CN107764644A - The Analysis of Asphalt Pavement Structure equivalent method of model is relied on based on ground surface material modulus stress and strain - Google Patents
The Analysis of Asphalt Pavement Structure equivalent method of model is relied on based on ground surface material modulus stress and strain Download PDFInfo
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Abstract
The present invention relates to a kind of Analysis of Asphalt Pavement Structure equivalent method that model is relied on based on ground surface material stress and strain, according to the asphalt pavement structure form and material type for intending analysis, determine each thickness degree, Poisson's ratio and ground surface material modulus stress (strain) rely on model, model is relied on using ground surface material modulus stress (strain) and characterizes each layer modulus of asphalt pavement structure, established with reference to calculating load and Coating combination condition and calculate analysis system, point is calculated using each layer stress least favorable point position of asphalt pavement structure as equivalent, the final modulus of each structure sheaf is obtained by iterating to calculate, the stress at any point inside asphalt pavement structure is calculated according to elastic layer system theory on this basis, strain and displacement.This method considers to be influenceed caused by material non-linearity question road pavement Mechanics Calculation, makes asphalt pavement structure force analysis more rational and perfect.
Description
Technical Field
The invention mainly relates to the field of road engineering, in particular to a stress analysis problem of an asphalt pavement structure caused by the nonlinear characteristic of a pavement material.
Background
The real mechanical response of the pavement structure under the action of load is always a basic theoretical problem in the research of the pavement structure analysis theory and design method. Due to the diversity and complexity of the component materials, the mechanical response of the pavement structure under the action of vehicle load and natural environment mostly shows obvious nonlinear characteristics. For years, in order to reveal the evolution mechanism of the service performance of a pavement structure and establish a design theory which is more in line with the actual pavement structure and the mechanical response behavior of materials, researchers at home and abroad try to explore the real mechanical response of the pavement structure under the action of load, but because of the nonlinear characteristic of the pavement material, a satisfactory result cannot be obtained.
At the present stage, in the road surface structure analysis method based on the linear elasticity hypothesis, due to the fact that the physical equation cannot correctly describe the nonlinear constitutive relation of the asphalt road surface material and the diversity and the uncertainty of the value of the structural layer modulus test method, the real stress state of the road surface structure is difficult to accurately and objectively evaluate, and the method is not beneficial to guiding the design of a newly-built road surface and the service life evaluation of the in-service road surface.
According to the classical linear elastic mechanics theory, the modulus of a material is an inherent property of the material, is independent of environment and external force and is generally a constant value. However, a large number of indoor and outdoor tests show that the modulus of a pavement material is closely related to indexes such as stress, strain and strength, and changes with the change of a load level, the modulus value difference under different stress paths and different test conditions is large, and the pavement material shows quite obvious nonlinear characteristics, the modulus of the pavement material is not a constant value, but is a function expression related to the stress, strain or strength, namely a stress (strain) dependent model, and in order to obtain the real mechanical response of a pavement structure, the influence of the material nonlinearity problem on the pavement mechanical calculation must be considered.
Disclosure of Invention
The invention discloses an equivalent analysis method for an asphalt pavement structure based on a pavement material modulus stress (strain) dependency model, which is characterized by adopting the pavement material modulus stress (strain) dependency model to represent the material modulus of each layer of the asphalt pavement structure according to the nonlinear characteristic of a pavement material, and provides a brand new asphalt pavement structure mechanics analysis method by taking the most unfavorable point of stress of each layer of the asphalt pavement structure as an equivalent calculation point.
