Jean Christophe Le Coze
email: christophe.lecoze@ineris.fr

BP Texas City accident: weak signais or sheer power?

The aim of this paper is to discuss the interprétation of the BP Texas City accident. While bringing a lot of empirical data on a wide range of dimensions, the US Chemical Safety Board investigation did not import the normalisation of déviance concept for sensitising the data. It however clearly indicated a référence to the Columbia Accident Investigation Board where this concept was influential (i.e. chapter 8 of the Columbia report, 2003). The aim of this paper is to see nevertheless how valuable the concept could be for this case. The Baker Panel report (2007) will be used as a second source for this purpose. It will also be the opportunity to introduce the complex debate of the relationship between culture and power. Some, such as Perrow, hâve indeed criticised the cultural rationale of the normalisation of déviance, at the expense of power "We miss a great deal when we substitute culture for power". This paper is not a judgement of the reports used hère as inputs but rather a way of interrogating the case with an alternative, and hopefully, complementary angle.

INTRODUCTION

The CSB report on BP Texas City accident (CSB, 2007) provided a deep account of the organisational genesis of the disaster. Based on a similar framework of the accident investigation model of CAIB (Columbia Accident Investigation Board), several dimensions are covered, linking technology, human, organisational and environmental factors. The historical approach applied by the report allows a description of the events that shaped the situation prior to the events. Main outcomes of this investigation are linked with BP organisational way of dealing with proeess safety, through leaming from expérience (i.e. poor root causes analysis, poor completion of actions for identifîed deficiencies), management of change (i.e. budget cuts, organisational changes such a merger and leadership turnover). Other identifîed items were human factors (i.e. design of control rooms and interfaces, procédures updates, communication and fatigue issues), safe design and maintenance of barriers (i.e. blowdown System size, level transmitters failures), but also relationship with regulators (OSHA and lack of enforcement and inspections throughout the years).

One of the key finding (at the organisational level) and lengthy development in the report ("BP Safety culture", p 149 to 174) concerns the way signais about risks were handled by the management of the plant and by corporate levels. Indeed, following the accident, as outsiders and readers of the report, messages such as thèse ones seemed quite clear: there was a risk, according to the HSSE business plan from March 15 (few days before the accident -23 rd of march) that the refïnery "kills someone in the 12-18 months". There was also the following message from the Texas City plant HSSE manager "/ truly believe that we are on the verge of something bigger happening" (from an email of February 20, 2005).

It is true that the state of the installations and safety management implementation appear as rather more than inadéquate through the descriptions found in the report. When reading the findings of the report, one can not help wondering why was the plant maintained in this apparently degraded level of safety while information was available and opportunities for action obvious (for instance the replacement of the blowdown system by a flare system). But at the same time, some similar reports of investigations of past accidents, such as the presidential commission on the space shuttle Challenger, were revised by social scientists while introducing principle of rétrospective fallacy, but also by stressing the associated systemic nature of thèse types of accidents.

INTERPRETATIVE PRINCIPLES OF ACCIDENTS

Rétrospective fallacy (and normalisation of déviance)

The rétrospective fallacy advocates that signais présent in the past only appear quite clear in retrospect 1 . They are not as clear for the decision-makers at the time of the events as they are for investigators. "This warning is the warning of the rétrospective fallacy understanding organisational failure dépends on systematic research that avoids the rétrospective fallacy by going beyond secondary sources and summaries, relying instead on personal expertise based on original sources that reveal ail the complexity, the culture, the culture of the task environment, and the meaning of actions to insiders at the time." [START_REF] Vaughan | The challenger launch décision: risky technology, culture and déviance at NASA[END_REF]. Thus, based on this rétrospective fallacy argument, Vaughan's "normalisation of déviance" (1996) suggested to revise some of the challenger commission findings. A main principle of this model is that signais at the time were weak rather than strong, and that décision to launch was strongly biased by past expérience of engineers regarding joints behaviour as well as biased by their socialisation. This pattern was created and maintained by the production of a culture, a culture of production and a structural secrecy.

The production of a culture occurs with the uncertainties of the technologies. Engineers introduced the technological uncertainties into qualitative and quantitative behavioural models, offering the ability to predict or to anticipate. Anomalies or signais about the gap between the anticipated behaviours and the observations were closely monitored. Thèse signais triggered the need for new explanations or were rationalised so that they found their place in the worldview or paradigm developed by engineers. For [START_REF] Vaughan | The challenger launch décision: risky technology, culture and déviance at NASA[END_REF], thèse signais could either be mixed signais, routine signais or weak ones. The production of a culture is thus the establishment of a prevailing paradigm constraining the way engineers or scientists interpret phenomena and make sensé of them. The culture of production refers to the bureaucratie (daily importance of paper and procédures for dealing with subcontractors, with régulations etc) and political (imperative of cost and schedules) accountabilities of NASA. Culture of production was also based on the "can do" culture of NASA, anchored in the past successes of Apollo program and the ability of the organisation to be successfully meeting its purposes despite technological challenges. The structural secrecy introduces the classical problems of organisations such as spécialisation of functions, géographie distances and difficulty for control functions to ensure oversights due to problems of independence but also compétence given the complexity of the technologies involved.

Culture and power. However, this model of normalisation of déviance, introducing a strong cultural perspective, was not favoured by other social scientists such as [START_REF] Perrow | Organisation à hauts-risques et "normal accidents[END_REF]. Perrow still saw in the Challenger accident an example of sheer power rather than a cultural manifestation « They were told to take off their engineering hats and put on their managerial hats and make a managerial and not engineering décision. To me, that is a case of sheer power, it is not the routinisation of déviance » [START_REF] Perrow | Organisation à hauts-risques et "normal accidents[END_REF]. Perrows' sentence introduces the question in social science of the relationship between culture and power.

It is interesting to notice that culture as a safety issue has been debated quite a lot, maybe at the expense of power which is however a key dimension in any debates on organisations, and more widely in any debate on society. [START_REF] Weick | Normal accident theory as frame, link, and provocation[END_REF] made a point on this issue, when commenting on Perrow's assertion regarding some interprétations of his 1984 normal accident book "/ would say that much of the work in the risk area today is systematically detoxing the power aspects of tny book". Weick makes the following remark ( 2004) "So we are ail provoked to remember that power matters and that it matters differently depending on the plurality of the powerful organizational interests (p 385) and we are provoked to work out the mechanism by which this happens, something that has not been done well. We are also provoked to take a second look at organisational culture. "A focus upon a culture of reliability is a luxury in the world of risky Systems" (p 360); "We miss a great deal when we substitute culture for power" (p 380). Perhaps we need another Snook-like tour de force to show us that culture and power are not opposed explanations, but rather that culture shapes the way for power, defines power, is shaped by power, masks power, embodies power. Culture is not just breezy social constructionist talk (my phrase, not Perrow's), it makes power possible and is made binding through acts of power". It was not the first time that Perrow illustrated his point of view on the relationship between power and culture. We find an earlier sentence from Perrow (1985), in Scott (2000) in which he disapproves "this infatuation with cultural myths and symbols to the neglect of power and group interesf. Normalisation of déviance introduces thus the interesting problem of the relationship between culture and power. It seems that a cultural perspective would favour normalisation of déviance as an explanatory principle whereas an emphasis on power would reject the rationale behind it (but this is a simplification).

Systemic dimension of accidents

The systemic nature of the accident refers to the fact that such events do not happen in isolated organisations but in wider contexts including outside actors and forces. The open System perspective introduced is a powerful analogy for organisational studies (Scott, 2003). Thèse actors and forces can be professions (i.e. engineering profession), nation states (i.e. régulation and control authorities) or also industries and associations (i.e. petrochemical industry). Thèse external forces due to the open property of organisations permit for normalisation of déviance to occur and to be maintained, so the rétrospective fallacy and the systemic nature of thèse accidents are closely linked as principles for interpreting accidents.

According to [START_REF] Vaughan | The challenger launch décision: risky technology, culture and déviance at NASA[END_REF], some of thèse outside influences were missed in the Challenger commission report. The part played by the Congress in constraining the space agency was not identified whereas NASA depended on congress and had little freedom. The influence of the engineering culture, which can be considered as a societal influence through profession, was also not mentioned in the report however contributed to the normalisation of déviance pattern. "Engineering as a craft and as a bureaucratie profession contributed to the work group's normalization of technical déviation in officiai launch décision making venues by providing basic assumptions that were elaborated in the NASA organisation culture" (Vaughan, 2002, 18).

Following the Columbia shuttle destruction and given the similarity of this accident with her analysis of Challenger, Vaughan insisted on thèse types of external forces constraining the possibility of avoiding répétitive négative pattern (Vaughan, 2005, 56). "Cultures of production, whether production of police statistics, war, profits or timely shuttle launches, are a product of larger historical, cultural, political, ideological and économie institutions. Making organisational changes that contradict them is difficult to implement, but in the face of continuing and consistent institutional forces even more difficult as time passes. Attributing repeating négative patterns to declining attention and forgetting of lessons learned as a crisis recèdes into history neglects the sustaining power of thèse institutionalised external forces. The extent to which an organisation can resist to this condition is likely to vary as its status and power vary". She found empirical and theoretical support in new institutionalism for such a position (Powell & Dimaggio, 1991, Scott, 2001). For Scott, "/ see the ascendance of institutional theory as simply a continuation and extension of the intellectual révolution begun during the mid 1960s, which introduced open Systems conceptions into the study of organisations (...) Organisations were seen as more than production Systems; there were social and cultural Systems" (Scott, 2001). Institutions constrain (but also enable, in a dual relationship) organisations in différent manners with différent mechanisms that Scott distinguishes between regulative, normative and cultural-cognitive. New institutionalism, by opposition to the old institutionalism (Di Maggio & Powell, 1991a), introduces the latter one, the culture-cognitive forces existing within spécifie fields, at macro levels with impact at micro levels, such as professions (i.e. engineering professions in Vaughan's analysis). This approach is contemporary and influenced by theoretical developments in social sciences such as Garfïnkel (1967), [START_REF] Berger | The social construction of reality[END_REF]Luckmann, (1967), Bourdieu (1977) or Giddens (1984) introducing and stressing the cognitive dimensions of the relationship between individuals and society.

