  Infrastructure systems, such as power, transportation, telecommunication, and
water systems, are composed of multiple components which are interconnected and
interdependent to produce and distribute essential goods and services. So, the
robustness of infrastructure systems to resist disturbances is crucial for the
durable performance of modern societies. Multilayer networks have been used to
model the multiplicity and interrelation of infrastructure systems and
percolation theory is the most common approach to quantify the robustness of
such networks. This survey systematically reviews literature published between
2010 and 2021, on applying percolation theory to assess the robustness of
infrastructure systems modeled as multilayer networks. We discussed all network
properties applied to build infrastructure models. Among all properties,
interdependency strength and communities were the most common network property
whilst very few studies considered realistic attributes of infrastructure
systems such as directed links and feedback conditions. The review highlights
that the properties produced approximately similar model outcomes, in terms of
detecting improvement or deterioration in the robustness of multilayer
infrastructure networks, with few exceptions. Most of the studies focused on
highly simpliffied synthetic models rather than models built by real datasets.
Thus, this review suggests analyzing multiple properties in a single model to
assess whether they boost or weaken the impact of each other. In addition, the
effect size of different properties on the robustness of infrastructure systems
should be quantiffied. It can support the design and planning of robust
infrastructure systems by arranging and prioritizing the most effective
properties.