The method for analyzing the equivalent weight of the asphalt pavement structure based on the pavement material modulus stress and strain dependence model comprises the following steps:
1) Selecting the structural form and the material type of the asphalt pavement to be analyzed, and determining the calculated load type, the interlayer combination condition and the thickness h of each layer i And poisson ratio mu i (ii) a Wherein: the parameter i represents the number of the asphalt pavement structure layers and is a positive integer;
2) According to the structural form and the material type of the asphalt pavement to be analyzed, determining an asphalt mixture complex modulus strain dependence model, a semi-rigid base layer and a roadbed soil resilience modulus stress dependence model through an indoor test, taking the model group as a modulus value basis of each layer during the structural analysis of the asphalt pavement, and obtaining the model group by adopting the following steps:
(1) Determination method of complex modulus strain dependence model of asphalt mixture
(1) Carrying out complex modulus tests on the asphalt mixture at different strain levels, different loading frequencies and different test temperatures;
(2) acquiring an asphalt mixture complex modulus main curve based on temperature parameters under different strain levels by taking a certain frequency as a reference frequency according to the following method;
(i) Under a certain strain level, a Boltzmann function is adopted to represent the correlation between the temperature and the complex modulus logarithm of the asphalt mixture at a certain frequency,
(ii) Taking Boltzmann function relation in (i) as a reference, introducing a temperature shift factor alpha according to a time-temperature equivalent principle, carrying out translation processing on test data of temperature and complex modulus at the strain level and other frequencies to obtain a new group of temperature-complex modulus tests after translation,
(iii) The regression analysis is carried out on the data in the step (ii) by adopting a formula (1), so that a main complex modulus curve of the asphalt mixture based on temperature parameters with a certain frequency as a reference frequency under the strain level can be obtained, the functional expression is the formula (1),
in the formula: t-temperature, in units of ℃;
e is the complex modulus logarithm of the asphalt mixture with the base of 10;
A 1 、A 2 、x 0 and dx is a regression parameter,
(iv) By adopting the methods in (i), (ii) and (iii), the main complex modulus curve of the asphalt mixture based on temperature parameters with a certain frequency as a reference frequency under other strain levels can be obtained,
(3) sorting the translated temperature-complex modulus test data in the step (2) into a data format with independent variable of temperature and strain level and dependent variable of complex modulus logarithm, and performing regression analysis on the data format by adopting a formula (2) to obtain an asphalt mixture complex modulus strain dependence model based on temperature parameters;
in the formula: t-temperature, in units of ℃;
e is the complex modulus logarithm of the asphalt mixture with the base of 10;
ε -Strain, unit 1X 10 2 με；
a、b、c、x 0 Dx-regression parameter;
(2) Method for determining semi-rigid base layer resilience modulus stress dependence model
[1] Determining the type of the inorganic binder of the semi-rigid base layer, the type of the stabilized material and the life-preserving period of the test piece according to the structural form and the material type of the asphalt pavement to be analyzed, and obtaining the semi-rigid base layer materials with different strength levels by adjusting the dosage of the inorganic binder and the grading composition of the stabilized material;
[2] adopting the semi-rigid base material with different strength levels in the step (1) to respectively carry out the strength and the resilience modulus test of the compression stress mode and the strength and the resilience modulus test of the bending and pulling stress mode;
[3] according to the stress mode, the test data in the step (2) are arranged into a data format with independent variable of strength and stress level and dependent variable of resilience modulus;
[4] performing regression analysis on the data in the compression stress mode in the step [3] by adopting a binary quadratic model of a formula (3), and performing regression analysis on the data in the bending and pulling stress mode in the step [3] by adopting a power function model of a formula (4) to obtain a semi-rigid base layer resilience modulus stress dependence model based on the intensity level expressed by the formula (3) and the formula (4);
E＝f(σ,R)＝a·σ 2 + b.sigma + c.R + d formula (3)
E＝f(σ,R)＝a·R c ·(σ+1) b Formula (4)
In the formula: e-compression or bend tensile modulus of elasticity in MPa;
σ -stress level, in MPa;
r-compressive or tensile strength in MPa;
a. b, c, d are regression parameters;
(3) Roadbed soil resilience modulus stress dependence model determination method
<1>, at different confining pressures (sigma) 3 ) And bias stress (σ) d ) Performing a dynamic triaxial resilience modulus test on the roadbed soil;
<2&at the step<1>, different confining pressure (sigma) 3 ) Next, performing a triaxial failure strength test on the roadbed soil;
the test data in the step <1> and the step <2> are arranged into a data format with independent variable of bias stress and failure strength and dependent variable of dynamic rebound modulus;
and (4) performing regression analysis on the data in the step <3> by adopting the formula (5) to obtain a roadbed soil resilience modulus stress dependence model based on the strength index expressed by the formula (5).
