No system carries risks that cannot be eliminated completely through preventive measures. Although the lower the risk of a system the higher the level of security, it is increasingly difficult and costly to further reduce the risk level. Given China’s economic and social development level and the public’s willingness to accept risks, a trade-off can be made between the risk level and the cost of a system. Therefore, the ALARP principle was selected to establish risk standards in China.

This principle stands divides risks into three zones: intolerable, ALARP, and broadly acceptable (Langdalen et al., 2020). If the risk falls into an intolerable zone, measures must be taken to reduce the risk. If it falls into the ALARP zone, taking risk control measures depends on whether risk reduction is feasible and whether the benefits outweigh the costs. If a risk falls into the broadly acceptable zone, no risk-control measures are required. This principle is illustrated in Figure 1.

In 1967, Farmer proposed a limit curve for the acceptable risk of various accident types using probability theory, known as the famous F-N curve (Pei et al., 2018). The F-N curve is a limiting curve based on probability theory that allows various accidents to occur. It is based on probabilistic analysis and expected benefits, and takes into account the current state of risk in which it is located as well as people’s aversion to risk, and it is highly scientific and versatile. It was first used for risk assessment in nuclear power plants and was later widely applied in the construction of social life risk standards for dam engineering. The expression for this curve is as follows: 1 − F N x < C x n (1) where F _N (x) is the distribution function of the annual mortality rate, representing the probability of x deaths; 1−F _N (x) is the probability of ≤N deaths; C is a constant that determines the position of the risk control line; and n is the slope that represents the degree of aversion to risk, with a larger slope indicating greater ecosystem to risk and less acceptability.

According to the Chinese State Council’s “Regulations on Reporting and Investigating Production Safety Accidents,” one death is equivalent to a direct economic loss of 3.3–5 million RMB (Li et al., 2015). Therefore, it is suggested to construct China’s economic risk standards for reservoir dams based on a ratio of 4 million RMB per person. Although measuring human life values in economic terms is often considered inhumane and has gained strong criticism and opposition, it is reasonable to use life risk standards as a basis for constructing economic risk standards under the premise of controlling life risks at socially acceptable levels.

Constructing the environmental risk criteria for dam failure on the basis of the life and economic risk criteria avoids over-complicating the criteria on the one hand, and on the other hand allows for a strong correlation between the different criteria. Therefore, it is proposed to analyze the economic perspective by simplifying the environmental loss to the money needed to compensate the environmental risk, then the relationship between the loss of environmental value and its exceeding probability is as follows: 1 − F N ′ x < C x n (2) where F N ′ x is the probability distribution function in which the funds needed to compensate for ecological and environmental risks <x, C is a constant, and n is the slope of the standard line

Owing to substantial differences in politics, economics, culture, and other aspects among different countries (Li et al., 2018; Ge et al., 2020b), foreign risk standards cannot be directly applied to China (Ge et al., 2017; Ge et al., 2020c). Based on relevant domestic and foreign achievements and China’s national conditions, the following principles were used to construct risk standards for dams:

(1) Compliance with the safety status of Chinese dams. Several of China’s active reservoir dams were built from the 1950s to the 1970s. They were limited by economic and technological levels at that time, and several have hidden safety hazards. If standards are too strict, more reservoirs will be classified as “dangerous or sick.” In the current situation, where funding is relatively tight, several reservoirs will not be able to receive timely reinforcement against risks and will be forced to change operating conditions or stop operating, which will degrade the local economic development environment. It is also not conducive to effectively distinguish the degree of danger between “dangerous and sick” reservoirs.

C is a constant that determines the starting position of the standard line. The acceptable risk C values adopted by some countries and institutions are listed in Table 2. As seen from table, the value of C is primarily 10⁻³/year. The values of C in Table 2 include various application categories such as nuclear power plants, hazardous chemicals, factories, all types of buildings (hospitals, schools, and residential buildings), slopes, and dams. Considering that accidents involving hazardous chemicals, factories, and buildings during new construction, reconstruction, expansion, and in-service production and storage processes are primarily caused by human factors, natural factors beyond human control are also important components of uncertainty during the construction and operation of reservoir dams. Therefore, according to the suggestion of Li et al. (2015), the standard for dam safety can be appropriately lowered to C = 10⁻². The acceptable risk standard can be one order of magnitude smaller than this; thus C = 10⁻³.

The value of n represents the degree of risk preference. Considering the vast territory of China, there may be considerable differences in economic development, ecological environment quality, and social and cultural backgrounds among the different regions. Therefore, the degree of risk preference varies across the regions; thus, a risk matrix was introduced. This method was proposed by the US Air Force Electronic Systems Center in the mid-to-late 1990s, and has been widely used in US military weapon system development projects as a structural method for identifying the importance of project risks. It can evaluate the potential risks of projects and is currently widely used in research fields, such as project risk assessment and safety risk rating (Koulinas Georgios et al., 2021).

The higher the per capita GDP in a region, the higher the demand for quality of life; and the more emphasis it places on the surrounding ecological environment, the more averse it is to risk (Francis et al., 2022). The higher the quality of the ecological environment, the higher the losses caused by disasters, and the more averse they are to risk. The per-unit area average ESV and the per capita ecological environment value reflect the ecological environment quality of a region from different perspectives. The higher the per capita ESV, the stronger sustainable development capability of the region. However, this does not necessarily mean that the ecological damage caused by disasters is more severe. For example, in areas with poor land quality, floods may not cause considerable ecological damage; however, the per capita ESV may still be relatively high because of low population density (Peter et al., 2022). Therefore, the average ESV per unit area is a better indicator of the importance of a region’s ecological environment. The higher the average ESV per unit area, the greater are the losses caused by floods. Therefore, per capita GDP and per unit area average ESV were selected to construct a risk preference matrix. Based on statistical data released by the National Bureau of Statistics in 2020 (National Bureau of statistics of the people’s Republic of China, 2020), the per capita GDP and per unit area average ESV of each province are shown in Table 3.

