CN104598669A - Method for forecasting permanent deformation of bituminous mixture pavement - Google Patents
Method for forecasting permanent deformation of bituminous mixture pavement Download PDFInfo
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Abstract
In order to better simulate the practical stress state of a pavement structure and more accurately estimate permanent deformation of a bituminous mixture pavement, the invention provides a method for forecasting permanent deformation of the bituminous mixture pavement. According to the method for forecasting permanent deformation of the bituminous mixture pavement, the temperature of the bituminous mixture pavement is divided into m sections, the bituminous mixture pavement is structurally divided into n sub-layers, average deviatoric stress and creep compliance of the sub-layers in different temperature sections and under different load conditions are calculated, and permanent deformation of the bituminous mixture pavement is calculated according to the formula (please see the formula in the specification). The method for forecasting permanent deformation of the bituminous mixture pavement has the technical advantages that coupling effects of the pavement temperature, traffic axle loads and pavement material characteristics are analyzed comprehensively, analysis results accord with reality better, accuracy is high, and the application range is wide.
Description
Technical Field
The invention relates to the technical field of road engineering construction, in particular to a method for predicting permanent deformation of a bituminous mixture pavement.
Background
The road surface structure generates excessive permanent deformation under the action of repeated load, so that unevenness affecting comfort and driving safety can appear on the road surface, and even the road surface cracks. Therefore, limiting the amount of permanent deformation of a pavement structure is a fundamental requirement that must be considered in the design of pavement structures.
The basic methods for estimating the permanent deformation of the asphalt mixture pavement at home and abroad can be classified into an empirical method, an empirical-theoretical method and a theoretical analysis method according to different bases when a model is established.
(1) Empirical method
The general empirical method is also called statistical method, and is based on a large amount of observation data of a test road section and combined with an indoor test to establish an estimation empirical formula of the relationship between the permanent strain of an asphalt mixture layer and the load and material characteristics to determine the deformation of the asphalt mixture road surface under the long-term repeated action of the load. A representative model is an empirical formula established in the 80 s of the 20 th century a. wijerthe et al:
lgp＝c0+c1lgN type (1)
Wherein,pis the permanent vertical strain of the asphalt mixture; n is the repeated action times of the axle load; c. C0，c1Is a parameter of material performance and stress state.
The empirical method is obtained by regression analysis of test path measurement data, and the actual situation of the path is compared and conformed to, so that the empirical method has the characteristics of strong pertinence and high estimation precision under specific conditions; but the whole effect of the pavement structure is not considered, the formula of the estimated deformation has poor ductility and poor universality, and the method is only suitable for estimating the permanent deformation of the asphalt mixture pavement in a specific area under specific conditions. Therefore, the method is limited to be used for popularizing and evaluating the permanent deformation of the asphalt mixture pavement.
(2) Semi-empirical-semi-theoretical method
Compared with the empirical method, the semi-empirical-semi-theoretical method reduces the limitation on the use range to a certain extent and improves the universality. Generally, an elastic layered system theory or a viscoelastic layered system theory is adopted to solve the stress and displacement of the road surface, and then an empirical relation between the permanent deformation of the asphalt layer and the deflection of the road surface, material performance parameters and load is calculated by combining indoor and outdoor related tests. A representative model of the method is an estimation model proposed by Jacob Uzan:
Wherein RD is permanent deformation of the asphalt layer, and is mm; omega is the road surface deflection coefficient (dimensionless); the road surface deflection under the dynamic load of the double wheels is realized; n is the repeated loading times; a is1、a2Road surface structure and size parameters.
There are also some interesting aspects in semi-empirical-semi-theoretical methods. First, the development of the constitutive model of bituminous mixtures is very important for studying the plastic deformation of the model. The study of this aspect was conducted at Arizona State university, Purdue university, UC Berkeley, et al. Secondly, the reaction of the material upon environmental changes is also taken into account. Third, plastic strain is considered in combination with other types of strain or stress by elastic or viscoelastic modeling.
(3) Theoretical analysis method
The theoretical analysis method is based on a layered elastic system theory or a viscoelastic system theory, calculates stress in a pavement system, and calculates pavement permanent strain by using the relationship between the pavement asphalt mixture permanent strain and the stress.
