Tunnel Slope Research Articles

Numerical Study on the Influence of the Slope Composition of the Asymmetric V-Shaped Tunnel on Smoke Spread in Tunnel Fire

Asymmetrical V-shaped tunnels often appear in tunnels crossing the river or urban underground road tunnels. The smoke flow inside is affected by a lot of factors. A full understanding of the smoke flow in this kind of tunnel is the basis of the smoke control. In this study, the effects of slope composition and fire heat release rate (HRR) on the longitudinal induced airflow velocity, the smoke back-layering length at the small slope side, and the maximum ceiling temperature were studied by the numerical method. The results show that when the fire occurs at the slope change point of the V-shaped tunnel, the maximum ceiling temperature decreases with the increase in the slope of the large-slope side tunnel. The longitudinally induced velocity is primarily related to the slope of the large-slope side tunnel and the fire HRR. When the slope difference between the side tunnels or the slope of the large-slope side tunnel is large, the smoke in the small-slope side tunnel flows back toward the fire source after reaching its maximum dispersion distance and then reaches a quasi-steady state. The smoke back-layering length is mainly affected by the slope and length of the large-slope side tunnel. When the slope of the large-slope side tunnel is 9%, the induced airflow velocity from the small-slope side can prevent the spread of smoke. The empirical models of the smoke back-layering length and the longitudinal induced airflow velocity in the small-slope side tunnel are drawn, respectively, by the theoretical analysis and the numerical results. This study can provide technical support for the design and operation of smoke control systems in V-shaped tunnels.

Numerical study on smoke temperature distribution in naturally ventilated inclined tunnels: Effects of tunnel width and tunnel slope

Inclined tunnel fires exhibit unique characteristics compared to horizontal tunnel fires as a result of the stack effect. Nevertheless, there is still a lack of consensus among previous scholars regarding the smoke temperature distribution in inclined tunnel fires. This work conducts a numerical investigation on the smoke back-layering length upstream of the fire source and the temperature decay downstream of the fire source in naturally ventilated inclined tunnels with varying widths and slopes. Results indicate that as the tunnel slope increases from 0° to 8°, the smoke back-layering length first decreases and then continues at a constant value of 1.47H4/3/W1/3, while the effect of tunnel width is negligible. The decay factor in the one-dimensional flow stage (x/H≥4) exhibits two distinct patterns related to tunnel width: it initially remains constant and then drops when the tunnel is wide, whereas it monotonically drops when the tunnel is narrow. Two empirical models are developed to identify the segmented characteristics and verified through the relevant data from existing literature with similar fire scenarios. This work offers a method for estimating the smoke temperature distribution in inclined tunnels, providing crucial insights for fire prevention, smoke detection, and safety strategies in tunnel engineering.

A Mixed Convection Model for Estimating the Critical Velocity to Prevent Smoke Backlayering in Tunnels

AbstractA novel mathematical model for the critical ventilation velocity to prevent smoke backlayering in tunnels is presented, addressing limitations of prior approaches. The basis of the model is a rigorous characterisation of the physical processes by the characteristic quantities. Empirical parameters within the new model are determined, to align with results from both full-size and small-scale tunnel experiments. Data from numerical simulations (CFD, Computational Fluid Dynamics), validated by known test data, are then used to estimate the effects of tunnel slope and other parameters on the critical velocity. The model is seen to approximate the critical velocity well, following all trends identified by test data and CFD parameter studies. The empirically calibrated equation permits prediction of the critical velocity beyond the narrow range of tunnel geometries where known results already give an answer. The resulting equation has practical application for tunnel design.

The forecasting of surface displacement for tunnel slopes utilizing the WD-IPSO-GRU model

