Experimental Study on the Forced Ventilation Safety during the Construction of a Large-Slope V-Shaped Tunnel

Abstract

The special large-slope V-shaped structure of underwater tunnels changes the ventilation characteristics during tunnel construction, making the traditional experience limited. Therefore, it is urgent to study the influence of the special structure on the safety of the air environment during construction. In this paper, a series of small-scale experiments were conducted to investigate the ventilation characteristics of V-shaped tunnels. The coupled effects of ventilation parameters (distance of duct outlet from working face $L_0$, air velocity at the duct outlet $u_0$) and structural characteristics (digging length $L_d$, slope of the uphill section $\theta$) were considered. The extreme slope of the V-shaped tunnel of 8% was considered. The flow field and pollutant transport law were determined by using CO as a tracer in the experiments. The results show that $u_0$ has a positive impact on the air return velocity, while $L_d$ has a negative impact, and neither of the other two factors has a significant effect. The transport characteristics of CO in V-shaped tunnels differ from those in flat tunnels, with the former tending to cause unconventional areas of high pollutant concentrations in the horizontal sections. Furthermore, the correlations between CO concentration and distance, ventilation time, and the influence factors discussed in this paper are derived from the experimental results. The conclusions provide guidance for the construction of V-shaped tunnels to prevent air pollution in the construction environment and to improve the working conditions of laborers. Additionally, it can also enrich the ventilation experience in tunnel construction.

1. Introduction

The number of underwater tunnels has been increasing in recent years, and a large number of underwater tunnels with special V-shaped structures are under construction [1,2]. The single-ended closure of tunnels during construction often makes it difficult for pollutants to be exhausted and fresh air to enter. This leads to poor air quality and endangers the lives of construction workers [3,4]. As shown in Figure 1, the V-shaped tunnel is bored single-ended and sequentially through a downhill section, a horizontal section, and an uphill section. Due to the different structures and the corresponding differences in the flow characteristics during tunnel construction, the previous experience of ventilation in normal flat tunnels is no longer applicable. Therefore, it is necessary to carry out a systematic study of the ventilation characteristics during the construction of V-shaped tunnels.

In the past few years, many scholars have studied the flow field and pollutant transport law in tunnels [5,6,7,8,9,10]. Previous studies have shown that the structure of the ventilation flow field during tunnel construction can be divided into the jet zone, vortex zone, and return zone. The characteristics of the return zone are often the focus of research, as it relates to the ability of pollutants to be discharged smoothly during tunnel construction. Further, the air return velocity $u_{\mathrm{return}}$ has been widely studied as an important parameter for measuring the return zone, with the advantages of being easy to measure and having a direct effect on the emission of pollutants. Nan et al. [11] studied the flow form of backflow in ventilated tunnels and derived a semi-empirical equation for the distribution law of the mean air backflow velocity. The equations demonstrate that the mean air backflow velocity is related to the tunnel width, height, duct diameter, and jet velocity. Then, Li et al. [12] investigated the applicability of the backflow velocity requirement (0.15 m/s) under conventional size tunnels in the construction of super-large cross-section underground works by constructing a numerical model. The results indicated that this wind speed was not sufficient to keep CO concentrations in the tunnel below an acceptable level. Chang et al. [13] studied the distribution of air velocity values in the tunnel ventilation area by varying the ventilation parameter settings. The study showed that increasing the cross-sectional area of the tunnel reduced the velocity of the airflow in the return zone. Furthermore, other scholars have evaluated the optimal level of $u_{\mathrm{return}}$ in tunnels by utilizing concepts like dead zones and the average age of air [14,15]. Additionally, some scholars have also conducted a lot of research on the distribution of wind speed in tunnel construction ventilation under high-temperature environmental hazards [16,17].

In the contaminant transport study, Rodriguez and Lombardia [18] used parameters such as the TBM (Tunnel Boring Machine) advance rate to predict pollutant influx into the tunnel based on coal mine experience. However, more studies have focused on the distribution patterns of pollutants in tunnels [19,20,21]. The effects of ventilation parameter settings have been frequently emphasized. Xie et al. [22] considered the effects of the air supply volume and the distance of the duct outlet from the working face on the distribution of dust concentration. The study revealed that for the optimal ventilation effect, each air supply volume corresponds to a specific installation location of the air duct outlet. Fang et al. [23] investigated the gas distribution characteristics in tunnels under full-section excavation and step excavation methods under the influence of the distance between the duct outlet and the working face. Zhou et al. [24] carried out a series of subscale experiments by additionally considering the effects of the tunnel structure such as the angle between the inclined shaft and the construction section, the inclined shaft slope, and the length of the tunnel, as well as ventilation parameter settings such as the location of the duct outlet. Xie et al. [25] concluded that the relationship between ventilation time and the three variables of the upper limit of dust concentration, volume flow rate of the forced air duct, and total explosive mass satisfy logarithmic, power, and logarithmic functions, respectively. Chang et al. [13] derived the ventilation time as a function of distance ($x$) and pollutant concentration ($C$) for the entire tunnel construction period through a series of numerical simulations. Later, some scholars studied the calculation of the CO distribution function during tunnel construction in high-altitude environments [26].

