Prediction method of concrete freeze-thaw damage by coupling freeze-thaw cycle temperature and saturation

Abstract

The present invention provides a method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation, which belongs to the field of concrete durability. The method specifically comprises the following steps: conducting freeze-thaw tests on concrete with different freeze-thaw cycle temperatures and different saturations; proposing an equivalent damage age calculation formula that simultaneously reflects the freeze-thaw temperature history and concrete saturation by analogy with the equivalent age theory, and establishing a fractional-order prediction model for freeze-thaw damage of hydraulic concrete based on the equivalent damage age; combining freeze-thaw cycle test data of hydraulic concrete with different freeze-thaw cycle temperatures and different saturations, optimizing and inverting the parameters of the new model using the Grey Wolf optimization algorithm; and predicting freeze-thaw damage of hydraulic concrete under different freeze-thaw cycle temperatures and saturations based on the optimized fractional-order freeze-thaw degradation model of hydraulic concrete.

Description

Technical Field

[0001] The present invention belongs to the research field of hydraulic concrete durability, and in particular relates to a concrete freeze-thaw damage prediction method that couples freeze-thaw cycle temperature and saturation. Background Art

[0002] Freeze-thaw cycles are a significant factor affecting the durability of concrete structures in high-latitude and high-altitude regions. To study the freeze-thaw degradation characteristics of concrete, domestic and international researchers often conduct freeze-thaw tests on saturated or highly saturated concrete according to concrete testing procedures, and then conduct concrete durability design and evaluation. However, engineering practice shows that, in actual hydraulic concrete structures, concrete in the water-facing, underwater areas, and backwater areas is often unsaturated, while concrete in areas with fluctuating water levels, above-water areas, and behind-water areas is often saturated. Furthermore, my country's vast territory results in reservoirs and dams located in different climatic regions experiencing varying frequency and degree of freeze-thaw damage, and extreme climate change may exacerbate these differences. Therefore, freeze-thaw cycle temperature and saturation are two important factors affecting the frost resistance of hydraulic concrete.

[0003] Extensive research has been conducted on freeze-thaw degradation models for concrete. However, most existing models are based on freeze-thaw cycle test data from saturated or highly saturated concrete under current standards. Furthermore, most research on the frost durability of hydraulic concrete conducted domestically and internationally has been conducted at a center temperature of -17°C for the frost-resistant specimens, which raises questions about the applicability of this center temperature. Furthermore, most existing models are discrete prediction models based on the number of freeze-thaw cycles, and their expressions change when the freeze-thaw cycle temperature changes. Although Yuan Bin et al. proposed a continuous degradation model that reflects variable freeze-thaw cycle temperatures, this model does not consider the saturation factor. Therefore, current concrete freeze-thaw degradation models are unable to reasonably reflect the freeze-thaw degradation behavior of hydraulic concrete with varying saturations under variable freeze-thaw cycle temperatures. Therefore, when predicting the durability of freeze-thaw-damaged hydraulic concrete, the effects of both freeze-thaw cycle temperature and saturation on the performance of hydraulic concrete should be considered simultaneously. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a concrete freeze-thaw damage prediction method that couples freeze-thaw cycle temperature and saturation, while taking into account the influence of freeze-thaw cycle temperature and saturation on the performance of hydraulic concrete, thereby solving the shortcoming that the existing freeze-thaw degradation model cannot reasonably reflect the freeze-thaw degradation properties of hydraulic concrete with different saturations under variable freeze-thaw cycle temperature.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation, comprising the following steps:

[0006] Step 1: Design and carry out freeze-thaw cycle tests on concrete with different saturations at different freeze-thaw cycle temperatures to obtain test data on the compressive strength and splitting tensile strength of hydraulic concrete at different freeze-thaw cycle temperatures and different saturations;

[0007] Step 2: By analogy with the equivalent age theory, establish an equivalent damage age calculation formula that takes into account saturation and freeze-thaw cycle temperature;

[0008] Step 3: Combine the equivalent damage age calculation formula in step 2 to establish a fractional freeze-thaw degradation model for hydraulic concrete;

[0009] Step 4: Establish a parameter optimization mathematical model for the fractional freeze-thaw degradation model of hydraulic concrete;

[0010] Step 5: Based on the compressive strength and splitting tensile strength test data obtained from the freeze-thaw test in step 1, the Gray Wolf optimization algorithm is used to optimize the parameters in the equivalent damage age calculation formula and the freeze-thaw degradation model;

[0011] Step 6: Based on the optimized fractional freeze-thaw degradation model of hydraulic concrete, freeze-thaw damage prediction of concrete with different freeze-thaw cycle temperatures and saturations is performed.