What is the situation of the BP Texas City refinery in regards with this type of model and debate that followed the Challenger investigation report (rétrospective fallacy, systemic nature of accident)? How can an accident of this scale happen when "The panel observes, however, that during the course of its review, it saw no information to suggest that anyone, from BP's board members to its hourly workers acted in anything other than good faith" (Baker panel, 2007, 15). How does it complément the CSB report that has not made much référence to this spécifie model of weak signais and normalisation of déviance? Can we apply thèse to the data and findings? In the next parts, some éléments from the report will be extracted for this purpose. They will offer a partial perspective (hence the brackets in the headings "some éléments of') for each items in the scope of this paper. Eléments showing how the company is opened to its environment hâve been also favoured, in order to stress some of the systemic dimensions shaping the accident.

A normalisation of déviance (some éléments of)?

One approach to answer to this question is to look for information that could fit in the rationale of normalisation of déviance, and then to look for data to fit the production of culture, culture of production and structural secrecy model. Do we find a normalisation of déviance in the BP Texas City accident? It is indicated that the refinery is "Considered one of the world's most complex refineries, it includes 29 oil refining units and four chemical units, largest BP's refineries Worldwide (1800 BP employées, 6000 subcontractors) (Bake panel, 2007, 43). From the reports (especially part 9, "BP Safety culture"), it seems quite clear that many assessments of the state of the installations were performed throughout the years preceding the accident. Table 1 contains some extracts of the différent studies carried out and some comments from the CSB.

GHSER audit (2003)

"There were serious concerns about the potential for a major site incident due to the large number of hydrocarbon releases (over 80 in the 2000-2001 period). The study also found that many inspections were overdue and that known reliability issues including instrumentation, needed to be addressed."

"The analysis concluded that the budget cuts did not consider the spécifie maintenance needs of the Texas City refinery" the prevailing culture at the Texas City refinery was to accept cost réductions without challenge and not to raise concerns when operational integrity was compromised"

In October 2002, the BP group refining VP sent a communication saying that the financial condition of refining was much worse than expected,, and that from a financial perspective, refining was in a "crisis mode" (...) During this same period, Texas City managers decided not to eliminate atmospheric blowdown Systems.

"the units and staff are actively managing infrastructure risks but the current condition of the infrastructure and assets is poor at the texas city refinery""

The 1000 days goal reflected the continuée focus by site leadership on Personal safety and cost-cutting rather than on process safety" SHIFT prograin -1000 days goal (2003)

Repositioning project (2004)

The project team, led by BP personal outside the refinery, found that the refinery contributed only to 10 percent of the Global refining profits while consuming 18 percent of capital expenditure needed to meet environmental and safety compliance. The Texas City refinery faced additional challenges due to its unique complexity and interconnectedness. Management stated that the refinery was the most complex in the world by a factor of two.

Golden rules (2004)

The golden rules addresscd primarily personal safety issues related to work activities such as working at heights, lifting opertaions, and entering confined spaces. Although MOC (management of change) is one of the élément of the golden rules, process safety was not specifically addressed.

Safety Reality (November 2004)

poor safety level, wake up call for plant supervisors

Key Risks

The refinery would likely "kill someone in the 12-18 months"

This part of the CSB report reminds the reader of a pattern. Problems were identified; signais were strong (in retrospect) about the state of the installations, especially the warning from some whistle blowers and from the many officiai reports. Thèse signais could be said strong because they were clearly acknowledged by management. "Seeing the brutal facts so clearly was hard to digest, including the concern around the conflict between production and safety. The évidence was strong and clear and I accept my responsibility for the resuit" (CSB report, 2007, 171). However, we also know that some were not communicated to higher levels. "Serious safety failures were not communicated in the compiled reports. For example, the "2004 R&M segment risks and opportunities" report to the group chief executive States that there were "real advancements in improving segment wide HSSE performance in 2004", but failed to mention the three major incidents and three fatalities in Texas City that year" (CSB report, 2007, 145).

A sign of normalization of déviance in the Challenger case was the fact that information about potential serious problems (cold température potential impact on joint behaviour) was not transmitted to higher décision raaking levels. Instead of revealing a decision-making problem pointing at individual faulty managers, it was indeed, for [START_REF] Vaughan | The challenger launch décision: risky technology, culture and déviance at NASA[END_REF] a sign that insiders collectively constructed an inadéquate level of risk. Were risks at Texas City in gênerai therefore also normalized? Were they identified and treated through spécifie measures, each time establishing a new norm while stepping outside safe boundaries? Do we hâve the production of culture; a culture of production and a structural secrecy combining together to produce and maintain a slippery slope (Vaughan, 2005)?

3.2 The production of a culture (some éléments of)

Behavioural safety as a solution. The behavioural safety approach was also favoured as an answer to the technological problems " The Texas City site's response to the "control of work review", which occurred after two major accidents in spring 2004, focused on ensuring compliance with safety rules. The response stated that the review findings support "our objective to change our culture to hâve zéro tolérance for wilful non compliance to our safety policies and procédures. (...) the Texas city business unit leader announced that he was implementing an educational initiative and accelerated the use of punishment to create a "culture of discipline" (CSP report, 2007, 164).

An institutional influence. The inadequacy of the answer to the problem faced by BP through a focus on behavioural compliance with rules could be the sign of one of thèse external forces contributing to create isomorphic pattern among companies such as put forward by new institutionalism (Di Maggio and Powell, 1991b, 70). " Models may be diffused unintentionally, indirectly through employées transfer or turnover, or explicitly by organisations such as Consulting firms or industry trade associations. Even innovation can be accounted for by organisational modelling (...) organisations tend to model themselves after similar organisations in their field that they perceive to be more legitimate or successfuF'.

This behavioural and disciplinary approach seems indeed to hâve become a norm in the industry for dealing with human factors in safety. This is clearly performed at the expense of other approaches targeting more cognitive and contextual approaches of work such as promoted by ergonomics or sociology (Le Coze and Dupré, 2008). We find confirmation of this prevailing way of thinking in BP with comments from employées regarding accident investigations within BP. "A number of hourly employées at Texas City and Toledo, for example, expressed the belief that management is more interested in assigning blâme than identifying the root cause of an incident" (Baker Panel, 2007, p 201). But while in this particular case the accident reveals the inadequacy of response through behavioural compliance with rules to identified safety problems, this can't be seen only as the BP company level but more widely as an industry level, at a systemic level, influencing BP's practices.

A culture of production (some éléments of)

A "Making do" culture institutionalized. Do we now find éléments regarding the présence of a culture of production? It certainly is something that is made explicit in the two reports. As it is obvious that the degraded state of the installations can be traced back to the budgets cuts throughout the preceding years of the accidents, the Baker Panel ask the following questions: Did the refinery plant managers and their staff fail to see the need to spend more? Did they believe that they were more likely to be rewarded for meeting aggressive cost-cutting goals ?(...) the panel is unable to answer to thèse questions". Short of answer to thèse questions, it nevertheless found some support from Browne, the CEO of BP, who suggest a "make do" mentality as an explanation for the poor state of the installations. "Browne commented that for a number of years, BP had a "make do" mentality when times in the refinery business were tough and there was not much money to go around. Browne also commented that the otherside of "making do " is the fact that if a business gets used to not having something, it does not notice Us absence. If the business makes do for a long time, it begins to become blind of the risks that the business faced because the business just got used to them" (Baker panel, 2007, 84). As Vaughan analysed in a her case about production pressures that they "became institutionalised and thus taken-for-granted aspect of the worldview that ail participant brought to NASA decision-making venues" (Vaughan, 1996, xiv)". Similarly, BP Texas City culture of production through "making do" principle became institutionalised and created forces constraining practices of managers.

Unclear tradeoffs as a contributory factor. The fact that corporate levels created more pressure on the tradeoffs processes at refinery levels did not help to ensure a better use of the resources. As indicated in the Baker Panel report "While initiative has been well intentioned, collectively they hâve overloaded refinery management and staff. BP's corporate organisation has provided the refineries with little guidance on how to prioritise thèse many initiatives and the refineries do not receive additional funding to implement each initiative. " (Baker Panel, 2007, p 86).

Structural secrecy (some éléments of)

A gulf between actual performances and perception of it. BP is a huge company that "opérâtes in more than 100 countries across six continents and employs more than 96000 people. BP's corporate structure has been complex for many years" (Baker Panel, 2007, p27). The size and complexity of BP's organisations participated in creating a deep gap between many of the objectives of the refineries and the current practices. "The information available to the panel indicates that a substantial gulf appears to hâve existed between the actual performance of BP's process safety management system and BP's perception of that performance. The gulf did not occur at any one particular point in time and did not exist only at particular point within the organisation. Instead, the information available to the Panel appears to indicate a more systemic breakdown occurring at multiple levels and in différent line and functional positions." (Baker panel, 2007, 228).

