Method and application of asphalt mixture semi-circular bending index prediction and anti-cracking evaluation based on splitting test

Abstract

The application relates to the technical field of road engineering, and discloses a method and application for predicting a semi-circular bending index and evaluating crack resistance of asphalt mixture based on a splitting test. The method comprises the following steps: S1, taking an AC-13 graded SBS modified asphalt mixture standard test piece, performing a splitting test on the standard test piece in a low-temperature brittle interval of-20 DEG C to 0 DEG C, and measuring at least one splitting test index; S2, selecting a preset linear conversion model corresponding to the temperature of the current splitting test according to the temperature; and S3, substituting the measured splitting test index into the preset linear conversion model to calculate an index of a semi-circular bending test of the asphalt mixture at the corresponding temperature. The method solves the core contradiction between the difficulty in obtaining high-precision fracture parameters and the urgent requirement for on-site rapid detection in the field of road engineering.

Description

Technical Field

[0001] This invention relates to the field of road engineering technology, and in particular to a method and application for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests. Background Technology

[0002] Asphalt mixtures are the primary surface layer material for high-grade highways and urban roads, and their crack resistance directly affects the service life and driving safety of the pavement. During service, asphalt pavements are subjected to multiple effects, including vehicle loads, temperature changes, and moisture intrusion, making them highly susceptible to reflective cracking, low-temperature shrinkage cracking, and fatigue cracking. Therefore, accurately evaluating the fracture characteristics of asphalt mixtures is of great significance for optimizing mix design, selecting crack-resistant modifiers, predicting pavement life, and formulating maintenance strategies.

[0003] Currently, the test methods for evaluating the crack resistance of asphalt mixtures in the laboratory are mainly divided into two categories: the semi-circular bending test and the splitting test.

[0004] The semicircular bending test (SCB test) is a recognized method for directly obtaining the fracture mechanics parameters of materials (such as fracture energy, fracture toughness, and crack resistance index). These indicators can objectively reflect the fracture resistance and brittle behavior of asphalt mixtures, and are therefore considered the gold standard in scientific research and evaluation of high-grade pavement materials. However, this test has significant limitations: specimen preparation is complex, requiring core sampling from the field or the formation of cylindrical specimens in the laboratory, followed by cutting into semicircular discs of a specific thickness and machining a precise pre-crack (depth 15mm ± 0.5mm, width no more than 1.5mm). The requirements for cutting accuracy and pre-crack size are extremely high, and deviations in machining accuracy can easily lead to specimen test failure; the test equipment is demanding and the operation is cumbersome, with the installation, alignment, preloading, and formal testing of a single specimen being time-consuming and labor-intensive; and it is not suitable for rapid on-site testing, requiring the processed specimens to be sent to the laboratory for testing. This leads to a technical problem: in the field of road engineering material testing, although the semicircular bending test can provide high-precision fracture mechanics parameters, its specimen preparation is complex, costly, and time-consuming, which cannot meet the needs of rapid quality sampling inspection at the engineering site; while the splitting test is easy to operate, it cannot directly provide equivalent fracture mechanics parameters, and the evaluation systems of the two are disconnected.

[0005] The splitting test is much simpler to operate. It only requires applying a load along the diameter of a standard Marshall specimen or cylindrical core sample, and then measuring the failure load and displacement to obtain indicators such as splitting strength and splitting fracture energy. The equipment is simple and the operation is quick, making it suitable for large-scale quality sampling inspection. However, the mechanical indicators of the splitting test and the semi-circular bending test belong to different failure modes: the splitting test involves indirect loading, creating a tensile-compressive composite stress field inside the specimen; the semi-circular bending test involves three-point bending loading, with the pre-existing crack tip dominated by Type I tensile stress. Because the two failure modes differ, the physical meanings of the indicators also differ. Currently, there is no universally accepted quantitative conversion formula with engineering precision, making it difficult to interoperate between the two evaluation systems.

[0006] Furthermore, at both normal and high temperatures, asphalt mixtures exhibit viscoelastic properties, with complex failure mechanisms. The failure modes of splitting and semicircular bending tests differ significantly, making it difficult to establish stable and reliable quantitative relationships. Therefore, existing research is mostly limited to qualitative analysis with single temperatures and small samples, lacking systematic statistical modeling and temperature correction, and failing to provide specific conversion formulas and prediction intervals with statistical significance and engineering application value.

[0007] There is an urgent need to construct a systematic statistical modeling and temperature correction method for key fracture performance indicators of asphalt under low-temperature conditions, such as fracture energy and fracture toughness, derive corresponding quantitative conversion formulas, and establish scientifically reliable prediction ranges. Simultaneously, the crack resistance of asphalt mixtures should be analyzed based on these rapidly predicted semi-circular bending test indicators. Summary of the Invention

[0008] One of the objectives of this invention is to provide a method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting crack tests. This invention targets AC-13 graded SBS modified asphalt mixtures, focusing on the low-temperature brittle range of -20℃ to 0℃, and solves the technical problem of cumbersome and inefficient existing evaluation methods. It relies on splitting crack tests to quickly obtain the predicted values ​​of the semi-circular bending index of the mixture before and after modification, thereby achieving a rapid and accurate evaluation of the effect of the modifier application.

