Analysis of the Stability of the Double-Hole Complementary Ventilation and Ventilation Network of the Tunnel Constructed by Drilling and Blasting Method

Abstract

Currently, double-hole complementary ventilation is a mature ventilation method for operating tunnels, but how to carry out it in the construction tunnel poses a new challenge. Due to the desynchronization in the construction period of the double-hole tunnel, there is an instantaneous difference in the air flow demand between the two working faces. The study analyzes the impact of geometric parameters, specifically L_t (the distance from the traffic cross passage to the working face of the advance side tunnel), L_p (the distance between the pedestrian cross passage and the working face of the advance side tunnel), H_t (height of the upper step), and L_w (safe step distance of the double-hole working face) on ventilation network stability. The results show that with the increase of L_t and L_p, the R_m resistance of each branch changes non-uniformly, and the stability of the ventilation network is significantly different. Then, when L_t, L_p = 80 and 180 m, the air flow directions of the double-hole tunnel are the same. Finally, when L_t and L_p = 130 m, the air flow directions are inconsistent, which indicates that in the range of 80 m < L_t or L_p < 180 m, the cross-section size of the cross passage affects the stability of the ventilation network. However, when 2.5 m < H_t < 3 m, or 30 m < L_w < 50 m, the stability of the ventilation network is not affected, and the flow field of the double-holes does not interfere with each other. The conclusions obtained confirm that the double-hole complementary ventilation method is available in construction tunnels, and has potential for implementation.

1. Introduction

In recent years, China has implemented the Western Development Policy, the construction of transportation infrastructure has shifted westward, and the scale and structure of the road network in the western region have been continuously improved. Due to the dense mountains and ravines in the western region, tunnel engineering is developing in the direction of “deep burial, long distance, and large cross-section” [1,2,3]. The complex construction technology and harsh conditions of the long highway tunnel have brought new challenges to the tunnel ventilation. If the ventilation is not smooth, pollutants such as CO and dust cannot be removed from the tunnel effectively. This situation may cause dyspnea for construction workers and lead to death by suffocation in severe cases [4,5,6]. In the selection of ventilation methods for long highway tunnels, full diameter air flow ducts are mostly used to match high-power forced ventilations in foreign countries [7], while in China, inclined shafts, parallel pilot tunnels, and shafts are usually built and a combination of forced and roadway ventilation methods are adopted [8,9]. Through numerical simulation and on-site monitoring, scholars discussed the above ventilation measures and ventilation effects, and summarized the air flow and pollutant migration laws in the tunnel under the forced ventilation method [4,10,11]. At the same time, the correction coefficients of key parameters such as air flow demand, fan efficiency, air flow duct leakage rate, and air flow duct resistance during tunnel construction ventilation are also studied, which provides theoretical guidance for tunnel construction [12,13,14,15,16]. However, most of the above-mentioned studies focus on single-hole tunnels, and few scholars focus on the construction and ventilation of double-hole tunnels.

In contrast, the double-hole tunnel has the following advantages: (1) During the construction period, the construction difficulty is small, and the probability of collapse is small [17]; (2) During operation, the piston air flow can be fully utilized to achieve the complementarity of the two holes [18]; (3) In terms of disaster prevention and rescue, when a major accident occurs in one tunnel, the other tunnel can operate normally and can be used for rescue and evacuation [19]. Based on the above advantages, the construction of a double-hole tunnel has shown a new trend. A double-hole tunnel includes an advance side tunnel, undercut side tunnel, pedestrian crossings, and traffic crossings [20,21]. When ventilating the tunnel, the maximum air flow demand of tunnels should be determined by a number of factors; for example, the smoke discharged from the working face of the double tunnel, the maximum number of workers, the minimum allowable air flow velocity, the degree of dilution of exhaust gases from internal combustion engines. Then fresh air flow should be directed to the working face through forced air flow ducts to meet the ventilation demand [22,23,24]. After fresh air flows back twice, air flow resistance R_m of each branch of the double-hole tunnel must be overcome before it can be discharged into the atmosphere. At present, the influence of factors such as the difference in the air flow demand of the two holes, the distance from the cross passage to the working face, and the safe layout distance between the double-hole working faces caused by the asynchronous construction period on the stability of R_m and ventilation network is not clear.

