Smoke Movement in a Sloping Subway Tunnel Under Longitudinal Ventilation with Blockage

Critical velocity and smoke back-layering length are two of the determining parameters to the fire risk assessment of subway tunnel. These two parameters of a sloping subway tunnel with train blockage were investigated both experimentally and numerically in this paper. To address the influences of slope, the slopes of 0, 3, 6, 9, 12, 15% in downhill subway tunnel were studied and the height (H) of the tunnel was replaced by the inclined tunnel height (\( H/\cos \theta \)). The train model with a dimension of 2 m (length) × 0.3 m (width) × 0.38 m (height) was also chosen in simulations and experiments for the tunnel blockage. Thenceforward, 30 reduced-scale experimental and 150 numerical scenarios were analyzed to predict the critical velocity and smoke back-layering length in various sloping subway tunnels. Six different heat release rates including 5.58, 11.17, 16.67, 22.35, 27.94, and 33.52 kW were considered in the experiments and five different heat release rates including 2.79, 5.58, 8.38, 11.17 and 16.67 kW were considered in the simulations. Based on the comparison in the horizontal tunnel, numerical results were quite consistent with the experiments. The results showed that train blockage influenced the smoke back-layering length, and the critical velocity increases with the tunnel slope. Finally, empirical models were developed to predict the critical velocity and smoke back-layering length in a sloping subway tunnel with train blockage.     

Fire Whirl Experimental Facility with No Enclosure of Solid Walls: Design and Validation

In this work, a fire whirl facility with no enclosure of solid walls was designed, for experimental simulation of fire whirls in open field. Air curtains were used to produce the generating eddy of fire whirl. Tests were conducted to evaluate the capability of the new facility. It was found that there was an optimal tilt angle for the air curtains to produce stable fire whirls. Experiments of fire whirls under different pool diameters showed that the mass loss rate \( \dot{m} \) depended on the circulation \( \varGamma \) by \( \dot{m}\sim \varGamma^{1.18} \) and the dimensionless flame height satisfied \( H^{*} \sim \varGamma^{*0.71} \) (where the asterisks denote dimensionless variables). It was also found that the ratio of the continuous flame height to the whole flame height for different pool diameters was 0.67. The centerline temperatures varied with the normalized height \( Z \) by \( Z^{0.08} \), \( Z^{ - 1.30} \) and \( Z^{ - 2.18} \), respectively in the regions of the continuous flame, intermittent flame and plume. The radiative fraction was calculated to be close to 44%. All these results fit well with literature data, thereby the capability of the new facility for producing stable fire whirls was fully validated. Some potential applications of the new facility were discussed in detail. Especially, instruments such as infrared camera can be used to investigate the flame radiation of fire whirls by the new facility.     

CFD Simulations of Pool Fires in a Confined and Ventilated Enclosure Using the Peatross–Beyler Correlation to Calculate the Mass Loss Rate

