A method for obtaining the interlayer shear strength of asphalt pavement under real working conditions
By constructing a pavement structure model and converting it into indoor oblique shear fatigue test parameters, the problem of insufficient correlation between pavement working conditions and indoor test parameters in the existing technology was solved, and accurate assessment of interlayer shear performance and identification of defects were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2022-11-07
- Publication Date
- 2026-06-30
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Figure CN115758813B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of interlayer performance testing of asphalt pavement, and specifically to a method for obtaining the interlayer shear strength of asphalt pavement under real working conditions. Background Technology
[0002] The interlayer bonding state of asphalt pavement is one of the important factors determining the service life of the pavement. Good interlayer bonding can effectively improve the overall integrity of the pavement structure and extend its fatigue life. Literature shows that road sections with steep longitudinal slopes, curves, intersections, bus stops, tunnel entrances / exits, high temperatures, heavy loads, and low speeds are prone to numerous early-stage defects, resulting in a service life far shorter than expected. Therefore, quantifying the impact of different pavement operating conditions on interlayer performance is of great significance.
[0003] Factors affecting the interlayer shear performance of asphalt pavements can be broadly categorized into internal and external factors. Internal factors include interlayer treatment methods, bonding materials, interface contamination, and interface morphology; external factors include the stress environment at the interlayer interface, stress duration, and temperature environment. In actual road conditions, the external factors to consider are more complex. Axle load, vehicle speed, vehicle acceleration, curves, road longitudinal slope, and pavement friction coefficient all affect interlayer durability. Previous studies typically simplified actual pavement conditions to four factors at the interlayer interface: compressive stress, shear stress, loading period, and temperature, and investigated their impact on interlayer performance.
[0004] Existing technologies utilize indoor compressive-direct shear fatigue tests to investigate the interlayer shear fatigue performance under different compressive stresses, shear stresses, loading frequencies, and temperatures, simulating the evolution of interlayer performance under various road conditions. However, the correlation between the test parameters and road condition factors is weak, making it impossible to translate these parameters into the influence of road condition factors on interlayer performance. Existing technologies, after comparing the interlayer stress state in compressive-direct shear and oblique shear tests with the interlayer stress state under moving road loads, propose that the constant compressive stress in the compressive-direct shear test enhances interlayer performance, leading to overestimation of test results. The oblique shear test, therefore, better reflects the actual stress state between pavement layers.
[0005] Some existing technologies suggest that a 25.5° angle between the interlayer interface and the horizontal plane can be used to simulate conventional traffic loads on asphalt pavements. Others use a 45° angle to simulate conventional traffic loads on bridge decks and a 60° angle to simulate extreme braking conditions on bridge decks. It is evident that existing studies lack a correlation between actual pavement conditions and laboratory shear test parameters, making accurate conversion between the two impossible. A single oblique shear angle can only simulate one type of road condition, making it difficult to quantify the impact of different pavement conditions on interlayer performance. Therefore, to study the influence of different pavement conditions on interlayer performance, a method is needed that can design and calculate laboratory oblique shear test parameters based on actual pavement conditions and obtain shear performance data. Summary of the Invention
[0006] To address the aforementioned shortcomings in the prior art, this invention provides a method for obtaining the interlayer shear strength of asphalt pavement under real-world working conditions, which solves the problem that the prior art struggles to quantify the impact of different pavement working conditions on interlayer performance.
[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:
[0008] A method for obtaining the interlayer shear strength of asphalt pavement under real working conditions is provided, which includes the following steps:
[0009] S1. Obtain the structural and material parameters that conform to the real road surface, and construct the road surface structure model through simulation software;
[0010] S2. By changing the values of vertical compressive stress and horizontal frictional resistance in the simulated road structure model, the shear stress and compressive stress at the most unfavorable load point can be obtained.
[0011] S3. Obtain the pavement structure coefficients based on the relationships between shear stress and compressive stress and vertical compressive stress and horizontal frictional resistance, respectively.
[0012] S4. Based on the pavement structure coefficient, the factors in the actual working conditions are converted into indoor oblique shear fatigue test parameters, and the interlayer shear resistance of asphalt pavement under real working conditions is obtained through the indoor oblique shear fatigue test results.
