CN113486510A - Asphalt mixture pavement rut estimation method based on rut mechanical model - Google Patents

Asphalt mixture pavement rut estimation method based on rut mechanical model Download PDF

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CN113486510A
CN113486510A CN202110751708.0A CN202110751708A CN113486510A CN 113486510 A CN113486510 A CN 113486510A CN 202110751708 A CN202110751708 A CN 202110751708A CN 113486510 A CN113486510 A CN 113486510A
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曹玮
但汉成
杜银飞
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Central South University
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Abstract

The invention relates to the technical field of road engineering, and discloses an asphalt mixture pavement rut estimation method based on a rut mechanical model, which comprises the following steps: s1, establishing a rut mechanical model considering time, loading history dependency and confining pressure dependency; and S2, estimating the rutting depth of the target pavement according to the vertical pressure stress pulse in the target pavement and the rutting mechanical model. The method comprehensively considers two main influence mechanisms of the time of viscoplasticity deformation accumulation, the loading history dependence and the confining pressure dependence, wherein the time of viscoplasticity deformation accumulation is represented by viscoplasticity creep compliance or relaxation modulus, and the dependence of viscoplasticity deformation accumulation is represented by a parameter E∞In consideration, the rutting performance of the asphalt mixture pavement can be effectively predicted.

Description

Asphalt mixture pavement rut estimation method based on rut mechanical model
Technical Field
The invention relates to the technical field of road engineering, in particular to an asphalt mixture pavement rut estimation method based on a rut mechanical model.
Background
Ruts are a main disease type of asphalt pavements, can seriously affect the driving safety and comfort, and are factors to be considered in the pavement material and structure design of high-temperature areas and heavy-load road sections in summer, so that the ruts of the asphalt mixture pavements need to be estimated reasonably. The rutting disease of the asphalt pavement in China mainly originates from the permanent deformation of an asphalt surface layer material, namely the constraint on a mineral aggregate framework is reduced due to asphalt softening at high temperature, so that the viscoplasticity deformation of an asphalt mixture is accumulated under the action of external load. The method has relatively abundant research on the rutting evolution of the asphalt mixture, but most of prediction models belong to phenomenological or empirical models, so that the applicability, popularization and application of the prediction models are greatly limited. The establishment of the rutting mechanical model mainly faces two great challenges, namely that the viscosity of asphalt endows the time and loading history dependence of the mixture in the permanent deformation process, and the porosity of a mineral aggregate framework endows the confining pressure dependence of the permanent deformation, and the existing mechanical model considers or considers the influence mechanisms of the two aspects rarely. The evolution law of the viscoplastic deformation of the asphalt mixture is mastered, the action mechanism of each influencing factor is ascertained, and a rutting mechanical model is established, which is a precondition and a key for guiding the material and structural design of an asphalt pavement to fundamentally prevent rutting diseases.
Disclosure of Invention
The invention aims to provide an asphalt mixture pavement rut estimation method based on a rut mechanical model, and aims to solve the problem that the rut estimation accuracy is poor due to the fact that the existing mechanical model considers little or gives consideration to time, loading history and confining pressure dependence.
In order to achieve the purpose, the invention provides the following technical scheme:
an asphalt mixture pavement rut estimation method based on a rut mechanical model comprises the following steps:
s1, establishing a rut mechanical model considering time, loading history dependency and confining pressure dependency;
s2, estimating the rutting depth of the target pavement according to the vertical pressure stress pulse in the target pavement and the rutting mechanical model;
the expression of the rut mechanical model is as follows:
Figure BDA0003144880440000011
in the formula (1), epsilonvp(t) is the viscoplastic strain, Dvp(t) is the viscoplastic creep compliance equation; sigmadIs partial stress, in the form of triaxial stressIn the state has sigmad＝σ1－σ3，σ1For axial stress, σ3Is confining pressure; t represents time, ξ is an integral variable of time,<>macaulay brackets are indicated to ensure irreversibility of viscoplastic deformation;
the vertical compressive stress pulse comprises a plurality of loading cycles, and each loading cycle comprises a half-sine pressure pulse and a period of pause time.
