A dynamic-static modulus conversion model of asphalt pavement material based on tension-compression difference

Abstract

The application discloses a kind of asphalt pavement material dynamic-static modulus conversion models based on tension-compression difference.The model is by testing asphalt mixture and semi-flexible pavement material under different loading frequency or different loading rate tension-compression dynamic, static modulus respectively constructs the correlation model of static modulus-loading rate and dynamic modulus-loading frequency, then based on equivalent principle, constructs the correlation model of dynamic modulus-equivalent loading rate, again with static modulus-loading rate correlation model fitting, namely obtains.The conversion model structure is clear, data source is wide, easy to operate, and effectively combines theoretical model and experimental data, comprehensively reflects the correlation between loading rate and tension-compression dynamic-static modulus, with wide application range and accuracy, and has important guiding significance to asphalt pavement structure design.

Description

Technical Field

[0001] This invention relates to a dynamic and static modulus conversion model, specifically a dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compression differences, belonging to the field of road engineering technology. Background Technology

[0002] Currently, both domestic and international pavement structure mechanical analysis employs traditional linear elastic theory, and the dynamic compressive resilient modulus of the surface layer material is used in design and verification, without fully considering the tensile-compressive differences in the material's properties, leading to significant errors in the calculation results. my country has a long history of research on static modulus, resulting in mature theories and experimental methods. Studies have shown that the dynamic modulus of pavement materials is approximately 2 to 3 times the static modulus, and the mechanical properties of pavement under actual dynamic loads differ significantly from those in the static model. Therefore, it is necessary to establish the conversion relationship between the tensile-compressive dynamic and static moduli of asphalt pavement materials, verifying the accuracy of dynamic modulus test results while achieving rapid conversion between dynamic and static moduli.

[0003] Some researchers have considered the tensile and compressive differences of materials when calculating pavement structures. They have conducted mechanical analyses on typical asphalt pavement structures and found that the difference in mechanical response between structural calculations using compressive modulus and tensile / compressive dual modulus as material stiffness parameters can reach more than 50%. Other researchers have conducted compressive dynamic modulus tests on seven different asphalt mixtures and found that the dynamic modulus of asphalt mixtures is affected by various factors such as temperature and loading frequency, and that it has a significant velocity dependence.

[0004] Although some scholars have conducted some research on the relationship between the dynamic and static moduli of asphalt pavement materials under standard testing methods, the test results of the dynamic and static moduli are affected by a variety of factors, and the one-sided establishment of the relationship curve is unreasonable.

[0005] Therefore, how to consider the influence of various internal and external factors on the dynamic and static modulus of asphalt pavement materials and realize the conversion of the dynamic and static modulus of asphalt pavement materials under complex conditions is a key problem that needs to be solved by those skilled in the art. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to provide a dynamic and static modulus conversion model for asphalt pavement materials based on the tension-compression difference. This model is based on the tension-compression difference characteristics of the material. It constructs correlation models between static modulus and loading rate, and dynamic modulus and loading frequency using experimental data of the material. Then, based on the equivalence principle, it constructs a correlation model between dynamic modulus and equivalent loading rate. Finally, it fits this model to the static modulus-loading rate correlation model to obtain the final conversion model. This conversion model has a clear structure, broad data sources, and is easy to operate. It effectively combines theoretical models with experimental data, comprehensively reflecting the correlation between loading rate and the tension-compression dynamic and static moduli. It has a wide range of applications and high accuracy, and provides important guidance for asphalt pavement structure design.

[0007] To achieve the above technical objectives, the present invention provides a dynamic and static modulus conversion model for asphalt pavement materials based on tension-compression differences, including: Step S1: According to the test requirements of the "Test Procedures for Asphalt and Mixtures in Highway Engineering" (JTG E20-2011), determine the mix proportions of asphalt mixture and semi-flexible pavement material composed of raw materials including asphalt mixture, and obtain the test specimens required for both.

[0008] Step S2: After the specimens obtained in Step S1 are kept at a constant temperature, the tensile and compressive dynamic and static moduli of asphalt mixtures and semi-flexible pavement materials are tested under different loading frequencies or different loading rates.

