Dynamics of harmful factors in inclined road tunnels according to the results of numerical modeling of up to 50 MW fires in terms of natural ventilation

. The present paper explores the change of the harmful factors by means of full-scale numerical models. In the numerical models, the tunnel length is 400 m; the slope gradient varies within 0-9%, with a 2% step; and the heat release rate is within 5-50 MW. The outdoor air temperature on the models was assumed to be 20℃, while the pressure difference between the portals on different models varied depending on the slope, and the variation range was 50-400 Pa. The modeling results show that the propagation of the harmful factors is characterized by stabilization as demonstrated by the fact that the distance of descending propagation of the harmful factors decreases for each specific tunnel gradient and eventually shows a pronounced asymmetry with respect to the seat of fire. This confirms the preferential and pronounced ascending movement of the ventilation flow with toxic products of combustion. Thus, the worst results during the natural ventilation are expected for ascending flows. Based on the isolines of temperature, as well as the concentrations of carbon monoxide and oxygen, the gradient factor can be calculated, which can be used to design ventilation systems for engine tunnels, ensure their safe operation and save human lives during the fire.


Introduction
In the next 3-5 years, more than 50 new road tunnels are planned to build in Georgia.If looking at their design solutions, it is clear that the only expected risk-factor for them is fires.Generally, the question of fires is topical all over the world because more tunnels mean greater traffic and higher probability of fires.By considering the major tunnel fires in the world, the European Union has paid special attention to the Trans-European Transport Network, in which the safety of existing and future tunnels is a top priority.For tunnels on this network that are longer than 500 meters, the European Parliament and the Council of Europe have issued EU Directive 2004/54 on the minimum safety level.The total length of such tunnels in the EU countries is more than 1000 km.The EU countries have been given a clear recommendation to extend the requirements of the Directive to tunnels that are not part of the Trans-European Transport Network.In fact, the minimum safety level for them is defined by the organizational and technical requirements for tunnels.
In December of 2021, the European Commission proposed a new regulation on new guidelines [the European Commission's proposal for a new Regulation on TEN-T guidelines (COM 2021/821)], that included the Black Sea and Aegean Sea in the list of newly agreed transport corridors [1].Therefore, the above-mentioned road tunnels to build in Georgia should be considered as part of the Trans-European Transport Network.
These tunnels are built on mountainous terrain to overcome the most difficult sections of the roads.In the future, with the construction and operation of new tunnels, freight turnover and traffic intensity will naturally increase.As for the traffic increase, it directly increases fire risks.It should also be noted that the lengths of the existing and future tunnels vary.There are also short tunnels with different inclinations among them, and they must be ventilated by natural traction.Therefore, studying different scenarios of fire development in similar circumstances is necessary.

Fire strength and considered harmful factors
Scenarios of fire development in tunnels are studied using computer modeling.The process are analyzed using the results obtained by CFD models, what, in our opinion, makes it possible to adequately predict rapidly changing underground situations with lower expenses.A transport tunnel is presented as a complex engineering structure with limited spatial dimensions extending in one direction with a concentrated traffic flow.This circumstance makes the emergency management in a tunnel specific -the emergency management in a confined space.
For life saving purposes during the fire, the present article considers the following harmful factors: high temperature, high concentrations of carbon monoxide and carbon dioxide, and sharply reduced concentration of oxygen.
The change in the average time of onset of hyperthermic human shock caused by one of the harmful factors, the abnormal temperature, is given in Table 1, and the data on fire strength by the number of burning vehicles are given in Table 2.These tables are useful in planning and implementing evacuation.

Numerical modeling
The magnitude and direction of natural traction vary greatly depending on the hypsometric location of tunnel portals, their geometry, location, spatial orientation and other similar conditions.Therefore, in most cases natural traction cannot be calculated theoretically, but its reliable measurement is possible only by natural observations.To build numerical models during the fire, the pressure difference between the portals can be determined with barometric formula, since in this case the direction of combustion products is dictated by their lower density and, hence, their ascending movement along the tunnel centerline.In this case, it is possible to calculate the pressure difference between the tunnel portals using the hypsometric data of the portals necessary to realize the boundary conditions for the numerical models.The barometric formula is as follows Where  ℎ is the pressure value for the portal located at altitude ℎ asl, Pa;  0 is the numerical value of atmospheric pressure at sea level, in the realized numerical problems,  0 =101 325 Pa;  is the air molecular mass, kg;  is the of gravity acceleration, m/s 2 ; ℎ is the height difference relative to sea level, m;  is the Boltzmann constant, J/;  is the absolute air temperature at given level, , in the realized numerical problems:  = 293.2.
The difference between hypsometric levels of the portals can be calculated using a simple formula that was used to realize the boundary conditions for the models Where ∆ℎ is the height difference between the portals, m;  is the tunnel slope, %; the range of slope variation in the realized numerical problems was 1-9 %;  is the tunnel length, m; the tunnel length in the realized numerical problems was 400 m.
In accordance with Georgian regulations, up to 400-meter-long tunnels do not necessarily require artificial ventilation systems.So, in this case, the fire-induced harmful factors will propagate in natural ventilation conditions.It should be noted that in case of natural ventilation in inclined tunnels, like with artificial ventilation, the propagation of toxic combustion products is characterized by pronounced asymmetry along the axial line of the tunnel [2,3].
It is known that in order to investigate the mentioned problem, we created a numerical model of the tunnel with the following geometrical and physical parameters: 1. tunnel length: 400 m; 2. power strength modeled in the tunnel: 5, 10, 15, 20, 30, 50 MW; 3. tunnel crosssection area: 42.5 m 2 ; 4. tunnel slope: 0, 1, 3, 5, 7, 9 %; 5. duration of the simulated process: 180 s; 6. minimum size of a finite volume cell: 0.25 x 0.25 x 0.25 m; 7. combustible substance polyurethane M 27; 8. burning surface area: 5-10 m 2 ; 9. fire location: central part of the tunnel; 10. harmful factors and processes typical of the fire studied: a sharp increase in temperature and in the concentrations of carbon monoxide and carbon dioxide, as well as a sharp decrease in oxygen concentration.
In order to bring numerical models closer to real natural conditions, boundary conditions were provided in advance to ensure the barometric pressure difference between the tunnel portals.The basic requirement was to consider standard atmospheric conditions according to formulas (1) and ( 2).The baseline values required for the calculation and the numerical values obtained are given in Table 3.

