A generalized Drucker–Prager viscoplastic yield surface model for asphalt concrete

Abstract

A Generalized Drucker-Prager (GD-P) viscoplastic yield surface model was developed and validated for asphalt concrete. The GD-P model was formulated based on fabric tensor modified stresses to consider the material inherent anisotropy. A smooth and convex octahedral yield surface function was developed in the GD-P model to characterize the full range of the internal friction angles from 0 to 90 degrees. In contrast, the existing Extended Drucker-Prager (ED-P) was demonstrated to be applicable only for a material that has an internal friction angle less than 22 degrees.Laboratory tests were performed to evaluate the anisotropic effect and to validate the GD-P model. Results indicated that 1) the yield stresses of an isotropic yield surface model are greater in compression and less in extension than that of an anisotropic model, which can result in an under-prediction of the viscoplastic deformation; and 2) the yield stresses predicted by the GD-P model matched well with the experimental results of the octahedral shear strength tests at different normal and confining stresses. By contrast, the ED-P model over-predicted the octahedral yield stresses, which can lead to an under-prediction of the permanent deformation. In summary, the rutting depth of an asphalt pavement would be underestimated without considering anisotropy and convexity of the yield surface for asphalt concrete. The proposed GD-P model was demonstrated to be capable of overcoming these limitations of the existing yield surface models for the asphalt concrete.

Modeling Stress-Dependent Anisotropic Elastoplastic Unbound Granular Base in Flexible Pavements

“…A Generalized Drucker-Prager (GD-P) yield surface model was developed by the authors to allow a smooth and convex yield surface when frictional angle varies from 0 to 90 degrees for granular materials such as asphalt, aggregate base, sand or soil materials (14). This GD-P model can remove the inherent limitations of the existing models, e.g., the non-smoothness for the Mohr-Coulomb yield surface or the non-convexity for the extended Drucker-Prager yield surface when the frictional angle is greater than 22 degrees.…”

“…Several studies have indicated that β < α is valid for geo-materials such as soils, sands, and asphalt mixtures ( 15, 16 ). Here β is derived to be a function of anisotropy ( 14 ):…”

Viscoelasticplastic–Fracture Modeling of Asphalt Mixtures Under Monotonic and Repeated Loads

“…However, most used a yield surface like Mohr-Coulomb, Drucker-Prager (D-P) or extended D-P models which have some significant limitations such as non-smooth or non-convex surfaces when internal frictional angle is greater than 22°. To remove these limitations, the author has developed a generalized Drucker-Prager (GD-P) yield surface model as shown in Equations 8 to 12 (15,25), allowing a smooth and convex surface for frictional angles varying from zero to 90°.…”

“…However, the coupling of deformation and cracking at a high temperature has not appropriately modelled by the existing models especially under a compressive load. This is due to that 1) yield surface was not used, e.g., VEPCD uses Schapery's VP theory which implicitly assumes that plasticity occurs even at a very tiny load, which is not accurate for asphalt mixtures; or yield surface was used inappropriately, e.g., an asphalt mixture normally has a friction angle larger than 22, however the CDM models employ the extended Drucker-Prager model which is effectively applicable only for a material with a friction angle less than 22 (15); 2) the initiation of damage/cracking was not well defined, e.g., both assume that damage is initiated from the beginning of the load, which may be a reasonable assumption in tension and at low/intermediate temperatures but not in compression or at high temperatures. The cracks don't grow in compression until the material has been hardened due to the accumulation of the VP deformation to a level that a viscoelastic Griffith energy criterion is satisfied (4); and 3) the FE simulations for both models require significant laboratory tests to calibrate model parameters and also need extensive experiences in programming material subroutines.…”

“…• Yield surface was not used (e.g., viscoelastic-plastic continuum damage uses Schapery's viscoplastic theory, which implicitly assumes that plasticity occurs even at a very tiny load, which is not accurate for asphalt mixtures), or yield surface was used inappropriately [e.g., an asphalt mixture normally has a friction angle larger than 22°; however, the CDM models use the extended Drucker-Prager model, which is effectively applicable only for a material with a friction angle less than 22° (15)].…”