“Computational Civil Engineering - "Intersections" International Journal

188 M. Balcu, Şt.M. Lazărcomputation. The application of viscoplastic parameters, however, is not sostraightforward. They are associated with the determination of the fluidityparameter γ in Eq. (9). To evaluate γ , derivative ε of Eq. (3) with respect toloading time t, we havewhere ( N ) N b − ( N − ) bvpβ −1( N ) ⋅σ ω ⋅ β ⋅t& ε = B ⋅ f(38)vpf = 1 . The average value of ε&vp during loading period t canbe approximated by1 −tωβ −1ω β 1( N ) ⋅σ⋅ β ⋅τdτ= B ⋅ f ( N ) ⋅σ⋅ t& ε vp = B ⋅ ft ∫(39)0Compare the above equation with Eq. (3) and the fluidity parameter can then beapproximated byβ −1( N ) ⋅ tγ = B ⋅ f(40)Three points are noted for Eq. (40). Firstly, the fluidity parameter of an asphaltmixture is an average value over the loading period t. This means that γ in theiteration is a variable which changes with the increase of loading time t. Thischaracteristic is different from that of many other materials for which constantfluidity parameters can be employed. Secondly, the fluidity parameter is associatedwith parameter β . If β ≥1. 0 , it may indicate the steady plastic flow or collapse ofthe sample which Bonnier [3] described as the second or the tertiary creep. Forβ