Further, said Dvp(t) is characterized by the Prony sequence and is expressed as:
Figure BDA0003144880440000012
in the formula (2), N is the number of terms of Prony sequence, D0、Dj、τjThe visco-plastic compliance parameters are respectively expressed as instantaneous creep compliance, each compliance component and corresponding characteristic delay time.
Further, said Dvp(t) viscoplastic relaxation modulus E characterized by the Prony sequencevp(t) calculating by solving a matrix equation;
the expression of the viscoplasticity relaxation modulus characterized by the Prony sequence is as follows:
Figure BDA0003144880440000021
in the formula (3), M is the number of terms of Prony sequence, E∞、Ei、ρiThe parameters are viscoplasticity relaxation parameters which respectively represent long-term relaxation modulus, each modulus component and corresponding characteristic relaxation time, and the viscoplasticity relaxation spectrum conforms to the lognormal distribution:
Figure BDA0003144880440000022
in the formula (4), xi＝ln(ρi/ρm)，ρmDenotes the mean relaxation time, Δ EvpAnd
Figure BDA0003144880440000023
measuring the height and width of the lognormal distribution respectively;
the expression of the matrix equation is:
AkjDj＝Qk (5)
in formula (5), k is 1,2, … p, and p is the number of time nodes determined in advance in the collocation method (collocation method);
Figure BDA0003144880440000024
Figure BDA0003144880440000025
Figure BDA0003144880440000026
further, in step S2, according to the vertical compressive stress pulse in the target road surface and the rutting mechanical model, the target road surface rutting depth is estimated, which specifically includes:
loading phase in the first cycle: initial conditions are t ═ 0, σd(0)＝0，εvp(0) 0, viscoplastic strain epsilonvpThe iterative calculation method of (1) is that, assuming that the viscoplastic strain at the nth time step is known, there is
Figure BDA0003144880440000027
In the formula (9), the state quantity R at the (n + 1) th time stepjIs calculated iteratively as
Figure BDA0003144880440000031
Wherein σdFor external bias stress loads, σintTo characterize the internal stresses of plastic hardening of pavement materials,
Figure BDA0003144880440000032
t is time, having:
Figure BDA0003144880440000033
unloading and intermittent phases in the cycle: viscoplastic strain epsilonvp(t) maintenance of constant, internal stress σintIs calculated as follows:
Figure BDA0003144880440000034
Figure BDA0003144880440000035
wherein the iterative calculation formula of the state quantity Rj is
Figure BDA0003144880440000036
Loading stage after the first cycle:
when an external load sigmadLess than or equal to the internal stress σintStrain of viscoplasticity ofvp(t)Maintained unchanged and internal stress sigmaintCalculated according to the formulas (12) to (14);
when an external load sigmadGreater than internal stress sigmaintIn time, namely at the nth and n +1 time steps, the following relationship is satisfied:
Figure BDA0003144880440000037
the viscoplastic strain ε at time step n +1vp(t)Calculated according to equation (9), but wherein the state quantity RjIs calculated iteratively as
Figure BDA0003144880440000038
Internal stress sigmaintIs in accordance with the bias stress loading, i.e.
Figure BDA0003144880440000039
Compared with the prior art, the invention has the beneficial technical effects that:
the model considers the visco-plastic relaxation modulus E for a given asphalt mixturevp(t) is the intrinsic property of the material, independent of the loading conditions, and the influence of the confining pressure is completely determined by the parameter E∞And (5) characterizing. The model parameters have E∞、ΔEvp、
Figure BDA00031448804400000310
ρmDetermining the viscoplastic relaxation modulus in the form of a lognormal distribution, selecting M Prony terms at equal intervals on a logarithmic scale, and determining Ei、ρiThe viscoplastic creep modulus Dvp (t) can be calculated according to the expressions (5) - (8) and substituted into the model expression (1) to determine the viscoplastic strain epsilonvp(t) of (d). Most of the existing models only aim at monotonous loading or continuous cyclic loading, cannot be used for intermittent repeated loading which is more suitable for the actual action characteristic of traffic load, or can only describe the viscoplasticity strain response of the asphalt mixture under a very limited intermittent loading action frequency. The method comprehensively considers two main influence mechanisms of time of viscoplasticity deformation accumulation, loading history dependence and confining pressure dependence, wherein the time of viscoplasticity deformation accumulation is represented by viscoplasticity relaxation modulus, and the confining pressure dependence is represented by parameter E∞In consideration, the concept of internal stress represents the plastic hardening of the material in the loading stage and the softening of the material in the unloading and intermittence periods, so that the rutting performance of the asphalt mixture pavement under the condition of more fitting with the actual triaxial stress and traffic load characteristics (discontinuity and high repeatability) can be effectively predicted, and the support for fundamentally preventing rutting diseases is provided for the material and structure design of the asphalt pavement.
