Variation of heat release rate with forced longitudinal ventilation for vehicle fires in tunnels

Fire Safety Journal 36 (2001) 569–596

Variation of heat release rate with forced longitudinal ventilation for vehicle fires in tunnels R.O. Carvela,*, A.N. Bearda, P.W. Jowitta, D.D. Drysdaleb a

Department of Civil & Offshore Engineering, Heriot-Watt University, Edinburgh, Scotland EH14 4AS, UK b Department of Civil & Environmental Engineering, University of Edinburgh, Edinburgh, Scotland EH9 3JN, UK Received 22 August 2000; received in revised form 20 November 2000; accepted 12 February 2001

Abstract Many tunnels are equipped with longitudinal ventilation systems to control smoke in the event of a fire. However, the influence of such ventilation on fire development and fire spread has rarely been considered. This paper presents the results of a study using a Bayesian methodology to estimate the effect of forced longitudinal ventilation on heat release rate (HRR) for fires in tunnels. The behaviour of car and heavy goods vehicle (HGV) fires with a range of forced ventilation velocities is investigated. Results are presented and the implications are discussed. It has been found that forced ventilation has a great enhancing effect on the HRR of HGV fires, but has little effect on the HRR of car fires. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Tunnel fires; Ventilation; Bayesian methods; Fire growth; Fire size; Heat release rates

1. Introduction Over the past few years the issue of fire in transport tunnels has become an important concern, not only for tunnel designers, operators and regulators, but also for the general public. The fires in the Tauern Tunnel in Austria [1], the Mont Blanc Tunnel joining France to Italy [2], the Channel Tunnel joining the UK to France [3] and the underground railway in Baku, Azerbaijan [4] have highlighted the issue and shown the devastating effect of such fires, in terms of loss of life, damage to facilities and destruction of vehicles. *Corresponding author. Tel.: +44-131-449-5111; fax: 44-131-451-5078. E-mail address: [email protected] (R.O. Carvel). 0379-7112/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 1 0 - 8

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Even though fatal fires in tunnels are rare, and the majority of fires that do occur in tunnels are small, rarely involving more than one vehicle, there is always the need to increase our level of understanding of the behaviour of fire in tunnels. This is because traffic density in tunnels is increasing all the time, and tunnel systems are continuing to grow in size, length and complexity. In many tunnels one of the most important parts of fire safety management is control of the ventilation system, the main concern usually being to control the smoke in the event of a fire to such an extent that there is a smoke free escape route from the fire location. Tunnel ventilation systems fall into two main categories: transverse and longitudinal. In transversely ventilated tunnels, fresh air is supplied from a duct (either under the roadway or above the ceiling) at periodic points along the length of the tunnel. In some cases the exhaust air is only extracted at one or two points at or near the portals, this is described as ‘‘semi-transverse ventilation’’. In other cases there is a separate duct to extract air at periodic points along the length of the tunnel, this is described as ‘‘fully transverse ventilation’’. In longitudinally ventilated tunnels, air is forced along the tunnel, often by jet fans installed on the ceiling at periodic points along its length. Jet fans are a comparatively recent invention, so older tunnels tend to be transversely ventilated. However, installation of longitudinal ventilation systems tends to cost less than transverse ventilation, so many recently constructed tunnels are equipped with longitudinal ventilation. In the USA the majority of tunnels are transversely ventilated, in the far east the majority are longitudinally ventilated, whereas in Europe both types of system are commonplace. In tunnels with longitudinal ventilation the concern in the event of a fire is generally to control the smoke so that there is no smoke flow upstream of the fire location, this is known as prevention of ‘‘backlayering’’ or ‘‘back-flow’’. Although it has been shown that the ‘‘critical’’ ventilation velocity required to prevent backlayering varies with fire size [5] and with tunnel shape [6], a recommendation used in many countries is that a fixed ventilation rate of 3 m s
1 be maintained in the event of any fire, to prevent the smoke backlayering [7]. The heat release rate (HRR) of a fire is considered by many to be the principal factor contributing to the severity of the fire [8]. It is dependent on a number of factors including the composition of the fuel and the availability of oxygen. It is therefore to be expected that the heat release rate of a fire in a tunnel will vary significantly with the forced ventilation velocity in the tunnel. Although a number of studies have been carried out to investigate the behaviour of smoke from fires in tunnels under a range of different ventilation conditions [9,10], few studies have been carried out to investigate the behaviour of the fires themselves, so the variation of the HRR of a fire in a tunnel with ventilation velocity is not adequately known. In 1976, Heselden estimated the HRR of a heavy goods vehicle (HGV) fire in a tunnel to be approximately 20 MW [11] and this figure has tended to become an accepted value. Some tunnels have been built with a ‘‘design fire’’ of approximately 20 MW in mind [12] (although other tunnels have been designed to withstand fires with HRRs of 50–100 MW). However, the only well documented fire test of a HGV in a tunnel, carried out in a longitudinally ventilated tunnel, exhibited a HRR well in excess of 100 MW [13]. Opinion is divided as to whether the huge

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difference between these two figures is due to underestimation in the first instance, or the dramatic intensifying effect of the longitudinal ventilation in the experimental results. In order to increase the level of safety in vehicle tunnels, it is necessary to understand how fires behave in tunnels with longitudinal ventilation systems. Specifically it is important to understand how fires involving vehicles will respond to changes in the ventilation velocity. This is particularly significant as the majority of fire experiments in tunnels have been carried out with fuel pools rather than with solid fuels or actual vehicles, and while test series like the Memorial Tunnel Fire Ventilation Test Program [9] have greatly increased the level of understanding of smoke behaviour in tunnels with different ventilation configurations, they reveal nothing about how vehicle fires will respond to forced ventilation. The mechanism of burning of a fuel pool is very different from that of a solid fuel. For a vehicle fire or a wooden crib fire, for example, forced ventilation may blow through the fire load, causing the fire to spread and grow in intensity in a very different manner than if there were no forced ventilation. This is not the same for a pool fire where all the combustion occurs at (or above) the surface, not inside the load. That is not to say that the influence of longitudinal ventilation on a pool fire is not important or significant, just that it is different to the influence of ventilation on a vehicle fire. Pool fires have been considered in a separate part of this study and the results have been published elsewhere [14]. There have been very few fire tests of real vehicles in tunnels, and the tests that have been carried out have used a number of different tunnel sizes, vehicle types and ventilation conditions, which give no coherent picture of fire behaviour overall. Yet it would be desirable to use all the experimental data that are available to investigate the relationship between fire size (HRR) and ventilation velocity. There is no way to use such a diverse set of data using conventional statistical analysis, but one method that may be used is to consider the problem probabilistically and use Bayes’ theorem. 1.1. Bayes’ theorem Bayesian methods have been used for many years as a way to determine estimates of probability given expert judgement and ‘‘evidence’’ [15]. An unknown variable of a system, designated k in this instance, is considered to be a random variable with a probability function PðkÞ. The function may be considered to be continuous or comprised of a number of discrete possible values of k. For a number of reasons, which will be covered in Section 3 of this paper, a discrete methodology has been used in this study. In its discrete form, Bayes’ theorem assumes that the random variable can take any of a number of values: k1 , k2 , k3 , . . ., kn . Estimates of the probabilities Pðk ¼ ki Þ can then be refined by considering an experimental test result, denoted I. Rev. Thomas Bayes (1702–1761) considered the product rule, as applied to conditional probabilities: Pðk ¼ ki j IÞPðIÞ ¼ PðI j k ¼ ki ÞPðk ¼ ki Þ;