This paper takes the air flow direction of the double-hole tunnel as the main research object, explores the diffusion law of air flow under the difference of air flow demand in the double-hole tunnel and the influence of multiple factors on the stability of the double-hole tunnel ventilation network, and provides theoretical guidance for the measurement of ventilation effect and the formulation of construction procedures in the construction of double-hole tunnel on the basis of the Qinlan Tunnel of Tianba Expressway and the method of combination of numerical simulations and field tests.

2. Engineering Background

2.1. Project Overview

The Qinlan Tunnel area belongs to the karst cluster depression landform, the tunnel passes through the mountain, and the designed tunnel is a long tunnel with small clear separation, which is a deep-buried, double-hole six-lane tunnel with a maximum buried depth of about 356.7 m. The design length of the advance side tunnel is 2170 m, of the undercut side tunnel, 2160 m, of the cross passage, 20 m. Among them, the advance side tunnel and the undercut side tunnel are semicircular arches with a width of 15 m and a height of 7.5 m, the grade of the surrounding rock of the cave body is mainly III~IV, and according to The Code for Construction Design of Highway Tunnels [25], the short step method is selected for excavation, and the step length is 30 m. At the same time, the diameter of the forced air flow duct is 1.5 m, and the distance from the inlet to the working face is 30 m, which can make the fresh air flow outside the tunnel reach the working face smoothly.

Both tunnels are ventilated by forced ventilation. The tunnel construction mainly includes drilling, blasting, slag removal, secondary lining, and other processes; the on-site construction schematic diagram is shown in Figure 1. Forced ventilation should consider the exhaust of blasting gases from the working face, the maximum number of workers in the tunnel, the minimum allowable air flow velocity, the degree of dilution and discharge of exhaust gas from the internal combustion engine, etc, and then comprehensively determine the maximum value of the required air flow volume; the required air flow volume of the unilateral tunnel is shown in

Table 1. Calculation of air flow demand of working face under different working conditions.

	Exhaust the Blasting Gases	Maximum Number of Workers	The Minimum Permissible Air Flow Velocity	Dilution of Internal Combustion Engine Exhaust Gases
Calculations	$Q_{\mathrm{y}}=\frac{7.8}{t}\sqrt[3]{{G\left({AL}_{\mathrm{p}}\right)}^2}$	$Q_{\mathrm{p}}=k_{\mathrm{f}}m{q}_{\mathrm{f}}$	$Q_{\mathrm{w}}=60\mathrm{v}A$	$Q_{\mathrm{f}}=q{\displaystyle \sum \mathrm{w}}$
air flow demand	1769.4 m3/min	202.4 m3/min	796.5 m3/min	1824.6 m3/min

[8].

As can be seen from Table 1, the maximum air flow demand of the unilateral tunnel is 1824.6 m³/min, and the air flow supply volume of the forced ventilator is calculated considering the air flow leakage volume of the forced ventilation pipe. The air flow supply volume of the fan is calculated by the following formula:

$$Q_{\mathrm{j}}=P_{\mathrm{b}}{Q}_Z$$

(1)

Among them, Q_z is the air flow demand of the working face, m³/s; Q_j is the air flow supply volume of the fan, m³/s; P_b is the air flow leakage rate of the forced duct, % is calculated as follows:

$$P_{\mathrm{b}}=\frac{1}{1-\frac{L_{\mathrm{g}}}{100}{P}_{100}}$$

(2)

Among them, L_g is the length of the pipe, take the longest pipe length, m; P₁₀₀ is the average air flow leakage rate of 100 m, take 1%.

Accordingly, the 2 × 75 kW axial flow fan SDF (C)-NO11.5 was selected to supply fresh air flow to the tunnel, with a rated air flow volume of 1171 m³/min~2285 m³/min and an air flow pressure of 727 Pa~4629 Pa, which could meet the ventilation requirements of the unilateral tunnel.

2.2. On-Site Measurement

In order to visually analyze the ventilation situation in the double-hole tunnel, the TSI air flow velocity measuring instrument was used to measure the air flow velocities of the six measuring points shown in Figure 2, and air flow velocities were recorded once every 20 m, so as to obtain the velocity distribution law of the double-hole tunnel. During the measurement process, the slag is transported in the advance side tunnel, and the forced fan outside the tunnel is turned on at high velocity. The undercut side tunnel is lined twice, and the ventilator outside the tunnel is turned on at low velocity.