The Baker Panel report indeed dedicates two parts on corporate and board oversights. For the Panel "BP typically did not receive short term négative feedback on its reorganisations or job réductions, and as a resuit, BP apparently believed that the refinery opérations continued to hâve the necessary capabilities in place" (Baker panel, 2007, 81). This is clearly the symptom of effect from structural secrecy, where relevant information to steer the organisation is not provided.

Turnover in the industry as an institutional influence. An aggravating factor of structural secrecy at the refinery came from the fréquent changes of leadership. "The panel believes that the high turnover at the plant manager position has contributed to the process safety culture leadership weaknesses at those refineries. (...) Texas City interviewées also noted the differing personalities and priorities of the plant managers. (Baker Panel, 2007, 73). But turnover in managerial position is a current practice in the industry. It is not spécifie to BP and could be traced back to an évolution of practices in the whole industry, a standard that has been pointed at and criticised after the BP Texas City accident for its impact on safety. « Jeroen van der Veer, Shell's chief executive, has imposed a job-tenure rule of four to six years for ail but the most junior staff. Last week BP followed the Dutch company, signalling that the here-today, gone-tomorrow culture of the globe-hopping oil executive had to corne to an end.(...) Shell now expects mid-career and senior executives to spend four to six years in a post, but when Mr van der Veer joined the company in 1971, rapid job movement was the rule. In a récent interview with The Times, he said that the industry had changea over the past two décades and needed much greater professionalism." (The Times, May 7, 2007) 2 .

CONCLUSION

4.1 Preventing « data that should fit model » Historical events such as industrial accidents are unique, they never repeat in the exact same ways. They happen at différent time, within différent technologies, with différent people, etc. But it is also possible to think nevertheless that patterns repeat themselves. As Hughes wrote "History does not repeat itself in détail, but drawing analogies between past and présent allow us to see similarities" (Hughes, 2004, p 2). The two positions are défendable. There will indeed probably be always enough similarities and différences between historical cases to maintain one or the other position. One important principle for accident investigation, and for both thèse positions, is to be sensitive to the "data that should fit the modeF symptom (Le [START_REF] Coze | Complexity and learning from expérience[END_REF]. This principle warns observers not to attempt to force data to fit preexisting models. Enough sensitivity should be therefore granted. It is clear that this applies to this paper and this interprétative exercise. There is always a risk to use a case from which the data hâve been collected without in mind the spécifie model one is trying to apply.

Strong signal or sheer power ?

Yet, treating the Texas City accident with the normalisation of déviance concept is also a useful exercise for the question raised between strong/weak signais and power, between culture and power. We found useful complementary data to the CSB report in the Baker Panel report (pressures from corporate levels to make tradeoffs without guidance, "making do" principle etc) to perform a very partial analogy. It is also an analogy at a macro level, considering risks from the plant perspective and not from a spécifie technology. It is not completely convincing though, given the limits pointed at through the "data that should fit the modeF issue and because of the limited nature of the exercise. There is a bit of a twist in doing so especially when not working on primary sources (direct interviews and observations) but indirect ones (reports already organising their findings).

We could nevertheless say that it is interesting to try to look through the event with the production of a culture, a culture of production and structural secrecy in mind. But we could also see that this company was under abnormal and extrême production pressures. With this stated, is a focus upon a culture of reliability (with ail the conceptual refinements of normalisation of déviance) as Perrow suggested then a luxury? Does this accident not explain itself simply by targeting misused power by élites, the power of few to enforce production pressures way out of known good practices? Is it the power of few, regardless of potential conséquences (conséquences of which they are not themselves exposed)? The power of high level

The two examples of institutional forces, behavioural approaches and high turnover of managers, are clearly detrimental to safety. They do not appear in retrospect to be very rational responses to process safety issues. But they are nevertheless implemented. officiais taking way too many risk, gambling, while managing complex and highly hazardous plants? We won't be able to definitely answer this question hère but we also understand that personal opinion on human nature and society strongly influences the type of interprétation one would favour.

A sort middle position could be satisfying hère. It is indeed rather difficult to analytically distinguish culture from power. Wouldn't it be indeed a réduction of the ase to summarise it as a resuit of power when it is an entire System which revealed its weaknesses? Accidents of this scale are complex events, with psycho, cognitive, social, economical, cultural and political dimensions (Le [START_REF] Coze | Complexity and learning from expérience[END_REF]. As Weick put it " culture and power are not opposed explanations, but rather than culture shapes the way for power, defines power, is shaped by power, masks power, embodies power". Resilience engineering as an applied field, would probably gain in trying to incorporate into its models the constant intertwined présence of power and culture as shapers of organisational behaviour.

Table 1 .

 1 A number of assessments of the Texas City situation (from CSB report)

	Veba report (2002)
	Rétrospective	analysis
	(2002)
	Financial Crisis mode
	(2002)

This is also known as the « hindsight bias ».


Benjamin Daudonnet

/ Baker

Frédéric Mercier

Krzysztof Woznica

MODELING OF THE LARGE DEFORMATION AND RUPTURE OF A METALLIC PLATE SUBJECTED TO EXPLOSIVE LOADING

Thin walled metal pressure vessels or pipes commonly used in industry can burst under certain circumstances: as a result, the pressure envelope may undergo large deformations, which may eventually lead to a rupture. The response of these vessels to static and quasi-static loads is relatively well-understood but their response to highly dynamic pressure loading conditions is not. This paper describes a numerical study of the response of circular metal plates to the dynamic loads produced by hydrogen-oxygen explosions. In this study, a range of dynamic responses and rupture criteria models are considered and compared with the results of experiments. The ability of MSC MARC software to model the rupture phase and, in some cases, the post-rupture phase (i.e., fragment production) is also discussed.

INTRODUCTION

A wide range of vessel rupture models models are available in the open literature. Some models, (i.e., Qiu et al. [START_REF] Qiu | A model for the dynamic fracture toughness of ductile structural steel[END_REF], Recho [START_REF] Recho | Rupture par fissuration des structures[END_REF], Su et al. [START_REF] Su | Elastic fracture properties of all-steel gas cylinders with different axial crack types[END_REF]) rely on the mechanical aspects of the failure such as crack propagation, while other models (i.e., Haque et al. [START_REF] Haque | Rapid depressurization of pressure vessels[END_REF], Leung [START_REF] Leung | Two-phase flow discharge in nozzles and pipes -a unified approach[END_REF], Woodward and Mudan [START_REF] Woodward | Liquid and gas discharge rates through holes in process vessels[END_REF], Fthenakis et al. [START_REF] Fthenakis | A simple model for predicting the release of a liquid-vapor mixture from a large break in a pressurized container[END_REF]) treat the failure using fluid mechanics. Few models are available that consider both aspects of the failure. Where they exist, most studies in this behaviour are focussed on pipeline rupture, (i.e., Iung [START_REF] Iung | Propagation rapide et arrêt des fissures dans les aciers pour gazoducs. Rupture par clivage et rupture ductile[END_REF], Emery [START_REF] Emery | An experimental and analytical investigation of axial crack propagation in long pipes[END_REF] andRivalin [START_REF] Rivalin | Développement d'aciers pour gazoducs à haute limite d'élasticité et ténacité élevée: mécanique et mécanismes de la rupture ductile à grande vitesse[END_REF], [START_REF] Rivalin | Ductile tearing of pipeline-steel wide plates II. Modeling of in-plane crack propagation[END_REF]).

In addition the modelling efforts listed, several experimental studies of structures subjected to a dynamic load have also been performed, for both simple ( [START_REF] Florence | Circular plate under a uniformly distributed impulse[END_REF], [START_REF] Nurick | Deformation of thin plates subjected to impulsive loading -a review -Part II: Experimental studies[END_REF], [START_REF] Nurick | The deformation of thin plates subjected to impulsive loading, In Inelastic Behaviour of Plates and Shells[END_REF], [START_REF] Teeling-Smith | The deformation and tearing of thin circular plates subjected to impulsive loads[END_REF], [START_REF] Pennetier | Structures minces face à une explosion, application à la gestion de risques industriels[END_REF]) and complex structures ( [START_REF] Beltman | The structural response of cylindrical shells to internal shock loading[END_REF], [START_REF] Emery | An experimental and analytical investigation of axial crack propagation in long pipes[END_REF]). In this paper, experiments to measure the response of thin plates to various dynamic loads are presented. The experimental results illustrate the dynamic behavior and the rupture of the structure. These results were then compared to the results of a numerical model. The conclusions and the possible future use of the model are also presented.

EXPERIMENTS Experimental device

The experimental device to test the metal plates, based on the one used in [START_REF] Woznica | Experiments and numerical simulation on thin metallic plates subjected to an explosion[END_REF], is shown in Figure 1. Two stainless steel tubes were used: Tube 1 is 800 mm long and Tube 2 is 400 mm long. Each tube has an inside diameter of 194 mm and a wall thickness of 12.5 mm. The metal plate to be tested is clamped between these two tubes. Some experiments were performed with a rounded edge between the tube and the plate, in order to prevent the circumferential rupture caused by the sharp edge.