Layer strain method
The layer strain method was first proposed by Barksdale and roman. The principle of this method is to divide each layer of the pavement into smaller sub-layers, calculate the sub-layers on the basis of the theory of the elastic layer system, and then estimate the permanent deformation of each layer of the pavement by linking to a laboratory test. The permanent deformation of the asphalt layer is estimated according to the elastic layered system, and the Shell method has the most influence internationally. The method is established on the basis of a large number of creep tests, a track test and a series of assumptions. The model assumes that the relationship between the stiffness of the asphalt mixture and the stiffness of the asphalt obtained in the creep test is equal to the relationship between the stiffness of the viscous part of the mixture and the stiffness of the viscous part of the asphalt, and then the stiffness of the mixture is used for replacing the stiffness of the viscous part of the asphalt mixture reflecting the permanent deformation of the asphalt. The model has the following defects: the effect of using the modified asphalt on reducing the ruts of the newly-built pavement cannot be explained; the phenomenon that the road surface generates different tracks under the conditions of different axle loads, different configurations and the same contact pressure cannot be explained; only the elastic response is accurate, the stiffness parameter is taken as the elastic parameter, and the viscosity and the plastic response of the mixture are not considered; the introduction of the dynamic image correction factor increases the prediction permanent deformation by 30 to 100 percent.
The advantages of the layer strain method are: the theory is simplified, and the requirement of engineering precision can be basically met. The disadvantages are that: 1) only the stress strain of the lower area of the center of the tire is considered, and the shear deformation of the wheel track edge is not considered; 2) the permanent deformation depends only on the elastic stress of the road surface; 3) using elastic theory, linear or non-linear, is not consistent with some practical behavior that causes permanent deformation (e.g., shear flow at the footprint edge).
Theoretical method of viscoelasticity
In a pavement structure design viscoelasticity system VESSYS proposed by the Federal public road administration and the Massachusetts institute of technology, a permanent deformation estimation model based on a viscoelasticity theory is established. In this model, the permanent deformation of the pavement material is considered as a function of stress, loading time, temperature, moisture content. Suppose that: 1) between the load repeated action times m and m +1, the viscoelastic deformation of the pavement material has enough recovery time; 2) the deflection of each layer is not changed under the action of each load.
③ finite element method
The finite element method can well simulate the deformation of the road surface with nonlinear characteristics. Currently, many researchers use finite element programs including ABAQUS, ANSYS, etc. to create an estimated model of permanent deformation. For example, Huang, H.M et al, university of Puff, USA, uses a creep model for rutting finite element analysis; the Jian Fang Hua utilizes a viscoelastic finite element method to estimate rutting and compares APT (accessed behavior testing) and PURWHell test results, thereby proving the validity of estimating rutting by the finite element method; the Zhong Wu utilizes a finite element method to simulate the characteristics of the asphalt mixture pavement material, particularly simulate the track deformation of Superpave, and proves the feasibility of the viscoelastic finite element method in the wide application of pavement structure analysis and design. With the great improvement of the calculation capacity and the calculation time of the computer, the method is more reasonable and economic, and the finite element method can be used for simulating the whole deformation area of the pavement under the load action, thereby being a development direction for estimating the permanent deformation of the asphalt mixture pavement.
Disclosure of Invention
The invention provides a method for predicting the permanent deformation of an asphalt mixture pavement, which aims to better simulate the actual stress state of a pavement structure and more accurately predict the permanent deformation of the asphalt mixture pavement. The method for predicting the permanent deformation of the asphalt mixture pavement comprises the steps of dividing the temperature of the asphalt pavement into m intervals, dividing the structure of the asphalt mixture pavement into n sub-layers, respectively calculating the average offset stress and creep compliance of each sub-layer under different temperature intervals and load conditions, and calculating the permanent deformation of the asphalt mixture pavement by adopting the following formula (1).