[0013] Furthermore, the structural parameters that conform to real pavement include the thickness of each layer of the pavement structure; the material parameters that conform to real pavement include material type, elastic material parameters, and viscoelastic material parameters; among which, the elastic material parameters include dynamic modulus, density, and Poisson's ratio; and the viscoelastic material parameters include the Prony series.
[0014] Furthermore, the specific method for step S3 is as follows:
[0015] According to the formula:
[0016] τ=k1·P+k3·T
[0017] σ=k2·P+k4·T
[0018] Obtain the pavement structure coefficients k1, k2, k3, and k4; where τ is the shear stress at the most unfavorable load point on the interlayer interface under pavement working conditions; σ is the compressive stress at the most unfavorable load point under actual pavement working conditions; P is the vertical compressive stress in the simulation; and T is the horizontal frictional resistance in the simulation.
[0019] Furthermore, the specific method for converting the factors in the actual working conditions into indoor oblique shear fatigue test parameters based on the pavement structure coefficient in step S4 is as follows:
[0020] According to the formula:
[0021]
[0022]
[0023] Obtaining indoor oblique shear fatigue test parameters (F) * ,θ * ); where F * The fatigue loading force parameters for indoor oblique shear fatigue tests; θ * denoted as α, where m is the shear angle in the indoor oblique shear fatigue test; m is the axle load; g is the acceleration due to gravity; a is the vehicle acceleration; A1 is the contact area between the tire and the road surface under standard axle load; α is the road surface slope; and A is the area of the interlayer interface of the specimen in the indoor oblique shear fatigue test.
[0024] Furthermore, when the scenario is emergency braking of a vehicle, the vehicle acceleration a = gμ; μ is the coefficient of sliding friction of the road surface.
[0025] Furthermore, when the scenario involves a winding road, according to the formula:
[0026]
[0027] Update the vehicle acceleration to obtain a new vehicle acceleration a*; where v is the vehicle speed and R is the curve radius.
[0028] Furthermore, the specific method for obtaining the interlayer shear resistance of asphalt pavement under real working conditions through indoor oblique shear fatigue test results in step S4 is as follows:
[0029] The amplitude of the sine wave of the fatigue loading force in the indoor oblique shear fatigue test is set as F. * The shearing angle of the oblique shear is set to θ. *The loading frequency was set according to the driving speed, and the ambient temperature of the test chamber was set according to the road surface temperature. The fatigue failure test was carried out to obtain the interlayer shear fatigue life, and then the interlayer shear performance of asphalt pavement under real working conditions was obtained.
[0030] Furthermore, the loading frequency is obtained as follows:
[0031] According to the formula:
[0032] f = 0.227v 0.944
[0033] Get the loading frequency f.
[0034] The beneficial effects of this invention are as follows: This invention constructs a mapping equation between actual road surface working conditions and indoor oblique shear test parameters, realizes the conversion between road surface working conditions and oblique shear test parameters, and uses this equation to accurately evaluate the interlayer shear fatigue performance under different road surface working conditions through indoor oblique shear tests. Attached Figure Description
[0035] Figure 1 This is a flowchart illustrating the method.
[0036] Figure 2 This is a schematic diagram of the apparatus used in the interlayer oblique shear test in the embodiment;
[0037] Figure 3 The example shows the time history curves of interlayer stress (σ,τ).
[0038] Figure 4 This is a schematic diagram of the inter-story stress (σ,τ) at the most unfavorable load point in the embodiment.
[0039] Figure 5 Time history curves showing the evolution of interlayer stress (σ,τ) under different vertical compressive stress (P);
[0040] Figure 6 A schematic diagram showing the evolution of interlayer stress (σ,τ) under different levels of frictional resistance (T);
[0041] Figure 7 This is a schematic diagram of the ABAQUS road surface structure model in the embodiment;
[0042] Figure 8 The results of the oblique shear fatigue test obtained in the examples are shown. Detailed Implementation
[0043] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0044] like Figure 1 As shown, the method for obtaining the interlayer shear strength of asphalt pavement under real working conditions includes the following steps:
[0045] S1. Obtain the structural and material parameters that conform to the real road surface, and construct the road surface structure model through simulation software;
[0046] S2. By changing the values of vertical compressive stress and horizontal frictional resistance in the simulated road structure model, the shear stress and compressive stress at the most unfavorable load point can be obtained.