[0009] To achieve the above-mentioned objectives, the specific technical solution is as follows: A method for predicting the semi-circular flexural properties and assessing the crack resistance of asphalt mixtures based on splitting tests includes the following steps: S1 Take AC-13 graded SBS modified asphalt mixture standard specimens and conduct splitting tests on the standard specimens in the low temperature brittle range of -20℃ to 0℃ to obtain at least one splitting test index. S2 selects a preset linear transformation model corresponding to the current splitting test temperature; S3 substitutes the measured splitting test index into the preset linear transformation model to calculate the index of the asphalt mixture semi-circular bending test at the corresponding temperature. The splitting test indicators include splitting test fracture energy and splitting strength; the semicircular bending test indicators include semicircular bending test fracture energy, semicircular bending test stress intensity factor, semicircular bending test fracture resistance, and semicircular bending test crack resistance index.

[0010] According to embodiments of the present invention, one of the technical solutions has at least one of the following advantages or beneficial effects: This invention proposes for the first time a predictive scheme for the conversion of indicators between different test methods for the crack resistance of asphalt mixtures in the low-temperature brittle range of -20℃ to 0℃. This fundamentally solves the core contradiction in road engineering—the difficulty in obtaining high-precision fracture parameters and the urgent need for rapid on-site testing. Simultaneously, by focusing on low-temperature brittle fracture as the failure mode, it completely overcomes the technical challenge of establishing a stable conversion relationship between the two failure modes at normal and high temperatures due to their significant differences. Previously, the splitting test method only addressed the testing speed issue and could not provide fracture mechanics parameters; single-temperature qualitative correlation studies could only partially reveal the correlation of indicators and could not form a quantitative tool usable in engineering. This invention solves two originally independent technical problems simultaneously, achieving an organic unity of speed and high precision.

[0011] Specifically, this invention reveals that within the temperature range of -20℃ to 0℃, the viscoelastic effect of asphalt mixtures almost disappears, and the failure mode transforms from viscoplastic fracture at room temperature to ideal brittle fracture. At this temperature, the mechanical responses of the indirect tensile failure in the splitting crack test and the pure bending tensile failure in the semi-circular bending test exhibit a highly stable linear positive correlation, fundamentally eliminating the root cause of the unstable conversion relationship. Based on this, by pre-establishing a linear conversion model of temperature-dependent characteristics, readily obtainable splitting crack test indicators are directly and quantitatively converted into semi-circular bending fracture mechanical parameters, completely breaking down the technical barriers between the two evaluation methods. This invention, through innovative technical thinking, transforms two previously unsolvable contradictions into an achievable solution.

[0012] According to one embodiment of the present invention, splitting strength is the maximum tensile stress at specimen failure, reflecting the material's ultimate bearing capacity against tensile failure, and has a direct mechanical relationship with fracture toughness (the ability to resist crack initiation) in the semi-circular bending test; splitting fracture energy is the total energy consumed per unit area during specimen fracture, reflecting the material's ability to resist crack propagation, and has an essential intrinsic connection with fracture energy (the energy consumed throughout the crack propagation process) in the semi-circular bending test. These two indicators reflect the low-temperature crack resistance of asphalt mixtures from different dimensions, and are the splitting test parameters with the highest correlation to the semi-circular bending test indicators and the clearest physical meaning.

[0013] According to one embodiment of the present invention, the preset linear transformation model in S2 is pre-established by the following method: S21 prepared multiple asphalt mixture specimens and subjected them to 0-12 freeze-thaw cycles to obtain specimen groups under different freeze-thaw cycle periods. S22 In each freeze-thaw cycle, multiple parallel specimens are taken from the specimen group for splitting test and multiple parallel specimens are taken for semi-circular bending test. The measured values ​​of the splitting test index and the semi-circular bending test index of each parallel specimen are measured respectively. S23 For each test temperature, iterates through each freeze-thaw cycle at the test temperature, takes the arithmetic mean of the measured values ​​of the splitting test index of all parallel specimens in the same cycle, and takes the arithmetic mean of the measured values ​​of the semicircular bending test index of all parallel specimens in the cycle. The two arithmetic means are used to form a set of paired data points corresponding to the cycle; finally, multiple sets of independent paired data points with the same number of freeze-thaw cycles at each temperature are obtained. S24 uses the least squares method to perform univariate linear regression analysis on paired data points at each test temperature to establish a linear regression model between the splitting test index X and the semicircular bending test index Y: Y=a+bX, where a is the intercept and b is the slope. S25 performs a significance test (p<0.05) and a residual normality test (Shapiro-Wilk test p>0.05) on each linear regression model, and retains the linear regression model that passes the test as the preset linear transformation model corresponding to the temperature described in S2.

[0014] In the low-temperature brittle range (-20℃ to 0℃), the failure mechanism of both the splitting and semi-circular bending tests is dominated by tensile stress, and the fracture energy and other indicators of the two tests have an inherent linear correlation. The linear regression model established by this invention using the least squares method (Y=a+bX) can capture this inherent relationship, making the model simple and easy to apply in engineering. Freeze-thaw cycles can cause microcracks and moisture intrusion within asphalt mixtures, leading to cumulative damage and a decline in the material's mechanical properties. By incorporating paired freeze-thaw cycle data into regression analysis, the established model implicitly includes the impact of freeze-thaw damage on the conversion relationship, making it applicable for predicting crack resistance under different freeze-thaw histories.

[0015] According to one embodiment of the present invention, the number of freeze-thaw cycles includes 0, 3, 6, 9, and 12 freeze-thaw cycles. Freeze-thaw cycles exceeding 12 are not applicable to the model of the present invention.