In the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the pavement temperature interval number; n is the sub-layer number of the asphalt mixture pavement structure; h isiThe thickness of the ith sublayer of the asphalt mixture pavement is in mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be obtained by subtracting the major stress and the minor stress of each unit obtained by finite element analysis and calculation of the asphalt mixture pavement structure under the action of dynamic load; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value of the creep test model is obtained by repeatedly loading a corrected Burgers model and combining the interpolation and fitting of the indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
Further, the method for predicting the permanent deformation of the asphalt mixture pavement, disclosed by the invention, comprises the step of predicting the creep compliance (J) of the ith sub-layer of the asphalt mixture pavementvp)iRelation J ofvp＝f(T,N,σ0) The method comprises the following steps:
s71, taking eta (t) as AeBtCarrying out nonlinear correction on a first viscous element eta in a constitutive equation of the Burgers model;
the constitutive equation of the Burgers model is as follows (2):
the modified Burgers model equation is as follows (3):
e.g. at t ═ t0And the unloading is carried out at the moment, then,
s72, simulating the loading and unloading process of the wheel pair asphalt mixture pavement by adopting half sine wave intermittent load, wherein the half sine wave intermittent load can be expressed as a piecewise function, namely
Viscous flow deformation strain after N times of loading:
s73, correcting the creep compliance of the viscoelastic unit in the Burgers model, namely, the creep compliance of the viscoelastic unit in the Burgers model is expressed by the following formula (7):
according to the Boltzmann linear superposition principle, the viscoelastic deformation generated by the ith half-sine wave intermittent load is finished to the action moment of the Nth half-sine wave gap load, and the residual viscoelastic deformation is as follows:
after N loads, the residual viscoelastic deformation was:
order to <math>
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Then at the end of the nth half sine wave pause, the permanent deformation is:
at the end of the nth half sine wave intermittent action, the creep compliance is:
s74, combining the asphalt mixture pavement material with different temperature ranges and different axle loads, and performing a triaxial repeated load creep test by adopting a semi-versine wave load simulation loading and unloading process, namely equivalently converting the semi-versine wave load stress into equivalent static load offset stress, namely multiplying the equivalent static load offset stress by 2/pi times, and respectively equating the three offset stresses of 300kpa, 500kpa and 700kpa to 191.1kpa, 318.5kpa and 445.8 kpa; load time t00.2s, pause time td0.8s, total period T1 s, σ0Corresponding to the axial offset stress in the test, a viscoelastic mechanical model for describing the permanent deformation of the triaxial repeated load creep test can be obtained:
wherein:
s75, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the asphalt mixture mechanical model;
s76, step SThe i-th sublayer creep compliance (J) can be obtained by carrying the interpolation fitting parameters obtained by 75 fitting into formula (11)vp)iRelation J ofvp＝f(T,N,σ0)；
In the above formulas, σ0Axial bias stress in MPa; t is the load application time, 0<t≤t0The unit is s; E. e1Modulus in MPa; eta, eta1Is a viscoelasticity parameter in mpa.s; A. b is a kettle sticking parameter; t is the total period of load action, T is T0+td；σtIs the axial offset stress at the time t, sigma is the maximum stress value of the axial offset stress wave crest, t0Is the loading time in units of s; t is tdIs the pause time in units of s; n is the load action frequency; k is the viscosity of the kettle.
Further, the method for predicting the permanent deformation of the asphalt mixture pavement comprises the following steps:
s1, dividing the area where the asphalt mixture pavement is located into m temperature intervals according to the annual actual temperature condition of the area, and taking the middle value of the interval as the representative temperature value of the temperature interval to obtain the annual pavement temperature distribution frequency; wherein the annual pavement temperature distribution frequency is the percentage of the annual hours of each temperature interval to the annual total hours; m is a natural number greater than 1 and takes a value of 5-10;
s2, obtaining temperature values of different asphalt mixture pavement depths in each temperature interval by adopting an actual measurement method; the temperature values of different asphalt mixture pavement depths are actual measurement temperature values of different temperature intervals at different asphalt mixture pavement depths;
s3, determining the elastic modulus of the asphalt mixture pavement at different depths in each temperature interval according to the relationship between the temperature and the modulus of the asphalt mixture pavement material;
s4, determining temperature axle load distribution, dividing vehicle axle load grades according to the actual running conditions of roads and the axle load size, calculating axle load distribution frequency of different axle load grades, and calculating equivalent axle load grades and equivalent axle load distribution frequency of different temperature areas within a design year according to the accumulated equivalent axle load on one lane within the design year and the road surface temperature distribution frequency and the axle load distribution frequency, namely the temperature axle load distribution;