[0012] The present invention provides a method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation, which has the following beneficial effects:

[0013] 1. In view of the fact that the existing freeze-thaw degradation model cannot comprehensively reflect the freeze-thaw degradation properties of hydraulic concrete under different freeze-thaw cycle temperatures and saturations, the present invention first proposes an equivalent damage age expression for coupling freeze-thaw cycle temperature and saturation by analogy with the equivalent age theory. Secondly, a fractional-order freeze-thaw degradation model is established based on the equivalent damage age. Finally, the gray wolf optimization algorithm is used to fit the model parameters.

[0014] 2. Based on the principles of freeze-thaw testing and model establishment, the present invention invents a model establishment method that couples freeze-thaw cycle temperature and saturation, which solves the shortcoming that the existing freeze-thaw degradation model cannot comprehensively reflect the freeze-thaw degradation properties of hydraulic concrete under different freeze-thaw cycle temperatures and saturations. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The present invention will be further described below with reference to the accompanying drawings and examples:

[0016] Figure 1 This is the flowchart of the Gray Wolf algorithm;

[0017] Figure 2 Comparison of average compressive strength loss at different freeze-thaw temperatures;

[0018] Figure 3 Comparison of average splitting tensile strength loss at different freeze-thaw temperatures;

[0019] Figure 4 Comparison between the experimental and predicted values ​​of fractional freeze-thaw damage of unsaturated hydraulic concrete;

[0020] Figure 5 Comparison between the experimental value and the predicted value of fractional freeze-thaw damage of saturated hydraulic concrete. DETAILED DESCRIPTION

[0021] A method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation, comprising the following steps:

[0022] Step 1: Design and carry out freeze-thaw cycle tests on concrete with different saturations at different freeze-thaw cycle temperatures to obtain test data on the compressive strength and splitting tensile strength of hydraulic concrete at different freeze-thaw cycle temperatures and different saturations.

[0023] Combined with the design mix ratio of hydraulic concrete for the concrete water project to be investigated, three or more different freeze-thaw cycle temperatures and three or more different saturations of concrete sealed freeze-thaw and water freeze-thaw tests were carried out indoors to obtain freeze-thaw test data for concrete with different freeze-thaw cycle temperatures and different saturations.

[0024] Step 2: By analogy with the equivalent age theory, establish an equivalent damage age calculation formula that takes into account saturation and freeze-thaw cycle temperature.

[0025] The concrete equivalent age theory shows that within a certain temperature range (-10℃~80℃), the hydration rate of concrete increases with increasing temperature. This process is often expressed by the Arrhenius function:

[0026]

[0027] Where, k(T) is the hydration reaction rate; A is the constant coefficient; E a is the activation energy, kJ / mol; R is the gas constant, generally taken as 8.314J / (mol·K); T is the concrete temperature, ℃.

[0028] The relative humidity inside concrete also affects the equivalent age. For this reason, Zhu Bofang and Bazant et al. proposed an equivalent age expression that takes both temperature and humidity into consideration:

[0029]

[0030] Where, τ e is the equivalent age, d; β T is dependent on the concrete temperature; β θ It depends on the internal humidity of concrete; T0 is the reference temperature, generally 20℃; U his the activity energy, kJ / mol; h is the relative humidity inside the concrete, %; the meanings of other parameters are the same as above.