To quickly assess slope stability based on field displacement monitoring data, this paper constructs a hybrid optimization model that predicts surface displacement during tunnel excavation in base-overburden slopes. The model combines Wavelet Decomposition (WD) with a Gated Recurrent Unit (GRU), and the GRU's hyperparameters are optimized using an Improved Particle Swarm Optimization algorithm (IPSO). The specific steps are as follows: First, the Wavelet Decomposition (WD) technique is applied to decompose the raw displacement data, extracting features at different time–frequency scales. Next, the Dropout technique is incorporated into the GRU model to prevent overfitting. Additionally, nonlinear inertia weight ω improved cognitive factor c1, and social factor c2 are introduced. The PSO algorithm is improved by integrating crossover and mutation concepts from genetic algorithms. Finally, the IPSO is used to optimize the number of neural units hN, HN, LN and dropout rates D1 and D2 in the GRU network architecture. After constructing the WD-IPSO-GRU model, a comprehensive comparison is made with various swarm intelligence algorithms and state-of-the-art models. The experimental results demonstrate that the WD-IPSO-GRU model significantly improves the prediction accuracy of surface displacement in slopes during tunnel excavation. Compared to directly using raw data for prediction, the introduction of the WD preprocessing technique improved the prediction accuracy at measurement points 01 and 02 by 28% and 45.9%, respectively. Additionally, with the model optimized by IPSO, the prediction accuracy at measurement points 01 and 02 increased by 76% and 56.7%, respectively. The WD-IPSO-GRU model effectively addresses the challenges of extracting features from univariate displacement time-series data and determining the parameters of the GRU network. It improves the prediction accuracy of surface displacement in base-overburden type slopes and demonstrates excellent generalization ability and reliability. The research results validate the potential application of the model in geotechnical engineering and provide strong support for assessing slope stability during tunnel excavation.

Study on the maximum ceiling temperature and downstream temperature distribution in inclined tunnel fire

Constrained by various factors, including terrain, tunnels frequently exhibit slopes. While existing research on fires in inclined tunnels predominantly focuses on the characteristics of smoke flow in large slope tunnels, there is a notable lack of attention given to the study of micro-slope tunnels and important factors such as induced air inflow. Therefore, in this paper, the numerical simulation method is used to study the maximum ceiling temperature rise and downstream temperature distribution in inclined tunnel fire under the conditions of micro-slope and large slope. The results show that the main factors affecting the ceiling temperature rise are not only the tunnel slope, but also the HRR and the downstream length. These effects can be expressed by the stack effect intensity. When the inclined tunnel fire occurs, the maximum ceiling temperature and the downstream temperature distribution characteristics show two states. When the stack effect in the tunnel is diminished, there is no significant alteration in the maximum ceiling temperature and temperature distribution within the tunnel when compared to a horizontal tunnel. In a tunnel with a strong stack effect, the maximum temperature decreases as the stack effect increases, and the temperature distribution differs greatly from a horizontal tunnel. The theoretical analysis of this paper identifies the demarcation point of the two state changes as the dimensionless induced air inflow velocity of 0.1. On this basis, a piecewise prediction model for the maximum ceiling temperature of the inclined tunnel fire is established. Because the temperature distribution between the fire source and the maximum temperature position is not regular. Thus, using the maximum ceiling temperature as a reference point, an accurate segmented prediction model of temperature distribution is proposed for downstream Region 1. This study offers guidance for designing tunnel structures with high-temperature resistance and assessing safety conditions within the tunnel.

Seismic response and damage evolution process of a bedded slope‒tunnel system via the continuum‒discontinuum element method

To investigate the failure evolution process and failure mechanism of the bedded slope‒tunnel system under earthquakes, this work examines a specific layered slope at a tunnel portal in southeast China and conducts a 2D dynamic analysis with the continuum‒discontinuum element method (CDEM). It investigates the slope's dynamic behavior and potential for instability by evaluating the wave patterns, acceleration, displacement, Hilbert‒Huang transform (HHT) spectral analysis, and equivalent crack ratio. The research results indicate that the analysis of acceleration and displacement over time provides insights into wave propagation within a slope. During minor earthquakes (< 0.3 g), the slope experiences dynamic amplification at the surface and elevation-dependent effects, which are less evident during stronger seismic events. This work also revealed a positive correlation between the tunnel's dynamic amplification and elevation. A method leveraging HHT energy analysis, in conjunction with the slope's equivalent fracture ratio, is introduced to trace the progression of seismic damage across temporal and spatial dimensions. The progression of seismic intensity is characterized by stages of local failure initiation, expansion, and eventual holistic failure. Similarly, the temporal dynamics of instability are categorized into phases of initial instability, acceleration, and eventual sliding. Furthermore, this work explores the impact of tunnels on slope stability by comparing the equivalent fracture ratios and dynamic displacement patterns of slopes both with and without tunnels, revealing the evolution process of seismic damage to slope‒tunnel systems. This work provides a reference for the seismic design of complex slope‒tunnel systems.

