Construction and application of concrete nonlinear microscopic fracture analysis model under temperature change

Abstract

The invention relates to construction and application of a concrete nonlinear microscopic fracture analysis model under temperature change. In order to solve the technical problem that in the prior art, the coupling effect of the temperature change and the size effect is not considered at the same time, so that the size-effect-free tensile strength and fracture toughness of the concrete after high temperature are accurately determined through small-size test data, relative size and temperature coupling variables are introduced; constructing a virtual crack propagation amount calculation model aiming at the lightweight aggregate concrete and the common concrete; establishing a microscopic fracture theory based on small-size test piece test data inversion size-effect-free material parameters; introducing normal statistical analysis to determine a 95% guarantee rate confidence interval; and constructing a fracture failure whole curve and a peak load prediction model. Unification of test standards is achieved, the influence of the size effect is effectively eliminated, the prediction precision of the mechanical property of the concrete after high temperature is remarkably improved, and reliable technical support is provided for safety evaluation of the concrete structure after a fire disaster.

Description

Technical Field

[0001] This invention relates to the field of building material performance testing technology, and in particular to the construction and application of a nonlinear microscopic fracture analysis model for concrete under temperature changes. Background Technology

[0002] Fire is one of the most destructive accidents that concrete structures may suffer during their lifespan, posing a serious threat to public safety and the lives and property of the victims. Due to the low thermal diffusivity of concrete, its internal temperature rises rapidly under the high temperatures of a fire, leading to a significant deterioration in its strength, modulus of elasticity, and other mechanical properties. Furthermore, the vapor pressure accumulated in the pores of the concrete under high temperatures can easily trigger explosive spalling, causing concrete fragments to break off from the surface and gradually detach, ultimately leading to structural collapse. Therefore, post-fire safety assessments of concrete structures are crucial, and the impact of high temperatures on the fracture toughness of concrete (…) is particularly important. K IC ) and tensile strength ( f t The influence of ) is a key parameter for structural analysis and evaluation.

[0003] In existing technologies, many scholars have conducted experimental studies on the effects of high temperatures on concrete. K IC and f t The influence of [various factors]. For example, Yu et al. used wedge splitting tests to find that concrete [had a certain effect]. K IC The fracture toughness of concrete decreases with increasing temperature. Prokopski and Abdel-Fattah et al. confirmed through three-point bending tests that the fracture toughness of concrete further decreases at high temperatures and after cooling. Mi et al. revealed through wedge splitting tensile tests that the fracture parameters of concrete decrease with increasing temperature. Pirmohammad et al. studied asphalt concrete and similarly observed that the fracture toughness and fracture energy decrease with increasing temperature. Liang et al. conducted static splitting tensile tests on ultra-high performance fiber-reinforced concrete and found that the tensile strength decreases sharply when the temperature exceeds 400℃. These studies all indicate that temperature changes have a significant impact on the fracture toughness and tensile strength of concrete.

[0004] However, existing technologies have the following problems or shortcomings: First, different researchers use inconsistent specimen types and calculation methods, leading to a lack of comparability and consistency in test results; second, concrete test results exhibit a significant size effect, meaning that the fracture toughness calculated by linear elastic fracture mechanics is unstable in small-sized specimens, only stabilizing when the specimen height exceeds 2000 mm; third, although existing studies have proposed theoretical models based on the concept of relative size, capable of simultaneously determining the absence of size effects in concrete from small-sized test results... ft and K IC However, this model is only applicable to normal temperature conditions and does not consider the influence of temperature changes; fourth, the failure mechanism of concrete under high temperature is more complex, involving microstructural evolution such as porosity changes, and there is currently no theoretical model reported that can quantitatively describe the fracture failure of concrete after high temperature.

[0005] Therefore, the existing technology lacks a unified theoretical model that can simultaneously consider temperature changes and size effects, and accurately determine the size-effect-free tensile strength and fracture toughness of concrete from small-scale test results. This has become a technical problem that urgently needs to be solved in this field.