[0047] S3. Obtain the pavement structure coefficients based on the relationships between shear stress and compressive stress and vertical compressive stress and horizontal frictional resistance, respectively.
[0048] S4. Based on the pavement structure coefficient, the factors in the actual working conditions are converted into indoor oblique shear fatigue test parameters, and the interlayer shear resistance of asphalt pavement under real working conditions is obtained through the indoor oblique shear fatigue test results.
[0049] In the specific implementation process, such as Figure 2 As shown, the interlayer oblique shear test can be performed using the apparatus disclosed in patent number ZL201910335110.6. This test assesses the interlayer shear fatigue resistance by subjecting a double-layer asphalt mixture sample to fatigue shear with a shear angle θ. The shear angle θ is the angle between the interlayer interface of the double-layer sample and the axis of the applied force. In order for the compressive stress and shear stress at the interlayer interface in the test to meet the theoretical requirements, the shear angle θ and the applied force F need to satisfy equation (1).
[0050]
[0051] In equation (1), F is the fatigue loading force (kN) provided by the loading device in the fatigue shear test, which is provided by the dynamic servo loading system; τ is the shear stress (MPa) at the interlayer interface under actual road conditions; σ is the compressive stress (MPa) under actual road conditions; and A is the area (m2) of the interlayer interface of the specimen. In the oblique shear fatigue test, different shear angles θ and fatigue loading forces F represent different interlayer stress states, and different road conditions can be mapped by adjusting the shear angle θ and fatigue loading force F.
[0052] The interlayer stress state varies under different pavement conditions. The interlayer stress state under actual pavement conditions can be calculated using simulation analysis software. When conducting simulation analysis, the established model needs to conform to the actual pavement structure and material parameters, such as the thickness of each pavement layer, material type, and corresponding material parameters (elastic material parameters: dynamic modulus, density, Poisson's ratio; viscoelastic material parameters: Prony series). On this simulation model, moving vertical pressure P and horizontal frictional resistance T are used to simulate traffic loads, and the time history curves of interlayer stress between the upper and middle layers of the pavement structure directly below the wheel are calculated, as shown below. Figure 3 and Figure 5 As shown.
[0053] like Figure 4 and Figure 6 As shown, the maximum shear stress τ max The inter-story stress state (σ, τ) at the corresponding location is taken as the most unfavorable load point. In the simulation analysis, the values of vertical compressive stress P and horizontal frictional resistance T are changed to obtain the inter-story stress (σ, τ) at the most unfavorable load point. Substituting the results into equation (2), the structural coefficients k1 to k4 can be calculated.
[0054]
[0055] In equation (2), P is the moving vertical compressive stress (MPa) in the simulation analysis, T is the moving horizontal frictional resistance (MPa) in the simulation analysis, τ is the shear stress (MPa) at the most unfavorable load point on the interlayer interface under the pavement working condition; σ is the compressive stress (MPa) at the most unfavorable load point under the actual pavement working condition, and k1~k4 are pavement structure coefficients, which are related to the number of layers, type, thickness of each layer, and material parameters of each layer of the pavement structure, and are calculated from the simulation calculation results.
[0056] After obtaining the structural coefficients k1 to k4, the interlayer stress state (σ, τ) at the most unfavorable load point under different road conditions (P, T) can be accurately calculated using equation (2). In actual road conditions, the vertical compressive stress value P and the horizontal frictional resistance value T are related to the road friction coefficient, road longitudinal slope, vehicle axle load, and vehicle acceleration, and can be converted according to the theory of classical mechanics.
[0057] (1) Axle load conversion
[0058] When rolling friction is ignored and only the vehicle is traveling at a constant speed is considered, the vertical compressive stress P and the horizontal frictional resistance T are calculated as shown in equation (3).
[0059]
[0060] In equation (3), m is the axle load (kg); g is the acceleration due to gravity (m / s²). 2A1 is the contact area between the tire and the road surface under standard axle load. Substituting equation (3) into equations (1) and (2) yields:
[0061]
[0062] According to equation (4), the interlayer stress state at the most unfavorable load position of the interlayer interface under different axle load conditions can be calculated, as well as the values of the shear angle θ and the loading force F required in the corresponding indoor oblique shear test.