A large number of scholars have made outstanding contributions in the field of ventilation during the construction of tunnels. However, the majority of prior research has focused primarily on analyzing the influence of ventilation parameters on the flow field, with less attention given to the conjoined impact of ventilation parameters and tunnel structure. The former conclusions are more applicable to ordinary flat tunnels, and research on ventilation in recent years has predominantly relied on numerical simulation, with limited systematic experimental verification. Systematic experimental research on the ventilation of tunnels with special structures is needed.

Therefore, a series of small-scale ventilation experiments focusing on the process of forced ventilation for the construction of a V-shaped tunnel were conducted. The changes in the return flow and pollutant distribution under the influence of ventilation parameters (distance between the duct outlet from working face $L_0$, air velocity at the duct outlet $u_0$) and tunnel structure (digging length $L_d$, slope of the uphill section of the V-shaped tunnel $\theta$) were investigated in this paper. The effects of each factor are discussed in detail. The difference between the ventilation characteristics of a V-shaped tunnel and a normal flat tunnel is clarified. Finally, the formula of CO concentration and air return velocity applicable to V-shaped tunnels are derived. This work aims to address the research gap in traditional experience during the construction of V-shaped special-structure tunnels. It also helps to ensure the environmental safety and respiratory health of personnel during the construction of special-structure tunnels.

2. Experimental Study

2.1. Tunnel Model

The prototype tunnel is the cross-harbor tunnel from Guangzhou to Zhanjiang, China, which exhibits the unique V-shaped characteristics. The ventilation flow field in tunnel construction can be simplified as a viscous constant and incompressible fluid flow. Therefore, the Reynolds number is used as a similarity criterion, with a critical value of 5 × 10⁴ based on experience [27,28]. The wind speed in the model must be at least 2 m/s to ensure similarity between the model and the prototype (the critical wind speed is calculated by $Re=uD/\nu$, where $Re$ is the Reynolds number; $u$ is the fluid flow rate, m/s; $D$ is the equivalent diameter of the tunnel model, m; and $\nu$ is the air kinematic viscosity, m²/s, which is taken as 1.57 × 10⁻⁵ m²/s here). Based on the similarity theory [24,29] and considering the convenience of practical operation and realistic conditions, the similarity ratio in this study was set at 1:25. A tunnel model with a length of 20 m was constructed. The physical drawings and specific dimensions can be seen in Figure 2 and

Table 1. Dimensions of prototype tunnel and subscale model (1:25).

Types	Inner Diameter of the Tunnel (m)	Inner Diameter of the Ventilation Duct (m)	Distance from the Duct Outlet to the Closed End of the Tunnel (m)
Prototype tunnel	12.6	2.0	25/50/75
Small-scale model	0.50	0.08	1/2/3

, respectively. The model consisted of four parts, which were the main body of the tunnel model, the ventilation system, the pollutant-generating device, and the data-monitoring system. Later experiments were conducted on this ventilation platform.

As shown in Figure 2a and Figure 3, the main body was made of 10 sections of 2 m-long galvanized iron pipe, closed at one end and open at the other. The closed end was used to mimic the working face in an actual construction tunnel and the main body was placed on several height-adjustable supports in order to change the slope of the model. As shown in Figure 2b and Figure 4a, the ventilation system included a PVC air duct, a fan capable of a maximum capacity of 2326 m³/h, and a frequency modulator. The air duct was suspended at the top of the model. The fan frequency was adjusted to control the wind velocity at the duct outlet through a frequency modulator. As shown in Figure 2c, the pollutant generation device included a CO cylinder, a pressure-reducing valve, and a flow meter with a range of 0.1–1 L/min. The pollutant generation device was connected to the closed end of the model by a hose, and CO could be injected into the model.

Likewise, the data-monitoring system is presented in Figure 2d, which acquired both wind speed and CO concentration within the model. Wind speed detection consisted of a hot-wire anemometer and fixed Pitot tubes (see Figure 4b,c). The hot-wire anemometer was used to calibrate the exit velocity of the air duct. The Pitot tubes were used as fixed-wind-speed test points in the model and were arranged according to the equal-area method, and the Pitot tubes were coupled to micro-differential pressure transmitters, which were connected to data acquisition modules to transfer the data to a PC. As indicated by the red arrow in Figure 2, starting at 1 m from the closed end of the model, a wind speed measurement section was set up at 2 m intervals along the horizontal direction of the model, for a total of 10 sections. The detection of CO concentration was accomplished by a pumped CO detector (see Figure 4d). The CO measurement point was located in the center of the cross-section as shown by the green triangle in Figure 2. Starting at 1.6 m from the closed end, a CO measurement point was placed every 4 m at equal intervals for a total of 5 measurement points.