In the formula: e-dynamic triaxial resilience modulus in MPa;
σ d -triaxial test offset stress in MPa;
p a -atmospheric pressure, taking 0.10138MPa;
r-triaxial failure strength in MPa;
a、b、K 1 、K 2 、K 3 -a regression parameter;
3) According to the structural form and the material type of the asphalt pavement to be analyzed, a set of initial values E of the modulus of each layer of material is given i 0 Combined with the thickness h in step 1) i And Poisson ratio mu i Taking the most unfavorable stressed point positions of each layer of the asphalt pavement structure as equivalent calculation points, and calculating the Mises equivalent stress and equivalent strain of each equivalent calculation point by adopting an elastic layered system theory;
4) Substituting Mises equivalent strain of equivalent calculation points of each asphalt layer in the step 3) into an asphalt mixture complex modulus strain dependence model formula (2), substituting Mises equivalent stress of equivalent calculation points of each semi-rigid base layer into a semi-rigid base layer rebound modulus stress dependence model formula (3) or formula (4), substituting Mises equivalent stress of equivalent calculation points of the roadbed layer into a roadbed soil rebound modulus stress dependence model formula (5), and obtaining a new group of material modulus values of each layer
5) ComparisonAndwhen the two are equal or the relative error reaches the minimum value, the calculation is finished; otherwise, repeating the step 3) and the step 4) to carry out iterative calculation until the convergence precision requirement is met;
6) Adopting modulus values of each layer when the convergence precision requirement is met in the step 5)Final modulus E as structural layer i ；
7) And 6) calculating the stress, strain and displacement of any point in the asphalt pavement structure according to the elastic layered system theory by adopting the final modulus of each structural layer in the step 6), thereby obtaining the asphalt pavement structure analysis result based on the pavement material modulus stress (strain) dependence model and the equivalent method.
The method starts from the nonlinear characteristic of a pavement material, adopts a pavement material modulus stress (strain) dependency model to represent the modulus of each layer of an asphalt pavement structure, takes the most unfavorable stress point of each layer of the asphalt pavement structure as an equivalent calculation point, obtains the final modulus of each structure layer through iterative calculation, and calculates the stress, strain and displacement of any point in the asphalt pavement structure according to an elastic layered system theory on the basis. Because the method considers the influence of the nonlinear problem of the material on the pavement mechanics calculation, the stress analysis of the asphalt pavement structure is more reasonable and perfect.
The strain level of the complex modulus strain-dependent model determination method of the asphalt mixture in the step 2) is usually 30, 60, 90, 120 and 150 mu epsilon, the loading frequency is usually 10, 15, 20, 25, 30, 35 and 40Hz, the test temperature is usually 0,5, 10, 15, 20, 25, 30, 35, 40 and 45 ℃, and the reference frequency is 10Hz.
The inorganic binder type of the semi-rigid base layer resilience modulus stress dependence model determining method in the step 2) is cement, lime or fly ash, the type of the stabilized material is gravel, sand or soil, the life-span of the test piece is usually 7d, 28d, 90d or 180d, the strength level is usually more than 5, the compression stress mode refers to an axial unconfined compression test, the bending and pulling stress mode refers to a three-point or four-point beam type bending and pulling test, and the strength and resilience modulus values are representative values.
Different confining pressures (sigma) of the method for determining the resilience modulus stress dependence model of the roadbed soil in the step 2) 3 ) Usually at 3-5 levels, at pressures ranging from 0-0.5MPa; different bias stress (sigma) d ) Typically at 5 levels, at pressures in the range of 0-1.0MPa.
The stress worst point position (equivalent calculation point) of each layer of the asphalt pavement structure in the steps 3) and 4) refers to: the asphalt layer and the semi-rigid base layer are the intersection point of the load central line and the bottom of each layer, and the roadbed layer is the intersection point of the load central line and the position 40cm below the top surface of the roadbed.
The convergence precision in the step 5) and the step 6) is required to be equal to the modulus of the nth time and the modulus of the (n-1) th time of each layer or the minimum relative error.
The invention provides a brand new asphalt pavement structure mechanics analysis method based on a pavement material modulus stress (strain) dependence model by taking the most unfavorable stressed point of each layer of an asphalt pavement structure as an equivalent calculation point from the nonlinear characteristic of a pavement material, so that the stress analysis of the asphalt pavement structure is more reasonable and perfect.
