Damage model building method of recycled brick-concrete aggregate

Abstract

The invention belongs to the technical field of construction waste resource utilization, and particularly relates to a method for establishing a damage model of recycled brick-concrete aggregate. The invention discloses a method for establishing a damage model of recycled brick-concrete aggregate. The method comprises the following steps: selecting a recycled brick-concrete aggregate concrete standard test piece; determining an initial damage variable of the recycled brick-concrete aggregate concrete standard test piece; determining a uniaxial loading damage variable of the recycled brick-concrete aggregate concrete standard test piece; determining the total damage variable of the recycled brick-concrete aggregate concrete standard test piece; and determining the freeze-thaw damage constitutive model of the recycled concrete. According to the method, factors such as the freezing and thawing cycle times, the load level and the self characteristics of the regenerated brick-concrete aggregate are comprehensively considered, and the damage model capable of accurately reflecting the mechanical property change rule of the regenerated brick-concrete aggregate concrete under the freezing and thawing-load coupling effect is constructed; a solid theoretical support is provided for recycled concrete structure design and safety evaluation in cold regions or complex stress environments, and long-term safe and reliable operation of building structures is guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of resource utilization of construction waste, and in particular relates to a method for establishing a damage model of recycled brick-concrete aggregate. Background Art

[0002] In recent years, as the construction industry develops towards high efficiency, environmental protection and sustainability, the application of recycled concrete as a green and environmentally friendly material in the construction field has shown an increasingly widespread trend. It not only effectively solves the problem of construction waste disposal, but also alleviates the pressure of shortage of natural aggregate resources to a certain extent. However, in actual engineering application scenarios, the use environment of recycled brick-concrete aggregate concrete is complex. Especially in cold areas, or in building structures that are subjected to complex stress conditions, recycled brick-concrete aggregate concrete is often subjected to the coupling of freeze-thaw and load. This freeze-thaw cycle process will cause pore pressure and osmotic pressure inside the concrete, leading to the generation and expansion of microcracks; and the load acting at the same time will further aggravate the development of these microcracks and change the stress distribution state inside the concrete. This coupling of freeze-thaw and load affects and promotes each other, which has an extremely significant impact on the mechanical properties of recycled brick-concrete aggregate concrete. For example, its key mechanical performance indicators such as compressive strength, tensile strength, and elastic modulus will change, thereby affecting the bearing capacity and stability of the structure.

[0003] At present, although the academic and engineering communities have conducted some research on the mechanical properties of recycled concrete under the influence of a single factor (such as freeze-thaw alone or load alone), there is still a lack of accurate, comprehensive and highly adaptable model descriptions for the change laws of the mechanical properties of recycled brick-concrete aggregate concrete under such complex working conditions, that is, the coupling of freeze-thaw and load. The lack of such a model is largely not conducive to the scientific design and safety assessment of recycled concrete structures in cold regions or complex stress environments. When designing such structures, engineers often cannot accurately predict the performance changes of the structure during long-term use due to the lack of accurate theoretical basis, which may lead to problems of over-design or under-design; in terms of safety assessment, it is also difficult to accurately judge the safety margin of the structure under complex working conditions, which brings potential risks to the long-term safe use of the building structure. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to provide a method for establishing a damage model of recycled brick-concrete aggregate. The present invention comprehensively considers multiple factors such as the number of freeze-thaw cycles, load level, and the characteristics of the recycled brick-concrete aggregate itself, and constructs a damage model that can accurately reflect the change law of the mechanical properties of recycled brick-concrete aggregate concrete under freeze-thaw-load coupling. It provides a solid theoretical support for engineers to carry out recycled concrete structure design and safety assessment in cold areas or complex stress environments, thereby effectively avoiding over-design or under-design, more accurately controlling the safety margin of the structure under complex working conditions, and ensuring the long-term safe and reliable operation of the building structure, thereby promoting a wider and scientific application of recycled concrete technology in the construction industry.