[0006] The information disclosed in this background section is intended only to enhance the understanding of the background technology of this disclosure and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] This invention addresses the lack of existing technologies that can simultaneously consider the coupling effect of temperature change and size effect, thereby accurately determining the size-effect-free tensile strength and fracture toughness of concrete after high temperature from small-scale test data. By employing key technical means such as introducing relative size and temperature coupling variables, constructing a virtual crack propagation calculation model, establishing a microscopic fracture theory inversion method, and normal statistical analysis, significant technical effects have been achieved, including unified testing standards, elimination of the influence of size effect, accurate prediction of the mechanical properties of concrete after high temperature, and provision of reliable confidence intervals.

[0008] According to one aspect of this disclosure, a method for constructing a nonlinear microstructural fracture analysis model for concrete is provided, comprising the following steps: (1) Establish the virtual crack propagation amount Δ a fic The calculation model, where Δ a fic It is temperature T and relative size parameters ( W - a 0) / d max The function, W For the height of the specimen, a 0 represents the initial crack length. d max Maximum aggregate particle size; (2) Based on the virtual crack propagation amount Δ a fic Calculate the nominal stress σ n ; (3) Based on the nominal stress σn and equivalent crack length a e The size-free tensile strength of concrete is determined by a preset relationship. f t and fracture toughness K IC .

[0009] In some embodiments of this disclosure, the virtual crack propagation amount Δ a fic Calculate as follows: For lightweight aggregate concrete: ; For ordinary concrete: .

[0010] In some embodiments of this disclosure, the nominal stress σ n Calculate using the following formula: ; In the formula, S For the span of the specimen, B For the specimen thickness, P max For peak load, α For the seam height ratio, α = a 0 / W .

[0011] In some embodiments of this disclosure, the equivalent crack length a e Calculate using the following formula: ; In the formula, a 0 represents the initial crack length of the specimen; α It is the seam height ratio of the specimen. α=a 0 / W , W The height of the specimen; Y ( α ) represents geometric parameters, determined based on indoor testing.

[0012] In some embodiments of this disclosure, in step (3), the method of linear fitting is used to determine... f t and K IC This includes: establishing relational expressions: ; simultaneously determined through linear regression f t and K IC .

[0013] In some embodiments of this disclosure, in step (3), the determination is made by statistical analysis. f t and K IC ,include: Based on characteristic crack length With the maximum aggregate particle size d max Based on the following quantitative relationship, calculate the personalized fracture parameters: ; ; Normal distribution statistical analysis was performed on the calculation results of multiple specimens: mean deviation μ and standard deviation σ, And establish a confidence interval as μ ±2 σ The prediction range.

[0014] In some embodiments of this disclosure, the method also includes constructing a full fracture failure curve: With log a e x-axis, log σ n The vertical axis is based on a defined... f t and K IC Plot the theoretical curve; mark the 95% confidence interval on the curve.

[0015] In some embodiments of this disclosure, a peak load prediction model is also included: Build P max and f t , K IC The linear relationship: , ; in A e 1 , A e 2 The effective area is related to the specimen's geometric parameters.

[0016] According to another aspect of this disclosure, a method for post-fire safety assessment of concrete structures is provided, comprising the following steps: (1) Obtain the temperature history and geometric dimensions of the concrete structure after the fire; (2) Based on the test data of small-sized specimens, the nonlinear micro-fracture analysis model of concrete constructed by the above method is used to determine the size-free material parameters of concrete at the corresponding temperature; (3) Construct a full fracture failure curve to evaluate the fracture behavior of the structure under different load conditions; (4) Use the peak load prediction model to predict the bearing capacity of key parts of the concrete structure; (5) Based on the confidence interval of 95% guarantee rate, conduct a reliability assessment of structural safety.

[0017] In some embodiments of this disclosure, the method further includes: constructing a structural performance evaluation model under a temperature gradient field based on the differences in material parameters in different temperature regions, so as to achieve an accurate assessment of the overall safety of the concrete structure after a fire.

[0018] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. Consistency and Accuracy: By considering the coupling effect of temperature and relative size, a method was established that can simultaneously determine the size-effect-free tensile strength from small-scale test results. f t and fracture toughness K IC The newly developed microscopic fracture model addresses the issues of inconsistent testing methods and the influence of size effects in existing technologies. This model is applicable at various high temperatures, enabling accurate prediction of concrete fracture parameters.