Drawings
Figure 1 is a schematic diagram of a computational analysis system,
FIG. 2 Boltzmann function of temperature versus complex modulus at a frequency of 10Hz (strain level 30. Mu. Epsilon.),
FIG. 3 shows the translation results of the temperature and complex modulus test data at different frequencies (strain levels 30. Mu. Epsilon. And 10Hz are reference curves),
FIG. 4 is a main complex modulus curve of asphalt mixture based on temperature parameters (strain level 30 mu epsilon and 10Hz are reference curves),
FIG. 5 is a main curve of complex modulus of asphalt mixture (10 Hz as reference frequency) based on temperature parameters at all strain levels,
FIG. 6 is a graph of the calculation results of the maximum principal stress at each point on the axis z,
FIG. 7 is a graph of the calculation of the maximum principal strain at each point on the axis z,
FIG. 8 is a graph showing the results of vertical displacement calculations for each point on the axis z.
Detailed Description
Taking a certain asphalt pavement structure as an example, the method for analyzing the equivalent weight of the asphalt pavement structure based on a pavement material modulus stress (strain) dependence model is described, and the specific steps are as follows:
step 1, selecting the structural form, the material type and a calculation analysis system of the asphalt pavement to be analyzed.
(1) A semi-rigid base long-life asphalt pavement structure as shown in fig. 1 was selected as the pavement structure to be analyzed. The structure has 7 layers, the thickness of the pavement and the materials from top to bottom are respectively as follows: the cement stabilized macadam comprises a 4cm SBS-AC13 asphalt layer, a 8cm HMAC20 asphalt layer, a 20cm cement stabilized macadam CBG25 semi-rigid base layer, a 20cm cement stabilized soil CS semi-rigid base layer and a roadbed layer.
(2) The Poisson ratio of SBS-AC13 to cement stabilized soil CS is 0.25, the Poisson ratio of HMAC20 to cement stabilized macadam CBG25 is 0.20, and the Poisson ratio of roadbed is 0.35.
(3) The calculation load type is single-circle uniformly-distributed load, the load size p =0.7MPa, and the load circle radius =15cm. A three-dimensional coordinate system is established by taking a single-circle load central point as a coordinate system origin O, taking the horizontal rightward direction as the x-axis forward direction, taking the vertical paper outward direction as the y-axis forward direction, and taking the vertical downward direction as the z-axis forward direction, as shown in figure 1.
(4) The interlayer bonding condition of each structural layer of the pavement is completely continuous.
And 2, determining a stress (strain) dependence model of each layer of modulus of the asphalt pavement through a test.
(1) Determination of strain dependence model of complex modulus of SBS-AC13 asphalt layer
(1) The complex modulus test of the asphalt mixture SBS-AC13 is carried out, the strain level is 30, 60, 90, 120 and 150 mu epsilon, the loading frequency is 10, 15, 20, 25, 30, 35 and 40Hz, the test temperature is 0,5, 10, 15, 20, 25, 30, 35, 40 and 45 ℃, and the obtained complex modulus test result of the asphalt mixture is shown in Table 1. The complex modulus data in Table 1 are logarithmized and the results are shown in Table 2.
TABLE 1 asphalt mixture SBS-AC13 complex modulus test results
TABLE 2 asphalt mixture SBS-AC13 Complex modulus test results (logarithm of complex modulus)
(2) A main curve of complex modulus of the asphalt mixture based on temperature parameters with 10Hz as a reference frequency when the strain level is 30 mu epsilon is obtained according to the following steps.
(i) Based on the data in table 2, a relationship between the temperature and the complex modulus logarithm of the asphalt mixture at a strain level of 30 mu epsilon and a frequency of 10Hz is established by adopting a Boltzmann function, and is shown in figure 2.
(ii) Calculating a temperature shift factor alpha under each loading frequency according to a time-temperature equivalent principle by taking a Boltzmann function relation of temperature and complex modulus at a frequency of 10Hz as a reference curve i,j (results are shown in Table 3), the test data of temperature and complex modulus at different frequencies were translated, and the results after translation are shown in FIGS. 3 and 4.
