## 5 Methods
### Crash Modification Factors  
CMFs  
The crash prediction for 'base' conditions should be adapted to real site conditions by applying Crash Modification Factors (CMFs). CMFs assume different values as follows:  
* \(CMF>1\), if site-specific conditions are worse than 'base' conditions;
* \(CMF=1\), if site-specific conditions are the same as 'base' conditions;
* \(CMF<1\), if site-specific conditions are better than 'base' conditions.  
'Base' conditions in terms of geometric-functional road characteristics are defined both for segments and intersections. Different CMFs are defined with the relative 'base' conditions and data availability, as detailed in Table 5.  
The CMF for each site is calculated whenever data are available according to HSM prescriptions [9]. When the mean CMF values are greater than 1, the conditions of the Italian roads are on average worse than the 'base' conditions of the US roads. In order to use the model to simulate future scenarios, the CMFs must be recalculated for the new traffic values and new geometric-functional characteristics. Average CMFs values for the existing road and the redesigned road are reported in Table 6. The most critical conditions for the existing road, in terms of geometric characteristics, were recorded for horizontal curvature and driveway density, which have the highest average CMFs values.  
\begin{table}
\begin{tabular}{c c} \hline
**Minor Road Importance** & \(\boldsymbol{AADT_{min}}\) \\ \hline High & 15\% of \(AADT_{maj}\) \\ Medium–High & 10\% of \(AADT_{maj}\) \\ Medium & 7.5\% of \(AADT_{maj}\) \\ Medium–Low & 5\% of \(AADT_{maj}\) \\ \hline \end{tabular}
\end{table}
Table 4: Assumption for minor road traffic at junctions.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Facility Type** & **Severity Level** & **SPF–Safety Performance Function** & \(N_{SPF}\)**[cashes/year]** \\ \hline \multirow{3}{*}{**Segments \({}^{\star}\)**} & **All** & \(N_{SPF}=AADT.L.365.10^{-6}.e^{(-0.312)}\) & 39.13 \\  & **KABC** & \(N_{SPF}=exp[-9.006+0.977\cdot\ln(AADT)+ln(L)]\) & 14.64 \\  & **KAB** & \(N_{SPF}=exp[-8.499+0.852\cdot\ln(AADT)+ln(L)]\) & 7.60 \\ \hline \multirow{6}{*}{**Segments \({}^{\star}\)**} & **All** & \(N_{SPF}=\exp[-9.86+0.79\cdot\ln\left(AADT_{maj}\right)+0.49\cdot\ln(AADT_{min})]\) & 66.39 \\  & **KABC** & \(N_{SPF}=\exp[-9.628+0.725\cdot\ln\left(AADT_{maj}\right)+0.312\cdot\ln(AADT_{ min})]\) & 14.08 \\  & **KAB** & \(N_{SPF}=\exp\left[-10.241+0.581\cdot\ln\left(AADT_{maj}\right)+0.468\cdot\ln(AADT _{min})\right]\) & 5.58 \\ \cline{2-4}  & **All** & \(N_{SPF}=\exp[-8.56+0.60\cdot\ln\left(AADT_{maj}\right)+0.61\cdot\ln(AADT_{ min})]\) & 4.08 \\  & **KABC** & \(N_{SPF}=\exp[-8.747+0.825\cdot\ln\left(AADT_{tot}\right)]\) & 0.40 \\  & **KAB** & \(N_{SPF}=\exp[-8.511+0.723\cdot\ln(AADT_{tot})]\) & 0.19 \\ \cline{2-4}  & **All** & \(N_{SPF}=\exp[-5.13+0.60\cdot\ln\left(AADT_{maj}\right)+0.20\cdot\ln(AADT_{ min})]\) & 4.81 \\  & **KABC** & \(N_{SPF}=\exp[-12.337+1.028\cdot\ln\left(AADT_{maj}\right)+0.231\cdot\ln(AADT_{ min})]\) & 0.21 \\  & **KAB** & \(N_{SPF}=\exp[-11.059+0.981\cdot\ln\left(AADT_{tot}\right)]\) & 0.13 \\ \hline \end{tabular} \({}^{\star}\) 278 homogeneous segments and 36 intersections (32 \(\times\) 3 ST, 1 \(\times\) 4 ST, 3 \(\times\) 4 SG).  
\end{table}
Table 3: Considered safety performance functions for different severity levels.  
The planned redesign, composed by the rehabilitated road and bypasses, shows safer characteristics in terms of horizontal curvature, shoulder type and width and roadside hazard rating. In fact, according to Table 6, the CMFs associated with these characteristics for the redesigned road are significantly reduced compared to the state of the art. It should also be noted that the bypasses are characterized by the absence of intersections and driveways.