Advances in Permanent Deformation Modeling of Asphalt Concrete—A Review
Abstract
:1. Introduction
2. Objective and Scope
3. Permanent Deformation Prediction
3.1. Analytical Models
3.2. Calibration Tests
Model (Equation) | Variables | Description | Reference | Calibration Test |
---|---|---|---|---|
a, b | Accurate for secondary stages, small stress/strain deformation | Creep, creep-recovery | ||
Where, | A, B, C, D | Most widely used analytical model for permanent deformation in all three creep stages; the first part is a power function (for low stresses). and the second part is for high stresses (tertiary stage). (—maximum stress, – plastic failure threshold; , —axial and lateral stress, —stiffness) | Francken [40] | Repeated triaxial compression |
, | , S, m | Analytical Power Model based on dissipated energy rate; is a function of resilient modulus and applied stress | Khedr Safwan [41] | Multiple step dynamic test |
, β, | Widely used analytical model to fit all creep stages | Tseng and Lytton [42] | Triaxial creep-recovery test | |
,
, , | Analytical model for three creep stages, mainly developed for unbound materials (, —scale primary and tertiary strain; δ2, —rate parameters) | Wilshire and Evans [43] | Creep tests | |
, , | Mechanistic-empirical (MEPDG) Model —resilient strain, T—temperature | Triaxial creep-recovery test | ||
; ; | a, b, c, d, k | Three-stage rutting model (Modified Francken model) for accurate flow number identification | Zhou et al. [28] | Triaxial creep-recovery test |
A, B, C, D | Two phase, Linear exponent model (mainly for unbound granular materials) | Cerni et al. [44] | Triaxial creep-recovery test | |
A, B, C, α | Incremental model: mechanistic based as a function of viscoplastic hardening (H and α), loading time, deviatoric stress, and rest period (A, C contain the parameters related to initial behavior of permanent deformation) | Choi et al. [45] | Triaxial creep-recovery | |
, , , , , , A, B, C, | A mechanistic shift model based on the load time and stress–shift function (master curve). is atmospheric pressure, is reduced loading time, and is deviatoric stress | Choi et al. [46] | Triaxial creep-recovery | |
a, b, c | A three-stage model modified from Francken model | Fang et al. [4] | Wheel tracking, Uniaxial cyclic compression |
4. Permanent Deformation Damage Modeling
4.1. Stress–Strain Response
4.2. Constitutive Models
Analogical Models
4.3. Continuum Based Models
4.3.1. Damage Density
4.3.2. Viscoplasticity
4.4. Mechanistic Methods
4.4.1. Pavement Analysis Using the Nonlinear Damage Approach (PANDA)
- (1)
- First, the linear and nonlinear viscoelastic variables are obtained from dynamic modulus (for linear viscoelastic) and creep-recovery tests (nonlinear viscoelastic). The nonlinear viscoelastic strain is formulated using the well-known Schapery’s viscoelastic constitutive equation [68].
- (2)
- Secondly, the viscoelastic strain is deducted from the total strain to extract the viscoplastic strain from the same creep-recovery test data using the strain decomposition principle. Then, the classic Perzyna’s viscoplasticity [66] theory is adopted to predict the viscoplastic strain evolution. The Drucker–Prager yield surface function is often used [23,74].
- (3)
- The third foundation of the PANDA constitutive model is the viscodamage model [64] using the continuum damage mechanics (CDM) theory. The effective strain is used in effective configuration. The viscodamage model mainly predicts the permanent deformation in the tertiary creep.