[0016] According to one embodiment of the present invention, the freeze-thaw cycle is performed as follows: the specimen is first placed in a water bath at room temperature for 20-26 hours to be saturated with water, then frozen at -18±2℃ for 12-20 hours, and finally thawed in a constant temperature water bath at 60℃±0.5℃ for 20-26 hours, thereby completing one freeze-thaw cycle.

[0017] According to one embodiment of the present invention, the asphalt-aggregate ratio of the AC-13 graded SBS modified asphalt mixture is 5.02%. The mechanical properties of mixtures with different gradations, asphalt types, and asphalt-aggregate ratios vary significantly. The conversion model of the present invention is based on AC-13 graded SBS modified asphalt mixtures and is therefore directly applicable to this type of mixture.

[0018] According to one embodiment of the present invention, in S2, the temperature of the test is 0°C, -10°C or -20°C, and the standard specimen is kept at the test temperature for no less than 4 hours.

[0019] According to one embodiment of the present invention, in S2, when the temperature of the experiment is 0°C, the linear transformation model is selected from at least one of the following formulas: Fracture energy: ; CRI: ; K IC : ; R C : ; G f1 Fracture energy (J / m) in a semi-circular bending test 2 G f2 The fracture energy in the splitting test is J / m. 2 CRI is the crack resistance index for the semi-circular bending test, which is dimensionless; K IC Stress intensity factor for semicircular bending test ;R T The splitting strength (MPa) in the splitting test; R C Fracture resistance in semi-circular bending test (MPa).

[0020] According to one embodiment of the present invention, in S2, when the temperature of the experiment is -10°C, the linear transformation model is selected from at least one of the following formulas: Fracture energy: ; CRI: ; K IC : ; R C : .

[0021] According to one embodiment of the present invention, in S2, when the temperature of the experiment is -20°C, the linear transformation model is selected from at least one of the following formulas: Fracture energy: ; CRI: ; K IC : ; R C : .

[0022] According to one embodiment of the present invention, in the splitting test, five parallel specimens are tested at each test temperature and each freeze-thaw cycle, and the average value is taken as a data point.

[0023] According to one embodiment of the present invention, the standard specimen in step S1 is a Marshall specimen or cylindrical core sample with a diameter of 101.6 mm ± 0.2 mm and a height of 63.5 mm ± 1.3 mm. For AC-13 graded asphalt mixture, the size of the Marshall specimen with a diameter of 101.6 mm ± 0.2 mm and a height of 63.5 mm ± 1.3 mm is already larger than its characteristic fracture size, and the measured fracture performance parameters are stable inherent material parameters, unaffected by the specimen size.

[0024] According to one embodiment of the present invention, S4 is included after S3: determining the prediction interval of the key indicators of the semicircular bending test based on a preset 95% confidence interval. The present invention introduces statistical confidence intervals into the prediction of indicator conversion between different testing methods for asphalt mixtures, quantifying the uncertainty of the prediction results and solving the problem of high engineering decision-making risk caused by only providing single-point prediction values ​​in the prior art, thus providing a more comprehensive and scientific basis for engineering evaluation.

[0025] According to one embodiment of the present invention, the splitting test adopts the standard method for splitting tests (T0716-2025 in JTG 3410-2025) with a loading rate of 50 mm / min; the semi-circular bending test adopts the standard method for semi-circular bending tests (T0765-2025 in JTG 3410-2025) with a loading rate of 10 mm / min. The loading rate affects the material's failure behavior. Using a uniform standard loading rate (50 mm / min for splitting tests and 10 mm / min for semi-circular bending tests) ensures the consistency and comparability of the test results, allowing test results from different laboratories and different batches to be used in the same conversion model. The model described in this method is only applicable to the above-mentioned standard loading rates; changing the loading rate requires recalibration.

[0026] The second objective of this invention is to provide an application of the method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on the splitting test.

[0027] The specific technical solution is as follows: A rapid evaluation system for the crack resistance of asphalt mixtures, employing the aforementioned method for predicting and assessing the semi-circular bending index of asphalt mixtures based on splitting tests, includes: The data input module is used to input the splitting test parameters and the test low temperature; The model storage module is used to store the linear transformation model and its coefficients at different temperatures; The calculation module calls the corresponding linear transformation model based on the input temperature to calculate the predicted values ​​of the semicircular bending test index and calculates the 95% prediction interval. The output module displays or exports the prediction results and prediction ranges, and supports the generation of prediction reports. The linear transformation models stored in the model storage module include transformation models at three temperatures: 0℃, -10℃, and -20℃. The models at each temperature include fracture energy transformation model, CRI transformation model, stress intensity factor transformation model, and fracture resistance transformation model.

[0028] According to one embodiment of the present invention, the formula for calculating the 95% prediction interval is: G f1 ±1.96×σ; or CRI±1.96×σ; or K IC ±1.96×σ; or R C ±1.96×σ. Where σ is the standard deviation of the residuals.

[0029] The present invention also provides the application of the method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on the splitting test in the mix design optimization of asphalt mixtures.

[0030] The method of this invention can quickly evaluate the crack resistance of different mix proportion schemes through a simple splitting test, which greatly shortens the mix proportion optimization cycle and reduces the test cost.

[0031] The present invention also provides the application of the method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on the splitting test in the on-site spot inspection of asphalt pavement construction quality.

[0032] On-site assessments of asphalt mixture quality are crucial for quickly determining whether they meet standards, but the semi-circular bending test cannot be performed on-site. This invention allows for on-site splitting tests, rapid prediction of key semi-circular bending test indicators, and real-time on-site control of construction quality.