The aim of this paper is to analyse the application of the Peatross–Beyler (P&B) correlation (Fire and safety science—Proceedings of the fifth international symposium, 1997) to calculate the Mass loss rate (MLR) for a pool fire in a confined and ventilated enclosure for a range of conditions.The experimental references considered are the PRISME-SI-D1, D2 and D6 tests (Prétrel et al. in 9th International seminar on fire safety in nuclear power plants and installations, 2005), conducted by the Institut de Radioprotection et de Sûreté Nucléaire.The dimensions of the enclosure used in the experiment are 5 m in length, 6 m in width and 4 m in height. A pool fire, \(0.4\,\hbox {m}^2\) hydrogenated tetrapropylene (TPH, \(\hbox {C}_{12}\hbox {H}_{26}\)), is located in the center of the room. The compartment is connected to the outside through an inlet and outlet. The P&B correlation is implemented as a boundary condition in computational fluid dynamics calculations. The MLR outcome depends on the average \(\hbox {O}_2\) concentration in a predefined volume and the characteristics of the fuel. The influence of the size and location of the predefined volume, the ventilation branch position (at 1 m and 3.65 m from the floor) and the Renewal Rate (\(R_r\)) (\(4.7\,\hbox {h}^{-1}\) and \(8.4\,\hbox {h}^{-1}\)) are studied. Two types of \(\hbox {O}_2\) predefined volumes have been tested: layer and ring. The layer volume is located in the low part of the compartment, the base of the volume spanning the compartment floor. The ring is a volume around the pit. It is assumed for both approaches that the measured \(\hbox {O}_2\) is representative of the available oxygen for the flame. The P&B boundary condition predicts the influence of the vitiation on the MLR. Other methods, such as imposing the MLR expected in open condition, overpredict the amount of injected fuel. The results show that the P&B correlation provides good agreement with the experimental data. The deviation between experimental data and numerical prediction for the average MLR in the best case is ?5.0% with absolute values of 0.004 kg/s and 0.0038 kg/s for the experiment and the simulation respectively for case PRS-SI-D1. The MLR calculation is influenced by the position of the ventilation opening and the \(R_r\). The temperature and \(\hbox {O}_2\) concentration profiles are significantly influenced by the ventilation configuration. These differences are related to the transport of the injected air from the inlet to the floor by density difference.     

Measurement of the Thermal Parameters of Composite Materials During Fire Tests with Quantitative Infrared Imaging

A fire resistance test, as performed on plates of carbon fibre reinforced polymer composites, is conceptually analogous to a step heating, and can be modelled by the one-dimensional heat equation. Thus modelled, the plate operates as a linear system with an impulse response function that relates temperatures at the front face (the one exposed to fire) and the rear face, and depends on two parameters, namely thermal diffusivity (\(\alpha \)) and effective Biot number (Bi). Taking as input the time evolution of temperature at the front face, the output of the model for each (\(\alpha \), Bi) couple is a predicted temperature for the rear side of the plate. At each point of the plate, \(\alpha \) and Bi can be retrieved by fitting the predicted temperature to the experimental one. These parameters are good quantitative indicators of thermal damage, and therefore its measurement has a particular interest to understand degradation processes associated with fire action. To perform their retrieval as described, temperature measurement for both faces of the plate during the experiment are made with a specifically developed infrared imaging system, composed by two synchronized infrared cameras that image both sides of the sample during the fire test and provide surface temperature maps, spatially co-registered and with the flame effects filtered out. Applying the fitting procedure described to these temperature maps makes possible, for the first time, to measure \(\alpha \) and Bi in situ during the fire test. The value of \(\alpha \) obtained by this procedure (varying from \(\approx 0.5 \times 10^{-7} \, \mathrm{m}^{2} \, \mathrm{s}^{-1}\) in the region most affected by fire, to \(\approx 7 \times 10^{-7} \, \mathrm{m}^{2} \, \mathrm{s}^{-1}\) near sample edges) has been compared to those measured after the test, on samples at room temperature, with the classical flash method. A good general agreement has been found, with differences that can be attributed to the temperature dependence of diffusivity. From this comparison a critical temperature of \(T = 450^{\circ }\)C has been identified, that separates two different regimes, probably related to different degradation states, with slopes of \(-\,1.5 \times 10^{-9} \, \mathrm{m}^{2} \, \mathrm{s}^{-1} \, \mathrm{K}^{-1}\) for \(T<450^{\circ }\)C and \(3 \times 10^{-10} \, \mathrm{m}^{2} \, \mathrm{s}^{-1} \, \mathrm{K}^{-1}\) for \(T>450^{\circ }\)C.     

