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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-HRT-08-073
Date: September 2009

Development of A Multiaxial Viscoelastoplastic Continuum Damage Model for Asphalt Mixtures

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Chapter 8. Conclusions and Future Work

8.1. Conclusions

The approach adopted in this research to characterize asphalt concrete over a wide range of temperatures and loading rates encountered in the field divided the problem into two components: (1) characterizing the viscoelastic response and (2) characterizing the viscoplastic response. The VECD model described the time-dependent behavior of asphalt concrete with growing microcrack damage. The irrecoverable (whether time-dependent or independent) strain was described by the VP model. These two models were integrated based on the strain decomposition principle to form the VEPCD model. This model was found to be applicable to the tension mode and, in principle, to the compression mode of loading.

Through the model characterization procedures, it was also found that the dynamic modulus, if it was determined according to strict guidelines so that the linear limits of the material were not exceeded, was not dependent upon loading direction (tension compression or compression only). Further, it was found that this loading direction independence held under different confined stress states. From these confined dynamic modulus tests, a state-dependent model similar to the one used for unbound paving materials was developed and characterized.

The viscoelastic damage characteristics were found to differ in the compression and tension loading modes, with the compression mode showing the more favorable results (i.e., less reduction in the pseudo stiffness, C, for the same amount of increase in the damage parameter, S). These results were also consistent with the hypotheses that the damage parameter, S, was related to cracking density or crack volume and that the primary direction of this cracking was perpendicular to the tensile loading direction or parallel to the compressive loading direction. A simple, empirically-based viscoplastic model was found to be sufficient for explaining the tensile behavior of asphalt concrete, but it did not explain the compressive behavior.

For the compressive behavior, a rate-dependent softening mechanism, which operated during unloading, was found to be a significant factor that affected the viscoplastic characteristics of asphalt concrete. Several existing viscoplastic models that included flow rules and a yield criterion had been evaluated, but they were found to be insufficient for describing this softening behavior. To account for this characteristic behavior, the rate-dependent, hardening-softening function was suggested using Perzyna's flow rule. The relaxation modulus determined from the linear viscoelastic characterization was utilized in this process. It was shown that the developed model could account for the effects of rest periods and loading sequence on viscoplastic strain development.

In light of practical concerns related to the use of constant rate tests in the AMPT and due to the complexities of performing true time-dependent analysis of cyclic fatigue tests, a simplified VECD model was presented. This model utilized results from fatigue tests performed at nominal levels that were possible with the AMPT equipment, as well as the VECD model that specialized in such loading so as to arrive at a simple formulation to characterize the model. This formulation was found to generally agree with the results from the constant rate tests, particularly under conditions of minimal viscoplastic strain.

Another major finding in this research was the verification of the time-temperature superposition principle with growing damage, both in compression and tension, in a confined stress state. This principle was proven valid using constant rate tests under various temperatures and strain rates with an applied confining stress. Therefore, the response of a mixture with growing damage at one temperature could be predicted by shifting its response at another temperature using the time-temperature shift factor determined from the LVE complex modulus tests.

The major contribution of the time-temperature superposition principle and the damage characteristic curve was the significant reduction in testing requirements. The model allowed the prediction of the material's behavior at any temperature from a test result obtained from a single temperature and the time-temperature shift factors obtained from temperature sweep complex modulus tests. The experimental results from the previous FHWA project (DTFH61-03-H-00116) and this project verified that the time-temperature superposition principle with growing damage was valid in both tension and compression, regardless of the confined state (i.e., unconfined or confined).

To realize the full potential of the VEPCD material model for predicting pavement performance, a robust FEP++ was developed to account for the effects of loading and boundary conditions. FEP++ was designed using a top-down, object-oriented approach with great care so that further enhancements could be made by the research team in an efficient manner. Furthermore, special elements and implementation techniques were employed to increase the computational efficiency. The 2D version of the resulting software has the ability to predict stresses, strains, and damage of the pavement under repeated traffic loading. FEP++ was also extended to 3D stress analysis with the ultimate goal of 3D damage modeling of moving traffic loads. All these capabilities were made accessible to the user through carefully designed and powerful graphical pre and postprocessors. As part of the ongoing HMA-PRS project sponsored by the FHWA (DTFH61-08-H-00005), FEP++ is now being molded into an integrated software tool that can be used for robust pavement performance predictions.

To illustrate the capabilities of FEP++ and its preprocessor, a full 3D finite-element analysis was carried out. The effects of temperature, material, and wheel speed were studied and found to be in accordance with the expected results. Namely, the pavement showed an increased viscous response with increased temperature and decreased speed. The simulations also showed lower strains with higher temperatures, increased wheel speed, and a stiffer asphalt concrete material.

8.2. Future Work

The following items are recommended for future research:

  • Modeling multiaxial VEPCD: Sensitivity analyses considering true in-field conditions should be carried out for both tensile and compressive loading to determine the influence of simplifications to and the need for the complete multiaxial formulation. If complete multiaxial modeling does not substantially change the predicted performance of the asphalt concrete, then less testing is needed for accurate pavement performance modeling.
  • Further Simplifying VECD model development: Although constant rate tests are simple to perform, the capacity of the recently developed AMPT equipment limits the use of such tests. A simplified model further specialized for more moderate load amplitude cyclic tests and derived rigorously will expand the application of the VECD model for further routine testing and analysis.
  • Hardening in the MVECD compression model: A possible drawback to the current MVECD model for compression is the lack of a function to account for hardening due to aggregate interlock. It is known that such a function becomes important, especially at low confinement levels and high temperatures, but the implication of aggregate interlocking under more moderate conditions is unknown.
  • Yielding criteria in the VP compression model: In this research, the model parameters were determined for each specific confining pressure condition. Although these parameters are not sufficient to explain the general behavior of HMA pavements, which experience an almost uniform confining pressure for certain time periods, they are, nonetheless, reasonable for introducing a yield criterion that can account for the entire confining pressure.
  • Hardening-softening of the function in the VP compression model: Even though the current hardening-softening function reasonably accounts for the rate-dependent softening of HMA, some over and underpredictions were observed for certain stress histories. These observations may be explained by an inaccuracy in the hardening-softening function, and therefore, more research into the hardening-softening function is required.
  • Refining analysis program: Current VEPCD modeling is aided by a software package developed at NCSU. The program is currently in the development stage and is considered to be research-grade software. Usability, therefore, is somewhat limited. Refinement of this program into a complete black box package will greatly aid the implementation of VEPCD modeling at the industrial level.
  • Advancing material models with FEP++: Currently the 3D FEP++ code includes modules for linear elastic and linear viscoelastic materials. The MVECD model should be implemented along with other material models and functions. To model unbound paving materials accurately, a module should be added to include a nonlinear elastic material model. In addition, models that account for the effects of temperature and moisture gradients in pavement systems and the effects of aging of the HMA layer on pavement performance need to be incorporated into the FEP++. Additionally, anisotropy of the HMA and slip elements at the pavement-base interface should be included. The modular design of the 3D FEP++ allows for incorporation of new modules that pertain to advanced materials, more efficient solution techniques, and fast solvers with little or no change to the existing code.

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