[0031] During the freeze-thaw cycle, the lower the freeze-thaw cycle temperature, the greater the reduction in concrete material properties, which is opposite to the effect of curing temperature on the equivalent age; and the lower the concrete saturation, the slower the reduction in concrete material properties, which is the same as the effect of the relative humidity inside the concrete on the equivalent age of concrete. For this reason, a negative sign is added to formula (1) to describe the effect of freeze-thaw temperature, and the equivalent damage age calculation formula is designed with reference to the above calculation formula of the effect of the relative humidity inside the concrete on the equivalent age of concrete. Since the concrete activation energy in formula (1) is no longer applicable when the concrete suffers freeze-thaw damage, the damage coefficient k is used instead of the ratio of the concrete activation energy to the gas constant (E a / R). Therefore, for unsaturated hydraulic concrete in the water level fluctuation area, the water area and the back water area, the equivalent damage age formula of concrete under the sealed freeze-thaw mode considering the freeze-thaw temperature history and saturation is:

[0032]

[0033] Where, τ e d is the equivalent damage age of freeze-thaw of hydraulic concrete with different saturations under sealed freeze-thaw mode; β T is dependent on the concrete temperature; β θ is dependent on the concrete saturation; k is the damage coefficient to be inverted; T is the actual temperature of concrete, ℃; T0 is the reference temperature, ℃; k1 and k2 are parameters to be inverted; θ is the concrete saturation, %. The meanings of other parameters are the same as above.

[0034] For the underwater hydraulic concrete, the saturation inside the concrete is close to 100%. When it is damaged by freeze-thaw cycles, the mechanical properties show a large rate of decline. Therefore, based on formula (3), an acceleration coefficient β is introduced. w , in order to characterize the acceleration of the freeze-thaw equivalent damage age of hydraulic concrete with a saturation of 100% relative to the freeze-thaw equivalent damage age of unsaturated hydraulic concrete, the freeze-thaw equivalent damage age formula of saturated hydraulic concrete under the freeze-thaw mode considering the freeze-thaw temperature history is:

[0035]

[0036] Where, τ' e is the freeze-thaw equivalent damage age of saturated hydraulic concrete under the freeze-thaw mode, d; β w is the acceleration coefficient to be determined. The meanings of other parameters are the same as above.

[0037] Since the freeze-thaw temperature changes with time during the test and Equations (3) and (4) are integral equations, the equivalent damage age of the temperature is calculated using a segmented calculation method and the Simpson formula is used for calculation.

[0038]

[0039] Based on Matlab (R2020a) platform, the Simpson formula is used to calculate the equivalent damage age. Since k, k1, k2 and β in the equivalent damage age expression are w In order to obtain the parameters to be inverted, it is necessary to combine the measured data and optimize the inversion of the concrete freeze-thaw degradation model parameters based on the freeze-thaw damage age.

[0040] Step 3: Combine the equivalent damage age calculation formula in step 2 to calculate the equivalent damage age, and then establish a fractional freeze-thaw degradation model for hydraulic concrete.

[0041] Fractional calculus is the study of calculus with fractional orders of operation. It is a generalization of conventional integer-order calculus and has been successfully applied in many fields. Among them, the Riemann-Liouville-type fractional calculus operator theory uses a differential-integral form, avoiding limit solutions and significantly reducing computation time. Based on the Riemann-Liouville-type fractional calculus operator theory, the fractional freeze-thaw degradation model for unsaturated hydraulic concrete is expressed as follows:

[0042]

[0043] Where, P is the strength loss rate, %; t e is the equivalent damage age of hydraulic concrete during freeze-thaw, d, for the sealed freeze-thaw mode t e Using τ e , for the water freezing and thawing mode, t e Using τ' e r and λ are the parameters to be fitted. The meanings of the other parameters are the same as above.

[0044] Step 4: Establish a parameter optimization mathematical model for the fractional freeze-thaw degradation model of hydraulic concrete.

[0045] The mathematical model for parameter optimization of the fractional freeze-thaw degradation model of hydraulic concrete under the unsaturated sealed freeze-thaw mode is:

[0046]

[0047] Where X is the parameter set to be determined; Z is the objective function; P c To calculate the strength loss rate, %; P mis the measured strength loss rate, %; St is the constraint; Find is the solution; Let is so that; min is the minimum value; the subscripts l and u represent the upper and lower limits of the parameter to be fitted, respectively. The meanings of the remaining parameters are the same as above.

