# A Multiobjective Decision-Making Model for Risk-Based Maintenance Scheduling of Railway Earthworks
## 3 Multiobjective Decision-Making Model for Maintenance Planning
### Attributes  
#### 3.2.1 Safety-Change in Reliability Index Due to an Intervention  
In order to estimate the benefit of an intervention (maintenance activity), the difference in reliability index before and after the intervention was used. Utility theory can find the optimal balance between the benefit of increased reliability and incurred costs. The change in the reliability index due to the intervention is defined in Equation (12):  
\[\Delta\beta=\beta_{2}-\beta_{1} \tag{12}\]  
where: \(\beta_{1}\) and \(\beta_{2}\) are the reliability index before and after the intervention, respectively. In this paper, the reliability indices of all individual earthworks on the Irish Rail network were determined based on the approaches described in Section 3. [PERSON] and [PERSON] (2017) suggest that for earth slopes outside urban areas, a minimum target reliability index \(\beta_{\text{T}}=2.0\), corresponding to a probability of failure of 2.23%, is acceptable. Although this reliability index would classify the performance as poor in accordance with ([PERSON], 2018) USACE, it is consistent with conventional practice in geotechnical engineering (S \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Maintenance Levels** & **Description of Damage** & **Maintenance Option** & \begin{tabular}{c} **Maintenance Cost** \\ **(Unit Cost)** * \\ \end{tabular} & \begin{tabular}{c} **Downline/Duration** \\ **(days)** \\ \end{tabular} & \begin{tabular}{c} **Reduced Speed** \\ **(km/h)** \\ \end{tabular} & \begin{tabular}{c} **Failure** \\ **Mechanism** \\ \end{tabular} & \
\begin{tabular}{c} **Reliability** \\ **Index after** \\ \end{tabular} &
\begin{tabular}{c} **Expected Lifespan** \\ **(year)** \\ \end{tabular} \\ \hline
**Minimum** & \begin{tabular}{c} **Roleed drains** \\ **overwong vegetation** \\ \end{tabular} & \begin{tabular}{c} **Vegutation** \\ **GE000** **, 45/m** \\ \end{tabular} & 1 & 0 & Planar & 4 & 5 \\ \cline{2-10}  & \begin{tabular}{c} **Insufficient or** \\ **overwong vegetation** \\ \end{tabular} & \
\begin{tabular}{c} **Vegutation** \\ **GE000** **, 45/m** \\ \end{tabular} &
\begin{tabular}{c} **Mechanism** \\ **GE000** **, 45/m** \\ \end{tabular} & 0 & 25 & Planar & 4 & 10 \\ \hline
**Medium** & \
\begin{tabular}{c} **Tension cracks** \\ **overwong vegetation** \\ \end{tabular} &
\begin{tabular}{c} **Passive debris barrier** \\ **Passive debris barrier** \\ **Passive debris barrier** \\ **Reliability** \\ **GE000** **, 45/m** \\ \end{tabular} & 1 & 0 & Planar & 3 & 20 \\ \hline
**Maximum** & \
\begin{tabular}{c} **Roleing requirements** \\ **(domance widening)** \\ \end{tabular} &
\begin{tabular}{c} **Reliability** \\ **GE000** **, 45/m** \\ \end{tabular} & 1 & 0 & Rotational & 3 & 20 \\ \hline
**\
\begin{tabular}{c} **Mechanism** \\ **Landslide** \\ \end{tabular} &
\begin{tabular}{c} **Reliability** \\ **GE000** **, 45/m** \\ \end{tabular} & 4 & 0 & Rotational & 5 & 30 \\ \hline
**\
\begin{tabular}{c} **Oversberg asset** \\ \end{tabular} &
\begin{tabular}{c} **Reliability** \\ **GE000** **, 45/m** \\ \end{tabular} & 3 & 0 & Rotational & 3 & 40 \\ \hline
**\
\begin{tabular}{c} **Mechanism** \\ **Cambridge asset** \\ \end{tabular} &
\begin{tabular}{c} **Reliability** \\ **GE000** **, 45/m** \\ \end{tabular} & 3 & 0 & Both & 3.5 & 50 \\ \hline
**
\begin{tabular}{c} **\({}^{*}\)**unit cuts are calculated per m/m for linear assets and should be multiplied by the sloped height. \\ \end{tabular}
\end{table} 
Table 1: Intervention rules for earth slopes (cutings and embankments).