Figure 3 shows the air flow velocity distribution at the measurement points of the double-hole tunnel; Figure 3a is the air flow velocity distribution at measurement points of the undercut side tunnel; and Figure 3b is the air flow velocity distribution of the advance side tunnel. It can be seen from Figure 3a that in the range of 60 m~120 m from the working face, the air flow velocity at the measuring points in the undercut side tunnel show a downward trend as a whole. In the range of 120 m~180 m, the air flow velocity at the measuring points rise first and then stabilize. As can be seen from Figure 3b, the air flow velocity at the measurement points of the advance side tunnel show an overall downward trend. It is worth noting that the distance between the central axis of the cross passage and the working face of the advance side tunnel is 130 m, and the air flow velocity fluctuates around the cross passage in Figure 3a, indicating that the cross passage may have an impact on the flow field of the double-hole tunnel.

3. Theoretical Analysis and Numerical Model

3.1. Theoretical Analysis of Air Flow Direction

The air flow in the ventilation network of the double-hole tunnel follows the law of resistance, the law of energy conservation, the conservation of nodal air flow volume, and the law of loop energy balance. Figure 4 is a ventilation network diagram of a double-hole, single-cross passage, wherein the junction of the cross passage and the advance side tunnel is node 3, the junction of the cross passage and the undercut side tunnel is node 4, the air flow direction in the tunnel depends on the pressure of nodes 3 and 4, the air flows from the node with high energy level to the node with low energy potential, and when the energy potential of the two nodes is the same, the air flow is stagnant.

According to the law of energy balance of the loop, Equation (3) can be obtained:

R₁Q₁² + R₃Q₃² = R₂Q₂² + R₄Q₄²

(3)

The pressure energy difference between node 3 and node 4 is:

E_3–4 = R₁Q₁² − R₂Q₂²

(4)

When there is no air flow in the traffic cross passage, E_3–4 = 0:

R₁Q₁² = R₂Q₂², R₃Q₃² = R₄Q₄²

(5)

From (5), it can be obtained:

$$\frac{R_1{R}_4}{R_2{R}_3}={\left(\frac{Q_2{Q}_3}{Q_1{Q}_4}\right)}^2=1$$

(6)

When the air flow direction in the cross passage is from node 3 → node 4, the pressure energy of node 3 is higher than that of node 4, E_3–4 > 0, which is:

R₁Q₁² > R₂Q₂², R₃Q₃² > R₄Q₄²

(7)

From (7), it can be obtained:

$$\frac{R_1{R}_4}{R_2{R}_3}<{\left(\frac{Q_2{Q}_3}{Q_1{Q}_4}\right)}^2<1$$

(8)

In the same way, when the air flow direction in the cross passage is changed from node 4 → node 3, the relation is:

$$\frac{R_1{R}_4}{R_2{R}_3}>{\left(\frac{Q_2{Q}_3}{Q_1{Q}_4}\right)}^2>1$$

(9)

Combining (6), (8), and (9) gives discriminant (10):

$$K=\frac{R_1{R}_4}{R_2{R}_3}\left\{\begin{array}{l}>1,\hspace{1em}\mathrm{The} \mathrm{wind} \mathrm{direction} \mathrm{in} \mathrm{the} \mathrm{transverse} \mathrm{channel} \mathrm{is} \mathrm{from} \mathrm{node} 4 \mathrm{to} \mathrm{node} 3;\\ =1,\hspace{1em}\mathrm{The} \mathrm{wind} \mathrm{flow} \mathrm{in} \mathrm{the} \mathrm{transverse} \mathrm{channel} \mathrm{is} \mathrm{stagnant};\\ <1,\hspace{1em}\mathrm{The} \mathrm{wind} \mathrm{direction} \mathrm{in} \mathrm{the} \mathrm{transverse} \mathrm{channel} \mathrm{is} \mathrm{from} \mathrm{node} 3 \mathrm{to} \mathrm{node} 4.\end{array}\right.$$

(10)

Through numerical simulation, the flow Q_m of A-A, B-B, C-C, and D-D sections in the four branches is obtained, as well as the resistance h_m of each branch and the air flow resistance R_m of each branch, and then the air flow resistance R_m of each branch is substituted into Equation (10) for theoretical calculation, and the air flow direction of the double-hole tunnel can be determined by the K obtained.

