## 1 Introduction  
The natural hazard chain refers to a series of secondary hazards induced by a single natural hazard [1]. Compared with a single hazard, a hazard chain has the characteristics of a long time scale, broad scope, and immense destructiveness and results in enormous losses of life and economic losses, and harmful social and environmental effects [2]. Heavy rains, debris flows, earthquakes, landslides, landslide dams, and outburst floods are all individual hazards, but sometimes, they can be in a hazard chain and cause more severe hazards. A landslide is usually caused by heavy rains or geological effects such as earthquakes and occurs suddenly, with huge impacts on human production and life [3]. When there is a river in the direction of the landslide, the landslide can easily block the river and form a landslide dam. The landslide dam causes the upstream water level to keep rising and also causes the submersion of the upstream residential area. Once the landslide dam breaches, the large amount of water accumulated in the barrier lake will be released quickly and will cause enormous hazards downstream. In recent years, frequent earthquakes and heavy rains have led to a global outbreak of landslides [4]. The Tangjiashan landslide dam formed in the 2008 Wenchuan earthquake and collapsed 29 days later. The dam forced nearly 200,000 people downstream to evacuate [5]. In 2009, heavy rainfall caused by a typhoon led to landslides and debris flows in Hsiaolin Village. The landslides buried the village and blocked the gorge of the Cishan River, and the peak outflow rate reached 70,649 m\({}^{3}\)/s after the landslide dam breached [6]. In 2018, landslides blocked the Jinsha River twice at the same location. The outburst flood caused road damage and extensive damage to large areas of farmland and houses [7]. Therefore, a risk assessment method needs to be proposed to reduce the economic loss, loss of life, and social and environmental effects of the hazard chain. In the existing research, scholars from China and overseas have mostly used mathematical methods, such as the analytic hierarchy process, the Poisson probability model, and information models, to evaluate the vulnerability and risk of landslide disasters. However, the existing risk assessments have focused primarily on single hazards, including forecasts of landslide movements [8; 9], dam formation [10; 11; 12; 13], dam stability [14; 15; 16; 17], and outburst floods [3; 10; 18; 19]. With the development of science and technology, more and more advanced methods are used for forecasting hazards. [PERSON] et al. [20] proposed the inverse FORM algorithm and, based on this, a geographic information system extension tool was developed for probabilistic physical modeling and forecasting landslides [21]. [PERSON] [22; 23] analyzed the responses of the medium-sized mountainous Mesochora catchment to climate change and proposed a multi-stage method for selecting input variables for ANN forecasts of river flows. For assessing the risk of a hazard chain, a conceptual risk assessment model of a regional hazard chain was proposed based on [PERSON]'s permanent deformation model and applied to predicting a disaster chain induced by the Wenchuan earthquake [24]. [PERSON] [25] summarized the hazard chain mode of river blockages induced by avalanches on the basis of a hazard chain structure. A risk assessment of the Layue landslide dam was carried out from the aspects of risk and vulnerability. These studies have mainly focused on the concept of a hazard chain, but have yet to emphasize a systematic risk assessment model. Although the remedy for a hazard chain lies in blocking it before expansion/transformation, sometimes, it is inevitable [26]. Therefore, a risk assessment model is needed to reduce the losses caused by the hazard chain. This study aimed to explore a risk assessment model of hazard chains and to apply it to the case of landslides. A database was established for statistical analysis.