[0019] 2. Wide applicability: The model is applicable to a variety of concrete materials such as lightweight aggregate concrete (LWC) and ordinary concrete (NWC), and covers a temperature range from room temperature to high temperature (e.g., 20℃ to 800℃), expanding the application scenarios of existing models.

[0020] 3. Strong robustness: By introducing normal statistical analysis, a confidence interval for the fracture failure curve with a 95% guarantee rate was constructed, effectively handling the dispersion of experimental data and improving the reliability and engineering applicability of the model. All experimental data fell within the confidence interval, verifying the rationality of the model.

[0021] 4. Simplified prediction: Peak load was established. P max With material parameters f t and K IC The simple linear relationship between them facilitates rapid prediction and evaluation in engineering applications, reducing the need for complex calculations.

[0022] 5. Clear Mechanism: By calculating the virtual crack propagation, the influence of temperature on the microstructure of concrete was quantified, revealing the mechanism of concrete fracture failure at high temperatures, and providing theoretical support for the safety evaluation of concrete structures after a fire.

[0023] In summary, through technological innovation, this invention has achieved accurate and unified determination of concrete fracture parameters at high temperatures, solved key problems in the prior art, and achieved significant technological progress and practical value. Attached Figure Description

[0024] Figure 1 Δ is the embodiment of this application a fic Simplified diagram ( W - a 0 / d max ≈10, T =250℃).

[0025] Figure 2 Δ in the embodiments of this application a fic Follow T Three-dimensional surface plot showing the relative dimensional changes of the specimen.

[0026] Figure 3 Δ is the embodiment of this application a fic Follow T Changes in the extended plan view ( W - a 0 / d max ≈10).

[0027] Figure 4 The stress of cracks is considered in the embodiments of this application. σ n Calculation diagram.

[0028] Figure 5 The crack tip Δ at different high temperatures in the embodiments of this application a fic A schematic diagram of the normal distribution.

[0029] Figure 6 This is a schematic diagram of the experimental loading in an embodiment of this application.

[0030] Figure 7 This is the linear fitting result in the embodiments of this application.

[0031] Figure 8 This is one of the results of normal statistical analysis in the embodiments of this application.

[0032] Figure 9This is the second result of normal statistical analysis in the embodiments of this application.

[0033] Figure 10 This is a comparison chart of the results of the two methods in the embodiments of this application.

[0034] Figure 11 The fracture failure curves of NWC and LWC at different high temperatures are shown in the embodiments of this application.

[0035] Figure 12 This is one of the peak prediction curves of NWC and LWC at different high temperatures in the embodiments of this application.

[0036] Figure 13 This is the second peak prediction curve of NWC and LWC at different high temperatures in the embodiments of this application. Detailed Implementation

[0037] To better understand the technical solution of this application, the above technical solution will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Example 1: Construction of a microscopic fracture model considering the effects of high temperature 1. Virtual crack propagation Δ at high temperature a fic calculate For three-point bending specimens with precast cracks, the macroscopic cracking in concrete is actually the process of crack initiation and eventual penetration at the aggregate-cement matrix interface transition zone (FPZ) at the microscopic level. Under peak load... P max At the initial crack a At the tip, irregular and intermittent crack propagation zones will appear, i.e., the virtual crack propagation amount Δ. a fic For concrete specimens of the same size, Δ a fic The value typically extends from the bluntest crack tip to the most active crack tip (Δ). a fic - ∼Δ a fic + ). To quantify Δ a fic Specifically, in this example, the value is the relative specimen size at a high temperature of 250℃. W - a 0 / d max Taking the LWC group with a value of ≈10 as an example, for Δ a fic It has been simplified, such as Figure 1 As shown. Furthermore, in existing studies, the virtual crack propagation amount Δa fic The calculations only considered the effects of the relative size of the specimen and the aggregate particle size, without taking into account high temperature. T The specific mechanisms by which these changes occur are investigated. Extensive research indicates that high temperature significantly affects concrete crack propagation. Therefore, this study considers the coupled effects of specimen relative dimensions and high temperature, proposing a virtual crack propagation amount Δ that accounts for the influence of high temperature. a fic The calculation method.