Table 2. Ranges and accuracy of experimental measuring instruments.

Instruments	Range	Accuracy
Hot-wire anemometer	0.3~30 m/s	1%
Micro differential pressure transmitters	−25 to 25 Pa	0.4%
CO flow meter	0.1 to 1 L/min	4%
CO detector	0 to 1000 ppm	3%

demonstrates the range and accuracy of all the measuring instruments used in the experiment.

2.2. Working Conditions and Experimental Procedures

Table 3. The detail of test conditions.

Test No.	Slope of the Uphill Section  $\mathsf{\theta }$(%)	Tunneling Length  ${\mathit{L}}_{\mathit{d}}$(m)	Distance from the Duct Outlet to the Closed End  ${\mathit{L}}_0$(m)	Air Velocity at the Duct Outlet  ${\mathit{u}}_0$(m/s)
1–45	2	12, 16, 20	1, 2, 3	2, 4, 6, 8, 10
46–90	4	12, 16, 20	1, 2, 3	2, 4, 6, 8, 10
91–135	6	12, 16, 20	1, 2, 3	2, 4, 6, 8, 10
136–180	8	12, 16, 20	1, 2, 3	2, 4, 6, 8, 10

shows the experimental working conditions. Four factors were considered in this study: the digging distance $L_d$, the distance from the duct outlet to the closed end $L_0$, the slope of the uphill section $\theta$, and air supply speed $u_0$. In addition, the slope of the downhill section was set to 2% in the experiment.

The experimental steps can be performed as follows: (1) Start the fan, calibrate the wind speed at the duct outlet, and carry out the next steps after the value has stabilized. (2) Open the software for acquiring wind speed and CO concentration detectors. Then turn on the fan to a specific working condition. (3) Open the CO cylinder valve and regulate the gas flow meters after the wind flow field has stabilized. Release at 600 mL/min for 25 s of quantitative CO. (4) Save the data after all CO detectors show a concentration of 0. (5) Turn off the fan. For other conditions, repeat steps (1) to (5) after adjusting the tunnel model. Additionally, the moment when the release of CO starts has been defined as moment 0 s (at this moment, “ventilation time” = 0 s). Repeat the experiment 3 times for each working condition.

2.3. Repeatability Verification and Error Analysis

2.3.1. Repeatability Verification

Pre-experiments were conducted to verify the performance of the experiment. Firstly, the wind speed at the duct outlet was tested to ensure the stability of the air supply of the fan. As shown in Figure 4b, the velocity measurement points were arranged according to the equal cross-section method. Figure 5a shows the fluctuation of wind speed at each test point when the fan frequency was 40 Hz. As shown in Figure 5b, the turbulence intensity (standard deviation/average value) at each test point did not exceed 3.92%. The above test indicated that the stability of wind flow at the duct outlet could be ensured [30].

To illustrate, the average velocity $u_0$ of the outlet cross-section is calculated by Equation (1):

$$u_0=\frac{Q}{A}=\frac{{\displaystyle \sum \left(u_i\times A_i\right)}}{{\displaystyle \sum A_i}},$$

(1)

where $Q$ is the air volume at the outlet of wind duct, m³/s. $A$ is the cross-sectional area of the wind duct outlet, m²; $A_i$, $u_i$ represent the area and wind speed of each part of the equal-area partition, respectively. The correlation between the fan frequency and $u_0$ was determined by repeated tests. As can be seen in Figure 5c, there was a strong linear relationship between them, demonstrating that adjusting the fan frequency effectively controlled the velocity at the duct outlet.

2.3.2. Error Analysis

The experimental errors were demonstrated by the air velocity characteristics and CO transport patterns in the model. The results of multiple repetitive tests under a specific working condition ($L_d=20 \mathrm{m}$, $L_0=1 \mathrm{m}$, $\theta =2 \%$, $u_0=6 \mathrm{m}/\mathrm{s}$) are presented in Figure 6. The curves for each point match well, and the error band is relatively small. Therefore, it is concluded that the experimental error meets the requirements and will not be further discussed.

3. Results and Discussion

3.1. Flow Field

The air return velocity $u_{\mathrm{return}}$ is often focused on because of its ease of measurement and direct contribution to pollutant removal. However, it has been less studied in V-shaped tunnels.

