WO2023284112A1 - 一种沥青路面模量梯度确定方法、装置及电子设备 - Google Patents

一种沥青路面模量梯度确定方法、装置及电子设备 Download PDF

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WO2023284112A1
WO2023284112A1 PCT/CN2021/120074 CN2021120074W WO2023284112A1 WO 2023284112 A1 WO2023284112 A1 WO 2023284112A1 CN 2021120074 W CN2021120074 W CN 2021120074W WO 2023284112 A1 WO2023284112 A1 WO 2023284112A1
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modulus
asphalt pavement
dynamic
specimen
gradient
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PCT/CN2021/120074
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French (fr)
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罗蓉
汪彪
刘安刚
王锦腾
于晓贺
李冲
束裕
房晓斌
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武汉理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • the invention relates to the technical field of asphalt pavement evaluation, in particular to a method, device, electronic equipment and computer-readable storage medium for determining the modulus gradient of asphalt pavement.
  • the asphalt in the asphalt pavement chemically reacts with the oxygen in the air, and a series of changes occur in its properties, causing the asphalt pavement to age.
  • the aged asphalt pavement becomes hard and brittle, its durability is reduced, and it is more prone to fatigue cracking.
  • the oxygen in the air first reacts with the asphalt mixture on the surface of the asphalt pavement, and then reacts with the asphalt mixture inside the asphalt pavement through the gap. Because it takes more time for the oxygen in the air to diffuse into the deep pavement through interconnected gaps, the oxygen concentration deep in the pavement structure is low, and the aging rate is slow, which makes the asphalt pavement appear non-uniform aging along the depth direction.
  • the dynamic modulus of asphalt mixture is related to its aging and damage degree, the higher the aging degree of asphalt mixture, the greater the value of dynamic modulus.
  • the dynamic modulus of the aged asphalt pavement changes along the depth direction of the road, which makes the modulus of the asphalt pavement non-uniform.
  • the non-uniform aging phenomenon of asphalt pavement can be characterized.
  • the dynamic modulus gradient of asphalt mixture is an important parameter in the design and evaluation of asphalt pavement, which can be applied to the mechanical response analysis of asphalt pavement. Using the analysis results of the mechanical response, it is possible to predict the permanent deformation, fatigue cracking and other phenomena of the asphalt pavement, so as to design and evaluate the asphalt pavement and serve the road engineering construction.
  • the invention provides a method for determining the modulus gradient of asphalt pavement, comprising:
  • the asphalt pavement modulus gradient model parameters and the ratio of the top and bottom dynamic moduli of the test piece are programmed and solved to obtain the initial ratio of the asphalt pavement modulus gradient model parameters and the top and bottom dynamic modulus of the test piece;
  • the modulus gradient of the asphalt pavement under the condition of set temperature and frequency is obtained.
  • fitting the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula specifically includes: fitting the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula
  • L is the side length of the cross section
  • d is the thickness of the specimen
  • t is the loading time
  • F m (t), G m (t), and H m (t) are the transverse strain value, vertical strain value and rotation angle, respectively
  • l d/2 is the height of the top surface of the specimen after deformation
  • l -d/2 is the height of the bottom surface of the specimen after deformation.
  • the asphalt pavement modulus gradient model parameters and the ratio of the dynamic modulus at the top and the bottom of the specimen are programmed and solved, specifically including: through the fitting formula and the planning formula, the asphalt pavement modulus
  • the gradient model parameter n, the initial ratio k of the dynamic modulus k at the top of the specimen and the bottom dynamic modulus are used for planning and solving, and the planning formula is
  • the dynamic modulus master curve is obtained according to the asphalt pavement modulus gradient model parameters and the initial ratio of the top and bottom dynamic moduli of the specimen, specifically including: obtaining the dynamic modulus of the bottom, middle and top of the specimen, and according to the asphalt
  • the parameters of the pavement modulus gradient model, the initial ratio of the dynamic moduli at the top and bottom of the specimen, and the dynamic moduli at the bottom, middle and top of the specimen are used to obtain the dynamic modulus master curve.
  • the dynamic modulus of the bottom, middle and top of the test piece is obtained, according to the asphalt pavement modulus gradient model parameters, the initial ratio of the top and bottom dynamic moduli of the test piece, the dynamic modulus of the bottom, middle and top of the test piece Obtain the dynamic modulus master curve, including:
  • E- d/2 * ( ⁇ ) is the dynamic modulus of the bottom surface of the specimen, is the dynamic modulus of the top surface of the specimen, is the dynamic modulus in the middle of the specimen, n is the modulus gradient model parameter of the asphalt pavement, k is the initial ratio of the dynamic modulus at the top and bottom of the specimen, w is the frequency, J′ -d/2 ( ⁇ ), J′′ -d /2 ( ⁇ ) are the real part and imaginary part of the creep compliance respectively, and the formula of the dynamic modulus master curve is
  • E * ( ⁇ ) is the dynamic modulus
  • ⁇ is the loading frequency
  • ⁇ is the minimum value of the dynamic modulus
  • ⁇ is the difference between the vertical coordinates of the upper and lower asymptotes of the main curve
  • ⁇ , ⁇ , and ⁇ are the shape parameters
  • ⁇ T is the time-temperature shift factor
  • the method for determining the modulus gradient of the asphalt pavement also includes obtaining the time-temperature shift factor through the time-temperature shift factor formula, and the time-temperature shift factor formula is Among them, C 1 and C 2 are the fitting parameters, t is the test temperature, t 0 is the reference temperature, and a T is the time-temperature shift factor.