[0039] It is worth noting that concrete can be classified into ordinary concrete (NWC) and lightweight aggregate concrete (LWC) based on density. Studies by Chen et al. have shown that the physical properties of LWC, such as water absorption, differ from those of NWC. Dabbaghi ​​et al. have also confirmed through research that LWC and NWC exhibit significant differences in fracture toughness and tensile strength at different high temperatures. Therefore, this example establishes a Δ value for virtual crack propagation considering the relative size of the specimen, the maximum aggregate size, and the effects of high temperature for both LWC and NWC concrete types. a fic The calculation method is shown in Equation (1) and Equation (2).

[0040] LWC (1); NWC (2); in, T Temperature (°C); W The height of the specimen is in mm. a 0 represents the initial crack length (mm); d max The maximum aggregate particle size (mm) is given in this example. d max =12.5mm.

[0041] exist Figure 2 The paper shows the virtual crack propagation Δ of NWC and LWC. a fic Depending on the relative size of the specimen and the high temperature T A changing 3D surface plot. For a more intuitive view, Figure 3 The relative dimensions are given respectively. W - a 0 / d max Virtual crack propagation Δ of NWC and LWC approximately 10 a fic A schematic diagram showing the changes with high temperature is provided, along with a simplified schematic diagram of aggregate expansion. It was found that as... T The increase of virtual crack propagation Δ in NWC and LWC afic It gradually increases, but the growth becomes slower and slower, and eventually its value tends to be constant.

[0042] 2. Linear fitting method to determine concrete at high temperatures f t and K IC Currently, many scholars have conducted in-depth research on the fracture properties of concrete at room temperature, and based on the results of laboratory tests on small-sized specimens, have simultaneously determined the fracture toughness and tensile strength of concrete without size effects. The boundary effect model describes the material's fracture failure as follows: (3); In the formula, The nominal stress that takes into account the effect of structural cracks; f t The tensile strength of the material; The characteristic crack length of the material can be determined by the material strength. f t and fracture toughness K IC As shown in equation (4). a e The equivalent crack length is given by equation (5): (4); (5); In the formula, a 0 represents the initial crack length of the specimen; α It is the seam height ratio of the specimen. α=a 0 / W , W The height of the specimen; Y ( α () represents the geometric shape parameter. Based on indoor tests, for the span-to-depth ratio... S / W The concrete specimen with a strength of 2.5 is shown in equation (6): (6).

[0043] At peak load P max The nominal stress distribution at the three-point bending point is as follows Figure 4 As shown, based on the equilibrium of forces, we can obtain the result considering the initial crack. a 0 impact, virtual crack propagation Δ a fic nominal stress of the range The expression is shown in equation (7).

[0044] (7); In the formula, S For the span of the specimen, B The thickness is the specimen thickness.

[0045] Calculate according to formula (5) a e Substituting equations (1) and (2) into equation (7) yields the result considering high temperature. T changing The calculation formulas are shown in equations (8) and (9) respectively: LWC (8); NWC (9).

[0046] Substituting equation (4) into equation (3) yields the expression for the linear fitting method, as shown in equation (10): (10).

[0047] The equivalent crack length is calculated according to equations (5), (8), and (9). and nominal stress Substituting into equation (10), the true tensile strength of concrete without size effect can be determined simultaneously using the linear fitting method. f t and fracture toughness K IC parameter.

[0048] 3. Concrete at high temperatures f t and K IC Statistical analysis model Related studies have shown that even for specimens cast in the same batch, the virtual crack propagation Δ a fic The dispersion of the test load will lead to the peak value of the test load. P max The discreteness of LWC and NWC makes it impossible to determine the true fracture parameters under laboratory conditions. To obtain the true fracture parameters of LWC and NWC at different high temperatures... f t and K IC This example considers Δ at different high temperatures a fic The changes all follow a normal distribution, such as Figure 5 As shown, peak load P max The fracture parameters also follow a normal distribution.

[0049] Studies by Hu et al. have shown that for quasi-brittle materials such as concrete and rock, the characteristic crack length... Its fracture process zone width FPZ W The two are approximately equal, that is ≈ FPZ W However, Bazant's research indicates that, for various types of concrete, there is an approximate existence of this phenomenon. w c ( FPZ W )≈ nd a ( d max The quantities are equal, but for ordinary concrete, n The value is usually taken as 3. Based on the research results of the above scholars, this example uses the characteristic crack length of concrete. With the maximum aggregate particle size d max The ratio between them is taken as 3, as shown in equation (11): (11); Substituting equation (11) into equation (3) and rearranging, we can obtain: f t The expression for is shown in equation (12). Substituting equation (12) into equation (4), we can further obtain . K IC The specific expression is shown in equation (13).