According to the 2020 income classification standard of the World Bank, most provinces in China have an annual per capita income in the middle-to high-income range, whereas the remaining provinces have a per capita income in the high-income range (Shah et al., 2022). To differentiate the per capita GDP income of each province more precisely, the middle-to high-income range was evenly divided into three categories: 2.58–5.29, 5.29–8, and >8 yuan per capita GDP. The average ecological service value per unit area (ESV) for each province was determined by setting the highest and lowest values as the upper and lower limits of the range and equally dividing the range into three categories: 8–14, 14–21, and 21–28 yuan per unit area. The resulting risk-preference matrices are presented in Table 4.

When falling into zone Z, n = 2 is assigned, indicating risk aversion; when falling into zone Y, n = 1.5 is assigned, indicating slight risk aversion; and when falling into zone X, n = 1 is assigned, indicating risk neutrality. Based on the per capita GDP and average ESV per unit area of each province in 2020, the risk preference of each province was determined using a risk matrix, as shown in Figure 3.

As shown in Figure 3, the regions with risk preference X primarily include some western and central provinces of China and Jilin Province. Western regions, such as Xinjiang, Tibet, Qinghai, Gansu, and Ningxia, have relatively underdeveloped economies. People in these areas tend to focus more on economic development than on the ecological environment, resulting in a risk preference of X. In central provinces, such as Hebei, Henan, Shanxi, and Shandong, although the total economic output is large, the population is large, and the per capita GDP is relatively small, resulting in a risk preference of X. Among the three northeastern provinces, only Jilin Province has a risk preference of X. Upon comparison, although Jilin’s per capita GDP is higher than that of Heilongjiang, Heilongjiang has important ecological protection areas, such as the Greater and Lesser Khingan Mountains, with higher ecological value and lower risk tolerance. Therefore, among the three northeastern provinces, only Jilin Province has a risk preference of X.

The risk preference of most provinces in China is Y, where some areas have high ecological environment quality despite being economically underdeveloped, whereas others have moderate ecological environment quality despite being economically developed (i.e., Beijing). Additionally, some regions, such as Hunan, have good overall economic development and ecological environment quality; however, a large population means that their per capita GDP has not reached the high-income range, resulting in a Y risk preference.

Only Shanghai, Hong Kong, Guangdong, Fujian, Zhejiang, and Taiwan have a Z-risk preference and are concentrated in the southeastern coastal region of China. These areas are economically developed and have a high ecological environment quality, resulting in a lower tolerance for risk.

Most countries or regions have set extreme value lines for the risk standards of the two types. First, the probability extreme value line set by Australia indicates that there is no need to consider the consequences of an accident if its probability is below a certain value (ANCOLD Australia National Committee on Large Dams, 2003). The other, such as the loss extreme value line set by Hong Kong, indicates that if the accident loss exceeds a certain value, then the risk is intolerable. Considering the safety status of Chinese dams, management levels, and levels of economic and social development, it is currently not feasible to set extreme accident value lines (Li et al., 2015). Therefore, the following two points should be considered when setting the accident probability extreme value line:

(1) Probability of dam accidents in China. According to (Li et al., 2015; Fan and Jiang, 2005), the annual average probability of dam failure can be considered as 10% for the tolerable risk extreme value line and 1% for the acceptable risk extreme value line. From 1954 to 2018, 3,541 dam failures occurred in China, with an annual failure rate of 6.29 × 10⁻⁴. Therefore, the tolerable and acceptable extreme value lines were 6.29 × 10⁻⁵ and 6.29 × 10⁻⁶, respectively.

Where Φ ⋅ represents the standard normal distribution function.

Assuming that the reliability function is a random variable following a normal distribution (Wilde and Johansson, 2013; Li S. et al., 2015; Ge et al., 2017). The current reliability standards in China are relatively consistent with the dam safety situation, so 10% of P _f can also be used as the tolerable risk extreme line and 1% as the acceptable risk extreme line.

As people’s concern for the ecological losses caused by dam failures is significantly lower than that for the loss of life and economic losses, these requirements can be appropriately reduced. Moreover, the funding guarantees and management levels of large reservoirs were better than those of medium and small reservoirs. Among the 84 dam failures from 2000 to 2018, there were no failures in large reservoirs, 7 in medium-sized reservoirs, and the remainder in small reservoirs (Li H. et al., 2021). Therefore, to avoid excessive complexity in standards, large (I) reservoirs can adopt the same standards as large (II) and medium reservoirs. Thus, for large- and medium-sized reservoirs, the tolerable and acceptable risk probability extreme value lines are 1.08 × 10⁻⁵ and 1.08 × 10⁻⁶, respectively, whereas for small reservoirs, the tolerable and acceptable risk probability extreme value lines are 7 × 10⁻⁵ and 6.29 × 10⁻⁶, respectively.

To simultaneously meet the extreme value lines determined according to the safety level of the dam and current reliability standards, a smaller value was considered as the risk standard. Finally, the tolerable and acceptable risk probability extreme value lines for medium-sized reservoirs are 1.08 × 10⁻⁵ and 1.08 × 10⁻⁶, respectively, whereas the tolerable and acceptable risk probability extreme value lines for small reservoirs are 6.29 × 10⁻⁵ and 6.29 × 10⁻⁶, respectively.