# Long-Term Monitored Road Degradation Functions as a Tool to Increase Quality of Pavement Design
## 1 Introduction
### Related Research
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Country** & **Evaluation Function** & **Explanation of Function** \\ \hline \multicolumn{3}{c}{**Overview of Approaches for Rut Calculation**} \\ \hline \hline Austria & \(t=a\sqrt{N}\) & \(N\) is the number of loads equivalent to a standard axle (10 t), \(a\) is an empirically determined factor depending on the road structure. \\ \hline Finland & \(RD_{p}\) is predicted rut depth, \(RD_{m}\) is measured rut depth, \(AGE_{\textit{errn}}\) is the number of years from the last road  reinforcement to the year of measurement, \(AGE_{\textit{mp}}\) is number of years from measurement to year of  wheel path depth forecast \\ \hline Hungary & \(RUT=e^{a+b\times AGE}\) \(RUT=e^{a+b\times FORG}\) & \(AGE\) is age of the road abrasive layer, \(ROD_{m}\) is measured rut depth, \(AGE_{\textit{errn}}\) is the number of years from the last road  reinforcement to the year of measurement, \(AGE_{\textit{mp}}\) is number of years from measurement to year of  wheel path depth forecast \\ \hline Ireland & \(IR_{l}=\) \(IR_{l-1}+(a+b\times ESAL_{t}\times 0.41\times 10)\) & \(ESAL_{t}\) is number of passes of uniaxial design axles (80 kN), \(IR_{l}\) is value IRI in year \(t\), \(a\), \(b\) are calibration parameters \\ \hline HIDM 4 & \(\Delta RDM\) is the annual increment in the total average wheel  path depth in both wheel paths \(\Delta RDM=RDO+\Delta RDPD+\Delta RDWT\) is the annual increment due to structural  deformations, \(\Delta RDM=\Delta RDST+\Delta RDPD+\Delta RDWT\) is the annual increase due to plastic deformations, \(\Delta RDW\), \(for\)\(AGE\) \(>1\) & \(\Delta RDM\) is the annual increment in the total average wheel  path depth in both wheel paths \(\Delta RDM=RDO+\Delta RDPD+\Delta RDWT\) is the annual increment due to structural  deformations, \(\Delta RDM=\Delta RDST+\Delta RDPD+\Delta RDWT\) is the annual increase due to past and tear, \(AGE4\) is the number of years since the last road  reconstruction or construction \\ \hline \multicolumn{3}{c}{**Overview of Approaches for IRI Calculation**} \\ \hline Finland & \(IR_{l+1}=a+b\times IR_{l}\) \(IR_{l+1}\) \(a\), \(b\) are the parameters of the model according to the type of  road construction \\ \hline Hungary & \(IRI=e^{a+b\times AGE}\) \(IRI=e^{a+b\times FORG}\) \(RIO\) is number of repeated crossings of equivalent  passenger cars \(a\), \(b\) are constants \\ \hline Ireland & \(RD_{t}=a\times(0.41\times cumESAL_{t})^{b}\) \(RIO\) is transverse evenness in mm \(cumESAL_{t}\) is cumulative number of passes of uniaxial  design axles (80 kN) per year \(t\), \(a\), \(b\) are calibration parameters \\ \hline HIDM 4 & \(\Delta RI\) is incremental change of IRI \(K_{\textit{gr}}\) is calibration factor for the development of longitudinal  roughness, \(\Delta RI_{s}\) is contribution of the structural component of  roughness, \(\Delta RI_{c}\) is the contribution of cracks to inequalities, \(\Delta RI_{r}\) is the contribution of variations in transverse  inequalities to longitudinal  inequalities, \(\Delta RI_{l}\) is contribution of pressures to inequalities, \(\Delta RI_{e}\) is the contribution of the environment to inequalities \\ \hline Poland & \(IRI=IR_{0}.e^{b.003(t-t_{0})}\) \(IRI\) is predicted value IRI in year \(t\), \(IR_{0}\) is measured IRI in year \(t_{0}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of approaches for evaluating the quality of roads and their parameters [24,26].