Risk-informed based comprehensive path-planning method for radioactive materials road transportation
Introduction
According to the U.S. Department of Transportation (DOT)’s hazardous material table, there are nine classes of hazardous materials (HAZMAT), in which RADMAT is defined as the hazard class 7 [1]. Currently, with the rapid development of nuclear energy and nuclear technology, the transport volume of the RADMAT has increased dramatically [2], [3], [4]. RADMAT transportation differs from the transportation of the other eight classes of HAZMAT. Due to the radiation characteristics of RADMAT and its accidental radioactive release, RADMAT transportation accidents have the potential of causing radiological damages to the affected population, public property, and the environment. Particularly, the principle and objective of RADMAT transportation route selection are different from that of general cargo transportation. The transport of RADMAT is based on the basic principle that the radiation exposure received by the staff and the general public can be reasonably reached to the lowest level as far as possible, and the safe implementation of the transportation is the prime goal [4]. On this basis, other specific targets such as the shortest distance, the least cost, and the shortest time are considered. Therefore, it is essential to determine a safe and economical route for the transportation of RADMAT by considering its transportation risks and costs, comprehensively.
To date, HAZMAT transportation has attracted increasing attention from scholars at home and abroad [5], [6], [7], [8], [9], [10]. Among them, the problems of risk assessment [11], [12], [13] and route optimization [14], [15], [16] are the most commonly tackled. However, most studies were focused on the transportation of non-radioactive HAZMAT, including explosives, compressed gasses, flammable liquids [17], and toxic materials, while few studies were devoted to solving the route optimization problems of RADMAT transportation. So far, several works have already been devoted to the risk assessment of non-radioactive HAZMAT road transportation [18], [19], [20] and railway transportation [[11], [12], [13],21,22]. Recently, some works have been devoted to the risk assessment of RADMAT transportation, including marine [23] and road [24] modes. Yet, several limitations exist in the risk models in these works. Christian and Kang [25,26] proposed a probabilistic risk assessment (PRA) methodology to assess and reduce the risks of spent nuclear fuel maritime transportation. Ship collision probability and transport cask damage probability were obtained through a non-linear finite element analysis. Nevertheless, the accident consequence was ignored and thus the risk was not quantified. Tao et al. [27,28] proposed an integrated probabilistic safety assessment for spent nuclear fuel road transportation. The comprehensive risk factors were identified and the population exposure dose was considered to evaluate the radioactive risks. However, the radiological damage to the surrounding environment was not considered. Although some previous researches on HAZMAT road transportation risk analysis incorporated the consequence indicators of population vulnerability and environmental vulnerability to evaluate the accident consequences [20,22,29], the risk models were aimed at the chemical materials (e.g., liquid chlorine) and thus were not applicable to the radioactive materials.
Currently, both single-objective and multi-objective route planning [30], [31], [32], [33], [34], [35] models were explored by scholars. Some were based on the risk indicators, others were not. Generally, risk analysis is an important tool for informed decision-making [36,37]. As transportation risk is a subject with much uncertainty and has considerable meanings for decision-makers, much attention should be focused on risk quantification when it comes to route optimization. However, the risk indicator in some routing studies has not been fully considered. For instance, some studies mainly focused on the single-objective-based route optimization under the consideration of accident probability [14], consequence cost [30,31], or economical cost [33,38], while the risk involved in the optimization model was not sufficiently quantified. Other studies selected the optimal route based on the coupling of methods including fuzzy comprehensive evaluation (FCE), analytic hierarchy process (AHP) [39], nearest neighbor (NN) method [39], and entropy weight [40]. Actually, a single-objective approach is not enough in most instances. At present, some researches have been conducted to optimize the HAZMAT transportation route by considering multi-objective including transportation risk and cost [41], risk equity [42], and value-at-risk (VAR) [43], [44], [45]. Nevertheless, the accident probability indicators and consequence indicators are not sufficiently considered and quantified in the existing risk-based route optimization models. Chen et al. [16] developed a multi-objective geographic information system (GIS) for nuclear waste transport route selection considering the travel time, transportation risk, and exposed population. In their work, the transportation risk was calculated just simply by employing prevailing traffic volume per hour. Shen [46] considered three objectives of minimizing transportation risk, transportation time, and transportation cost to optimize the route for Liquefied Petroleum Gas (LPG) road transportation by using the GRA model. Similar optimal methods can be seen in [47,48], in which the transportation risk was not fully quantified because the accident probability was obtained based on the historical traffic accident statistical data and the accident consequence was obtained by estimating the total number of affected populations [43,[48], [49], [50]]. Yun et al. [51] selected an optimized route from three routes for transportation of spent nuclear fuel based on the lowest risk calculated by considering the accident probability and consequence in Korea. Yet, the probabilities were obtained using abroad existing data and statistical models, and the population dose consequences were obtained using Gaussian plume model which the geographical features and local wind pattern were not considered. The previous HAZMAT transportation route optimization works are summarized and depicted in Fig. 1.