TABLE 3 temperature Shift factor at different frequencies (Strain level 30. Mu. ε)
TABLE 4 temperature and Complex modulus test data after translation at different frequencies (Strain level 30. Mu. ε)
(iii) Regression analysis of the data in table 3 using the formula (1) can obtain the complex modulus main curve of the asphalt mixture based on the temperature parameter when the strain level is 30 mu epsilon (as shown in figure 4), and the expression of the main curve is shown in the formula (6).
(3) The main complex modulus curve of the asphalt mixture based on the temperature parameter with the 10Hz reference frequency can be obtained according to the method of the step (2) when the strain level is 60, 90, 120 and 150 mu epsilon, as shown in figure 5. The values of the various regression parameters in the master curve are shown in Table 5.
TABLE 5 regression parameters in temperature vs. Complex modulus master curve relationships at different strain levels
| Regression parameters | 30με | 60με | 90με | 120με | 150με |
| A 1 | 4.4854 | 4.4829 | 4.5013 | 4.4959 | 4.5656 |
| A 2 | 2.3733 | 2.1677 | 1.9868 | 1.9865 | 1.7653 |
| x 0 | 29.5071 | 30.9691 | 32.0580 | 31.2562 | 32.2689 |
| dx | 14.1723 | 14.0073 | 14.5849 | 14.4002 | 16.0970 |
(4) And (3) sorting the translation results of the temperature and complex modulus test data under different strain levels in the step (3) into a data format with independent variables of temperature and strain level and dependent variables of complex modulus logarithm, and showing in table 6.
Table 6 arrangement table of temperature and complex modulus test data translation results under different strain levels
(5) And performing regression analysis on the data in the table 5 by adopting the formula (2) to obtain an asphalt mixture complex modulus strain dependence model of the asphalt mixture SBS-AC13 based on temperature parameters, which is shown in the formula (7).
(2) Determining a complex modulus strain-dependent model of HMAC20 asphalt layer
By adopting the method in the step (1), a complex modulus strain dependence model of the HMAC20 asphalt layer can be determined by the same method, see formula (8).
(3) Model for determining rebound modulus stress dependence of cement stabilized macadam CBG25 semi-rigid base course
As can be seen from the structural form and material type of the asphalt pavement shown in FIG. 1, the flexural-tensile stress mode of the semi-rigid base course in the structure is more unfavorable than the compressive stress mode, so that the flexural-tensile stress mode is selected to determine a stress dependence model of the rebound modulus of the cement-stabilized macadam.
(1) The type of the cement stabilized macadam CBG-25 binder is cement, the stabilized material is macadam, and the life-span of the test piece is 90d. 5 materials with different strength levels in a bending and pulling stress mode are obtained by adjusting the dosage of the inorganic binder and the grading composition of the stabilized material.
(2) And (3) carrying out a bending-pulling stress mode strength and resilience modulus test by using the cement stabilized macadam CBG-25 in the step (1), and the results are shown in Table 6.
(3) And performing regression analysis on the data in the bending and pulling stress mode in the table 7 by adopting the formula (4) to obtain a formula (9).
E＝11272.5×R 0.84 ×(σ+1) -0.29 Formula (9)
The formula (9) is a strength level-based inorganic binder stabilizing material modulus of resilience stress dependence model of the cement stabilized macadam CBG-25 under different stress modes.
TABLE 7 test results of strength and resilience modulus of cement stabilized macadam in CBG-25 bending-pulling stress mode
(4) Model for determining resilience modulus stress dependence of cement stabilized soil CS semi-rigid base layer
And (4) determining a CS (modulus of elasticity) stress dependence model of the cement stabilized soil by adopting the method in the step (3) in the same way, and taking the formula (10).
E＝7951.2×R 0.53 ×(σ+1) -0.36 Formula (10)
(5) Determining roadbed soil resilience modulus stress dependence model
(1) Carrying out different confining pressures (sigma) 3 ) Sum bias stress (σ) d ) And (3) performing dynamic triaxial resilience modulus test on the foundation soil of the lower road. Confining pressure level (sigma) 3 ) The number of the plants is 3: 0.14MPa, 028MPa, 042MPa, bias stress (sigma) d ) The levels were 5: 0.2MPa, 0.3MPa, 0.4MPa, 0.5MPa, 0.6MPa, and the test results are shown in Table 8.