[0009] Step S3: Based on the test results of Step S2, establish correlation models between the tensile and compressive static modulus and loading rate of asphalt mixtures and semi-flexible pavement materials, respectively.

[0010] Step S4: Based on the test results of Step S2, establish correlation models between the tensile and compressive dynamic modulus and loading frequency for asphalt mixtures and semi-flexible pavement materials, respectively.

[0011] Step S5: Based on the correlation models obtained in Steps S3 and S4, establish a dynamic modulus-equivalent loading rate model, and then fit it with the correlation model of static modulus-loading rate to obtain a dynamic-static modulus conversion model.

[0012] As a preferred embodiment, the process of determining the mixing ratio in step S1 includes:

[0013] Step S1-1: Determine the optimal asphalt-aggregate ratio for asphalt mixtures using the Marshall design method;

[0014] Step S1-2: The optimal asphalt content of the matrix asphalt mixture in the semi-flexible pavement material is determined by using the results of the Schellenberg leakage test and the Kentenberg fly-through test, and the mix proportion of cement mortar is determined by using orthogonal design test.

[0015] As a preferred embodiment, the test specimens required in step S1 include uniaxial compression test specimens and direct tensile test specimens.

[0016] As a preferred embodiment, the uniaxial compression test specimen is prepared using a rotary compactor.

[0017] As a preferred embodiment, the direct tensile test specimen is formed by a hydraulic rutting specimen forming machine, cut into beam-shaped specimens, and then filled with cement mortar.

[0018] As a preferred embodiment, the static modulus testing process in step S2 is as follows: the asphalt mixture and the semi-flexible pavement material are subjected to progressive loading and unloading tests to obtain the static modulus under each load level.

[0019] As a preferred embodiment, the dynamic modulus testing process in step S2 is as follows: applying offset sine wave or semi-sine wave axial compressive stress to asphalt mixture and semi-flexible pavement material at a certain temperature and loading frequency to test the recoverable axial strain, thereby obtaining the dynamic modulus under different conditions.

[0020] As a preferred embodiment, the correlation model between the tensile / compressive static modulus and the loading rate is established as follows: Based on the test results of the tensile / compressive static modulus of asphalt mixtures and semi-flexible pavement materials and their corresponding loading rates, a relationship model between the static modulus and the loading rate is established, and the calculation process is as follows:

[0021] Formula 1:

[0022] Formula 2:

[0023] In Equations 1 and 2: E c E is the uniaxial compressive static modulus, with dimensions in MPa. t The direct tensile static modulus, with dimensions in MPa; a c b c a t and b t is the fitting parameter, dimensionless; v is the loading rate, with dimensions in MPa / s.

[0024] As a preferred embodiment, the correlation model between the tensile / compressive dynamic modulus and the loading frequency is established as follows: Based on the test results of the tensile / compressive dynamic modulus of asphalt mixtures and semi-flexible pavement materials and their corresponding loading frequencies, a relationship model between the dynamic modulus and the loading frequency is established, and the calculation process is as follows:

[0025] Formula 3:

[0026] Formula 4:

[0027] In equations 3 and 4: E* cd E* is the uniaxial compressive dynamic modulus, with dimensions in MPa. td The dynamic modulus is directly tensile, with dimensions in MPa; a cd b cd a td and b td is the fitting parameter, which is dimensionless; f is the loading frequency, which is in Hz.

[0028] As a preferred embodiment, the process of establishing the dynamic modulus-equivalent loading rate model is as follows: based on the equivalence principle, the loading time is obtained according to the loading frequency, and then the equivalent loading rate of the dynamic modulus is calculated by combining the peak stress applied during the test and the contact area of ​​the specimen.

[0029] As a preferred embodiment, the specific calculation process of the dynamic modulus-equivalent loading rate model is as follows:

[0030] Formula 5:

[0031] Formula 6:

[0032] Formula 7:

[0033] Formula 8:

[0034] In equations 5-8: t is the loading time, in seconds; f is the loading frequency, in Hz; P max σ is the peak stress, in kN; s is the contact area of ​​the specimen, in mm². 2 ;a' cd b' cd 、a' td and b' td These are the fitting parameters, which are dimensionless.