s5, establishing a three-dimensional finite element calculation model of the pavement structure based on ANSYS software according to the actual condition of the pavement structure of the asphalt mixture, and dividing the pavement structure of the asphalt mixture into n sub-layers vertically according to the set depth interval; the asphalt layer is divided according to the interval of 1cm, and the sub-layer dividing interval of the base layer and the sub-layer dividing interval of the subbase layer are increased;
s6, carrying out stress analysis on the road surface structure three-dimensional finite element calculation model established in the step S5 by using ANSYS software at representative temperatures of all temperature intervals to obtain stress distribution in sub layers of the asphalt mixture road surface, extracting and analyzing large and small principal stresses in a load action range, and subtracting the large and small principal stresses of all units to obtain the average partial stress (sigma) of each sub layer of the asphalt mixture road surface at each representative temperature0)iWherein i is equal to 1, 2, 3, …, n;
s7, carrying out a triaxial repeated load creep test on the asphalt mixture pavement in combination with different temperature intervals and different axle loads, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the mechanical model of the asphalt mixture pavement under different temperatures and different axle loads;
wherein:
in the formula, σ0Axial bias stress in MPa; A. b is a kettle sticking parameter; e1Modulus in MPa; eta1Is a viscoelasticity parameter in mpa.s;
s8, the i-th sub-layer creep compliance (J) can be obtained by taking the interpolation fitting parameters obtained by the fitting in the step S7 into the formula (11)vp)iRelation J ofvp＝f(T,N,σ0)，
In the formula, σ0Axial bias stress in MPa; b is a kettle sticking parameter; t is t0For load time, 0<t≤t0The unit is s; t is the total period of load action and is expressed by s; k is a kettle sticking parameter;
s9, adopting the following formula (1) to calculate the permanent deformation of the asphalt mixture pavement,
in the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the interval number of pavement temperature divisions; n is the sub-layer number of the asphalt mixture pavement; h isiIs the thickness of the ith sub-layer of the asphalt mixture pavementIs mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be obtained by subtracting the major stress and the minor stress of each unit obtained by finite element analysis and calculation of the pavement structure under the action of dynamic load; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value is obtained by modeling through a repeated loading correction Burgers model and combining the interpolation and fitting of indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
The method for predicting the permanent deformation of the asphalt mixture pavement has the advantages that the method can comprehensively analyze the coupling effect of the pavement temperature, the traffic axle load and the pavement material characteristics, the analysis result is more practical, the accuracy is higher, and the application range is wide.
Drawings
FIG. 1 is a block diagram of the design process of the method for predicting the permanent deformation of the asphalt mixture pavement;
FIG. 2 is a graph of annual road surface temperature distribution frequency in different temperature ranges;
FIG. 3 is a graph showing the temperature variation of each temperature zone with the depth of the pavement structure;
FIG. 4 is a graph of temperature versus modulus;
FIG. 5 is a graph showing the elastic modulus curves of asphalt mixture road surfaces at different road surface depths in different temperature intervals;
FIG. 6 is a graph of axle load distribution frequency;
FIG. 7 is a graph of temperature distribution on axis;
FIG. 8 is a schematic view of the asphalt mixture pavement structure of the present embodiment;
FIG. 9 is a schematic diagram of a three-dimensional finite element model constructed in the present embodiment;
FIG. 10 is a graph of the deflection stress at 20 ℃ for different axle loads and different road depths in this example.
The method for predicting the permanent deformation of the asphalt mixture pavement is further described with reference to the accompanying drawings and specific examples.
Detailed Description
FIG. 1 is a block diagram showing the design process of the method for predicting the permanent deformation of an asphalt mixture pavement according to the present invention, which can be seen from the figure that the method for predicting the permanent deformation of an asphalt mixture pavement divides the temperature of the asphalt mixture pavement into m intervals, divides the asphalt mixture pavement into n sub-layers, calculates the average offset stress and creep compliance of each sub-layer under different temperature and load conditions, calculates the permanent deformation of the asphalt mixture pavement by the following formula (1),
in the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the interval number of pavement temperature divisions; n is the sub-layer number of the asphalt mixture pavement; h isiThe thickness of the ith sublayer of the asphalt mixture pavement is in mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be obtained by subtracting the major stress and the minor stress of each unit obtained by finite element analysis and calculation of the asphalt mixture pavement structure under the action of dynamic load; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value of the creep test model is obtained by repeatedly loading a corrected Burgers model and combining the interpolation and fitting of the indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
Creep compliance (J) for the ith sublayer of asphalt pavementvp)iRelation J ofvp＝f(T,N,σ0) The method comprises the following steps:
s71, taking eta (t) as AeBtCarrying out nonlinear correction on a first viscous element eta in a constitutive equation of the Burgers model;
the constitutive equation of the Burgers model is as follows (2):
the modified Burgers model equation is as follows (3):
e.g. at t ═ t0And the unloading is carried out at the moment, then,