  • the dynamic modulus of the top surface and the bottom surface, the asphalt pavement modulus gradient under the condition of set temperature and frequency is obtained, specifically including:
  • top surface, bottom surface dynamic modulus and modulus gradient model formula obtain the asphalt pavement modulus gradient under the condition of set temperature and frequency, and the described modulus gradient model formula is:
  • E(z) is the dynamic modulus value at the depth z of the road surface
  • E d/2 is the surface modulus of the specimen
  • E -d/2 is the modulus of the bottom surface of the specimen
  • d is the thickness of the specimen
  • n is the model parameter
  • k 1 is the test ratio of dynamic modulus at the top and bottom of the specimen.
  • the present invention also provides a device for determining the modulus gradient of asphalt pavement, including a specimen data processing module, a planning solution module, a dynamic modulus acquisition module and a modulus gradient determination module;
  • the specimen data processing module is used to obtain the lateral strain value, vertical strain value and rotation angle of the pavement core sample specimen, and fit the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula;
  • the planning solution module is used to plan and solve the asphalt pavement modulus gradient model parameters, the ratio of the top and bottom dynamic moduli of the specimen through the fitting formula, and obtain the asphalt pavement modulus gradient model parameters, the top and bottom dynamic moduli of the specimen. initial ratio of dynamic moduli at the bottom;
  • the dynamic modulus acquisition module is used to obtain the dynamic modulus master curve according to the asphalt pavement modulus gradient model parameters, the initial ratio of the top and bottom dynamic moduli of the test piece, and obtain the set temperature and temperature according to the dynamic modulus master curve. Dynamic moduli of the top and bottom surfaces under frequency conditions;
  • the modulus gradient determination module is used to obtain the modulus gradient of the asphalt pavement under the condition of set temperature and frequency according to the parameters of the asphalt pavement modulus gradient model and the dynamic modulus of the top surface and the bottom surface.
  • the present invention also provides an electronic device, including a memory and a processor, and a computer program is stored in the memory, and when the computer program is executed by the processor, the asphalt pavement as described in any of the above technical solutions can be realized.
  • Modulus Gradient Determination Method including a processor, and a computer program is stored in the memory, and when the computer program is executed by the processor, the asphalt pavement as described in any of the above technical solutions can be realized.
  • the present invention also provides a computer-readable storage medium, on which a computer program is stored.
  • a computer program is stored on which a computer program is stored.
  • the computer program is executed by a processor, the method for determining the modulus gradient of an asphalt pavement as described in any of the above-mentioned technical solutions is realized.
  • the beneficial effect of adopting the above embodiment is: by obtaining the lateral strain value, vertical strain value and rotation angle of the pavement core sample specimen, fitting the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula; Through the fitting formula, the asphalt pavement modulus gradient model parameters and the ratio of the top and bottom dynamic moduli of the test piece are programmed and solved to obtain the initial ratio of the asphalt pavement modulus gradient model parameters and the top and bottom dynamic modulus of the test piece; According to the asphalt pavement modulus gradient model parameters, the initial ratio of the top and bottom dynamic modulus of the specimen to obtain the dynamic modulus master curve, according to the dynamic modulus master curve to obtain the top and bottom dynamic modulus under the condition of set temperature and frequency quantity; according to the asphalt pavement modulus gradient model parameters, the dynamic modulus of the top surface and the bottom surface, the asphalt pavement modulus gradient under the condition of set temperature and frequency is obtained; the determination of the asphalt pavement modulus gradient is realized.
  • Fig. 1 is the schematic flow chart of an embodiment of the method for determining the modulus gradient of asphalt pavement provided by the present invention
  • Fig. 2 is the schematic diagram of the cutting of the overall pavement core sample provided by the embodiment of the present invention.
  • Fig. 3 is the schematic diagram of cutting of the test piece provided by the embodiment of the present invention.
  • Fig. 5 is a schematic diagram of collection of strain changes with loading time at different positions of the test piece provided by the embodiment of the present invention.
  • Fig. 6 is the schematic diagram of the main curve of dynamic modulus provided by the embodiment of the present invention.
  • Figure 7 is a schematic diagram of the modulus gradient provided by the embodiment of the present invention.
  • Fig. 8 is a structural block diagram of an asphalt pavement modulus gradient determination device provided by an embodiment of the present invention.
  • a specific embodiment of the present invention discloses a method for determining the modulus gradient of an asphalt pavement, a schematic flow chart thereof, as shown in FIG.
  • Step S1 obtaining the lateral strain value, vertical strain value and rotation angle of the pavement core sample specimen, and fitting the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula
  • Step S2 using the fitting formula to program and solve the modulus gradient model parameters of the asphalt pavement and the ratio of the dynamic modulus at the top and bottom of the test piece to obtain the modulus gradient model parameters of the asphalt pavement and the dynamic modulus at the top and bottom of the test piece initial ratio;
  • Step S3. Obtain the dynamic modulus master curve according to the asphalt pavement modulus gradient model parameters and the initial ratio of the dynamic moduli at the top and bottom of the specimen, and obtain the top surface and Dynamic modulus of the bottom surface;
  • Step S4 according to the parameters of the asphalt pavement modulus gradient model and the dynamic moduli of the top surface and the bottom surface, obtain the modulus gradient of the asphalt pavement under the condition of set temperature and frequency.
  • the on-site core sample (core sample diameter can be 15cm) is drilled at the shoulder of the asphalt pavement.
  • the core sample structure includes the pavement asphalt mixture surface layer and part of the base layer, and the service time of the pavement is considered to be the aging time of the pavement core sample. ; Cut the overall pavement core sample, and separate the upper layer, middle layer and lower layer of the pavement with different types of asphalt mixture.
  • the schematic diagram of the overall pavement core sample cutting is shown in Figure 2.
  • the cutting diagram of the specimen is shown in Figure 3.
  • the cutting process is mainly divided into the following three steps , the rough upper surface of the pavement core sample is ground to reduce the loss of the thickness of the test piece as much as possible in the process.
