Reconstruction of the Grenfell tower fire—Part 6—Numerical simulation of the Grenfell tower disaster: Contribution to the understanding of the tenability conditions inside the common areas of the tower

The recent dramatic events at Grenfell Tower in London involving a combustible façade system have raised concerns regarding the fire risk that these systems pose. The spread of fire over the façade of the Tower was previously modelled numerically and the results of this modelling were validated by comparison with observations of the real fire. This model was used to determine the fire behaviour of the façade and the propagation of the façade fire into the apartments through windows. The modelling used an impact model according to ISO 13571 and included fire loads from the façade and, when relevant, from apartment contents. Tenability levels inside the apartments were quantified by an analysis of the toxic and thermal conditions due to the combustion of the façade materials and the apartment contents. In the present paper, the conditions inside the lobbies and stairs of the Tower are investigated, building on the previous analysis of the apartments. This allows an understanding of the evolution of toxic and thermal conditions whilst the fire spread, and their impact on egress during the fire event.

(CO), hydrogen cyanide (HCN) and carbon dioxide (CO 2 ), depends on the inhaled dose over a period of time and, thus, on the concentrations of these species and the duration of the exposure. Effects depend on the variability of human responses to toxicological injuries.
Depleted oxygen may also be a parameter driving tenability. 8 Thus, the contribution of any burning materials in terms of mass loss rate, yields of products released, etc., as well as the conditions under which they burn (well-or under-ventilated conditions), must be considered, in order to evaluate tenability in terms of toxicity and thermal effects. [9][10][11][12][13][14][15][16][17][18][19][20][21][22] Observations from the disaster have shown that the fire spread over the Tower can be split in different periods. During the period from 01:08 a.m. to 01:29 a.m., approximately, external flames spread over its east face. After this, dense irritant smoke started to accumulate in the burning apartments, and spread via the front doors of these apartments into common lobbies and stairwell, because of the weak fire performance of the doors, and because the doors were left open during egress or because of the actions of firefighters. The smoke gradually caused occupants to evacuate their apartments, and moved, either to apartments on the same floor or to apartments on lower or upper floors via the stairs. Occupants who remained in their apartments were affected by increasing amounts of toxic smoke from outside (from the façade fire and from the burning contents of lower apartments) and from the lobbies. As the fire spread over the façade, window failures led to the development of more and more apartment content fires. The applicable Building Regulations required prescribed levels of fire resistance between apartments and between each apartment and common areas, such as the lobbies, and the façade was supposed to "adequately resist the spread of fire." The common lobbies should be fire resisting and be able to remain separated from the main escape stair for at least for 30 min, in a fully developed fire. Naturally, this value is highly theoretical and does not consider smoke leakage, such as the opening of a door during a fire. Regardless, these measures should prevent smoke from entering the lobbies and stairs, allowing occupants to evacuate in safe conditions without exposure to toxic smoke and heat.
Numerical simulation is a useful investigative tool to understand and analyse such a disaster, and it makes the evaluation of particular phenomenon easier. The fire behaviour of the Grenfell Tower façade build-up was simulated using the computational fluid dynamics (CFD) code Fire Dynamics Simulator (FDS) [23][24][25][26] to determine the vertical and later horizontal fire spread over the façade in references 28 and 29.
The model was validated 29,30 6 The simulation allowed the evaluation of local concentrations of effluents and temperature conditions in each room (kitchen, living room and bedroom) of each apartment. In reference 34, an impact model was considered including fire loads from the façade system and from apartment contents, where relevant. This allowed the quantification of the conditions inside the Tower, by an analysis of the toxic and thermal contributions from combustion of both the façade components and each apartment's contents. The analysis of tenability conditions inside Grenfell Tower showed that the same conclusion can be made regardless of the input data for toxic gas yields or the model used, within the limits of the studied dataset and conditions. The overall conclusion was that the effluent from burning apartment contents quickly drove tenability conditions. This multi-step research was performed with highly interdependent parts, both experimental and numerical. The diagram in Figure 1 describes the whole approach from the very first step of this research.
In the present paper, a detailed model of the four uppermost floors (20 th to 23 rd ) of the Tower is addressed, because the higher floors of the Tower experienced the worst tenability conditions. An additional model for the lower floors (10 th to 13 rd ) was developed to provide adequate boundary conditions to upper floors, since both firefighters and occupants reported untenable conditions in lobbies and the stairwell between the 10 th and the 16 th floors. Floors 14 th to 19 th were not modelled since it is assumed that there was no contribution from these lobbies because no occupants left these floors after 01:50 a.m.
The simulation takes into account the real geometry of each apartment, lobby and stairs. For each room in each apartment, the effluent concentrations and temperature are fixed by prior analysis of the horizontal fire spread over the Tower. The tenability conditions, in terms of carbon monoxide, hydrogen chloride, hydrogen cyanide and gas temperature can thence be evaluated for each lobby and the stairwell.
This investigation sheds light on the impact of toxic and thermal conditions inside the Tower depending on the evolution of the fire spread over the four faces of the Tower. This publication does not assess tenability conditions for individual occupants, for two reasons. First, such analysis requests a lot of behavioural and movement data that is not necessarily available and may be highly speculative, reducing the validity of the analysis. Second, individual cases are ethically difficult to analyse in such recent fire with many fatalities and an inquiry still undergoing. So, only general tenability conditions are presented hereafter. In this research, individual situations are not addressed. The work presented is very sensitive to the assumptions made, and it is our decision not to extrapolate to individual cases.