[0005] The technical solution of the present invention is: a method for establishing a damage model of recycled brick-concrete aggregate, comprising the following steps:

[0006] S1: Select the standard specimen of recycled brick-concrete aggregate concrete, and the initial damage of the standard specimen of recycled brick-concrete aggregate concrete is 0;

[0007] S2: Determine the initial damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows:

[0008] S21: The standard specimen of recycled brick-concrete aggregate concrete was subjected to several freeze-thaw-load couplings. The initial damage variable of the standard specimen of recycled brick-concrete aggregate concrete was:

[0009]

[0010] Where: D0 is the initial damage variable of the material after freeze-thaw-load coupling; E0 is the elastic modulus of the standard specimen of recycled brick-concrete aggregate concrete; E n is the elastic modulus of the material after several freeze-thaw cycles;

[0011] S22: Considering that the stress level applied in the freeze-thaw-load coupling will cause an acceleration effect on the damage caused by freeze-thaw, the initial damage variable in step S2 is corrected, specifically:

[0012]

[0013] Where: D n Modify the initial damage variable for the material after freeze-thaw-load coupling; α s is the correction coefficient of the initial elastic modulus at different stress levels in the freeze-thaw-load coupling action; the elastic modulus of recycled brick-concrete aggregate concrete with stress levels S=0, S=0.2, S=0.4, and S=0.6 is fitted with the S=0 group as the standard, and the relationship between the stress level S and the correction coefficient is finally obtained:

[0014] αs =0.98027-1.12742S,R 2 =0.99067 (3)

[0015] Finally, the modified initial damage variable function of recycled brick-concrete aggregate concrete after freeze-thaw-load coupling is obtained:

[0016]

[0017] S3: Determine the uniaxial loading damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows:

[0018] The bearing surface of the standard specimen of recycled brick-concrete aggregate concrete is composed of countless microelements. Some microelements are damaged and then withdrawn from work. The damage caused by stress in the freeze-thaw-load coupling is defined as the ratio of the number of damaged microelements to the total number of microelements on the surface:

[0019]

[0020] Where: D c A is the damage generated during uniaxial compression; i is the number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete; A is the total number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete;

[0021] According to the Lemaitre strain equivalence principle, the relationship between stress and strain is:

[0022] σ=(0.98027-1.12742S)E n ε(1-D c ) (6)

[0023] The uniaxial compressive damage constitutive relation of the standard specimen of recycled brick-concrete aggregate concrete under freeze-thaw-load coupling is:

[0024]

[0025] S4: Determine the total damage variable of the standard specimen of recycled brick-concrete aggregate concrete as:

[0026]

[0027] The interface micro-element strength obeys the Weibull distribution, and its probability density function is:

[0028]

[0029] Where: F is the distribution variable of the micro-element strength; λ and k are distribution parameters;

[0030] Under certain strain conditions, the number of damaged interface microelements Ai The relationship with the total number of interface elements A can be expressed as:

[0031]

[0032] Substituting into formula (5) we can get:

[0033]

[0034] Substituting equation (4) and equation (11) into equation (8) yields the total damage:

[0035]

[0036] Combining equations (6) and (11), it can be seen that the constitutive relationship of recycled brick-concrete aggregate concrete subjected to different freeze-thaw-load levels is:

[0037]

[0038] S5: Determine the freeze-thaw damage constitutive model of recycled concrete. The specific process is as follows:

[0039] According to the boundary conditions of the stress-strain curve, the model distribution parameters are determined as:

[0040] ①ε=0,σ=0

[0041] ②ε=ε p , σ=σ p

[0042] ③ε=ε p ,

[0043] By taking the derivative of formula (10), we can get:

[0044]

[0045] According to boundary condition ②, we can get:

[0046]

[0047] According to boundary condition ③, we can get:

[0048]

[0049] Combining the above formula (14), formula (15), and formula (16), we can get the scale parameter Shape parameters

[0050] Substituting into formula (13), the freeze-thaw damage constitutive model of recycled concrete is obtained as follows:

[0051]

[0052] Thus, the freeze-thaw damage constitutive model of recycled concrete is established.