  • the boundary line of the structural layer cuts off the base layer, and cuts and separates the upper, middle, and lower layers; cuts the cylindrical specimens of each structural layer along the section into cuboid specimens with a cross-section of 100mm ⁇ 100mm.
  • 6 groups of LVDTs are installed on the surface of the test piece to measure the strain at different positions of the test piece during the test.
  • the schematic diagram of the strain measurement is shown in FIG. 4 .
  • the LVDTs (linear displacement transducers) on the front and rear sides of the vertical direction are used to test the vertical strain on the top and bottom surfaces of the specimen, and the two sets of vertical LVDTs attached to the other two sides are used to measure the strain in the middle of the specimen, and the horizontal
  • the two sets of LVDTs in the direction are used to measure the lateral deformation of the specimen.
  • the gauge length of the LVDT in the vertical direction is 70mm
  • the gauge length of the LVDT in the horizontal direction is the thickness of the specimen.
  • the material tester (MTS) is used to carry out the uniaxial compression creep test, and the test temperatures are selected as 5°C, 20°C, and 35°C, respectively, and are carried out in sequence from low temperature to high temperature. Medium-cure for 4 hours to ensure that the internal temperature of the specimen reaches equilibrium.
  • the appropriate loading force is determined through exploratory tests before the test, so that the total strain of the specimen during the test does not exceed 150 ⁇ . Three parallel tests were carried out on each specimen, and the acquisition schematic diagram of the change of strain with loading time at different positions of the specimen is shown in Figure 5.
  • the average value of the three results was taken for subsequent analysis; the interval between each group of tests was 15 minutes to ensure the complete recovery of the viscoelastic strain on the specimen.
  • the lateral strain value, vertical strain value and rotation angle are fitted to obtain a fitting formula, which specifically includes: fitting the lateral strain value, vertical strain value and rotation angle to obtain Fitting formula
  • L is the side length of the cross section
  • d is the thickness of the specimen
  • t is the loading time
  • F m (t), G m (t), and H m (t) are the transverse strain value, vertical strain value and rotation angle, respectively
  • l d/2 is the height of the top surface of the specimen after deformation
  • l -d/2 is the height of the bottom surface of the specimen after deformation.
  • the lateral strain value, the vertical strain value and the rotation angle are fitted to obtain the fitting formula
  • the asphalt pavement modulus gradient model parameters and the ratio of the dynamic modulus at the top and bottom of the test piece are programmed and solved through the fitting formula, which specifically includes: through the fitting formula and the planning formula,
  • the asphalt pavement modulus gradient model parameter n, the initial ratio k of the dynamic modulus k at the top of the specimen and the bottom dynamic modulus are used for planning and solving, and the planning formula is
  • L is the side length of the cross section
  • d is the thickness of the specimen
  • the dynamic modulus master curve is obtained according to the asphalt pavement modulus gradient model parameters, the initial ratio of the top and bottom dynamic moduli of the test piece, which specifically includes: obtaining the bottom, middle and top dynamic moduli of the test piece,
  • the dynamic modulus master curve is obtained according to the asphalt pavement modulus gradient model parameters, the initial ratio of the dynamic moduli at the top and bottom of the test piece, and the dynamic moduli at the bottom, middle and top of the test piece.
  • the dynamic modulus of the bottom surface, the middle part and the top surface of the test piece is obtained.
  • Surface dynamic modulus to obtain the dynamic modulus master curve including:
  • E- d/2 * ( ⁇ ) is the dynamic modulus of the bottom surface of the specimen, is the dynamic modulus of the top surface of the specimen, is the dynamic modulus in the middle of the specimen, n is the modulus gradient model parameter of the asphalt pavement, k is the initial ratio of the dynamic modulus at the top and bottom of the specimen, w is the frequency, J′ -d/2 ( ⁇ ), J′′ -d /2 ( ⁇ ) are the real part and imaginary part of the creep compliance respectively, and the formula of the dynamic modulus master curve is
  • E * ( ⁇ ) is the dynamic modulus
  • ⁇ is the loading frequency
  • ⁇ is the minimum value of the dynamic modulus
  • ⁇ is the difference between the vertical coordinates of the upper and lower asymptotes of the main curve
  • ⁇ , ⁇ , and ⁇ are the shape parameters
  • ⁇ T is the time-temperature shift factor
  • the loading frequency J′ -d/2 ( ⁇ ), J′′ -d/2 ( ⁇ ) are real and imaginary parts of creep compliance
  • the method for determining the modulus gradient of the asphalt pavement further includes obtaining the time-temperature shift factor through the time-temperature shift factor formula, and the time-temperature shift factor formula is Among them, C 1 and C 2 are the fitting parameters, t is the test temperature, t 0 is the reference temperature, and a T is the time-temperature shift factor.
  • E * ( ⁇ ) is the dynamic modulus, MPa; ⁇ is the loading frequency, rad/s; ⁇ is the minimum value of the dynamic modulus, MPa; ⁇ is the difference between the ordinates of the upper and lower asymptotes of the main curve, MPa; ⁇ , ⁇ , and ⁇ are shape parameters; ⁇ T is the time-temperature shift factor, which is calculated by the following formula;
  • C 1 and C 2 are fitting parameters; t is the test temperature, °C; t 0 is the reference temperature, °C
  • the dynamic modulus of the top surface and the bottom surface is obtained, specifically including:
  • top surface, bottom surface dynamic modulus and modulus gradient model formula obtain the asphalt pavement modulus gradient under the condition of set temperature and frequency, and the described modulus gradient model formula is:
  • E(z) is the dynamic modulus value at the depth z of the road surface
  • E d/2 is the surface modulus of the specimen
  • E -d/2 is the modulus of the bottom surface of the specimen
  • d is the thickness of the specimen
  • n is the model parameter
  • k 1 is the test ratio of dynamic modulus at the top and bottom of the specimen.