3.1.1. Effect of $L_0$ on the Flow Field

Three types of $L_0$ (distances between the wind duct outlet and the closed end of the model) were considered, which were 1 m, 2 m, and 3 m, respectively. Figure 7 shows the variation in the cross-section average wind speed along the model for different digging lengths $L_d$ at different $L_0$ values. The positive and negative values of the wind speed represent the direction of the speed. As depicted in Figure 7, the average wind speed profiles under varying $L_0$ influences showed significant differences within a distance of 4 m from the closed end. This part of the region is conventionally defined as the vortex zone. Then, a stable return flow developed behind this zone, which is often referred to as the return zone. The curves of $u_{\mathrm{return}}$ for different $L_0$ conditions are in good overall agreement. This phenomenon indicates that the influence of $L_0$ on the flow field in the V-shaped tunnel mainly lies in the vortex zone near the closed end, and $L_0$ does not have a significant effect on whether or not a stable returning wind is formed or the size of $u_{\mathrm{return}}$ in this experiment. This conclusion is consistent with Chang et al. [13].

3.1.2. Effect of $u_0$ on the Flow Field

Correspondingly, a total of five wind speed $u_0$ magnitudes of the forced air duct outlet, namely 2, 4, 6, 8, and 10 m/s, were considered. Figure 8 illustrates the effect of $u_0$ on the flow field within the model under different $L_d$ values. As can be seen, each wind speed curve under different $u_0$ values exhibits a similar pattern. It shows a significant pattern in the return zone; the higher $u_0$ is, the higher $u_{\mathrm{return}}$ is.

3.1.3. Effect of $L_d$ on the Flow Field

Three cases with $L_d$ values of 12, 16, and 20 m were studied. As Figure 8 shows, the effect of $L_d$ on cross-sectional average wind speed is most obvious in the vortex zone. The synthesis in Figure 7 shows that the growth of $L_d$ does not significantly increase the length of the vortex zone. However, $L_d$ affects $u_{\mathrm{return}}$ in the return zone, even though the total length of the model is not very long. At the same $u_0$, the steady $u_{\mathrm{return}}$ measured by the model tends to decrease as $L_d$ grows.

3.1.4. Effect of $\theta$ on the Flow Field

Figure 9a,b shows the wind speed profiles within the model at each slope $\theta$ for $u_0$ values of 2 m/s and 10 m/s, respectively. The results show that the slope has no significant impact on the capacity to generate a steady reflux or the magnitude of the $u_{\mathrm{return}}$ within the model. The effect of $\theta$ on the flow field is not monolithic. There is a superimposed effect of $\theta$ and $u_0$ on the behavior of $u_{\mathrm{return}}$ in the model. The turbulence of the flow field measured in the model is not obvious, with high $u_0$ values corresponding to small $\theta$ values. In contrast, it is more difficult to form a stable $u_{\mathrm{return}}$ curve in the case of large $\theta$ and low $u_0$ values.

3.1.5. Derivation of the Air Return Velocity

According to the previous discussion, the return wind speed is not significantly affected by $L_0$ or $\theta$, but is more significantly affected by $L_d$ and most significantly affected by $u_0$. Considering that there are fewer $L_d$ variables, only the effect of $u_0$ is considered, and the experimental results are fitted to obtain a functional relationship between $u_0$ and $u_{\mathrm{return}}$. As shown in Figure 10, the $u_{\mathrm{return}}$ is a primary function of $u_0$, and it increases linearly with $u_0$. The fitting function is specified as follows:

$$u_{\mathrm{return}}=0.03355u_0+0.03632,$$

(2)

where $u_{\mathrm{return}}$ is the air return velocity within the model, m/s; $u_0$ is the velocity of the wind duct outlet, m/s.

3.2. CO Diffusion Law

The experimental findings indicate a distinction in the CO transportation pattern between V-shaped tunnels and flat tunnels. Figure 11a,b shows the work of Tao et al. [31] and the conclusions drawn in this study, respectively. The work of Tao et al. [31] shows the CO transport law under the construction of a flat tunnel. The peak CO concentration in the flat tunnel decays progressively with increasing distance from the closed end. Instead, the peak CO concentration within the V-shaped tunnel undergoes a fluctuating decrease along the longitudinal direction of the model. As illustrated in Figure 11b, the peak CO concentrations at 5.8 m and 13.8 m from the closed end of the model are higher than the previous measurement point, but still show a decreasing trend in general. This makes V-shaped tunnels, such as underwater tunnels, prone to generating additional pollutant accumulation areas behind the working face, making the safety of ventilation in the rear space of such structural tunnels a concern. A subsequent analysis of the effects of the four influences mentioned earlier on CO transport in the V-shaped tunnel is made.