[0035] As a preferred embodiment, the specific expression of the dynamic-static modulus conversion model is as follows:

[0036] Formula 9: E=A+B|E * |;

[0037] In Equation 9, E is the static modulus, A and B are fitting parameters, and |E| * | is the dynamic modulus.

[0038] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0039] 1) The dynamic-static modulus conversion model provided by this invention is based on the tensile-compressive difference characteristics of materials. It constructs a correlation model between static modulus and loading rate and dynamic modulus and loading frequency using experimental data of materials. Then, based on the equivalence principle, it constructs a correlation model between dynamic modulus and equivalent loading rate. Finally, it is fitted with the correlation model between static modulus and loading rate to obtain the conversion model. This conversion model has a clear structure, a wide range of data sources, is easy to operate, and effectively combines theoretical models with experimental data. It comprehensively reflects the correlation between loading rate and tensile-compressive dynamic and static moduli, and has a wide range of applications and high accuracy. It has important guiding significance for the design of asphalt pavement structures.

[0040] 2) In the technical solution provided by this invention, the power function is selected to construct the correlation models of static modulus-loading rate, dynamic modulus-loading frequency, and dynamic modulus-equivalent loading rate, which can accurately reflect the nonlinear relationship between independent and dependent variables. Then, the static modulus-loading rate correlation model is constructed through linear fitting. The fitting results are highly consistent with the experimental results, with a fitting coefficient ≥0.99 and excellent regression performance. It can accurately realize the rapid conversion between dynamic and static modulus, effectively solving the data distortion problem caused by the single dependent variable and the narrow range when converting dynamic and static modulus in the prior art. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0042] Figure 1 This is a graph showing the variation of the static modulus of direct tension with loading rate in Embodiment 1 of the present invention;

[0043] Figure 2 This is a graph showing the variation of uniaxial compression static modulus with loading rate in Embodiment 1 of the present invention;

[0044] Figure 3 This is a graph showing the variation of the dynamic modulus of direct tension with loading frequency in Embodiment 1 of the present invention;

[0045] Figure 4 This is a graph showing the variation of uniaxial compression dynamic modulus with loading frequency in Embodiment 1 of the present invention;

[0046] Figure 5 This is a graph showing the variation of the uniaxial compression dynamic modulus of SFP-16 with loading rate in Embodiment 1 of the present invention;

[0047] Figure 6This is a fitting diagram of the dynamic and static modulus conversion model of asphalt pavement materials in Embodiment 1 of the present invention;

[0048] Figure 7 This is an independent dataset for asphalt pavement materials at loading rates of 0.2, 0.3, and 0.4 MPa / s in Example 1 of this invention;

[0049] Figure 8 This is a graph showing the relative error between the measured values ​​and the calculated values ​​from the conversion model at loading rates of 0.2, 0.3, and 0.4 MPa / s in Embodiment 1 of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Example 1

[0052] This embodiment provides a dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences. The specific process is as follows:

[0053] Step S1: According to the test requirements of the "Test Procedures for Asphalt and Mixtures in Highway Engineering" (JTG E20-2011), the aggregates that have been screened layer by layer are dried and mixed with asphalt to prepare dense-graded asphalt mixture (AC-16) and large-pore asphalt mixture. For the uniaxial compression test of the asphalt mixture, a rotary compactor is used to prepare cylindrical specimens with a height of 100±2mm and a diameter of 100±2mm. For the direct tensile standard specimen, a hydraulic rutting specimen forming machine is used to form rutting plates with a length of 300mm × width of 300mm × height of 50mm. The dense-graded asphalt mixture is then cut into 5 pieces with a length of 250mm × width of 50mm × height of... Beam-type specimens with a height of 50mm; cylindrical specimens of large-pore asphalt mixture and rutting slabs were demolded after being laid horizontally and cooled at room temperature for 12 hours, and then placed into custom-made test molds. The bottom of the test molds was tightly sealed with plastic wrap and tape, and then pre-made cement mortar was poured in. After the cement mortar was vibrated and seeped in, the excess mortar on the surface was scraped off. The specimens and test molds were placed in an environment with a humidity of not less than 90% and a temperature of 20℃±3℃ for 28 days for curing. Finally, semi-flexible pavement material (SFP-16) was formed, and its rutting slabs were cut into beam-type specimens of the same size as AC-16.

