Modelado de las solicitaciones de los elementos estructurales de hormigón en edificios de gran altura en incendios reales

The fire of the Windsor Building in Madrid represents a paradigm in High Rise Building Fires. The present Work analyzes the origin, growth and propagation conditions of natural fires in tall buildings. The Study has been focused on the determination of the thermal exposure conditions (temperatures T , heat fluxes q ,, , etc.) on the structural members of high rise buildings, at end use conditions, under natural fires using fire computer modeling techniques. 
Work allowed: 1) validate the predictive capacity of the fluid-dynamics computer models used, 2) apply these models to a specific fire scenario to assess the thermal and the mechanical response of the structural members of a high rise building.


RESUMEN
El incendio de la Torre Windsor de Madrid constituye un suceso paradigmatico de incendios en edificios de gran altura. En el presente Estudio se analizan las condiciones de origen, desarrollo y propagacion de incendios reales en este tipo de edificaciones, asi como la determinacion de las condiciones de exposicion (temperaturas T,, flujos de calor q", etc.) a las que se encuentran sometidos los elementos estructurales, en condiciones de uso final en este tipo de estructuras, mediante la utilizacion de tecnicas de modelado y simulacion computacional de incendios.

INTRODUCTION
When the effects of fires in a building are examined by utilizing of modelling tools and computational simulation, it should be recognised, firstly, that the behaviour of a structure in case of fire is very connected with the effect that the fire can have on the structural elements that compose it and second, that the redundancy inside the structure can permit that the loads be distributed even when individual structural members fail.
In the present work, the fire in the Windsor Tower is taken as a basis to carry out different types of analysis: 1) determination of the start and development of the first phases of the fire considering as reference the fire in the office of origin (2109), and 2) the propagation on the floor of the fire, selecting the 21 st floor. This permits determination of the severity reached as a result of the completely developed fire, due to the combustion of the present materials.
Subsequently calculations were carried out by means of an FEM (Finite Element Method) model, using the thermal loads calculated to provide of the gas-phase boundary conditions to the structural members. The use of this type of study permits calculation of the global impact of the temperature inside the structure, focusing on, by means of detailed analysis, the behaviour of the elements inside the structural frame. On 12-13 February 2005, the Windsor Tower  was involved in a major fire, of duration 18-20 hours. This broke out in an office on the 21 st floor of the building, causing extensive structural damage to the upper floors of the building. The Windsor Tower was built in 1978 and was at one time the tallest building in Madrid.

DESCRIPTION OF THE BUILDING
The upper section of the building, above floor three, was a tower block containing offices and consisted of a concrete core, several interior concrete columns, exterior steel columns and a concrete waffle slab floor with permanent clay formwork (see Figure 1).
At the time of the fire a programme of fire protection upgrading was being undertaken, and the steel columns up to the second transfer floor had been protected, except on the 9 th floor where two adjacent sides of the building remained unprotected due to the sequential nature of the upgrades to the building. An additional fire escape was also added to the west side of the building.

MODELLING AND COMPUTATIONAL SIMULATION OF THE FIRE
The modelling of the fire is a very complex discipline due to the large number of variables involved. When applying fire exposures to a structure, a number of methods are available [4], as described below.
The simplest approach is to specify a uniform temperature for the surface of the structural elements. This temperature can either be estimated from observational or experimental data, taking into account for example the colour of the flames or the post-fire condition of the exposed materials. In the case of the Windsor Tower, video evidence is consistent with gas-phase temperatures reaching around 800-1000°C after flashover.
In the absence of measurements, it is possible to represent the approximate conditions of fire development by means of modelling tools and computational simulation of the fires. Within these are different approaches based on steady-state and transient simulations.
In Transport, Finland. The Smokeview software [2] was used to display the result of the FDS simulations and create images and animations of these results.
'Fire Dynamics Simulator (FDS)' is a Computational Fluid Dynamics (CFD) model that was designed specifically for fire simulations. FDS solves numerically a form of the Navier-Stokes equations appropriate for low-speed, thermally-driven flow with an emphasis on smoke and heat transport from fires. The core algorithm is an explicit predictorcorrector scheme, second-order accurate in space and time. Turbulence is treated by means of the Smagorinsky form of Large Eddy Simulation (LES).

Analysis of the validation of the predictive capability of the model
Before commencing the analysis of the scenario of the floor fire, the processes of validation of the predictive capability of the computational simulation model was developed, taking for a reference the full-scale fire tests carried out in a tall building at Dalmarnock (Glasgow, UK), a study lead by the University of Edinburgh (UK) (4).
The results produced by the simulations showed a great disparity between the prediction of the simulation models of simulation and the experimental measurements, nevertheless, the results obtained in the simulations of the general behavior of the fire are deemed sufficiently reliable to be utilized in a simplified engineering analysis.
In order to improve the predictive capability of the model, the sensitivities exit choice have been previously analysed with FDS and have improved the parameters introduced to the model to advance to the maximum the calculations of the dynamics of the fire (5). Likewise, the influence of the turbulence was studied and the spatial refinement in the accuracy of the results (6,7). This analysis have permitted to determine a consensus on the importance of the correct selection of the input parameters of in the model and the spatial refinement of the grid, in the accuracy of the results of the calculations of the dynamics of the fire.