Figure 1: Experimental Device

Photo 1 displays the setup for the experiment. In addition to the elements already described above, a high speed camera (shown in the foreground) was used to record the crack propagation and pattern of the tested plates at 10000 frames/second. The experiments were conducted as follows. Once the testing plate was clamped between the tubes, a vacuum was simultaneously created in Tubes 1 and 2. A stoichiometric hydrogen-oxygen mixture was then introduced in Tube 1, while air was fed into Tube 2, to balance the pressure across the plate. Two kinds of explosion could then be produced:

• a "deflagration", in which the mixture was ignited by a low energy discharge (mJ range), such as an electric spark, or • a "detonation", in which the mixture was ignited by a stronger ignition energy (50 J in our experiment). In this case, the shock wave is supersonic and very stable, resulting in a very repeatable dynamic loading condition, whereas deflagration case produced a more stochastic load. When the shock wave reaches the tested plate, its velocity and overpressure peak are not those of a real detonation. For the purposes of discussion, the term "deflagration" also is used to refer to an explosion produced using the low energy ignition systems and the term "detonation" is used to describe the high ignition energy event, even though these terms are not exact for describing the two explosion modes. A sample pressure trace from a detonation test is provided in Figure 2. The successive peaks represent the reflections of the wave inside the tube.

Experimental results

Different plate thicknesses (2 mm, 1 mm and 0.5 mm) and materials (Al5754, Al2017, DC01) were tested. With the sharp edge, the plates were either bulged or split along the edge. With the rounded edge, the plates were also bulged but larger deformations were observed (Photo 2), as higher loadings could be applied without resulting in a circumferential rupture.

For the Al5754 (1 mm) plates with the rounded edge, caps of different size (Table 1) were ejected (Photo 3): the rupture was not a shear rupture, as observed with the sharp edge.

Material behaviour -Chaboche model

The elastoviscoplastic law of Chaboche [START_REF] Lemaitre | Mécanique des matériaux solides[END_REF] was chosen to describe the material behavior. It was demonstrated that this law gives accurate results, comparable to those obtained in experiments [START_REF] Woznica | Experiments and numerical simulation on thin metallic plates subjected to an explosion[END_REF]. The relations introduced in this law are, for the inelastic strain rate s 1 :

i 3 . s'-X £ =3 p& s \ (1) 2 Jls'-X'
where p is the accumulated inelastic strain rate,

(2)

K

Rupture criteria

The damage model proposed by Chaboche and Lemaitre [START_REF] Lemaitre | Mécanique des matériaux solides[END_REF] is a fully coupled model. It is based on the damage parameter D which can be expressed as a ratio between the Young's Modulus modified by the damage and its initial value.

D = l-E (5)

MODELING

Characteristics of the modeling

The numerical modeling of the experiments was performed using the commercial software package MSC.MARC [START_REF]MENTAT, Version[END_REF]. Since the plate thickness is much smaller than its radius, thin shell elements were used to create the plate model. In addition, one-dimensional axisymmetric shell elements were used in order to reduce processing times. The load function was defined using the pressure data recorded during the experiments: the pressure-time history was defined as a pressure force normal to the surface.

The value D = 0 corresponds to a non-damaged state, while D=1 corresponds to a fully damaged (i.e., failed) state.

D = 2Ea(l-D) 2 (6)
where fis a function of the stress triaxiality.

The parameters a and /3 corresponding to this damage law are expressed in equation [START_REF] Fthenakis | A simple model for predicting the release of a liquid-vapor mixture from a large break in a pressurized container[END_REF]. They can be using tensile loading/unloading tests where, fis a constant, [START_REF] Daudonnet | Etude numérique de la rupture d'éléments de structures constituant des réservoirs sous chargement dynamique[END_REF].

While Chaboche was used as the basis for this study, other rupture criteria could also be used. To evaluate some of these alternatives, the following rupture criteria were also considered and defined into MSC Software: • strain limit a simple strain limit obtained from tensile tests was used to define the rupture. • strain rate: Another limit, based on the strain rate was also defined [START_REF] Johnson | Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures[END_REF]:

e f = + D 2 exp(D 3 o *)]x ]1 + D 4 ln(è)]x [l + D 5 T (7)
where Sf is the strain at rupture, a* is the triaxiality and è is the non-dimensional strain rate,

• triaxiality damage: this criteria was used by Lee and Wierzbicky [START_REF] Lee | Fracture prediction of thin plates under localized impulsive loading. Part II : discing and petalling[END_REF] for rupture of a thin plate under projectile loading as follows:

D = Jo a -de (8)
where a H is the hydrostatic stress, and G the Von Mises equivalent stress.

RESULTS

The numerical modeling and analysis were compared to the experimental results for both the ruptured and unruptured plate conditions.

Tests with no rupture

The MSC software model was validated by comparing the results obtained with those of Woznica et al. [START_REF] Woznica | Experiments and numerical simulation on thin metallic plates subjected to an explosion[END_REF]. The close agreement between these results ( [START_REF] Daudonnet | Modeling of damage in a circular plate subjected to dynamic excitation[END_REF]) indicates that the model is appropriate. Additional comparisons to the experiments were then made:

• the final plate deflection along the radius was measured and compared to the numerically-predicted value at different times. As shown in Figure 3, good agreement between the numerical and the experimental results was observed. the large displacement and deformation of the plate observed when introducing a rounded edge plate holder also showed good agreement with the numerical results (Figure 4).

Tests with rupture

Three different rupture tests were studied: un-notched plate with the rounded edge, notched tensile test specimen, notched explosive test specimen.

Un-notched Plate under Explosive Load

The rupture that occurs at high loadings with the rounded edge was studied using axisymmetric shell elements. Comparing the results obtained using different rupture criteria (i.e, strain, strain rate, damage) we notice that the best results (see Table 2) were obtained for criteria that take into account the strain rate or the damage (i.e., Chaboche-Lemaitre). These results illustrate the importance of the strain rate and the damage effect on the material response.

Notched Tensile Test Specimen

Before the studying of the failure of the notched plates under explosive loading, tensile test specimens were modelled. The aim of this experiment was to verify the adequacy of a method to model the rupture. We applied the strain criteria combined with the deletion of elements, as illustrated in Figure 5.

Notched Explosive Test Specimen

As presented above, a notch was created in the center of the plate in order to initiate and control the location of the rupture. The result of this experiment can be observed in Photo 4 for Al5754. Good results were obtained numerically, as shown in Figure 8 and Figure 9. The general shape of the crack predicted is very similar to that observed experimentally. The discontinuities observed in the crack velocity prediction are attributed to the discontinuities inherent to the modeling (i.e., the deletion of an element cannot be continuous). Once the abnormal values of crack velocity are excluded, the numerical result appears to be of the same order as the measured value (between 200 and 300 m/s).

For Al2017, the crack length and velocity measured were compared to the calculated results. As presented in Figure 6 and Figure 7, good agreements were obtained, relative to the complexity of the phenomenon. This method could be applied for more elaborate arrangement, but any such model must be applied carefully as it can be subject to variation (for example if the size of the element is too large).

CONCLUSION

This paper compares experimental results to results obtained using numerical simulations for metallic plates subjected to explosive loads. The numerical prediction used an axisymmetric model for a metallic plate subjected to a dynamic load. The material deformation was predicted using the Chaboche viscoplastic law, where the material characteristics have been identified from tensile tests. Accounting for the strain rate or the damage was shown to improve the accuracy of the prediction of the rupture (compared to a basic strain criterion). Combining such a criterion with the deletion of elements provides a good match to experimental data (shape, velocity) for this complex phenomenon. These results indicate that this method could be a viable means of studying rupture.

RECOMMENDATIONS FOR FUTURE WORK

While this study has shown good agreement for thin plates in a fixed geometry, a more detailed analysis of the limits of validity of this method is recommended. Another extension of this work would be to further study the projection of a fragment and its initial velocity once the rupture occurs. Indeed, in the case of the axisymmetric elements, the deletion of the failed element would lead to the creation of a fragment, which is then projected.

Photo 1 :Figure 2 :

 12 Photo 1: Photograph of the Experimental Device

  Photo 2: Bulged Plate (AL5754, Detonation, Pi=1.1 bar, Rounded Edge)

Figure 3 :

 3 Figure 3: Plate Deflection at Different Times (Deflagration, Pi=0.8 bar, Sharp Edge)

Figure 4 :

 4 Figure 4: Numerical Displacement and Final Experimental Deflection at the Center of a Plate (Detonation, Pi= 1.1 bar, Rounded Edge)

Figure 5 :Figure 7 :

 57 Figure 5: Numerical result for a notched specimen: Equivalent Total Strain

Figure 8 :Figure 9 :

 89 Figure 8: Numerical Result for Al5754 notched plate: Equivalent Total Strain (Deflagration -Pi=0.8 bar)

Table 1 : Diameter of Caps for Different Loads

 1

	Initial pressure [bar]	1.1	1.2	1.4
	Cap diameter [mm]	0	37	150

Another way to initiate the rupture and control its starting location was to create a notch. Notches of different widths, from 0.3 mm to 1.6 mm, were created in the center of the plate. Photo 4 is an example of the results obtained for a 1 mm Al5754 notched plate.

Photo 4:

Experimental Result for Al5754 Notched Plate (Deflagration, Pi=0.8 bar, Sharp edge)

  and n are viscous parameters, y=l [s-1 ]. The parameter k is the initial yield limit. s' denotes the deviator of stress tensor s, J(...) is the scalar equivalent of deviatoric stress invariant. R is a drag stress.

