Fire Resistance of Materials & Structures - Modelling of Fire Scenario

Fire Resistance of Materials & Structures
Modelling of Fire Scenario
Date of Submission
2016
Submitted by
Seyed Mohammad Sadegh Mousavi
836 154
Submitted to
Prof. P. G. Gambarova
Prof. R. Felicetti
Dr. P. Bamonte
Structural Assessment & Residual Bearing
Capacity, Fire & Blast Safety
Civil Engineering for Risk Mitigation
Politecnico di Milano
[ 2 n d H o m e w o r k - M o d e l l i n g o f f i r e s c e n a r i o ]

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Politecnico di Milano – Lecco Campus
Prof. R. Felicetti & Prof. P. G. Gambarova & Dr. P. Bamonte
Seyed Mohammad Sadegh Mousavi (836154)
Fire Resistance of Materials and Structures
Prof. R. Felicetti, Prof. P.G. Gambarova and Dr. P. Bamonte
2nd Homework - Modelling of the fire scenario
The figure below shows the plan of a library room, whose structural elements are to be checked (in terms of
bearing capacity, R criterion) in fire conditions. The dimensions of the room and windows are given in
centimeters; the height of the room is 3.50 m.
The active protection measures of the room are as follows:
· NO automatic fire suppression;
· NO independent water supplies;
· Automatic detection and alarm systems, by smoke;
· NO automatic transmission to Fire Brigade;
· NO on site Fire Brigade.
· The library is provided with safe access routes and fire-fighting devices.
The thermal characteristics of the walls, floor and ceiling (thick layers) are as follows:
· Mass per unit volume: ρ = 1100 · (1 + F/50) [kg/m3]
· Specific heat: c = 950 [J/ (kg K)]
· Thermal conductivity: λ = 0.5 · (1 - L/50) [W/ (m K)]
Evaluate the possible fire scenario, in terms of temperature-time curve, following:
a) The parametric approach given in the standard EN 1991-1-2 (with two alternative cooling stages);
b) The two/one-zone numerical model implemented in the Ozone 2.2.5 software according to the two
following hypotheses for the vents opening (according to the Luxenbourg Authorities):
- Scenario 1: windows are constantly 90% open from the beginning of the fire
- Scenario 2: double glazing failure: 50% opening beyond 200°C and 90% opening beyond 400°C
F = number corresponding to the 3rd letter of the first name
L = number corresponding to the 3rd letter of the last name

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Thermal characteristics of walls, floor and ceiling:
F= 25 (Y), L= 21 (U)
 Mass per unit volume :
𝜌 = 1100 (1 +
25
50
) = 1650 [
𝑘𝑔
𝑚3⁄ ]
 Specific Heat: c= 950 [J/(kgK)]
 Thermal Conductivity:
𝜆 = 0.5 (1 −
21
50
) = 0.29 [ 𝑊
𝑚 𝐾⁄ ]
Opening Area: 𝐴 𝑣 = 𝐵 × 𝐻𝑣 (𝑚2
) (𝐻𝑣=Opening Height)
Segment Data
Floor Area 𝑨 𝒇 8 × 12 = 96 𝑚2
Total area of the enclosure 𝑨𝒕 2 × (8 × 3.5 + 12 × 3.5 + 8 × 12) + 9 = 341 𝑚2
Average Height of openings 𝑯 𝑽 1.5 𝑚
Area of vertical openings 𝑨 𝒗 3 × 2 × 1.5 = 9 𝑚2
1. The Parametric Approach (given in standard EN1991-1-2)
Fire load density is the maximum energy released per 𝑚2
.
𝑞 𝑓,𝑘 =
𝑄 𝑓𝑖,𝑘
𝐴 𝑓
(MJ/𝑚2
) is refered to the area of the floor 𝐴 𝑓.
𝑞𝑡 =
𝑞 𝑓,𝑑 𝐴 𝑓
𝐴 𝑡
(MJ/𝑚2
) is refered to the total area 𝐴 𝑡 of the enclosure (Walls, Openings & Ceiling included)
In case of the type of occupancy is known, 𝑞 𝑓,𝑘 is provided by the tables in books & recommendations.
For library, value of characteristic fire load density (80% fractile) has been chosen from table in Fig.1:
𝑞 𝑓,𝑘 = 1824
𝑀𝐽
𝑚2⁄
Under the assumption: 𝛿 𝑞2 = 1
(Unit value of the danger of fire activation factor)