  • the uniaxial compression test is carried out on the pavement core sample upper layer, middle surface layer and lower layer test piece, and determine n, k and the dynamic modulus E -d/2 of the bottom surface, middle part and top surface of the test piece E 0 , E d/2 ; through the formula Determine the change of dynamic modulus with depth of the pavement surface, middle layer and lower layer, so as to obtain the change trend of dynamic modulus of the entire asphalt pavement with depth.
  • the pavement core sample includes the upper layer, middle layer and lower layer.
  • the pavement structure of the Hubei section of the Beijing-Hong Kong-Macau Expressway is the Superpave-12.5 structure with a thickness of 4cm on the upper layer, and AC-20I with a thickness of 6cm in the middle layer.
  • Type structure, the lower layer is AC-20S type structure with a thickness of 6cm.
  • the actual upper, middle, and lower layers of the core sample are 3.5cm, 5.6cm, and 5.6cm, and the dimensions of each structural layer are 100mm long x 100mm wide x 35mm high, 56mm high, and 56mm high; , 20°C, and 35°C, the strain changes with time under constant load on the top, middle, bottom, and lateral sides of the specimen, as shown in Figure 3.
  • the strains at the top, middle, and bottom of the specimen are different, indicating that the material properties at different depths of the asphalt pavement are different. Due to the non-uniform aging phenomenon, the dynamic modulus of the specimen is non-uniformly distributed along the depth direction, and there is a modulus gradient phenomenon.
  • the top surface, middle part, bottom surface, lateral strain of each test piece and the change of the test piece rotation angle with the loading time are used for fitting to determine the model parameters, so as to determine that the bottom surface, middle part and top surface of each structural layer are at 0.004rad/s-0.01 Dynamic modulus in the range of rad/s; according to the results of pavement modulus gradient derivation, it can be determined that the dynamic modulus of the upper layer, the middle layer and the lower layer of the asphalt pavement vary with depth at each frequency and take a curve, where 0.01rad/ s
  • the change formula of the dynamic modulus of each structural layer is, for the upper layer, For the middle level, For the lower layer, In order to obtain the dynamic modulus in a wider frequency range, the main curve of dynamic modulus is drawn, the schematic diagram of the main curve of dynamic modulus is shown in Figure 6, and the parameters of the main curve of dynamic modulus of each structural layer are obtained, as shown in Table 1;
  • the dynamic modulus at 20°C and 10 Hz is used, and the modulus gradient of asphalt pavement at this frequency can be determined according to the dynamic modulus master curve, as shown in Table 2;
  • the dynamic modulus of asphalt pavement at 20°C and 10Hz can be plotted with depth, as shown in the figure.
  • modulus heterogeneity of the asphalt pavement it can be determined that after 16 years of aging, the asphalt pavement has a modulus gradient phenomenon in the upper, middle and lower layers.
  • the schematic diagram of the modulus gradient is shown in Figure 7.
  • the embodiment of the present invention provides a device for determining the modulus gradient of asphalt pavement. Its structural block diagram is shown in FIG. Quantity gradient determination module 4;
  • the specimen data processing module 1 is used to obtain the lateral strain value, vertical strain value and rotation angle of the pavement core sample specimen, and fit the lateral strain value, vertical strain value and rotation angle to obtain a fitting formula ;
  • the planning solution module 2 is used to plan and solve the asphalt pavement modulus gradient model parameters, the ratio of the top and bottom dynamic moduli of the test piece through the fitting formula, and obtain the asphalt pavement modulus gradient model parameters, the top of the test piece and the initial ratio of the bottom dynamic modulus;
  • the dynamic modulus acquisition module 3 is used to obtain the dynamic modulus master curve according to the asphalt pavement modulus gradient model parameters, the initial ratio of the top and bottom dynamic moduli of the specimen, and obtain the set temperature according to the dynamic modulus master curve and the dynamic moduli of the top and bottom surfaces under frequency conditions;
  • the modulus gradient determination module 4 is used to obtain the modulus gradient of the asphalt pavement under the condition of set temperature and frequency according to the modulus gradient model parameters of the asphalt pavement and the dynamic modulus of the top surface and the bottom surface.
  • An embodiment of the present invention provides an electronic device, including a memory and a processor, and a computer program is stored in the memory, and when the computer program is executed by the processor, it can realize the functions including pitch described in any of the above embodiments.
  • An embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored.
  • the computer program is executed by a processor, the method for determining the modulus gradient of an asphalt pavement as described in any of the above-mentioned embodiments is implemented. .
  • the invention discloses a method, a device, an electronic device and a computer-readable storage medium for determining the modulus gradient of an asphalt pavement.
  • the vertical strain value and the rotation angle are fitted to obtain the fitting formula;
  • the asphalt pavement modulus gradient model parameters and the ratio of the dynamic modulus at the top and bottom of the specimen are programmed and solved to obtain the asphalt pavement modulus Gradient model parameters, the initial ratio of the dynamic modulus at the top and bottom of the specimen;
  • the curve obtains the dynamic modulus of the top surface and the bottom surface under the condition of the set temperature and frequency; according to the asphalt pavement modulus gradient model parameters, the dynamic modulus of the top surface and the bottom surface, obtain the modulus of the asphalt pavement under the condition of the set temperature and frequency Gradient; realize the determination of the modulus gradient of asphalt pavement.
  • the modulus gradient of the asphalt pavement determined by the technical scheme of the present invention can characterize the non-uniform aging phenomenon of the asphalt pavement after long-term service, and the pavement evaluation and design work can be improved by determining the non-uniformity of the pavement dynamic modulus after long-term aging, which is beneficial to road engineering Construction is of great significance.
  • the processes of the methods in the above embodiments can be implemented by instructing related hardware through computer programs, and the programs can be stored in a computer-readable storage medium.
  • the computer-readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, and the like.

