## 1 Introduction  
As an electrical product for transmitting electricity, information, and electromagnetic energy, cables have been widely used in various areas of the modern economy, which is the basic guarantee for the normal operation of the modern economy and society. As the insulation and the sheathing of cables are generally made of plastic or rubber and other flammable materials, they can easily be damaged under high temperature conditions [1]. For example, the fire accident in the Dalian's oil depot on 16 July 2010 caused damage to the power supply lines and distribution rooms at the initial stage of the fire. All the low-voltage power supply was interrupted, so all of the oil tank emergency shut-off valves could not be electrically shut off. The manual operation of the electric valve was slow and dangerous, which caused great difficulties in firefighting [2, 3]. Therefore, in the case of fire, some key cables connected to the firefighting and safety equipment became the weak point of the emergency system. Therefore, it is of great significance to improve the fire resistance of such key cables [4, 5]. There are two common methods to improve the fire resistance of key lines: one is to use fire-resistant cables, and the other is to bury the cable [6]. These two methods are not suitable for the existing cables that have already been laid. The amount of work and economic loss caused by shutdown construction is large, and the second method is not convenient for the maintenance and replacement of individual cables. Therefore, it is necessary to consider other schemes for the fire-resistant transformation of a cable system. At present, the research on cable fires mainly focuses on the combustion characteristics of a cable. These articles describe the carrying out of experiments or numerical simulations on the propagation direction and velocity of the flame on a cable, the combustion temperature distribution, toxic gas diffusion, and other parameters, and they reveal the characteristics of cable fire [7; 8; 9; 10; 11; 12; 13; 14]. Some experimental research studies and numerical calculations about cable failure have mainly focused on the direct fire protection of cables [15; 16; 17; 18; 19; 20; 21; 22]. [PERSON] et al. [15] used fire barriers made from mica glass tape and from ceramifiable silicone rubber to protect cables and to monitor the insulation state of cables during fire testing. This study provided ideas for the fire-resistant design of cable insulation sheaths, and it proved that it was appropriate to judge the state of cables by measuring the insulation resistance of cables. [PERSON] et al. [16] studied the insulation failure time of VV cables and ZC-YV cables coated with different thicknesses of fire-retardant coatings under standard fire conditions. The results showed that the application of fire-retardant coating could delay the insulation failure time of a cable when heated. [PERSON] et al. [17] also studied the relationship between the thickness of a fire-retardant coating and the failure time when a cable was directly coated with the fire-retardant coating. The results showed that the failure time increased with the increase of the coating thickness. However, the cable failed in less than 10 min in the experiment. Therefore, the method of directly coating fire-retardant coating onto the cable surface could delay the failure time of the cable, but the time was not enough. [PERSON] et al. [23] considered using different conduits to protect cables. The results showed that when the heat flux of the environment was low, the protection effect of the threading flame retardant polyvinyl chloride (PVC) conduits was slightly better than that of metal conduits, and when the heat flux was high, the result was the opposite. Through previous field investigation in an oil storage company, it was found that most of the cables in the fire dike of the company's oil tank area were laid in cable trays.