[0033] The present invention also provides the application of the method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on the splitting test in the crack resistance evaluation of asphalt mixtures.

[0034] Evaluating the crack resistance of asphalt mixtures requires comparing their crack resistance indices. The method of this invention can quickly obtain predicted values ​​of the semi-circular bending index before and after modification through a splitting test, enabling rapid evaluation of the crack resistance of asphalt mixtures and providing rapid data support for evaluating their crack resistance.

[0035] The principle of this invention is as follows: The existing semi-circular bending test route can accurately obtain fracture mechanics parameters, but it cannot meet the requirements of high efficiency and low cost, and is not suitable for rapid on-site testing.

[0036] Existing technologies can address the needs for high efficiency and low cost in splitting tests, but they cannot address the need for high precision because their failure modes (indirect tension) differ from those of the semicircular bending test (pure bending). The two tests cannot be directly applied to each other, and there is a lack of universally accepted conversion formulas.

[0037] The key to this invention's ability to solve both problems simultaneously lies in its utilization of two important mechanical mechanisms: First, the mechanism of convergence of failure mechanisms under low-temperature brittleness: In the low-temperature brittleness range of -20℃ to 0℃, the failure of asphalt mixtures is solely dominated by tensile stress. In the splitting test, the maximum horizontal tensile stress is generated at the center of the specimen, and in the semi-circular bending test, bending tensile stress is generated at the tip of the pre-cast crack. Both are essentially triggered by the single mechanism of tensile stress reaching the material's tensile limit. Therefore, the convergence of failure modes in the two tests makes statistical prediction possible.

[0038] Second, the mechanism of fracture energy as an intrinsic material property: For brittle materials, regardless of whether the fracture occurs via a combined tensile-compression path or a pure bending path, the total energy consumed in the material's failure (fracture energy) is an intrinsic material property. Therefore, splitting fracture energy and semi-circular bending fracture energy are essentially measuring the same type of fracture resistance energy, only measured in different ways. This explains why a strong linear correlation can be established between the two.

[0039] Based on the above mechanism, this invention adopts a technical solution of systematic data statistical regression + temperature-based modeling + statistical significance test + residual normality test. It not only utilizes the high efficiency advantage of splitting test, but also ensures the accuracy of prediction results through scientific statistical modeling, thus achieving a balance between high efficiency and high precision.

[0040] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0041] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at 0℃. Figure 2 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at -10℃. Figure 3 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at -20℃. Figure 4 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at 0℃. Figure 5 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at -10℃. Figure 6 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at -20℃. Figure 7 Splitting strength at 0℃ and K IC Linear relationship diagram; Figure 8 Splitting strength and K at -10℃ IC Linear relationship diagram; Figure 9 Splitting strength and K at -20℃ IC Linear relationship diagram; Figure 10 Splitting strength and semi-circular bending test at 0℃ C Linear relationship diagram; Figure 11 Splitting strength and semi-circular bending test at -10℃ C Linear relationship diagram; Figure 12 Splitting strength and semi-circular bending test at -20℃ C Linear relationship diagram. Detailed Implementation

[0042] When a numerical range is disclosed herein, the range is considered continuous and includes the minimum and maximum values ​​of the range, as well as every value between the minimum and maximum values. Furthermore, when the range refers to integers, it includes every integer between the minimum and maximum values ​​of the range. Additionally, when multiple ranges are provided to describe a feature or characteristic, the ranges may be combined. In other words, unless otherwise specified, all ranges disclosed herein should be understood to include any and all subranges to which they are incorporated.

[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of the present invention.

[0044] Unless otherwise specified, the reagents, methods and equipment used in this invention are all conventional reagents, methods and equipment in this technical field.

[0045] The specimens used in the examples were standard Marshall specimens of AC-13 graded SBS modified asphalt mixture (diameter 101.6 mm ± 0.2 mm, height 63.5 mm ± 1.3 mm). The AC-13 graded SBS modified asphalt mixture used in the above specimens was purchased from Guangxi Jiaoke Group Co., Ltd., with an asphalt-aggregate ratio of 5.02%. The performance indicators are shown in Table 1.

[0046] Table 1

[0047] In this embodiment, the freeze-thaw cycle was performed according to the standard T0729-2025 "Asphalt Mixture Splitting Strength Ratio Test" in the People's Republic of China industry standard "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025). For the freeze-thaw cycle conditions, the specimen was first placed in a water bath at room temperature for 24 hours to be saturated with water, then frozen at -18±2℃ for 16 hours, and finally thawed in a constant temperature water bath at 60℃±0.5℃ for 24 hours, thus completing one freeze-thaw cycle.

[0048] In this embodiment, the splitting tensile test was performed according to T0716-2025 "Split Tear Test of Asphalt Mixtures" in the People's Republic of China industry standard "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025). Standard Marshall specimens (diameter 101.6 mm ± 0.2 mm, height 63.5 mm ± 1.3 mm) were used, with a loading rate of 50 mm / min. The test temperatures were 0℃, -10℃, and -20℃. The failure load and load-displacement curves for each specimen were recorded, and the splitting tensile strength (Rf) was calculated. T ) and splitting fracture energy (G f2 ).

[0049] In this embodiment, the semicircular bending test was performed according to T0765-2025 "Asphalt Mixture Crack Propagation Test" in the People's Republic of China industry standard "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025). The specimen was a semicircular disc (101.6 mm in diameter and 50 mm in thickness), with a pre-fabricated crack depth of 15 mm ± 0.5 mm and a crack width not exceeding 1.5 mm. The loading method was three-point bending with a span of 120 mm and a loading rate of 10 mm / min. The test temperature was consistent with that of the splitting test.