3.2.1. Effect of $L_0$ on the CO Diffusion

Figure 12 shows the variation in CO concentration under the influence of $L_0$. From the longitudinal height of each curve, it can be seen that the CO concentration at the same measurement point decreases with the increase in $L_0$. In general, the peak CO concentration shows a pattern of $C_{L_0=1 \mathrm{m}}>C_{L_0=2 \mathrm{m}}>C_{L_0=3 \mathrm{m}}$. However, there is an exception, such as the curve “13.6 m from the closed end” in Figure 12, which shows a pattern of increasing and then decreasing with the increase in $L_0$. Similarly, in terms of the horizontal width of the curves, there is a time lag in the appearance of the CO concentration curves at each measurement point at different $L_0$ values. With little difference between the CO concentration profiles at $L_0=1 \mathrm{m}$ and $L_0=2 \mathrm{m}$, the CO concentration profiles at $L_0=3 \mathrm{m}$ appear later. This means that it takes longer for an equal amount of CO to be transported to a given point when $L_0$ is particularly large and inappropriate. This also affects the total time required to remove all quantitative CO from the model. It can be seen from Figure 12 that the ventilation time ($t$) required to remove all the CO from the model has the pattern of $t_{L_0=3 \mathrm{m}}>t_{L_0=2 \mathrm{m}}\approx t_{L_0=1 \mathrm{m}}$. Therefore, it can be summarized that there exists a suitable range for $L_0$ in practical engineering. Within the suitable range, $L_0$ has little effect on pollutant transportation, but beyond it, the total time of pollutant discharge will be greatly increased. This increase in the total duration of ventilation further supports the conclusion that the wider vortex zone slows down the process of releasing harmful gases near the working face [21], and this conclusion remains applicable to the ventilation of V-shaped tunnels.

3.2.2. Effect of $u_0$ on the CO Diffusion

Figure 13 demonstrates a significant effect of the $u_0$ range from 2 m/s to 10 m/s on CO concentration. Under the condition of small $u_0$ values, the CO concentration increases rapidly to a fairly high peak concentration in a short time, and then starts to decrease at a rate lower than the concentration increase. Additionally, the higher the $u_0$ value, the lower the peak concentration that can be measured at each test point, and the shorter the $t$ required for all concentration profiles to fall to 0. This means that as $u_0$ increases, the emission rate of CO also increases, and the pollutant transport function in the model strengthens.

3.2.3. Effect of $\theta$ on the CO Diffusion

Figure 14 indicates the CO concentration at five different positions along the tunnel under the influence of $\theta$. The CO concentration profiles exhibit varying peak values and appearance times under the influence of $\theta$. Vertically along the axes, the CO concentration exhibits a difference in peak height (Figure 14a,c,d). This shows that the greater the $\theta$ value, the lower the peak height. Horizontally on the axes, there is a time difference in the appearance of the CO concentration curves, and it is evident that the CO concentration increase can be detected earlier at the same measurement point for small $\theta$ values (Figure 14c,d).

For more intuition, the integrated numerical simulation approach was used for further qualitative discussion. Ultra-extreme cases with $\theta$ values of 12%, 16%, and 20% were considered. The software Ansys Fluent 20.2 [32] was used and the basic parameters were set as shown in

Table 4. Basic parameter settings for numerical simulation.

Parameter Type	Parameter	Parameter Setting
Mesh	Quantity and quality	3.2 × 105, 0.35–0.99
General	Time	Transient
	Solver type	Pressure-based
	Gravity	X: 0, Y: −9.81, Z: 0 (m/s2)
Model	Viscous model	Standard $k-\epsilon$ (2 eqn)
	Species (Species transport model)	Mixture template (CO, air) Density: volume–weight mixing law Viscosity: constant
Materials	CO (fluid)	Density: constant, 1.1233 kg/m3
	Air (fluid)	Density: constant, 1.225 kg/m3
Boundary	Velocity inlet	6 m/s
	CO inlet (mass-flow inlet)	0.00752 kg/s (release for 25 s)
	Tunnel model and duct (wall)	No slip wall
	Open end (pressure outlet)	101.325 kPa, Turbulence intensity 5%
Solution	Pressure–velocity coupling scheme	Simple
	Gradient	Least-squares cell-based
	Pressure	Second-order
	Momentum	Second-order upwind
	Turbulent kinetic energy	First-order upwind
	Turbulent dissipation rate	First-order upwind
	CO	Second-order upwind
	Solution controls	Pressure 0.3, Density 1, CO 1
Initialization	Initialization methods	Standard
	Initial values	CO: 0
Calculation	Type	Fixed
	Time steps (s)	1
	Max iterations	50

. Figure 15 shows the simulation results at t = 80 s, while Figure 16 validates them.