[0063] (2) Road slope α conversion
[0064] When the road has a longitudinal slope α, the frictional resistance T between the road surface and the tire is used to balance the component of gravity caused by the longitudinal slope. The calculation methods for the vertical compressive stress P and the horizontal frictional resistance T are as shown in equation (5).
[0065]
[0066] In equation (5), m is the axle load (kg); g is the acceleration due to gravity (m / s²). 2 ); α is the longitudinal slope of the road (rad); A1 is the contact area between the tire and the road surface under standard axle load. Substituting equation (5) into equations (1) and (2), we get:
[0067]
[0068] According to equation (6), the interlayer stress state at the most unfavorable load position of the interlayer interface under different road slope conditions can be calculated, as well as the values of the shear angle θ and the loading force F that need to be adjusted in the corresponding indoor oblique shear test.
[0069] (3) Conversion of vehicle acceleration a
[0070] When a vehicle accelerates or decelerates, the vertical compressive stress P and the horizontal frictional resistance T are calculated as shown in equation (7):
[0071]
[0072] In equation (7), m is the axle load (kg); g is the acceleration due to gravity (m / s²). 2 ); a is the vehicle acceleration (m / s²) 2 A1 is the contact area between the tire and the road surface under standard axle load. Substituting equation (7) into equations (1) and (2) yields:
[0073]
[0074] If a vehicle slides on the road surface due to emergency braking, the vehicle's acceleration is a = gf, where f is the coefficient of sliding friction of the road surface. At this point, equation (8) transforms into equation (9), as shown below:
[0075]
[0076] Based on equations (8) and (9), the interlayer stress state at the most unfavorable load position of the interlayer interface under different driving acceleration a conditions can be calculated, as well as the values of the shear angle θ and the loading force F that need to be adjusted in the corresponding indoor oblique shear test.
[0077] By combining the conversion methods of equations (4), (6), (8), and (9), the road surface condition mapping equation (Equation 10) can be established, which is to obtain the indoor oblique shear fatigue test parameters (F). * θ * The equation (10) can be used to convert factors such as axle load, longitudinal slope, cross slope, curves, acceleration / deceleration, and road friction coefficient in actual road conditions into shear test parameters: fatigue loading force F and shear angle θ. The influence of different road conditions on interlayer performance can be studied through indoor interlayer shear test results.
[0078]
[0079] Obtaining indoor oblique shear fatigue test parameters (F) * θ * ); where τ * The interstory shear stress at the most unfavorable load point; σ * The interstory compressive stress at the most unfavorable load point; F * The fatigue loading force parameters for indoor oblique shear fatigue tests; θ * 1 is the shear angle in the indoor oblique shear fatigue test; m is the axle load (kg); g is the acceleration due to gravity (m / s²). 2 ); a is the vehicle acceleration (m / s²) 2 A1 is the contact area between the tire and the road surface under standard axle load; α is the road surface slope (rad); A is the area of the interlaminar interface of the specimen in the indoor oblique shear fatigue test (m²). 2 ). τ * and σ * It does not participate in the indoor oblique shear fatigue test itself, but τ * and σ * It can be used as an auxiliary parameter to confirm the experimental parameter F. * and θ * Is it correct, such as τ? * and σ * If the value is abnormal, it indicates that F * and θ * There are problems that need to be corrected.
[0080] It should be noted that when the vehicle brakes suddenly, the vehicle acceleration 'a' needs to be replaced with...
[0081] a=gμ Formula (11)
[0082] In equation (11), μ is the coefficient of sliding friction of the road surface; g is the acceleration due to gravity.
[0083] When there is a curve in the road, since the driving acceleration 'a' and the centripetal acceleration 'a' are in different directions, it is necessary to use vector synthesis of acceleration 'a'. * ,at this time
[0084]
[0085] In equation (12), a * The resultant acceleration (m / s²) 2 ); a is the vehicle acceleration (m / s²) 2 a′ is the centripetal acceleration of the curve (m / s²). 2 v is the vehicle speed (m / s); R is the radius of the road curve (m).