Drawings
Fig. 1 is a flowchart of an asphalt mixture pavement rut estimation method based on a rut mechanical model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of measured values and model fitting values of viscoplastic strains under different bias stresses and confining pressures in a first experiment according to an embodiment of the present invention;
FIG. 3 is a parameter E in the first experiment provided by the embodiment of the present invention∞A graph of stress ratio as a function of time;
FIG. 4 is a schematic diagram of a visco-plastic strain measurement value and a model prediction value in a random loading experiment in the first experiment according to the embodiment of the present invention;
FIG. 5 is a schematic diagram of measured values of viscoplastic strain and model fitting values under different bias stresses and a confining pressure of 138kPa in a second experiment according to an embodiment of the present invention;
fig. 6 is a schematic diagram of the visco-plastic strain measurement value and the model prediction value under the 0.1 s and 1.6s stress pulse conditions in the second experiment according to the embodiment of the present invention;
fig. 7 is a schematic diagram of a visco-plastic strain measurement value and a model prediction value in a random loading experiment in the second experiment according to the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and embodiments:
as shown in fig. 1, a rut estimation method for an asphalt mixture pavement based on a rut mechanical model includes:
s1, establishing a rut mechanical model considering time, loading history dependency and confining pressure dependency;
s2, estimating the rutting depth of the target pavement according to the vertical pressure stress pulse in the target pavement and the rutting mechanical model;
the expression of the rut mechanical model is as follows:
Figure BDA0003144880440000041
in the formula (1), epsilonvp(t) is the viscoplastic strain, Dvp(t) is viscoplasticityCreep compliance equations; sigmadIs partial stress, has sigma under triaxial stress stated＝σ1-σ3，σ1For axial stress, σ3Is confining pressure; t denotes time and ξ is an integral variable of time.<>Macaulay brackets are shown to ensure irreversibility of viscoplastic deformation. That is, for any variable
Figure BDA0003144880440000044
Macaulay brackets are defined as:
Figure BDA0003144880440000042
in this model, the time and loading history dependence of viscoplastic strain is described by convolution and macauliy brackets. As can be seen from equation (1), the model largely retains the form of the visco-elastic convolution model.
Further, Dvp(t) is characterized by the Prony sequence and is expressed as:
Figure BDA0003144880440000043
in the formula (2), N is the number of terms of Prony sequence, D0、Dj、τjThe visco-plastic compliance parameters are respectively expressed as instantaneous creep compliance, each compliance component and corresponding characteristic delay time.
Further, said Dvp(t) viscoplastic relaxation modulus E characterized by the Prony sequencevp(t) calculating by solving a matrix equation;
the expression of the viscoplasticity relaxation modulus characterized by the Prony sequence is as follows:
Figure BDA0003144880440000051
in the formula (3), M is the number of terms of Prony sequence, E∞、Ei、ρiIs a viscoplastic relaxation parameter, each of which is represented byLong-term relaxation modulus, each modulus component and corresponding characteristic relaxation time, and for the convenience of parameter calibration, it is assumed that the viscoplasticity relaxation spectrum conforms to the lognormal distribution:
Figure BDA0003144880440000052
in the formula (4), xi＝ln(ρi/ρm)，ρmDenotes the mean relaxation time, Δ EvpAnd
Figure BDA0003144880440000053
measuring the height and width of the lognormal distribution respectively; therefore, the Prony coefficient of the viscoplastic relaxation modulus can be completely determined from only these three parameters.