| UNDERSTANDING THE TENABILITY CONDITIONS INSIDE THE APARTMENTS FOLLOWING THE FAÇADE FIRE
The study addressed in this paper is the culmination of a multi-step research approach (Figure 1). A brief summary of this approach is addressed in this section. It allows synthetizing the assumptions and results from the previous steps that are used in the present research.
The three-dimensional CFD model of Grenfell Tower, addressed in references 27, 28 (Figures 2 and 3), was constructed using component data that had been validated by a study of the thermal and combustible characteristics of façade systems at experimental scales. 29,30 The heat release rates of apartment content fires detailed in reference 32 were used for each floor of the Tower. The apartments are numbered as follows: X1 for the one bedroom apartment on the east face of the Tower, X2 for the south east two bedrooms apartment, X3 for the south west two bedrooms apartment, X4 for the one bedroom apartment on the west face of the Tower, X5 for the north west two bedrooms apartment and X6 for the north east two bedrooms apartment. The failure criteria of windows assessed in reference 33 were implemented for each apartment opening. In the global model of the Tower, no path was provided for fire spread between apartments by F I G U R E 1 Synthesis of the whole approach from the very first step of this research to the actual paper-highly interdependent parts, both experimental and numerical F I G U R E 2 Numerical models of the south/north and east/west faces of the Tower-Overview of the spatial arrangement of apartments and columns ducts, HVAC systems, or by holes in ceilings or walls. Fire propagation between apartments (horizontally or vertically) could only occur via the façade and subsequent window failure. This work calculated the fire conditions, over time, at every location on the façade and inside the apartments, in terms of burning condition, window failure, heat release rate and effluent concentrations ( Figure 4). This whole approach allowed the understanding of the interactions between apartments and the façade fire, 34 Table 1.
The analysis of tenability conditions inside Grenfell Tower showed that, within the limits of the studied dataset and conditions, the same conclusion can be made regardless of the input data for toxic gas yields and the model used. The overall conclusion was that fires involving apartment contents quickly drive tenability conditions, independently of the dataset and model used, and even if noncombustible insulant is used instead of PIR as façade insulant. Thus, the temperature and toxicity conditions were evaluated numerically in every apartment of the Tower, and the authors have estimated the most severe and the most probable of the nine scenarios that were calculated.
In this paper, based on these conclusions, a further analysis of conditions in the uppermost four storeys (floor 20 th to 23 rd ) of the Tower is described. It was on these floors of the Tower where the most fatalities occurred and for which observational data exists on the opening and closing of apartment front doors and the evolution of tenability conditions. Furthermore, the worst tenability conditions occurred in the higher floors of the Tower. The simulation takes into account the real geometry of each apartment, lobby and stair. For each of those rooms, the local effluent concentrations as well as the local temperature are set numerically from the previous analysis of the tenability conditions in each apartment. 34 Carbon monoxide, hydrogen cyanide and hydrogen chloride concentrations, and gas temperature can thus be evaluated in the lobbies and stairwell.  Unlike the analysis performed in reference 34, which was based on tenability models applied in each room of the different apartments, the analysis performed in lobbies and stairs is limited to gas concentrations and temperatures. A toxicity model presupposes a behavioural scenario; in lobbies and stairs individuals were mobile, and the pattern of their movement is only partly understood but variable. For this reason, the tenability models are not applied but the gas concentrations and temperatures provided allow such analysis in the future.

| INITIAL CONDITIONS IN THE APARTMENTS, LOBBIES AND STAIRWELL
The simulation takes into account the real geometry of each apartment, lobby and the stairwell as shown in Figure 6.    Table 2.
The main assumptions in the simulation of the toxicity scenario are: • the different times of window failure are known for each room (kitchen, living room, and bedroom) of each apartment 32,33 ; • the fire starts in a room 4 min after window failure, corresponding to the delay for flame re-entry and local furniture ignition 32 ; • when a door between an apartment and lobby is closed, due to the This confirms the observations reported in experts' reports and occupants' testimonies (Table 3). However, evacuation is thought to be  Table 3.