ð1Þ

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where Pðk ¼ ki j IÞ is the conditional probability of k being equal to ki given I, and so on. He rearranged this to give Pðk ¼ ki j IÞ ¼

PðI j k ¼ ki ÞPðk ¼ ki Þ : PðIÞ

ð2Þ

In Bayesian notation, Pðk ¼ ki Þ is the ‘‘prior’’ estimate of probability, that is the probability before the experimental evidence is considered, Pðk ¼ ki j IÞ is the ‘‘posterior’’ estimate of probability and PðI j k ¼ ki Þ is the ‘‘likelihood’’ of the evidence if k ¼ ki . PðIÞ is clearly the probability of the evidence for all values of k, so Bayes’ theorem can be expressed as PðI j k ¼ ki ÞPðk ¼ ki Þ Pðk ¼ ki j IÞ ¼ Pn : i¼1 PðI j k ¼ ki ÞPðk ¼ ki Þ

ð3Þ

As the ‘‘likelihood’’ of the evidence features in both the top and bottom of the right hand side of Eq. (3), the sum of all likelihood values need not equal one, that is, the likelihood of the evidence is not necessarily expressed as a probability. In this study, likelihood values will be given arbitrary values relative to each other, for example the likelihood that k ¼ 1 may be given a value four times the value given to k ¼ 2, and so on. The posterior probabilities represent a refined estimate of the probability distribution of k. As new experimental data become available the process may be repeated using the posterior probability distribution from the previous calculations as the prior distribution in the new calculations. This may be repeated as and when new experimental data become available. As Lindley put it ‘‘today’s posterior distribution is tomorrow’s prior distribution’’ [16]. To determine the mean value of k, known as the ‘‘expectation of k’’, the Bayesian estimator can be used: X EðkÞ ¼ ki Pðk ¼ ki j IÞ: ð4Þ 1.2. Methodology To describe the variation of HRR with ventilation velocity, the heat release rate coefficient k will be used, defined by Qvent ¼ kQnat ;

ð5Þ

where Qvent is the HRR of a vehicle fire in a tunnel with forced ventilation and Qnat is the HRR of a similar fire in a similar tunnel with natural ventilation. For the purposes of this study it is assumed that ‘‘natural’’ ventilation has a fairly low velocity, this would not necessarily be the case on a windy day or in a tunnel with a significant slope. By considering the coefficient k, rather than the absolute HRR of a fire, factors such as the composition of the vehicle may be bypassed. Thus if k ¼ 1:5 for a car fire in a certain tunnel with a 2 m s
1 airflow, then a small car, which would be expected to burn at 2 MW in a tunnel with natural ventilation, would probably burn at about 3 MW whereas a larger car, which might burn at 5 MW in a naturally ventilated tunnel, would be expected to burn at about 7.5 MW. It should be noted that Qnat for a vehicle fire would probably not be the same as the HRR of a fire

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involving a similar vehicle carried out under a calorimeter hood in a laboratory; when fires in tunnels are compared to similar fires outside of tunnels a significant enhancement of HRR, due to the confining geometry of the tunnel, is generally observed [17,18] unless the fire is underventilated, in which case Qnat may be significantly reduced. Vehicles that pass through tunnels come in all shapes and sizes, however experimental fire testing of vehicles in tunnels has not yet covered the whole range of vehicle sizes, so it was decided to consider only passenger cars and HGVs in this study. Data from the following fire tests were used in the study: * * * * * * * * *

HGV fire test in the Hammerfest tunnel}forced ventilation [13,19]; simulated truck load in the Hammerfest tunnel}natural ventilation [19, 20]; reduced scale HGV simulation test in the HSE tunnel}forced ventilation [21]; car fire tests in the Hammerfest tunnel}natural ventilation [19,20]; car fire test in the Des Monts Tunnel}forced ventilation [22]; wooden crib tests in the VTT tunnel}forced ventilation [23]; wooden crib tests in the Hammerfest tunnel}natural and forced ventilation [19]; car and wooden crib tests in a ‘‘blasted rock tunnel’’}natural ventilation [24]; wooden crib test in the HSE tunnel}forced ventilation [25].

Data from each fire test with forced ventilation were compared with data from equivalent fire tests with natural ventilation, to determine approximate values of k for each forced ventilation test. For the reduced scale tests, HRR and ventilation velocity values were scaled up to ‘‘full size’’ using Froude scaling laws [26]. For car fires it was decided to consider the following discrete values of k: 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0. However, it quickly became apparent that the spread of possible k values for HGV fires subject to forced ventilation was far greater than for car fires. In order to keep the number of discrete values of k to a meaningful and manageable level, it was decided to consider that k for a HGV fire would fall into one of the following ranges of values: 0.5–1, 1–2, 2–4, 4–8, 8–16, 16–32, 32–64 and 64+. This includes the possibility that k may take any value above 0.5, but also gives enough resolution at small values of k to be useful. It may be that there is an upper limit to the value of k, beyond which the fire would be blown out. As this has not happened in any of the experimental tests used in this study there is no way of predicting where this limit, if it exists, might occur, so it will not be considered further in this paper. The prior probability distribution functions for this study were intended to be representative of ‘‘expert opinion’’ and to this end a panel of eight experts in the fields of fire safety engineering, fire dynamics and fire fighting was organised. The expert panel contained representatives from the UK Health & Safety Executive (who have carried out experimental fire tests in tunnels and modelling of fires in tunnels), the Fire Research Station (experimental and theoretical modelling), Kent Fire Brigade (experience of the ‘‘real life’’ fire in the Channel Tunnel), fire consultants (experimental fires in tunnels carried out for Eurotunnel and in the EUREKA test series) and experts in fire dynamics from Edinburgh and Heriot-Watt Universities. For financial reasons it was not possible to include experts from countries other than