[0053] The technical effect of the present invention is that: the present invention comprehensively considers multiple factors such as the number of freeze-thaw cycles, load level and the characteristics of recycled brick-concrete aggregates themselves, and constructs a damage model that can accurately reflect the change law of the mechanical properties of recycled brick-concrete aggregate concrete under freeze-thaw-load coupling. It provides solid theoretical support for engineers to carry out recycled concrete structure design and safety assessment in cold areas or complex stress environments, thereby effectively avoiding over-design or under-design, more accurately controlling the safety margin of the structure under complex working conditions, and ensuring the long-term safe and reliable operation of the building structure, thereby promoting a wider and scientific application of recycled concrete technology in the construction industry.

[0054] The following is a further description with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a linear fitting diagram of the model parameter λ and the number of freeze-thaw cycles in the embodiment of the present invention.

[0056] Figure 2 It is a linear fitting diagram of the model parameter k and the number of freeze-thaw cycles in the embodiment of the present invention.

[0057] Figure 3 Embodiment E of the present invention n Fitting plot of the functional relationship between freeze-thaw cycles and stress level.

[0058] Figure 4 This is a diagram showing the influence of the number of freeze-thaw cycles on the damage variables in an embodiment of the present invention.

[0059] Figure 5 Graph showing the influence of stress level on damage variables according to an embodiment of the present invention.

[0060] Figure 6 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0-0 test block.

[0061] Figure 7 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0-40 test block.

[0062] Figure 8 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0-80 test block.

[0063] Fig. 9 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0-120 test block.

[0064] Fig.10 It is a comparison chart of the constitutive model curve after correction of the embodiment of the present invention and the test data of the RB-CAC-0-160 test block.

[0065] Fig.11 It is a comparison chart of the constitutive model curve after correction of the embodiment of the present invention and the test data of the RB-CAC-0.2-40 test block.

[0066] Fig.12 It is a comparison chart of the constitutive model curve after correction of the embodiment of the present invention and the test data of the RB-CAC-0.2-80 test block.

[0067] Fig.13 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.2-120 test block.

[0068] Fig.14 It is a comparison chart of the constitutive model curve after correction of the embodiment of the present invention and the test data of the RB-CAC-0.2-160 test block.

[0069] Fig.15 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.4-40 test block.

[0070] Fig.16 It is a comparison chart of the constitutive model curve after correction of the embodiment of the present invention and the test data of the RB-CAC-0.4-80 test block.

[0071] Fig.17 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.4-120 test block.

[0072] Fig.18 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.6-20 test block.

[0073] Fig.19 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.6-40 test block.

[0074] Fig. 20 It is a comparison chart of the constitutive model curve after correction in the embodiment of the present invention and the test data of the RB-CAC-0.6-60 test block. DETAILED DESCRIPTION

[0075] Example 1

[0076] A method for establishing a damage model of recycled brick-concrete aggregate comprises the following steps:

[0077] S1: Select the standard specimen of recycled brick-concrete aggregate concrete, and the initial damage of the standard specimen of recycled brick-concrete aggregate concrete is 0;

[0078] S2: Determine the initial damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows:

[0079] S21: The standard specimen of recycled brick-concrete aggregate concrete was subjected to several freeze-thaw-load couplings. The initial damage variable of the standard specimen of recycled brick-concrete aggregate concrete was:

[0080]

[0081] Where: D0 is the initial damage variable of the material after freeze-thaw-load coupling; E0 is the elastic modulus of the standard specimen of recycled brick-concrete aggregate concrete; E n is the elastic modulus of the material after several freeze-thaw cycles;

[0082] S22: Considering that the stress level applied in the freeze-thaw-load coupling will cause an acceleration effect on the damage caused by freeze-thaw, the initial damage variable in step S2 is corrected, specifically:

[0083]

[0084] Where: D n Modify the initial damage variable for the material after freeze-thaw-load coupling; α s is the correction coefficient of the initial elastic modulus at different stress levels in the freeze-thaw-load coupling action; the elastic modulus of recycled brick-concrete aggregate concrete with stress levels S=0, S=0.2, S=0.4, and S=0.6 is fitted with the S=0 group as the standard, and the relationship between the stress level S and the correction coefficient is finally obtained:

[0085] α s =0.98027-1.12742S,R 2 =0.99067 (3)