[0086] The loading frequency f in the oblique shear fatigue test is obtained by converting the road traffic speed, as shown in the following formula:
[0087] f = 0.227v 0.944 Equation (13)
[0088] Through the mapping equations (10) to (13), the complex road surface conditions can be transformed into shear test parameters: fatigue loading force F and shear angle θ. In the oblique shear test, the amplitude of the sine wave of the fatigue loading force is set to F, and the shear angle of the oblique shear is θ. Then, the loading frequency f and the temperature of the ambient chamber are set according to the driving speed and the road surface temperature. Based on this, a fatigue failure test is performed to obtain the interlayer shear fatigue life N. f This allows for the evaluation of the interlayer shear fatigue performance under the road surface conditions mapped by the parameters (F, θ).
[0089] In one embodiment of the present invention, a certain highway has a high traffic volume, an average speed of 50 km / h, and a large number of heavy-duty trucks. Surveys revealed numerous interlayer pavement defects on steep longitudinal slope sections and at traffic light intersections. An investigation was conducted on the general pavement condition, steep longitudinal slope pavement condition, and traffic light intersection pavement condition of this road section; the results are shown in Table 1. Indoor oblique shear fatigue tests are needed to determine the differences in interlayer shear fatigue resistance under the three pavement conditions shown in Table 1.
[0090] Table 1: Road Surface Condition Data Collection
[0091] Road conditions average speed Road slope average acceleration Axle load Road surface temperature General road conditions 50km / h 0% <![CDATA[0m / s 2 ]]> 10000kg 40℃ Slope road conditions 50km / h 7% <![CDATA[3m / s 2 ]]> 10000kg 40℃ Traffic light intersection 25km / h 0% <![CDATA[5m / s 2 ]]> 10000kg 40℃
[0092] like Figure 7As shown, based on the pavement structure and materials of each layer of the highway, a simulation analysis model was established using Abaqus finite element analysis software. The pavement structure and the thickness of each layer are shown in the figure. Figure 7 The material parameters for each layer are shown in Tables 2 and 3. The material parameters for each layer are determined by indoor standard tests or obtained from existing references.
[0093] Table 2: Mechanical parameters of pavement structure materials
[0094]
[0095] Table 3: Prony grade of asphalt surface materials (g) I )
[0096]
[0097] In the simulation calculation, assuming the vertical compressive stress P1 = 0.7 MPa and the horizontal frictional resistance T1 = 0 MPa, the stress state at the most unfavorable load point of the interlayer interface is obtained (σ1 = 0.293 MPa, τ1 = 0.270 MPa); again assuming the vertical compressive stress P2 = 0.7 MPa and the horizontal frictional resistance T2 = 0.49 MPa, the stress state at the most unfavorable load point of the interlayer interface is calculated (σ2 = 0.430 MPa, τ2 = 0.441 MPa). Substituting (σ1, τ1), (P1, T1), (σ2, τ2), (P2, T2) into equation (2) yields:
[0098]
[0099]
[0100] The structural coefficients are: k1 = 0.386, k2 = 0.419, k3 = 0.349, k4 = 0.280.
[0101] Substituting the pavement conditions and structural coefficients (k1~k4) in Table 1 into equations (10) and (13), the oblique shear test parameters are shown in Table 4.
[0102] Table 4. Parameters for the Road Surface Condition Mapped Inclined Shear Test
[0103] Road surface conditions F(kN) θ° f(Hz) Temperature (°C) General road conditions 7.04 47.4 10 40 Longitudinal slope working conditions 9.04 45.4 10 40 Traffic light intersection 9.78 44.9 5 40
[0104] Based on the oblique shear fatigue test parameters in Table 4, the oblique shear fatigue test was set up. The amplitude of the cyclic fatigue loading force of the sine waveform provided by the dynamic loading device was set to F, the loading frequency to f, the shear angle of the specimen fixture to θ, and the test temperature was controlled at 40℃. Based on these parameters, the oblique shear fatigue failure test was conducted, and the fatigue life Nf (number of load cycles) at failure was recorded. The test results are shown in [Table 4]. Figure 8Comparing the interlayer shear fatigue life under three different road conditions, it can be seen that the present invention can effectively distinguish the interlayer shear fatigue performance under different road conditions. The interlayer fatigue performance of steep longitudinal slope sections and traffic light intersections is much lower than that of general road conditions. Therefore, in actual engineering, the pavement of these sections is prone to interlayer separation-type defects.