As shown in Figure 15, the diffusion distance is longer on the side near the top and shorter on the side near the ground, and the CO concentration at the cross-section is higher near the top and lower near the ground, as indicated by the red box. The results demonstrate that the distribution of CO exhibits an inverted trapezoidal shape with high concentrations in the upper part and low concentrations in the lower part. As $\theta$ increases, the area of CO contamination along the tunnel generally increases, and the vertical diffusion area also increases (red box in Figure 15). The lowest concentration of CO at the cross-section increases gradually, while the highest concentration decreases, and the vertical concentration gradient becomes smaller.

As shown by the red dots in Figure 15, the position of the pollution front is further forward for $\theta$ values of 4% and 8% than for $\theta$ values of 12%, 16%, and 20%, and this pattern is not consistent, as it is observed that $\theta =8\%$ is earlier than $\theta =4\%$. This phenomenon indicates a general trend that the smaller the $\theta$ value, the earlier the pollutant front reaches the open end. The simulation results are in agreement with the experimental results. As for the phenomenon of low peaks at large $\theta$ values, this is due to the relatively lower concentration as the diffusion distance becomes larger.

Therefore, based on the combined results of experiments and numerical simulations, it can be concluded that the distribution of CO is in an inverted trapezoidal shape. The larger the $\theta$ value, the larger the contamination range becomes, while causing the CO concentration at specific points to decrease. Meanwhile, at smaller slopes, there is a general tendency for CO to be transported to the open end earlier.

3.2.4. Effect of $L_d$ on the CO Diffusion

Figure 17 shows the CO concentration profiles at each point within the model for $L_d$ values of 12 m, 16 m, and 20 m, respectively. From the lateral view, the appearance of CO concentration and the first concentration wave peak (black lines) are detected at almost the same moment for different $L_d$ values. At the open end of the model, the moment of CO emergence is delayed with the increase in $L_d$. This is due to the objective effect of the model length, which implies that the larger the $L_d$ value, the longer the time required for all CO to be discharged from the model.

3.3. Derivation of the CO Distribution Function

In previous studies, CO transport is often categorized into three phases, which are the mixing phase in the control zone, the diffusion phase of the peak CO in the tunnel, and the diffusion phase after the peak CO leaves the open end of the tunnel [13,26]. In order to clarify the transportation process of CO and other pollutant gases during V-shaped tunnel construction, the ventilation distribution function of CO concentration is derived in this paper.

3.3.1. Control Zone

The space between the air duct outlet and the working face is usually defined as the control zone, where the fresh air flow is usually mixed with the dirty air generated by construction. To facilitate subsequent quantitative analyses, the initial CO concentration (C₀) was used in this study as the dimensionless CO concentration (C). Figure 18 shows the relationship between ln(C/C₀) and $t$ in the control zone during the ventilation process in the V-shaped model. Starting from the release of CO, ln(C/C₀) climbs rapidly to the peak value in a short time, and then with the increase in $t$, ln(C/C₀) decreases uniformly. After that, it decreases to a certain determined value and starts to fluctuate in a generally decreasing trend, and different working conditions show similar patterns. As shown in Figure 18, ln(C/C₀) decreases to −5 and then begins to fluctuate in a decreasing trend. At this time, the corresponding CO concentration is about 5 ppm, which can be regarded as the CO being almost completely discharged in the model, and the subsequent fluctuating decline in each condition does not show a more consistent pattern. Therefore, it is meaningless to study the CO distribution function after ln(C/C₀) is reduced to −5. Thus, this study investigated the main stage of the ventilation process, the stage of uniformly decreasing concentration of CO, as shown by the red line segment in Figure 18.

Figure 19 illustrates the variation in ln(C/C₀) in the control zone at different moments by varying $L_d$, $L_0$, $\theta$, and $u_0$, respectively, while other variables remain constant. Considering that the variation in $L_0$ makes the relative positions of measurement points in the control zone differ, and it is not strictly a single-variable case, the flow field patterns and CO transport patterns within the model are similar for $L_0=1 \mathrm{m}$ and $L_0=2 \mathrm{m}$, with the latter being more consistent with the actual construction environment. Therefore, the condition of $L_0=2 \mathrm{m}$ is used here as an example for subsequent analysis. According to the previous research and related analysis, it is known that ln(C/C₀) is a function of $L_d$, $\theta$, $t$, and $u_0$. The following assumptions are made:

$$\ln \left(\frac{C}{C_0}\right)=f(L_d,\theta ,u_0,t),x<L_0,$$

(3)

By analyzing Figure 18 and Figure 19, ln(C/C₀) satisfies parabolic, linear, linear, and linear functions for the four factors $L_d$, $\theta$, $t$, and $u_0$, respectively. Therefore, the distribution function of CO concentration in the control area of the V-shaped tunnel is obtained from the experimental results:

$$\ln \left(\frac{C}{C_0}\right)=f(L_d,\theta ,u_0,t)=a\frac{L_d}{D}+b{\left(\frac{L_d}{D}\right)}^2+c\theta +d{u}_{0}t+e{u}_0,x<L_0,$$

(4)

where a, b, c, d, and e are constant coefficients, and the results of the fitting can be seen in

Table 5. Results of fitting the CO distribution function in the control zone.