[0054] Step S2: Place the prepared specimen in a constant temperature chamber at 20℃ for 4-5 hours. Then place it in the direct tensile and uniaxial compression fixture of the Multifunctional Material Testing System (MTS-Landmark), and adjust the fixture position so that the indenter of the test specimen makes initial contact with the specimen. The top tension rod is fully connected to the Multifunctional Material Testing System, and the entire test process is completed in the constant temperature chamber. Using the built-in program of the Multifunctional Material Testing System and setting the applied load, the test is performed according to the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG). In accordance with the relevant requirements of E20-2011, both AC-16 and SFP-16 specimens were subjected to direct tensile and uniaxial compressive static modulus tests at loading rates of 0.01 MPa / s, 0.02 MPa / s, 0.05 MPa / s, 0.1 MPa / s, and 0.5 MPa / s. The test results are shown in Table 1. For the direct tensile and uniaxial compressive dynamic modulus tests of AC-16 and SFP-16, six different loading frequencies (0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, and 25 Hz) were selected according to the specification to apply sinusoidal axial tensile and compressive loads to the specimens. The test results are shown in Table 2.

[0055] Table 1. Static modulus test results (MPa)

[0056]

[0057] Table 2. Dynamic modulus test results (MPa)

[0058]

[0059] Step S3: Based on the test results obtained in Step S2, establish correlation models of tensile and compressive static modulus-loading rate for SFP-16 and AC-16 at 20℃, respectively, using a power function to describe the above models; establish correlation models of direct tensile static modulus-loading rate and uniaxial compressive static modulus-loading rate for SFP-16 and AC-16 based on the data in Table 1, and the results are as follows. Figure 1 and Figure 2 As shown, the specific calculation formula is as follows:

[0060] Formula 1:

[0061] Formula 2:

[0062] In Equations 1 and 2: E c E is the uniaxial compressive static modulus, with dimensions in MPa. t The direct tensile static modulus, with dimensions in MPa; a c b c a t and b tis the fitting parameter, dimensionless; v is the loading rate, with dimensions in MPa / s.

[0063] Step S4: Based on the test results obtained in Step S2, establish the correlation models of tensile and compressive dynamic modulus-loading frequency for SFP-16 and AC-16 at 20℃ respectively; establish the correlation models of direct tensile dynamic modulus-loading frequency and uniaxial compressive dynamic modulus-loading frequency for SFP-16 and AC-16 based on the data in Table 2. The results are as follows. Figure 3 and Figure 4 As shown, the specific calculation formula is as follows:

[0064] Formula 3:

[0065] Formula 4:

[0066] In equations 3 and 4: E* cd E* is the uniaxial compressive dynamic modulus, with dimensions in MPa. td The dynamic modulus is directly tensile, with dimensions in MPa; a cd b cd a td and b td is the fitting parameter, which is dimensionless; f is the loading frequency, which is in Hz.

[0067] Step S5: Based on the correlation model obtained in steps S3 and S4, establish a dynamic modulus-equivalent loading rate model. To facilitate the demonstration of the model establishment process, the dynamic modulus of SFP-16 uniaxial compression is calculated as an example under the conditions of 20℃ and a loading frequency of 10Hz. The calculation process is as follows:

[0068] Formula 5:

[0069] Formula 6:

[0070] Based on the conversion relationship between loading rate and loading frequency, the equivalent loading rates for each loading frequency in the SFP-16 uniaxial compression dynamic modulus test are: 0.11 MPa / s (0.1 Hz), 0.55 MPa / s (0.5 Hz), 1.1 MPa / s (1 Hz), 5.5 MPa / s (5 Hz), 11 MPa / s (10 Hz), and 27.5 MPa / s (25 Hz). A correlation model between the SFP-16 uniaxial compression dynamic modulus and the equivalent loading rate is established, and the results are as follows: Figure 5 As shown, the specific calculation process is as follows:

[0071] Formula 7:

[0072] Formula 8:

[0073] In equations 5-8: t is the loading time, in seconds; f is the loading frequency, in Hz; P max σ is the peak stress, in kN; s is the contact area of ​​the specimen, in mm². 2 ;a ’ cd b ’ cd a ’ td and b ’ td These are the fitting parameters, which are dimensionless.

[0074] Depend on Figure 5 It can be seen that the uniaxial compression dynamic modulus of SFP-16 increases with the increase of the equivalent loading rate, and the growth rate gradually decreases, exhibiting a power function relationship. Moreover, the fitting coefficient is greater than 0.99, indicating a high degree of fitting. The dynamic modulus at each loading rate can be obtained through the fitting relationship, and the calculation results are shown in Table 3.

[0075] Table 3 Static and Dynamic Modulus of Pavement Materials (Tensile and Compressive)

[0076]

[0077] Based on the tensile and compressive dynamic and static moduli of SFP-16 and AC-16 in Table 3, the results are fitted to obtain a dynamic-static modulus conversion model, the results of which are as follows: Figure 6 As shown, the specific calculation process is as follows:

[0078] Formula 9: E=A+B|E * |;

[0079] In Equation 9, E is the static modulus, A and B are fitting parameters, and |E| * | is the dynamic modulus.

[0080] To further verify the accuracy and precision of the conversion model, the tensile and compressive dynamic and static moduli of SFP-16 and AC-16 were tested at loading rates of 0.2 MPa / s, 0.3 MPa / s, and 0.4 MPa / s. Independent datasets were used for discrimination and evaluation, and the test results were plotted on [the graph]. Figure 7 Based on the dynamic modulus test results, the static modulus is calculated according to the transformation model, thereby calculating the relative error between the two, such as... Figure 8 As shown, the maximum relative error between the measured value and the calculated value of the conversion model does not exceed 3.5%, indicating that the dynamic and static modulus conversion model of asphalt pavement material based on tension-compression difference of this invention has high accuracy.

[0081] As described above, the dynamic-static modulus conversion model provided by this invention fully considers the correlation between dynamic and static models and loading rate and frequency. It effectively solves the problem that existing technologies only perform simple quantitative analysis on the mechanical parameters such as the modulus of asphalt pavement materials, rarely studying the variation law of material mechanical parameters under the influence of multiple factors, thus leading to the problem of single-factor consideration and incomplete scope. Furthermore, this model is applicable to the conversion of dynamic and static moduli at different loading frequencies, overcoming the difficulty of existing technologies that only consider the dynamic-static correspondence at a loading frequency of 10Hz, making it impossible to achieve a one-to-one correspondence between dynamic and static moduli at different loading frequencies. This model makes the selection of pavement material mechanical parameters more reasonable and the pavement structure design more accurate and scientific, providing a theoretical basis for the selection of mechanical parameters and structural design of asphalt pavement materials.