s72, simulating the loading and unloading process of the wheel pair asphalt mixture pavement by adopting half sine wave intermittent load, wherein the half sine wave intermittent load can be expressed as a piecewise function, namely
Viscous flow deformation strain after N times of loading:
s73, correcting the creep compliance of the viscoelastic unit in the Burgers model, namely, the creep compliance of the viscoelastic unit in the Burgers model is expressed by the following formula (7):
according to the Boltzmann linear superposition principle, the viscoelastic deformation generated by the ith half-sine wave intermittent load is finished to the action moment of the Nth half-sine wave gap load, and the residual viscoelastic deformation is as follows:
after N loads, the residual viscoelastic deformation was:
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Then at the end of the nth half sine wave pause, the permanent deformation is:
at the end of the nth half sine wave intermittent action, the creep compliance is:
s74 asphaltThe mixed material pavement material is combined with different temperature intervals and different axial loads, a three-axis repeated load creep test is carried out by adopting a semi-versine wave load simulation loading and unloading process, namely, the semi-versine wave load stress is equivalently converted into equivalent static load bias stress, namely multiplied by 2/pi times, and the three bias stresses of 300kpa, 500kpa and 700kpa are respectively equivalent to 191.1kpa, 318.5kpa and 445.8 kpa; load time t00.2s, time to unload td0.8s, total period T1 s, σ0Corresponding to the axial offset stress in the test, a viscoelastic mechanical model for describing the permanent deformation of the triaxial repeated load creep test can be obtained:
wherein:
s75, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the asphalt mixture mechanical model;
s76, fitting the interpolation obtained by the fitting in the step S75The creep compliance (J) of the i-th sublayer is obtained by several passes (11)vp)iRelation J ofvp＝f(T,N,σ0)；
In the above formulas, σ0Axial bias stress in MPa; t is the load application time, 0<t≤t0The unit is s; E. e1Modulus in MPa; eta, eta1Is a viscoelasticity parameter in mpa.s; A. b is a kettle sticking parameter; t is the total period of load action, T is T0+td；σtIs the axial offset stress at the time t, sigma is the maximum stress value of the axial offset stress wave crest, t0Is the loading time in units of s; t is tdIs the pause time in units of s; n is the load action frequency; k is the viscosity of the kettle.
The invention discloses a method for predicting permanent deformation of an asphalt mixture pavement, which comprises the following steps of:
s1, dividing the area where the asphalt mixture pavement is located into m temperature intervals according to the annual actual temperature condition of the area, and taking the middle value of the interval as the representative temperature value of the temperature interval to obtain the annual pavement temperature distribution frequency; wherein the annual pavement temperature distribution frequency is the percentage of the annual hours of each temperature interval to the annual total hours; m is a natural number greater than 1 and takes a value of 5-10;
in this embodiment, the road surface temperature is divided into 9 temperature intervals at 5 ℃, the equivalent temperature is the median of the temperature intervals, then the total number of hours occupied by each temperature interval in the whole year is counted, and the total number of hours in the whole year (365 × 24) is divided by the value to obtain the road surface temperature distribution frequency of the whole year in different temperature intervals, as shown in fig. 2.
S2, obtaining temperature values of different asphalt mixture pavement depths in each temperature interval by adopting an actual measurement method; the temperature values of different asphalt mixture pavement depths are actual measurement temperature values of different temperature intervals at different asphalt mixture pavement depths;
in this embodiment, sensors are arranged along the depth of the asphalt mixture pavement, and the temperature values of different asphalt mixture pavement depths in each temperature interval are obtained by collecting, processing and analyzing related data. Then, plotting the depth from the road surface as the vertical axis (unit is mm) and the temperature as the horizontal axis (unit is degree centigrade) to obtain the variation curve of the temperature of each temperature area along with the structural depth of the road surface, as shown in fig. 3.
S3, determining the elastic modulus of the asphalt mixture pavement at different depths in each temperature interval according to the relationship between the temperature and the modulus of the asphalt mixture pavement material;
in this embodiment, the asphalt mixture pavement material shown in fig. 8 is used, the relationship between the temperature and the modulus is shown in fig. 4, and the elastic modulus of the asphalt mixture pavement at different pavement depths in each temperature interval can be calculated through fig. 4 and fig. 3, as shown in fig. 5.
S4, determining temperature axle load distribution, dividing vehicle axle load grades according to the actual running conditions of roads and the axle load size, calculating axle load distribution frequency of different axle load grades, and calculating equivalent axle load grades and equivalent axle load distribution frequency of different temperature areas within a design year according to the accumulated equivalent axle load on one lane within the design year and the road surface temperature distribution frequency and the axle load distribution frequency, namely the temperature axle load distribution;
in this embodiment, the traffic volume is divided into 10 axle load grades, which are 0-2, 2-4, 4-8, 8-10, 10-12, 12-14, 14-16, 16-18, > 18, and the unit is T. The distribution frequency is shown in fig. 6.