Due to Evp(t) and Dvp(t) satisfies the following relation:
Figure BDA0003144880440000054
from the Prony sequence of the relaxation modulus, the Prony sequence corresponding to the creep compliance was calculated by solving the following matrix equation according to the above formula.
The expression of the matrix equation is:
AkjDj＝Qk (5)
in formula (5), k is 1,2, … p, and p is the number of time nodes determined in advance in the collocation method (collocation method);
Figure BDA0003144880440000055
Figure BDA0003144880440000056
Figure BDA0003144880440000061
furthermore, the axial load acting characteristic in the actual road surface is considered, and the vertical compressive stress pulse in the road surface approximately conforms to a semi-sinusoidal shape. Therefore, the vertical compressive stress pulse in step S2 includes several loading cycles, each of which includes a half-sine pressure pulse and a pause duration for simulating the discontinuity of traffic axle load on the actual road surface.
Step S2 specifically includes:
loading phase in the first cycle: this phase is similar to monotonic loading with the initial condition t-0, σd(0)＝0，εvp(0) 0, the viscoplastic strain continues to increase, Macaulay brackets are not activated, εvpDetermined by convolution in formula (1), viscoplastic strain εvpThe iterative calculation method of (1) is that, assuming that the viscoplastic strain at the nth time step is known, there is
Figure BDA0003144880440000062
In the formula (9), the state quantity R at the (n + 1) th time stepjThe iterative calculation of (a) is:
Figure BDA0003144880440000063
wherein σdFor external bias stress loads, σintTo characterize the internal stresses of plastic hardening of pavement materials,
Figure BDA0003144880440000064
t is time, having:
Figure BDA0003144880440000065
Rjthe initial condition of the iterative computation is
Figure BDA0003144880440000066
In the loading phase, for tablesInternal stress of plastic hardening of material
Figure BDA0003144880440000067
Stress offset from external load
Figure BDA0003144880440000068
And the consistency is maintained.
Unloading and intermittent phases in the cycle: the convolution calculation is reduced in equation (1) and Macaulay brackets are activated when the internal stress σ is presentintUnder the action of (2), viscoplastic strain epsilonvp(t) maintenance of constant, internal stress σintIs calculated as follows:
Figure BDA0003144880440000069
Figure BDA0003144880440000071
wherein the iterative calculation formula of the state quantity Rj is
Figure BDA0003144880440000072
Loading stage after the first cycle:
when an external load sigmadLess than or equal to the internal stress σintStrain of viscoplasticity ofvp(t)Maintained unchanged and internal stress sigmaintCalculated according to the formulas (12) to (14);
when an external load sigmadGreater than internal stress sigmaintIn time, namely at the nth and n +1 time steps, the following relationship is satisfied:
Figure BDA0003144880440000073
the viscoplastic strain ε at time step n +1vp(t)Calculated as equation (9), but where the state quantity Rj is iteratively calculated as:
Figure BDA0003144880440000074
internal stress sigmaintIs in accordance with the bias stress loading, i.e.
Figure BDA0003144880440000075
Experiment one
The conventional dense-graded asphalt mixture is adopted, the maximum nominal particle size is 9.5mm, and the performance grade of asphalt is PG 52-34. Preparing a rotary compaction test piece, and cutting and coring to obtain the test piece with the diameter of 100mm and the height of 150 mm. In the experiment, the test piece is wrapped up by the Latex film, and both ends are fixed with the clamp plate through O type circle to ensure that the test piece only receives the effect of even confined pressure in the triaxial chamber from the outside. The axial strain is measured by four LVDTs fixed on a sticky nail, the sticky nail penetrates through a film and is stuck on the surface of a test piece by adopting epoxy resin glue, and the contact part of the sticky nail and the film is sealed by acrylic latex caulking materials. The experimental temperature was 48 ℃, the confining pressure used was 69, 138, 207kPa, the bias stress used a cyclic loading pattern, each cycle consisting of a 0.4s half-sinusoidal pressure pulse and a rest period, and the bias stress amplitude was 483, 689, 896 kPa. To ensure sufficient recovery of viscoelastic strain during the rest period, the rest period of each cycle was set to 100s, and the strain at the end of each rest period was collected as the viscoelastic strain. Two parallel tests are adopted under each loading condition, and the obtained results are used for parameter calibration and model verification.