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Figure 1 – Type of occupancy
According to the Annex E (informative) EN 1991-Part 1-2, design fire load density is:
𝑞 𝑓,𝑑 = 𝑞 𝑓,𝑘 . 𝑚 . 𝛿 𝑞1. 𝛿 𝑞2. 𝛿 𝑛 (
𝑀𝐽
𝑚2⁄ )
Where:
m = Combustion factor, function of a type of fire load. For Cellulosic fire ≅ 0.8.
Danger of fire activation factors:
𝛿 𝑞1 = Considering the compartment size.
𝛿 𝑞2 = Considering the type of occupancy.
Figure 2 – Compartment floor area (At)
For 𝐴 𝑓 = 96 𝑚2
→ {
𝛿 𝑞1 = 1.33
𝛿 𝑞2 = 1.0

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𝛿 𝑛= Factors which consider the effect of the active fire fighting measures.
𝛿 𝑛 = ∏ 𝛿 𝑛𝑖
10
𝑖=1
Figure 3 – Active fire fighting measures
The active fire fighting measures of the room with respect to the Fig.3, are as follows:
 NO Automatic fire suppression  𝛿 𝑛1 = 1.0
 NO Independent water supplies  𝛿 𝑛2 = 1.0
 Automatic detection & Alarm System, by Smoke  {
𝛿 𝑛3 = 1.0
𝛿 𝑛4 = 0.73
 No Automatic transmission to fire bridge  𝛿 𝑛5 =1.0
 No on site fire bridge  𝛿 𝑛7 = 0.78
 Library provided with safe access route  𝛿 𝑛8 = 1.0
 Library provided with fire fighting devices  𝛿 𝑛9 = 1.0
 No smoke exhaust system  𝛿 𝑛10 = 1.5
𝛿 𝑛 = ∏ 𝛿 𝑛𝑖
10
𝑖=1
= 0.73 × 0.78 × 1.5 = 0.8541
Design fire load density:
𝑞 𝑓,𝑑 = 1824 × 0.8 × 1.33 × 1 × 0.8541 = 1657.58 (
𝑀𝐽
𝑚2⁄ )
Design fire load related to total area of enclosure: (Must be in the range 50 ≤ 𝑞𝑡,𝑑 ≤ 1000 𝑀𝐽
𝑚2⁄ )
𝑞𝑡,𝑑 =
𝑞 𝑓,𝑑 𝐴 𝑓
𝐴 𝑡
=
1657.58 × 96
341
= 466.65 (
𝑀𝐽
𝑚2⁄ )