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Fig. 1. Theoretical test tunnel for HGV case.

the UK in this study. It is possible that this panel may have a cultural bias and it is acknowledged that an international panel might have given slightly different estimates. Each panel member was independently asked to estimate various factors relating to fire size and k for vehicle fires in specific tunnel situations subject to ventilation velocities of 2, 4, 6 and 10 m s
1 in the case of the HGV fire and of 1.5 m s
1 in the case of the car fire. These estimates were combined to give the prior distribution functions used in this study. As all the experimental tests that are relevant to the case of a HGV fire in a tunnel were carried out in single lane tunnels, only HGV fires in single lane tunnels have been considered in this study. The dimensions of the hypothetical test tunnel, for which the estimates were made, are based on the Channel Tunnel, and are shown in Fig. 1. Car fire tests were carried out in both single lane and twin lane tunnels so estimates were sought for a typical twin lane tunnel, as shown in Fig. 2. In order to refine the prior estimates of k, it is necessary to estimate the ‘‘likelihood’’ of each experimental test for each discrete value of k. Initially it had been hoped that the members of the expert panel would be able to provide these estimates, but after a short pilot study was carried out it became clear that some people considered any evidence as support for their own prior estimates, so this was not done. It was decided that the first author of this paper was the best person to estimate the likelihood values as he was independent from all the prior estimates and also familiar with all the experimental test results. The likelihood of an experimental test is not an easy concept to grasp. The question one must ask oneself is of the form How likely is it that this experiment would have happened, in the way it did, if the value of k for the hypothetical test tunnel was assumed to be 2.0 for a forced ventilation rate of 4 m s
1? Making precise estimates of likelihood values for each value of k would be a very complex process, and may not be justifiable; it is also unnecessary. Instead each

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Fig. 2. Theoretical test tunnel for car fire case.

likelihood value has been allocated only a ‘‘high’’, ‘‘medium’’ or ‘‘low’’ rating, which not only simplifies the process but takes much of the individual opinion out of the process. The ratio of high : medium : low was originally set at 4 : 2 : 1 but has also been varied to test the sensitivity of the posterior results. This will be discussed later in the paper.

2. Results For the case of a HGV fire in a tunnel, the development of the fire was studied at two points: (i) in the growth phase and (ii) at maximum heat release rate. 2.1. HGV fire in the growth phase The experts were asked to consider a HGV loaded with furniture in a tunnel. It is assumed that a fire breaks out at the front of the trailer and grows until it involves the whole vehicle. Under natural ventilation conditions the fire grows from 1 to 5 MW in time tg . The experts were asked to consider a similar vehicle in a similar tunnel with forced longitudinal ventilation and were asked about their expectation of the HRR of the fire at time tg after the fire was 1 MW in size. On average the expectation of the experts was that the HRR would probably be between 1.5 and 2 times greater at time tg after the fire was 1 MW for all ventilation velocities considered. A prior probability distribution was built for each of the four ventilation velocities considered from these estimates, as shown in Fig. 3. The following experimental tests were considered to be relevant to this case: *

* *

*

EUREKA simulated truck load test in the Hammerfest tunnel (full scale, natural ventilation); EUREKA HGV fire test in the Hammerfest tunnel (full scale, forced ventilation); EUREKA wooden crib tests in the Hammerfest tunnel (full scale, forced and natural ventilation); FOA wooden crib tests in the ‘‘blasted rock tunnel’’ (reduced scale, natural ventilation);

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Fig. 3. Prior probability distributions for a HGV fire in the growth phase.

* *

wooden crib test in the HSE tunnel (reduced scale, forced ventilation); simulation of HGV fire in the HSE tunnel (reduced scale, forced ventilation).

Not all these tests were carried out at the same scale, and although k is a dimensionless coefficient and is the same at full and reduced scale, ventilation velocity is not and the airflow velocities of the reduced scale tests require to be scaled up to full scale in order to easily compare the tests. Froude scaling rules [26] were used. By conserving the Froude number, defined by Fr ¼ u2 =gL

ð6Þ

(where u is the flow velocity, g is the acceleration due to gravity and L is a characteristic dimension of the tunnel) the ventilation velocity scales as L1=2 and heat release rate scales as L5=2 . It has been demonstrated that the mean hydraulic diameter, H% (the ratio of four times the tunnel cross-sectional area to tunnel perimeter), of a tunnel is the characteristic dimension in critical velocity experiments [6], and this is the dimension used in scaling calculations here. The reduced scale test data were scaled up to an equivalent size to the full scale tests for comparison. Each forced ventilation test was then compared to each natural ventilation test to gain an approximate value of k for that test at the test airflow velocity. Estimates of the likelihood functions for each forced ventilation test were then made for each of the four ventilation velocities considered. In the initial stages of the HGV fire test, the ventilation velocity was 6 m s
1. The fire in this case was ignited in the cab, not at the front of the trailer, and so the HRR of the fire was between 10 and 15 MW when the fire spread to the trailer. However the fire then grew to well over 100 MW in under 2 min, which is substantially faster than the growth of any of the natural ventilation tests. Comparing the rate of increase of HRR of the HGV test with the initial stages of the naturally ventilated simulated truck load test suggests a k value of about 25, possibly much greater, for a HGV in the Hammerfest tunnel with a forced ventilation velocity of 6 m s
1. For forced ventilation rates of 6 and 10 m s
1 a ‘‘high’’ likelihood has therefore been given for k values in the 16–32 range, whereas for ventilation rates of 2 and 4 m s
1, a ‘‘high’’ likelihood has been given for k values in the 8–16 range. ‘‘Medium’’ and