The parameter to be calibrated is E∞、ΔEvp、
Figure BDA0003144880440000076
ρmThe visco-plastic strain data obtained from each parallel experiment under all conditions were used for parameter calibration with an error function of
Figure BDA0003144880440000077
In the above formula,. psi.Total number of experiments, psi, for parameter calibrationjFitting the model to the jth experimental data to obtain an error, P is the number of cyclic loads in the jth experiment,
Figure BDA0003144880440000078
and
Figure BDA0003144880440000079
respectively representing the viscoplastic strain measurement value and the model fitting value of the ith cycle in the jth experiment.
Fig. 2 shows the comparison of the measured values of the viscoplastic strain at different ambient pressures with the fitted values of the model, and it can be seen that the model well describes the nonlinear influence of the ambient pressure and the bias stress on the accumulation of the viscoplastic deformation. FIG. 3 shows a parameter E characterizing the effect of confining pressure∞Correlation with stress ratio (ratio of confining pressure to bias stress) and curve fitting.
The effectiveness of the model is further verified by a random loading experiment, the experiment temperature is the same, the number of loading cycles is 1500, the stress pulse duration in each cycle is different from 0.1 to 1.6s, the stress amplitude is randomly changed within the range of 491-904 kPa, the stress pulse duration and the stress amplitude are randomly combined after being determined by the generated random numbers, the intermittence duration is 10s, and the experiment is respectively carried out under the two ambient pressure conditions of 103 kPa and 172 kPa. Fig. 4 shows the comparison between the viscoplastic strain measurement value and the model prediction value in the random loading experiment, and it can be seen that the model prediction effect is good.
Experiment two
The conventional dense-graded asphalt mixture is adopted, the nominal maximum particle size is 12.5mm, and the performance of the asphalt is graded as PG 70-22. The blend was coarser graded and more viscous than the material used in case 1. The preparation and experimental method of the test piece are similar to those of the experiment I, except that the experimental temperature is set to 54 ℃ corresponding to the high-viscosity asphalt, and only 138kPa is considered in confining pressure. In each loading cycle, the stress pulse duration is 0.1 s, 0.4s and 1.6s, the stress amplitude is 620 kPa, 827 kPa and 1034kPa, and the pause duration is constant at 100 s. The 0.4s stress pulse experimental data are used for calibrating model parameters, other experiments are used for verifying the model, and 2-3 parallel experiments are executed under each condition. Fig. 5 shows that the model and experimental data agree well under all bias stress conditions during the parameter calibration. Fig. 6 shows the actual visco-plastic strain and the model predicted value under the stress pulse conditions of 0.1 s and 1.6s, and the model predicted effect is better. Fig. 7 shows the results of random loading experimental verification, which indicates that the model gives a good prediction of the accumulation of viscoplastic strain under random loading.
The foregoing is merely an example of the present invention and common general knowledge in the art of designing and/or characterizing particular aspects and/or features is not described in any greater detail herein. It should be noted that, for those skilled in the art, without departing from the technical solution of the present invention, several variations and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.

Claims (4)

1. The method for estimating the ruts of the asphalt mixture pavement based on the rut mechanical model is characterized by comprising the following steps of:
s1, establishing a rut mechanical model considering time, loading history dependency and confining pressure dependency;
s2, estimating the rutting depth of the target pavement according to the vertical pressure stress pulse in the target pavement and the rutting mechanical model;
the expression of the rut mechanical model is as follows:
Figure FDA0003144880430000011
in the formula (1), epsilonvp(t) is the viscoplastic strain, Dvp(t) is the viscoplastic creep compliance equation; sigmadIs partial stress, has sigma under triaxial stress stated＝σ1-σ3，σ1For axial stress, σ3Is confining pressure; t represents time, ξ is an integral variable of time,<>denotes MacaulayBrackets to ensure irreversibility of viscoplastic deformation;
the vertical compressive stress pulse comprises a plurality of loading cycles, and each loading cycle comprises a half-sine pressure pulse and a period of pause time.