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Part a - Parametric fires according to Eurocode 1:
The Time-Temperature is a function of fire load, Ventilation and wall lining
 The limitation of fire load is for compartments of floor area (𝐴 𝑓) < 500 𝑚2
 The limitation of height of the compartment < 4 m
 The limitation of the wall lining, only vertical vent (no ceiling windows)
They have been worked out by interpolating the burning phase of the Swedish curves.
Temperature-time dependency for parametric fire is:
𝑇(℃) = 20 + 1325(1 − 0.324𝑒−0.2𝑡∗
− 0.204𝑒−1.7𝑡∗
− 0.472𝑒−19𝑡∗
)
Where:
𝑡∗
= Fictitious time, 𝑡∗
= Γ. t and t is the time in hours.
The sequence of step is:
1- Evaluate the wall factor (b) – (Square root of thermal inertia)
𝑏 = √𝜆𝜌𝑐 (100 < b < 2200)
𝑏 𝑟𝑒𝑓 = 1160 (Reference value of thermal inertia)
b Factor - Thermal Inerta
Section Area (m^2) ρ [kg⁄m^3 ] c [J/Kg°C ] λ [W/m °C ] bi bi.Ai
Walls 140 1650 950 0.29 674 94391
Floor 96 1650 950 0.29 674 64725
Ceiling 96 1650 950 0.29 674 64725
Total 332 674.223 223842
(Opening Excluded) 𝑊𝑆
1
2⁄
𝑚2°C
Figure 4 – Wall factor (b)
2- Evaluate Openin factor (O)
𝑂 = 𝐹𝑣 =
𝐴 𝑣√ 𝐻 𝑣
𝐴 𝑡
=
9×√1.5
341
= 0.0323 (0.02 < O < 0.20)
O = Opnenig (Ventilation) factor EN1991-2002 (𝐹𝑣 in Buchanan’s Book)
𝑂𝑟𝑒𝑓 = 0.4 (Reference value of the ventilation factor)

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3- Evaluate the factor (𝚪)
Γ = (
𝑂
𝑂𝑟𝑒𝑓
𝑏
𝑏 𝑟𝑒𝑓
)
2
= (
0.0323
0.04
674.223
1160
)
2
= 1.93
Γ = Distortion of the time scale that takes into account of the fact that fire is expected to be faster or
slower than in normal conditions.
So, Γ = 1.93 > 1.0 (high ventilation, low thermal inertia) will yield a faster heating phase compared to
the ISO curve (and vise versa).
4- Determine the shortest possible duration of the heating phase (𝒕𝒍𝒊𝒎) in hours:
According to the Fig.6 that is given from the minimum time for propagation (𝑡𝑙𝑖𝑚) in excel sheet and
code:
Minimum Time for Propagation (𝑡𝑙𝑖𝑚)
Slow 25
Medium 20
Fast 15
Figure 5 – Minimum time for propagation (𝒕𝒍𝒊𝒎)
So, In our case for the library (Fast fire growth rate) is 𝒕𝒍𝒊𝒎 = 𝟏𝟓 𝒎𝒊𝒏
Figure 6 – Fire growth rate cases