Experimental study on the effect of longitudinal ventilation on spill fire characteristics in sloped tunnels

A series of spill fire tests were carried out in a reduced-scale tunnel (6 m × 0.6 m × 0.45 m), considering different discharge rates (60–140 ml/min), ventilation rates (0∼1.26 m/s), and tunnel slopes (3 %, 5 %, 7 %). Some crucial characteristic parameters during the quasi-steady combustion stage of tunnel spill fires were analyzed, including the diffusion shape of the liquid fuel, mass burning rate per unit area, flame morphology and plume temperature, and the critical ventilation velocity. The results show that as the tunnel slope increases, the diffusion shape of the liquid fuel transitions from circular to an ellipse shape and then to rectangular or linear shape. Moreover, the mass burning rate per unit area decreases with increasing ventilation rates at low ventilation (V < 0.5 m/s), while it remains almost constant at high ventilation rates (V ≥ 0.5 m/s). This could be attributed to variations in flame tilt behavior under different ventilation conditions. Predictive models for the flame tilt angle and the vertical temperature distribution of tunnel spill fires under the effect of ventilation were further established and verified. Furthermore, the critical ventilation velocity of tunnel spill fires remains essentially unchanged as the discharge rate (or fire source power) increases. This phenomenon was explained by analyzing the resistance of the spill fire plume and the buoyancy generated by the smoke temperature. This work could serve as a critical reference for assessing disaster risks and executing emergency rescue operations during tunnel spill fires.

Study of the Thermal Buoyancy on the Smoke Flow in Tunnel Fires under the Coupled Effects of the Longitudinal Air-flow and the Tunnel Slope

Study of the Thermal Buoyancy on the Smoke Flow in Tunnel Fires under the Coupled Effects of the Longitudinal Air-flow and the Tunnel Slope

The Effect of Slope on Smoke Characteristics of Natural Ventilation Tunnel with Shafts

Tunnels with natural ventilation and extraction have become the focus of ventilation research in recent years. It is significant to study the characteristics of smoke in tunnel fires to ensure the safety of people and the tunnel structure. Previous research has mainly focused on natural ventilation in horizontal tunnels, and there are few studies on sloped tunnels. In this paper, we studied the smoke characteristics of natural ventilation extraction in slope tunnel fires both experimentally and theoretically. The small-scale experimental results showed that the position of the fire source, heat release rate (HRR), and the size of the shaft had little effect on the deflection angle of the fire plume. The deflection angle of fire plume was only related to the tunnel slope and increased with the tunnel slope. The slope had no effect on the smoke temperature distribution on the downside of the tunnel, while the smoke temperature on the upside decreased with the increase in the slope. The calculation models of the maximum smoke temperature rise and the smoke temperature distribution were obtained based on the experimental results and theoretical analysis. Compared with the experimental data, the developed semi-empirical models could provide a reliable prediction of smoke temperature.

Badanie efektu dławienia w pożarze tunelu

As per the emergency ventilation strategy, air velocity of 3 m/s in case of the longitudinal ventilation is sufficient for smoke control in all fire conditions. Numerical experiments were carried out with FDS software to estimate the numerical value of the critical velocity. Numerical models were realized in 0-6% slope tunnels with a 1% step for 5, 10, 20, 30 and 50 MW fires for four types of fuel: gasoline, diesel fuel, oil and firewood. The paper notes that the dynamic pressure induced by a strong fire is much higher than the static pressure of tunnel jet fans. As a result, following the algebraic summation of positively-directed ventilation flows and the negatively-directed flows induced by fire, an intense back layering occurs, which casts doubt on the suitability of the specified emergency ventilation strategy when designing the fire ventilation. The critical ventilation speed of 3 m/s cannot cope with the traction caused by fire, expressed by the ascending movement of the high-temperature and low-density combustion products. The paper discusses the numerical modelling results with an adiabatic underground heat exchange model and presents typical tunnel fire modelling plans, which correspond to an inclined tunnel for ascending and descending ventilation flows as well as a horizontal tunnel. The article gives the regularities obtained by the numerical models of changes in the variables of average air temperature and density, average carbon monoxide, average carbon dioxide and soot concentrations. According to the emergency ventilation strategy, critical velocity is an important value and a major determinant of back layering prevention in sloping tunnels. Although many papers have been devoted to this problem, the obtained results differ much. The present paper shows that strong fires induce much greater dynamic pressures than the static pressures of the tunnel jet fans are. Consequently, the flows caused by these forces, as they move in different directions, following their algebraic summation, cause a strong back-layering in case of positive ventilation flows, i.e., when the ventilation flow is descending and the fire seat is found at a lower point compared to the air supply portal. The new results can be used to develop fire ventilation plans as well as life-saving and emergency control solutions in the operating tunnels for personnel and rescuers.

