## 1 Introduction
However, this system is characterised by a significantly higher migration of air to the goaves with caving compared to the U-type ventilation system. This offers more favourable conditions for the self-heating of coal left in the goaves, which, in turn, may cause an endogenous fire to arise. The research conducted by [PERSON] (2018) revealed that the total migration of air to the goaves with caving depending on the type of roof rocks filling the goaves with caving may, in extreme cases, amount to as much as approximately 40% (for rocks with the highest value of tensile strength). The air stream migrating to the goaves with caving poses a risk for a low-temperature process of coal oxidation to be initiated, which may lead to spontaneous combustion of the coal left in the goaves. The prerequisites for this process to be initiated, besides the presence of coal, include the flow of air with a specific speed and appropriate oxygen concentration. When these conditions are met, it is possible for the reaction of low-temperature coal oxidation to be initiated, during which heat is produced and then accumulated by the coal, thereby causing its temperature to rise. If these conditions continue for a specific period of time (the incubation time), spontaneous combustion of coal, i.e., an endogenous fire, may occur. The most essential factor affecting the process of heat accumulation is the speed of the air stream flowing through the goaves with caving in the longwall. This speed depends on the type of roof rocks forming the caving (since they influence their sealing degree) as well as on the volumetric flow rate of the air supplied to the longwall. However, the issue of how the volumetric flow rate of the air supplied to the longwall impacts the risk of endogenous fires has been discussed in several publications [PERSON] (2018); [PERSON] (2018); [PERSON] (2018). Nevertheless, no conclusive range has been determined for the air speed flowing through the goaves that would contribute to the initiation and maintenance of the coal oxidation process. In the paper by [PERSON] et al., this value was assumed to range from 0.004 to 0.0016 m/s [PERSON] et al. (2018). [PERSON] et al. (2018), on the other hand, assumed that the critical speed value ranges from 0.015 to 0.0017 m/s, whereas [PERSON] reported that this value is between 0.015 and 0.0015 m/s S. On the other hand, [PERSON] et al. [PERSON] et al. (2018) indicated that this value ranges from 0.001 to 0.02 m/s. The speed ranges indicated are quite extensive. Therefore, the present paper assumes that this speed ranges from 0.02 m/s to 0.0015 m/s. In the case of the oxygen concentration in the air flowing through goaves with caving, it has been demonstrated that the lower limit for self-combustion of coal is 8%. The results of the tests carried out by [PERSON] (2018) indicate that no spontaneous combustion of coal occurs below this value due to the insufficient concentration of oxygen. Coal oxidation in the goaves with caving may occur only in the area of the goaves which meets both of the above conditions, namely the presence of crushed coal susceptible to spontaneous combustion and the air flowing through the goaves at a specific speed and with a specific oxygen concentration. This area could be termed as the zone with a particularly high risk of endogenous fires. In this zone, the physical and chemical parameters of the air reach values conducive to the initiation of the oxidation process. This was used as the basis for formulating the risk criterion for spontaneous coal combustion (endogenous fire) in the goaves with caving, which includes:  
* the presence of fragmented coal left in the goaves with caving. * the speed of the air flowing through the goaves with caving must range from 0.0015 to 0.02 m/s. * the level of oxygen concentration in the air flowing through the goaves with caving should be higher than 8%. Works involving determination of the distribution of physical and chemical parameters of the air flowing through the goaves with caving have already been published.