## 5 Restoring Original Low-Temperature Performance to Aged Asphalt Pavements  
Oxidative aging leads to an increase in stiffness, loss of ductility and cohesion of binders, and warmer embrittlement temperatures, see Table 1 and Figure 8. As a result, oxidative aging lowers the resistance to fracture of oxidized mixtures as compared to their virgin state [37; 46; 47; 48]. To restore the crack-resistant state of oxidized asphalt concrete pavements, measures such as pavement surface milling and/or the application of rejuvenators are taken. Asphalt rejuvenators are asphalt additives and modifiers that are used to revitalize, provide sealing, and restore the physical and chemical properties of the aged asphalt concrete [49; 50; 51]. Rejuvenators address the issue of oxidative hardening by softening the aged asphalt binder through restoration of the asphaltenes to maltenes ratio [6]. After applying a thin layer of rejuvenator over the top surface of pavement, the rejuvenator penetrates the asphalt concrete using the pore and tortuosity structure via gravity and capillary action, and diffuses through the asphalt concrete to chemically react with the asphalt binder. The rejuvenator/binder reaction restores the binder's material properties to its original state, i.e., the material properties of the virgin material. As the asphalt binder is softened, it also increases its adhesive properties and reduces the susceptibility of the asphalt pavement to thermal cracking. As described by [PERSON] [49], with the exception of visual inspection, there is no standardized method to evaluate the performance of rejuvenators when applied in the field. Currently, the ability of rejuvenators to improve pavements' durability is typically evaluated by (1) estimating the penetration in samples at 25 \({}^{\circ}\)C using asphalt binder extracted from untreated and treated cores, (2) comparing the viscosity at 60 \({}^{\circ}\)C of asphalt binder samples extracted from untreated and treated cores, and (3) comparing the percentage of aggregate loss when untreated and treated samples are subjected to a pellet abrasion test. Mainly because these tests are cumbersome and time consuming, they are not often used. Here, AE source location is used to characterize and evaluate the rejuvenators' ability to restore mixtures to their original low-temperature performance grading, i.e., their original crack resistant state. Because of the granular nature of asphalt concrete mixtures, the [PERSON]'s iterative source location technique [51; 52] was used to accurately locate the source of each event. The [PERSON]'s method is the application of the Gauss-Newton algorithm, which requires data from at least four AE sensors to build the following arrival time function of the \(i\)th sensor:  
\[f_{i}(x,y,z,t)=T_{s}+\frac{1}{v}\sqrt{\left(x_{i}-X_{s}\right)^{2}+\left(y_{i} -Y_{s}\right)^{2}+\left(z_{i}-Z_{s}\right)^{2}} \tag{3}\]  
in which \(\left(X_{s},\ Y_{s},\ Z_{s}\right)\) represent the spatial coordinates of the source, \(\left(x_{i},\ y_{i},\ z_{i}\right)\) represent the coordinates of the ith sensor, \(v\) is the known wave velocity, and \(T_{s}\) and \(t_{i}\) are the unknown source event occurring time and the known receiving time by the \(i\)th sensor, respectively. Equation (3) can be expanded using Taylor series at a point \(\left(x_{0},y_{0},z_{0}\right)\), near the actual source, resulting in Equation (4):  
\[f_{i}(x,y,z,t)=f_{i}(x_{0},y_{0},z_{0},t_{0})+\epsilon_{i} \tag{4}\]  
in which \(\epsilon_{i}\), the residual term, a.k.a. the correction vector, is the difference between the calculated arrival time and the observed arrival time with respect to the \(i\)-th sensor. It can be calculated using the first order derivatives of the arrival time function. By going through several iterations of Equation (5), the [PERSON]'s method tries to minimize the correction vector.