TABLE 8 roadbed soil dynamic triaxial resilience modulus test results
(2) Carrying out different confining pressures (sigma) by adopting the confining pressure level in the step (1) 3 ) The results of the triaxial breaking strength test of the lower road foundation soil are shown in Table 9.
TABLE 9 triaxial destructive strength test results for roadbed soil
| σ 3 /MPa | 0.14 | 0.28 | 0.42 |
| R/Mpa | 0.076 | 0.103 | 0.130 |
(3) The test data in step (1) and step (2) are arranged into a data format with independent variable of bias stress and failure strength and dependent variable of dynamic rebound modulus, and are shown in table 10.
TABLE 10 summary of dynamic triaxial resilience modulus and breaking strength test results of roadbed soil
(4) And (3) performing regression analysis on the data in the table 10 by adopting the formula (5), wherein the numerical values of all regression parameters are shown in the table 11, and substituting the numerical values into the formula (5) can obtain a roadbed soil resilience modulus stress dependence model of certain roadbed soil based on the strength index, which is expressed by the formula (11).
E＝f(σ,R)＝157.2274·(9.8639·σ d +1) -1.3721 (R) 0.4189 (11)
TABLE 11 regression parameters of stress-dependent model in roadbed soil triaxial test mode
| Regression parameters | a | b | K 1 | K 2 | K 3 | Coefficient of correlation R 2 |
| Numerical value | 3.36331 | 0.24598 | 4.04214 | -1.37211 | 1.70298 | 0.90 |
(6) Summary of modulus stress (strain) dependence model of each layer of material in pavement structure
Thus, a stress (strain) dependent model of each layer of the pavement structure to be analyzed for modulus of the material can be obtained, as shown in table 12.
TABLE 12 modulus stress (Strain) dependence model of pavement materials
Step 3, calculating the modulus of the pavement material as an initial valueThen, the mies equivalent stress and equivalent strain at each equivalent point are calculated.
(1) Giving a set of initial values of modulus of each layer materialIn connection with step 1, the material parameters for the structural analysis of the bituminous pavement can be determined, see table 13.
TABLE 13 initial values of modulus of each layer of asphalt pavement
(2) Determining equivalent computing point locations
Taking the most unfavorable stressed point position of each layer of the asphalt pavement structure as an equivalent calculation point, wherein: the asphalt layer and the semi-rigid base layer are the intersection point of the load central line z-axis and the bottom of each layer, and the roadbed layer is the intersection point of the load central line z-axis and the position 40cm below the top surface of the roadbed, namely point A in figure 1 1 To A 7 . In the three-dimensional coordinate system, the coordinates of each equivalent calculation point are (0,0,4), (0,0,12), (0,0,32), (0,0,52), (0,0,72), (0,0,92), (0,0,132) in cm.
(3) The Mises equivalent stress and equivalent strain at each equivalent calculation point were calculated using elastic layer system theory, and the results are shown in table 14.
TABLE 14 Mises equivalent stress and equivalent strain at equivalent calculated points for initial values of modulus
Step 4, substituting the Mises equivalent stress or equivalent strain in the table 14 into the pavement material modulus stress (strain) dependence model in the table 12, and calculating new modulus values of materials of all layersSee table 14.
TABLE 15 new modulus values for road surface layers
Step 5, determining the final modulus E of each structural layer i 。
(1) ComparisonAndthe relative error between the two is calculated and is shown in Table 16. As can be seen from table 16, the relative error between the two is large, and the convergence accuracy requirement is not satisfied, so that the iterative calculation needs to be performed by repeating step 3 and step 4 until the convergence accuracy requirement is satisfied.
TABLE 16Andrelative error
(2) The iterative calculation process is shown in table 17. As can be seen from Table 17, when the convergence accuracy requirement is satisfied by the iteration calculation to the 7 th time, the modulus value of each layer at this timeI.e. the final modulus E i 。
TABLE 17 results of iterative computations
Step 6, adopting the final modulus E of each structural layer in the step 5 i And calculating the stress, strain and displacement of any point in the asphalt pavement structure according to the elastic layered system theory, so as to obtain the asphalt pavement structure analysis result based on a pavement material modulus stress (strain) dependence model and an equivalent method. The maximum principal stress, maximum principal strain and vertical displacement calculations are only listed here for each point on the z-axis, see fig. 6-8.