[0086] Finally, the modified initial damage variable function of recycled brick-concrete aggregate concrete after freeze-thaw-load coupling is obtained:

[0087]

[0088] S3: Determine the uniaxial loading damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows:

[0089] The bearing surface of the standard specimen of recycled brick-concrete aggregate concrete is composed of countless microelements. Some microelements are damaged and then withdrawn from work. The damage caused by stress in the freeze-thaw-load coupling is defined as the ratio of the number of damaged microelements to the total number of microelements on the surface:

[0090]

[0091] Where: D c A is the damage generated during uniaxial compression; i is the number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete; A is the total number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete;

[0092] According to the Lemaitre strain equivalence principle, the relationship between stress and strain is:

[0093] σ=(0.98027-1.12742S)E n ε(1-D c ) (6)

[0094] The uniaxial compressive damage constitutive relation of the standard specimen of recycled brick-concrete aggregate concrete under freeze-thaw-load coupling is:

[0095]

[0096] S4: Determine the total damage variable of the standard specimen of recycled brick-concrete aggregate concrete as:

[0097]

[0098] The interface micro-element strength obeys the Weibull distribution, and its probability density function is:

[0099]

[0100] Where: F is the distribution variable of the micro-element strength; λ and k are distribution parameters;

[0101] Under certain strain conditions, the number of damaged interface microelements A i The relationship with the total number of interface elements A can be expressed as:

[0102]

[0103] Substituting into formula (5) we can get:

[0104]

[0105] Substituting equation (4) and equation (11) into equation (8) yields the total damage:

[0106]

[0107] Combining equations (6) and (11), it can be seen that the constitutive relationship of recycled brick-concrete aggregate concrete subjected to different freeze-thaw-load levels is:

[0108]

[0109] S5: Determine the freeze-thaw damage constitutive model of recycled concrete. The specific process is as follows:

[0110] According to the boundary conditions of the stress-strain curve, the model distribution parameters are determined as:

[0111] ①ε=0,σ=0

[0112] ②ε=ε p , σ=σ p

[0113] ③ε=ε p ,

[0114] By taking the derivative of formula (10), we can get:

[0115]

[0116] According to boundary condition ②, we can get:

[0117]

[0118] According to boundary condition ③, we can get:

[0119]

[0120] Combining the above formula (14), formula (15), and formula (16), we can get the scale parameter Shape parameters

[0121] Substituting into formula (13), the freeze-thaw damage constitutive model of recycled concrete is obtained as follows:

[0122]

[0123] Thus, the freeze-thaw damage constitutive model of recycled concrete is established.

[0124] Example 2

[0125] The damage model of XX recycled brick-concrete aggregate is established by adopting the damage model establishment method of the recycled brick-concrete aggregate as in Example 1. The specific process is as follows:

[0126] Recycled brick aggregate concrete test blocks with different stress levels (S = 0, S = 0.2, S = 0.4, S = 0.6) and different freeze-thaw times (such as 0, 20, 40, 60, 80, 120, 160, etc.) were prepared and marked as RB-CAC-[stress level value]-[freeze-thaw times], such as RB-CAC-0–40. The test blocks were subjected to uniaxial compression tests, and the stress and strain data during the test were recorded. At the same time, the acoustic emission signals of the test blocks during the uniaxial compression failure process were collected, as shown in Table 1;

[0127] Table 1 Characteristic points of stress-strain curves of each group of recycled concrete test blocks

[0128]

[0129]

[0130] According to the peak stress and peak strain in the uniaxial compression results of recycled brick-concrete aggregate concrete under different freeze-thaw load times in Table 1, the corresponding distribution parameters are calculated in combination with the above formula, and the results are listed in Table 2:

[0131] Table 2 Weibull distribution parameters

[0132] Group λ k RB-CAC-0-0 2.710640 2.002381 RB-CAC-0-40 2.913300 2.273282 RB-CAC-0-80 3.073279 2.508149 RB-CAC-0-120 3.247240 2.549108 RB-CAC-0-160 3.471759 3.095126 RB-CAC-0.2-40 3.008712 3.922664 RB-CAC-0.2-80 3.395420 3.420329 RB-CAC-0.2-120 3.616806 4.356823 RB-CAC-0.2-160 3.910824 3.918963 RB-CAC-0.4-40 3.536775 4.310336 RB-CAC-0.4-80 3.855353 5.084125 RB-CAC-0.4-120 4.322492 4.442894 RB-CAC-0.6-20 4.085294 4.159549 RB-CAC-0.6-40 4.520380 5.556954 RB-CAC-0.6-60 4.934520 6.634264

[0133] The model parameters and the number of freeze-thaw cycles were linearly fitted, and the fitting results were shown in Figure 1 , Figure 2 ,Depend on Figure 1 , Figure 2 It can be seen that the distribution parameters and the number of freeze-thaw cycles satisfy a linear function relationship and have a good correlation. From the fitting results, it can be seen that the model distribution parameters and increase with the increase of freeze-thaw cycles, indicating that the brittleness of recycled brick-concrete aggregate concrete increases with the increase of freeze-thaw cycles.

[0134] Taking the initial tangent modulus under 0 freeze-thaw cycles as the standard, the initial tangent modulus of recycled brick-concrete aggregate concrete under different freeze-thaw cycles was normalized, and a linear function was used for fitting to establish the E n The functional relationship between the freeze-thaw times and the stress level is shown in the following figure. Figure 3 As shown. Figure 3 It can be seen that the correlation coefficients of the fitting are all greater than 0.95, which proves that the fitting results are good. It proves that the initial tangent modulus E of recycled brick-concrete aggregate concrete that has experienced a certain number of freeze-thaw-load coupling is n It satisfies a linear relationship with the freeze-thaw number N and the stress level S: as the freeze-thaw-load coupling effect increases, the initial tangent modulus of recycled brick-concrete aggregate concrete decreases.

[0135] According to the test data, the initial damage variables, uniaxial loading damage variables, model distribution parameters, etc. are calculated according to the above model construction steps. For the initial damage variables, the elastic modulus of the test block after different freeze-thaw load coupling is measured, and combined with the elastic modulus of the standard specimen RB-CAC-0-0, it is calculated according to formula (4). The uniaxial loading damage variable is calculated according to the micro-element damage of the pressure-bearing surface through formula (5) and subsequent related derivations. The model distribution parameters are calculated by the stress-strain curve boundary conditions and related formulas to obtain the scale parameters and shape parameters, and then determine the model.

[0136] According to the damage mechanics theory, the accumulation of damage inside the material leads to the final destruction of the material. Combining equation (11) with Figure 3 It can be obtained that the functional relationship between the total damage variable and N and S is:

[0137]

[0138] The damage of the material during freeze-thaw-load coupling is calculated by the above formula, and the results are as follows: Figure 4 , Figure 5 shown. Figure 4 , Figure 5 They are respectively the changing rules of total damage under the same stress level and different freeze-thaw times and the changing rules of total damage under the same freeze-thaw times and different stress levels. It can be seen that the initial damage of the RB-CAC-0-0 group of test blocks calculated by the model is 0, which is consistent with the hypothesis. With the increase of freeze-thaw times and stress levels, the initial damage of recycled brick-concrete aggregate concrete shows an upward trend, and the initial damage of the RB-CAC-0.6-40 group of test blocks is about 0.74. Analysis Figure 4 It can be seen that when the stress level S = 0, the rapid growth of material damage is approximately between 0.0015 and 0.003. As the number of freeze-thaw cycles increases, the damage enters the rapid growth stage more slowly, but the rate of reaching the damage peak speeds up. Figure 5 There is the same change rule: as the stress level increases, the damage enters the rapid growth stage more slowly, but the rate of reaching the damage peak speeds up.