	This law introduces an isotropic hardening:
	R = b(R 1 -R)p	(3)
	where R1 and b are material parameters.
	A kinematic hardening is expressed through the evolution of
	the back stress X,
	= -aé'-cXp	(4)
		viscoplastic
	model:
	E=71.11 GPa,	r=ls 1 ,
	n= 8.9;	K = 13.97 MPa,
	k=101.64 MPa,	c= 2478.3,
	a=54049GPa,	b=14.68,
	R1= 178.45 MPa.

where a and c are the law parameters. The following material data, validated for Al 5457 at T= 20°C (Woznica et al.,

[START_REF] Woznica | Experiments and numerical simulation on thin metallic plates subjected to an explosion[END_REF]

), were used in the Chaboche

Table 2 : Cap Radius Predictions

 2

				Cap radius (mm)
				Detonation	Detonation
				Pi=1.2bar	Pi=1.4bar
		Experimental Result	18.5	75
	Predicted	Cap Radius	Strain Strain Rate ( S ) Triaxiality Damage Chaboche Lemaitre Damage Model	39 24 52,5 30	59,52 56 62,6 72


INERIS Fabien Fouihen

INERIS Stéphane Duplantier

PRESSURIZATION OF FIXED ROOF STORAGE TANKS DUE TO EXTERNAL FIRES

INTRODUCTION

This study deals with one of the phenomena which is able to generate fire balls like the one which was observed during the 1987 Edouard Herriot port of Lyon fire. Reflections led on this accident have pushed to consider the phenomenon of tank pressurization as a potential initiating event of the fire ball observed. In concrete terms, when a fixed roof storage tank is surrounded by a pool fire, and when the vents or the insulation are not correctly designed, the inside pressure can raise until the mechanical limits of the structure are reached. The aim of this study is to develop a tool which will allow to follow the variations of the pressure and temperature in the gas phase, highlighting if a pressure increase is possible or not. This will help the sizing of new tank vents and insulation of the walls, or evaluating the risk of already build structures, by solving the question occurrence of the accident, regarding the estimated external fire duration. The model also gives the temperature distribution in the liquid phase, at each time step. In case of rupture, this information will be useful to describe the phenomenological aspect of the accident after the rupture of the tank. It means that qualifying and quantifying the fire ball generated and its effect on persons and structures will be possible. Currently, although a few analytical models exist to quantify the fire ball and its effects after the rupture, none is able to describe with accuracy the pre-rupture phenomena. This model is a work in progress, and at the end, the tool will take into account the two phases of the accident and will allow to study complete and consistent scenarios. After a description of the numerical model developed, this paper presents its application on the study of the influence of various parameters.

DESCRIPTION OF THE MODEL AND INPUT DATA

The modelling tool presented is a dynamic model which represents the axisymmetric behavior over time of a cylindrical tank, when this one is impacted by a pool fire. The approach which has been followed in all building steps of the model was to "forget" the empiric assumptions, laws or formulas used in current standards, and to consider only the basic equations of thermodynamic and fluids mechanic. As the literature doesn't present experimental tests or accidents analysis allowing to check the evolution of different parameters, it is essentially the study of energy balance and trends evolutions

Figure 1. Input data and considered heat transfers

As stated previously, the studied geometry is considered axisymmetric. The input parameters written in italic on Figure 1, are the specific dimensions of the tank: its height, diameter and thickness. The thickness of the wall is supposed uniform. It's also necessary to input the filling rate of the tank, expressed as a percentage. The vent itself is defined by its surface and its discharge coefficient. A minimum opening pressure must also be provided. This latter parameter allows to take into account the safety valves. It is possible to consider several substances: water, ethanol, hexane (Cs), decane (Cio), undecane (Cn) or dodecane (C12). In all cases, the substance is considered pure. The characteristics of the substances are intrinsic functions of temperature. To model the fire that impacts the tank, the radiative flux per unit area of flame must be defined. It is possible to define two types of aggression: a uniform distribution of the radiative flux along the entire height of the flame, or a radiative flux function of the height. In all cases, the flame height is limited to the height of the tank.

MESH

The mesh put in place is axisymmetric. The volume of liquid is divided into m x n identical sub-volumes. There are m volumes along the height, and n following the radius of the tank. So as to work with volumes of the same capacity, the spatial distribution is done following the equations (1) and (2) :

m (1) (2)
The gas is supposed to have homogeneous pressure and temperature on the entire free volume. Therefore, it is composed of a single computational ceil. As for the walls of the tank, it is represented with m+1 cells along the height, with a width along the radius equal to the thickness of the wall, as shown in Figure 2.

HEAT TRANSFERS

Thermodynamics allows us to predict the total amount of energy that a system should share with the outside to move from one equilibrium state to another. Thermokinetic is used to describe quantitatively the changes in characteristics of the system, particularly temperature, between the initial state of equilibrium and final steady state. At each time step, the calculation of heat transfers leading to a variation of pressure in the gas phase is done. The Figure 3 shows which equations are used in each cell so as to equilibrate the energy balance. The numbers in this Figure refers to the numbering of equations which are all defined later in the paper.

(13)

(5)

t '/• • • 'al l (5)
Vent Roof (4) Gas

(6) (11) (11) (11)
T (4)

Figure 3. Equations taken into account

The various equations used correspond to the first thermodynamic law applied to each defined system, i.e. to the following energy balance:

<Pl+<P* ! =<P,,+<Ps l (3)
With <pi the incoming heat flux, (p ge the generated heat flux, q> Q the outgoing heat flux, <Pst the stocked heat flux. Solving this equation leads to a differential equation which allows to determine the evolution of the temperature at a given point during time. The heat flux are calculated the following ways:

-The generated heat flux: it occurs when another form of energy (chemical, electrical, mechanical, nuclear) is converted into thermal energy. The system considered here is not concerned by this type of flux. -The stocked heat flux: it is linked to an augmentation of the internal energy of the system during time. It can be written as (4):

ot (4)
-The incoming and outgoing heat flux: heat transfers can occur by: Conduction: it is the favorite way of energy transfer in opaque medium. It occurs without material movement, along the temperature gradient. It is calculated following the Fourier hypothesis (for example in the x direction) by the equation ( 5):

<P = -M^-(5) ox

Convection: it is the transfer of heat between a solid and a fluid, obtained by the displacement of the fluid. This phenomenon is governed by the Newton law ( 6): <p = hS(T,,-Tj [START_REF]Documentation File for API Manual of Petroleum Measurement Standards[END_REF] Radiation: it is an electromagnetic transfer of energy between two surfaces. It is calculated with the equation ( 7):

<p=oe P sfà-TÏ) (7)
Evaporation, condensation and convection inside the liquid are important heat transfer modes. Taking them into account is more complex their modeling is detailed in the next sections.

CONVECTION ALGORITHM INSIDE THE LIQUID

The convection algorithm developed is based on the use of the dimensionless Grashof's number. A static fluid in contact with a wall brought from a temperature 7~to a higher temperature T+AT, will overheat by conduction. The density of a fluid volume will increase from pto p+Ap. This unit volume will be subjected to a lifting force. While (3 is the cubic expansion coefficient, pAT represents the module of the acceleration produced by thermal expansion due to changes in temperature. This movement of fluid caused by differences in density will give rise to convection currents. By equalizing the variation of kinetic energy to the variation of potential energy, the number of Grashof allows to calculate the rising speed (ms 1 ), for a unit volume of liquid:

f L ( 9
)
This algorithm is based on the principle that the phenomenon of convection is initiated and amplified by the volume of liquid moving upward. The downward movements are the result of the imbalance caused. According to equation (9), the fraction of volume which comes out of a cell is defined by:

dV = S h dz = S h udt (10)
Mass conservation law is used to define step by step, for each cell, the fraction of liquid volume entering or leaving the considered cell, as well as its origin or its direction. The contribution of convection for calculating the temperature of a fluid cell density can be determined following the approach detailed in Figure 4.

Cell (i j) of volume V at temperature T(t)
DV_ a > 0 =>Volume of liquid getting in the cell (i.j)

\7

Calculation of DV_a

Getting in or out From cells a to Ceil (ij) at temperature T_ a(t) (a=L2 : 3and4)

INTEGRATION OF EVAPORATION AND CONDENSATION

At each time step, and for each cell volume, the vapor pressure at the liquid temperature is compared to the partial vapor pressure in the gaseous volume of the tank. This allows to evaluate the mass transfer between phases in order to determine the contribution of evaporation and condensation to variations of:

-Pressure; -Liquid level; -Temperature. The total number of moles of liquid which have to be evaporated is calculated so that the balance is achieved between the liquid and gas phases. To do so, the equation ( 11) is used. In this formula, Brepresents the second virial coefficient.

