## 1 Introduction  
In recent decades, the increasing intensity and frequency of earthquakes have posed a significant risk to operational tunnels [1]. For instance, in China, after the 2008 Wenchuan earthquake, numerous tunnels were reported to have suffered from different degrees of damage [2], causing significant economic losses and casualties. Moreover, tunnels constitute crucial elements of transportation infrastructure worldwide; seismically induced damage of tunnels may thus have substantial consequences on the operation of the global transportation network after a significant event [3]. Therefore, a thorough study of the resilience evaluation of tunnels is of paramount importance to the development of better seismic infrastructure planning and interventions.  
Seismic resilience describes the capability of a tunnel and associated organizations and communities to mitigate damage induced by earthquake loading [4], these factors constituting the key components in vulnerability and risk analyses for metro systems. Tunnels that are resilient to earthquakes can maintain and even enhance their crucial functionality by responding and adjusting to seismic events. In this sense, resilience can be associated with organizational, technical, social, and economic dimensions [5]. Critical infrastructure assessments based on the concept of resilience have been at the forefront of research for decades [6, 7] and are gradually being integrated into the design practices and operational procedures of transport infrastructure stakeholders [8, 9].  
Quantifying infrastructure resilience is typically associated with the so-called resilience indexes, which describe the assets' ability to absorb the effects of damage, adjust to new circumstances, and return to normal after failure [9, 10]. Moreover, indexes related to the resilience curve, which describes how well a structure recovers after an earthquake event and how quickly it can return to full functionality, are widely used [8; 9; 10]. The resilience assessment frameworks for single and multiple hazards have been developed and applied to a variety of infrastructures, such as hospital facilities [11; 12], schools [13; 14], transportation networks [9; 10], buildings [15; 16] and bridges [17; 18]. These existing works have been conducted with various assumptions and have some limitations [19; 20; 21]; thus, there is a need for further studies related to the development of more rigorous resilience assessment frameworks for different types of infrastructure. Additionally, there have been recent introductions of resilience considerations for tunnels that account for the effects of extreme surcharge discussed by [PERSON] and [PERSON] [22]; nevertheless, to the author's best knowledge, such an evaluation framework related to the seismic resilience of tunnels has not been considered in the literature.  
To bridge this gap, this study extends the author's previous investigation published at the 4 th International Conference on Performance-Based Design in Earthquake Geotechnical Engineering (PBD-IV) [23] to further shed light on the resilience of shallow circular tunnels subjected to earthquakes using fragility functions. This study focuses on the probabilistic seismic resilience evaluation of circular tunnels in typical soft soil areas. The seismic resilience of the examined tunnel is quantified based on the developed fragility functions and existing restoration functions. The effects of various fragility functions proposed by different researchers on tunnels' resilience are also highlighted. The findings of this study are expected to assist consultants, operators, and stakeholders in enhancing seismic risk management as part of the development of more resilient metro systems.