Study on the influence of branch slope on smoke movement mechanism in bifurcated tunnel fire under natural ventilation

In order to investigate the impact mechanism of branch slope on fire smoke in underground bifurcation spaces, a series of small-scale fire experiments were conducted. This study measured relevant data under natural ventilation conditions for four different branch slopes and six fire power levels, focusing on the highest ceiling temperature in the tunnel and the attenuation pattern of ceiling temperatures along the longitudinal direction in both the main and branch tunnels. It also analyzed the temperature field, velocity field, and pressure field at the bifurcation. The results indicate that a decrease in branch slope leads to an increase in the highest temperature in the main tunnel, primarily due to the enhanced chimney effect that intensifies the entrainment of smoke and accelerates the flow of fire smoke. A modified model for the highest temperature, considering the influence of branch slope, was proposed. Branch slope has a certain impact on the longitudinal temperature attenuation of the tunnel ceiling, with a relatively weaker effect on the main tunnel. Based on empirical formulas, a formula for longitudinal temperature attenuation involving slope, including both the main and branch tunnels, was developed. Fire smoke accelerates at the bifurcation point, a phenomenon that intensifies with an increase in the slope of the branch tunnel. The research in this paper provides a reference for fire safety issues in bifurcated tunnel structures.

Study on the smoke flow characteristics in inclined tunnel with an upstream shaft under natural ventilation

The rapid expansion of urban highway tunnels has led to a significant increase in the risk of fire incidents. Moreover, the urban highway tunnels often have inclinations, which further exacerbates the complexity of the smoke flow. In contrast to the extensive research on natural ventilation in horizontally tunnels, there is still a lack of studies on the natural ventilation of shaft in inclined tunnels. Therefore, this study employed numerical simulations and theoretical analysis to investigate the length of smoke back-layering and flow patterns in inclined tunnel fires with an upstream shaft. By comparing the induced air inflow velocity and smoke back-layering length in inclined tunnels, both with and without an upstream shaft, three types of smoke flow states were identified. State 1: smoke spreading to the upstream shaft, State 2: smoke being limited between the shaft and the fire source, State 3: no smoke backflow in the inclined tunnel. In State 1, the shaft discharges smoke outward. The downstream length and the distance between the shaft and the fire source determined smoke back-layering length. In States 2 and 3, the shaft fills the air inward. The shaft has no obvious effect on the smoke back-layering length. Furthermore, the effects of HRR, fire source position and shaft position on smoke flow characteristics are analyzed. As a result of the analysis, a segmented prediction model for smoke back-layering length and a quantitative method for predicting smoke flow state are proposed. By fine-tuning the tunnel slope, two critical values between the three smoke flow states are obtained. The research results can provide a useful reference for ventilation and evacuation design of inclined tunnels.

Limitations in Tunnel Portal Design: An Evaluation Using Numerical Models and Line Surveys

In this study, engineering geology and geotechnical design studies of a highway tunnel project, located on the route of Zonguldak-Amasra-Kurucasile, was expressed. Owing to the low overburden thickness the subjected slope tunnel, especially the right tube in accordance with the project kilometer incremental direction, will be exposed to asymmetrical load after commence of the excavation. Besides, thicknesses between right tube right wall and the slope face in this section has decreased up to 6 m level. Moreover, as the tunnel is passing under the 1st grade archeological protection area, some of the site investigation studies, such as geotechnical drilling and site laboratory works could not have been performed. Thus, this study is explaining the determination of excavation support system of slope tunnel by using engineering geology studies and numerical models. As the tunnel site is located under the 1st grade archeological protection area, any of the required geotechnical site investigation drilling studies and corresponding site testing was not performed on the tunnel axis. Instead of this, line surveys, local sampling, and internationally accepted rock mass classification studies (RMR, Q, GSI) were performed on the rock mass outcrops, which are positioned against to the Black Sea. At the conclusion of these studies, rock mass engineering properties were determined through the utilization of empirical equations that incorporate data derived from site investigation studies and laboratory test results as input.

