## 2 Materials, Test Methods and Analysis Methods  
In this study, one soft binder PG 58-28 was used for blending with RAP mortars. The rheological properties are shown in Table 1. In addition, six RAP types including 2 high-stiffness RAPs, 2 medium-stiffness RAPs and 2 low-stiffness RAPs which were denoted as A through F were selected to yield the modified asphalt mortars. The extracted aged binders from six RAPs were tested in BBR first and categorized as high-, medium- and low-stiffness RAPs. These values were based on the stiffness values of these extracted aged binders. These RAP materials were initially sieved to a size which passed through a #50 (0.3-mm) sieve and was retained on a #100 (0.15-mm) sieve, and then were mixed with base binders at various aged states accordingly. The aged binder contents of the total binder in these RAP materials were obtained by using an ignition oven to burn all the asphalt for each RAP source. These aged binder contents of the total binder in the RAP mortar are 6.07%, 7.10%, 6.50%, 5.86%, 5.25%, and 8.3% for RAP sourcesA-F, respectively. These aged binder percentages were defined the ratio of burned aged binder to the total RAP before burning (in mass). It should be noted that the tested samples were produced with pure binder (PG 58-22 binder) and fine RAP mortar (filler and aged binder) in this study. In this research study, the base binders (virgin, rolling thin film oven (RTFO), and pressure-aged vessel (PAV)) blended with various sieved RAPs were used to produce RAP mortars, which were employed to fabricate the BBR beams. The trial and error procedures were performed to obtain the proper percentage of RAP (in terms of aged binder percentage). A percentage over 15% of aged binders was very stiff and could not be poured at a high temperature of over 165 \({}^{\circ}\)C. Therefore, in this study, a percentage of up to 15% aged binder (i.e., sieved RAP including 15% aged binder) was used to produce the modified mortar. The value of 15% was the ratio of the aged binder from RAP to the total binders (aged binder with pure soft binder). In addition, two more concentrations (5% and 10%) were utilized to help explore the performance characteristics of these mortars in this study. The BBR test generally provides a low temperature measure of the stiffness and relaxation properties of an asphalt binder. The obtained results are typically used to provide an indication of an asphalt binder's ability to resist low temperature cracking. The creep stiffness of asphalt binder from the BBR test is usually as a function of time, which is a measure of the thermal stresses in the asphalt binder resulting from thermal contraction. A higher creep stiffness value indicates higher thermal stresses. Originally, the crucial values included creep stiffness values at 60 sand the slope of the master curve at 60 s, commonly defined the \"m-value\" in Superpave system. In this study, three test temperatures of \(-18\)\({}^{\circ}\)C, \(-12\)\({}^{\circ}\)C, and \(-6\)\({}^{\circ}\)C were utilized to test the stiffness/deflection values of various RAP mortars in terms of soft binder aging states. These stiffness values and m-values were used to determine the minimum low temperatures of these asphalt RAP mortars. The virgin binder PG 58-28 was blended with RAP mortars concluding three aged binders (5%, 10% and 15%) from six RAP sources (A-F). The fabricated BBR samples were tested at three temperatures (\(-6\)\({}^{\circ}\)C, \(-12\)\({}^{\circ}\)C and \(-18\)\({}^{\circ}\)C). The Superpave criteria for characterizing low temperature cracking of an asphalt binder are based on the definition of a critical cracking temperature, which is the maximum temperature below which cracking occurs as a result of a single cooling cycle. Therefore, cracking would happen when an asphalt binder reached a critical stiffness value. This critical temperature is typically defined the limiting stiffness temperature. The Superpave binder specification uses BBR to measure the stiffness of asphalt binder at specified temperatures.