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‘‘low’’ likelihood values are allocated around these ranges in accordance with the amount of uncertainty (as the test was carried out at 6 m s
1, the estimated likelihood function for 2 m s
1 has more uncertainty than for 4 m s
1). It has been observed that the arrangement of the fuel in the simulated truck load test was significantly different from the arrangement of the fuel in the HGV test and so the two may not be directly comparable; perhaps if cribs of a different geometry or porosity had been used in the truck load test the HRR development would have been faster. However, even if the arrangement of the fuel had caused the fire to develop two or three times faster, the apparent value of k in comparison with the HGV test would still have been more than eight, which is more than twice the value expected by the majority of the expert group. A wooden crib test was carried out in the Hammerfest tunnel with a forced ventilation velocity of 2.9 m s
1. Comparing data from this test with data from the naturally ventilated wooden crib test in that tunnel and with naturally ventilated crib tests in the blasted rock tunnel, suggests a k value of between 1.3 and 1.7, in the growth phase, for ventilation velocities about 3 m s
1. A high likelihood has therefore been allocated for k ranges 1–2 and 2–4 at 2 and 4 m s
1. Medium likelihoods have been given for ranges 0.5–1 and 4–8 at 2 and 4 m s
1 and for all ranges from 1 to 8 for 6 and 10 m s
1 ventilation rates. All other ranges have been allocated a low likelihood. Although the wooden cribs used in these experiments are not of comparable size to a real HGV load, the test has been considered relevant to the initial stages of fire development on a HGV load. For the purposes of this study it is assumed that the initial rate of growth on a large crib (before the fire involves the whole crib) is similar to the rate of growth in the initial stages of a fire on a larger load (e.g. a HGV trailer). A wooden crib test was carried out in the HSE tunnel at 13 scale, with a ventilation velocity equivalent to 2.0 m s
1 at full scale. Comparing data from this test with data from all the naturally ventilated wooden crib tests suggests a k value of between 8 and 20 for the initial stages of the fire. A high likelihood has therefore been allocated to k range 8–16 for a 2 m s
1 forced airflow, and to k range 16–32 for all other airflow velocities. Medium likelihoods have been allocated to the ranges on either side of the highs and all other ranges have been allocated a low likelihood. A 13 scale HGV simulation test was also carried out in the HSE tunnel. This involved a replica of a HGV carrier wagon from the Channel Tunnel complete with HGV tractor and trailer. Part of the fuel load in this test was supplied by a liquid fuel pan. The initial ventilation velocity was equivalent to 6.3 m s
1 at full scale, after 16 min this was reduced to the equivalent of 2.5 m s
1 and after a further 12 min it was again reduced to the equivalent of 1.7 m s
1. Comparing data from this fire test with data from all the naturally ventilated tests suggests a k value of above 25 for a ventilation velocity of about 6 m s
1 during the growth phase, although it must be noted that the development of the fire in the fuel pan in this test would be significantly different from the development of a fire in a wooden crib or a real vehicle, so these observations should be used with caution. A high likelihood has been allocated to k range 16–32 at 4, 6 and 10 m s
1 and to k range 8–16 at 2 m s
1. Medium likelihoods have been allocated to the 4–8 range at 2 and 4 m s
1, to the 8–

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16 range at 4, 6 and 10 m s
1, to the 16–32 range at 2 m s
1 and to the 32–64 range at 4, 6 and 10 m s
1. All other ranges have been allocated a low likelihood. Results will be discussed both using and discounting this test. The likelihood values used to refine the prior probability distribution of k in the growth phase of a HGV fire are summarised in Table 1. The prior probability distributions, based on the estimates of the expert panel, were refined using Bayes’ theorem with the likelihood values allocated for the four pieces of experimental evidence described above. The posterior probability distributions are shown in Fig. 4. To calculate the expectation of the probability distribution it is necessary for the unknown quantity to fall into equally sized ranges. As the k ranges used in the HGV study are not of equal size, it is not possible to calculate the expectation of k directly. Instead, the probability distribution was expressed in ranges of the variable n, defined by k ¼ 2n . The k ranges used in the study may then be expressed in terms of n as:
0.5  0.5, 0.5  0.5, 1.5  0.5, . . ., 5.5  0.5 and 6.5  0.5. The expectation of n was calculated for each ventilation velocity using Eq. (4). The expectation of k was calculated using EðkÞ ¼ 2EðnÞ . The variation of the expectation of k with ventilation velocity is shown in Fig. 5. 2.2. HGV fire at maximum heat release rate The experts were asked to consider the same HGV fires once the fire was fully involved. They were asked to estimate probable values of k at the maximum heat release rate. On average the expectation of the experts was that the HRR would probably be between 2 and 4 times greater for all ventilation velocities considered. A prior probability distribution was built for each of the four ventilation velocities considered from these estimates, as shown in Fig. 6. The following experimental tests were considered to be relevant to this case: *

* *

* *

EUREKA simulated truck load test in the Hammerfest tunnel (full scale, natural ventilation); EUREKA HGV fire test in the Hammerfest tunnel (full scale, forced ventilation); FOA wooden crib tests in the ‘‘blasted rock tunnel’’ (reduced scale, natural ventilation); wooden crib test in the HSE tunnel (reduced scale, forced ventilation); simulation of HGV fire in the HSE tunnel (reduced scale, forced ventilation).

Although the wooden crib tests carried out in the Hammerfest tunnel were considered to be relevant to the initial stages of fire development on a HGV, the cribs used were not large enough to give any information on the fire behaviour of a HGV, so these tests have not been used in this part of the study. The airflow velocity during the Hammerfest HGV test was reduced from 6.0 to 2.9 m s
1 once the fire had engulfed the entire vehicle. Comparing the maximum HRR of the fire at each of these ventilation velocities with the HRR of the simulated truck load, gives k values of approximately 7–10 and 8–9 at 6 and 3 m s
1, respectively. High likelihood values have therefore been allocated to the 8–16 range

Test with forced ventilation

Compared to these natural ventilation tests

Equivalent ventilation velocity (m s
1)

High likelihood at 2 m s
1

High likelihood at 4 m s
1

High likelihood at 6 m s
1

High likelihood at 10 m s
1

EUREKA HGV test EUREKA crib test HSE crib test HSE simulation test

EUREKA simulated truck load EUREKA crib test FOA crib tests FOA crib tests, EUREKA simulated truck load

6.0 2.9 2.0 6.3

8–16 1–2, 2–4 8–16 8–16

8–16 1–2, 2–4 16–32 16–32

16–32 n/a 16–32 16–32

16–32 n/a 16–32 16–32

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Table 1 Summary of k ranges allocated a high likelihood for a HGV fire in the growth phase

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Fig. 4. Posterior probability distributions for a HGV fire in the growth phase.