(p -P )v jwY; ;\ -V i«/'_ îû ' partial vap) f \p _ sal partial _ vap / g ( 11
)
Two cases may arise: either the cell (i, j) is likely to contribute to the change of mole number in the gas phase, and the algebraic value of /Vis calculated, or it isn't, and /Vis equal to zero. This approach prevents from the presence of liquid with temperature above the equilibrium temperature corresponding to the partial pressure in the gas,

TAKING THE VENT INTO ACCOUNT

The gas is composed of a mixture of air and vapor due to the evaporation of the liquid inside the tank. The pressure in the tank is a function of four interdependent parameters: the temperature of the gas mixture, the rate of evaporation/condensation, the flow rate of the vent, the liquid level. At each time step, evaporation contributes to the change in the partial pressure of vapor, and increasing the total pressure in the gas. When it reaches and exceeds the trigger pressure of the vent, a certain amount of gas is evacuated outside of the tank. This volume of matter is calculated with the Bernoulli's equation:

V m = 2C n S, D'-'venl ( 12
)
With CD the discharge coefficient of the vent, S ven t its surface and AP the differential pressure between the inside and the outside of the tank. Knowing the number of moles of liquid at a temperature Ti(iJ) evaporated, and the number of moles of gas at temperature T g evacuated by condensation or through the vent, it is possible to determine the contribution of gas transfers to the variations of gas temperature:

IN -L-N 4. A/ _ A/ -AT IT M+V 1 Af ( V /ïrf; /I /• , \ V V 111»/ _ m/> ^ J V ill»/ w ^ J V mol ciulil J V /»»/ frur IT//) J V /M«/ flflt _a/f/ J s"/ / -«1»/ V ' •/ / J / V f ' -/ / A/ + A/ + A/ -A 7 -A 7 " +VA/ fz /I tnoJ _ va/j ' J rii«/ _ «//• mw/ _ cond «1»' _ ivac _ vap mol _ évac _ air £^ mol V ' J !

INFLUENCE OF THE DIFFERENT PARAMETERS

So as to determine the influence of the accessible parameters on the behavior of the system, a reference case has been used. The parameters corresponding to this reference case are:

-The height of the tank: 14 m;

-The diameter of the tank: 24 m;

-The thickness of the walls: 10 mm;

-The filling ratio: 50% of the tank capacity;

-The substance: hexane;

-The vent surface: 0,1 m 2 ;

-The maximal radiative flux of the fire: 50 kW.m" 2 .

The variations of the pressure of the gas phase are presented in Figure 5. The maximum pressure obtained here is called Pmax_ref. Pmax_ref keeps the same value all along the present section. During the first 15 h, the size of the vent is sufficient to compensate the vaporization rate. The maximal overpressure is observed after 30 h of fire, where a 5 h plateau is reached. After, the pressure starts to decrease with the level of the liquid.

The influence of the followings parameters has been evaluated:

-The stored substance; -The liquid level;

-The diameter of the tank;

-The vent surface.

The detailed graphs of the results obtained are presented from Figure 6 to Figure 9. They show the variation of the pressure in the gas phase when only one of the parameters previously defined varies. The blue curve is always the reference case. : These curves show that for hydrocarbons, the overpressure is nearly the same in each case studied. The length of the carbon chain has an overall influence on the kinetic of the phenomenon. The pressure raise occurs later for the heavy substances than for the light ones. The case of a low molecular weight alcohol has been modeled too, and the results in this case show that the impact is also on the intensity of the overpressure.

"• • • • • , • -. \ u v« ..V. / • J 1 > • t i ^ i i 0
The next parameter studied is the level of the liquid at the beginning of the accident. The scenarios modeled concerned tanks filled with 25, 50 and 90 % of liquid. The gas phase is composed of a mixture of air and vapor, considering the partial pressure of the vapor of the stored substance.

Figure 7. Influence of the tank filling

It seems that an initially full tank leads to a quicker phenomenon, with a really bigger overpressure. This is partially due to the limited amount of gas which is needed to obtain equivalent conditions of pressure in each case. Moreover, the behavior of the system doesn't appear as a linear function of the tank filling. The same study has been done concerning the diameter of the tank:

Figure 8. Influence of the tank diameter

Increasing the diameter of the tank has for effect to increase the overpressure obtained. This can be partially explained by the exchange surface between the liquid and gas phase, which increases with bigger diameters. However, as the total volume of liquid increases too, the overpressure is observed later.

The two previous parameters directly impact the area of wetted wall, which seems to be the dominant factor causing the observed peak pressure, due to an efficient heat transfer from the fire. The effect of diameter on time duration seems to also be explained by the ratio wall area / tank volume, which decreases as diameter increases.

The last study done concerned the dimension of the vent. It has overall been done in order to check the behavior of the model. Results follow the good sense trends: a limitation of the vent size leads to a higher overpressure.

INDUSTRIAL APPLICATION

The results of the previous parametric study have highlighted the predominance of two parameters: the wetted wall area (linked here to the diameter of the tank) and the surface of the vent. In order to establish a general behavior chart, various simulations have been run with different configurations regarding these two input data. The output data will allow to:

-Either in a design phase, calculate the vent size needed to prevent any accident due to pressure increase inside the tank;

-Or for already built tanks, supply input data for the phenomenological study of the potential fireball generated, based on the temperatures mapping in the liquid at the bursting pressure.

For the production of a first general behavior chart, the following conditions were chosen. The fixed parameters are the height of the tank (14 m), the tank wall thickness (10 mm), the filling ratio of the tank (90% of the total height), the substance stored (decane), the maximum radiative flux of the fire (50 kW.m-2) with a progressive loading on the wall. The varying parameters are the vent size and the tank diameter.

A typical result obtained is represented on Figure 10, as a function of time. This curve corresponds to the smallest tank (12 m diameter) with the smallest vent (0,025 m 2 ) studied.

0.15 0.05 Time(h)

Figure 10. Example of output data

In this Figure, the 2D maps represent the distribution of temperatures in the liquid phase, at different time steps. The "discontinuity" which appears is due to the approach taken to model the fire, with a non uniform loading along the height of the tank. These maps will allow to determine the quantity of liquid which will participate to the potential fire ball at a given failure pressure. Pmaxjnax is the maximum pressure reached during the parametric study presented in this section, it means for the smallest vent size and maximum tank diameter.

Figure 11 shows the results obtained for the influence of the vent size on the behavior of the pressure, for a 48 m diameter tank. The tank has vents with surfaces varying from 0,025 m 2 to 0,500 m 2 .

CONCLUSION

The model presented in this paper is a tool developed by INERIS, to determine the surface of vents which should be put in place to compensate the vaporization flow of the content of a fixed roof tank caught in a pool fire. The results obtained with the first parametric studies seem to be consistent with the trends that could be expected. The behavior of the liquid, the heat balance and the kinetic of simulated phenomenon suggest that the computed code works correctly. However, the sensitivity of results to various parameters makes unavoidable the implementation of experimental trials. These parameters have been identified during the development of the model, and the experimental approach will help to adjust them, in order to obtain a model as close as possible to the real behavior. Further to these trials, the next step of this study will be to assess the effects resulting from the rupture of the pressurized tank and from the generation of the fireball.

  which have been considered to validate each step of conception of the model. The heat transfers taken into account in the model are represented on Figure1.

Figure 2 .

 2 Figure 2. Axisymmetric mesh used

  getting out of the cell (ij)Contribution C2 : [V-IDV a] .T(t)

Figure 4 .

 4 Figure 4. Participation of natural convection in liquid temperature calculation

Figure 5 .

 5 Figure 5. Evolution of pressure for the reference case

Figure 6 .

 6 Figure 6. Influence of the substance stored

Figure 9 .

 9 Figure 9. Influence of the vent surface

Figure 11 .Figure 12 .

 1112 Figure 11. Influence of the vent size for a 48 m diameter tank


Turbulent energy Turbulent energy dissipation rate Volume flow rate Mass flow rate Density Generalised diffusion coefficient Source

INTRODUCTION

This study is a part of the EGSISTES research project that aims to improve the understanding of dangerous phenomena in underground infrastructures. For the présent case, it deals with fîre in tunnels.

Récent large fires in tunnels hâve induced a modification of the régulation relative to the driver's protection. Mainly, smoke management in case of fire was defïne on the base of the smoke stratification for bidirectional tunnels and for congested unidirectional ones. For both cases, smoke generated by the fïre has to be pushed out of the tunnel without invading the whole section because of people présence. As an illustration of this strategy, the French régulation (1) imposes for congested unidirectional tunnel, a maximum velocity of 2 m/s in order to keep the stratification during the évacuation procédure. Such a velocity will generated backlayering flow that must also keep stratified.

As that appears clearly in this above description, stratification must be strictly ensured during the évacuation period, not only for the downstream flow but also for the backlayering layer too, It must however be kept in mind that the stratification of the flow is based on an equilibrium between buoyancy effect and sheer stress.

In above described tunnels, two main disturbance sources were identifïed: jet fans located upstream the fire, which are used to control the air flow velocity, and turbulence induced by vehicles.

The aim of this paper is to study the influence of those two kinds of perturbations on the stratification.

The whole study, in the context of the EGSISTES project is based on both expérimental and numerical works.

The experiments, achieved in the INERIS fire gallery are used to improve physics understanding. Moreover, numerical approach enables to go further and reveals some détails that can hardly be enlighten by the experiment.

The aim of this paper is mainly to describe the numerical work based on two Computational Fluid Dynamics codes: the Fire Dynamics Simulator (FDS) and Phoenics.

First of ail, the numerical approach is briefly described comparatively for the two codes. Then, the expérimental geometry, which was retained as the numerical one, is described.

Next, before describing comparatively the results of those two codes, a comparison with available expérimental resuit is achieved. This comparison concerns the backlayering flow and its properties.

At the end, the two disturbance source effects were tracked. Results obtained with both codes are detailed and the influence of disturbance on the stratification phenomena is discussed.

NUMERICAL APPROACH

Conservation équation

The smoke behavior in tunnel in case of fîre is governed by the fluid mechanic équations.

Thèse équations are the mass, momentum, and energy conservation that can be written in the conservative gênerai form as on [1].

[l]

Thèse équations cannot be solved analytically and require a numerical approach. The complexity of the géométrie real domain leads to introduce in this numerical approach, some physical models.

In fire modeling, main physical phenomena that hâve to be modeled are turbulence and fîre heat release.