[0050] (12); (13).

[0051] Furthermore, substituting equations (12) and (13) into equation (7) respectively, we can further obtain equations (14) and (15). f t and K IC Calculation formula: (14); (15).

[0052] The calculations based on the microscopic fracture model proposed above are as follows: The material parameters of LWC and NWC can be calculated using equations (14) and (15). f t & K ICPersonalized values. Furthermore, equation (16) is used to evaluate the material parameters of LWC and NWC. f t & K IC By performing normal statistical analysis on the personalized values, material parameters can be obtained. f t & K IC mean difference μ and standard deviation σ .

[0053] (16); In the formula, x The fracture parameter, i.e., the concrete's... f t or K IC ; σ This represents the standard deviation of the set of parameters; μ This is the average value of the set of parameters.

[0054] Example 2: Experimental Verification of the Model 1. Experimental setup The LWC uses fine ceramsite with a maximum particle size of 4.75 mm as fine aggregate and coarse ceramsite with a maximum particle size of 12.5 mm as coarse aggregate. The NWC uses crushed stone with a maximum particle size of 12.5 mm as coarse aggregate and natural sand with a maximum particle size of 4.75 mm as fine aggregate. To evaluate the fracture parameters of the LWC and NWC, according to the requirements of RILEM FMC50, Dabbaghi ​​et al. designed and fabricated 32 groups of 96 notched beams of different sizes for three-point bending loading tests. Four different heights were fabricated. W The width of the specimen B Both are 38.1mm, with a span-to-height ratio S / W =2.5, seam height ratio a 0 / W =0.2, and the specific information on the specimen dimensions is shown in Table 1.

[0055] The experiment used a servo-controlled testing machine with displacement control, and applied load by displacement rate control. A schematic diagram of the specific experiment is shown below. Figure 6 As shown. The ambient temperature was 25℃. When heating the specimens, specimens at 250℃, 500℃, and 750℃ were first exposed to 100℃ for 24 hours to remove surface moisture, and then placed in an electric furnace to be heated to the specified temperature and cooled in the furnace until the ambient temperature was reached.

[0056] Table 1 Specimen dimensions, peak load and Δ a fic Summary table of calculated values

[0057] Wherein, L represents lightweight aggregate concrete, N represents ordinary concrete; T1 represents 25℃, T2 represents 250℃, T3 represents 500℃, T4 represents 750℃; W1 represents 38.1mm, W2 represents 76.2mm, W3 represents 152.4mm, and W4 represents 304.8mm.

[0058] 2. Linear Fitting Method Based on the concrete microstructure fracture models of LWC and NWC considering the influence of high temperature changes proposed in Example 1, the Δ values ​​of LWC and NWC at different high temperatures can be calculated according to Equations (1) and (2), respectively. a fic Personalized values ​​are shown in Table 1. Then, based on the linear fitting formula in equation (10), a linear fitting graph can be plotted. The true fracture parameters without size effects can be obtained simultaneously from the intercept and slope of the fitted line. f t and K IC A 95% confidence band was established in the fitted plot to characterize the accuracy of the data fitting, and a 95% prediction band was established to consider the discreteness of concrete fracture parameters. The specific linear fitting plot is shown below. Figure 7 As shown.

[0059] The true fracture parameters obtained by linear fitting f t and K IC Table 2 provides a detailed summary, and the experimental data were compared and verified with those from the original literature. The comparative analysis revealed that linear fitting... f t and K IC The data is very close to that in the original literature. Regarding tensile strength... f t In general, except for the L-T1 group, all other groups f t The fitted values ​​all fall within the discrete range (S1~S3) of the original literature data. The fitted value for the L-T1 group is 2.91 MPa, which is very close to the experimental data range of 2.52~2.85 MPa. Regarding fracture toughness... K ICFor most of the data, the data are also within the discrete range. However, for groups L-T3, L-T4, N-T1, N-T3, and N-T4, which are not within the S1~S3 range, the relative errors between their fitted values ​​and the mean values ​​of the corresponding experimental data are 17.3%, 17.8%, 4.0%, 5.9%, and 23.4%, respectively. The reason for this error is that only three specimens were prepared for each group in the indoor tests, which is insufficient to truly reflect the discrete range of the fracture parameters of LWC and NWC. Furthermore, it is easy to see that, except for group L-T1 with a relative error of 4.0%, the rest were tested in high-temperature environments of 500℃ and 750℃. This is because high temperatures exacerbate internal defects in concrete, further increasing the discreteness of the fracture parameters.