Fig. 5. The expectation of k for a HGV fire in the growth phase.

Fig. 6. Prior probability distributions for a fully involved HGV fire.

for 4, 6 and 10 m s
1 and to the 4–8 range for 2m s
1. Medium likelihoods have been allocated to the 4–8 range at 4, 6 and 10 m s
1, to the 16–32 range at 6 and 10 m s
1 and to the 2–4 and 8–16 ranges at 2 m s
1. All other ranges have been allocated a low likelihood. Between the 6.0 and 2.9 m s
1 ventilation phases of the fire there was a short period of time when the forced ventilation was switched off and the HRR of

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the fire diminished. This has not been used as the ‘‘natural ventilation’’ comparison for two reasons. The HRR of the fire appears to have been still dropping when the forced ventilation was restarted, so the value to which it would have dropped is not known, and also this period of ‘‘natural ventilation’’ followed a period of intense heat release from the fire, so the ceiling, walls and floor of the tunnel would have been radiating a lot of energy back into the fire during this period probably enhancing the HRR significantly. A constant ventilation velocity, equivalent to 2 m s
1 at full scale, was maintained during the wooden crib test in the HSE tunnel. Comparing the HRR data from this test with data from naturally ventilated wooden crib tests suggests a k value of approximately 2 at 2 m s
1. High likelihoods have therefore been given to the 1–2 and 2–4 ranges at 2 m s
1 and to the 2–4 range at 4 m s
1. Medium likelihoods have been allocated to the 1–2 and 4–8 ranges at 4 m s
1. All other ranges have been allocated a low likelihood. During the HSE simulation test, the airflow velocity was reduced from a full scale equivalent of 6.3 to 2.5 m s
1 and again to 1.7 m s
1. Comparing these HRR data with the naturally ventilated tests suggests k values of approximately 13, 9.5 and 5.4 for each of those ventilation velocities. High likelihood values have therefore been allocated to the 4–8 range at 2 and 4 m s
1, to the 8–16 range at 4, 6 and 10 m s
1 and to the 16–32 range at 10 m s
1. Medium likelihoods have been allocated to the 4–8 range at 6 and 10 m s
1, to the 8–16 range at 2 m s
1 and to the 16–32 range at 6 m s
1. The likelihood values used to refine the prior probability distribution of k at maximum heat release rate for a HGV fire are summarised in Table 2. The prior probability distributions, based on the estimates of the expert panel, were again refined using Bayes’ theorem with the likelihood values allocated for the three pieces of experimental evidence described above. The posterior probability distributions are shown in Fig. 7. The expectation of k was again calculated by means of first determining the expectation of n, calculated using Eq. (4). The variation of the expectation of k with ventilation velocity is shown in Fig. 8.

2.3. Car fires in tunnels Unlike the HGV case, the experimental fire tests that are relevant to the behaviour of car fires in tunnels were not carried out across a range of different ventilation velocities. To date, there have been no well documented fire tests of cars in tunnels subject to longitudinal ventilation velocities above 2 m s
1, so there is no way of refining estimates of probability at higher ventilation velocities. Given the experimental evidence available, it was decided to study the influence of forced longitudinal ventilation at 1.5 m s
1 only. Given the available evidence it was not possible to be precise about the HRR development in the growth phase of the fire, so k values during the growth phase cannot be determined. It is however possible to learn something about the influence of forced ventilation on the development of a car fire if the time taken to reach

582

Test with forced ventilation

Compared to these natural ventilation tests

Equivalent ventilation velocity (m s
1)

High likelihood at 2 m s
1

High likelihood at 4 m s
1

High likelihood at 6 m s
1

High likelihood at 10 m s
1

EUREKA HGV test

EUREKA simulated truck load

4–8

8–16

8–16

8–16

HSE crib test HSE simulation test

FOA crib tests FOA crib tests, EUREKA simulated truck load

6.0 2.9 2.0 6.3

1–2, 2–4 4–8

2–4 4–8, 8–16

n/a 8–16

n/a 8–16, 16–32

2.5 1.7

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Table 2 Summary of k ranges allocated a high likelihood for a HGV fire at maximum heat release rate

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Fig. 7. Posterior probability distributions for a fully involved HGV fire.

Fig. 8. The expectation of k for a fully involved HGV fire.

maximum heat release rate is compared between fire tests with forced and natural ventilation. 2.4. Heat release rate of a fully involved car fire The expert panel provided estimates of their expectations of HRR values for car fires in tunnels subject to natural and forced ventilation. Estimates were made for five different tunnel sizes and shapes and also for ‘‘mini’’ and ‘‘family’’ cars. After combining the estimates and calculating values for k, it became apparent that while the experts expected that the absolute HRR of a car fire in a small tunnel would be higher than the absolute HRR of a similar fire in a larger tunnel, and the absolute HRR of a family car fire would be higher than the absolute HRR of a mini car fire, the expected values of k were approximately the same for all cases. Given the lack of available data for car fires in tunnels with forced ventilation, it is assumed at this time that the opinion of the experts is correct}that k is not significantly dependent on car size or tunnel dimensions. It is hoped that more

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experimental data will become available in the future so that this assumption may be tested. A prior probability distribution for k was devised, based on the estimates of the experts. The available experimental evidence used to refine this probability distribution were * * * * * *

EUREKA car fire test in the Hammerfest tunnel}natural ventilation; CETU car fire test in the Des Monts Tunnel}forced ventilation at 1.3 m s
1; FOA car fire test in the ‘‘blasted rock tunnel’’}natural ventilation; FOA wooden crib fire tests in the ‘‘blasted rock tunnel’’}natural ventilation; VTT wooden crib fire tests in a mine tunnel}forced ventilation at 1.3 m s
1; EUREKA wooden crib fire tests in the Hammerfest tunnel}natural and forced ventilation at 2.9 m s
1.