2.2

Numerical solvers PHOENICS is based on the finite volume method which solves the équations on a staggered grid. The solutions of the resulting coupled differential équations are obtained in an itérative manner using the SIMPLEST algoiïthm (2).

FDS is based on a second order finite différence scheme for the spatial discretization. The temporal resolution uses prédictive corrective scheme (3).

2.3

Turbulence modelling The two codes used in this paper are based on two différent turbulence models.

To account for turbulence in Phoenics code, the Chen-Kim (4) modified RANS k-e model (5) (6) is used. In this model, turbulence is represented by the turbulent kinetic energy k and its dissipation rate e. Both of thèse variables require solving two équations of the generic form presented in [l].The effects of gravity on the turbulence are modelled by the introduction of buoyancy source ternis into the équations for k and s.

In FDS, the turbulence closure is based on the LES Smagorinsky static approach (7). In such a model, the largest scales are directly solved while phenomena smaller than the eut scale are modeled.

Before going any further in the code results cornparison, it must be notice that LES provide instantaneous values while RANS results gives temporal, which can be considered as statistical, means quantities. So, it is important, for the results comparisons, to average LES results along the steady phase. This is done only for comparison purposes, underlying the fact that providing instantaneous results, in the case of an LES model enables to capture some détails that cannot be trapped using a RANS approach. Instantaneous température pick, for example, will not be enlightened by the averaged method while LES will be able to show it. Secondly, characteristics frequencies of the flow, such as vortex formation, can also be revealing by the LES approach.

2.4

Fire Représentation Physically, a fire could be modeled as a séries of complex chemical reactions that induced species transformation and the release of energy, only the thermal effect is taken into account in this study, species production is not discussed. It can be numerically represented in many différent ways.

A classical approach to represent fire in tunnel (2) consists in imposing a source term in the energy équation associated with a kinetic évolution. This approach was, for example, retained by the French ministry of transport [START_REF]Guide des dossiers de sécurité des tunnels routiers, Fascicule 4 : Les études spécifiques de dangers[END_REF]. The species source terms is defïned proportionally to the heat source term.

As discussed above, the way to represent the fire is to define a source term in the energy équation to represent the heat release rate of the fire. The energy équation that is solved is given on [2];

^ + V • {pVH) = V • (F H VH) + S R [2]
In Phoenics, the energy source term S H is the convective heat release rate of the fire per unit of volume as the fire is modeled by a volumetric source of heat; the radiation part is not modeled. In simulations presented in this paper, the heat release rate density retained is 1 MW/m 3 , which is the value advocate for this code.

In FDS the fire is represented by a surface of emitted combustible products. The heat released is next distributed in différent cells using a simple combustion model [START_REF]Fire Dynamics Simulator (Version 5) Technical référence Guide[END_REF]. This method enables to represent exactly the expérimental fire source. Radiant heat transfer is modeled in FDS using a 1-flux approach.

2.5

Boundary conditions Walls are considered as adiabatic and rough. Standard wall-functions are used with the Phoenics k-s model. A 3 mm roughness scale is imposed, this corresponds to the concret roughness. In the LES approach, using FDS, there is no particular model for the wall. The smoke layers are not as long as the roughness should hâve an impact on the results. Furthermore, in the expérimental part, the higher probe is not installed in the boundary layer.

At the inlet, the atmospheric pressure and the ambient température are imposed. This boundary condition allows the smoke to go out if the backlayering predicted length is too important. The fan is represented by a flow rate imposed on the chimney base.

EXPERIMENTAL DOMAIN

This expérimental study is carrying out using the INERIS fire gallery: a 1/3 scale tunnel with a maximum clearance cross section of 5.4 m 2 and with a total length of 50 m.

The expérimental set up is schemed on Figure 1. The upper part is a smoke duct which permits to ventilate using a transversal ventilation System, system that is not used in the présent paper.

The ground is not regular (approx. ±1%) that was modeled in the différent simulations. Ail parameters of this study are calculated using Froude similarity to take in account of the reduced scale.

During experiments, the fire is generated by an heptane pool fire. The expérimental heat release rate of the fire is computed from the mass consumption measurement and reaches 352kW in reduced scale, this corresponds to a heat release rate of 5,5 MW in full scale.

The radiative fraction was also computed on the basis of the expérimental resuit. To do that, velocity and température profiles were measured downstream the fire, this gives the convected part. Knowing both total and convective energy, the radiative fraction was evaluate to 0.39, value in accordance with standard value for 0,25 m 2 heptane pool fire [START_REF]Scale Dependency of Radiation and Smoke Emission from Large Pool Fires, KOSEKI[END_REF].

The ventilation is supplied by the fan installed in the chimney. It is important to note that the fan is far from the fire and downwind an air washer. This means that the température at the fan is constant during one experiment. The fresh air would arrived by the open extremity on the left on the scheme.

NUMERICAL REPRESENTATION OF THE DOMAIN

Because of numerical constraints, the geometrical model is based on rectangular cross sections. In such a model, the lower part of the fire gallery is correctly represented because its section is a square of 3 m width by 1.8 m height.

After having checked that the chimney does not affect simulations and in order to reduce the cells number, i.e. the CPU time for each computation, this chimney was not modeled.

Then, a study of the influence of the grid sensibility was achieved and the independence of the results was checked, focused on the backlayering length. Following this study, for both FDS and Phoenics, the same number of cells was used: 250 cells in the length, 60 in the width and 40 in the height, which gives a total number of 600,000 cells. This gives characteristic size for the cell of: 20 cm in the length, 5 cm in the width and 4.5 cm in the height.

Two phenomena were studied, upstream and downstream stratification, so two flre positions were tested: • To obtain an upstream smoke layer in the gallery (backlayering), the fire was placed at 10 m of the chimney; • To evaluate the downstream layer stratification, the fire was located 10 m from the inlet.

At first, the stratification of both upstream and downstream smoke layers are characterized.

Then, the influence of the perturbation on the stratification is analyzed. For the backlayering, the perturbation corresponds to a jet fan. For the downstream smoke layer, the perturbation is due to the présence of vehicles blocked by the traffic jam downstream the fire. The vehicles are represented by cube to avoid cutting cells. The vehicles position studied représenta the traffic of an unidirectional tunnel.

STRATIFICATION QUANTIFICATION

To discuss about stratification, Newman (13) lias introduced two stratification parameters:

A7 ^[4] T -T c f * Tj,-T 0
Where T c is the température at the height of 0.88h, T f the température at 0.12h and T h is the température in the smoke layer. AT avg is the gas température rise relative to ambient condition and is defined in (13).

Thèse two parameters inform on the amplitude of the température différences, and on the relative thickness of the hot and cold layers.

The study of the stratification using those two parameters can be done for both upstream and downstream smoke layers.

For the downstream study, the function between those two parameters defmes two régions that dépend on the stratification characteristics [START_REF] Newman | Expérimental évaluation of Fire-Induced stratification[END_REF].

In the région II (Figure 2), for St < 1.7, buoyancy dominated the température stratification. This leads to a destruction of stratification. If S 2 approaches values of the order of 0.1, the smoke layer is completely destratified.

In the région I, for S! > 1.7, S2 is roughly equal to 1. This implies that the gas at the floor is at the fresh air température.

S1

Figure 2: Evolution of the two stratification parameters, reproduced from ( 14).

For the upstream flow, the évolution of the function is supposed to be uniform following a power low (15).

COMPARISON BETWEEN NUMER1CAL AND EXPERIMENTAL RESULTS FOR THE BACKLAYERING

Before going any further in the physical and numerical analysis, it is important to ensure that the numerical results are in good agreement with expérimental values.

This comparison is based on the expérimental measurement of the backlayering. The experiment use a fire located at 10 m of the base of the chimney and the ventilation flow rate was chosen to respect French régulation for a longitudinally ventilated congested tunnel (1). The air flow velocity at reduced scale is 0.93 m/s, this corresponds to one of 1.6 m/s in full scale.

Expérimental and numerical results comparison

Représentative quantities for the backlayering phenomena are température and velocity. First of ail, maximum température reached under the roof above the fire was compared because the backlayering effect directly dépends on this parameter.

The expérimental value of 285°C was quite correctly reproduced by the two CFD codes (245°C for FDS and 240°C for Phoenics).

Two température profiles were measured: 10 m and 17 m upstream the fire and one velocity profile was measured 17 m upstream the fire. Those three profiles were compared with the numerical prédiction. Figure 3 shows the température profile comparison between both FDS and Phoenics prédiction and the expérimental one. This graph enables to compare the thickness of the thermal layer. The interface between the hot smoke and the fresh air layers height is calculated by the N-rule method (12). Thèse interface heights are represented on the figure by stars. It is shown on this figure that the thickness of the backlayering layer is over predicted by the two CFD codes.

It is also shown on this figure that the température is under predicted with FDS in the upper layer. Whereas, the maximum température of the backlayering layer is well predict by Phoenics. Nevertheless, the température of the upper part of the smoke layer is not well predicted by Phoenics. This can be partially explained by the ceiling model in Phoenics simulations that do not take in account the heat transfer between the ceiling and the smoke layer. Next, as discussed earlier, an expérimental profile of velocity is available 17 m upstream the fîre, Figure 4 shows the comparison between numerical prédictions and expérimental measurements for the température and the velocity profiles. The interface heights on the température profile are represented by stars.