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Abstract

本发明涉及一种沥青路面模量梯度确定方法、装置、电子设备及计算机可读存储介质，所述沥青路面模量梯度确定方法包括：获取路面芯样试件的横向应变值、竖向应变值及转角，得到拟合公式；通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。本发明公开的沥青路面模量梯度确定方法，实现了对沥青路面模量梯度的确定。

Description

一种沥青路面模量梯度确定方法、装置及电子设备 技术领域
本发明涉及沥青路面评价技术领域，尤其涉及一种沥青路面模量梯度确定方法、装置、电子设备及计算机可读存储介质。
背景技术
服役期间，在温度、紫外线、氧气浓度等环境因素作用下，沥青路面中的沥青与空气中的氧气发生化学反应，性质发生一系列的变化，使得沥青路面发生老化。老化后的沥青路面变硬、变脆，耐久性降低，更易产生疲劳开裂。老化过程中，空气中的氧气先与沥青路面表面的沥青混合料发生化学反应，再通过空隙与沥青路面内部沥青混合料产生化学反应生。因空气中的氧气通过相互连接的空隙进入路面深处扩散需要更多时间，路面结构深处的氧气浓度较低，老化速率较慢，使得沥青路面沿深度方向出现非均匀老化现象。
沥青混合料的动态模量与其老化和损伤程度存在关联性，沥青混合料的老化程度越高，其动态模量值越大。老化后的沥青路面的动态模量沿道路深度方向发生变化，使得沥青面层模量存在非均匀性。通过对沥青路面老化后的模量非均匀性进行研究，能够表征沥青路面的非均匀老化现象。同时，沥青混合料的动态模量梯度是沥青路面设计和评价中的重要参数，可以被应用于沥青路面的力学响应分析。运用力学响应的分析结果，能够对沥青路面的永久变形、疲劳开裂等现象进行预估，从而对沥青路面进行设计和评价，为道路工程建设服务。然而，现阶段在对沥青路面进行设计和评价时，往往忽略了非均匀老化作用对沥青路面动 态模量参数的影响，认为各结构层模量均匀，从而使得其分析结果与路面的实际服役状况存在差异。而现有技术确少沥青路面模量梯度的确定方案。
发明内容
有鉴于此，有必要提供一种沥青路面模量梯度确定方法、装置、电子设备及计算机可读存储介质，用以实现对沥青路面模量梯度的确定。
为了实现上述目的，本发明提供了一种沥青路面模量梯度确定方法，包括：
获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
进一步地，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式，具体包括：对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式
Figure PCTCN2021120074-appb-000001
Figure PCTCN2021120074-appb-000002
Figure PCTCN2021120074-appb-000003
其中，
Figure PCTCN2021120074-appb-000004
为参数，
Figure PCTCN2021120074-appb-000005
L为横截面边长，d为试件厚度，t为加载时间，所述F m(t)、G m(t)、H m(t)分别为横向应变值、竖向应变值及转角，l d/2为变形后试件顶面高度，l -d/2为变形后试件底面高度。
进一步地，通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，具体包括：通过所述拟合公式及规划公式，对沥青路面模量梯度模型参数n、试件顶部和底部动态模量的初始比值k进行规划求解，所述规划公式为
Figure PCTCN2021120074-appb-000006
Figure PCTCN2021120074-appb-000007
Figure PCTCN2021120074-appb-000008
其中，
Figure PCTCN2021120074-appb-000009
Figure PCTCN2021120074-appb-000010
进一步地，根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，具体包括：获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线。
进一步地，获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线，具体包括：
利用动态模量公式获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部、顶面动态模量及动态模量主曲线公式获取动态模量主曲线，所述动态模量公式为
Figure PCTCN2021120074-appb-000011
Figure PCTCN2021120074-appb-000012
Figure PCTCN2021120074-appb-000013
其中，E -d/2 *(ω)为试件底面动态模量，
Figure PCTCN2021120074-appb-000014
为试件顶面动态模量，
Figure PCTCN2021120074-appb-000015
为试件中部动态模量，n为沥青路面模量梯度模型参数，k为试件顶部和底部动态模量的初始比值，w为频率，J′ -d/2(ω)、J″ -d/2(ω)分别为蠕变柔量的实部和虚部，所述动态模量主曲线公式为
Figure PCTCN2021120074-appb-000016
其中，E *(ω)为动态模量，ω为加载频率，δ为动态模量最小值，α为主曲线上下渐近线的纵坐标的差值，β、γ、λ为形状参数，α T为时-温移位因子。
进一步地，所述沥青路面模量梯度确定方法还包括，通过时-温移位因子公式获取时-温移位因子，所述时-温移位因子公式为
Figure PCTCN2021120074-appb-000017
其中，C 1、C 2分别为拟合参数，t为试验温度，t 0为参 考温度，a T为时-温移位因子。
进一步地，根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度，具体包括：
根据所述沥青路面模量梯度模型参数，顶面、底面动态模量及模量梯度模型公式，获取设定温度及频率条件下的沥青路面模量梯度，所述模量梯度模型公式为
Figure PCTCN2021120074-appb-000018
Figure PCTCN2021120074-appb-000019
其中，E(z)为路面深度z处的动态模量值，E d/2为试件表面模量，E -d/2为试件底面模量，d为试件的厚度，n为模型参数，k 1为试件顶部和底部动态模量的测试比值。
本发明还提供了一种沥青路面模量梯度确定装置，包括试件数据处理模块、规划求解模块、动态模量获取模块及模量梯度确定模块；
所述试件数据处理模块，用于获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
所述规划求解模块，用于通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
所述动态模量获取模块，用于根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