[0048] The mechanical properties of hydraulic concrete with a saturation of 100% have a large decline rate, so a parameter to be inverted β is added to the calculation formula of the equivalent damage age of unsaturated hydraulic concrete. w , to characterize its damage acceleration effect (β w >0), and delete the two parameters to be inverted, k1 and k2, and the damage coefficient k is taken as the inversion result of the fractional freeze-thaw degradation model of unsaturated hydraulic concrete. At this time, for the parameter optimization mathematical model of the fractional freeze-thaw degradation model of saturated hydraulic concrete under the water-freeze-thaw mode, X=[r,λ,β w ].

[0049] Specifically, the mathematical model for parameter optimization of the fractional freeze-thaw degradation model of saturated hydraulic concrete under the freeze-thaw mode is:

[0050]

[0051] Step 5: Based on the compressive and splitting tensile strength test data obtained from the freeze-thaw tests in Step 1, the Gray Wolf Optimization Algorithm (GWA) is used to optimize the parameters in the equivalent damage age calculation formula and the freeze-thaw degradation model. The GWA is a new swarm intelligence algorithm proposed by Mirjalili et al., inspired by the leadership hierarchy and pack hunting behavior of gray wolves in nature. Due to its simple principles, few parameters, ease of programming, support for distributed parallel computing, and powerful global search capabilities, the GWA has been widely used in global optimization problems in fields such as computer science, engineering, and management.

[0052] The gray wolf social hierarchy is a pyramid. The alpha wolf is at the top, responsible for decision-making and other overall affairs; the beta wolf is at the second level, assisting the alpha wolf in decision-making and commanding other lower-ranking wolves; the delta wolf is at the third level, obeying the orders of the alpha and beta wolves and responsible for scouting, guarding, and other matters; the omega wolf is at the lowest level, responsible for balancing relationships within the group. In the gray wolf hunting process, the behavior of surrounding prey is defined as follows:

[0053]

[0054] Where, and Represent the position vectors of the target and the gray wolf respectively, t is the current iteration number, and is a coefficient vector, calculated as follows:

[0055]

[0056] In the formula, the parameters is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations decreases. and is a random vector between [0,1].

[0057] In the gray wolf population, α wolves, β wolves, and δ wolves are the groups closest to the prey and most able to perceive prey information. The positions of the remaining gray wolf individuals are determined based on these three types of wolves.

[0058] In the parameter optimization, α, β, and δ are the three best solutions obtained so far. The positions of these three are used to determine the position of the next target, and the remaining gray wolves are forced to update their positions according to the position of the best gray wolf. The mathematical model is shown in formula (15):

[0059]

[0060] Where D α 、D β 、D δ represents the distance between the α, β, and δ wolf packs and other individuals; Represent the current positions of α, β, and δ respectively; C1, C2, and C3 are random vectors;

[0061] The position update formula of the gray wolf individual is as follows:

[0062]

[0063] Where X1, X2, and X3 represent the position of the gray wolf ω that needs to be adjusted due to the influence of the wolf packs in the α, β, and δ layers. The average value is taken here, that is:

[0064]

[0065] The Gray Wolf Algorithm starts with a set of random solutions and searches for the optimal parameter set in continuous iterations. When the accuracy is met, it automatically stops outputting the optimal solution. Figure 1 shown.

[0066] Step 6: Based on the optimized fractional freeze-thaw degradation model of hydraulic concrete, freeze-thaw damage prediction of concrete under different freeze-thaw cycle temperatures and saturations is performed.

[0067] Combined with the variable freeze-thaw cycle temperature and variable saturation conditions, the equivalent damage age is calculated and then substituted into the optimized fractional freeze-thaw degradation model of hydraulic concrete to predict the freeze-thaw damage of concrete under different freeze-thaw cycle temperatures and saturations.