[0060] 3. Normal statistical analysis Based on the description in Example 1, using indoor test information, the fracture toughness of all LWC and NWC specimens can be calculated based on equations (14) and (15). K IC and tensile strength f t Personalized calculation results. Then, normal statistical analysis was performed on the personalized calculation results to obtain the material parameters of LWC or NWC at different high temperatures. f t & K IC Statistical analysis of specimens mean μ、 variance σ And the coefficient of variation (CV), specifically as follows: Figure 8 , Figure 9 As shown.

[0061] For material parameters ( f t & K IC Normal analysis mean μ A summary is provided in Table 2. (Based on...) f t Analysis revealed that only the fitted value of 2.92 MPa for the L-T1 group was outside the discrete range, but it was very close to the fitted value of 2.91 MPa from the linear fitting method, indicating to some extent that the linear fitting method and the normal method can mutually verify each other. K IC Analysis revealed that only groups L-T1 and N-T1 fell within the S1-S3 discrete range. This is because only three concrete specimens were prepared for each group, insufficient to reflect the true discrete range of the concrete. The remaining groups... K ICAlthough there is a certain relative error compared to the experimental results, the error is relatively small. For LWC, the relative errors of the normal statistical results compared to the experimental mean are 11.6%, 19.2%, and 12.3%, respectively, while for NWC they are 3.9%, 5.5%, and 11.7%, respectively. It is easy to see that the fitting error of LWC is relatively large compared to NWC. This may be because LWC contains a large number of lightweight aggregate particles with high porosity. These particles have a greater difference in thermal expansion coefficient at high temperatures compared to the mortar matrix, which leads to more active development and more uneven distribution of ITZ microcracks. In addition, it was found that the fitting effect is better at lower temperatures (T1), but the relative error of the fitting effect generally increases with increasing temperature (T2~T4). This is because with higher temperatures... T As the temperature rises, damage to microcracks, pores, and interfacial transition zones within the concrete gradually worsens, leading to an increase in the virtual crack propagation amount Δ. a fic The dispersion of the corresponding fracture parameters increases significantly. In addition, high-temperature-induced debonding of the aggregate-mortar interface, decomposition of chemical products, and uneven thermal expansion make the stress field distribution inside the specimen more complex, thereby further amplifying the deviation between experimental measurements and model assumptions.

[0062] Table 2 Comparison of fitted values ​​and original data using normality analysis and fitting methods. .

[0063] Based on the data summarized in Table 2, the fitting results of the two methods are compared graphically, as follows: Figure 10 As shown. Through comparison, it was found that... T Rising, LWC and NWC f t and K IC Both methods showed a clear downward trend, exhibiting the same trend, and their calculation results were quite close, with small relative errors compared to the indoor experimental results S1~S3 for each group. Furthermore, both methods... f t The calculation results differed by only 0~0.09 MPa, further validating the accuracy of the proposed microstructure models considering LWC and NWC at different high temperatures. Furthermore, for both types of concrete, it was found that… f t The fitting effect is significantly better than K IC This is because K IC Characterizing a material's resistance to crack propagation is highly dependent on the fracture process at the crack tip. High temperatures further exacerbate local damage, thereby increasing the dispersion of crack propagation and consequently worsening the fitting effect.

