Energy dissipation and the deformation resistance of bituminous mixtures

Abstract

A B S T R A C T R i~ S U M I ~The use of energy dissipation has been extended for assessing the resistance to permanent deformation of bituminous mixtures. The method is found beneficial for accurately determining the end of the linear region from the curves of permanent strain versus number of loading cycles, where the strain rate is constant. An analysis procedure based upon a combined technique of strain rate and energy dissipation method is presented. BACKGROUNDDuring the deformation of a viscoelastic material, part of the total energy required to perform the work is dissipated through viscous losses, with the remainder of the deformational energy being stored elastically. Tschoegl [1] states that "the rate of absorbed energy per unit volume of a viscoelastic material during deformation is equal to the stress power, i.e. the rate at which the work is performed" (see equation (1)):where dW/dt is the rate of absorbed energy per unit volume, o(t) is the applied stress as a function of loading time t, and dg/dt is the strain rate. The total work of deformation, which is the mechanical energy absorbed per unit volume of material in the deformation up to time t, can be formulated as:where W(t) is the total work of deformation and u is the number of load applications as a function of the loading time t. The total energy, W(t), is the combination of both the stored (elastic) energy, We(t ) , and the dissipated energy, Wa(t ). How much of the total energy can be stored and how much can be dissipated depend on the type of deformation and on the properties of the material. W(t) = We(t ) + Wd(t ) Differentiation of the above equation results in:dW _ dWe dWdThe rate at which energy is absorbed by the material during the deformation at time t equals the sum of the rates at which energy is stored and dissipated.In Fig. 1, a load is applied at O and reaches its peak load value at A; the load is maintained until B and then is released to allow the corresponding strain to recover from the deformation. Eventually, if there is no permanent deformation, the strain will return to its original position O (plot I), or otherwise it goes to O'(plot II). In the case of reversible deformation (plot I), the energy stored during the deformation is completely released during the recovery. The dissipated energy is the area within the hysteretic loop (OAB), and the storage (ehstic) energy is the area below the recovery curve (OBC). However, the energy stored in the deformation may not be completely released during the recovery, and hence a permanent (plastic) deformation occurs (plot II). In this case, the dissipated energy is the sum of the areas within the hysteretic energy (O'A'B) and the plastic energy sections (OAA'O'), and the storage (elastic) energy is the 1359-5997/99 9 RILEM 2 1 8

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