3.2. Physical Models and Meshing

According to the actual working conditions of the tunnel, the ventilation model of the double-hole, single-cross passage tunnel is established at a scale of 1:1. The forced fan is about 30 m outside the tunnel, not reflected in the model. The model includes the advance side tunnel, the undercut side tunnel, the cross passage, the second lining platform car, and the forced duct. Among them, the cross passage is divided into a pedestrian cross passage and a traffic cross passage, the pedestrian cross passage is 2.5 m wide and 3.7 m high, and the traffic cross passage is 6.25 m wide and 6.97 m high. In Figure 5, the distance from the traffic cross passage to the working face of the advance side tunnel is L_t, the distance between the pedestrian cross passage and the working face of the advance side tunnel is L_p, the safe distribution distance of the working faces of the double-hole tunnel is L_w, and the height from the upper step to the tunnel floor is H_t.

The quality of the mesh affects the accuracy of the simulation results, so it is important to verify the independence of the mesh, and the air flow velocity is the primary metric for verifying the independence of the mesh. Import the model into ANSYS Workbench and mesh the entire model by Mesh, including low (1,091,336 elements), medium (1,909,446), and high (4,225,884) mesh quality. Under the three different meshing schemes, the velocity distribution of different measurement points in the advance side tunnel and the undercut side tunnel is shown in Figure 6.

Considering the computer performance and simulation error, the medium grid quality scheme is adopted with a total of 1,909,446 grids, with an average grid size of 0.83, a maximum of 1, and a minimum of 0.15.

3.3. Mathematical Models

The air flow velocity in the tunnel is not large and the pressure change is small, so the compressibility of the air flow can be ignored. Therefore, the air flow in the tunnel is considered as a three-dimensional incompressible and stable viscous turbulence. The model of turbulent flow is a high Reynolds number k-ε model. Mathematical models include continuity equations, momentum equations, and k-ε model equations [26,27].

Incompressible Continuity Equation:

$$\frac{\partial \rho {\overline{u}}_i}{\partial x_i}=0$$

(11)

Incompressible Momentum Equation:

$$\frac{\partial (\rho {\overline{u}}_i)}{\partial t}+\frac{\partial (\rho {\overline{u}}_i{\overline{u}}_j)}{\partial x_i}=\rho f_i-\frac{\partial p}{\partial x_i}+\frac{\partial }{x_i}(\mu \frac{\partial {\overline{u}}_i}{\partial x_i})-\frac{\partial (\rho {\overline{u}}_i^{\prime }{\overline{u}}_j^{\prime })}{\partial x_j}$$

(12)

Realizable k-ε Turbulence model:

$$u_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$

(13)

k equation:

$$\frac{\partial k}{\partial t}+{\overline{u}}_j\frac{\partial k}{\partial j}=v_t\left(\frac{\partial {\overline{u}}_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)\frac{\partial {\overline{u}}_i}{\partial x_j}-\frac{\partial }{\partial x_j}\left[\left(\frac{v_t}{{\sigma }_k}-v\right)\frac{\partial k}{\partial x_j}\right]-\epsilon$$

(14)

ε equation:

$$\frac{\partial \epsilon }{\partial t}+{\overline{u}}_j\frac{\partial \epsilon }{x_j}=-C_{{\epsilon }_1}\left(\partial {\overline{u}}_i{\overline{u}}_j\right)\frac{\partial {\overline{u}}_i}{\partial x_j}-\frac{\partial }{\partial x}\left[\left(\frac{v_t}{{\sigma }_{\epsilon }}-v\right)\frac{\partial \epsilon }{\partial x_j}\right]-C_{{\epsilon }_2}\frac{{\epsilon }^2}{K}$$

(15)

In Equations (11)–(15), ρ is the fluid density, kg/m³; u_i and u_j are the velocity components of the fluid, m/s, respectively; p is the pressure on the fluid microelement, Pa; μ is the dynamic viscosity, Pa·s; μ_t is the turbulent viscosity Pa·s; k is the turbulent flow energy, m²/s²; ε is the dissipation rate, m³/s; σ_k and σ_ε are the Prandtl numbers corresponding to k and ε equations, respectively. According to the relevant experiments, the model constants were C_μ = 0.09, C_ε1 = 1.44, C_ε2 = 1.92, σ_k = 1.0, and σ_ε = 1.3.