| INVESTIGATION OF THE CONDITIONS ON FLOORS 20-23
A detailed numerical model, illustrated in Figure 6 Table 4.
When analysing the contribution of the different toxic effluents in Figures 14 and 15, it is of interest to compare the main effluents (CO, HCN and HCl) on a common scale based on toxicity contribution.
For acute toxicity, and in a first approach, one can consider a toxic • Light increase in temperature ($5 C).
• Light increase in toxic gas concentrations (CO, HCN, HCl) mainly from the façade fire.
• Smoke from façade fire and "X6" burning apartments started to fill the lobbies, but the smoke is still reported as light. • Mass-evacuation noticed at same time, leading to constant opening of doors between apartments and lobbies, and then between lobbies and stairwell as observed by firefighters. • Numerous people were in the stairwell where the conditions were reported better than in lobbies.
• Increase in temperature ($20 C) in all lobbies from 10th to 13th floors. • Increase in toxic gas concentrations, in particular in the 11th floor lobby, mainly CO from the façade fire.
• Hot and thick smoke filled the lobbies, where conditions worsened in less than 10 min. • Degraded conditions also reported in the stairwell, but evacuation was still possible.
• Quick increase in temperature ($20 C) in all the lobbies from 10th to 13th floors. • Increase in toxic gas concentrations, in 12th and 13th floor lobbies, mainly from the apartment contents fires. • Lobbies were reported full of smoke although temperature conditions seemed better. • No more occupants evacuated during this period, the doors between stairwell and lobbies remained closed. Lower apartments ceased burning.
• Decrease in temperatures and toxic gas concentrations.
• Burning of "X6" apartments decreasing and front doors probably missing. • Front door of Flat 75, on the 10 th floor is also reported as open. • However, because no more evacuation happened during this period, the doors between stairwell and lobbies remained closed while lower apartments were no longer burning.
• Increase in temperature and toxic gas concentrations in lobbies. • Sudden decrease of toxic gas concentrations in stairwell, with temperatures between 25 C and 40 C.
• Decay phase of "X6", "X1" and "X5" fires, while "X4" apartments, mainly bedroom and kitchen, and "X5" kitchens were locally on fire. • Around 03:30 a.m., one person evacuated from the 21 st floor and reported better conditions in the stairwell at 10th floor while descending.
• Lower temperature and toxic gas concentrations in lobbies and stairwell.
effect equivalence between CO and HCN with approximately a factor between 18 and 246. In the same way, one can consider a toxic equivalence level between CO and HCl with a factor 3. This is calculated using toxic loads from ISO 13571 7 and from SLOT values as proposed in reference 41, as well as for other toxicological thresholds such AEGLs 10 min or IDLH. In Figure 16, an example of the toxic effluent   • Light increase of temperature ($5 C).
• Light increase of toxic gas concentrations (CO, HCN, HCl) mainly from the façade fire and from lower floors.
• Beginning of horizontal fire spread.
• Smoke from façade fire and "X6" burning apartments started to fill the lobbies, but the smoke is still reported as light. • Mass-evacuation occurred, leading to constant opening of doors between apartments and lobbies, and then between lobbies and the stairwell as observed by firefighters. • Numerous people were in the stairwell where the conditions were reported better than in lobbies. • Increase of temperature ($25 C) in all lobbies and the stairwell from 20th to 23rd floors. • Increase of toxic gas concentrations, in particular in the 23rd floor lobby and stairwell, mainly CO from the façade fire.
• Hot and thick smoke filled the lobbies, where conditions worsened in less than 10 min. • Degraded conditions also reported in the stairwell.
• One person evacuated from the 23rd floor around 02:00 a.m. and reported degraded conditions in stairwell.
• Temperatures of up to 50 C, mainly in 20th floor lobby, associated with high carbon monoxide concentration.
• Conditions were untenable both in lobbies and stairwell. • No evacuation during this period; • Temperatures of up to 60 C, mainly in 20th floor lobby. • Associated with high CO and HCN concentrations, mainly from apartment fires.
• Lobbies were reported full of smoke between 02:40 a.m. and 03:30 a.m. • All the apartments located on the east and north faces ("X6," "X1" and "X5" apartments) were involved in the fire. • The fire was spreading to the south and west faces. • Around 03:30 a.m., one person evacuated from the 21 st floor and reported hot conditions in lobbies and stairwell while descending until 10 th floor. • After 03:30 a.m., fires were decreasing and no more occupants evacuated from these floors. • The doors between the stairwell and lobbies remained closed and lower apartments were no longer burning.
• Increase in temperature and toxic gas concentrations both in lobbies and stairs.