The cumulative equivalent axle number of the highway on one lane in the design year is 1.88 multiplied by 107And then, combining the road surface temperature distribution frequency of the 9 temperature zones obtained in the step S1 and the axle load distribution frequency shown in fig. 6 to calculate equivalent axle numbers of different axle load grades and different temperature zones within the design years. Plotting the axle load grade as the horizontal axis and the equivalent axle times as the vertical axis to obtain the temperature axle load distribution diagram, as shown in figure 7.
S5, establishing a three-dimensional finite element calculation model of the pavement structure based on ANSYS software according to the actual condition of the pavement structure of the asphalt mixture, and dividing the pavement structure of the asphalt mixture into n sub-layers vertically according to the set depth interval; the asphalt layer is divided according to the interval of 1cm, and the sub-layer dividing interval of the base layer and the sub-layer dividing interval of the subbase layer are increased;
the asphalt pavement structure of this embodiment includes an asphalt layer, a base layer, and a sub-base layer, as shown in fig. 8. The three-dimensional finite element model is shown in fig. 9.
S6, carrying out stress analysis on the road surface structure three-dimensional finite element calculation model established in the step S5 by using ANSYS software at representative temperatures of all temperature intervals to obtain stress distribution in sub layers of the asphalt mixture road surface, extracting and analyzing large and small principal stresses in a load action range, and subtracting the large and small principal stresses of all units to obtain the average partial stress (sigma) of each sub layer of the asphalt mixture road surface at each representative temperature0)iWherein i is equal to 1, 2, 3, …, n;
the length, width and height of the finite element calculation model of the embodiment are all 3m, and it is assumed that:
(1) the crack failure surface is composed of unconnected points, other layers are composed of linear elastic materials, Poisson ratio is mu, and elastic modulus is E;
(2) the roadbed is assumed to be free of constraint and wireless in the downward direction and the horizontal direction, the layers above the roadbed are constrained, and the driving direction is infinite;
(3) the road surface structure acts on vehicle load, and the effect generated at the infinite distance and the horizontal infinite distance below the road surface structure can be ignored;
(4) the facing and underlying layers are semi-continuous, while the other layers are fully continuous.
The relationship between axle load and tire pressure is set as shown in Table 1, i.e., different axle loads produce different stresses on the road surface (the tire pressure area is calculated as the standard vehicle tire contact patch)
TABLE 1 axle load vs. tire pressure relationship
The finite element calculation model is analyzed and calculated to obtain the offset stress curve graphs of different axle loads and different road depths under the temperature representative condition of each temperature interval, the offset stress curve graphs are limited to space, and the offset stress curve graphs of different axle loads and different road depths at 20 ℃ are listed, as shown in figure 10. Extracting the principal stress sigma of each sublayer in the finite element model1、σ3According to (σ)0)i＝(σ1-σ3)iThe average partial stress (sigma) of the ith sub-layer of the asphalt mixture pavement can be obtained0)i；
S7, carrying out a triaxial repeated load creep test on the asphalt mixture pavement in combination with different temperature intervals and different axle loads, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the mechanical model of the asphalt mixture pavement under different temperatures and different axle loads;
wherein:
in the formula, σ0Axial bias stress in MPa; A. b is a kettle sticking parameter; e1Modulus in MPa; eta1Is a viscoelasticity parameter in mpa.s;
the interpolation fitting parameters of the sub-layers of the partial mechanical models of the three asphalt mixtures of SMA-13, AC-20 and ATB-30 in the embodiment are shown in Table 2.
TABLE 2 interpolation fitting parameters of three mechanical models of asphalt mixture
S8, the i-th sub-layer creep compliance (J) can be obtained by taking the interpolation fitting parameters obtained by the fitting in the step S7 into the formula (11)vp)iRelation J ofvp＝f(T,N,σ0)，
In the formula, σ0Axial bias stress in MPa; b is a kettle sticking parameter; t is t0For load time, 0<t≤t0The unit is s; t is the total period of load action and is expressed by s; k is a kettle sticking parameter;
the creep compliance of a part of the sub-layer in this example can be determined by equation (11) and Table 2 (J)vp)iI.e. creep compliance J of the i-th sublayervp＝f(T,N,σ0) See table 3.