This figure shows that the layer thickness is well predicted by FDS farther from the fîre while for Phoenics the thickness is over predicted. This figure confirms the under prédiction of the température of the layer by FDS.

The température of the backlayering layer is over predicted by Phoenics, this could be explained by the over prédiction of the upper part of the smoke layer nearer the fire.

Before concluding, the measured length of the backlayering layer is about 25 m, which is in great accordance with the corrélation given by (12).

The predicted lengths using the two CFD codes are compared to this expérimental resuit.

The two results are reproduced on Figure 5. FDS simulation predicts a backlayering length of 21 m upstream the fire and Phoenics a length of 26 m, lengths in good agreement with the expérimental measurements. and Phoenics (down).

Conclusion of the expérimental confrontation

This first comparison permits to conclude that the k-a Chen-Kim model is probably inappropriate to predict the smoke layer thickness whereas the LES model permit to obtain a resuit in better accordance with the expérimental measurements.

The smoke températures obtained with Phoenics are over predicted. Whereas, FDS under predicts the hot smoke température. In FDS, the radiant heat transfer between hot smoke layer and the ceiling is probably over predicted. In Phoenics, the fact that the heat exchanges at the ceiling (adiabatic boundary condition) are not modeled can explain the over prédiction of hot layer températures. Whereas, the sides model would not affect the resuit as the smoke layer has negligible heat exchange with the sides. In fact, the contact surface between the smoke layer and the sides is small. Moreover, the sides are made of refractory concrète.

For next experiments, it will be important to refîne the température profile in the smoke layer and to détermine the évolution of the ceiling température during expérience to check the level of heat exchange between the hot layer and the ceiling.

Next sections are based only on numerical simulations. Expérimental results for following configurations are not yet available and will be published later.

7.

COMPARISON OF THE TWO CODE RESULTS FOR THE PERTURBATION 1NDUCED BY A JET FAN

In longitudinally ventilated tunnels, jet fans, located under the ceiling, are used to generate the air flow. The momentum source generated by such an apparatus can hâve an influence on the stratified backlayering layer.

The aim of this part of the study is to characterize this influence. To prevent for complex coupled physical effects, the jet was designed to prevent from rotational effect in the expérimental situation.

The same approach, i.e. a plane jet without rotational effect, was used in the numerical approach. This simplifîed approach enables to represent the vertical gradient of velocity that propagates into the tunnel to the backlayering layer.

The jet will be generated at the entrance of the fire gallery using a ventilation box. The output velocity of the ventilation box was set to 3 m/s.

The charactenstics of the backlayering layer are then compared with and without jet in terms of température distribution, velocity profile and backlayering length. In order to compare the hot smoke layer characteristics, it is necessary to conserve an air flow velocity of 0.93m/s for the cases with and without jet.

First, the vertical température distribution is plotted on Figure 6 for numerical results obtained with FDS and Phoenics. Thèse results show that the backlayering layer is slightly affected by the jet near the fire. The jet influences greatly the part of the smoke layer near the front. The comparison of the Figure 5 and Figure 8 shows the modification of the backlayering front due to the jet.

The hot smoke layer in this part is thicker with the jet than without. This implies that the backlayering layer is longer with the jet than without.

Moreover, the front layer température distribution is perturbed by the jet. The smoke with température between 20 and 50°C takes a thicker layer on the front with the jet than without. The FDS code predicts a lower influence of the fan on the jet with a small impact on the head of the backlayering layer. This lower influence should be explain by the fact that the length of the layer compute with FDS is smaller than the one obtained with Phoenics and, consequently, the distance between the backlayering front and the fan is more important with FDS, so the effect of the fan is diminished. Moreover, the turbulence models used with Phoenics and FDS are not the same and should affect the influence of jet on backlayering layer.

MT\ i ! ! '_n

Expériences will be achieved to explain this influence of the jet located just near the backlayering front.

COMPARISON OF THE TWO CODE RESULTS FOR THE PERTURBATION INDUCED BY THE VEHICLE PRESENCE

The two previous sections dealt with the backlayering layer.

The présent part objective is to evaluate the stratification of the downstream smoke layer and the influence of vehicles on its stratification. This point is particularly important in case of longitudinally ventilated congested tunnel. In such a case, vehicles can be blocked under the smoke layer and their influence could be important as shown on some previous studies (10) and ( 16). The aim of this part of the study is to evaluate this importance and the ability of numerical CFD code to predict this influence. Those results will be compared with future expérimental work. The numerical simulations are released in the gallery with an air flow velocity of 0.93 m/s.

For convenient reasons, vehicles are based on cubic forms for both the numerical and the expérimental approach. The vehicle distribution includes 13 cars and 2 lorries. The vehicles are assumed to be blocked downstream the fire in a congested tunnel. They are distributed as reproduced on Figure 9. The comparison between the two configurations, with and without vehicles, is based on the two stratification parameters, Si and S 2 , defined earlier.

The évolution of S 2 =f(S!) was plotted along the gallery for both codes in the two configurations (Figure 10).

The results show that, according ( 14), the flow is stratified for both configurations but with two différent zones: • Above vehicles, the stratification is improve by a diminution of the layer height; • Downstream of the vehicles, the stratification stability is altered because of turbulence génération. The température profile will give more detailed information about the effect of vehicles on the stratification.

The température profile for both codes in the two configurations is plotted hereafter on Figure 11 in the centreline section behind the first lorry. The turbulence induced by vehicles, and mainly the recirculation downstream a lorry, was well capture by the two CFD codes Figure 13. The intensity of those structures is not important enough to affect greatly the stratification.

This conclusion is probably also due to the reduce power of the fire (352 kW), in case of larger smoke volume production, this effect may not be observed.

This will be checked by future numerical simulations. Finally, it was observed that the réduction of the smoke layer thickness decrease while increasing the distance from the fire and, consequently, an effect on the stratification stability downstream the vehicles.

CONCLUSIONS AND PERSPECTIVES

This article is the beginning of a larger study that aims to improve the understanding of the physical phenomena responsible of the smoke propagation in tunnels. To reach this objective, an expérimental campaign is achieved in accordance with a numerical one.

The first part of this study aims to quantify, using two CFD codes, the impact of a perturbation on the stratification phenomena. This also enables to compare the ability of the two codes to predict smoke behaviour in the context of a fire in tunnel.

After having briefly described the numerical models and the geometry used for the expérimental campaign, the Newman parameters that can be used for describing the stratification are presented [START_REF] Newman | Expérimental évaluation of Fire-Induced stratification[END_REF]. Those parameters are used to evaluate the influence of obstacles on the smoke layer behaviour and stability.

Before going any further, the confrontation between experiment and numerical modelling hâve shown that both codes are able to predict with a quite good accuracy the length of the backlayering smoke layer. However, the two CFD codes with the model used in the simulations do not permit to represent with good accuracy the température distribution in the smoke layer. More expériences are required to détermine more accurately the température smoke layer profile and the évolution of the température on ceiling.

Finally, the influence of two types of external perturbation was numerically studied.

The first kind of perturbation is an air flow coming, in real situation; from jet fans located upstream the fire. To prevent for complex interaction and enable to understand the influence of a velocity gradient coming from such a fan, the jet was generated in order to remove ail rotational effects. The numerical approach has shown that a plane jet has no effect on the backlayering layer near the fire. Nevertheless, the jet influences the smoke layer front: the hot layer is thicker than the one without jet and the front starts to destratify. Thus, the backlayering layer tends to be longer than the one without jet.

The second type of perturbation consists in vehicles blocked in the traffic jam downstream the fire. The numerical comparison between the référence case, that is to say without vehicle, and the smoke propagation above the vehicle has shown that just above vehicle, the stratification is not altered by cars and lorries but can be altered downstream thèse vehicles.

As indicate above, this part is the beginning of a larger study. The next step of it is to achieve the experiment which corresponds to the modelled situation. Those experiments will not only enable to validate the two codes but also provide a complète expérimental work concerning the smoke propagation in tunnel.

Next, the numerical stiidy will be extended to real size tunnels. Compiling ail the results will permit to hâve a great improvement of the understanding of the physical phenomena involved in the smoke propagation in tunnels and then, to propose a simple model to reproduce this phenomena.

Figure 1 :

 1 Figure 1 : Scheme of the expérimental set-up.

Figure 3 :

 3 Figure 3: Température profile comparison at 10 m upstream the tïre.

Figure 4 :

 4 Figure 4: Température and velocity profiles comparison at 17 m upstream the fire.

Figure 5 :

 5 Figure 5: Visualization of the backlayering length obtained with FDS (up)

Température [°C]Figure 6 :

 6 Figure 6: Vertical profile of température with and without jet fans at 17 m upstream of the fire obtained with Phoenics (left) and FDS (right).

Figure 7 :

 7 Figure 7: Velocity profile 17 m upstream the fire source obtained with Phoenics (left) and FDS (right).

Figure 8 :

 8 The backlayering layer front obtained with Phoenics

Figure 9 :

 9 Figure 9: Vehicles distribution in the tunnel.

Figure 10 :

 10 Figure 10: Plot of S2=f(Sl).

Figure 11 :Figure 12 :

 1112 Figure 11: Vertical profile of température with and without vehicle obtained with FDS (left) and Phoenics (Right).

Figure 13 :

 13 Figure 13: Détail zoom on the recirculation behind a lorry.

ACKNOWLEDGMENT

The authors thanks the ANR, "Agence Nationale pour la Recherche" for funding the projects and ail the other partners of the projects: CEA, LME and RATP for their involvement in the EGSISTES project.