Claims (6)
1. The method for analyzing the equivalent weight of the asphalt pavement structure based on the pavement material modulus stress and strain dependence model comprises the following steps:
1) Selecting the structure form and material type of the asphalt pavement to be analyzed, and determining and calculating the load type, interlayer bonding condition and thickness h of each layer i And poisson ratio mu i . Wherein: the parameter i represents the number of the asphalt pavement structure layers and is a positive integer;
2) According to the structural form and the material type of the asphalt pavement to be analyzed, determining an asphalt mixture complex modulus strain dependent model, a semi-rigid base layer and a roadbed soil resilience modulus stress dependent model through an indoor test, taking the model group as modulus value-taking basis of each layer in the structural analysis of the asphalt pavement, and obtaining the model group by adopting the following steps;
(1) Determination method for complex modulus strain dependence model of asphalt mixture
(1) Carrying out complex modulus tests of the asphalt mixture at different strain levels, different loading frequencies and different test temperatures;
(2) acquiring an asphalt mixture complex modulus main curve based on temperature parameters under different strain levels by taking a certain frequency as a reference frequency according to the following method;
(i) Under a certain strain level, a Boltzmann function is adopted to represent the correlation between the temperature and the complex modulus logarithm of the asphalt mixture at a certain frequency,
(ii) Taking Boltzmann function relation in (i) as a reference, introducing a temperature shift factor alpha according to a time-temperature equivalent principle, carrying out translation processing on test data of temperature and complex modulus at the strain level and other frequencies to obtain a new group of temperature-complex modulus tests after translation,
(iii) Performing regression analysis on the data in the step (ii) by adopting a formula (1) to obtain an asphalt mixture complex modulus main curve based on temperature parameters by taking a certain frequency as a reference frequency under the strain level, wherein a function expression is the formula (1),
in the formula: t-temperature in units of;
e, the complex modulus logarithm of the asphalt mixture with the base of 10;
A 1 、A 2 、x 0 dx-the regression parameter,
(iv) By adopting the methods in (i), (ii) and (iii), the complex modulus master curve of the asphalt mixture based on temperature parameters with a certain frequency as a reference frequency under other strain levels can be obtained,
(3) and (3) sorting the translated temperature-complex modulus test data under different strain levels in the step (2) into a data format with independent variable of temperature and strain level and dependent variable of complex modulus logarithm, and performing regression analysis on the data format by adopting a formula (2) to obtain an asphalt mixture complex modulus strain dependence model based on temperature parameters.
In the formula: t-temperature in units of;
e, the complex modulus logarithm of the asphalt mixture with the base of 10;
ε -Strain, unit 1X 10 2 με；
a、b、c、x 0 Dx-regression parameter;
(2) Method for determining semi-rigid base layer resilience modulus stress dependence model
[1] Determining the type of the inorganic binder of the semi-rigid base layer, the type of the stabilized material and the life-preserving period of the test piece according to the structural form and the material type of the asphalt pavement to be analyzed, and obtaining the semi-rigid base layer materials with different strength levels by adjusting the dosage of the inorganic binder and the grading composition of the stabilized material;
[2] adopting the semi-rigid base material with different strength levels in the step (1) to respectively carry out the strength and the resilience modulus test of the compression stress mode and the strength and the resilience modulus test of the bending and pulling stress mode;
[3] according to the stress mode, the test data in the step (2) are arranged into a data format with independent variable of strength and stress level and dependent variable of resilience modulus;
[4] performing regression analysis on the data in the compression stress mode in the step [3] by adopting a binary quadratic model of a formula (3), and performing regression analysis on the data in the bending and pulling stress mode in the step [3] by adopting a power function model of a formula (4) to obtain a semi-rigid base layer resilience modulus stress dependence model based on the intensity level expressed by the formula (3) and the formula (4);
E＝f(σ,R)＝a·σ 2 + b.sigma + c.R + d formula (3)
E＝f(σ,R)＝a·R c ·(σ+1) b Formula (4)
In the formula: e-compression or bend tensile modulus of elasticity in MPa;
σ -stress level, in MPa;
r is the compressive or bending tensile strength in MPa;
a. b, c, d-regression parameters;
(3) Method for determining roadbed soil resilience modulus stress dependence model
<1&At different confining pressures sigma 3 Sum bias stress σ d Performing a dynamic triaxial resilience modulus test on the roadbed soil;
<2&at the step<1&Different confining pressure sigma of gt 3 Next, performing a triaxial failure strength test on the roadbed soil;
the test data in the step <1> and the step <2> are arranged into a data format with independent variable of bias stress and failure strength and dependent variable of dynamic rebound modulus;
and (4) performing regression analysis on the data in the step <3> by adopting the formula (5) to obtain a roadbed soil resilience modulus stress dependence model based on the strength index expressed by the formula (5).