At present, there are no fully documented fire tests of cars in tunnels with forced ventilation. The only recorded car fire test with forced ventilation was carried out in the Des Monts Tunnel in France, with a longitudinal ventilation velocity of 1.3 m s
1. The only details reported about that fire were that the maximum HRR, recorded 4 min after ignition, was approximately 2 MW. Comparing this with the car fire tests in the naturally ventilated Hammerfest and blasted rock tunnels suggests a k value of approximately one at maximum heat release, for the forced ventilation velocity of 1.5 m s
1. A high likelihood value has therefore been allocated to a k value of 1.0 and low likelihoods to all other values. All the other tests used to refine the probability distribution involved wooden crib fires. Eight wooden crib ‘‘mock-ups’’ of cars were arranged in a quarry tunnel at Lappeenranta in Finland to investigate the possibility of fire spread between cars in a longitudinally ventilated tunnel. The ventilation velocity was 1.3 m s
1 throughout the test. The two cribs at the front of the queue were ignited and a maximum HRR of slightly over 4 MW per crib was achieved after about 15 min. The fire did not spread between ‘‘vehicles’’ and after the first two cribs had burned out, the two cribs at the back of the queue were ignited. Once again the fire did not spread. A maximum HRR of almost 2 MW per crib was achieved after about 20 min. Comparing HRR data from these tests with data from the naturally ventilated crib fire tests in the Hammerfest and blasted rock tunnels, suggests k values of approximately one for the initial crib fires and significantly less than one for the later crib fires. Thus a high likelihood value has been allocated to the k value 1.0, a medium value to 0.5 and low values to all other values of k for the initial fires and a high likelihood value has been allocated to the k value 0.5, a medium value to 1.0 and low values to all other values of k for the later crib fires. Two wooden crib fire tests were carried out in the Hammerfest tunnel with identical cribs, equivalent in size to large passenger cars, one with natural ventilation and one with forced ventilation of 2.9 m s
1. Comparing the HRR data from the two tests suggests a k value of 2.8 for a forced airflow near 3.0 m s
1. As the velocity of interest is 1.5 m s
1, high likelihood values have been allocated to k values of 1.5 and 2.0, medium to 1.0 and 2.5 and low to all other values.

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The likelihood values used to refine the prior probability distribution of k at maximum heat release rate for a car fire are summarised in Table 3. The prior probability distribution, based on the estimates of the expert panel, was refined four times using Bayes’ theorem with the likelihood values allocated for the experimental evidence described above. The prior and posterior probability distributions are shown in Fig. 9 and the variation of the expectation of k, calculated using Eq. (4), with each successive refinement is shown in Fig. 10. 2.5. Time to maximum HRR for a car fire The expert panel was also asked to estimate the time required for a car fire in a tunnel to reach maximum heat release rate with natural ventilation and with a forced ventilation of 1.5 m s
1. A ‘‘timescale coefficient’’ kt was considered, defined by tvent ¼ kt tnat ;

ð7Þ

where tvent and tnat are the time taken to maximum heat release rate for a car fire in a tunnel with forced ventilation and natural ventilation respectively. Discrete values for kt of 0.5, 0.6, 0.7, . . ., 1.4 and 1.5 were considered. A prior probability distribution was devised from the estimates. The likelihood of each of the experiments used as evidence in the above HRR calculations was used to refine the prior probability distribution. The prior and posterior probability distributions are shown in Fig. 11. The prior expectation of the experts was that the ventilation would probably cause a car fire to reach maximum HRR in 20% less time than natural ventilation would; however the posterior expectation is that a forced ventilation velocity of 1.5 m s
1 would have little effect on the timescale of the fire, with Eðkt ) having a value very near one. 2.6. Sensitivity and uncertainty issues Any calculation based on estimated values must be tested to determine how sensitive the final results are to variations in the estimates themselves. In this study the results are dependent on a number of estimated factors including the original prior probabilities and the ratio of high : medium : low likelihood used in the refining process. The sensitivity of results to both these factors must be considered. 2.7. Sensitivity to likelihood ratio All results presented so far have been calculated using a likelihood ratio of 4 : 2 : 1. As it is important to test the sensitivity of the calculations to this ratio, the calculations have also been carried out using ratios of 10 : 5 : 1, 3 : 2 : 1 and 4 : 3 : 2. A graph of the expectation of k for a fully involved HGV fire using each of these ratios is shown in Fig. 12. Selected posterior distributions are compared in Fig. 13. It can be seen that while the spread of the distribution varies slightly with the likelihood ratio, the expectation of k is not significantly affected by the ratio used except in the

586

Test with forced ventilation

Compared to these natural ventilation tests

Ventilation velocity (m s
1)

High likelihood

Medium likelihood

Low likelihood

CETU car fire test VTT crib test 1 VTT crib test 2 EUREKA crib fire test

EUREKA EUREKA EUREKA EUREKA

2.0 1.3 1.3 2.9

1.0 1.0 0.5 1.5 and 2.0

n/a 0.5 1.0 1.0 and 2.5

All All All All

and FOA car fire tests and FOA crib tests and FOA crib tests crib fire test

others others others others

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Table 3 Summary of values of likelihoods used for the case of a car fire

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Fig. 9. Prior and posterior probability distributions for a car fire in a tunnel.

Fig. 10. Variation of the expectation of k with increasing evidence for a car fire in a tunnel.

Fig. 11. Prior and posterior probability distributions for the timescale of a car fire in a tunnel.

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Fig. 12. The sensitivity of the expectation of k to variations in the likelihood ratio.

Fig. 13. Posterior probability distributions for a HGV fire in the growth phase at 6 m s
1 using different likelihood ratios.

extreme case of 10 : 5 : 1. Although some preliminary results were published using this ratio [27] it appears that it may produce slightly exaggerated results. 2.8. Sensitivity to prior estimates The sensitivity to the prior estimates is also of interest. To test this, the calculations were performed using a uniform prior, that is all ranges having equal probability in the first instance. Fig. 14 compares the expectation of k for a fully involved HGV fire calculated using a uniform prior with that calculated using the estimated prior. Selected posterior distributions are compared in Fig. 15. It can be seen that after four Bayesian refinements, the posterior probability distribution is still significantly dependent on the prior distribution. The expectation of k based on calculations using the expert prior is much smaller than using the uniform prior. When the likelihood ratio 10 : 5 : 1 was used in these calculations, the difference between the posterior distributions based on the expert and diffuse priors was insignificant.

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Fig. 14. The sensitivity of the expectation of k to variations in the prior probability function.

Fig. 15. Posterior probability distributions for a HGV fire in the growth phase at 6 m s
1 using expert and uniform prior probability functions.