Combination of Kriging methods and multi-fractal analysis for estimating spatial distribution of geotechnical parameters

Spatial variability (randomness, correlation, and singularity) within the geotechnical parameters of complicated geological movements influences the estimation quality that depends on how well mathematical tools can account for variability through limited observations of a spatial field. Classical statistical methods depict randomness well, but cannot account for the problems associated with spatial correlations. Geostatistical methods such as ordinary Kriging (OK), universal Kriging (UK), and co-Kriging (CK) can produce predictions based on spatial auto-correlation and cross-correlation, but are always accompanied by average smoothing effects; a local singularity created by nonlinear geo-processes, therefore, requires special methods to be properly evaluated. In this study, a shallow load-bearing stratum of silt clay (length = 525 m, width = 80 m) at the former 2010 Expo Park in Shanghai was explored by performing 42 borehole laboratory experiments, which provided the key geotechnical parameters: the cohesion coefficient (\( C \), in kPa), the friction angle (\( \varphi \), in ^o), and the compression modulus (\( E_{\text{S}} \), in MPa). First, Kriging methods such as OK, UK, and CK estimated these geotechnical parameters, then a multi-fractal analysis was employed to measure the local singularity. Cross-validation illustrates that multi-fractal analysis has the ability to depict a local anomaly, and further that the auxiliary information utilized in CK improves spatial estimation accuracy.     

Computational modeling of natural ventilation in low-rise non-rectangular floor-plan buildings

Natural ventilation (NV) is a relevant passive strategy for the design of buildings in seek of energy savings and the improvement of the indoor air quality and the thermal comfort. The main aim of this work is to present a comprehensive NV modeling study of a non-rectangular floor-plan dwelling. Given the arbitrary shape of the building, recourse is made to computational fluid dynamics (CFD) to determine the surface-averaged pressure coefficients (\(\overline {{C_p}} \)). The CFD model was calibrated to match experimental data from an extensive wind tunnel database for low-rise buildings. Then, \(\overline {{C_p}} \) computation via CFD is used to feed the building performance simulation software EnergyPlus, in replacement of the built-in Swami and Chandra parametric model that is only valid for estimating \(\overline {{C_p}} \) in rectangular floor-plan buildings. This computational tool is used to investigate the effect of NV on the thermal performance and the airflow rate in a social housing located in the Argentine Littoral region. Simulation results of the considered building show that NV enables to reduce even more than 65% of the cooling degree-hours. Furthermore, regarding to the \(\overline {{C_p}} \) source (either CFD or Swami and Chandra’s), it is also found that this data has a considerable effect on the airflow rates, but a little effect on the thermal performance.     

A Finite Element Model for the Simulation of the UL-94 Burning Test

The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation is a promising methodology for predicting this behaviour. In this paper, a computational procedure that aims at analyzing the combustion, melting and flame spread of polymer is presented. The method models the polymer using a Lagrangian framework adopting the particle finite element method framework while the surrounding air is solved on a fixed Eulerian mesh. This approach allows to treat naturally the polymer shape deformations and to solve the thermo-mechanical problem in a staggered fashion. The problems are coupled using an embedded Dirichlet–Neumann scheme. A simple combustion model and a radiation modeling strategy are included in the air domain. With this strategy the burning of a polypropylene specimen under UL-94 vertical test conditions is simulated. Input parameters for the modelling (density, specific heat, conductivity and viscosity) and results for the validation of the numerical model has been obtained from different literature sources and by IMDEA burning a specimen of dimensions of \(148 \times 13 \times 3.2\,{\mathrm {mm}}^3\). Temperature measurements in the polymer have been recorder by means of three thermocouples exceeding the 1000 K. Simultaneously a digital camera was used to record the burning process. In addition, thermal decomposition of the material (Arrhenius coefficient \({\mathrm {A}}=7.14 \times 10^{16}\,{\mathrm {min}}^{-1}\) and activation energy \({\mathrm {E}}=240.67\,{\mathrm {kJ/mol}}\)) as and changes in viscosity (\(\mu \)) as a function of temperature were obtained. Finally, a good agreement between the experimental and the numerical can be seen in terms of shape of the polymer as well as in the temperature evolution inside the polymer.     