In the formula: e-dynamic triaxial resilience modulus in MPa;
σ d -triaxial test offset stress in MPa;
p a -atmospheric pressure, taking 0.10138MPa;
r-triaxial failure strength in MPa;
a、b、K 1 、K 2 、K 3 -a regression parameter;
3) According to the structural form of the bituminous pavement to be analyzedAnd material type, given a set of initial values of modulus for each layerCombining the thickness h in step 1) i And poisson ratio mu i Taking the most stressed point positions of each layer of the asphalt pavement structure as equivalent calculation points, and calculating Mises equivalent stress and equivalent strain of each equivalent calculation point by adopting an elastic layered system theory;
4) Substituting Mises equivalent strain of each asphalt layer equivalent calculation point in the step 3) into an asphalt mixture complex modulus strain dependence model formula (2), substituting Mises equivalent stress of each semi-rigid base equivalent calculation point into a semi-rigid base resilience modulus stress dependence model formula (3) or formula (4), substituting Mises equivalent stress of each road base equivalent calculation point into a road base soil resilience modulus stress dependence model formula (5) to obtain a new group of material modulus values of each layer
5) ComparisonAndwhen the two are equal or the relative error reaches the minimum value, the calculation is finished; otherwise, repeating the step 3) and the step 4) to carry out iterative computation until the convergence precision requirement is met;
6) Adopting modulus values of each layer when the convergence precision requirement is met in the step 5)Final modulus E as structural layer i ；
7) And 6) calculating the stress, strain and displacement of any point in the asphalt pavement structure according to the elastic layered system theory by adopting the final modulus of each structural layer in the step 6), thereby obtaining the asphalt pavement structure analysis result based on the pavement material modulus stress or strain dependence model and the equivalent method.
2. The method of claim 1, wherein the asphalt mix complex modulus strain-dependent model determination method has a strain level of typically 30, 60, 90, 120, 150 μ ∈, a loading frequency of typically 10, 15, 20, 25, 30, 35, 40Hz, a test temperature of typically 0,5, 10, 15, 20, 25, 30, 35, 40, 45 ℃, and a reference frequency of 10Hz.
3. The method according to claim 1, wherein the inorganic binder type of the semi-rigid base layer rebound modulus stress dependency model determination method is cement, lime or fly ash, the type of the stabilized material is crushed stone, gravel, sand or soil, the life span of the test piece is 7d, 28d, 90d or 180d, the strength level is more than 5, the compression stress mode refers to an axial unconfined compression test, the bending stress mode refers to a three-point or four-point beam bending test, and the strength and the rebound modulus values are representative values.
4. The method of claim 1, wherein the roadbed soil resilience modulus stress dependence model determines different confining pressures sigma of the method 3 Usually 3-5 levels, pressure range 0<σ 3 Less than or equal to 0.5MPa; different bias stress sigma d Typically 5 levels, pressure range 0<σ d ≤1.0MPa。
5. The method according to claim 1, wherein the most unfavorable stress point of each layer of the asphalt pavement structure, namely the equivalent calculation point, is as follows: the asphalt layer and the semi-rigid base layer are intersection points of a load central line and the bottoms of the layers, and the roadbed layer is an intersection point of the load central line and a position 40cm below the top surface of the roadbed.
6. The method of claim 1, wherein the convergence accuracy requirement is that each layer has an nth modulus equal to or a minimum relative error from the nth-1 st modulus.
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