# Effect of the Metro Train on the Smoke Back-Layering Length under Different Tunnel Cross-Sections
## 2 Literature Review  
The back layer of smoke is an important aspect of fire research in longitudinal ventilation tunnels. It has been extensively studied by researchers [4; 6; 7; 8]. [PERSON] [6] proposed an equation to predict the back-layering length based on theoretical analysis and the results of small-scale experiments. \[\frac{L}{H}\propto\frac{gHQ}{\rho_{a}c_{p}T_{f}V^{3}A} \tag{1}\]  
Figure 1: The research framework. Based on the theoretical analysis, [PERSON] et al. [7] proposed the back-layering length model by conducting full-scale experiments and FDS simulations results. \[ \begin{array}{c}L=\ln\left[K_{2}\left(\frac{C_{\rm L}H}{V^{2}}\right)\right]/0.019\\ K_{2}=g\gamma\left(\frac{G^{*2/3}}{F^{1/3}}\right)^{\epsilon}\\ \left\{\begin{array}{cc}\gamma=1.77,\epsilon=6/5&\left(Q^{*2/3}/F^{1/3}_{r} <1.35\right)\\ \gamma=2.54,\epsilon=0&\left(Q^{*2/3}/F^{1/3}_{r}>1.35\right)\end{array}\right. \end{array}  \tag{2}\]  
[PERSON] et al. [4] and [PERSON] et al. [8] proposed prediction models for back-layering length based on dimensionless analysis. The model proposed by [PERSON] et al. [3] is expressed as  
\[L^{*}=\left\{ \begin{array}{cc}18.5\ln\left(0.81Q^{*1/3}/V^{*}\right)&Q^{*} \leq 0.15\\ 18.5\ln\left(0.43/V^{*}\right)&Q^{*}>0.15\end{array} \right. \tag{3}\]  
The model proposed by [PERSON] et al. [8], considering the sectional coefficient \(\xi(\xi=A/H^{2})\), is expressed as,  
\[L^{*}=\left\{ \begin{array}{cc}6.41\ln\left(Q^{*}/V^{*3}\right)-3.58&\xi\geq 1 \\ 8.32\ln\left(Q^{*}/V^{*3}\right)-5.81&\xi<1\end{array} \right. \tag{4}\]  
Following these studies, many researchers have studied the effects of several other factors on the back-layering length, and proposed a series of new prediction models, such as tunnel slope [9], cross section [10], turning radius [11], ceiling extraction [12; 13; 14], branched tunnel [15], and ambient pressure [16; 17; 18]. In recent years, benefiting from the evolutions of artificial intelligence (AI) and big data, data-driven methods, especially artificial neural networks (ANNs) [19], have been increasingly applied in fire safety research. [PERSON] et al. [20] applied the framework of artificial intelligence (AI) and big data to predict fire sources in a numerical model of tunnels. [PERSON] et al. [21] proposed a method to automatically control fire-induced smoke by coupling a full-field CFD model and a PID algorithm. The ventilation system is controlled by the PID algorithm to automatically adjust the ventilation speed, so that the smoke back-layering is controlled within a certain range. Additionally, many scholars [22; 23; 24; 25; 26; 27; 28] have studied the influence of blockage on the smoke back-layering length. [PERSON] et al. [29] reviews recent research advances relating to critical velocity and the back-layering length of tunnel fires, mainly analyzing the experimental and theoretical studies on the effects of blockage, inclination, and fire source location. [PERSON] et al. [30] studied the effect of solid barriers and blockages on the length of smoke back-layering and critical velocity for a fire in a longitudinally ventilated tunnel. [PERSON] et al. [22] investigated the effect of (upstream) blockage-fire distance on the smoke back-layering length using experiments in a model tunnel, and a model for predicting the reverse layer was proposed, taking into account the distance coefficient between the fire and the obstacle. [PERSON] et al. [24; 25] considered the effect of metro trains on smoke back-layering. They found that the influence of metro trains on fires in tunnels cannot be neglected, and they proposed a new smoke back layer prediction model based on theoretical analysis through small scale experiments and numerical simulation results, respectively. The model proposed by the experiments is represented as [25],  
\[L^{*}=\left\{ \begin{array}{cc}6.956\ln\left(\frac{1.712Q^{*1/3}}{V^{*}/(1- \phi)}\right)&Q^{*1/3}\leq Q^{*1/3}_{L=L_{t}}\\ L^{*}_{t}+19.342\ln\left(\frac{0.935Q^{*1/3}_{b-T}}{V^{*}}\right)&Q^{*1/3}>Q^{*1 /3}_{L=L_{t}}\end{array} \right.