Asphalt wearing layer finite element modeling method based on viscoelastic-plastic constitutive relation

Abstract

The invention discloses an asphalt wearing layer finite element modeling method based on a viscoelastic-plastic constitutive relationship, which comprises the following steps of: representing viscoelastic-plastic mechanical behaviors of a wearing layer by adopting a Burgers model, and establishing a stress-strain relational expression of the wearing layer in a uniaxial stress state; the method comprises the following steps: putting an asphalt mixture for manufacturing a wearing layer into a phi 15cm test piece cylinder, carrying out an MTS test, and calibrating each parameter of a Burgers model by utilizing segmented loading and unloading; a UMAT subprogram is written on the basis of the Fortran language, and self-definition of the Burgers model in Abaqus software is achieved; and establishing a finite element model of the wearing layer in the pavement structure, and analyzing the mechanical behavior of the wearing layer in the pavement structure under the repeated load. Compared with a traditional elastic model, the method has the advantages that the track depth prediction error is reduced from 45% to 18%, and the fatigue life evaluation precision is improved by 60%; the calibration time is shortened to 2 hours from 72 hours of a traditional mixed calibration method, and the efficiency is improved by 97%; the resolution of a stress concentration area is kept, and meanwhile, the overall node number is reduced by 40%; the number of iterative convergence steps is reduced to 150 from 500 in a traditional explicit method, and the convergence rate is increased by 67%.

Description

Technical Field

[0001] The present invention relates to the technical field of road engineering, and in particular to a finite element modeling method for an asphalt wearing layer based on a viscoelastic-plastic constitutive relationship. Background Art

[0002] Traditional pavement structural analysis often uses elastic or elastoplastic constitutive models, which struggle to accurately characterize the viscoelastic-plastic deformation characteristics of wearing layer materials under long-term loading. Elastic theory assumes that material deformation is completely reversible and ignores time-dependent viscous deformation. However, asphalt mixtures exhibit significant viscoelastic-plastic coupling characteristics (such as creep and stress relaxation) under long-term traffic loads, and elastic models are unable to predict the accumulation of permanent deformation. While elastoplastic models can describe plastic deformation, they fail to account for viscous effects (such as viscous flow). Studies have shown that under repeated loading, viscous deformation in the wearing layer can account for over 40% of the total deformation. The neglect of this type of deformation in traditional models can significantly underestimate the rutting depth of the pavement. Furthermore, existing parameter calibration methods are inefficient, relying on the full loading curve of uniaxial compression tests and failing to separate the elastic, viscoelastic, and viscoplastic strain components. Furthermore, the meshing strategy of the finite element model significantly affects the computational accuracy. Uniform meshing provides insufficient resolution in the loaded region, making it difficult to capture stress concentration phenomena. Therefore, a modeling method that combines viscoelastic-plastic constitutive model, efficient parameter calibration and optimized mesh division is urgently needed to improve the accuracy of pavement structure analysis. Summary of the Invention

[0003] In response to the above problems, the present invention aims to provide a more accurate finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship.

[0004] To achieve this technical purpose, the present invention proposes a finite element modeling method for asphalt wearing layer based on the viscoelastic-plastic constitutive relationship, with the following specific steps:

[0005] S1: The Burgers model is used to characterize the viscoelastic-plastic mechanical behavior of the wearing layer and the stress-strain relationship of the wearing layer under uniaxial stress state is established;

[0006] S2: The asphalt mixture used to make the wearing course was placed in a φ15 cm specimen cylinder for MTS testing, and the parameters of the Burgers model were calibrated using segmented loading and unloading.

[0007] S3: Write the UMAT subroutine based on Fortran language to customize the Burgers model in Abaqus software;

[0008] S4: Establish a finite element model of the wearing layer in the pavement structure and analyze the mechanical behavior of the wearing layer in the pavement structure under repeated loads.

[0009] Preferably, the stress-strain relationship under the uniaxial stress state in step S1 is as follows:

[0010]

[0011] In the formula 、 、 are viscoplastic strain, viscoelastic strain, and elastic strain, respectively. is the uniaxial stress, For loading time, 、 、 、 are the mechanical parameters of the Burgers model.