2.9. Uncertainty due to likelihood estimation Due to the nature of the discrete Bayesian method used in this study there is also a degree of uncertainty introduced during the estimation of the likelihood of each piece of evidence. The influence of this uncertainty may best be seen by comparing the posterior distributions using the ratio 4 : 1 : 1 and the ratio 4 : 4 : 1 which may be considered to represent narrow and wide likelihood distribution functions. Selected posterior distribution functions and expectation graphs using these ratios are shown in Fig. 16. It can be observed that while the spread of the posterior distributions varies significantly, the expectation graphs show little variation. The wider likelihood functions tend to give slightly higher k values at low ventilation velocities, and lower k values at high ventilation velocities, compared to values obtained using the 4 : 2 : 1 ratio, whereas the narrow likelihood functions give slightly lower values at low ventilation velocities and slightly higher values at higher ventilation velocities. However the uncertainty introduced through this factor is small compared to other variations in the likelihood ratio.

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Fig. 16. The sensitivity of the expectation of k and posterior probability functions to variations in the likelihood function.

3. Discussion Although fire safety in tunnels has become an important issue in the past decade, there are still many large gaps in our understanding of fire behaviour in tunnels, the effect of ventilation systems on fire development and size is only one of many poorly understood aspects of fires in tunnels. Clearly the best way to fully understand influences like these would be to perform a series of fire tests in tunnels, and it is hoped that such a study will be carried out at some time in the future. In the meantime, it is important to try to learn as much as possible from all the experimental results that are available, and to implement changes in practice where applicable. At present there is no generally accepted consensus regarding the design or operation of ventilation systems for vehicle tunnels in the event of a fire. Where standards or recommendations do exist [7], they are largely based on individual judgement or experience and not on experimental results [28]. One of the issues highlighted by this study is the diversity of opinion amongst fire safety experts}very few of the experts expected the ventilation to have as dramatic an effect on the HRR of a HGV fire as the experimental evidence suggests, especially in the growth phase. It is clear that, if an engineering decision has to be made based on estimates alone, the opinion of one or two experts may not be enough. A method of combining expert judgement with what little experimental evidence is available is not merely desirable, but essential if the level of safety in vehicle tunnels is to be increased. 3.1. The value of Bayes’ theorem The Bayesian method has much to offer in fire safety engineering. The complexity of fire development makes the use of probabilistic methods necessary. Two ostensibly identical cases may produce fires which behave in widely different ways, and yet many of the fire models currently in use are deterministic in nature.

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Deterministic models may be valuable but they are not the sole answer, it may often be better to consider a problem from a probabilistic viewpoint. The Bayesian method has been used by statisticians for many years to aid decision-making on the basis of limited information. It has been shown to be scientifically sound, adaptable to many different situations and it has even been claimed that it is the best way of making any decision and indeed that we all subconsciously use Bayes-like reasoning when making everyday decisions [29]. In the present study, a Bayesian methodology has been used to refine estimates of probability with a diverse group of experimental data sets. The intention has been to come to an approximate understanding of the question of the effect of forced longitudinal ventilation on vehicle fires in tunnels. It is part of the Bayesian understanding that the results presented here are not the definitive results, they are merely the current beliefs, as more experimental evidence becomes available these results will be further updated and refined, and so on. The intention of this study was to begin to build a systematic foundation on which future engineering judgements may be built. It may appear unwise to base any important decision on a hypothetical estimate refined by only a few sets of experimental data, but after consideration of future tunnel fire experiments it is hoped that these estimates may be refined to a useable resource and also give a clearer understanding of the behaviour of pool fires in tunnels. At present it is hoped that these refined estimates are more realistic than expert judgement alone, having been refined using real experimental data. A similar Bayesian methodology may also be used with a specific case in mind; estimates can be sought for the particular tunnel size of interest and then these can be refined in a similar manner, yielding results that are specific to a real tunnel configuration. Of course, Bayes’ theorem is not restricted to the question of fire development in tunnels. Any estimated probability distribution may be refined using only a single experimental observation using this method. Bayes’ theorem has been used in a wide variety of contexts across the whole spread of engineering disciplines, from fire safety in nuclear plants [30] to pollution in water systems [31]. 3.2. The meaning of the results The purpose of the study was to estimate the probability distribution of the heat release rate coefficient, the random variable k, for hypothetical HGV and car fires in tunnels with longitudinal ventilation. From the probability distributions produced it should be possible to estimate the size of vehicle fires in tunnels given the influence of forced longitudinal ventilation. As there have been very few experimental fire tests on actual vehicles in tunnels, it is necessary to consider data from scale model fire tests and wooden crib fires in tunnels. Fires of these types may develop in significantly different ways to real vehicle fires, but as these provide most of the data that are available, they must be used until there are sufficient data from real vehicle fires. In the case of HGV fire development}the study of k in the growth phase, data from a real HGV fire test, a reduced-scale simulation test and a number of crib fire

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Fig. 17. The expectation of k and posterior probability distributions for a HGV fire in the growth phase both using and discounting the Buxton reduced scale simulation test data.

tests were used. As noted earlier, the reduced scale simulation test involved a liquid fuel pan as well as a solid fire load. Fire development in fuel pools is very different from fire development involving solid fuel, especially in the growth phase, so the data from this test have been used with caution. Posterior distributions of k in the growth phase were calculated both with and without these data. As shown in Fig. 17, there are significant variations between the posterior distributions and expectations of k. These variations are less significant if the 10 : 5 : 1 likelihood ratio is used. Using the 4 : 2 : 1 ratio, the posterior after three refinements is significantly more dependent on the prior distribution than after four refinements. Using the 10 : 5 : 1 ratio, the posterior after three refinements is not significantly dependent on the prior. The posterior distributions produced by the study suggest that k will increase dramatically with increasing ventilation velocity in the growth phase and for the fully involved fire. For each ventilation velocity considered in the study, the expected heat release rate of a HGV fire in the growth phase and at full involvement was several times larger than the experts’ expectation. In practical terms, the results of the study predict that a HGV fire in a tunnel subject to forced ventilation will release approximately 4, 5, 8 or 10 times more heat, at any given time within the growth phase, with ventilation rates of 2, 4, 6 or 10 m s
1 than with natural ventilation. The results of the study also predict that a fully involved HGV fire will release approximately 3, 5, 7 or 10 times more heat, at maximum heat release, with ventilation rates of 2, 4, 6 or 10 m s
1 than with natural ventilation. It has been observed that the results of this part of the study are highly dependent on the HGV test carried out as part of the EUREKA test series. This is indeed the case and will remain so until more fire tests of large vehicles are carried out, both in and out of tunnels. It is often unwise to try to learn too much from a single fire test; it may be that another fire test involving a similar vehicle under the same conditions would give very different results. However, our confidence that the EUREKA HGV test is not exceptional is increased by comparing the test data with data from the HSE