Study of fire in the room of origin
Before trying to establish a study to understand the development of the fire through the interior of the building, it was decided to focus attention on the fire development in the room of origin of the fire, with the purpose of understanding the fire development in terms of heat release rate.
The resulting technical elements of this analysis, besides obtaining useful results for the analysis in all the plant and between plants, facilitate verification of the hypothesis of the fire origin, and assist in determining the importance of the different factors that influence in the growth in an enclosure: dimensions of the enclosure, power of the ignition source, characteristics, distribution and types of flammable materials, conditions of ventilation, etc.
In the model the conditions of the room before the fire have been represented with two desks with its respective auxiliary desks in the position of the figure, three filing cabinets in front of the window and another two filing cabinets in the lateral walls. In addition each workstation had a computer and a papers tray, along with a wastebasket. Figure 2  The initial focus of the study was on the fire development in room 2109, the origin of the fire, making it possible to use refined grids for the CFD simulation. In this model the conditions of the room before the fire have been represented with a computational grid having a uniform cell size of 5 cm side, with 512,000 cells in the domain.
Once the computational domain was established, the characteristics of the materials of the interior finish were defined, with the heat release rate taken from the NIST cone calorimeter test in the research work 'Cook County Administration Building Fire, 69 West Washington, Chicago, Illinois, October 17, 2003: Heat Release Rate Experiments and FDS Simulations' [8]. Table 1 summarises the characteristics of the materials of the linings of the office.
To define the total heat release rate of these elements, the tests of National Institute of Standard and Technology NIST (USA) on 'Two Panel Workstation Fire Test' [9] were studied. Figure 4 shows this heat release rate curve. To characterize this element there was added also, between other parameters, an ignition temperature of 200 ºC.
Due to the importance of the definition of the window breaking times and for lack of more information, in this initial stage of the study two situations of ventilation were analyzed: (1) heat detectors were placed upon the glass which broke on having reached 150 ºC, and (2) the glasses partition were eliminated from the start.
Once all the input parameters were implemented in the model, the study proceeded to the calculation of the development of the fire dynamics of the fire in the floor. The Figure 3 is an example of the values of registered for temperature by the low thermocouples under the most unfavourable conditions during the first 1,800 seconds of the development of the fire simulation.
The results of the initial analysis demonstrated that it was possible to reach the status of a fully developed fire in this office from small sources of ignition, such as the wastebasket.
During the fire development there was verified the generalized ignition in the auxiliary desk close to the wastebasket before the first 30 minutes, and the breaking of the top windows in this interval of time, as well as the spread to the adjacent enclosures to the office 2109 across the nearest wall to the wastebasket.

Fire development on floor 21
The floor of the building was built around a central core of reinforced concrete, and steel columns were utilised around the perimeter. The reinforced concrete core was centred on the longer north-south facing axis but was slightly off-centred with regards to the eastwest axis. The core housed the stairwells, lift shafts and service ducts.
With the object of the present paper, the preliminary studies in the 21 st floor were centred in two specific targets, on the one hand (1) to study and to analyze the fire development in this floor and for other (2) to allow the calculation of the total heat release rate parametric curves representative of the real fires completely developed in the floor. In the Figure 4, a representation of the floor that will be object of this study with its initial layout can be observed. For the model a uniform grid size of 20 cm was adopted over the whole computational domain, with 729, 000 cells in total. The office containing the ignition source, which was analyzed in the initial study, above, is marked in the figure.
In this sense, it is apparent that attention must be paid to the conditions of oxygen depletion due to the fast growth of the fire, first in the room and later in the rest of the floor. This problem was solved by more detailed analyses by means of the introduction of the building ventilation system; however, these are not presented here due to reasons of space.
From the results obtained in the simulations, the total heat release rate curves were calculated in the floor for the conditions analyzed. This data provided an indicator of the magnitude and severity of the fire and of great importance to the analysis of the thermal stresses in the structural elements.
An analysis was realized to examine the results provided by parametric curves of heat release rate, in relation to the conditions of thermal attack (temperature, heat flux, etc.) necessary for collapsing the structure.
For the calculation process, the conditions of final use of the 21 st floor were simplified, considering only the structural elements together with the heat release rate curves previously calculated, taking these to be representative of the natural fire development. In the model, the characteristics curves of heat release rate were provided as an effective "design fire", placed over the whole surface of the floor. Different characteristics curves were studied; in this paper two extreme options of them will be described. The first one was mentioned in the previous paragraph, with a growth tsquared of approximately 225MW.
The second curve selected was approximately the double of the previous one in the value of peak (500 MW) with the purpose of considering an extremely severe situation (due, for example, to uncertainties in the modeling process). (see Figure 13). It should be noted that the size of this latter fire deliberately exceeds the approximate upper limit on a whole-floor ventilation-controlled fire, obtained from the expression   Figure 7 presents an overview of the thermal response in the structural elements after applying the parameter curve of heat release rate 500 MW. 5. Parametric curves for the adopted heat release rates. These results inform the consideration of the required input values for the finite element analysis, to determine the response of the structure, a process that is typically complex and that is explained more to the detail subsequently.

CONCLUSIONS
The initial phase of the investigative work has demonstrated the capacity of the computational fire models to undertake the analysis of the development of a fire inside small enclosures, such as the room of origin, as part of the larger zone of the complete floorplan. 9. Deflections in the 21st floor. 10 It has been shown, in qualitative terms, how the fire could grow and spread from the room of origin, and this then provided a basis for establishing a representation of a possible fullfloor fire. Besides analyzing the development of the fire, these models permitted comparison of the computed thermal exposures with those that it was assessed the structure had been submitted to. These thermal loads were employed in the subsequent phases to analyze the mechanical response (stresses and deformations) of the structure via finite elements models (FEM).
A global study has been carried out to assess the behavior of the main concrete structure of the Windsor Tower. This has permitted an appraisal of the impact of representative thermal exposures, referencing data obtained from the assessment of the structure after the fire and various methods based on computational simulation models of the fire. The thermal response of the structure was subsequently evaluated, in order to define the boundary conditions for the structural models, encompassing FEM. Based on this, a strategy has been developed to determine the mechanical response of the structure, with a view to analyzing the possible mechanisms of failure in relation to the effects of the fire.