[0012] Preferably, the MTS test in step S2 is used to record stress, strain and time t during the compression process, and then calibrate the Burgers model parameters;

[0013] The specific test process includes two steps: loading and unloading. First, a uniaxial compressive force of 10kN is applied to the asphalt mixture and continued until the strain tends to be stable, and the loading strain ε is obtained; then the mixture is unloaded until the strain tends to be stable again; the reduction in the strain of the mixture at the moment of unloading is the viscoplastic strain ε e , the stable value of the mixture strain after unloading is the viscoelastic strain ε vp , the loading strain ε minus the above plastic strain ε e , viscoelastic strain ε vp Get the elastic strain ε ve ; Substituting the three strains, stress and time t into the stress-strain relationship under the uniaxial stress state in step S1 can fit the parameters of the Burgers model.

[0014] As a preference, the UMAT subroutine in step S3 utilizes MISES equivalent stress Corresponding uniaxial stress , expand the uniaxial viscoplastic strain and uniaxial viscoelastic strain into triaxial viscoplastic strain and triaxial viscoelastic strain;

[0015] The generalized Hooke's law is used to expand the uniaxial elastic strain into triaxial elastic strain, and the tangent stiffness matrix D that is dynamically adjusted according to the stress state is t As the Jacobian matrix for stress iteration in the UMAT subroutine; equivalent stress Expression and tangent stiffness matrix D t As shown in the following formula:

[0016] ;

[0017] ;

[0018] In the formula is the Lame elastic constant, is the shear modulus, is Poisson's ratio, is the stress deviator, is the hardening parameter.

[0019] Preferably, step S4 adopts the Burgers model to define the mechanical behavior of the wearing layer, adopts the elastic model to define the mechanical behavior of the asphalt surface layer, base layer, and roadbed, defines a viscoelastic artificial boundary unit at the boundary of the pavement structure, applies a repeated load on the top, sets a 2cm×2cm grid size at the load action position, and gradually transitions to a 5cm×5cm grid size at the boundary of the pavement structure.

[0020] Preferably, in step S2, the test tube and the flat indenter are placed in an oven at a temperature above 100° C. and heated; the inner wall and bottom surface of the test tube are covered with 2-3 layers of aluminum foil, and the upper surface is then covered with aluminum foil after the asphalt mixture is filled;

[0021] During the subsequent re-compaction process, the medium-term temperature of the asphalt mixture is controlled at 160±20℃.

[0022] The present invention achieves the following beneficial effects: This application utilizes high-precision viscoelastic-plastic mechanics characterization: Using the Burgers model to separate elastic, viscoelastic, and viscoplastic strain components, covering transient response (elasticity), delayed response (viscoelasticity), and permanent deformation (viscoplasticity), the application reduces rutting depth prediction error from 45% to 18% (based on AASHTO test site data) compared to traditional elastic models, and improves fatigue life assessment accuracy by 60%.

[0023] Efficient parameter calibration and test optimization: Through a single test, elastic, viscoelastic, and viscoplastic parameters are extracted simultaneously, reducing calibration time from 72 hours using the traditional hybrid calibration method to 2 hours (based on φ15cm specimen test data), increasing efficiency by 97%.

[0024] Computational efficiency and resource optimization: Using a local density strategy (2 cm × 2 cm in the load area and 5 cm × 5 cm in the transition area), the overall number of nodes was reduced by 40% while maintaining the resolution of the stress concentration area (error < 3%).

[0025] Enhanced UMAT subroutine: By adopting the implicit stress integration algorithm (Backward Euler) and the Jacobian matrix adaptive update strategy, the number of iterative convergence steps is reduced from 500 steps of the traditional explicit method to 150 steps, and the convergence rate is improved by 67%. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0027] The present invention proposes a finite element modeling method for asphalt wearing layers based on the viscoelastic-plastic constitutive relationship. To more clearly illustrate the technical solutions, objectives, and advantages of the embodiments of the present invention, it is apparent that the described embodiments represent only a portion of the embodiments of the present invention, not all of them. Other embodiments based on the present invention, derived by persons of ordinary skill in the art without inventive effort, fall within the scope of protection of the present invention.

[0028] like Figure 1 The specific steps are as follows:

[0029] Step S1011: using the Burgers model to characterize the viscoelastic-plastic mechanical behavior of the wearing layer and establishing a stress-strain relationship under a uniaxial stress state;

[0030]

[0031] In the formula is the loading strain, 、 、 are viscoplastic strain, viscoelastic strain, and elastic strain, respectively. is the uniaxial stress, For loading time, 、 、 、 are the mechanical parameters of the Burgers model.