4.4.2. Microstructural Based Models
4.4.3. Finite Element Simulation
5. Permanent Deformation and Fatigue Interaction Damage
6. Summary, Conclusions, Further Research
6.1. Summary
6.2. Conclusions
6.3. Further Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Physical Meaning | Theory/Domain | Calibration Test |
---|---|---|---|
Viscoelastic Model Parameters [68,82] | |||
Instantaneous creep compliance. Characterizes the instantaneous elastic part of the viscoelastic strain | Linear viscoelastic | Creep compliance or Dynamic Modulus | |
nth retardation time. A measure of the required time for the viscoelastic material to relax the induced stress | |||
nth coefficient of the Prony series associated with the nth retardation time kn. These parameters characterize the transient compliance of the material | |||
, , | Nonlinear viscoelastic parameters, where measures the reduction or the increase in the instantaneous compliance; defines the nonlinearity effects in the transient compliance; and is the nonlinear parameter accounting for the loading rate effects on the creep response | Schapery’s Nonlinear viscoelastic | Creep-recovery |
Viscoplastic Model Parameters [64,66,69] | |||
Viscoplastic fluidity parameter, such that is a measure of viscoplastic viscosity | Perzyna’s Viscoplastic (with Drucker–Prager yield criteria) | Creep, creep-recovery (creep part), constrain strain rate test | |
, , | Isotropic hardening parameters, where defines the initial yield strength; defines the saturated limit of the hardening function; and defines the hardening rate and controls the shape of the hardening function versus the effective viscoplastic strain () | ||
Viscoplastic rate sensitivity exponent and describes the nonlinear rate dependency of viscoplastic response | |||
, | Govern the pressure sensitivity of the yield surface and plastic potential functions. Related to the angle of friction in the asphalt concrete | ||
Model parameter distinguishing viscoplastic responses in extension and contraction modes of loading | |||
Visco-damage Model Parameters [64] | |||
Visco-damage fluidity parameter ( is a measure of damage viscosity) | CDM (Tertiary creep) | Creep tests | |
Stress dependency parameter. Defines the sensitivity of the damage evolution due to stress level | |||
The reference damage force obtained at a reference stress of a creep test | |||
Strain exponent parameter. Defines the sensitivity of the damage evolution due to strain level | |||
Model parameter distinguishing visco-damage responses in extension and contraction modes of loading | |||
Micro-damage healing model Parameters [83] | |||
Micro-damage healing fluidity parameter, such that is a measure of healing viscosity | CDM for healing | ||
, | Healing model parameters that describe the effect of the damage and healing histories on the healing evolution | ||
Temperature coupling terms parameters [64] | |||
, , | Temperature sensitivity model parameters for viscoplastic, viscodamage and microdamage healing, respectively | Time–temperature superposition | Dynamic Modulus, Creep compliance |
Reference temperature | |||
Hardening–relaxation Model Parameters [24,25] | |||
The hardening–relaxation fluidity parameter, such that 1/ is the hardening–relaxation retardation time controlling the rate of the hardening–relaxation | Creep-recovery (at different rest periods) | ||
, , | Hardening–relaxation rate-sensitivity parameters that describe the relaxation behavior of viscoplastic hardening due to recoverable potential during rest period | ||
Moisture damage Model Parameters [84] | |||
Adhesion or cohesion moisture damage parameter | CDM for moisture damage | Pull-off test | |
Parameter that describes the moisture damage history |
Advantages | Disadvantages |
---|---|
|
|
Loading Approach | ||||
---|---|---|---|---|
Mode | Load Configuration | Pulse Loading | Equivalent Loading | Moving Loading |
2D | Single wheel (plane strain) | √ | √ | √ |
Single wheel (axisymmetric) | √ | √ | √ | |
Single wheel (moving loading) | √ | |||
Multiple wheel (moving loading) | √ | |||
3D | Single wheel (rectangular) | √ | √ | √ |
Whole wheel path | √ | √ | ||
Single wheel (circular) | √ | √ | ||
Single wheel (moving) | √ | |||
Multiple wheel | √ |
Approach | ||||
---|---|---|---|---|
Properties, Theories, Methods | PANDA | Microstructure | Analogical | Empirical |
Continuum damage mechanics | √ | √ | - | - |
Viscoelastic | √ | - | √ | √ |
Viscoplasticity | √ | √ | √ | √ |
Micromechanics | † | √ | - | - |
Finite element simulation | √ | √ | √ | - |
Time–temperature superposition | √ | √ | √ | - |
Coupling (healing, moisture) | √ | √ | - | - |
Coupling fatigue–rutting damage | - | - | - | - |
Full pavement deformation model | √ | √ | - | - |
Hardening–relaxation mechanism | √ | √ | - | - |
Uniaxial and triaxial repeated load test | √ | √ | √ | √ |
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Alamnie, M.M.; Taddesse, E.; Hoff, I. Advances in Permanent Deformation Modeling of Asphalt Concrete—A Review. Materials 2022, 15, 3480. https://doi.org/10.3390/ma15103480
Alamnie MM, Taddesse E, Hoff I. Advances in Permanent Deformation Modeling of Asphalt Concrete—A Review. Materials. 2022; 15(10):3480. https://doi.org/10.3390/ma15103480
Chicago/Turabian StyleAlamnie, Mequanent Mulugeta, Ephrem Taddesse, and Inge Hoff. 2022. "Advances in Permanent Deformation Modeling of Asphalt Concrete—A Review" Materials 15, no. 10: 3480. https://doi.org/10.3390/ma15103480