## 1 Introduction  
Noise is an important environmental issue affecting a large part of the European population. Prolonged exposition to noise may affect health [1, 2, 3, 4, 5, 6, 7] or cause annoyance [8, 9, 10] and sleep disturbances [11]. Among different noise sources, road noise is one of the most impactful. In Europe, the Environmental Noise Directive (END) [12] prescribes the periodical noise mapping of main road infrastructures to monitor citizen's exposure to noise, while the member states themselves have enacted laws to set noise emission limits for infrastructures. Thus, road noise emission reduction is an important research topic. The sound emitted from the vehicles come from the following three different sources: engine and mechanical noise; aerodynamic noise; and rolling noise, on which this work focused. Indeed, rolling noise is the most important for speeds over 40 km/h concerning lightweight vehicles and for speeds over 60 km/h concerning trucks and other heavy vehicles [13]. Rolling noise is generated by the interaction between the tire and the road pavement, and it is affected by several noise generation, amplification, and modification mechanisms. In particular, the pavement characteristics are the most interesting because they can be defined in the design phase by technicians, while tire properties vary from vehicle to vehicle, leading to the average behavior. For this, the European Commission recently issued a regulation setting the minimum requirement in terms of noise for road paving within public procurement [14]. So an understanding of the parameters involved in rolling noise is crucial. Over the years, those relationships have been investigated; however, a complete and comprehensive understanding of all the involved parameters, especially with regard to pavement stiffness, is yet to be achieved. Dynamic stiffness (DS) is an important parameter for road pavement resistance to stress, but it is also correlated with rolling noise [15]. The stiffness of a material is a measure of its resistance to elastic deformation and is defined as the ratio of the applied force to the resulting displacement. Considering a sample with surface \(\Sigma\) and thickness \(l\), the stiffness \(s\) can be defined as follows:  
\[s\ =\ \frac{F}{\Delta l}\left[\mathrm{N/m}\right] \tag{1}\]  
where \(\Delta l\) is the thickness variation produced by the force \(F\). The stiffness is also linked to the elastic modulus so that the following stands:  
\[s\ =\ \frac{E\Sigma}{l}\left[\mathrm{N/m}\right] \tag{2}\]  
where \(E\) is the elastic or Young modulus, defined as the ratio between stress \(\sigma\) and axial strain \(\varepsilon\):  
\[E\ =\ \frac{\sigma}{\varepsilon}=\frac{F}{\Sigma}\ \frac{l}{\Delta l}\left[ \mathrm{N/m^{2}}\right] \tag{3}\]  
Stiffness influences impact noise generation mechanisms and the transmission of vibrations between the road surface and the tire [16]. In the last two decades, several scientific and independent research projects have reported evidence that lower DS can reduce TRN [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. A very similar quantity to DS is the mechanical impedance (MI), defined as the ratio between force and velocity. MI is correlated with the elasticity of the pavement and its energy dissipation capability, and it was seen that it has an effect on noise emission between 600 and 1600 Hz [26; 27]. Regardless of the number of works reporting the effect of DS and MI on TRN, all those results are not yet supported by a universally accepted and validated theoretical model. To validate a DS-TRN model, a large amount of reliable pavement DS measurements is needed, but at the moment, this is limited. The reasons are mainly the absence of a standardized methodology and the technical difficulties related to the measurement itself. The pavement stiffness measures can be classified into static or dynamic stiffness measurements.