“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International Symposium 181behaviour of a lined tunnel by the FEM. Later, Zienkiewicz [10] provided athorough review of finite element solutions to the time dependent materials. Heindicated that time dependent problems can be solved efficiently using a step-bystepapproach. To perform the computation, stress is assumed to be constant in asmall time interval. Strains can be evaluated and corrected at the end of the timeinterval. Step-by-step, strains in the whole time domain are then determined.Problems of utilizing the viscoplastic approach in the performance assessment offlexible pavements have been detailed by Barksdale [11]. He pointed out that oneof the key problems for viscous analysis of asphalt mixtures is the proper choice ofparameters required by the models. Goacolou [12] suggested that the viscoplasticstrain rate of asphalt mixtures can be directly related to the stress by a specialmatrix which is equal to the classical stiffness matrix multiplied by the threefunctions of temperature, loading cycle and the characteristics of stress nonlinearity.Based on experiments, Bonnier [3] proposed that strains of asphaltmixtures be resolved into viscoelastic and viscoplastic components. Kelvin-Woigtelements were used in the simulation of viscoelasticity while the general flow rulewas employed to model viscoplasticity.In this paper, mechanical models of asphalt mixtures are extended from onedimension to multi-dimensions on the basis of Perzyna’s theory of the viscoplasticflow rule [13]. A computer program of FEM denoted RAM (Rutting in AsphaltMixtures) is implemented and verified with respect to experimental data andtheoretical analyses. Using it in the pavement performance evaluation,development of permanent deformations within the surface layer of the road issimulated.2. MECHANICAL MODELS OF ASPHALT MIXTURESCreep and recovery tests are widely used in the determination of viscousparameters of asphalt mixtures. Sides et al. [7] suggested that recordeddeformations from compressive creep and recovery tests can be divided intoelastic, plastic, viscoelastic and viscoplastic components, according to whether thecomponents are time dependent and recoverable during unloading. Typical straintimerelationships during one loading cycle are illustrated in Figure 1, where ε e ,ε p , ε ve and ε vp denote the four components stated above. Due to the uncertaintyof loading magnitude, it is difficult to quantify stress and strain relationships duringthe period before the load reaches the designed value. Therefore, it is decided thatthe plastic component is not considered separately but is treated as a part of theviscoplastic component. In a uniaxial context, the constitutive models of asphaltmixtures during the Nth creep period can then be expressed as