[0139] The damage constitutive model is verified by combining the model distribution parameters and initial tangent modulus E of recycled brick-concrete aggregate concrete. n Substituting the functional relationship between freeze-thaw times and stress level into equation (17) for correction, the functional relationship between material stress, strain, N, and S is obtained as follows:

[0140]

[0141] The modified constitutive model curve is compared with the test data, such as Figure 6 to Figure 20 . As can be seen from the figure, the constitutive model established by the present invention can well reflect the stress-strain relationship of recycled brick-concrete aggregate concrete under different freeze-thaw-load coupling effects, and the consistency of the rising section of the model is higher than that of the falling section. During the use of recycled brick-concrete aggregate concrete, the mechanical properties of the material are mainly reflected in the curve change law before the peak stress. Therefore, the damage constitutive model established by the present invention can better describe the stress-strain change law of recycled concrete under different freeze-thaw cycles.

[0142] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for establishing a damage model of recycled brick-concrete aggregate, characterized in that: The following steps are involved: S1: Select the standard specimen of recycled brick-concrete aggregate concrete, and the initial damage of the standard specimen of recycled brick-concrete aggregate concrete is 0; S2: Determine the initial damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows: S21: The standard specimen of recycled brick-concrete aggregate concrete was subjected to several freeze-thaw-load couplings. The initial damage variable of the standard specimen of recycled brick-concrete aggregate concrete was: Where: D0 is the initial damage variable of the material after freeze-thaw-load coupling; E0 is the elastic modulus of the standard specimen of recycled brick-concrete aggregate concrete; E n is the elastic modulus of the material after several freeze-thaw cycles; S22: Considering that the stress level applied in the freeze-thaw-load coupling will cause an acceleration effect on the damage caused by freeze-thaw, the initial damage variable in step S2 is corrected, specifically: Where: D n Modify the initial damage variable for the material after freeze-thaw-load coupling; α s is the correction coefficient of the initial elastic modulus at different stress levels in the freeze-thaw-load coupling action; the elastic modulus of recycled brick-concrete aggregate concrete with stress levels S=0, S=0.2, S=0.4, and S=0.6 is fitted with the S=0 group as the standard, and the relationship between the stress level S and the correction coefficient is finally obtained: a s =0.98027-1.12742S,R 2 =0.99067 (3) Finally, the modified initial damage variable function of recycled brick-concrete aggregate concrete after freeze-thaw-load coupling is obtained: S3: Determine the uniaxial loading damage variables of the standard specimen of recycled brick-concrete aggregate concrete. The specific process is as follows: The bearing surface of the standard specimen of recycled brick-concrete aggregate concrete is composed of countless microelements. Some microelements are damaged and then withdrawn from work. The damage caused by stress in the freeze-thaw-load coupling is defined as the ratio of the number of damaged microelements to the total number of microelements on the surface: Where: D c A is the damage generated during uniaxial compression; i is the number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete; A is the total number of micro-elements on the surface of the standard specimen of recycled brick-concrete aggregate concrete; According to the Lemaitre strain equivalence principle, the relationship between stress and strain is: σ=(0.98027-1.12742S)E n e(1-D c ) (6) The uniaxial compressive damage constitutive relation of the standard specimen of recycled brick-concrete aggregate concrete under freeze-thaw-load coupling is: S4: Determine the total damage variable of the standard specimen of recycled brick-concrete aggregate concrete as: The interface micro-element strength obeys the Weibull distribution, and its probability density function is: Where: F is the distribution variable of the micro-element strength; λ and k are distribution parameters; Under certain strain conditions, the number of damaged interface microelements A i The relationship with the total number of interface elements A can be expressed as: Substituting into formula (5) we can get: Substituting equation (4) and equation (11) into equation (8) yields the total damage: Combining equations (6) and (11), it can be seen that the constitutive relationship of recycled brick-concrete aggregate concrete subjected to different freeze-thaw-load levels is: S5: Determine the freeze-thaw damage constitutive model of recycled concrete. The specific process is as follows: According to the boundary conditions of the stress-strain curve, the model distribution parameters are determined as: ①ε=0,σ=0 ②e=e p ,σ=σ p ③ε=ε p , By taking the derivative of formula (10), we can get: According to boundary condition ②, we can get: According to boundary condition ③, we can get: Combining the above formula (14), formula (15), and formula (16), we can get the scale parameter Shape parameters Substituting into formula (13), the freeze-thaw damage constitutive model of recycled concrete is obtained as follows: Thus, the freeze-thaw damage constitutive model of recycled concrete is established.

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