[0064] 4. Fracture Failure Curve For quasi-brittle materials such as concrete, fracture failure exhibits three control modes: strength-controlled, fracture toughness-controlled, and quasi-brittle fracture. These are respectively... Strength <0.1 f t Controlled intensity range, >10 o'clock K IC The controlled fracture toughness region that meets LEFM, and 0.1 < <10 o'clock f t and K IC A quasi-brittle fracture region is jointly controlled. However, under laboratory conditions, small-sized specimens typically exhibit a quasi-brittle fracture state, showing a significant size effect. The results were calculated using the aforementioned linear fitting method and normal statistical method, respectively. f t and K IC , with log a e The x-axis is log. σ n Plotting the best linear fit and normal distribution on the ordinate at different high temperatures, we can see the results. T The complete fracture failure curves of LWC and NWC are shown below. Figure 11 As shown. And based on the mean in the results of normal statistical analysis. μ and standard deviation σ By setting the 95% confidence interval for material parameters ( μ ±2 σ () is used to describe the dispersion of experimental data.

[0065] Depend on Figure 11 (a)~(h) It is easy to see that, except for the N-T4 group, the linearly fitted full curve and the normal statistical full curve basically overlap in the figure, which not only reflects the consistency and reliability of the two methods, but also demonstrates the accuracy of the proposed model. Furthermore, at different high temperatures... T Below, the experimental data points for NWC and LWC of different sizes are basically all within 0.1 < The region <10 is the quasi-brittle fracture region. With... T Growth, all experimental data for NWC and LWC are at a high level μ ±2 σ The accuracy of the proposed model was further verified within the region.

[0066] 5. Simplified prediction curves of concrete at different high temperatures By deriving and transforming formulas (14) and (15), the tensile strength can be obtained respectively. f t and fracture toughness K IC With peak load P max The simplified linear relationship between them is shown in equations (17) and (18). The effective area... A e 1 and A e 2 The x-axis is... P max Using the ordinate as the vertical axis, a scatter plot of experimental data from specimens of different sizes can be drawn. The slope of the straight line passing through the origin, fitted from the scatter plot, is then used as the concrete fracture parameter. f t or K IC Similarly, the linear fitting and normal statistical analysis methods obtained in the previous section were also used. f t and K IC The data were used to plot both the normal distribution curve and the best-fit curve, allowing for a comparative verification of the two methods. Furthermore, based on the mean of the normal statistical data... μ and standard deviation σ It has built a system with 95% reliability. μ ±2 σ )of P max - A e The curves, based on the scatter plot distribution, can verify the accuracy of the proposed mesoscopic model. Furthermore, if the fracture parameters are known... f t and K IC Alternatively, it can be based on P max - A e The curve represents the peak load of LWC and NWC specimens of different sizes. P max To make predictions, specifically as follows: Figure 12 , Figure 13 As shown.

[0067] (17), (18); in, A e1 , A e 2 It is the effective area of ​​the specimen, which is related to the size of the concrete specimen, the joint height ratio, the maximum aggregate size, and the virtual spread. Closely related to, etc.

[0068] like Figure 11 As shown in (a)~(h), except for group N-T4 K IC Apart from the larger relative error, the other groups f t and K IC The normal distribution curve and the optimal linear fitting curve are very close, and in most cases they almost overlap, reflecting the rationality of the proposed model. It was found that as... T With the increase of [variable name], the peak load fluctuation of LWC and NWC specimens increased, but all experimental data remained within the 95% confidence interval. μ ±2 σ This demonstrates that the proposed model can handle different high temperatures. T The good predictive performance of the model on LWC and NWC specimens of different sizes further verifies the rationality and accuracy of the model.

[0069] The above embodiments, based on indoor test data of NWC and LWC at high temperatures, establish a mesoscopic fracture model that can simultaneously determine the strength and fracture parameters of NWC and LWC at different high temperatures. Considering the discreteness of concrete experimental results, a statistical method for simultaneously determining the strength and fracture parameters of NWC and LWC from small-sized specimens under laboratory conditions is developed. The conclusions obtained are as follows: (1) Considering relative dimensions ( W - a 0) / d max and high temperature T The coupling effect of NWC and LWC is used to propose virtual crack propagation amounts. A calculation method was established to simultaneously determine the size-effect-free material parameters of NWC and LWC at different high temperatures using small-sized specimens. K IC & f t A microscopic fracture analysis model was constructed for NWC and LWC. Considering the discreteness of experimental results, the material parameters of NWC and LWC were further constructed. K IC & f t The normal statistical analysis model of ).

