The deaths of accident occurring in land hazardous material transport (rail and road) is a scale standard for judging accident severity in safety programmes. The f-N curve is a common practice to express the results from past scattered accident data through curve fitting method, which only estimate the overall trend. For this reason, this paper proposed a simple methodology by combination of normal distribution and f-N curve. To verify the method, the following three sets of statistical data were selected and analysed in this study: 1932 accidents in over 95 countries (1931–2004) and 322 accidents in China (2000–2008) available in the literature, and 2046 accidents investigated in China (2013–2017). It was found that the mean value curve is almost identical or even better than the best-fitted curve, while the predicted upper and lower limits with 96% reliability (±2σ) covering nearly all the statistical data are beyond the scope of common curve fitting. The result explains the inherent relation between accumulated frequency and deaths in different transport mode, in different country and at different period. This study also provides insights on the evolution of accident severity with the development of social economy and the requirement of safety.

This paper focuses on the application of higher-order and multilayer networks in identifying critical causes and relationships contributing to hazardous materials transportation accidents. There were 792 accidents of hazardous materials transportation that occurred on the road from 2017 to 2021 which have been investigated. By considering time sequence and dependency of causes, the hazardous materials transportation accidents causation network (HMTACN) was described using the higher-order model. To investigate the structure of HMTACN such as the importance of causes and links, HMTACN was divided into three layers using the weighted k-core decomposition: the core layer, the bridge layer and the peripheral layer. Then causes and links were analyzed in detail. It was found that the core layer was tightly connected and supported most of the causal flows of HMTACN. The results showed that causes should be given hierarchical attention. This study provides an innovative method to analyze complicated accidents, which can be used in identifying major causes and links. And this paper brings new ideas about safety network study and extends the applications of complex network theory.

In hazardous materials transportation systems, accident causation analysis is important to transportation safety. Complex network theory can be effectively used to understand the causal factors of and their relationships within accidents. In this paper, a higher-order network method is proposed to establish a hazardous materials transportation accident causation network (HMTACN), which considers the sequences and dependences of causal factors. The HMTACN is composed of 125 first- and 118 higher-order nodes that represent causes, and 545 directed edges that denote complex relationships among causes. By analyzing topological properties, the results show that the HMTACN has the characteristics of small-world networks and displays the properties of scale-free networks. Additionally, critical causal factors and key relationships of the HMTACN are discovered. Moreover, unsafe tank or valve states are important causal factors; and leakage, roll-over, collision, and fire are most likely to trigger chain reactions. Important higher-order nodes are discovered, which can represent key relationships in the HMTACN. For example, unsafe distance and improper operation usually lead to collision and roll-over. These results of higher-order nodes cannot be found by the traditional Markov network model. This study provides a practical way to extract and construct an accident causation network from numerous accident investigation reports. It also provides insights into safety management of hazardous materials transportation.

The Belt and Road has developed rapidly in recent years. Constructing a comprehensive traffic network is conducive to promoting the development of the the Belt and Road. To optimize the layout of the Belt and Road comprehensive traffic network, this paper identifies important cities. First, a weighted super adjacency matrix is defined, which includes sea, air, railway transportation and trans-shipment transportation between these transportation modes. With this matrix, the Belt and Road comprehensive traffic network (B&RCTN) is constructed. To identify important node cities, this paper proposes a method to calculate multi-layer centrality which considers inter-layer relationships. With the results of the above four centrality indexes, the Entropy Weight TOPSIS is used to synthesize the evaluation of the four indexes. Finally, the multi-layer comprehensive centrality rank of node cities is obtained. Result shows that there are 72 important cities in B&RCTN. These important cities are mainly distributed in the east and west of Eurasia. Eastern cities are located in East Asia and Southeast Asia, including 36 cities such as Singapore, Shanghai, Guangzhou, Shenzhen and Hong Kong. Western cities are concentrated in West Asia, Western Europe and North Africa along the Mediterranean coast, including 31 cities such as Istanbul, Dubai, Vienna, Trieste and Koper. There are few important cities in central Eurasia, except Almaty in Central Asia and Colombo in South Asia. In addition, important cities also include Moscow in Eastern Europe, Lagos and Lome in West Africa. Finally, based on the distribution of important cities, this paper puts forward some suggestions on the development of the Belt and Road comprehensive transportation.