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

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 Lo, air velocity at the duct outlet uo) and structural characteristics (digging length Ld, slope of the uphill section q) 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 uo has a positive impact on the air return velocity, while Ld 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.

Response characteristics of surrounding rock and segment structure of large longitudinal slope tunnel

Response characteristics of surrounding rock and segment structure of large longitudinal slope tunnel

Effect of width and slope of large cross-section tunnel on ceiling smoke temperature under natural ventilation

ABSTRACT When a fire occurs in a large cross-section tunnel with slope, the distribution characteristic of ceiling smoke temperature illustrates special laws under the effect of chimney effect, the thermal radiation feedback, and the air entrance limit from walls. A series of numerical simulations are conducted through FDS simulation software based on the actual size of highway tunnel. The influence of large cross-section tunnel width and slope on ceiling smoke temperature when fire occurs are discussed. The research results show that (1) as the tunnel slope increases from 5° to 20°, the distance between the maximum ceiling smoke temperature point and the fire source is 0.5 m, 1 m, 1.7 m, 2.4 m, respectively, and the distance between the ceiling impact point and the fire source is 1 m, 1.8 m, 2.3 m, 3 m, respectively. As the tunnel width increases from 10 m to 20 m, the distance between maximum ceiling smoke temperature point and fire source increases 0.9 m, 1.1 m, 1.3 m, 1.8 m, 2.5 m, and 2.6 m. (2) The prediction formula of maximum ceiling smoke temperature is modified, and a dimensionless relationship among the maximum ceiling smoke temperature and tunnel slope and tunnel width is established. (3) The formula of longitudinal ceiling smoke temperature distribution is modified, and the relationship among tunnel slope, tunnel width, tunnel height, and longitudinal ceiling smoke temperature distribution is established. The research conclusions can provide a theoretical basis for fire prevention design, smoke control and evacuation of this kind of large cross-section tunnel fire.

Study on the effect of width and slope of large cross-section tunnel on critical velocity of fire

When a tunnel fire occurs, due to the difference of tunnel width and slope, both smoke countercurrent length distribution law and critical velocity will become different, and these two are very important parameters in tunnel longitudinal ventilation design. Therefore, for the design of smoke control and longitudinal ventilation of the tunnel, based on actual highway tunnel size, this paper established and ran a series of numerical simulations through FDS simulation software to study tunnel width and slope?s effect on smoke countercurrent length and critical velocity. The results of this paper show that smoke countercurrent length decreases with tunnel slope?s increase and increases with tunnel width?s increase. Through dimensionless analysis, the prediction formulas of smoke countercurrent length and critical wind speed of large cross-section tunnel about tunnel width, slope and height are modified and established. The research conclusions can provide a theoretical basis for the longitudinal ventilation design, smoke prevention and exhaust measures and personnel evacuation in large cross-section tunnel fires.

Non-invasive (georadar) investigation of groundhog (Marmota monax) burrows, Pennsylvania, USA

Zoogenic impact plays a critical role in stream processes, especially bank stability and resulting channel dynamics. This study focuses on bioturbation by groundhogs (Marmota monax) along the riparian zone of Mill Creek (Bucks County, Pennsylvania, USA). Several complexes comprising at least 32 active burrows (average diameter: 25.9 cm) were geolocated, with morphometric measurements obtained at selected sites. Two networks were imaged using high-frequency 800 MHz ground-penetrating radar (GPR) and included: 1) a grid of parallel 3-m-long transects on the south bank, and 2) an 11-m-long profile on the north bank. Post-processed electromagnetic signal traces (A-scans) comprising 2D radargrams (B-scans) revealed voids as reverse-polarity anomalies (hollow inclined shafts and tunnels), allowing for a general assessment of burrow depth and orientation. At the southern cutbank site, a large burrow had an entrance diameter of 0.3 m and a westerly dip. A sloping tunnel section was detected at ~0.5 m depth, based on the geometry of point-source (transverse) hyperbolic diffractions corresponding to the roof and a floor ‘pull-up’. The second locality traversed three open burrow entrances adjacent to large tree roots. This survey along a tributary channel shows multiple hyperbolics below adjacent openings, with the latter showing the characteristic signal ‘breakout’. GPR data show hyperbolic signatures ~0.3–0.4 m below the ground surface. Along this transect, burrowing activity appears to increase with proximity to the northern bank of Mill Creek. An example of a depth slice (bedding-plane view) from a nearby riverbank demonstrates the potential for 3D visualization (C-scans) of burrow networks using a grid of closely spaced GPR profiles. Groundhog burrows constrain maximum long-term level of the groundwater table and serve as important zoogeomorphic structures in diverse ecotones, including developed landscapes. Abundant evidence of bank slumping, incision, and treefall suggests that burrowing activity likely weakens root systems and enhances groundwater flow, thereby initiating or accelerating geomorphic cascades leading to slope failure.