A Quantitative Infrared Imaging System for In Situ Characterization of Composite Materials in Fire Tests

A novel non-intrusive measurement system based on quantitative infrared imaging has been designed and developed specifically for the study of composite plates submitted to fire. The system consists of two synchronized infrared cameras that image both sides of the sample during a fire test, providing surface temperature maps spatially corregistered. Flame effects on measured temperature are minimized through selection of a spectral band with near negligible infrared absorption-emission (wavelength centre 9585 nm, full width at half maximum 135 nm), as well as software post-processing. An ad hoc experiment has shown that this procedure retrieves surface temperatures with an uncertainty of \(\pm 5\) K, compared to a systematic error larger than 60 K for a classic thermographic measurement. Surface emissivities of both sides of the sample are measured and included in the retrieval procedure. By adding a flash lamp, the system implements an adaptation of the classical Parker’s flash method to thermally thick samples, providing also a map of thermal diffusivities along the sample both before and after the burning. In the region most degraded by fire, the effective thermal diffusivity is reduced approximately one order of magnitude as compared to the pre-test value (from 5.9 × 10^?7 m² s^?1 to 0.5 × 10^?7 m² s^?1). Several composite samples have been analysed while exposed to fire in different conditions, showing that thermal diffusivity after the burning shows a strong correlation with the local maximum temperature reached during the test. More precisely, in the temperature range between \(\sim \)325 and 350\(^{\circ }\)C a drastic change in diffusivity seems to takes place, in a way that suggest a phase change.     

A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic

Recently, Ord and Getis (Ann Reg Sci 48:529–539, 2012) developed a local statistic \(H_i\) , called local spatial heteroscedasticity statistic, to identify boundaries of clusters and to describe the nature of heteroscedasticity within clusters. Furthermore, in order to implement the hypothesis testing, Ord and Getis suggested a chi-square approximation method to approximate the null distribution of \(H_i\) , but they said that the validity of the chi-square approximation remains to be investigated and some other approximation methods are still worthy of being developed. Motivated by this suggestion, we propose in this paper a bootstrap procedure to approximate the null distribution of \(H_i\) and conduct some simulation to empirically assess the validity of the bootstrap and chi-square methods. The results demonstrate that the bootstrap method can provide a more accurate approximation than the chi-square method at the cost of more computation time. Moreover, the power of \(H_i\) in identifying boundaries of clusters is empirically examined using the proposed bootstrap method to compute \(p\)  values of the tests, and the multiple comparison issue is also discussed.     

Effect of Wind on Smoldering Combustion Limits of Moist Pine Needle Beds

We studied moist pine needle beds burning under the effect of wind, in order to determine the upper moisture limit for which there is fire propagation for different wind velocities. For this purpose we built a wind tunnel that allowed us to burn a 600 mm by 150 mm by 40 mm bed under wind velocities between 0.5 m/s and 5.0 m/s and controlled air temperature. Results show an increase in moisture limit from 54% to approximately 140%, for the velocity range indicated. Combustion at limiting conditions proceeds mainly by smoldering with some periods of flaming combustion. It was observed that, for conditions close to extinction, the smoldering front is not quenched at the surface. Additionally, it was also observed that a strong flow of hot gases exit from the fuel bed at the free surface. These two observations lead to the conclusion that the main heat sink is moisture evaporation and that heat losses to the surroundings is reduced by the blowing effect of the hot gases coming off the bed. A dimensional analysis suggests a correlation between moisture limit and wind velocity of the form M = A ? B/ \( {v} \) _w ² , where M is moisture limit for fire propagation, A and B are constants, and \( {v} \) _w is wind speed. Two dimensionless numbers helped to plot the smoldering temperature and fire propagation velocity in a more meaningful way. They are \( \Uppi_{1} = {{T_{sml} c_{p,g} } \mathord{\left/ {\vphantom {{T_{sml} c_{p,g} } {v_{w}^{2} }}} \right. \kern-0pt} {v_{w}^{2} }} \) and \( \Uppi_{2} = {{Mh_{fg} } \mathord{\left/ {\vphantom {{Mh_{fg} } {v_{w}^{2} }}} \right. \kern-0pt} {v_{w}^{2} }} \) , where T _sml is smoldering temperature, c _p,g is the gas specific heat, M is fuel moisture content and h _fg is the latent heat of water evaporation. A relatively high moisture limit at 5 m/s wind velocity is possible due to the relatively high air flow into the smoldering front and the efficient heat feedback produced in forward smoldering.     