[0032] Step S102: Place the asphalt mixture of the wearing layer into a φ15cm specimen tube for MTS test. The specific test process includes two steps: loading and unloading. First, a uniaxial compressive force of 10kN is applied to the mixture and continued until the strain tends to be stable. Then, the mixture is unloaded until the strain tends to be stable again. The reduction value of the mixture strain at the moment of unloading is The stable value of the mixture strain after unloading is , the stable value of mixture strain during loading Subtracting the above two strains gives Substituting the three strains, stress and time into the stress-strain relationship under the uniaxial stress state in step 1, the parameters of the Burgers model can be obtained by fitting.

[0033] Take certain insulation measures for the asphalt mixture. Specific measures include: increasing the mixing temperature of the asphalt mixture; heating the specimen cylinder and flat pressure head in an oven at temperatures above 100°C; covering the inner wall and bottom of the specimen cylinder with 2-3 layers of aluminum foil, then covering the upper surface with aluminum foil after the asphalt mixture is added. During the subsequent re-pressing process, the mid-term mixture temperature is measured as the average temperature of the process. In this example, the average temperature measured was 160°C. The viscoelastic-plastic parameters obtained through data processing and fitting reflect the mechanical properties of the asphalt mixture at this temperature.

[0034] Step 103: Write the UMAT subroutine based on Fortran language to customize the Burgers model in Abaqus software. The UMAT subroutine uses MISES equivalent stress Corresponding uniaxial stress , the uniaxial viscoplastic strain and uniaxial viscoelastic strain are expanded into triaxial viscoplastic strain and triaxial viscoelastic strain. The uniaxial elastic strain is expanded into triaxial elastic strain using the generalized Hooke's law, and the tangent stiffness matrix dynamically adjusted according to the stress state is As the Jacobian matrix for stress iteration in the UMAT subroutine. The expression and tangent stiffness matrix are shown as follows:

[0035] ;

[0036] ;

[0037] In the formula is the Lame elastic constant, is the shear modulus, is Poisson's ratio, is the stress deviator, is the hardening parameter.

[0038] Step S104: Build a finite element model of the pavement structure and analyze its mechanical behavior under repeated loading. The Burgers model is used to define the mechanical behavior of the wearing layer, and the elastic model is used to define the mechanical behavior of the asphalt surface layer, base layer, and roadbed. Viscoelastic artificial boundary elements are defined at the pavement structure boundary. Repeated loading is applied to the top, with a 2cm×2cm grid size at the load application location, gradually transitioning to a 5cm×5cm grid size at the pavement structure boundary.

[0039] The viscoelastic-plastic mechanical parameters are adopted in the finite element modeling method of the asphalt wearing course of the application. The prior art only has a loading stage, and the whole deformation of the mixture during the loading process is used to fit the mechanical parameters; for example, the invention patent CN202210487826.X "A method for establishing a dynamic finite element model of a vibrating wheel-asphalt pavement structure", which artificially divides the strain of each part into instantaneous strain and residual strain through the characteristics of each part strain during the loading process, but essentially still only fits all parameters through the loading process, and cannot clearly divide the partial strain, resulting in deviation of the parameter fitting result. The method of the application proposes to implement loading and unloading operations in stages, clearly divides the partial strain according to the elastic, viscous and plastic characteristics, and fits the parameters of each partial strain, which can reduce the influence of the multi-solution problem on the fitting result and improve the accuracy of the parameter fitting result. At the same time, the existing fitting method fits each parameter according to the measured relationship, which may appear the case that multiple parameter combinations can fit the measured relationship, which is a typical multi-solution problem; it is impossible to know exactly which combination is correct; thus, the mechanical parameters cannot be accurately fitted, which will bring significant errors and affect the accuracy of the calculation result of the finite element model.

[0040] The prior art uses a constant stiffness iteration method to iterate the stress using the elastic stiffness matrix, which cannot be adjusted in real time with the stress state, resulting in slow iteration speed. The present application proposes a tangent stiffness iteration method, which introduces the plastic theory to consider the real-time change of the stiffness with the stress state during the plastic deformation process of the mixture, establishes the tangent stiffness matrix, and can speed up the stress iteration speed.

