Development of realistic design fire time-temperature curves for the testing of cold-formed steel wall systems

Abstract

Fire resistance rating of light gauge steel frame (LSF) wall systems is obtained from fire tests based on the standard fire time-temperature curve. However, fire severity has increased in modern buildings due to higher fuel loads as a result of modern furniture and light weight constructions that make use of thermoplastics materials, synthetic foams and fabrics. Some of these materials are high in calorific values and increase both the spread of fire growth and heat release rate, thus increasing the fire severity beyond that of the standard fire curve. Further, the standard fire curve does not include a decay phase that is present in natural fires. Despite the increasing usage of LSF walls, their behavior in real building fires is not fully understood. This paper presents the details of a research study aimed at developing realistic design fire curves for use in the fire tests of LSF walls. It includes a review of the characteristics of building fires, previously developed fire time-temperature curves, computer models and available parametric equations. The paper highlights that real building fire time-temperature curves depend on the fuel load representing the combustible building contents, ventilation openings and thermal properties of wall lining materials, and provides suitable values of many required parameters including fuel loads in residential buildings. Finally, realistic design fire time-temperature curves simulating the fire conditions in modern residential buildings are proposed for the testing of LSF walls.

Keywords

fire safety / standard fire curve / realistic design fire time-temperature curves / light gauge steel frame (LSF) walls / fuel load / fire resistance rating

Introduction

In recent times, light gauge steel frame (LSF) wall systems are commonly used in residential, industrial and commercial buildings as load bearing structural components. Fire resistance of LSF walls has been traditionally determined using the standard fire tests specified in international standards such as ISO 834 [ 1] and other national standards. Fire testing based on the standard time-temperature curve in ISO 834 [ 1] originated from the application of wood burning furnaces almost 100 years ago. In reality, modern residential and commercial buildings incorporate synthetic foams, fabrics and thermoplastic materials. During a fire, some of these thermoplastic materials melt and flow to the floor and burn faster with higher heat release rates resulting in more severe fires than standard fires [ 2, 3]. This means that the standard fire curve [ 1] used in testing of building elements does not accurately represent a building fire.

Recent research [ 3- 5] has shown that actual fire resistance rating (FRR) of building elements exposed to realistic fires is significantly less than indicated FRR from standard fire tests. Lennon and Moore’s [ 4] full scale fire tests at Cardington showed that the use of standard fire exposure would severely underestimate the severity of the fire in terms of maximum temperature and duration of fire exposure. Jones [ 5] also showed that actual fire resistance of building elements exposed to building fires can be significantly less than that obtained from exposing them to standard time-temperature curve [ 1]. A recent survey conducted within an Australian fire brigade unit also suggests that the effectiveness of containing a building fire within a room of fire origin has deteriorated over the last five years and it takes a longer time to bring the fire under control [ 6]. Further, over 80% of fire fighters believed that structural stability was lower in single and double storey modern style residential properties. This survey completed by experienced fire fighters believed that light weight construction, open plan design, lack of compartmentation and household furnishings had a significant impact on fire severity and loss of structural integrity [ 6].

Fire resistance of LSF walls depends on many factors, such as fire severity, geometry, wall lining material, support conditions and applied loads at the time of fire. Also a typical fire in a building starts in a single compartment and the severity of a fire depends on the usage of compartment, fuel load present and the sizes of openings and compartment [ 4, 6]. These parameters vary from compartment to compartment and have to be characterized to determine suitable realistic design fire curves. A real building fire curve has a decay phase (Fig. 1) whereas the standard fire curve rises continuously. Fire testing based on standard fire curve will give good comparative results for building systems tested under identical conditions. However, it has been shown that these results do not provide accurate FRR for residential and commercial buildings that have a high fire severity [ 4, 7].

This research was undertaken to study the characteristics of real building fires and to develop realistic design fire time-temperature curves for the testing of cold-formed LSF wall systems. In a building fire, the fire growth, fully developed and decay phases depend on the total fuel load in the room, fuel type and configuration, ventilation openings and thermal properties of compartment lining materials. Among them, the fuel load was selected first to represent the combustible contents in modern residential buildings. Using the available knowledge and data for other parameters, appropriate realistic building fire curves were then developed. This paper presents the details of the development of such realistic design fire time-temperature curves to obtain the FRR of LSF walls used in modern buildings.

Fire severity in modern buildings

Fire severity is a measure of the destructive impact of a fire in relation to temperature or time, which could cause failure. In the modern commercial and residential buildings, the increasing use of thermoplastic materials is clearly evident with the introduction of desktop computers, fabric coated drywall systems and upholstered furniture. Thermoplastic is a polymer made of plastic, and is malleable at high temperatures. Some polymers melt at temperatures between 300 and 450°C [ 2]. During a fire, they melt and burn faster with higher heat release rates resulting in more severe fires [ 2, 4, 7].

Bwalya et al. [ 7] conducted both individual and room-scale fire tests to evaluate the impact of new construction products on the fire safety of single-family residential dwellings. For this, a fuel package consisting of a mock-up sofa constructed with exposed polyurethane foam, upholstered furniture and wood cribs was selected. Individual fire tests were conducted using a cone calorimeter to measure the heat release rate. The fire growth rate for the mock-up sofa was fast and a rapid decay was observed following the peak heat release rate. The room scale fire test results showed that the rate of temperature rise during fire growth period was more rapid than that of standard time-temperature curve in [ 8].