所述模量梯度确定模块，用于根据所述沥青路面模量梯度模型参数、 顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
本发明还提供了一种电子设备，包括存储器和处理器，所述存储器上存储有计算机程序，所述计算机程序被所述处理器执行时，实现如上述任一技术方案所述的包括沥青路面模量梯度确定方法。
本发明还提供了一种计算机可读存储介质，其上存储有计算机程序，所述计算机该程序被处理器执行时，实现如上述任一技术方案所述的包括沥青路面模量梯度确定方法。
采用上述实施例的有益效果是：通过获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度；实现了对沥青路面模量梯度的确定。
附图说明
图1为本发明提供的沥青路面模量梯度确定方法一实施例的流程示意图；
图2为本发明实施例提供的整体路面芯样切割示意图；
图3为本发明实施例提供的试件切割示意图；
图4为本发明实施例提供的应变测量示意图；
图5为本发明实施例提供的试件不同位置处应变随加载时间变化的采集示意图；
图6为本发明实施例提供的动态模量主曲线示意图；
图7为本发明实施例提供的模量梯度示意图；
图8为本发明实施例提供的沥青路面模量梯度确定装置的结构框图。
具体实施方式
下面结合附图来具体描述本发明的优选实施例，其中，附图构成本申请一部分，并与本发明的实施例一起用于阐释本发明的原理，并非用于限定本发明的范围。
本发明的一个具体实施例，公开了一种沥青路面模量梯度确定方法，其流程示意图，如图1所示，所述沥青路面模量梯度确定方法包括：
步骤S1、获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
步骤S2、通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
步骤S3、根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
步骤S4、根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
一个具体实施例中，在沥青路面路肩处钻取现场芯样(芯样直径可为15cm)，芯样结构包括路面沥青混合料面层和部分基层，并认为路面服役时间为路面芯样老化时间；对整体路面芯样进行切割，将沥青混合 料类型不同的路面上面层、中面层和下面层分离，整体路面芯样切割示意图，如图2所示。
采用切割锯将直径15cm的路面芯样圆柱体试件，切割成长100mm，宽100mm，厚40-60mm的长方体试件，试件切割示意图，如图3所示，切割过程主要分为以下三步，对路面芯样粗糙的上表面进行磨平处理，过程中尽可能减少试件厚度的损失，磨平后的试件上下表面平整，使得试件表面在试验中受力均匀；沿芯样各结构层分界线将基层部分切除，并将上、中、下面层部分切割分离；沿截面将各结构层圆柱体试件切割成截面为100mm×100mm的长方体试件。
另一个具体实施例中，在试件表面安装有6组LVDT，用于测量试验过程中试件不同位置处的应变，应变测量示意图，如图4所示。竖直方向前后两侧的LVDT(直线位移传感器)用于测试试件顶面和底面的竖向应变，附在另外两侧的2组竖直方向的LVDT用于测量试件中部的应变，水平方向的2组LVDT用于测量试件的横向变形，竖直方向LVDT的标距为70mm，水平方向LVDT的标距为试件厚度。
采用材料测试仪(MTS)进行单轴压缩蠕变试验，选取试验温度分别为5℃、20℃、35℃，由低温向高温依次进行，在进行对应温度试验前，需将试件在环境箱中养生4个小时以保证试件内部温度达到平衡。为保证试件在加载过程中处于线性黏弹性阶段，在试验前通过探索性试验确定合适的加载力，使得试件在试验过程中产生的总应变不超过150με。对每个试件进行三次平行试验，试件不同位置处应变随加载时间变化的采集示意图，如图5所示。取三次结果的平均值用于后续分析；每组试验间隔15分钟，以保证试件受到的黏弹性应变完全恢复。通过上述方法可以得到路面芯样试件的横向应变值、竖向应变值及转角。
作为一个优选的实施例，对所述横向应变值、竖向应变值及转角进 行拟合，得到拟合公式，具体包括：对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式
Figure PCTCN2021120074-appb-000020
Figure PCTCN2021120074-appb-000021
Figure PCTCN2021120074-appb-000022
其中，
Figure PCTCN2021120074-appb-000023
为参数，
Figure PCTCN2021120074-appb-000024
L为横截面边长，d为试件厚度，t为加载时间，所述F m(t)、G m(t)、H m(t)分别为横向应变值、竖向应变值及转角，l d/2为变形后试件顶面高度，l -d/2为变形后试件底面高度。
一个具体实施例中，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式
Figure PCTCN2021120074-appb-000025
Figure PCTCN2021120074-appb-000026
Figure PCTCN2021120074-appb-000027
其中，
Figure PCTCN2021120074-appb-000028
为模型参数(拟合参数)，t为加载时间，s。
作为一个优选的实施例，通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，具体包括：通过所述拟合公式及规划公式，对沥青路面模量梯度模型参数n、试件顶部和底部动态模量的初始比值k进行规划求解，所述规划公式为
Figure PCTCN2021120074-appb-000029
Figure PCTCN2021120074-appb-000030
Figure PCTCN2021120074-appb-000031
其中，
Figure PCTCN2021120074-appb-000032
L为横截面边长，d为试件厚度，
Figure PCTCN2021120074-appb-000033
Figure PCTCN2021120074-appb-000034
作为一个优选的实施例，根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，具体包括：获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线。
作为一个优选的实施例，获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线，具体包括：
利用动态模量公式获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部、顶面动态模量及动态模量主曲线公式获取动态模量主曲线，所述动态模量公式为
Figure PCTCN2021120074-appb-000035
Figure PCTCN2021120074-appb-000036
Figure PCTCN2021120074-appb-000037
其中，E -d/2 *(ω)为试件底面动态模量，
Figure PCTCN2021120074-appb-000038
为试件顶面动态模量，
Figure PCTCN2021120074-appb-000039