[0068] Example analysis:

[0069] Taking a typical concrete high dam project as an example, the concrete mix ratio used in this test was designed based on the C30 concrete mix ratio in the non-foundation constraint area of ​​the project. Then, freeze-thaw cycle tests of concrete with different saturations at different freeze-thaw cycle temperatures were designed and carried out. Based on the test data of the compressive strength and splitting tensile strength of hydraulic concrete at different freeze-thaw cycle temperatures and different saturations, a fractional freeze-thaw degradation model was established in combination with the equivalent damage age established based on the equivalent damage age calculation formula. The Grey Wolf optimization algorithm was used to optimize the fitting of the equivalent damage age expression and the parameters in the freeze-thaw degradation model.

[0070] Step 1: Design and carry out freeze-thaw cycle tests on concrete with different saturations at different freeze-thaw cycle temperatures to obtain test data on the compressive strength and splitting tensile strength of hydraulic concrete at different freeze-thaw cycle temperatures and different saturations.

[0071] 1) Select the concrete water project to be investigated

[0072] The secondary concrete mix design for this test was based on the C30 concrete mix used in the non-foundation-constrained area of ​​a typical high concrete dam project. Details are shown in Appendix 1. The concrete had a water-binder ratio of 0.5, a sand content of 34%, a medium-sized stone to small stone ratio of 60:40, and a fly ash content of 35%.

[0073] Table 1 Test mix ratio Unit: kg / m 3

[0074]

[0075] 2) Freeze-thaw cycle test of unsaturated hydraulic concrete at different freeze-thaw cycle temperatures

[0076] By consulting the specifications and winter temperature change data of various regions, the three groups of cycle temperatures for this concrete rapid freeze-thaw cycle test were determined to be -18℃~6℃, -10℃~6℃ and -5℃~6℃. Based on the critical saturation theory, indoor rapid freeze-thaw cycle tests were carried out for sealed freeze-thaw (saturation 85%~91.7%, 91.7%~95%, 95%~100%) and water freeze-water thaw test groups (saturation of 100%).

[0077] The test specimens used were 100mm×100mm×100mm cubic concrete specimens. After forming, the specimens were placed in a standard curing room at (20±2)°C for one day before being demolded. Concrete specimens with design saturations of 85% to 91.7% and 91.7% to 95% were wrapped and cured for 21 and 14 days, respectively, before being immersed in a standard curing room water tank at (20±2)°C for 28 days. Concrete specimens with design saturations of 95% to 100% were directly placed in a standard curing room water tank at (20±2)°C for 28 days after demolding. Freeze-and-thaw specimens were wrapped and cured for 28 days. At the design age, the initial compressive and splitting tensile strengths of the specimens were measured as the starting values ​​for the frost resistance index. The hydraulic concrete specimens under three set saturations were subjected to freeze-thaw cycle tests in the form of "sealed freeze-thaw", that is, the specimens were wrapped in vacuum bags and placed in specimen boxes; the water-freeze and water-thaw specimens were directly placed in the specimen box, and the water surface should be immersed 20mm above the top surface of the specimen. The time for each freeze-thaw cycle is set at 2 to 4 hours according to the specification. Due to the large number of specimens in this test, a compressive and splitting tensile strength test was performed on the specimens every 50 cycles until 200 freeze-thaw cycles were completed. The test results are attached. Figure 2 and attached Figure 3 shown.

[0078] The sealed freeze-thaw specimens represent unsaturated hydraulic concrete, and the water-freeze-thaw specimens represent saturated hydraulic concrete.

[0079] Step 2: By analogy with the equivalent age theory, establish an equivalent damage age calculation formula that takes into account saturation and freeze-thaw cycle temperature.

[0080] Analogous to the equivalent age theory, the equivalent damage age calculation formula was designed. Since the concrete activation energy in formula (1) is no longer applicable when the concrete suffers freeze-thaw damage, the damage coefficient k is used instead of the ratio of the concrete activation energy to the gas constant (E a / R). The equivalent damage expressions of seal freeze-thaw and water freeze-thaw considering freeze-thaw cycle temperature and saturation are shown in Equation (3) and Equation (4), respectively, where θ takes the middle value of the three saturation ranges of 97.5%, 93.47%, and 88.3%.

[0081] Step 3: Combine the equivalent damage age established by the equivalent damage age calculation formula in step 2 to establish a fractional freeze-thaw degradation model for hydraulic concrete.