2. The asphalt mixture pavement rut estimation method based on the rut mechanical model according to claim 1, characterized in that: said Dvp(t) is characterized by the Prony sequence and is expressed as:
Figure FDA0003144880430000012
in the formula (2), N is the number of terms of Prony sequence, D0、Dj、τjThe visco-plastic compliance parameters are respectively expressed as instantaneous creep compliance, each compliance component and corresponding characteristic delay time.
3. The method for estimating the rutting of the asphalt mixture pavement based on the rutting mechanical model as claimed in claim 2, wherein D isvp(t) viscoplastic relaxation modulus E characterized by the Prony sequencevp(t) calculating by solving a matrix equation;
the expression of the viscoplasticity relaxation modulus characterized by the Prony sequence is as follows:
Figure FDA0003144880430000013
in the formula (3), M is the number of terms of Prony sequence, E∞、Ei、ρiThe parameters are viscoplasticity relaxation parameters which respectively represent long-term relaxation modulus, each modulus component and corresponding characteristic relaxation time, and the viscoplasticity relaxation spectrum conforms to the lognormal distribution:
Figure FDA0003144880430000014
in the formula (4), xi＝ln(ρi/ρm)，ρmDenotes the mean relaxation time, Δ EvpAnd
Figure FDA0003144880430000015
measuring the height and width of the lognormal distribution respectively;
the expression of the matrix equation is:
AkjDj＝Qk (5)
in formula (5), k is 1,2, … p, and p is the number of time nodes determined in advance in the collocation method (collocation method);
Figure FDA0003144880430000021
Figure FDA0003144880430000022
Figure FDA0003144880430000023
4. the method for estimating the rutting on the asphalt mixture pavement based on the rutting mechanical model according to claim 3, wherein in the step S2, the estimating of the rutting depth on the target pavement according to the vertical pressure stress pulse in the target pavement and the rutting mechanical model specifically comprises:
loading phase in the first cycle: initial conditions are t ═ 0, σd(0)＝0，εvp(0) 0, viscoplastic strain epsilonvpThe iterative calculation method of (1) is that, assuming that the viscoplastic strain at the nth time step is known, there is
Figure FDA0003144880430000024
In the formula (9), the state quantity R at the (n + 1) th time stepjIs calculated iteratively as
Figure FDA0003144880430000025
Wherein σdFor external bias stress loads, σintTo characterize the internal stresses of plastic hardening of pavement materials,
Figure FDA0003144880430000026
t is time, having:
Figure FDA0003144880430000027
unloading and intermittent phases in the cycle: viscoplastic strain epsilonvp(t)Maintained unchanged and internal stress sigmaintIs calculated as follows:
Figure FDA0003144880430000028
Figure FDA0003144880430000031
wherein the state quantity RjThe iterative calculation of (a) is:
Figure FDA0003144880430000032
loading stage after the first cycle:
when an external load sigmadLess than or equal to the internal stress σintStrain of viscoplasticity ofvp(t)Maintained unchanged and internal stress sigmaintCalculated according to the formulas (12) to (14);
when an external load sigmadGreater than internal stress sigmaintIn time, namely at the nth and n +1 time steps, the following relationship is satisfied:
Figure FDA0003144880430000033
the viscoplastic strain ε at time step n +1vp(t)Calculated according to equation (9), but wherein the state quantity RjThe iterative calculation of (a) is:
Figure FDA0003144880430000034
internal stress sigmaintIs in accordance with the bias stress loading, i.e.
Figure FDA0003144880430000035
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CN115758846A (en) * 2022-12-08 2023-03-07 山东大学 Calculation method of homogeneous viscoplasticity constitutive model

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Application publication date: 20211008