为试件中部动态模量，n为沥青路面模量梯度模型参数，k为试件顶部和底部动态模量的初始比值，w为频率，J′ -d/2(ω)、J″ -d/2(ω)分别为蠕变柔量的实部和虚部，所述动态模量主曲线公式为
Figure PCTCN2021120074-appb-000040
其中，E *(ω)为动态模量，ω为加载频率，δ为动态模量最小值，α为主曲线上下渐近线的纵坐标的差值，β、γ、λ为形状参数，α T为时-温移位因子。
一个具体实施例中，加载频率
Figure PCTCN2021120074-appb-000041
J′ -d/2(ω)、J″ -d/2(ω)为蠕变柔量的实部和虚部，
Figure PCTCN2021120074-appb-000042
Figure PCTCN2021120074-appb-000043
作为一个优选的实施例，所述沥青路面模量梯度确定方法还包括，通过时-温移位因子公式获取时-温移位因子，所述时-温移位因子公式为
Figure PCTCN2021120074-appb-000044
其中，C 1、C 2分别为拟合参数，t为试验温度，t 0为参考温度，a T为时-温移位因子。
需要说明的是，在路面设计与评价时，一般采用20℃、10Hz下的动 态模量，因此，通过绘制动态模量主曲线确定更广频率范围下沥青路面的动态模量，得到相应频率下沥青路面动态模量随路面深度的变化趋势，从而为后续分析长期服役沥青路面在车辆荷载作用下的力学响应情况提供依据。绘制动态模量主曲线，如下公式所示；
Figure PCTCN2021120074-appb-000045
其中，E *(ω)为动态模量，MPa；ω为加载频率，rad/s；δ为动态模量最小值，MPa；α为主曲线上下渐近线的纵坐标的差值，MPa；β、γ、λ为形状参数；α T为时-温移位因子，通过下式进行计算；
Figure PCTCN2021120074-appb-000046
其中，C 1、C 2为拟合参数；t为试验温度，℃；t 0为参考温度，℃
作为一个优选的实施例，根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度，具体包括：
根据所述沥青路面模量梯度模型参数，顶面、底面动态模量及模量梯度模型公式，获取设定温度及频率条件下的沥青路面模量梯度，所述模量梯度模型公式为
Figure PCTCN2021120074-appb-000047
Figure PCTCN2021120074-appb-000048
其中，E(z)为路面深度z处的动态模量值，E d/2为试件表面模量，E -d/2为试件底面模量，d为试件的厚度，n为模型参数，k 1为试件顶部和底部动态模量的测试比值。
一个具体实施例中，对路面芯样上面层、中面层和下面层试件进行 单轴压缩试验，确定n、k及试件底面、中部、顶面的动态模量E -d/2、E 0、E d/2；通过公式
Figure PCTCN2021120074-appb-000049
确定路面上、中、下面层动态模量随深度的变化，从而得到整个沥青面层动态模量随深度的变化趋势。
另一个具体实施例中，依托于京港澳高速公路湖北段，其建成通车于2002年，取芯时间为2018年，取芯时路面服役时间为16年，可认为其路肩处芯样的老化时间为16年，路面芯样包括上面层、中面层、下面层，京港澳高速公路湖北段路面结构为，上面层为厚4cm的Superpave-12.5型结构，中面层为厚6cm的AC-20I型结构，下面层为厚6cm的AC-20S型结构。实际芯样上、中、下面层3.5cm、5.6cm、5.6cm，各结构层试件尺寸分别为长100mm×宽100mm×高35mm、56mm、56mm；采用单轴压缩蠕变试验测定在5℃、20℃、35℃下，试件顶面、中部、底面和横向在恒定荷载下应变随时间的变化情况，如图3所示。试件顶面、中部和底面处应变不同，表明沥青路面不同深度处的材料性能不同，其顶面应变最小，底面应变最大，说明试件动态模量在顶面处最大，底面处最小，表明由于非均匀老化现象，试件动态模量沿深度方向非均匀分布，存在模量梯度现象。
将各试件顶面、中部、底面、横向应变以及试件转角随加载时间的变化情况采用进行拟合，确定模型参数，从而确定各结构层底面、中部和顶面在0.004rad/s-0.01rad/s范围内的动态模量；根据路面模量梯度推导的结果，可以确定沥青路面上面层、中面层和下面层在各频率下动态模量随深度的变化取曲线，其中0.01rad/s各结构层动态模量的变化公式为，对于上面层，
Figure PCTCN2021120074-appb-000050
对于中层面，
Figure PCTCN2021120074-appb-000051
对于下层面，
Figure PCTCN2021120074-appb-000052
为获取更广频率范围内的动态模量，采用绘制动态模量主曲线，动态模量主曲线示意图，如图6所示，得到各结构层动态模量主曲线参数，如表1所示；
表1
Figure PCTCN2021120074-appb-000053
在路面设计与评价时，采用20℃、10Hz下的动态模量，根据动态模量主曲线，可以确定沥青路面在该频率下的模量梯度情况，如表2所示；
表2
Figure PCTCN2021120074-appb-000054
由表2中相关参数，可以绘制沥青路面在20℃、10Hz下动态模量随 深度变化趋势，如图所示。通过对沥青路面模量非均性的测试，可以确定沥青路面在老化16年后，上面层、中面层和下面层均存在模量梯度现象，模量梯度示意图，如图7所示。
本发明实施例提供了一种沥青路面模量梯度确定装置，其结构框图，如图8所示，所述装置包括试件数据处理模块1、规划求解模块2、动态模量获取模块3及模量梯度确定模块4；
所述试件数据处理模块1，用于获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
所述规划求解模块2，用于通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
所述动态模量获取模块3，用于根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
所述模量梯度确定模块4，用于根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
本发明实施例提供了一种电子设备，包括存储器和处理器，所述存储器上存储有计算机程序，所述计算机程序被所述处理器执行时，实现如上述任一实施例所述的包括沥青路面模量梯度确定方法。
本发明实施例提供了一种计算机可读存储介质，其上存储有计算机程序，所述计算机该程序被处理器执行时，实现如上述任一实施例所述的包括沥青路面模量梯度确定方法。
本发明公开了一种沥青路面模量梯度确定方法、装置、电子设备及 计算机可读存储介质，通过获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度；实现了对沥青路面模量梯度的确定。
通过本发明技术方案确定的沥青路面模量梯度，可以表征沥青路面长期服役后的非均匀老化现象，通过确定长期老化后路面动态模量的非均匀性能够完善路面评价和设计工作，对道路工程建设具有重大的意义。
本领域技术人员可以理解，实现上述实施例方法的全部或部分流程，可以通过计算机程序来指令相关的硬件来完成，所述的程序可存储于计算机可读存储介质中。其中，所述计算机可读存储介质为磁盘、光盘、只读存储记忆体或随机存储记忆体等。