TABLE 3 relationship formula for calculating deformation of each sub-layer of asphalt mixture under different temperature, different axial load and different partial stress conditions
S9, adopting the following formula (1) to calculate the permanent deformation of the asphalt mixture pavement,
in the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the interval number of pavement temperature divisions; n is the sub-layer number of the asphalt mixture pavement; h isiThe thickness of the ith sublayer of the asphalt mixture pavement is in mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be obtained by subtracting the major stress and the minor stress of each unit obtained by finite element analysis and calculation of the pavement structure under the action of dynamic load; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value is obtained by modeling through a repeated loading correction Burgers model and combining the interpolation and fitting of indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention. Modifications and variations of the present invention will be apparent to those skilled in the art. Any changes, variations or equivalent substitutions made within the spirit and scope of the present invention should be included in the protection scope of the present invention.
Obviously, the method for predicting the permanent deformation of the asphalt mixture pavement has the advantages that the method can comprehensively analyze the coupling effect of the pavement temperature, the traffic axle load and the pavement material characteristics, the analysis result is more practical, the accuracy is higher, and the application range is wide.
Claims (3)
1. The method for predicting the permanent deformation of the asphalt mixture pavement is characterized by dividing the temperature of the asphalt pavement into m intervals, dividing the structure of the asphalt mixture pavement into n sub-layers, respectively calculating the average partial stress and creep compliance of each sub-layer under different temperature intervals and load conditions, and calculating the permanent deformation of the asphalt mixture pavement by adopting the following formula (1).
In the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the pavement temperature interval number; n is the sub-layer number of the asphalt mixture pavement structure; h isiThe thickness of the ith sublayer of the asphalt mixture pavement is in mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be obtained by subtracting the major stress and the minor stress of each unit obtained by finite element analysis and calculation of the asphalt mixture pavement structure under the action of dynamic load; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value of the creep test model is obtained by repeatedly loading a corrected Burgers model and combining the interpolation and fitting of the indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
2. The method of predicting permanent deformation of asphalt pavement according to claim 1, wherein the creep compliance (J) of the ith sublayer of asphalt pavementvp)iRelation J ofvp＝f(T,N,σ0) The method comprises the following steps:
s71, taking eta (t) as AeBtCarrying out nonlinear correction on a first viscous element eta in a constitutive equation of the Burgers model;
the constitutive equation of the Burgers model is as follows (2):
the modified Burgers model equation is as follows (3):
e.g. at t ═ t0And the unloading is carried out at the moment, then,
s72, simulating the loading and unloading process of the wheel pair asphalt mixture pavement by adopting half sine wave intermittent load, wherein the half sine wave intermittent load can be expressed as a piecewise function, namely
Viscous flow deformation strain after N times of loading:
s73, correcting the creep compliance of the viscoelastic unit in the Burgers model, namely, the creep compliance of the viscoelastic unit in the Burgers model is expressed by the following formula (7):
according to the Boltzmann linear superposition principle, the viscoelastic deformation generated by the ith half-sine wave intermittent load is finished to the action moment of the Nth half-sine wave gap load, and the residual viscoelastic deformation is as follows:
after N loads, the residual viscoelastic deformation was:
order to
Then at the end of the nth half sine wave pause, the permanent deformation is:
at the end of the nth half sine wave intermittent action, the creep compliance is:
s74, combining the asphalt mixture pavement material with different temperature ranges and different axle loads, and performing a triaxial repeated load creep test by adopting a semi-versine wave load simulation loading and unloading process, namely equivalently converting the semi-versine wave load stress into equivalent static load offset stress, namely multiplying the equivalent static load offset stress by 2/pi times, and respectively equating the three offset stresses of 300kpa, 500kpa and 700kpa to 191.1kpa, 318.5kpa and 445.8 kpa; load time t00.2s, pause time td0.8s, total period T1 s, σ0Corresponding to the axial offset stress in the test, a viscoelastic mechanical model for describing the permanent deformation of the triaxial repeated load creep test can be obtained:
wherein:
P2＝B；
s75, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the asphalt mixture mechanical model;
s76, the i-th sub-layer creep compliance (J) can be obtained by taking the interpolation fitting parameters obtained by the fitting in the step S75 into the formula (11)vp)iRelation J ofvp＝f(T,N,σ0)；
In the above formulas, σ0Axial bias stress in MPa; t is the load application time, 0<t≤t0The unit is s; E. e1Modulus in MPa; eta, eta1Is a viscoelasticity parameter in mpa.s; A. b is a kettle sticking parameter; t is the total period of load action, T is T0+td；σtIs the axial offset stress at the time t, sigma is the maximum stress value of the axial offset stress wave crest, t0Is the loading time in units of s; t is tdIs the pause time in units of s; n is the load action frequency; k is the viscosity of the kettle.