3.4. Boundary Condition Settings

The generated mesh was imported into Fluent for fluid simulation, solved using a pressure-based steady-state solver affected by elevation factors, and the turbulence model was selected as an achievable equation model, and the parameter properties and value settings are shown in

Table 2. Main parameters in the numerical simulation.

	Set Options		Parameter Setting
Boundary conditions	Inlet boundary conditions		Velocity inlet
	Outlet boundary conditions		Pressure outlet
	Qa > Qu	inlet1 (m/s)	8.16
		inlet2 (m/s)	16.18
	Qa < Qu	inlet1 (m/s)	16.18
		inlet2 (m/s)	8.16
Solver settings	Time		stable
	Solver type		Pressure-based
	Energy equation		Off
	Turbulence model		Realizable k-ε
	Pressure-velocity coupling scheme		simple

. The air flow demand of the advance side tunnel is Q_a, and the air flow demand of the undercut side tunnel is Q_u. In order to reflect the difference of the air flow demand of the double-hole tunnel: when Q_a > Q_u, inlet1 = 8.16 m/s and inlet2 = 16.18 m/s; when Q_a < Q_u, inlet1 = 16.18 m/s and inlet2 = 8.16 m/s.

3.5. Comparison between Measured and Simulated

Due to the possible differences between the tunnel model and the construction site, in order to verify the accuracy of the tunnel model, the measured values of E, F, and G measurement points at the human breathing height of 1.6 m in Figure 2 were compared with the simulated values, as shown in Figure 7. As can be seen in Figure 7, the relative error of the measured value and the numerical simulation value of each measurement point are within ±10%, and the air flow velocity and numerical simulation results at each measurement point of the double-hole tunnel are basically the same, and the tunnel flow field obtained by numerical simulation can be considered to be accurate.

Figure 8 is the vector diagram of the air flow of the tunnel at L_t = 130 m. It can be seen from Figure 8 that there is a vortex area in the air flow of the tunnel in the advanced side tunnel, which flows to the undercut side tunnel along the top of the traffic cross passage, and the air flow in the middle and lower part of the vortex is redirected and flows back into the advanced side tunnel; K = 22.49 > 1 is obtained by extracting the flow and resistance of each branch of the double-hole tunnel. Also, the air flow can be clearly determined from the undercut side tunnel to the advance side tunnel, which is consistent with the direction of smoke flow diffusion at the scene in Figure 4.

4. Analysis of Results

4.1. Effect of L_t on the Stability of Ventilation Network

According to the discriminant Equation (10), it can be seen that the air flow direction in the cross passage completely depends on the air flow–resistance ratio of the advance side tunnel and the undercut side tunnel, and has nothing to do with the air flow resistance of the cross passage itself.

The air flow resistance of each branch:

R_m = h_m/Q_m²

(16)

Among them, Q_m is the flow rate of each branch of the double-hole tunnel, and h_m is the resistance of each branch.

Figure 9 shows the comparison of the flow rate of each section of the tunnel under different L_t conditions. In Figure 9, if Q_a > Q_u, when the L_t is 80 m, 130 m, and 180 m, the air flow through the traffic cross passage decreases by 0.9, 1, and 0.23 m³/s (Q₁ − Q₃), respectively, and the cross-section flow rate of the undercut side tunnel increases by 2, 1.1, and 0.3 m³/s, respectively (Q₄ − Q₂). With the increase of L_t, the dynamic energy dispersion rate in the traffic cross passage increases, and the flow rate near the working face of the advance side tunnel continues to increase. If Q_a < Q_u, when the L_t is 80 m, 130 m, and 180 m, the air flow decreases by 16.7, 1.8, and 0.17 m³/s, respectively after the air flows through the cross passage, and the cross-section flow rate of the undercut side tunnel increases by 18.7, 2.1, and 0.19 m³/s, respectively.

Figure 10 shows the comparison of the resistance of each branch of the tunnel under different L_t conditions. In Figure 10, the resistance h_m of each branch decreases as L_t increases. Combined with the data in Figure 9 and Figure 10, the air flow resistance R_m of each branch can be calculated, and then K is obtained according to the discriminant Equation (10), which are summarized in

Table 3. Comparison of K and Rm of each branch under different L_t conditions.