Experiments and Numerical Simulations of Pressure Effects in Apartment Fires

The fire induced pressure and its influence on ventilation flows within a compartment have not been studied in detail previously. In this research work, we have investigated the development of gas pressure and the resulting flows in compartment fires first experimentally, by burning a series of heptane pool and polyurethane mattress fires inside a real, 58.6 m\(^2\) by 2.57 m high, apartment and then by carrying out numerical simulations of the experiments with the FDS code. The experiments were conducted with three different ventilation duct configurations to simulate three different airtightness conditions. The peak heat release rates were less than 1 MW and the burning times were about 180 s. The experimental results indicate that the gas pressure in relatively closed apartment can become high enough to revert the flows of the ventilation system, prevent escape through inwards-opening doors, and even break some structures. The peak gas temperatures under the ceiling of the burn room were about 300°C. The pool fires remained well-ventilated. The pressure ranges encountered in the experiments were between 100 Pa to 1650 Pa and the pressure occured within 50 s of ignition. We also report the FDS validation for this type of simulations and discuss the process of modelling the ventilation system and leakages.     

Failure of Fractional Horsepower Ventilation Fan Motors

Fractional horsepower motors are used to power exhaust fans such as those found in bathrooms and oven hoods. There was an increase in fires attributed to these motors shortly after the year 2000. Still, many argue that these motors cannot cause fires because they contain a thermal cutoff (TCO) unit that shuts off electrical current when the TCO reaches a specific temperature. In this paper we describe an unsafe failure mode that can occur after extended use. As fans age, the bearings wear out, resulting in heating of the coil wires. Excessive heating results in break down of the wire insulation, which can lead to a short between wires and create an autotransformer configuration. An autotransformer can support high current in only part of the wiring, resulting in resistive heating sufficient for ignition. With the low thermal conductivity of the coil (\(0.0162\,W/(\hbox {cm}\,{^{\circ }}\hbox {C})\)) and the poor performance of the TCO (no cutoff up to \(260{^{\circ }}\hbox {C}\)), a large temperature gradient is possible. The gradient allows for ignition in one part of the motor without activating the TCO. We experimentally validated the proposed mechanism in an isolated motor and a complete fan assembly resulting in ignition after 18 s and 23 s. The assembled fan burned for more than 6 minutes before we extinguished the flames for safety reasons. Our results are consistent with field results from actual fires.     

Floatation extraction of thinly-emulsified tributyl phosphate stabilized by silicic acid

We have studied regularities of floatation extraction of fine-emulsion tributyl phosphate stabilized by silicic acid. Most completely the floatation process occurs at pH 5–6. At the concentration of silicic acid 500–550 mg/dm³ the degree of floatation extraction of tributyl phosphate (α) reaches 70% (floatation time of tributyl phosphate is 10 min). In the presence of HNO₃ (1–5 mol/dm³) the value α passes through the maximum at \(C_{HNO_3 } \)= 3 mol/dm³. A conclusion was made about an important role in the studied floatation process of not only electrical, but also structural-mechanical properties of the surface of the air drops and bubbles.     

The socially optimal and equilibrium locations of two stores or libraries with consumer search

This paper examines the socially optimal (and also equilibrium) locations of two stores or libraries on a linear market of unit length. If each consumer has probability \(w\) of finding a desired product at each store, then the socially optimal locations are never completely centralized for full information, but are completely centralized for \(w \le 0.5\) when costly visit search is necessary. The Nash equilibrium locations of two stores, and various alternative models for the socially optimal locations of two stores, are also examined.     