After analyzing the previous works mentioned above, we can find that: (i) There is an absence of risk assessment-based route optimization methodology for radioactive materials road transportation though a lot of efforts are noticeable in the HAZMAT transportation domain. (ii) There is a lack of full consideration for multi-objective route optimization indicators. (iii) The accident occurrence probability indicators and consequence severity indicators are not sufficiently considered and quantified in the existing risk-based route optimization models.
Radioactive materials road transport system is a complex socio-technical system with dynamic changes. Due to the mobile characteristic of this transportation system, its transport safety is affected by the coupling and interactions among the risk factors such as human errors [52], machine failures, harsh environment, and poor management. Since the factors interacted dynamically, nonlinearly, and non-in-dependently in the system, the causal chains in an accident are not simply linear or independent [12]. Thus, it is significant to utilize a systematical risk assessment method to comprehensively analyze the radioactive material road transportation system and thereby assess the potential accident probability. Probabilistic safety assessment (PSA) methodology has the advantage of the systematic and global modeling characteristics, which can comprehensively consider the synergy and mutual influence of various internal and external factors in the complex socio-technical systems [53], [54], [55], [56], [57], [58]. The calculated risk is in line with the actual transportation situation and can truly reflect the risk level of the transportation route. Moreover, the ET/FT-based PSA could analyze the complex accident processes and identify underlying potential vulnerabilities to take the corresponding measures for accident prevention and risk reduction. In light of the demonstrated advantages, in this paper, we assess the transport risk by using the PSA methodology.
To overcome the aforementioned limitations, in this study, a risk-informed based comprehensive path-planning (RICPP) method for radioactive material road transportation (RMRT) has been successfully proposed by considering multi-objective including the transportation risk cost, time cost, and economical cost. Firstly, we develop an ET/FT-based PSA model to quantitatively calculate the occurrence probability of the RMRT accidents. After that, we establish the PEHR (personnel, environment, hazard target, and rescue force) comprehensive severity indexes for the accident consequence evaluation considering the vulnerability and resilience of the accident-affected entities. Subsequently, we quantify the severity index by using the AHP to obtain its importance weight and using the computational fluid dynamics (CFD)-based radionuclide dispersion model to assess its radiation dose. Secondly, we estimate the transportation radiological risk cost by coupling the potential accident probability and the associated consequences. Furthermore, the transport time cost and economical cost are estimated. Thirdly, we use the GRA model to select the optimal route by considering the transport risk cost, time cost, and economical cost comprehensively. Finally, we perform a case study of typical domestic road transportation of radioactive materials to verify the rationality and feasibility of the proposed RICPP method.
The main contribution and novelty of the proposed RICPP methodology lie in the following three aspects: (i) Multi-objective route planning indicators are established for the radioactive material road transportation considering radiological risk cost, transportation time cost, and economical cost; (ii) Among which, a novel integrated probabilistic safety assessment (PSA) methodology framework is proposed for the radiological risk cost estimation; (iii) To obtain the risk, the accident sequence-based probability analysis model and the PEHR comprehensive severity index-based radiological consequence evaluation model are established. The proposed RICPP methodology is beneficial for selecting a safer and more economical route for radioactive materials road transportation.
The remainder of this paper is organized as follows: Section 2 is devoted to the establishment of the RICPP methodology. In this part, radiological risks and transport costs are characterized and aggregated into a GRA model to select an optimal path. To demonstrate the effectiveness of the proposed method in this work, in Section 3, a case study for spent nuclear fuel road transportation is conducted and the calculation results and analysis results are presented and discussed. The final Section 4 is devoted to the conclusions and further work.
Section snippets
RICPP method
Radioactive material path-planning is essentially a multi-objective optimization problem. The government and the public are most concerned about the transportation safety of RADMAT. Transportation enterprise aims to reduce transportation costs as much as possible on the premise of ensuring transportation safety. At the same time, RADMAT transportation itself has the constraints of a time window. In this context, it is necessary to consider transportation safety, transportation time, and
Scenario description
To demonstrate the effectiveness of the proposed RICPP method, a typical domestic spent nuclear fuel road transportation is selected as the case study. In this study, assuming that there is a batch of spent nuclear fuel that needs to be transported from site S of the nuclear power plant to site D of the reprocessing plant and there are four transportation routes to choose from. It is assumed that spent fuel is loaded by the NAC-STC-type cask and transported by truck. During transportation,
Conclusions
This paper has proposed a risk-informed-based comprehensive path planning (RICPP) method for the optimal route selection problem of radioactive materials (RADMAT) road transportation. First, the three target quantities of radiation risk cost, transportation time cost, and transportation economic cost of transportation accidents were characterized and quantified, respectively. Then, the Gray Relation Analysis (GRA) model was utilized to select the optimal path. Finally, a case study of the
Author statement
The authors claim that none of the material in the paper has been published or is under consideration for publication elsewhere.
Declaration of Competing Interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (71901203), the Natural Science Foundation of Anhui province (2008085MA23), the National Key R&D Program of China (2018YFB1900301), and the Natural Science Foundation of the Anhui Higher Education Institutions of China (KJ2020A0110). In addition, the authors sincerely thank the editor and anonymous reviewers for their insightful comments that help us improve the quality of the article.
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