Experimental study on the inundation characteristics of flooding in a long straight subway tunnel

In recent years, the increase in extreme urban flooding events has caused severe property damage and safety problems. Subway tunnels are particularly vulnerable to underground space flooding. There have been traditional hydraulic experiments conducted to investigate unsteady turbulence properties of free surface flow in open channels. However, most experiments in flumes and pipes do not focus on the early formation process of inundation considering the unique structural configurations of subway tunnels. In this study, the general pattern that floodwater intrudes into a subway tunnel was studied by a scaled model experiment. Under different conditions of tunnel slope and inlet water discharge, the flood flow pattern, the water elevation, and flow velocity were investigated and analyzed. The results show that the flooding domain could be divided into three regions, including a Forming Region, a Uniform Region, and a Front Region. The unsteady Front Region performs an exponential rise in water elevation, and the velocity of flood propagation along the tunnel is nearly constant. The shape of the water surface profile is mainly influenced by tunnel slope, and the effect has a transition at the critical tunnel slope which was measured to be around 3‰. The classifications of flooding behavior under different conditions are described in detail. An empirical nondimensionalized formula for the tunnel inundation process in both unsteady and steady stages was proposed. This model enables rapid calculation of water depths with time in a subway tunnel. This research could provide an understanding of flood propagation in subway tunnels and facilitate the study of flooding detection and warnings in underground space. It also provides reference for evacuation decisions and subway flood control design.

Investigation of the fire hazard of underground space fire scenarios in urban metro tunnels under natural ventilation: Analysis of the impact of tunnel slope on smoke back-layering length

The smoke back-layering length is a crucial parameter for evacuating people in both road and subway tunnel fires. This study investigates the fire hazard induced by carriage fire in inclined metro tunnels under natural ventilation. The parameter ‘transition slope’ is defined to measure the smoke flow from the carriage head in the upstream direction to the tunnel or not due to the stack effect of the tunnel slope. The aim of this paper is to analyse the effects of changes in cross-section, downstream length, tunnel slope, and carriage side-door coupling on smoke behaviour characteristics by experiment and simulation methods. A piecewise function expression between dimensionless smoke back-layering length, downstream length, and tunnel slope for carriage fires in an inclined tunnel under natural ventilation is proposed by theoretical analysis. At the same time, a 1:15 scale model experiment was conducted to initially analyse the characteristics of smoke movement. Following this, full-scale numerical simulations were employed to complement the model experiment and quantify the principles governing smoke movement. The experimental results show that the tunnel slope has a significant effect on the smoke back-layering length. In contrast, the influence of the heat release rate was found to be relatively minor. In addition, simulation results show that the tunnel slope has no significant effect on the smoke back-layering length when the fire location is approximately 20 m from the train head, and the tunnel slope is in the range of 2.29° ∼ 3.43° (4% ∼ 6%). For small tunnel slopes, smoke spreads in the tunnel, and the smoke back-layering length produced by the virtual fire source shows a different law from the previous study model. Finally, the correlation coefficient of the piecewise function in theoretical analysis is fitted by combining the experimental and numerical simulation results. Practical application This study provides valuable insights into the practical implications of controlling and mitigating the impact of fires in inclined metro tunnels. By understanding the critical role of tunnel slope and providing a quantitative tool for smoke spread law assessment, this study contributes to the enhancement of safety measures and the protection of lives in tunnel environments during fire incidents.