Study of the Ultimate Load Capacity of K-Type Tube-Gusset Plate Connections

In order to investigate the ultimate load capacity of K-type tube-gusset plate connections with stiffened plate, the static tests of five full-scale specimens were conducted in this study. The results indicate that the end stiffened plate is critical for improving the load capacity of the connections. In addition, the parametric nonlinear finite element analysis of the K-type tube-gusset plate specimens was performed with account of such non-dimensional parameters as chord diameter-to-thickness ratio (γ), plate width-to-chord diameter ratio (α), plate thickness-to-chord thickness ratio (\(\tau_{1}\)), stiffened plate thickness (t_d), and nominal-to-yield stress ratio (η). The above analysis implies that the ultimate load capacity decreases with the increment of γ and increases with the increment of α and \(\tau_{1}\), while it is only slightly affected by the stiffened plate thickness. Compare the results of the finite element analysis with assessment by design guides existing. Based on the former results, an equation for estimating the load capacity of K-type tube-stiffened gusset plate is proposed.     

Examination on Fatigue Limit and Crack Growth Characteristic of SBHS700 Base Metal

The object of this study is to clarify fatigue limit and fatigue crack growth characteristic of SBHS700 base metal which is 780 MPa class steel. This study carried out the fatigue tests of SBHS700 base metal containing different defect size, and the fatigue limit was compared with that of the conventional steel. Test results indicate that the fatigue limit increased with decrease initial defect size, and can be precisely evaluated by using \(\sqrt {area}\) parameter model. This paper also presents that crack growth characteristic was almost the same as that of the conventional steel from the observation of striations by using Scanning electron microscope and length of beach marks.     

纵向通风与竖井自然排烟下隧道火灾烟气特性实验研究

中国逐渐发展成为世界上隧道和地下工程最多的国 家,其长隧道数量和长度跻身世界前列。据统计,火灾中85%的 人员死亡是由热烟气造成的,目前隧道中采用较为广泛的排烟系 统有纵向排烟系统、集中排烟系统和横向排烟系统,而针对长隧道 来说,我国广泛采用的是竖井式纵向通风,因此,研究纵向通风与 竖井排烟综合效应下隧道火灾烟气流动特性及温度分布规律具有 重要意义。本文建立了1：10 缩尺寸竖井隧道模型,主隧道长度 16.5 m,宽度1.3 m,高度0.65 m;竖井通过排烟横通道与主隧道 连接,排烟横通道设置在主隧道侧面中部,尺寸为1.2 m 长、0.6 m 宽、0.4 m 高;竖井横截面为半径0.6 m 的1/4 圆,高4.6 m。在 竖井隧道模型中开展了一系列油池火实验,选取2 种方形燃烧池 （20 cm×20 cm、23 cm×23 cm）作为火源,设置2 个纵向火源位置 （位置A：火源中心线与排烟横通道中心线距离0.375 m;位置B： 火源中心线与排烟横通道中心线距离1.375 m）,7 种纵向通风风 速（0,0.18,0.27,0.35,0.44,0.52,0.69 m/s）,定量分析不同工 况下温度分布及烟气逆流长度。研究结果表明：当无纵向通风时, 火焰与隧道地板垂直,且呈轴对称形态;当有纵向通风时,火焰向 下游偏移,且纵向通风风速越大,火焰向下游偏移越明显;当纵向 通风风速为0 m/s 时,由于竖井的存在,火源上、下游两侧烟气温 度分布并非对称,火源下游（竖井侧）烟气温度下降速度较快,与单 洞隧道烟气温度分布明显不同;随纵向通风风速增加,烟气逆流长 度和烟气温度减小,而最大温度偏移距离整体呈增加趋势;当无量 纲纵向通风风速v′＜0.19 时,主隧道最大温升△Tmax 与Q2/3/ Hef 5/3 呈正比,而当无量纲纵向通风风速v′＞0.19 时,主隧道最大 温升△Tmax 与Q? /(vb1/3Hef 5/3)呈正比,但常数系数均小于Li 等预 测模型中的常数系数;竖井隧道内无量纲纵向烟气温度分布符合 Fan 和Ji 等建立的纵向温度衰减模型,衰减系数k′在1.36~1.63 范围内变化,但其值明显大于单洞隧道纵向温度衰减系数k′;另 外,当火源位于位置A 时,最大烟气温度低于火源位于位置B 时 的最大烟气温度,无量纲纵向烟气温度衰减速度慢于火源位于位 置B 时衰减速度。     