Lt/(m)	Difference in the Air Flow Demand of Two Holes	R1/(N·s2/m8)	R2/(N·s2/m8)	R3/(N·s2/m8)	R4/(N·s2/m8)	K
80	Qa > Qu	3.0 × 10−3	5.4 × 10−3	5.5 × 10−5	6.9 × 10−5	0.69
	Qa < Qu	4.7 × 10−4	1.7 × 10−2	3.6 × 10−3	1.2 × 10−3	0.009
130	Qa > Qu	4.4 × 10−5	8.9 × 10−6	5.6 × 10−6	2.6 × 10−5	22.49
	Qa < Qu	1.1 × 10−4	4.6 × 10−4	9.1 × 10−6	3.8 × 10−5	1.26
180	Qa > Qu	6.5 × 10−6	8.4 × 10−6	1.7 × 10−6	9.3 × 10−6	4.19
	Qa < Qu	8.8 × 10−6	1.7 × 10−5	9.9 × 10−6	1.5 × 10−5	0.77

.

It can be seen from Table 3 that the R_m of each branch decreases with the increase of L_t, but the degree of decrease is different, resulting in an obvious difference in the K. When L_t = 80 m, Q_a > Q_u, K = 0.69 < 1; Q_a < Q_u, K = 0.009 < 1, it indicates that the air flows from the advance side tunnel to the undercut side tunnel. When L_t = 130 m, Q_a > Q_u, K = 22.49 > 1; Q_a < Q_u, K = 1.26 > 1, it indicates that the air flows from the undercut side tunnel to the advance side tunnel. When L_t = 180 m, if Q_a > Q_u, K = 4.19 > 1, the air flows from the undercut side tunnel to the advance side tunnel. If Q_a < Q_u, K = 0.77 < 1, the air flows from the advance side tunnel to the undercut side tunnel.

4.2. Effect of L_p on the Stability of Ventilation Network

Furthermore, in order to study the influence of different L_p on the air flow direction of the tunnel, the multi-section flow Q_m and resistance h_m of the tunnel were extracted, as shown in Figure 11 and Figure 12. If Q_a > Q_u, when L_p = 80 m, the cross-sectional flow rate of the advance side tunnel decreases by 2.2 m³/s (Q₁ − Q₃), and the cross-sectional flow rate of the undercut side tunnel increases by 1.5 m³/s (Q₄ − Q₂); when L_p = 130 m, the cross-sectional flow rate of the advance side tunnel increases by 0.11 m³/s, and the cross-sectional flow rate of the undercut side tunnel decreases by 0.11 m³/s; when L_p = 180 m, the cross-sectional flow rate of the advance side tunnel increases by 0.04 m³/s, and the cross-sectional flow of the undercut side tunnel decreases by 0.04 m³/s. If Q_a < Q_u, when L_p is 80 m, 130 m, and 180 m, the cross-sectional flow rate of the advance side tunnel decreases by 3.4, 0.5, and 0.04 m³/s, respectively, and the cross-sectional flow rate of the undercut side tunnel increases by 3.2, 0.5, and 0.07 m³/s, respectively.

In Figure 12, with the increase of L_p, the resistance h_m of each branch also decreases, but the trend of h_m is different from that in Figure 10. Combined with the data in Figure 11 and Figure 12, the R_m and K under different L_p conditions are calculated and summarized in

Table 4. Comparison of K and R_m of each branch under different L_p conditions.

Lp/(m)	Difference in the Air Flow Demand of Two Holes	R1/(N·s2/m8)	R2/(N·s2/m8)	R3/(N·s2/m8)	R4/(N·s2/m8)	K
80	Qa > Qu	9 × 10−4	1 × 10−2	1.4 × 10−4	7.4 × 10−4	0.45
	Qa < Qu	2.4 × 10−4	3.9 × 10−3	3.1 × 10−4	1.8 × 10−4	0.036
130	Qa > Qu	1.4 × 10−4	9.3 × 10−5	2.9 × 10−5	5.7 × 10−5	3.003
	Qa < Qu	2.7 × 10−5	7.6 × 10−5	2.3 × 10−5	3.6 × 10−5	0.551
180	Qa > Qu	1.8 × 10−5	2.2 × 10−5	6.6 × 10−6	1.8 × 10−5	2.257
	Qa < Qu	1.3 × 10−6	9.9 × 10−6	4.3 × 10−6	1.2 × 10−5	0.350

