# A Multiobjective Decision-Making Model for Risk-Based Maintenance Scheduling of Railway Earthworks
## 1 Introduction  
Traditionally rail infrastructure asset maintenance has been performed retroactively to correct, through replacement or remediation, failed elements. Naturally, this carries substantial safety implications for end-users and financial liability for infrastructure owners [1]. To limit their exposure, infrastructure owners have been trying to move towards more proactive asset maintenance approaches [2; 3; 4]. Such an approach would allow them to invest money in a prudent, sensible fashion, which maximizes utility and subsequently gives the best return on their investment [5]. Resulting in safer infrastructure which offers greater value to consumers and owners alike with less investment of resources [6]. Unfortunately, it is seldom clear how to most effectively allocate resources to achieve these goals. Railway networks are a significant global asset, with an estimated 200,063 km of track [7] in the EU alone, 95% of which was built before 1905. Individual structures along these railways, including bridges, tunnels and earthworks, were constructed prior to the adventof modern design and construction standards. Given their age, many have far exceeded typical design lifetimes, and their resilience to the impacts of increased traffic loading and extreme weather events is lower than comparable assets on modern networks like highways. Bridges and tunnels are discrete, high-value, visible assets, where the majority of safety problems are relatively easy to detect, and thus, budgets can be assigned with some certainty. As a result, these assets have undergone regular remediation and replacement since their initial construction, while most earthworks remain in their original condition [3]. This is problematic on several levels as the present-day structures are now carrying loads far above what was originally intended as part of everyday operation, while their long lifespans have left them at increased risk of deterioration from aging effects and extreme climate scenarios [8]. Aged embankments, in particular, due to their steep construction, are more susceptible to rainfall-induced shallow failures than their modern-day equivalents [9; 10]. This is because embankments constructed at slope angles in excess of their internal angle of friction rely on cohesion and matric suction for stability, the latter of which is inversely proportional to soil moisture [11; 12]. As a result, shallow shear failures often occur after heavy or prolonged rainfall [13]. [PERSON] et al. [14] found a strong correlation between earthwork failure and monthly rainfall in excess of the long-term average. Earthworks are often covered by vegetation, and their behavior varies temporally, being strongly influenced by both rainfall and drying events [15; 16; 17; 18]. The situation is complicated further by the scope of the networks involved and the presence of steep earthworks made of unknown material [19; 20; 21]. As a result, it is difficult for infrastructure managers to make effective maintenance decisions that utilize allocated resources in an optimum fashion. Although risk assessment for the management of earthwork slopes is now widely adopted, major failures are increasing [3]. This is partly due to issues such as aging, climate change and increased demand. However, an additional contributing factor is that current risk assessment approaches are overly reliant on the results of visual inspection for hazard assessment. When stability analyses are performed to compare the capacity (strength) to the demand (load), they tend to be deterministic with conservative estimates of input parameters. In reality, both the capacity and demand vary temporally in response to weather events and therefore, the choice of input parameters is neither straight-forward nor fixed, and a move towards probabilistic assessment where uncertainty is quantified to deliver a specific level of safety is preferred.