Engineering Approach for Designing a Thermal Test of Real-Scale Steel Beam Exposed to Localized Fire

This paper reports the design and results of a thermal test on heating of a 6 m long steel W beam subjected to a localized fire conducted at the National Fire Research Laboratory of the National Institute of Standards and Technology. A engineering approach was proposed to determine the heat release rate of the test fire. By the approach, a recently developed simple fire model was first used to approximately calculate the heat release rate and then a sophisticated model was used to check/refine the calculation. The concept of adiabatic surface temperature was used in the sophisticated model to represent the thermal boundary conditions at exposed surfaces in fire. The proposed approach successfully predicted the critical value of heat release rate of 500 kW to reach a target temperature of \(500^{\circ }\hbox {C}\) in the test specimen. A calibration test was also conducted to understand the difference between the predicted and measured steel temperatures in the investigated test, and found that the sophisticated model over-predict the adiabatic surface temperatures which would contribute to the over-prediction of the steel temperatures. The error of the predicted maximum steel temperature in the test specimen was within 10%. The study reported here is not necessarily a validation of the sophisticated model, rather the study provides a successful case study using current knowledge and tools to design realistic and controlled fire tests.     

Impact d’une galerie étanche peu profonde sur l’écoulement d’une nappe

While many studies have been achieved on the interactions between groundwater and deep tunnels, in order to identify the evolution of pore pressure around the structure and to characterize the flow to its leaky parts, few studies have dealt with the impact of the carrying out of an impervious gallery in a shallow aquifer. The induced change in the piezometric level of the aquifer and the one in the hydraulic gradient of the flow however can, in this case, have significant consequences, in particular when the linear structure is located in an urban environment. This paper investigates, in steady state, the case of a straight tunnel having a horizontal axis perpendicular to the direction of the regional groundwater flow and a circular or square cross section. The aim is to determine the additional lost head Δh _s due to the tunnel (i.e. additional to that resulting from the regional flow, supposed to be uniform with a hydraulic gradient i ₀). In the context of a horizontal confined aquifer having a thickness 2B and of a tunnel of radius R located in the middle part of the aquifer, an analogy can be established with the flow above a hydraulic threshold resulting from a local rise of the elevation of the base of an aquifer, having a thickness B, on a width 2R and with a vertical maximum amplitude R. When neglecting the vertical component of the hydraulic gradient compared to its horizontal component, analytical solutions are developed for various hydraulic threshold shapes (rectangular, triangular and circular), based on the equivalence with a local change in the transmissivity of an aquifer keeping a constant thickness. The corresponding formulas take the form: $ {\frac{{\Updelta h_{s} - \Updelta h_{0} }}{{\Updelta h_{0} }}} = f(a) $ , with $ a = {\frac{R}{B}} $ and Δh ₀ = 2Ri ₀. The use of these formulas shows that the additional lost head Δh _s due to the hydraulic threshold is proportional to i ₀ and that, for values of the ratio a < 0.5, the change in the piezometric surface is small. These conclusions are therefore limited by the fact that the vertical conductivity is supposed to be very large. In order to remove this hypothesis, numerical simulations are achieved using the MODFLOW code. It is considered a confined aquifer of length 2L = 110 m and thickness B = 10 m, a ratio $ a = {\frac{R}{B}} = 0.25 $ and a horizontal hydraulic conductivity $ K_{H} = 10^{ - 5} \,{\text{m}}\,{\text{s}}^{ - 1} $ . In the case of an isotropic medium ( $ \alpha = {\frac{{K_{H} }}{{K_{V} }}} = 1 $ ), the simulations allow to check the linearity of the