Parameter	Calculation Results
a	−0.03062
b	0.00147
c	−0.072
d	−5.289$A/V_0$
e	0.0447/$u_{\min }$
	R2 = 0.84

; C and C₀ are the CO concentration and the initial CO concentration within the model, respectively, in ppm; $L_d$ is the digging length of the model, m; $\theta$ is the slope of the uphill section of the model, %; $u_0$ is the average air velocity of the wind duct outlet, m/s; $t$ is the ventilation time, s; $D$ is the equivalent diameter of the tunnel model, m.

3.3.2. Diffusion Zone

In a flat tunnel, the CO distribution function in the diffusion zone is different for the two phases before and after the CO concentration peak reaches the tunnel exit [13,26]. Unlike flat tunnels, the CO transport in the diffusion zone of the V-shaped tunnel can be clearly divided into three stages. Figure 20 shows the values of ln(C/C₀) at different distances from the closed end of the V-shaped model in the diffusion zone for $L_d=20 \mathrm{m}$ and $u_0=6 \mathrm{m}/\mathrm{s}$.

Figure 20a shows stage Ⅰ of the diffusion. At this time, ln(C/C₀) in the uphill section shows a decreasing trend with time, and ln(C/C₀) in the horizontal section shows a pattern of increasing and then decreasing, while ln(C/C₀) in the downhill section is increasing. This shows the process of the peak of CO concentration moving from the closed end to the open end of the model. Figure 20b shows stage Ⅱ and stage Ⅲ within the model. At these two stages, the peak of the CO concentration wave leaves the model and ln(C/C₀) starts to decrease gradually at each measurement point. In this case, 180 s is the moment that distinguishes between stage Ⅱ and stage Ⅲ, which is influenced by multiple factors. As shown in Figure 20b, before 180 s, the ln(C/C₀) curve decreases with an almost uniform and parallel law. After this moment, ln(C/C₀) at the CO measurement point located 9.6 m from the closed end shows a bottoming-out pattern. It is observed that in this V-shaped tunnel model, the CO concentration at the measuring point located at the beginning of the uphill section often goes to 0 first. In addition, it is also observed that the larger the $\theta$ value, the earlier CO transport enters stage Ⅲ and the longer stage Ⅲ lasts. Therefore, the emergence of stage Ⅲ is clearly influenced by the structure of the tunnel model.

In this paper, a series of fitting analyses are carried out to analyze the main stages of the CO transport process in phase I and phase II, taking into account the $\theta$ value of the V-shaped tunnel. The relationship between CO concentration and $t$, $\theta$, and $x$ in the diffusion zone is derived as:

$$\ln \left(\frac{C}{C_0}\right)=\left\{\begin{array}{l}{f}_1\left(t\right){\left(\frac{x}{L_0}\right)}^3+f_2\left(t\right){\left(\frac{x}{L_0}\right)}^2+f_3\left(t\right)\left(\frac{x}{L_0}\right)+f_4\left(t\right)+k_1\theta ,x>L_0,t<T_0\\ f_5\left(t\right){\left(\frac{x}{L_0}\right)}^2+f_6\left(t\right)\left(\frac{x}{L_0}\right)+f_7\left(t\right)+k_2\theta ,x>L_0,t\ge T_0\end{array}\right.,$$

(5)

where $x$ is the distance from the closed end of the model, m; $L_0$ is the distance of the wind duct outlet from the closed end, m; $x/L_0$ is the dimensionless number of x; $T_0$ is the moment of peak CO concentration transport to the model outlet, $T_0=L_d/u_{\mathrm{co}}$, s. The fitting results are shown in

Table 6. CO transport function for stage I of the diffusion zone.

${\mathit{u}}_0$	Stage I
	${\mathit{f}}_1\left(\mathit{t}\right)$	${\mathit{f}}_2\left(\mathit{t}\right)$	${\mathit{f}}_3\left(\mathit{t}\right)$	${\mathit{f}}_4\left(\mathit{t}\right)$	${\mathit{k}}_1$	${\mathit{R}}^2$
4 m/s	0.011296t/T0 − 0.013823	−0.85433t/T0 + 1.15923	−10.0323(t/T0)2 + 20.02265t − 10.22568	30.48233(t/T0)2 − 63.12055t/T0 + 27.2187	−0.03046	0.892
6 m/s	0.01009t/T0 − 0.01396	−0.13118t/T0 + 0.21549	−2.95656(t/T0)2 + 6.12402t − 3.31801	16.52183(t/T0)2 − 38.29427t/T0 + 16.88465	−0.0015	0.924
8 m/s	0.08281t/T0 − 0.11163	−0.6216t/T0 + 0.89907	−5.59428(t/T0)2 + 12.78034t − 7.3066	13.52062(t/T0)2 − 33.28801t/T0 + 16.15787	−0.0498	0.884
10 m/s	0.04982t/T0 − 0.07595	−0.30228t/T0 + 0.53842	−4.02468(t/T0)2 + 9.31002t − 5.36407	9.88393(t/T0)2 − 26.43139t/T0 + 13.14085	−0.00224	0.935