[0050] In this embodiment, the preset linear transformation model is established in advance using the following method: S21 prepared multiple asphalt mixture specimens and subjected them to 0, 3, 6, 9 and 12 freeze-thaw cycles respectively to obtain specimen groups under different freeze-thaw cycle periods. S22 Under each freeze-thaw cycle, multiple parallel specimens were taken for splitting test and multiple parallel specimens were taken for semi-circular bending test to form multiple sets of parallel data pairs; S23 For each test temperature, iterate through each freeze-thaw cycle at the above test temperature, and take the arithmetic mean of the splitting test index and the semi-circular bending test index corresponding to all parallel specimens in the cycle to obtain a set of paired data points corresponding to the cycle; finally, obtain multiple independent paired data points at each temperature that are equal in number to the number of freeze-thaw cycles. S24 uses the least squares method to perform univariate linear regression analysis on paired data points at each test temperature to establish a linear regression model between the splitting test index X and the semicircular bending test index Y: Y=a+bX, where a is the intercept and b is the slope; S25 Perform a significance test (p<0.05) and a residual normality test (Shapiro-Wilk test p>0.05) on each linear regression model, and retain the linear regression models that pass the tests as the preset linear transformation models corresponding to the above temperature points; The linear fitting results, fitting curves, and 95% confidence intervals (shaded areas in the figure) for different indices at various temperatures are shown in this invention. Figures 1-12 ; in, Figure 1 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at 0℃. in, Figure 2 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at -10℃. in, Figure 3 The graph shows the linear relationship between the splitting fracture energy and the fracture energy of the semi-circular bending test at -20℃. in, Figure 4 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at 0℃. in, Figure 5 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at -10℃. in, Figure 6 The graph shows the linear relationship between splitting fracture energy and CRI in a semi-circular bending test at -20℃. in, Figure 7 Splitting strength at 0℃ and K IC Linear relationship diagram; in, Figure 8 Splitting strength and K at -10℃ IC Linear relationship diagram; in, Figure 9 Splitting strength and K at -20℃ IC Linear relationship diagram; in, Figure 10 Splitting strength and semi-circular bending test at 0℃ C Linear relationship diagram; in, Figure 11 Splitting strength and semi-circular bending test at -10℃ C Linear relationship diagram; in, Figure 12 Splitting strength and semi-circular bending test at -20℃ C Linear relationship diagram.

[0051] Example The method for predicting the semi-circular flexural properties and assessing the crack resistance of asphalt mixtures based on splitting tests includes the following steps: Standard Marshall specimens of AC-13 graded SBS modified asphalt mixture were taken and divided into 5 groups. These specimens were subjected to 0, 3, 6, 9, and 12 freeze-thaw cycles, respectively. The freeze-thaw cycle process was strictly performed in accordance with T0729-2025 "Test Procedure for Splitting Tensile Strength Ratio of Asphalt Mixtures" in the People's Republic of China industry standard "Test Procedure for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025). (1) Place the specimen in a constant temperature water bath at room temperature (25℃±1℃) for 24 hours to saturate it with water; (2) Remove the saturated specimen and freeze it in a low temperature chamber at -18℃±2℃ for 16 hours; (3) After freezing, the specimens were immediately transferred to a constant temperature water bath at 60℃±0.5℃ to thaw for 24 hours to complete one freeze-thaw cycle; After the freeze-thaw cycle, each group of specimens was placed in a high-precision constant temperature chamber at 0℃, -10℃, and -20℃ for at least 4 hours to ensure that the internal temperature of the specimens was completely consistent with the ambient temperature.

[0052] In this embodiment, specimens that have undergone three freeze-thaw cycles were selected for subsequent tests. At each test temperature, five parallel specimens were taken for both the splitting test and the semi-circular bending test, and the test results were taken as the arithmetic mean of the five specimens.

[0053] The average splitting crack index of the specimens after three freeze-thaw cycles in this embodiment is as follows: At 0℃: Fracture energy G in splitting test f2 =8000J / m 2 Splitting strength R in splitting test T =3.65MPa; At -10℃: Fracture energy G in splitting test f2 =7500J / m 2 Splitting strength R in splitting test T =4.20MPa; At -20℃: Fracture energy G in splitting test f2 =6500J / m 2 Splitting strength R in splitting test T =4.50MPa.

[0054] Based on the test temperature, the pre-established linear transformation model corresponding to the corresponding temperature in this invention is invoked. The above-mentioned splitting test indicators are substituted into the model to calculate the predicted values ​​and 95% prediction intervals of the key indicators of the semicircular bending test. All transformation models of this invention pass the significance test (p<0.05) and the Shapiro-Wilk residual normality test (p>0.05), and the reliability of the models meets the engineering requirements.

[0055] The temperature fracture energy G established in this inventionf1 The transformation model and prediction results are as follows: Under 0℃ conditions: the conversion model is: The normality test of the fracture energy residuals is shown in Table 2, and the standard deviation of the residuals σ = 86.15. Substitute the splitting fracture energy G f2 =8000J / m 2 The calculation yields: Gf1=21.734+0.6579x8000=5284.934 J / m 2 ; The 95% prediction interval is: [5284.934±1.96×86.15]=[5116.1,5453.8], which meets the requirements.

