## 1 Introduction  
The production and construction of road pavements need a substantial amount of energy and non-renewable materials. Therefore, the use of recycled materials and/or by-products seems to be necessary to create a more sustainable future for asphalt mixtures. The recycled materials and by-products that come from construction and demolition waste or urban and industrial waste can be introduced in asphalt mixes as recycled aggregates (e.g., RAP, steel slag, ceramics) instead of only using mineral aggregates [1]; on the other hand, waste polymers and oils can be used at the binder level as additives or modifiers of bitumen. Since the binder has a significant effect on asphalt mixture performances, the modification of bituminous binders has become the mainstream of research in recent decades [2]. Practical experiences and research have shown that rubber from end-of-life tires (ELTs) may be successfully used as bitumen modifiers to improve the binder response over a wide range of temperatures [3]. Without neglecting the several parameters that influence the physico-chemical properties of modified binders such as type, quantity, and characteristics of constituent materials, some studies have highlighted the feasible replacement for styrene-butadiene-styrene (SBS) polymers with recycled rubber [4, 5]. The rubberized binder shows good resistance to permanent deformations that turns into a high rutting resistance, which has been evaluated by the use of dynamic shear rheometer (DSR) device [4; 6]. Although, the SBS modified binder has the best resistance to crack, the binder that contains rubber shows the best anti-fatigue response [4]. In addition, based on rheological data, both virgin and waste polymers can decrease the brittleness of modified binders at intermediate temperature, and reduce the resulting stiffness at low temperatures [7]. However, the use of rubber has a disadvantageous aspect which is the overall increase in binder viscosity. This feature is important for pumpability and workability of modified binder [8]. The new candidates to improve low temperature properties and reduce the viscosity of the rubberized binders are oils that can have various origins (i.e., petroleum or bio-based oils, waste or refined used oils) [9]. Previous studies have highlighted the mitigation effect of oil when added to a modified binder regardless of its nature [10; 11; 12]. The oil modification alters the rheological and thermal behavior of bitumen, which has been observed through dynamic shear rheometer (DSR) and bending beam rheometer (BBR) analysis [9]. The introduction of oil leads to a decrease in the stiffness of binders, sometimes with adverse effects at high service temperature if overdosed. In detail, the study of [13] regarding the use of re-refined engine oil bottom (REOB) revealed that a limited concentration of the oil unaffected the thermal cracking performance of binders at low temperature and their fatigue cracking resistance at intermediate temperature. However, by increasing the concentration of REOB up to 15%, the binder strength and strain tolerance at intermediate temperature could be significantly influenced. Moreover, a large amount of oil may jeopardize the thermal cracking performance of binders [13]. Another study observed that blending standard bitumen with REOB at a rate of 9% did not compromise asphalt mixture stiffness and ageing [14]. On the other hand, a non-similar ageing susceptibility of fluxed and standard bitumens has been demonstrated, and the different binder responses were attributed to the composition of the various oils [9]. Therefore, the influence of oil has to be investigated deeply to minimize the related risks considering the maximum level that can be used and the variability of oil residues. Both wastes, ELTs and REOB, are engineering materials that represent a resource for further civil engineering applications.