[0082] Based on the Riemann-Liouville type fractional calculus operator theory, this method establishes a fractional freeze-thaw degradation model shown in Equation (7) based on the equivalent damage age.

[0083] Step 4: Establish a parameter optimization mathematical model for the fractional freeze-thaw degradation model of unsaturated hydraulic concrete.

[0084] Based on the above freeze-thaw degradation model, the unsaturated hydraulic concrete (sealed freeze-thaw) fractional parameter optimization mathematical model considering saturation and freeze-thaw cycle temperature is obtained as shown in formula (8). On this basis, the two parameters to be inverted, k1 and k2, are deleted and the damage acceleration coefficient β is introduced. w (β w >0), a fractional-order parameter optimization mathematical model for saturated hydraulic concrete (freeze-thaw) was established. The damage coefficient k in this model was derived from the inversion results of the sealed freeze-thaw fractional-order freeze-thaw degradation model. Based on previous research, the value ranges for the parameters to be fitted in the sealed freeze-thaw fractional-order freeze-thaw degradation model and the water-freeze-thaw fractional-order freeze-thaw degradation model are shown in Table 2.

[0085] Table 2 Range of parameters to be fitted for the fractional-order freeze-thaw degradation model of seal freeze-thaw and water freeze-thaw

[0086]

[0087] Step 5. Based on the compressive strength and splitting tensile strength test data obtained from the freeze-thaw test in step 1, the Gray Wolf optimization algorithm is used to optimize the fitting of the parameters in the equivalent damage age calculation formula and the freeze-thaw degradation model.

[0088] Combined with the measured data, based on the Matlab (R2020a) platform and the data in Table 3 and Table 4, the Grey Wolf optimization algorithm was used to optimize the fitting parameters in Equation (7) and Equation (8). In the Grey Wolf algorithm program, the solution range vector of the sealed freeze-thaw fractional-order freeze-thaw degradation model was set to [20, 10, 1, 0, 0.5] to [40, 30, 2, 1, 1.5], the problem dimension D was 5, the population size N was 30, the maximum number of iterations was 100, the iteration threshold for terminating the algorithm was 1000 times, and the accuracy of the termination algorithm was set to 1×10 -6 The solution range vector for the water-freeze-thaw fractional-order freeze-thaw degradation model is [x1, 0, 0.5, 1] ​​to [x1, 1, 1.5, 3], where x1 represents the inversion result of the damage coefficient k for the airtight freeze-thaw fractional-order freeze-thaw degradation model. The problem dimension D is always 3. The population size, maximum number of iterations, iteration threshold for the termination algorithm, and the accuracy of the termination algorithm are consistent with those for the airtight freeze-thaw fractional-order freeze-thaw degradation model. The parameter fitting optimization results and fitting accuracy of the fractional-order freeze-thaw degradation model are shown in Tables 5 and 6.

[0089] Table 3 Strength loss rate of sealed freeze-thaw specimens corresponding to equivalent damage age

[0090]

[0091] Table 4 Strength loss rate of water-freezing and water-thawing specimens corresponding to equivalent damage age

[0092]

[0093] Table 5 Fitting parameters and fitting accuracy of the unsaturated (sealed freeze-thaw) fractional-order freeze-thaw degradation model

[0094]

[0095] Table 6 Fitting parameters and fitting accuracy of saturated (freeze-thaw) fractional freeze-thaw degradation damage model

[0096]

[0097] Step 6: Based on the optimized fractional freeze-thaw degradation model of hydraulic concrete, freeze-thaw damage prediction of concrete with different freeze-thaw cycle temperatures and saturations is performed.

[0098] Combined with the variable freeze-thaw cycle temperature and variable saturation conditions, the equivalent damage age is calculated and then substituted into the optimized fractional freeze-thaw degradation model of hydraulic concrete to predict the freeze-thaw damage of concrete under different freeze-thaw cycle temperatures and saturations. The comparison between the measured and predicted values ​​of freeze-thaw damage of unsaturated hydraulic concrete is shown in the attached figure. Figure 4 As shown in the attached figure, the comparison between the measured and predicted values ​​of freeze-thaw damage of saturated hydraulic concrete is shown in the attached figure. Figure 5 shown.