[0056] At -10℃: the conversion model is: The normality test of the fracture energy residuals is shown in Table 2, and the standard deviation of the residuals σ = 259.4. Substitute the splitting fracture energy G f2 =7500J / m 2 The calculation yields: Gf1=-616.017+0.7502×7500=5010.490J / m 2 ; The 95% prediction interval is: [5010.490±1.96×259.4]=[4502.1,5518.9], which meets the requirements.

[0057] Under -20℃ conditions: the conversion model is: The normality test of the fracture energy residuals is shown in Table 2. The standard deviation of the residuals σ = 403.9. Substitute the splitting fracture energy G f2 =6500J / m 2 The calculation yields: Gf1=267.899+0.5704×6500=3975.499J / m 2 ; The 95% prediction interval is: [3975.499±1.96×403.9]=[3184.5,4767.8], which meets the requirements.

[0058] The crack resistance index (CRI) conversion model for the temperature-dependent semi-circular bending test established in this invention and the prediction results are as follows: Under 0℃ conditions: the conversion model is: The normality test of the fracture energy residuals is shown in Table 3 of this document, and the standard deviation of the residuals σ = 15.0. Substitute the splitting fracture energy G f2 =8000J / m2 The calculation yields: CRI=38.691+0.0291×8000=271.491; The 95% prediction interval is: [271.491±1.96×15.0]=[242.091,300.891], which meets the requirements.

[0059] At -10℃: the conversion model is: The normality test of the fracture energy residuals is shown in Table 3 of this paper, and the standard deviation of the residuals σ = 28.9. Substitute the splitting fracture energy G f2 =7500J / m 2 The calculation yields: CRI=-93.147+0.0491×7500=275.103; The 95% prediction interval is: [275.103±1.96×28.9]=[218.456,331.747], which meets the requirements.

[0060] Under -20℃ conditions, the conversion model is as follows: The normality test of the fracture energy residuals is shown in Table 3 of this paper, and the standard deviation of the residuals σ = 11.7. Substitute the splitting fracture energy G f2 =6500J / m 2 The calculation yields: CRI=-19.660+0.0218×6500=122.040; The 95% prediction interval is: [122.040±1.96×11.7]=[99.108,144.972], which meets the requirements.

[0061] The stress intensity factor (K) for temperature-dependent semicircular bending tests established in this invention IC The transformation model and prediction results are as follows: Under 0℃ conditions: the conversion model is: The residual normality test is shown in Table 4. The residual standard deviation of this model is σ=3.8. Substitute the splitting strength R T =3.65 MPa, calculated as follows: K IC =-0.029+8.9008×3.65=32.45892 ; The 95% prediction interval is: [32.45892±1.96×3.8]=[25.011,39.907], which meets the requirements.

[0062] Under -10℃ conditions, the conversion model is as follows: The residual normality test is shown in Table 4. The residual standard deviation of this model is σ=0.38. Substitute the splitting strength R T =4.2MPa, calculated as follows: K IC =-1.467+9.2507×4.2=37.38594 ; The 95% prediction interval is: [37.38594±1.96×0.38]=[36.641,38.131], which meets the requirements.

[0063] Under -20℃ conditions, the conversion model is as follows: The residual normality test is shown in Table 4. The residual standard deviation of this model is σ=1.297. Substitute the splitting strength R T =4.5MPa, calculated as follows: K IC =-5.896+10.2999×4.5=40.4535 ; The 95% prediction interval is: [40.4535±1.96×1.297]=[37.911,42.995], which meets the requirements.

[0064] The fracture resistance (R) of the temperature-controlled semi-circular bending test established in this invention C The transformation model and prediction results are as follows: Under 0℃ conditions: the conversion model is: The residual normality test is shown in Table 5. The residual standard deviation of this model is σ=31.4. Substitute the splitting strength R T =3.65 MPa, calculated as follows: R C =274.216+966.0320×3.65=3800.2328MPa; R 2 =0.962; The 95% prediction interval is: [3800.2328±1.96×31.4]=[3738.689,3861.777], which meets the requirements.

[0065] Under -10℃ conditions, the conversion model is as follows: The residual normality test is shown in Table 5. The residual standard deviation of this model is σ=37.5. Substitute the splitting strength R T =4.2 MPa, calculated as follows: R C=62.933+1021.9160×4.2=4354.9802MPa; The 95% prediction interval is: [4354.9802±1.96×37.5]=[4281.480,4428.480], which meets the requirements.

[0066] Under -20℃ conditions, the conversion model is as follows: The residual normality test is shown in Table 5. The residual standard deviation of this model is σ = 140.7. Substitute the splitting strength R T =4.5MPa, calculated as follows: R C =-499.530+1158.5508×4.5=4713.9486MPa; The 95% prediction interval is: [4713.9486±1.96×140.7]=[4438.177,4989.721], which meets the requirements.

[0067] Table 2. Normality test of fracture energy residuals

[0068] Table 3. Normality test of CRI residuals

[0069] Table 4 K IC Residual normality test

[0070] Table 5 R C Residual normality test

[0071] Comparative Example 1 The purpose of Comparative Example 1 is to demonstrate that the temperature-specific modeling strategy adopted in this invention, namely, establishing linear transformation models for -20℃, -10℃, and 0℃ respectively, has significantly higher prediction accuracy compared to a global single temperature model that ignores temperature differences.

[0072] Specifically, the only difference between Comparative Example 1 and the Example is that Comparative Example 1 combines 15 paired data points at all temperatures of -20℃, -10℃, and 0℃, with 5 freeze-thaw cycles at each temperature, into a single dataset to establish a single global linear regression model that is different from the Example.

