## 1 Introduction  
With the rapid development of the social economy, as an efficient public transit mode, urban rail transit (URT) has expanded greatly in the world. By the end of 2023, a total of 563 cities in 79 countries and regions had opened URT lines, with a total operating length of 43,400.39 km, and China ranks first in terms of the operating mileage [1]. However, as URT networks continue to expand, the threat from natural hazards has also become increasingly prominent, particularly extreme rainfalls. For example, on 20 July 2021, Zhengzhou, China, experienced a severe rainstorm, which flooded Metro Line 5, resulting in 14 passenger deaths. Considering the extreme weather is increasingly frequent due to global warming, conducting scientific and well-founded risk assessments before disasters has become crucial for minimizing disaster losses and enhancing a city's ability to prevent, mitigate, withstand, and respond to disasters effectively. Scholars have widely focused on this aspect in studies of urban heavy rainfall disaster risk assessment and zoning. [PERSON] et al. [2], using the contribution rate method, found that rainfall and terrain slope had the most significant impact on rain-induced landslides. Further research confirmed that slope was the main influencing factor for landslide disasters [3; 4; 5]. Meanwhile, [PERSON] et al. [6] applied the XGBoost model to assess the impact of various factors on flood risk, revealing that elevation and rainfall were the most prominent factors affecting flood risk. These studies highlight the potential risk of landslides and floods under the combined influence of rainfall and terrain features. Compared to flatland cities, mountainous cities are more prone to landslides and floods under extreme rainfall conditions due to their unique topographical features [3]. For instance, the frequency of landslides in Chongqing, a mountainous city in China, is the highest in the country [7], with rain-induced landslides accounting for over 90% [8]. Landslides [9] often occur along highways and railways, potentially leading to route blockages or damage, and even causing severe accidents such as train derailments. At the same time, floods caused by heavy rain [7] also can result in drowned trains, infrastructure damage, and even casualties. Therefore, enhancing the resilience of mountainous URT networks under extreme rainfall conditions has become a critical issue in the construction of safe transportation systems. Resilience is the ability of a system to maintain its basic functions and structures through resistance, mitigation, absorption, and recovery under extreme conditions [10]. Although the definition of resilience varies across different disciplines, its core content includes two aspects: the ability to withstand disruptions and the ability to return to normal after disruptions [11]. Since transportation is essential for the everyday functions of society, the resilience of transportation networks under extreme events has been attracting much attention recently. For example, [PERSON] et al. [12] analyzed the resilience of the New York City highway network faced with extreme storm surges by randomly removing nodes and examining changes in average node degree, clustering coefficient, and redundancy in the network topology. [PERSON] [13] analyzed the relationship between traffic network resilience and efficiency, pointing out that improving network resilience not only improves overall network efficiency but also reduces losses in the event of failures. Resilience is typically quantified through the resilience loss triangle, which is represented by the difference between the normal performance curve and the disrupted performance curve, as well as the durations of the disruption and recovery phases [14]. [PERSON] et al. [15] also proposed that transportation network resilience could be evaluated through both total performance loss and recovery speed.