3. The method for predicting the permanent deformation of an asphalt pavement according to claim 1, comprising the steps of:
s1, dividing the area where the asphalt mixture pavement is located into m temperature intervals according to the annual actual temperature condition of the area, and taking the middle value of the interval as the representative temperature value of the temperature interval to obtain the annual pavement temperature distribution frequency; wherein the annual pavement temperature distribution frequency is the percentage of the annual hours of each temperature interval to the annual total hours; m is a natural number greater than 1 and takes a value of 5-10;
s2, obtaining temperature values of different asphalt mixture pavement depths in each temperature interval by adopting an actual measurement method; the temperature values of different asphalt mixture pavement depths are actual measurement temperature values of different temperature intervals at different asphalt mixture pavement depths;
s3, determining the elastic modulus of the asphalt mixture pavement at different depths in each temperature interval according to the relationship between the temperature and the modulus of the asphalt mixture pavement material;
s4, determining temperature axle load distribution, dividing vehicle axle load grades according to the actual running conditions of roads and the axle load size, calculating axle load distribution frequency of different axle load grades, and calculating equivalent axle load grades and equivalent axle load distribution frequency of different temperature areas within a design year according to the accumulated equivalent axle load on one lane within the design year and the road surface temperature distribution frequency and the axle load distribution frequency, namely the temperature axle load distribution;
s5, establishing a three-dimensional finite element calculation model of the pavement structure based on ANSYS software according to the actual condition of the pavement structure of the asphalt mixture, and dividing the pavement structure of the asphalt mixture into n sub-layers vertically according to the set depth interval; the asphalt layer is divided according to the interval of 1cm, and the sub-layer dividing interval of the base layer and the sub-layer dividing interval of the subbase layer are increased;
s6, carrying out stress analysis on the road surface structure three-dimensional finite element calculation model established in the step S5 by using ANSYS software at representative temperatures of all temperature intervals to obtain stress distribution in sub layers of the asphalt mixture road surface, extracting and analyzing large and small principal stresses in a load action range, and subtracting the large and small principal stresses of all units to obtain the average partial stress (sigma) of each sub layer of the asphalt mixture road surface at each representative temperature0)iWherein i is equal to 1, 2, 3, …, n;
s7, carrying out a triaxial repeated load creep test on the asphalt mixture pavement in combination with different temperature intervals and different axle loads, compiling an iterative process related program by adopting 1stopt software, and fitting the test data with the formula (12) to obtain interpolation fitting parameters of each sublayer of the mechanical model of the asphalt mixture pavement under different temperatures and different axle loads;
wherein:
P2＝B；
in the formula, σ0Axial bias stress in MPa; A. b is a kettle sticking parameter; e1Modulus in MPa; eta1Is a viscoelasticity parameter in mpa.s;
s8, the i-th sub-layer creep compliance (J) can be obtained by taking the interpolation fitting parameters obtained by the fitting in the step S7 into the formula (11)vp)iRelation J ofvp＝f(T,N,σ0)，
In the formula, σ0Axial bias stress in MPa; b is a kettle sticking parameter; t is t0For load time, 0<t≤t0The unit is s; t is the total period of load action and is expressed by s; k is a kettle sticking parameter;
s9, adopting the following formula (1) to calculate the permanent deformation of the asphalt mixture pavement,
in the formula: delta h is the permanent deformation of the asphalt mixture pavement, and the unit is mm; m is the interval number of pavement temperature divisions; n is the sub-layer number of the asphalt mixture pavement; h isiThe thickness of the ith sublayer of the asphalt mixture pavement is in mm; (sigma)0)iThe average partial stress of the ith sublayer of the asphalt mixture pavement is expressed in MPa (sigma)0)i＝(σ1-σ3)iThe value can be calculated by finite element analysis of the road surface structure under the action of dynamic loadSubtracting the large and small principal stresses of each unit to obtain the stress; (J)vp)iCreep compliance of the i-th sub-layer of asphalt pavement, Jvp＝f(T,N,σ0) The value is obtained by modeling through a repeated loading correction Burgers model and combining the interpolation and fitting of indoor triaxial repeated load creep test data; m and n are both natural numbers larger than 1.
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