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5- Evaluate the duration of the ventilation-contorlled heating phase ( 𝒕 𝒎𝒂𝒙) in hours
Time needed in case of reaching the maximum temperature that is the maximum between the ventilation
controlled time to burn the fire load (Kawagoe formula) and the fuel controlled minimum time, 𝑡𝑙𝑖𝑚.
𝑡 𝑚𝑎𝑥 =
2 × 10−3
× 𝑞𝑡,𝑑
𝑂
=
2 × 10−3
× 467
0.0323
= 2.89 ℎ𝑟𝑠
6- a) If 𝑡 𝑚𝑎𝑥 > 𝑡𝑙𝑖𝑚 then the fire is ventilation controlled, as in this cases.
Determination the fictitious time to reach the maximum temperature, 𝑡 𝑚𝑎𝑥
∗
,via the relevant time scale
factor Γ for ventilation controlled fire:
𝑡 𝑚𝑎𝑥
∗
=
0.0002×𝑞 𝑡,𝑑
𝑂
. Γ =
0.0002×467
0.0323
× 1.93 = 5.581 hrs
𝑇 𝑚𝑎𝑥 = 20 + 1325(1 − 0.324𝑒−0.2𝑡 𝑚𝑎𝑥
∗
− 0.204𝑒−1.7𝑡 𝑚𝑎𝑥
∗
− 0.472𝑒−19𝑡 𝑚𝑎𝑥
∗
) = 1204 ℃
 Temperature during the heating phase, untill 𝑡 = 𝑡 𝑚𝑎𝑥 is given by:
𝜃𝑔 = 20 + 1325(1 − 0.324𝑒−0.2𝑡∗
− 0.204𝑒−1.7𝑡∗
− 0.472𝑒−19𝑡∗
)
𝑡∗
= Γ × 𝑡
 Temperaute during the cooling phase during the cooling down phase is given by: (EC1 & ISO)
𝜃𝑔 = 𝜃 𝑚𝑎𝑥 − 625. (𝑡 − 𝑡 𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 𝑡 𝑚𝑎𝑥
∗
≤ 0.5
𝜃𝑔 = 𝜃 𝑚𝑎𝑥 − 250. (3 − 𝑡 𝑚𝑎𝑥
∗ ). (𝑡 − 𝑡 𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 0.5 < 𝑡 𝑚𝑎𝑥
∗
< 2.0
𝜃𝑔 = 𝜃 𝑚𝑎𝑥 − 250. (𝑡 − 𝑡 𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 2.0 ≤ 𝑡 𝑚𝑎𝑥
∗
Where 𝑡 𝑚𝑎𝑥
∗
= (
0.2×10−3×𝑞 𝑡,𝑑
𝑂
). Γ
According to the value of 𝑡 𝑚𝑎𝑥
∗
= 5.581 ℎ𝑟𝑠, the 3rd
situation has been used.
 Buchanan formula for cooling rate:
According to Buchanan, it should be more accurate to correct the cooling rate with a time scale
different from Γ. So Buchanan proposed different furmula for this issue.
𝑑𝑇
𝑑𝑡
= (
𝑑𝑇
𝑑𝑡
)
𝑟𝑒𝑓
.
√ 𝑂
0.04⁄
√ 𝑏
1900⁄

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This is equivalent to using a second fictitious time, similar to that in the growth period, but in case of
better and accurare test results and computer simulations using square root rather than squared terms.
Thermal analysis should be performed taking into account also the cooling stage, as cooling is not
immediate inside the member and the damage can go up to the complete cooling of the member.
t/tmax* t* () real t. (h) T (°C) – EC1 P.F
0.00 0.0000 0.0000 20.0
0.05 0.2791 0.1444 767.7
0.10 0.5581 0.2887 856.4
0.15 0.8372 0.4331 916.8
0.20 1.1163 0.5775 961.1
0.25 1.3954 0.7218 995.0
0.30 1.6744 0.8662 1022.2
0.35 1.9535 1.0105 1044.8
0.40 2.2326 1.1549 1064.2
0.45 2.5116 1.2993 1081.4
0.50 2.7907 1.4436 1097.0
0.55 3.0698 1.5880 1111.2
0.60 3.3489 1.7324 1124.4
0.65 3.6279 1.8767 1136.6
0.70 3.9070 2.0211 1148.1
0.75 4.1861 2.1655 1158.9
0.80 4.4651 2.3098 1169.1
0.85 4.7442 2.4542 1178.7
0.90 5.0233 2.5985 1187.8
0.95 5.3024 2.7429 1196.3
1.00 5.5814 2.8873 1204.4
Figure 7 – EC1 Parametric Fire table
Figure 8 – ECI Time-Temperature fire curve comparing with ISO
0
200
400
600
800
1000
1200
1400
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Temperature(°C)
Time (hours)
EC1 parametric fire
ISO 834
EC1's cooling
Buchanan's cooling

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In the both ISO834 and EC1 time-temperature cases, there are a sharp increase in the time-temperature
curve during around the first 15 minutes. However, time scaling factor Γ accelerates the heating phase in
compression ISO834 fire. For EC1 fire, the time needed to reach maximum temperature is 2.8873h,
while for ISO834, that temperature at that time is around 10 percent less than EC1 fire.
According to the cooling stage and its plot, it is obvious that EC1 cooling is faster than the Buchanan’s
cooling. With respect to the slope calculation in excel, it provides that Buchanan’s cooling rate is
294.8°C/hour with cooling phase duration of 4.02h , while EC1 cooling rate is 483.3°C/hour with the
cooling phase duration of 2.45 hours.
O-ZONE
Part b – Time-Temperature Curve using O-Zone
To reach the aim of this homework, some implmentations were done in Ozone software. Ozone switches
autmatically from two zones [+localized fire] (Growth phase) to one zone (Fully developed fire).
Figure 9 – Zones
Figure 10 – Strategy

