freeze-thaw cycle.

7. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 6, characterized in that, Step 4 is followed by step 5, the specific process of which is as follows: Step 5.1, calculate the evolution function obtained through step 3. , , , , These parameters are converted into input parameters for the cohesive force model in the finite element method software. Step 5.2: Set the friction coefficient in the friction model of the finite element method software. Legal contact behavior; Among them, the coefficient of friction The results were obtained by fitting the Mohr-Coulomb criterion through interfacial direct shear tests under different normal pressures. The normal contact behavior adopts a hard contact model; Step 5.3: The cohesive force model after setting parameters in Step 5.1 and the friction model after setting parameters in Step 5.2 are coupled through the post-damage activation friction module in the finite element software, so as to activate them sequentially at different stages. Step 5.4: Model and perform numerical analysis in the finite element software after the processing in step 5.

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8. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 7, characterized in that, In step 5.1, the input parameters include tangential stiffness. Damage initiation stress Normal damage initiation stress, damage initiation displacement Completely destroy displacement ; in, In the formula, h is the thickness of the repair layer; The normal damage initiation stress adopts the maximum stress criterion, and is set to a value of [value missing]. 5% to 15% or determined by normal tensile testing; 。 9. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 7, characterized in that, In step 5.3, the activation process at different stages is as follows: Phase 1: When the interface is shifted At that time, only the cohesive force model is activated, when the shape parameter At this time, the nonlinearity in the pre-peak stage is not significant, and the cohesive model still adopts the general linear elasticity assumption. At that time, the cohesive force model adopts user-defined material embedding pre-peak stage constitutive model and post-peak stage constitutive model to achieve accurate nonlinear simulation; Phase Two: When At this time, the cohesive model dominates, and damage evolution degenerates according to the linear displacement softening criterion. At this point, the interfacial shear stress... from Gradually decrease to This corresponds to the constitutive model of the post-peak stage; Phase 3: When the interface shifts When the cohesive model completely fails, the friction model is activated, and the residual shear strength at the interface is determined by the friction coefficient. Together with the normal contact pressure, for pure shear loading conditions, the normal contact pressure is a constant generated by the clamp constraint, and the shear stress... Remaining as residual shear stress .

10. The method for constructing a constitutive model of a concrete repair interface considering freeze-thaw action according to claim 7, characterized in that, The specific process of step 5.4 is as follows: Step 5.4.1: Create a specimen in the finite element software. The specimen includes a base concrete component and a repair layer component. The specimen geometry is the same as that of the specimen in Step 1. Step 5.4.2: Apply the concrete damage plasticity model (CDP) to both the concrete and the repair layer materials; Step 5.4.3: Define a contact pair between the concrete and the repair layer, and simultaneously activate the cohesion model and the friction model in the contact properties; Step 5.4.4: Discretize the concrete and repair layer using three-dimensional eight-node hexahedral reduced integral elements, and refine the local mesh within a 5 mm thickness area at the repair interface; enlarge the element size in areas far from the interface. Step 5.4.5: Apply triaxial displacement constraint to the bottom of the base concrete and apply displacement control load to the top of the repair layer. The loading direction is parallel to the repair interface, and the loading rate is the same as the test conditions in Step 1. Step 5.4.6: Use the static universal analysis step, enable geometric nonlinearity, and set the initial increment step and minimum increment step to ensure convergence in the damage evolution stage; Step 5.4.7: Extract the reaction force and displacement at the loading end, convert them into shear stress and shear strain using equations (1) and (2), plot the interface shear stress-strain curve, and output the damage variable distribution cloud map to analyze the entire process of interface damage initiation, expansion and evolution.

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