and

Table 7. CO transport function for stage Ⅱ of the diffusion zone.

${\mathit{u}}_0$	Stage Ⅱ
	${\mathit{f}}_5\left(\mathit{t}\right)$	${\mathit{f}}_6\left(\mathit{t}\right)$	${\mathit{f}}_7\left(\mathit{t}\right)$	${\mathit{k}}_2$	${\mathit{R}}^2$
4 m/s	0.14269t/T0 − 0.19804	−1.64291(t/T0)2 + 3.02047t/T0 − 0.26269	6.99498(t/T0)2 − 20.7725t/T0 + 6.82536	−0.02483	0.909
6 m/s	0.22029t/T0 − 0.29843	−1.13271(t/T0)2+ 0.073205t/T0 + 1.67585	6.79006(t/T0)2 − 18.2798t/T0 + 5.34493	−0.03139	0.933
8 m/s	0.06615t/T0 − 0.09061	−0.31577(t/T0)2 + 0.17934t/T0 + 0.808	2.3919(t/T0)2 − 9.71992t/T0 + 3.34618	−0.03853	0.950
10 m/s	0.02331t/T0 − 0.02105	−0.41196(t/T0)2 + 1.18699 t/T0 − 0.60127	0.91471(t/T0)2 − 7.17993t/T0 + 3.69721	−0.05098	0.950

. The transport velocity $u_{\mathrm{co}}$ of the CO wave peak is fitted from the experimental results, which is calculated in the following equation:

$$u_{\mathrm{CO}}=0.0297u_0+0.0256,$$

(6)

where $u_{\mathrm{co}}$ is the transportation velocity of the CO concentration wave peak, m/s; $u_0$ is the wind velocity at the outlet of the wind duct, m/s. Under the conditions of special tunnel structures such as V-shaped underwater tunnels, pollutants such as CO will seriously affect the construction efficiency and the occupational health of workers. The formulas derived in this paper can provide an important reference for forced ventilation in tunnels of a similar type of structure.

4. Conclusions

In this paper, the ventilation safety in the construction of a large-slope V-shaped tunnel was investigated through a series of small-scale experiments for the first time, and the coupled effects of ventilation parameters and structural characteristics on construction tunnels, which have seldom been considered together, were taken into account. The effects of four variables, namely digging distance ($L_d$), the distance from the outlet of air duct to the closed end ($L_0$), the slope of the uphill section ($\theta$), and air supply speed ($u_0$), on the ventilation flow field and pollutant transport patterns in a V-shaped tunnel were investigated. The primary conclusions from this work are summarized as follows:

• The order of importance of the effect on the magnitude of the air return velocity is: $u_0>L_d>\theta \approx L_0$. Where increases in $u_0$ and $L_d$ cause $u_{\mathrm{return}}$ to increase and decrease, respectively. $\theta$ and $L_0$ have no significant effect on $u_{\mathrm{return}}$ to a limited extent. The $u_{\mathrm{return}}$ as a function of $u_0$ is derived.
• Pollutant transport characteristics of V-shaped tunnels and flat tunnels were compared. The peak of CO concentration along the longitudinal direction of the model does not decay unidirectionally as in the case of flat tunnels but shows fluctuating decay. Unconventionally high pollutant concentration occurs in the horizontal section of the model, making the V-shaped tunnel have critical ventilation areas other than the working area.
• Excessive levels of $L_d$ and $L_0$ lead to a significant increase in the time required for pollutant emission. In contrast, increasing $u_0$ without considering the flow field stabilization in the work area has the opposite effect. The discharge of pollutants is more favorable when the $\theta$ value is smaller. Conversely, a larger $\theta$ value results in a wider spread of pollutants.
• The functional relationship between CO concentration and each influencing factor in the control zone and diffusion zone is derived. The formula can be used to find the ventilation time required for similar projects.

This research employs reliable experiments to address the research gap in traditional ventilation and pollutant reduction experience during the construction of large-slope V-shaped tunnels. The results clarify the characteristics of the ventilation environment during the construction of V-shaped tunnels and provide a reference for the construction ventilation of other special-structure tunnels.