. When L_p = 80 m, Q_a > Q_u, K = 0.45 < 1; Q_a < Q_u, K = 0.036 < 1, indicating that the air flows from the advance side tunnel to the undercut side tunnel. When L_p = 130 m, Q_a > Q_u, K = 3.003 > 1, the air flows from the undercut side tunnel to the advance side tunnel, Q_a < Q_u, K = 0.551 < 1, and the air flows from the advance side tunnel to the undercut side tunnel. When L_p = 180 m, if Q_a > Q_u, K = 2.257 > 1, the air flows from the undercut side tunnel to the advance side tunnel, if Q_a < Q_u, K = 0.35 < 1, the air flows from the precedent tunnel to the undercut side tunnel.

In summary, when L_t, L_p = 80 and 180 m, the air flow direction of the tunnel is not restricted by the cross-section size of the cross passage: when L_t, L_p = 80 m, the air flows from the advance side tunnel to the undercut side tunnel; when L_t and L_p = 180 m, the air flows from the tunnel with small air flow demand to the tunnel with large air flow demand. When L_t = 130 m, the air flows from the undercut side hole to the advance side hole. However, when L_p = 130 m, the air flows from the tunnel with small air flow demand to the tunnel with large air flow demand, which indicates that the size of the cross passage affects the air flow direction of the double-hole tunnel.

4.3. Effect of H_t on the Stability of the Ventilation Network

The height of the upper step should be determined by the height of the tunnel section, the stability of mechanical equipment and the surrounding rock. The height of the upper step excavation H_t should be 2.5~3.5 m. The flow rate and resistance of each branch of the tunnel under different H_t conditions are shown in Figure 13 and Figure 14.

It can be seen from Figure 13 that when H_t = 2.5 and 3.5 m, Q₁ = 28.1 and 28 m³/s, respectively, after the air flowed through the cross passage, the cross-section flow of the advance side tunnel decreased by 1.1 and 1.9 m³/s (Q₁–Q₃), and the cross-section flow of the undercut side tunnel increased by 1.7 and 0.8 m³/s (Q₄–Q₂). When H_t = 3 m and Q₁ = 26.2 m³/s, the cross-section flow rate of the advance side tunnel increased by 1.7 m³/s, and the cross-section flow of the undercut side tunnel increased by 2 m³/s. In Figure 14, there was a significant difference in resistance under different operating conditions. Combined with Figure 13 and Figure 14,

Table 5. Comparison of R and K_m of each branch under different H_t conditions.

Difference in the Air Flow Demand of Two Holes	Lw/(m)	R1 (N·s2/m8)	R2 (N·s2/m8)	R3 (N·s2/m8)	R4 (N·s2/m8)	K
Qa > Qu	2.5	5.4 × 10−4	6.8 × 10−3	2.3 × 10−4	7.7 × 10−4	0.261
	3	3.0 × 10−3	5.4 × 10−3	6.9 × 10−5	5.5 × 10−5	0.687
	3.5	6.9 × 10−4	7.3 × 10−3	1.5 × 10−5	4.4 × 10−4	2.879

shows the K and R_m pair flows of each branch under different H_t conditions.

It can be seen from Table 5 that when H_t = 2.5 and 3 m, K = 0.261 and 0.687, both of which were less than 1, and the air flowed from the advance side tunnel to the undercut side tunnel. When H_t = 3.5 m, K = 2.879 > 1, the air flowed from the undercut side tunnel to the advance side tunnel. In fact, with the increase of H_t, the section area of the upper step decreased, and the local air flow resistance of the sudden expansion of the overflow section changed significantly, and the vortex area here changed the flow velocity of the section and the direction of air flow. Therefore, in the range of 3 m < H_t < 3.5 m, there may be a certain H_t that makes K = 1, and the air flow of the double-hole tunnel does not interfere with each other.

4.4. Effect of L_w on the Stability of the Ventilation Network

Based on the above analysis, it can be seen that the cross-section size of the cross passage affects the air flow direction of the double-hole tunnel in the range of 80 m < L_t, L_p < 180 m. However, when L_t and L_p = 80 m, the K is less than 1; the air flows from the advance side tunnel to the undercut side tunnel regardless of Q_a > Q_u or Q_u > Q_a. In order to explore the influence of L_w on the air flow direction of the double-hole tunnel, Q_a > Q_u and L_t = 80 m were kept unchanged, only the L_w (10, 20, 30, 40, 50 m) were changed, and the flow and resistance of each branch section were shown in Figure 15 and Figure 16.