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reduced scale fire test of a HGV-like fire load; when scaled to the same size the two tests give similar HRRs with similar forced ventilation velocities. In the case of the car fire, data from forced ventilation fire tests involving wooden cribs and a car were compared with data from natural ventilation fire tests of cars and wooden cribs in tunnels. Because of the lack of data at higher ventilation velocities, k was only determined for a ventilation velocity of 1.5 m s
1. It is not expected that ventilation at this rate will have any significant influence on the heat release rate or rate of development of a car fire in a tunnel. 3.3. The value of these results The study set out to answer a simple question and has produced fairly simple results, a question that must be addressed is are these results useful? Tunnel fires are very rare. The majority of fire fighters who work in areas near vehicle tunnels may have little or no experience of fighting such fires, and may not know what to expect in the event of such fires. Yet these fire fighters will probably have access to the controls of the tunnel ventilation systems in the event of a fire in a tunnel. Decisions on how to use the tunnel ventilation will be made. It is hoped that the results presented in this paper, together with results from other studies on tunnel fires, will enable the decision to be grounded in knowledge of fire behaviour, rather than just a ‘‘best guess’’. The primary concerns of the fire brigade are to help any people escape the fire to a place of safety and to control and extinguish the fire. Ventilation systems may be controlled in such a way as to blow all smoke produced by the fire to one side of the fire location. This will provide a smoke free escape route upwind of the fire location, but may also significantly affect the size of the fire. This study has shown that, for a HGV fire in a tunnel, forced ventilation causes an increase in fire size. Increasing the ventilation velocity will probably cause the fire to grow, possibly up to over 20 times larger. Without this knowledge it may seem reasonable to use the maximum possible ventilation to control the smoke; however, in the light of the results of this study, it would appear that the best solution would be to use the minimum ventilation velocity which is sufficient to control the smoke. It has been shown that the size of fires on HGVs can be greatly influenced by forced ventilation, it has also been shown that fires involving passenger cars are not significantly affected by forced ventilation. Results published elsewhere [14] have demonstrated that different sizes of pool fires in tunnels behave in different ways when forced ventilation is applied. Therefore it is clear that different ventilation strategies should be used when tackling different types of fire}ventilation should be kept to an absolute minimum if the fire involves a HGV or a large fuel spillage [14], whereas ventilation may be increased if the fire involves a passenger car or a smaller pool fire. Indeed it has been shown that high ventilation rates would be expected to cause a decrease in fire size for smaller pool fires [14]. Adopting the current recommendation of a 3 m s
1 airflow velocity in the event of any fire in a tunnel does not seem to be the most sensible option}if the fire type can be identified by the tunnel operators, the tunnel ventilation should be adjusted accordingly.

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It is hoped that the simple results presented here will be easily remembered and therefore may be recalled when decisions need to be made when fighting real fires in tunnels. 3.4. The use of Bayes’ theorem The methodology used in this study was the discrete form of Bayes’ theorem, it would also have been possible to use the continuous form of Bayes’ theorem. In the continuous methodology, the random variable k is assumed to have a continuous probability distribution PðkÞ. Bayes’ theorem is expressed as LðI j kÞPðkÞ Pðk j IÞ ¼ R ð8Þ LðI j kÞPðkÞ dk where PðkÞ is the prior probability function, Pðk j IÞ is the posterior probability function and LðI j kÞ is the likelihood function of the evidence I. A continuous approach has been used in studies such as that of Apostolakis [30], but was not used in this study due to the conceptual problems associated with evaluating a continuous likelihood function for each piece of evidence, and the necessary assumption that all the functions would be normal or lognormal distributions}the combined expert estimates did not give a normal or lognormal distribution in any case. The main reason Bayesian methods were chosen over other statistical methods is lack of data. In this study probabilities of k for various ventilation velocities have been estimated. Classically there is no method of estimating a probability distribution from as few data sets as were available. Also the data that were available came from a variety of tests in different tunnel configurations, again classically there is no way of using these together. The main advantage of Bayesian methods over classical estimation methods is the ability to incorporate expert judgement to compensate for lack of data. Bayesian methods also provide a simple way to refine estimates in the light of new evidence. Some critics of this method would argue that these results are ‘‘all guesswork’’, but by using Bayesian methods the experts estimates have been combined in a systematic way, which is scientifically justifiable, with all the available data. No ad hoc method of estimation can make such a claim. In their book ‘‘Scientific Reasoning’’ Howson and Urbach [29] contend that the Bayesian theory ‘‘is the only theory which is adequate to the task of placing inductive inference on a sound foundation’’.

4. Conclusions A Bayesian method has been used to determine the probable effect of forced longitudinal ventilation on fire size for vehicle fires in tunnels. The results predict that ventilation has a far more dramatic intensifying effect for HGV fires than experts in the field of fire safety predicted. It is clear that fire behaviour in tunnels is not adequately understood. In order to increase knowledge and understanding of fire

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behaviour, more experimental testing of vehicles in tunnels, with both forced and natural ventilation, is required. 4.1. Summary of main results For a HGV fire in a tunnel it is predicted that *

*

*

*

a 3 m s
1 airflow velocity may cause the fire size to increase up to five times in its growth phase; a 10 m s
1 airflow velocity may cause the fire size to increase up to 10 times in its growth phase; a 3 m s
1 airflow velocity may cause the size of a fully involved fire to increase up to four times; a 10 m s
1 airflow velocity may cause the size of a fully involved fire to increase up to 10 times. For a car fire in a tunnel it is predicted that

*

a 1.5 m s
1 airflow velocity will not significantly affect the fire size or rate of development of the fire.

Acknowledgements This study would not have been possible without the expert estimates and advice of the late H.L. Malhotra (Agniconsult), R. Chitty, S. Miles and M. Shipp (Fire Research Station), G. Atkinson and R. Bettis (HSE, Buxton), J. Beech (Kent Fire Service) and G. Grant (Grant Fire Consultants). This project was funded by the Engineering and Physical Sciences Research Council under grant GR/L69732.

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