Claims

1. A dynamic-static modulus conversion model for asphalt pavement materials based on tensile-compressive differences, characterized in that, include: Step S1: According to the test requirements of the "Test Procedures for Asphalt and Mixtures in Highway Engineering" (JTG E20-2011), determine the mix proportions of asphalt mixture and semi-flexible pavement material composed of raw materials including asphalt mixture, and obtain the test specimens required for both. Step S2: After the specimens obtained in Step S1 are kept at a constant temperature, the tensile and compressive dynamic and static moduli of asphalt mixtures and semi-flexible pavement materials are tested under different loading frequencies or different loading rates. Step S3: Based on the test results of Step S2, establish correlation models between the tensile and compressive static modulus and loading rate of asphalt mixtures and semi-flexible pavement materials, respectively. Step S4: Based on the test results of Step S2, establish correlation models between the tensile and compressive dynamic modulus and loading frequency for asphalt mixtures and semi-flexible pavement materials, respectively. Step S5: Based on the correlation models obtained in Steps S3 and S4, establish a dynamic modulus-equivalent loading rate model, and then fit it with the correlation model of static modulus-loading rate to obtain a dynamic-static modulus conversion model. The process of establishing the dynamic modulus-equivalent loading rate model is as follows: based on the equivalence principle, the loading time is obtained according to the loading frequency, and then the equivalent loading rate of the dynamic modulus is calculated by combining the peak stress applied during the test and the contact area of ​​the specimen. The specific calculation process of the dynamic modulus-equivalent loading rate model is as follows: Formula 5: ; Formula 6: ; Formula 7: ; Formula 8: ; In equations 5-8: t is the loading time, in seconds; f is the loading frequency, in Hz; P max σ is the peak stress, in kN; s is the contact area of ​​the specimen, in mm². 2 ;;a ’ cd b ’ cd a ’ td and b ’ td These are the fitting parameters, which are dimensionless. The specific expression for the dynamic-static modulus conversion model is as follows: Formula 9: ; In Equation 9, E is the static modulus, and A and B are the fitting parameters. It is a dynamic modulus.

2. The dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences according to claim 1, characterized in that: The process of determining the mix proportion in step S1 includes: Step S1-1: Determine the optimal asphalt-aggregate ratio for asphalt mixtures using the Marshall design method; Step S1-2: The optimal asphalt content of the matrix asphalt mixture in the semi-flexible pavement material is determined by using the results of the Schellenberg leakage test and the Kentenberg fly-through test, and the mix proportion of cement mortar is determined by using orthogonal design test.

3. The dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences according to claim 1, characterized in that: The test specimens required in step S1 include uniaxial compression test specimens and direct tensile test specimens; the uniaxial compression test specimens are prepared using a rotary compactor; the direct tensile test specimens are formed using a hydraulic rutting specimen forming machine, cut into beam-shaped specimens, and then filled with cement mortar.

4. The dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences according to claim 1, characterized in that: The static modulus test process in step S2 is as follows: the asphalt mixture and the semi-flexible pavement material are subjected to loading and unloading tests at each level to obtain the static modulus under each level of load. The dynamic modulus testing process in step S2 is as follows: applying offset sine wave or semi-sine wave axial compressive stress to asphalt mixture and semi-flexible pavement material at a certain temperature and loading frequency to test the recoverable axial strain, thereby obtaining the dynamic modulus under different conditions.

5. The dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences according to claim 1, characterized in that: The correlation model between the tensile and compressive static modulus and the loading rate is established as follows: Based on the test results of the tensile and compressive static modulus of asphalt mixtures and semi-flexible pavement materials and their corresponding loading rates, a relationship model between the static modulus and the loading rate is established, and the calculation process is as follows: Formula 1: ; Formula 2: ; In equations 1 and 2: E c E is the uniaxial compressive static modulus, with dimensions in MPa. t The direct tensile static modulus, with dimensions in MPa; a c b c a t and b t is the fitting parameter, dimensionless; v is the loading rate, with dimensions in MPa / s.

6. The dynamic and static modulus conversion model for asphalt pavement materials based on tensile-compressive differences according to claim 1, characterized in that: The correlation model between the tensile and compressive dynamic modulus and the loading frequency is established as follows: Based on the test results of the tensile and compressive dynamic modulus of asphalt mixtures and semi-flexible pavement materials and their corresponding loading frequencies, a relationship model between the dynamic modulus and the loading frequency is established, and the calculation process is as follows: Formula 3: ; Formula 4: ; In equations 3-4: E* cd E* is the uniaxial compressive dynamic modulus, with dimensions in MPa. td The dynamic modulus is directly tensile, with dimensions in MPa; a cd b cd a td and b td is the fitting parameter, which is dimensionless; f is the loading frequency, which is in Hz.

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