[0070] (2) Using the theoretical model constructed in this invention, experimental data of NWC and LWC at different high temperatures were analyzed. The material parameters of concrete were obtained by using linear fitting and normal analysis methods, respectively. K IC & f t The results show that the calculation results of the two methods are very close and agree well with the experimental results reported in the literature, fully verifying the rationality of the microstructural fracture analysis model proposed in this invention. The results are based on calculations using linear fitting and normal statistical methods. f t and K IC Construct different high temperatures T The complete failure curves for NWC and LWC fractures show that almost all experimental data points are within the 95% confidence interval.

[0071] (3) Based on peak load P max and equivalent area A e Material parameters of NWC and LWC at different high temperatures were constructed. K IC & f t A simplified prediction formula is used between NWC and LWC. Based on the simplified prediction formula, plots are made for NWC and LWC. P max - A e The predicted lines obtained by the fitting method and the normal analysis method were found to be very close, and the experimental data points were all distributed within the 95% prediction confidence interval. μ ±2 σ Within the scope of this invention, the rationality of the model constructed in this invention is further verified.

Claims

1. A method for constructing a nonlinear microstructural fracture analysis model for concrete, characterized in that, Includes the following steps: (1) Establish virtual crack propagation amount The computational model, in which It is temperature T and relative size parameters ( W - a 0) / d max The function, W For the height of the specimen, a 0 represents the initial crack length. d max Maximum aggregate particle size; (2) Based on the virtual crack propagation amount Calculate the nominal stress ; (3) Based on the nominal stress and equivalent crack length a e The size-free tensile strength of concrete is determined by a preset relationship. f t and fracture toughness K IC .

2. The construction method according to claim 1, characterized in that, The virtual crack propagation amount Δ a fic Calculate as follows: For lightweight aggregate concrete: ; For ordinary concrete: .

3. The construction method according to claim 1, characterized in that, The nominal stress σ n Calculate using the following formula: ； In the formula, S For the span of the specimen, B For the specimen thickness, P max For peak load, α For the seam height ratio, α = a 0 / W .

4. The construction method according to claim 1, characterized in that, The equivalent crack length a e Calculate using the following formula: ； In the formula, a 0 represents the initial crack length of the specimen; α It is the seam height ratio of the specimen. α=a 0 / W , W The height of the specimen; Y ( α ) represents geometric parameters, determined based on indoor testing.

5. The construction method according to claim 1, characterized in that, In step (3), the linear fitting method is used to determine... f t and K IC , Includes: Establishing relational expressions: ; simultaneously determined through linear regression f t and K IC .

6. The construction method according to claim 1, characterized in that, In step (3), statistical analysis is used to determine... f t and K IC ,include: Based on characteristic crack length With the maximum aggregate particle size d max Based on the following quantitative relationship, calculate the personalized fracture parameters: ； ； Normal distribution statistical analysis was performed on the calculation results of multiple specimens: mean deviation and standard deviation ， And establish a confidence interval as The prediction range.

7. The construction method according to claim 1, characterized in that, This also includes constructing the full fracture failure curve: by x-axis The vertical axis is based on a defined... f t and K IC Plot the theoretical curve; mark the 95% confidence interval on the curve.

8. The construction method according to claim 1, characterized in that, This also includes establishing a peak load prediction model: Build P max and f t , K IC The linear relationship: ， ； in A e 1 , A e 2 The effective area is related to the specimen's geometric parameters.

9. A method for safety assessment of concrete structures after a fire, characterized in that, Includes the following steps: (1) Obtain the temperature history and geometric dimensions of the concrete structure after the fire; (2) Based on the test data of small-sized specimens, the nonlinear micro-fracture analysis model of concrete constructed by any one of claims 1-8 is used to determine the size-free material parameters of concrete at the corresponding temperature; (3) Construct a full fracture failure curve to evaluate the fracture behavior of the structure under different load conditions; (4) Use the peak load prediction model to predict the bearing capacity of key parts of the concrete structure; (5) Based on the confidence interval of 95% guarantee rate, conduct a reliability assessment of structural safety.

10. The method for post-fire safety assessment of concrete structures according to claim 9, characterized in that, Also includes: Based on the differences in material parameters in different temperature regions, a structural performance evaluation model under a temperature gradient field is constructed to achieve an accurate assessment of the overall safety of concrete structures after a fire.

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