[0073] Using the least squares method, univariate linear regression models for the splitting index X and the semicircular bending index Y at various temperatures are established, in the form of: Y = a + b × X; where a is the intercept and b is the slope; The steps to establish a global single temperature model are as follows: All 15 data points were input into a univariate linear regression model, and the parameters were estimated using the least squares method. The global model is shown below, and the statistics of the global model are shown in Table 6. G f1 =-584.37+0.2611×G f2 ; Among them, G f1 Fracture energy (J / m) in a semi-circular bending test 2 G f2 The fracture energy in the splitting test is J / m. 2 .

[0074] Table 6 Global Model Statistics

[0075] Although the global model is statistically significant and the residuals are normal, its prediction accuracy varies greatly across different temperature ranges, as detailed below.

[0076] Prediction errors of the global model at various temperatures: Using the global model G f1 =-584.37+0.2611×G f2 Predictions were made based on measured data at -20℃, -10℃, and 0℃, and the errors at each temperature were calculated. The results are shown in Table 7. Table 7 Global Model Temperature Prediction Error

[0077] Where RMSE is the root mean square error, and the formula is: ; in: It is the first i Measured value of semi-circular bending fracture energy of each specimen (J / m) 2 ; It is the first i Predicted fracture energy of semicircular bending of one specimen (J / m) 2 ; n is the number of samples involved in the error calculation; RMSE reflects the average deviation between predicted and measured values, and its dimensions are the same as the original index (J / m²). 2 The smaller the RMSE, the higher the model's prediction accuracy.

[0078] MAPE is the Mean Absolute Percentage Error, and the formula is: ; The meanings of the symbols are the same as above.

[0079] MAPE presents the relative error as a percentage, is dimensionless, and facilitates comparisons of accuracy across different dimensions or indices. The smaller the MAPE, the higher the relative prediction accuracy of the model.

[0080] Using the temperature-specific model employed in the example, predictions were made for the data at their respective temperatures, and the results are shown in Table 8. Table 8. Temperature prediction errors of the full-temperature model

[0081] As shown in Tables 7 and 8, the MAPE of the temperature-specific model is less than 15% at all temperatures, which is far superior to the global model.

[0082] Based on the same set of original data, this comparative example demonstrates that while the global single model ignoring temperature differences is statistically significant, its prediction accuracy varies greatly across different temperature ranges, failing to meet practical engineering requirements. The temperature-specific modeling strategy proposed in this invention establishes transformation models for -20℃, -10℃, and 0℃, achieving high-precision predictions with a MAPE <15% at each temperature, without systematic bias. Therefore, temperature-specific modeling is an indispensable technical feature of this invention and a key means to reliably predict the crack resistance of low-temperature asphalt mixtures.

[0083] Comparative Example 2 The only difference between Comparative Example 2 and Example 1 is that Example 1 uses AC-13 graded SBS modified asphalt mixture, while Comparative Example 2 uses AC-13 graded No. 70 base asphalt (penetration 60 to 80, 0.1 mm, softening point ≥46℃, asphalt-aggregate ratio 5.02%).

[0084] Comparative Example 2 followed the exact same regression method as the Example: univariate linear least squares. Paired data of No. 70 base asphalt at various temperatures were modeled to obtain the following conversion formula. All models passed the significance test (p<0.05) and the residual normality test (Shapiro-Wilk p>0.05), constructing temperature-specific conversion formulas.

[0085] Under 0℃ conditions, the conversion model is as follows: ; The residual standard deviation of the model is σ = 0.92.

[0086] Under -10℃ conditions, the conversion model is as follows: ; The residual standard deviation of the model is σ = 0.81.

[0087] Under -20℃ conditions, the conversion model is as follows: ; The residual standard deviation of the model is σ = 0.74.

[0088] At 0℃, the CRI conversion model is: ; The residual standard deviation of the model is σ = 14.0.

[0089] At -10℃, the CRI conversion model is: ; The residual standard deviation of the model is σ = 11.9.

[0090] At -20℃, the CRI conversion model is: ; The residual standard deviation of the model is σ = 11.7.

[0091] Under the condition of 0℃, K IC The conversion model is as follows: ; The residual standard deviation of the model is σ = 3.8.

[0092] Under -10℃ condition, K IC The conversion model is as follows: ; The residual standard deviation of the model is σ = 0.38.

[0093] At -20℃, K IC The conversion model is as follows: ; The residual standard deviation of the model is σ = 1.297.

[0094] At 0℃, the RC conversion model is: ; The residual standard deviation of the model is σ = 23.4.

[0095] At -10℃, the RC conversion model is: ; The residual standard deviation of the model is σ = 37.5.

[0096] At -20℃, the RC conversion model is: ; The residual standard deviation of the model is σ=17.

[0097] Among them, G f1 Fracture energy (J / m) in a semi-circular bending test 2 G f2 Fracture energy in splitting test (J / m) 2 CRI: Crack resistance index for semicircular bending test, dimensionless; K ICStress intensity factor in semi-circular bending test ;R T Splitting strength (MPa) in splitting test; R C Fracture resistance in semi-circular bending test (MPa).

