# Determining the Safety Level of State Roads: An Italian Case Study
## 5 Case Study
### Preliminary Activity--Predictive Method
#### 5.2.2 Crash Modification Factors--\(Cmf_{s}\)  
As the proposed procedure involves the adoption of the HSM, it is necessary to consider the 'base' conditions defined by the HSM. The 'base' conditions represent some specific geometric-functional characteristics according to which the HSM model has been developed. The \(CMF_{s}\) are then introduced to adapt the specific site conditions to the 'base' conditions. In fact, \(CMF_{s}\) are multiplication factors that can assume values greater than one if the specific site conditions are worse than the 'base' conditions; conversely, the \(CMF\) value is less than one if the specific site conditions are better than the 'base' conditions. Table 2 summarizes the \(CMF_{s}\) 'base' conditions and the relative values computed for the investigated segments. It should be noted that the highest average \(CMF\) value is reported for horizontal curvature, with an extremely high maximum value. This means that, on average, Italian roads are characterized by small curve radii, leading to an increase in the predicted number of crashes. In addition, as expected, the \(CMF_{s}\) values for driveway density and roadside hazard rating are equal to one since the actual geometric conditions were unknown and the 'base' ones were assumed. Similarly, for lane width, a constant value slightly lower than the 'base' condition was assumed, so there is a constant \(CMF\) value slightly greater than one. Finally, for shoulder width and type, the average \(CMF\) value is greater than one, meaning that on average, Italian road conditions are more restricted than US roads. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Unit** & **Average** & **Std Deviation** & **Min** & **Max** \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} _AADT_\({}^{1}\) \\ Length \\ \end{tabular} } & \multirow{2}{*}{[vehicles/day]} & \multirow{2}{*}{14,885} & \multirow{2}{*}{6526} & \multirow{2}{*}{4919} & \multirow{2}{*}{31,979} \\  & & & & & & \\ \cline{1-1}  & & & & & & \\ \cline{1-1}  & & & & & & \\ \hline \multirow{8}{*}{
\begin{tabular}{c} _CMF\({}_{1}\)_ \\ _CMF\({}_{2}\)_ \\ _CMF\({}_{3}\)_ \\ _CMF\({}_{4}\)_ \\ _CMF\({}_{5}\)_ \\ _CMF\({}_{6}\)_ \\ \end{tabular} } & \multirow{2}{*}{[m]} & \multirow{2}{*}{399} & \multirow{2}{*}{259} & \multirow{2}{*}{24} & \multirow{2}{*}{948} \\  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary statistics of the geometric-functional characteristic and traffic volume data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**CMF**} & **CMF Description** & \multicolumn{2}{c}{**‘Base’ Conditions**} & \multicolumn{4}{c}{\(CMF_{s}\) for Investigated Segments \({}^{1}\)**} \\ \cline{3-8}  & & & **Average** & **Std Deviation** & **Min** & **Max** \\ \hline \multirow{2}{*}{
\begin{tabular}{c} \(CMF_{1}\)_ \\ _CMF\({}_{2}\)_ \\ _CMF\({}_{3}\)_ \\ _CMF\({}_{5}\)_ \\ _CMF\({}_{6}\)_ \\ \end{tabular} } & Lane width & 12 feet & 1.03 & 0.00 & 1.03 & 1.03 \\  & & 6 feet & 1.18 & 0.05 & 1.15 & 1.26 \\  & & \multicolumn{1}{c}{} & \multirow{2}{*}{None (\(R=\infty\))} & \multirow{2}{*}{1.74} & \multirow{2}{*}{1.91} & \multirow{2}{*}{1.00} & \multirow{2}{*}{27.08} \\  & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(CMF_{s}\) description, ‘base’ conditions (according to HSM [6]), and \(CMF_{s}\) values for the investigated segments. 2.3 Safety Performance Functions (\(SPF_{s}\)) and Non-Calibrated Predicted Crashes (\(N_{pred,n.c. }\))  
Before performing the model calibration, it is necessary to select and employ one or more \(SPF_{s}\) to calculate the number of predicted crashes in the 'base' conditions (\(N_{SPF}\)). This number of crashes only depends on the \(AADT\) and the segment length (\(L\)), as shown in Equation (2). Then, to account for the actual geometric-functional characteristics of each site, the \(CMF_{s}\) are applied, and the number of non-calibrated predicted crashes is obtained by Equation (3).