relationship between Δh _s and i ₀, with therefore a homogeneous variation in the proportionality coefficient compared to analytical solutions. Simulations also reveal that, in the case considered, the width of influence upstream and downstream L _i , corresponding to a value of the vertical component of the hydraulic gradient <1% of i ₀, is below 5.5R for the three hydraulic threshold shapes, and that it was few influenced by the hydraulic gradient i ₀. In the case of an anisotropy of the horizontal and vertical hydraulic conductivities, simulations reveal the significant importance of the anisotropy ratio $ \alpha = {\frac{{K_{H} }}{{K_{V} }}} $ when it is more than 1, the most common case, and indicate that the proposed analytical solutions give an asymptotic value of $ {\frac{{\Updelta h_{s} }}{{\Updelta h_{0} }}} $ for the isotropic case and for the values of the component α < 1. In the context of an unconfined aquifer, the hydraulic threshold model is not directly applicable. The model studied, using the Dupuit-Forchheimer assumption, is the one of a water table aquifer with a sloped base (slope value: p ₀). The simulations focus on an aquifer of length 2L = 85 m, with a tunnel of circular cross section having a diameter 2R = 5 m, bottom of which is located 5 m above the base of the aquifer, the isotropic hydraulic conductivity being equal to $ K = 10^{ - 5} \,{\text{m}}\,{\text{s}}^{ - 1} $ . The definitions of water heights d ₀ and d between the water table and the top of the tunnel are given in Fig. 7. The water table can be located above (fully submerged tunnel) or below (partially emerged tunnel) the top of the tunnel. The difference d ₀ ? d represents the half of the additional lost head Δh _s due to the tunnel. Simulations are performed for various values of p ₀ and d ₀. They provide the values of i ₀, d and Δh _s . In the case of a fully submerged tunnel (d > 0), a significant rise of the water table upstream of the tunnel is obtained only for high values of the hydraulic gradient (5 and 10%), but, even in this case, it remains less than the tenth of the wetted height of the aquifer h _m . It is also highlighted that the ratio $ {\frac{{\Updelta h_{s} }}{{i_{0} }}} $ varies as a linear function of (R + d) and that, in the studied case, there is no influence of the tunnel for d ≥ 4R. In the case of a partially emerged tunnel (d < 0), the aquifer is locally confined under the tunnel. It is suggested that an equivalence is possible with the case of a confined aquifer having a thickness equal to the wetted height in the unconfined aquifer. This is verified with one of the simulations. In the case of a partially emerged tunnel, the change in the water table due to the tunnel remains low.     

A computational study on effects of fire location on smoke movement in a road tunnel

In this work, a numerical model of tunnel fire is developed and aimed to investigate the influence of cross-sectional fire locations on critical velocity and smoke flow characteristic. It is shown that the critical velocity for a fire next to the wall is obviously higher than that for a fire in the middle or on the left/right lane. The ratio is estimated to be 1.12. The predictions of critical velocity from ‘small-fire’ models show a good agreement with that for a fire in the middle or on the left/right lane from CFD. The tunnel height at the fire location is proposed to be instead of the hydraulic tunnel height in the ‘big-fire’ model of Wu and Bakar for a fire next to the wall. The smoke moves backward in a tongue like form as the ventilation velocity is lower than the critical velocity. The back-layering length of a fire in the middle is shown to be approximate twice than that on the left/right lane under the same ventilation velocity, although they share the same critical velocity. Whereas a relatively short back-layering length for a fire next to the wall under the velocity of 2.6 and 2.7 m/s. In addition, a snaky high-temperature profile on the top wall at the initial downstream is observed for a fire on the left lane and next to the wall, and finally a steady and layered smoke flow. The likely cause of this phenomenon is subsequently explained in this study.