[0105] In summary, this invention constructs a mapping equation between actual road surface working conditions and indoor oblique shear test parameters, realizing the conversion between road surface working conditions and oblique shear test parameters. With the help of this equation, the interlayer shear fatigue performance under different road surface working conditions can be accurately evaluated through indoor oblique shear tests.
Claims
1. A method for obtaining the interlayer shear strength of asphalt pavement under real working conditions, characterized in that, Includes the following steps: S1. Obtain the structural and material parameters that conform to the real road surface, and construct the road surface structure model through simulation software; S2. By changing the values of vertical compressive stress and horizontal frictional resistance in the simulated road structure model, the shear stress and compressive stress at the most unfavorable load point can be obtained. S3. Obtain the pavement structure coefficients based on the relationships between shear stress and compressive stress and vertical compressive stress and horizontal frictional resistance, respectively. S4. Based on the pavement structure coefficient, the factors in the actual working conditions are converted into indoor inclined shear fatigue test parameters, and the interlayer shear resistance of asphalt pavement under real working conditions is obtained through the indoor inclined shear fatigue test results. The specific method for step S3 is as follows: According to the formula: Obtaining pavement structure coefficient pavement structure coefficient pavement structure coefficient and pavement structure coefficient ;in This refers to the shear stress at the most unfavorable load point on the interlayer interface under pavement conditions. This refers to the compressive stress at the most unfavorable load point under actual road conditions. P represents the vertical compressive stress in the simulation; T represents the horizontal frictional resistance in the simulation; The specific method for converting the factors in the actual working conditions into indoor oblique shear fatigue test parameters based on the pavement structure coefficient in step S4 is as follows: According to the formula: Obtaining parameters from indoor oblique shear fatigue tests ;in These are the fatigue loading force parameters for indoor oblique shear fatigue tests; The shear angle for indoor oblique shear fatigue testing; m For axle load; g It is the acceleration due to gravity; a For vehicle acceleration; This refers to the contact area between the tire and the road surface under standard axle load. The slope of the road surface; A This represents the area of the interlaminar interface of the specimen in the indoor oblique shear fatigue test.
2. The method for obtaining the interlayer shear strength of asphalt pavement under real working conditions according to claim 1, characterized in that, The structural parameters that conform to real pavement include the thickness of each layer of the pavement structure; the material parameters that conform to real pavement include material type, elastic material parameters, and viscoelastic material parameters; among which, the elastic material parameters include dynamic modulus, density, and Poisson's ratio; and the viscoelastic material parameters include the Prony order.
3. The method for obtaining the interlayer shear strength of asphalt pavement under real working conditions according to claim 1, characterized in that, When the scenario involves emergency braking of the vehicle, the vehicle acceleration... ; This is the coefficient of sliding friction of the road surface.
4. The method for obtaining the interlayer shear strength of asphalt pavement under real working conditions according to claim 1, characterized in that, When the scene involves a winding road, according to the formula: Update the vehicle acceleration and obtain the new vehicle acceleration. ;in v For driving speed; R The radius of the curve.
5. The method for obtaining the interlayer shear strength of asphalt pavement under real working conditions according to claim 1, characterized in that, The specific method for obtaining the interlayer shear resistance of asphalt pavement under real working conditions through indoor oblique shear fatigue test results in step S4 is as follows: The amplitude of the sine wave of the fatigue loading force in the indoor oblique shear fatigue test is set as follows: The shearing angle of the oblique shear is set to The loading frequency was set according to the driving speed, and the ambient temperature of the test chamber was set according to the road surface temperature. The fatigue failure test was carried out to obtain the interlayer shear fatigue life, and then the interlayer shear performance of asphalt pavement under real working conditions was obtained.
6. The method for obtaining the interlayer shear strength of asphalt pavement under real working conditions according to claim 5, characterized in that, The loading frequency is obtained as follows: According to the formula: Get loading frequency f .