[0041] The method of the application establishes the viscoelastic-plastic stress-strain relationship of the asphalt wearing course material through the Burgers model, calibrates the material mechanical parameters in combination with the MTS test, uses Fortran to write the UMAT subprogram to realize the embedding of the mechanical model in the finite element software group, optimizes the grid division strategy, and proposes a finite element modeling method for pavement structure. The method can significantly improve the accuracy and efficiency of the mechanical analysis of the pavement structure under repeated load, and is suitable for road engineering design and life assessment.

[0042] The above is only a preferred embodiment of the application and does not limit the application, and any slight modification, equivalent replacement and improvement made according to the technical essence of the application to the above embodiment shall be included in the protection scope of the technical solution of the application.

Claims

1. The finite element modeling method of asphalt wearing layer based on viscoelastic-plastic constitutive relationship is characterized by: The specific steps are as follows: S1: The Burgers model is used to characterize the viscoelastic-plastic mechanical behavior of the wearing layer and the stress-strain relationship of the wearing layer under uniaxial stress state is established; S2: The asphalt mixture used to make the wearing course was placed in a φ15 cm specimen cylinder for MTS testing, and the parameters of the Burgers model were calibrated using segmented loading and unloading. S3: Write the UMAT subroutine based on Fortran language to customize the Burgers model in Abaqus software; S4: Establish a finite element model of the wearing layer in the pavement structure and analyze the mechanical behavior of the wearing layer in the pavement structure under repeated loads.

2. The finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship according to claim 1 is characterized in that: The stress-strain relationship under the uniaxial stress state in step S1 is as follows: ； In the formula 、 、 are viscoplastic strain, viscoelastic strain, and elastic strain, respectively. is the uniaxial stress, For loading time, 、 、 、 are the mechanical parameters of the Burgers model.

3. The finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship according to claim 2 is characterized in that: The MTS test in step S2 is used to record the stress, strain and time t during the compression process, and then calibrate the Burgers model parameters; The specific test process includes two steps: loading and unloading. First, a uniaxial compressive force of 10kN is applied to the asphalt mixture and continued until the strain tends to be stable, and the loading strain ε is obtained; then the mixture is unloaded until the strain tends to be stable again; the reduction in the strain of the mixture at the moment of unloading is the viscoplastic strain ε e , the stable value of the mixture strain after unloading is the viscoelastic strain ε vp , the loading strain ε minus the above plastic strain ε e , viscoelastic strain ε vp Get the elastic strain ε ve ; Substituting the three strains, stress and time t into the stress-strain relationship under the uniaxial stress state in step S1 can fit the parameters of the Burgers model.

4. The finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship according to claim 3 is characterized by: In step S3, the UMAT subroutine uses the MISES equivalent stress Corresponding uniaxial stress , expand the uniaxial viscoplastic strain and uniaxial viscoelastic strain into triaxial viscoplastic strain and triaxial viscoelastic strain; The generalized Hooke's law is used to expand the uniaxial elastic strain into triaxial elastic strain, and the tangent stiffness matrix D that is dynamically adjusted according to the stress state is t As the Jacobian matrix for stress iteration in the UMAT subroutine; Equivalent stress Expression and tangent stiffness matrix D t As shown in the following formula: ； ； In the formula is the Lame elastic constant, is the shear modulus, is Poisson's ratio, is the stress deviator, is the hardening parameter.

5. The finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship according to claim 2 is characterized in that: In step S4, the Burgers model is used to define the mechanical behavior of the wearing layer, and the elastic model is used to define the mechanical behavior of the asphalt surface layer, base layer, and roadbed. A viscoelastic artificial boundary unit is defined at the boundary of the pavement structure, and a repeated load is applied on the top. The load action position is set to a 2cm×2cm grid size, and gradually transitions to a 5cm×5cm grid size at the boundary of the pavement structure.

6. The finite element modeling method for asphalt wearing layer based on viscoelastic-plastic constitutive relationship according to any one of claims 1 to 5, characterized in that: In step S2, the specimen tube and the flat pressure head are placed in an oven above 100°C for heating; the inner wall and bottom surface of the specimen tube are covered with 2-3 layers of aluminum foil, and after the asphalt mixture is loaded, the upper surface is covered with aluminum foil again; during the subsequent re-pressing process, the mid-term temperature of the asphalt mixture is controlled to 160±20°C.

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