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 In the next step, the compartment’s dimensions and wall openings were defined:
Figure 11 – Compartment’s Dimension
 Definition of materials for floor, cleiling, walls- One layer of normal weight concerete with
thermal properties assigned. Openings, for the walls that contain them, are also defined.
Figure 12 – Materials Property
 Openings: Walls 1 & 4 are defined in a same way:
Figure 13 – Walls 1 & 4

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Then, for the wall 2 (Fig. 14) was deifined an opening (window with its demension):
Figure 14 – Opening of wall 2
and also for wall 3 was defined two openings. As you can see in the following figure:
Figure 15 – Opening of wall 3

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 Definition of the curve:
Parametric fire curve, according to EN 1991-1-2 has been chosen. Existing fire fighting measures are
checked and accounted for.
Figure 16 – Parametric Fire Curve
 Definition of Paramaeters:
Calculation time was set to 8 hours, since we want to take cooling stage into account.
Two scenarios regarding openings have been defined:
Scenario 1: Time dependent openings (windows are constantly 90% opened from the beginning of the
fire).
Scenario 2: Temperature dependent openings - double glazing failure (50% opening beyond 200°C
and 90% opening beyond 400°C) - linear and stepwise.
As a result, 3 models were done with respect to the openings by changing the variation option:
1- Temperature dependent openings
 Linear
 Stepwise
2- Time dependent opening

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Figure 17 – Parameters
 Results – Comparisions among different models
The following graph is a gas temperature comparison among the 3 different models. According the
trends and global point of view all the 3 curves tend to overlap.
Figure 18 – Localised Fire Curves
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 50 100 150 200 250 300 350 400 450 500
Temperature(°C)
Time (min)
Time - Temperature Curve
Temp Dependent-Linear
Temp Dependent-Stepwise
Time Dependent

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Due to some flactuation in heating stage for three different cases in Fig. 18, it is necessary to check and
analyse the first few minutes more precisely. So, for reach to this aim the following graph (Fig. 19) will
be reperesented.
Figure 19 – Localised Fire Curves 2
According to the different scenarios regarding ventilation and openings, there are some differences
(flactuations) are dominant on the plot until around 8 min. while, all the curves will be almost the same
after that time.
For the temperature dependent openings (Linear & Stepwise) act very close to each other, but in case of
reaching the temperature of 500°C, linear temperature dependent openings is a bit faster than Stepwise
temperature dependent openings.
On the other hand, in case of time dependent scenario, there is a spike on the curve due to the failure of
the windows that it causes rapid decrease of the temperature because of fresh air is entering the
compartment and cools it and then immediately after that, again the temperature rise because of fresh air
increased the combustion.

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 Comparison of EC1-Parametric Approach and Ozone fire evolution:
Figure 20 – Comparison between EC1 & Ozone Fire Evolution
The behavior of EuroCode parametric fire and Ozone fire are the same in the first minutes of fire or
clearly under the 500°C temperature, so having high burning rates.
When the temperature of 500°C is achieved in the Ozone, model will be switched from two zones (Pre-
flashover, growth period) to one zone (Fully developed fire).
The rate of burning in the Pre-flashover is generally governed by the nature of burning fuel surfaces,
while in the burning period (fully developed fire), the temperature and the radiant heat flux within the
room are so great that all exposed surfaces are burning and the RHR is governed by the available
ventilation.
Ozone model supposed lack of oxygen while in parametric fire model, there is no such an assumption.
According to the cooling stage, in the Ozone model it is not linear as in EC and Buchanan models, it is
faster down to 200°C and then it is happening at a slower rate down to room temperature.
0
200
400
600
800
1000
1200
1400
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00
Temperature(°C)
Time [hours]
Comparison between EC1 & Ozone Fire Evolution
EC1 parametric fire
ISO 834
EC1's cooling
Buchanan's cooling
Time Dependent
Temp Dependent-Linear
Temp Dependent-Stepwise