以上所述，仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。

Claims (10)

  1. 一种沥青路面模量梯度确定方法，其特征在于，包括：
    获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
    通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
    根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
    根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
  2. 根据权利要求1所述的沥青路面模量梯度确定方法，其特征在于，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式，具体包括：对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式
    Figure PCTCN2021120074-appb-100001
    Figure PCTCN2021120074-appb-100002
    Figure PCTCN2021120074-appb-100003
    其中，
    Figure PCTCN2021120074-appb-100004
    为参数，
    Figure PCTCN2021120074-appb-100005
    L为横截面边长，d为试件厚度，t为加载时间，所述F m(t)、G m(t)、H m(t)分别为横向应变值、竖向应变值及转角，l d/2为变形后试件顶面高度，l -d/2为变形后试件底面高度。
  3. 根据权利要求2所述的沥青路面模量梯度确定方法，其特征在于，通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态 模量的比值进行规划求解，具体包括：通过所述拟合公式及规划公式，对沥青路面模量梯度模型参数n、试件顶部和底部动态模量的初始比值k进行规划求解，所述规划公式为
    Figure PCTCN2021120074-appb-100006
    Figure PCTCN2021120074-appb-100007
    Figure PCTCN2021120074-appb-100008
    Figure PCTCN2021120074-appb-100009
    其中，
    Figure PCTCN2021120074-appb-100010
    Figure PCTCN2021120074-appb-100011
  4. 根据权利要求1所述的沥青路面模量梯度确定方法，其特征在于，根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，具体包括：获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线。
  5. 根据权利要求1所述的沥青路面模量梯度确定方法，其特征在于，获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部和顶面动态模量获取动态模量主曲线，具体包括：
    利用动态模量公式获取试件底面、中部和顶面动态模量，根据所述沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值、试件底面、中部、顶面动态模量及动态模量主曲线公式获取动态模量主曲 线，所述动态模量公式为
    Figure PCTCN2021120074-appb-100012
    Figure PCTCN2021120074-appb-100013
    Figure PCTCN2021120074-appb-100014
    其中，E -d/2 *(ω)为试件底面动态模量，
    Figure PCTCN2021120074-appb-100015
    为试件顶面动态模量，
    Figure PCTCN2021120074-appb-100016
    为试件中部动态模量，n为沥青路面模量梯度模型参数，k为试件顶部和底部动态模量的初始比值，w为频率，J′ -d/2(ω)、J″ -d/2(ω)分别为蠕变柔量的实部和虚部，所述动态模量主曲线公式为
    Figure PCTCN2021120074-appb-100017
    其中，E *(ω)为动态模量，ω为加载频率，δ为动态模量最小值，α为主曲线上下渐近线的纵坐标的差值，β、γ、λ为形状参数，α T为时-温移位因子。
  6. 根据权利要求5所述的沥青路面模量梯度确定方法，其特征在于，还包括，通过时-温移位因子公式获取时-温移位因子，所述时-温移位因子公式为
    Figure PCTCN2021120074-appb-100018
    其中，C 1、C 2分别为拟合参数，t为试验温度，t 0为参考温度，a T为时-温移位因子。
  7. 根据权利要求1所述的沥青路面模量梯度确定方法，其特征在于，根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度，具体包括：
    根据所述沥青路面模量梯度模型参数，顶面、底面动态模量及模量梯度模型公式，获取设定温度及频率条件下的沥青路面模量梯度，所述 模量梯度模型公式为
    Figure PCTCN2021120074-appb-100019
    Figure PCTCN2021120074-appb-100020
    其中，E(z)为路面深度z处的动态模量值，E d/2为试件表面模量，E -d/2为试件底面模量，d为试件的厚度，n为模型参数，k 1为试件顶部和底部动态模量的测试比值。
  8. 一种沥青路面模量梯度确定装置，其特征在于，包括试件数据处理模块、规划求解模块、动态模量获取模块及模量梯度确定模块；
    所述试件数据处理模块，用于获取路面芯样试件的横向应变值、竖向应变值及转角，对所述横向应变值、竖向应变值及转角进行拟合，得到拟合公式；
    所述规划求解模块，用于通过所述拟合公式对沥青路面模量梯度模型参数、试件顶部和底部动态模量的比值进行规划求解，得到沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值；
    所述动态模量获取模块，用于根据沥青路面模量梯度模型参数、试件顶部和底部动态模量的初始比值获取动态模量主曲线，根据所述动态模量主曲线获取设定温度及频率条件下的顶面及底面动态模量；
    所述模量梯度确定模块，用于根据所述沥青路面模量梯度模型参数、顶面及底面动态模量，获取设定温度及频率条件下的沥青路面模量梯度。
  9. 一种电子设备，其特征在于，包括存储器和处理器，所述存储器上存储有计算机程序，所述计算机程序被所述处理器执行时，实现如权利要求1-7任一所述的包括沥青路面模量梯度确定方法。
  10. 一种计算机可读存储介质，其上存储有计算机程序，其特征在 于，所述计算机该程序被处理器执行时，实现如权利要求1-7任一所述的包括沥青路面模量梯度确定方法。
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