Results and Discussion
Given the interests of the practical application of the results obtained, it is advisable to present the results of the study as characteristics of transitional processes varying in time.
Along with the asymmetric nature of the propagation of toxic products of combustion, along the axial line of the tunnel, a similar pattern of the propagation of harmful factors should be noted.In particular, e.g. the pattern of smoke propagation in the underground space repeats the pattern of propagation of increased concentration of carbon monoxide, etc.So, the propagation pattern is similar for all harmful factors.Following the above-mentioned, it is possible to fully describe the dynamics of the propagation of harmful factors, in the first approximation, based on the characterization of only one of the factors.
Fig. 1 shows the variation of the backlayering length of smoke induced in the simulated problem in a 7% slope tunnel with a 50 MW fire.The presented graphs clearly show a qualitative picture of the propagation of the harmful factors induced by fire on the ascending and descending sides of natural ventilation.From the fire location on the ascending side, the harmful factors grow intensely, while on the descending side of fire, rapid transitional processes occur, with varying duration, intensity and backlayering distance of harmful factors.
It should also be noted that the strong turbulence on the ascending side practically eliminates the stratification of the ventilation flow because of different densities.As a result, each type of harmful factors in the entire cross section of the tunnel has its unique maximum concentration.
The maximum distance of descending propagation of toxic combustion products varies depending on tunnel slope and fire strength.This dependence is shown in Fig. 2. As the presented graphs show, the maximum variation range of the backlayering length of 100-150 m corresponds to the minimum tunnel slope between 1 and 3%.As the numerical value of the slope increases, the distance of backlayering decreases.In particular, the backlayering length is 50-70 m for 5-7% tunnel slopes, and is reduced to 35-50 m for 9% tunnel slope.
As the presented results of the numerical modeling show, the tunnel slope and fire strength are the main factors determining the backlayering length of toxic admixtures on a clean jet what is important to consider in saving lives.To save lives and control emergency situations in case of fire, it is also important to be able to estimate the duration of the nonstationary and transitional process of propagation of the harmful factors.Numerical studies have been conducted in this area, too, and the variation of the backlayering duration on the descending side of the tunnel depending on the fire strength and tunnel slope is shown in Fig. 3.

Fig. 3. Variation of backlayering duration on the descending side of the tunnel depending on fire strength and tunnel slope
The graph in Fig. 3 clearly shows that backlayering in tunnels with a 1% slope virtually lasts during modeling, i.e. for 180 seconds for any strength of fire modeled by us.In a tunnel with a 3% gradient, backlayering duration is reduced to 80-120 s, depending on the fire strength.Backlayering duration in tunnels with a 5% slope is within the range of 40-90 s; it is 40-75 s in 7%-sloping tunnels, and 30-50 s in 9%-sloping tunnels.Thus, tunnel slope and fire strength are inversely proportional to the sought values, which, as we have already pointed out, are the backlayering length and the backlayering duration.

Conclusion
-According to the results of the numerical modeling, the backlayering length of the combustion product and the duration of underground transitional processes in inclined road tunnels are strongly influenced by the slope of the tunnel, while the fire strength has less influence.Both tunnel slope and fire strength have an inverse effect on these values.-In case of 5-50 MW fire in a 400-meter-long tunnel with a slope of 1-9%, the range of the backlayering distance variation is 25-150 m and the backlayering duration is 30-180 s. -According to the results of numerical modeling, all other conditions being equal, a great slope of the tunnel should be considered as a negative factor from the point of view of tunnel ventilation and fire safety.

Fig. 1 .
Fig. 1.Variation of the backlayering length (a transitional process) in a 7% slope tunnel with a 50 MW fire

Fig. 2 .
Fig. 2. Variation of maximum backlayering distance depending on tunnel slope and fire strength This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSF) [Grant number FR-22-12 949].Title: Study of critical velocity and fire-induced back-layering to save lives in road tunnels.Special thanks to Ms. Thea Dolidze for her invaluable contribution to the English translation of the paper.

Table 1 .
Average time of onset of hyperthermic shock in humans

Table 2 .
Fire strength in a transport tunnel depending on the type and number of burning vehicles

Table 3 .
Barometric pressure difference between the portals