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 Results (Obtained by OZONE)
1st
Scenario – Temperature Dependent Opening (Linear Variation)
Fire Area: The maximum fire area ( 96.00m²) is greater than 25% of the floor area ( 96.00m²). The fire load is uniformly
distributed.
Switch to one zone: Lower layer Height < 20.0% ocompartment height at time [s] 207.53
Fully engulfed fire: Temperature of zone in contact with fuel >300.0°C at time [s] 332.80
Peak: 1255 °C At: 171 min
Figure 21. Hot and Cold Zone Temperature
According to the model passes from 2 zones to 1 zone (around 3 min), so the cold zone stops at the beginning.
Peak: 48.00 MW At: 17.3 min
Figure 22. RHR Data and Computed
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400 450 500
Time [min]
Hot Zone
Cold Zone
Analysis Name: Library
Gas Temperature
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0 50 100 150 200 250 300 350 400 450 500
Time [min]
RHR Data
RHR Computed
Rate of Heat Release

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According to the previous graph (Fig. 22), the theoretical Rate of Heat Release that is given by the code depends
on the type of compartment although calculated RHR related to the room’s envirinmental conditions and
ventilation factor of the openings.The area of the 2 curves should be the same while due to lack of Oxygen, at the
beginning there is low temperature. For theoretical RHR is around takes around 84 min and for computed RHR it
is around 310 min.
Figure 23. Zone Interface Elevation – Linear Variation
When the hot layer takes up more than 80 % of the total height of the compartment flashover will be happened
and as a result the seperation of 2 layers will be vanished.
Figure 24. Oxygen Mass – Linear Variation
The quantity of Oxygen in the room during the fire is change with time. According to the Fig. 24 at the beginning
the trend of Oxygen suddenly decrease because of the Oxygen is consumed by the combustion. At this step the
temperature is low but after breaking the windows and due to availablity of fresh air in the compartment that trend
is constant (zero) for some minutes and then Oxygen Mass tends to gradually increase in the room because the
combustile materials are consumed and they need less quantity of Oxygen for burning, that is Cooling Pahse.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5
[m]
Time [min]
Zone Interface Elevation - Linear
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300 350 400 450 500
(kg)
Time (min)
Oxygen Mass - Linear

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2nd
Scenario – Temperature Dependent Opening (Stepwise)
distributed.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400 450 500
Time [min]
Hot Zone
Cold Zone
Gas Temperature
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0 50 100 150 200 250 300 350 400 450 500
Time [min]
RHR Data
RHR Computed

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Figure 27. Zone Interface Elevation – Stepwise Variation
Figure 28. Oxygen Mass – Stepwise Variation
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3
[m]
Time [min]
Zone Interface Elevation - Stepwise
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
(kg)
Time (min)
Oxygen Mass - Stepwise

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3rd
Scenario – Time Dependent Opening
distributed.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400 450 500
Time [min]
Hot Zone
Cold Zone
Gas Temperature
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0 50 100 150 200 250 300 350 400 450 500
Time [min]
RHR Data
RHR Computed

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Figure 31. Zone Interface Elevation – Time-Dependent Opening
Figure 32. Oxygen Mass – Time-Dependent Opening
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7
[m]
Time [min]
Zone Interface Elevation - Time Dependent Opening
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
(kg)
Time (min)
Oxygen Mass - Time Dependent Opening

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