[0098] Cross-prediction error analysis: To quantify the prediction error of directly applying the SBS model of this invention to base asphalt No. 70, the following cross-prediction was performed: the SBS model (temperature-specific) of the embodiment was used to predict the semi-circular bending test index of base asphalt No. 70 in Comparative Example 2, and the result was compared with that. Based on data statistics and regression modeling, the following was calculated: At 0℃: Fracture energy G in splitting test f2 = 8000J / m²; Splitting strength R in splitting test T =3.65MPa; At -10℃: Fracture energy G in splitting test f2 = 7500 J / m²; Splitting strength R in splitting test T = 4.20MPa; At -20℃: Fracture energy G in splitting test f2 = 6500J / m²; Splitting strength R in splitting test T = 4.50MPa; The calculation results are shown in Tables 9-12 below: Table 9 Cross-prediction of fracture energy

[0099] Table 10 CRI Forecast Cross-Forecast

[0100] Table 11 K IC Forecast cross forecast

[0101] Table 12 R C Forecast cross forecast

[0102] As shown in Tables 9-12, the index values ​​of the No. 70 base asphalt are significantly lower than those of the SBS modified asphalt. Directly applying the SBS model results in a prediction error of approximately 42% to 43%. The cross-prediction error is substantial, far exceeding the acceptable range for engineering applications. Therefore, the formulas in this example are only applicable to AC-13 graded SBS modified asphalt with an asphalt-aggregate ratio of 5.02%.

[0103] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0104] The above embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

[0105] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests, characterized in that: Includes the following steps: S1 Take AC-13 graded SBS modified asphalt mixture standard specimens and conduct splitting tests on the standard specimens in the low temperature brittle range of -20℃ to 0℃ to obtain at least one splitting test index. S2 selects a preset linear transformation model corresponding to the current splitting test temperature; S3 substitutes the measured splitting test index into the preset linear transformation model to calculate the index of the asphalt mixture semi-circular bending test at the corresponding temperature. The splitting test indicators include splitting test fracture energy and splitting strength; the semicircular bending test indicators include semicircular bending test fracture energy, semicircular bending test stress intensity factor, semicircular bending test fracture resistance, and semicircular bending test crack resistance index. The preset linear transformation model described in S2 is pre-established using the following method: S21 prepared multiple asphalt mixture specimens and subjected them to 0-12 freeze-thaw cycles to obtain specimen groups under different freeze-thaw cycle periods. S22 In each freeze-thaw cycle, multiple parallel specimens are taken from the specimen group for splitting test and multiple parallel specimens are taken for semi-circular bending test. The measured values ​​of the splitting test index and the semi-circular bending test index of each parallel specimen are measured respectively. S23 For each test temperature, iterates through each freeze-thaw cycle at the test temperature, takes the arithmetic mean of the measured values ​​of the splitting test index of all parallel specimens in the same cycle, and takes the arithmetic mean of the measured values ​​of the semicircular bending test index of all parallel specimens in the cycle. The two arithmetic means are used to form a set of paired data points corresponding to the cycle; finally, multiple sets of independent paired data points with the same number of freeze-thaw cycles at each temperature are obtained. S24 uses the least squares method to perform univariate linear regression analysis on paired data points at each test temperature to establish a linear regression model between the splitting test index x and the semicircular bending test index y: Y=a+bX, where a is the intercept and b is the slope; S25 performs significance tests and residual normality tests on each linear regression model, and retains the linear regression models that pass the tests as the preset linear transformation models corresponding to the temperatures mentioned in S2.

2. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 1, characterized in that: The number of freeze-thaw cycles includes 0, 3, 6, 9, and 12 freeze-thaw cycles.

3. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 1, characterized in that: The asphalt-aggregate ratio of the AC-13 graded SBS modified asphalt mixture is 5.02%.

4. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 1, characterized in that: In S2, the test temperature is 0℃, -10℃ or -20℃, and the standard specimen is kept at the test temperature for no less than 4 hours.

5. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 4, characterized in that: When the temperature of the experiment is 0°C, the linear transformation model is selected from at least one of the following formulas: Fracture energy: CRI: K IC ： R C ： ； G f1 Fracture energy (J / m) in a semi-circular bending test 2 G f2 The fracture energy in the splitting test is J / m. 2 CRI is the crack resistance index for the semi-circular bending test, which is dimensionless; K IC Stress intensity factor for semicircular bending test ;R T The splitting strength (MPa) of the splitting test; R C The fracture resistance (MPa) for the semi-circular bending test.

6. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 4, characterized in that: In S2, when the temperature of the experiment is -10℃, the linear transformation model is selected from at least one of the following formulas: Fracture energy: CRI: K IC ： R C： 。 7. The method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests according to claim 4, characterized in that: In S2, when the temperature of the experiment is -20℃, the linear transformation model is selected from at least one of the following formulas: Fracture energy: CRI: K IC ： R C ： 。 8. A rapid evaluation system for the crack resistance of asphalt mixtures, employing the method for predicting the semi-circular bending index and evaluating the crack resistance of asphalt mixtures based on splitting tests as described in any one of claims 1-7, comprising: The data input module is used to input the splitting test parameters and the test low temperature; The model storage module is used to store the linear transformation model and its coefficients at different temperatures; The calculation module calls the corresponding linear transformation model based on the input temperature to calculate the predicted values ​​of the semicircular bending test index and calculates the 95% prediction interval. The output module displays or exports the prediction results and prediction ranges, and supports the generation of prediction reports. The linear transformation models stored in the model storage module include transformation models at three temperatures: 0℃, -10℃, and -20℃. The models at each temperature include fracture energy transformation model, CRI transformation model, stress intensity factor transformation model, and fracture resistance transformation model.

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