“Computational Civil Engineering - "Intersections" International Journal

190 M. Balcu, Şt.M. LazărMaterialsAsphaltconcreteHotrolledasphaltTable 1. Parameters of asphalt mixtures for computationE A ×B ×h a(MPa) 10 3 10 3 w b b613 0.488 0.716 0.290 1.222 0.795 0.190 0.2201377 0.816 0.842 0.449 2.110 0.750 0.338 0.344To investigate the development of rutting, values of viscoplastic displacement atvarious loading cycle n, say, at n = 10 1 , 10 2 , 10 3 , 10 4 , 10 5 , ..., are computed first.u n and loading cycle n canUsing the obtained values, viscoplastic displacement ( ) vpbe related by a regression equation. Now, replace integer n by a real x.Accumulation of viscoplastic deformations U(N) can therefore be viewed as apseudo-continuous function expressed asUN∑N( N ) = u( n) ≈ u( x)n=1Plot U(N) vs. N, the accumulation of viscoplastic deformations after the Nth wheelloading is determined. Further on, rutting after the Nth wheel loading can beestimated. The ( n) ~ n relationships can be determined using the least squareuvptechnique. Replaceu ( n) vpby ( x) vpvp∫0vpdx(41)u and substitute it into Eq. (41), and theaccumulation of viscoplastic deformations are evaluated. A plot at different loadingcycles allows one to see the development of permanent deformations along thepavement surface. With it, rutting and loading application relationships might beobtained. As expected, rutting under a specific length of loading time is a powerfunction with regard to the loading applications. This result is generally inagreement with the phenomena observed in practice, see, e.g. Thompson andNauman [14].7. CONCLUSIONConstitutive models of viscous behaviour of asphalt mixtures under repeated loadsare incorporated in a finite element code, RAM, using the general approach ofvisco-elastoplastic analysis. One of the main attractions of this work is the fact thatthe response of the material to the loads can be simulated during the whole loadingperiod and the development of deformations with time is hence accounted for. Acomputer program, RAM (Rutting in Asphalt Mixtures), is under completion todetermine the plastic deformation under cyclic loading. To date, an agreementbetween the model prediction and laboratory tests are under inspection.