In Figure 15, when L_w = 10 m, Q₁ = 27.5 m³/s, after the air flowed through the cross passage, Q₃ = 35.8 m³/s, the cross-section flow of the advance side tunnel increased by 8.3 m³/s (Q₃–Q₁), and the cross-section flow of the undercut side tunnel decreased by 8.2 m³/s (Q₂–Q₄). When L_w = 20, 30, 40, and 50 m, Q₁ = 28.2, 26.5, 30.9, and 27.7 m³/s, the cross-section flow of the advance side tunnel decreased by 4.6, 1.2, 3.3, and 4.4 m³/s, respectively, and the cross-section flow of the undercut side tunnel increased by 4.6, 1.6, 2.2, and 4.2 m³/s, respectively. In Figure 16, the resistance h_m of each branch was non-uniform. Combined with Figure 15 and Figure 16,

Table 6. Comparison of K and R_m of each branch under different L_w conditions.

Difference in the Air Flow Demand of Two Holes	Lw/(m)	R1	R2	R3	R4	K
Qa > Qu	1.6 × 10−3	1.5 × 10−3	5.1 × 10−4	2.1 × 10−3	4.499	1.6 × 10−3
	5.5 × 10−3	7.8 × 10−3	2.1 × 10−3	2.0 × 10−3	0.652	5.5 × 10−3
	3.0 × 10−3	5.4 × 10−3	6.9 × 10−5	5.5 × 10−5	0.687	3.0 × 10−3
	1.2 × 10−3	5.6 × 10−3	5.3 × 10−5	2.1 × 10−4	0.851	1.2 × 10−3
	1.6 × 10−4	4.6 × 10−3	9.4 × 10−5	6.8 × 10−4	0.253	1.6 × 10−4

shows the R and K_m pair flows of each branch under different L_w conditions.

It can be seen from Table 6 that when L_w = 10 m, K = 4.499 > 1, the air flowed from the undercut side tunnel to the advance side tunnel. When L_w = 20, 30, 40, and 50 m, the K are all less than 1, and the air flowed from the advance side tunnel to the undercut side tunnel. According to The technical code for highway tunnel construction (JTG F60-2009), the safe layout distance of the co-excavation working face for the excavation of two parallel tunnels should be determined according to the distance between the two tunnels and the surrounding rock, and should not be less than 2 times the diameter of the tunnel [25]. L_w = 30, 40, and 50 m meet the above requirements, but the K are all less than 1, indicating that within the allowable range of the regulations, changing L_w does not affect the air flow direction of the double-hole tunnel.

5. Conclusions

Based on the difference in the air flow demand between two working faces in a double-hole tunnel, this paper simulated the influence of structural parameters such as L_t (distance from the traffic cross passage to the working face), L_p (distance from the pedestrian cross passage to the working face), H_t (height of the upper step), and L_w (safe step distance of the working face of the double tunnel) on the structural stability of the ventilation network of the double-hole tunnel, and draws the following conclusions:

(1)

If there is a difference in the volume flow of the double-hole tunnel, the R_m of each branch in the ventilation network structure changes non-uniformly due to the influence of L_t, L_p, L_w, and H_t, resulting in significant differences in the K and the air flow direction of the tunnel under different working conditions.

(2)

When L_t and L_p = 80 m, the air flows from the advance side tunnel to the undercut side tunnel. When L_t and L_p = 180 m, the air flows from the tunnel with low air flow demand to the tunnel with large air flow demand. When L_t and L_p = 130 m, there is a difference in the air flow direction between the two. The results show that the size of the cross passage affects the stability of the ventilation network in the range of 80 m < L_t, L_p < 180 m.

(3)

In the construction regulations [25], the stability of the ventilation network has nothing to do with L_w. When 3 m < H_t < 3.5 m, there is an H_t that makes K = 1, and the ventilation network of the double-hole tunnel tends to be stable and the flow field does not interfere with each other.

The above studies prove the possibility of complementary construction ventilation of the two tunnels, which is conducive to replenishing the surplus air flow from the side with small air flow demand to the tunnel with large air flow demand. In the follow-up work, the curves of L_t and L_p and K values should be fitted to judge the application range of double-hole complementary ventilation.