[0099] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The embodiments and features in the embodiments of this application may be arbitrarily combined with each other unless they conflict. The scope of protection of the present invention shall be the technical solutions described in the claims, including equivalent alternatives to the technical features of the technical solutions described in the claims. Equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation, characterized in that: The steps include: Step 1: Design and carry out freeze-thaw cycle tests on concrete with different saturations at different freeze-thaw cycle temperatures to obtain test data on the compressive strength and splitting tensile strength of hydraulic concrete at different freeze-thaw cycle temperatures and different saturations; Step 2: By analogy with the equivalent age theory, establish an equivalent damage age calculation formula that takes into account saturation and freeze-thaw cycle temperature; For unsaturated hydraulic concrete in the water level fluctuation area, the water area, and the backwater area, the calculation formula for the equivalent damage age of concrete under the sealed freeze-thaw mode considering the freeze-thaw temperature history and saturation is: ；（1） Where, τ e is the equivalent damage age of freeze-thaw of hydraulic concrete with different saturations under sealed freeze-thaw mode; β T is dependent on the concrete temperature; β θ is dependent on the degree of concrete saturation; k is the damage coefficient to be inverted; T is the actual temperature of concrete; T 0 is the reference temperature; k 1 and k 2 is the parameter to be inverted; θ is the concrete saturation; The calculation formula for the freeze-thaw equivalent damage age of saturated hydraulic concrete under the freeze-thaw mode considering the freeze-thaw temperature history is: ；（2） Where, is the freeze-thaw equivalent damage age of saturated hydraulic concrete under the freeze-thaw mode; β w is the acceleration coefficient to be determined; Step 3: Combine the equivalent damage age calculation formula in step 2 to establish a fractional freeze-thaw degradation model for hydraulic concrete; Step 4: Establish a parameter optimization mathematical model for the fractional freeze-thaw degradation model of hydraulic concrete; Step 5: Based on the compressive strength and splitting tensile strength test data obtained from the freeze-thaw test in step 1, the Gray Wolf optimization algorithm is used to optimize the parameters in the equivalent damage age calculation formula and the freeze-thaw degradation model; Step 6: Based on the optimized fractional freeze-thaw degradation model of hydraulic concrete, freeze-thaw damage prediction of concrete with different freeze-thaw cycle temperatures and saturations is performed.

2. The method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation according to claim 1, characterized in that: In step 3, the expression of the fractional freeze-thaw degradation model of hydraulic concrete with different saturations is as follows: ；（3） Where, P is the strength loss rate, t e is the equivalent damage age of freeze-thaw of hydraulic concrete. For the sealed freeze-thaw mode t e use τ e , for the water freezing and thawing model, t e use , r 、 λ are the parameters to be fitted.

3. The method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation according to claim 2, characterized in that: In step 4, the mathematical model for optimizing the parameters of the fractional freeze-thaw degradation model of hydraulic concrete under different saturation sealed freeze-thaw modes is: ；（4） Where, X is the parameter set to be requested; Z is the objective function; P c To calculate the strength loss rate; P m is the measured strength loss rate; S . t . is the limiting constraint; Find To seek solutions; Indicates Minimum value; min is the minimum value; Subscript l 、 u Respectively represent the upper and lower limits of the parameters to be fitted; For the fractional freeze-thaw degradation model of saturated hydraulic concrete under the freeze-thaw mode, the formula (2) k Take the optimized inversion of formula (4) k The mathematical model for parameter optimization of the fractional freeze-thaw degradation model of saturated hydraulic concrete under the freeze-thaw mode is: ；（5）。 4. The method for predicting freeze-thaw damage of concrete by coupling freeze-thaw cycle temperature and saturation according to claim 1, characterized in that: In step six, the equivalent damage age is calculated in combination with the variable freeze-thaw cycle temperature and variable saturation working conditions, and then substituted into the optimized fractional freeze-thaw degradation model of hydraulic concrete with different saturations to predict the freeze-thaw damage of hydraulic concrete with different freeze-thaw cycle temperatures and saturations.

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