Recently, Bwalya et al. [ 9] conducted a survey of fuel loads in Canadian family dwellings to quantify the composition of the combustible contents in residential dwellings (Table 1). They were categorized into three main material groups: wood and paper (cellulose-based), synthetic plastics and textiles (or fabrics) for each type of room. Table 1 results show that wood-based materials form a significant proportion of the total combustible mass in residential dwellings. Although the cellulosic material makes up the highest contribution, plastics occupy nearly 13 to 39% by weight (kg) and contribute 20 to 48% of the fuel load (MJ). The increase in fuel load percentage was due to higher caloric values of synthetic plastics than cellulosic materials. This shows a significant contribution from synthetic plastic materials to the fuel loads in residential dwellings in recent times. Therefore there is a need to develop realistic design fire curves to simulate the modern compartment fires.

Review of fire time-temperature curves used in full scale fire tests

Standard design fires

Standard fire time-temperature curve

The origins of this curve (Fig. 2) date back to 1903 [ 10]. Many countries use ISO 834 [ 1] or have standards similar to ISO 834 and FRRs were calculated based on the above curve.

(1) T=\mathrm{345}{\log }_{\mathrm{10}}(\mathrm{8}t+\mathrm{1})+T_{\mathrm{0}},

where, T - Furnace temperature (°C) at time t (mins); T₂- Ambient temperature (°C) at the start (20°C)

External fire curve in Eurocode 1 Part 1.2 [ 11]

External fire curve is used for the design of structural members outside a burning compartment and is defined by Eq. (2) (Fig. 2).

(2) T=\mathrm{660}(\mathrm{1}-\mathrm{0.687}{e}^{-\mathrm{0.32}t}-\mathrm{0.313}{e}^{-\mathrm{3.8}t})+\mathrm{20.}

Hydrocarbon curve in Eurocode 1 Part 1.2 [ 11]

Hydrocarbon curve was developed for furnace testing of construction elements in the petrochemical industry and is defined by Eq. (3) (Fig. 2).

(3) T=\mathrm{1080}(\mathrm{1}-\mathrm{0.325}{e}^{-\mathrm{0.167}t}-\mathrm{0.675}{e}^{-\mathrm{2.5}t})+\mathrm{20.}

Non-standard design fires

Non-standard design fires are categorized into two main sections, namely; pre-flashover and post-flashover design fires. Post-flashover design fires are important in the design of building fire safety systems whereas pre-flashover fires mainly focus on the life safety of building occupants, especially the toxic gas production and fire spread around the buildings. Hence this section mainly reviews the available post-flashover fire models.

Pre-flashover design fires

Many researches were conducted to determine the growth rate of a fire and the most popular one was the t-squared method of estimating the heat release rate Q (MW) at time t (s) using Eq. (4) [ 12, 13].

(4) Q={\left({\displaystyle \frac{t}{k}}\right)}^{\mathrm{2}},

where, k is growth constant.

Equation (4) has also been simplified as follow:

(5) Q=\alpha t^{\mathrm{2}},

where, a is the fire intensity coefficient (kW/s²) and its values are given in [ 13].

Post-flashover design fires

Several equations and models have been developed in the past to simulate realistic time-temperature curves. These fully developed, post-flashover fires are used in the design and analysis of building fire safety systems, especially to obtain the FRR of structural elements.

(a) Experimental curves

Several experimental studies conducted in 1966 and the measured temperatures in post-flash over fires are reported in [ 12]. Figure 3 shows the developed time-temperature curves in terms of room area (ventilation proportion). These curves demonstrate the differences between realistic design and standard fires.

(b) Lie’s parametric curves

Lie [ 14] proposed a time-temperature curve to represent a building fire based on Eqs. (6) and (7) for lightweight construction.

(6) T=\mathrm{250}{(\mathrm{10}{F}_{\mathrm{v}})}^{\frac{\mathrm{0.1}}{F_v^{\mathrm{0.3}}}}{e}^{-F_v^{\mathrm{2}}t}[\mathrm{3}(\mathrm{1}-e^{-\mathrm{0.6}t})-(\mathrm{1}-e^{-\mathrm{3}t})+\mathrm{4}(\mathrm{1}-e^{-\mathrm{12}t})]+C{\left({\displaystyle \frac{\mathrm{600}}{F_{\mathrm{v}}}}\right)}^{\mathrm{0.5}},

where,

(7) F_{\mathrm{v}}={\displaystyle \frac{A_{\mathrm{v}}{(H_{\mathrm{v}})}^{\mathrm{1}/\mathrm{2}}}{A_{\mathrm{t}}}}({\mathrm{m}}^{\mathrm{1}/\mathrm{2}}),

A_v, H_v - Area (m²) and Height (m) of the ventilation opening; C- Constant based on the type of construction materials used in the compartment boundaries: C = 0 for heavy; and C = 1 for light building construction materials.

(c) Swedish curves

Swedish parametric curves given in [ 15] are the most popular time-temperature relationships used to represent realistic compartment fires. They are defined as follows [ 16]:

(8) T={\displaystyle \frac{\stackrel{.}{{\dot{q}}_c+\mathrm{0.09}{c}_p{A}_v{H}_v^{\mathrm{1}/\mathrm{2}}{T}_{\mathrm{0}}+(A_t-A_v){\left[{\displaystyle \frac{\mathrm{1}}{{\alpha }_i}}+{\displaystyle \frac{\mathrm{\Delta }x}{\mathrm{2}k}}\right]}^{-\mathrm{1}}(T_t-T_i)-{\dot{q}}_L}}{\mathrm{0.09}{c}_p{A}_v{H}_v^{\mathrm{1}/\mathrm{2}}+(A_t-A_v){\left[{\displaystyle \frac{\mathrm{1}}{{\alpha }_i}}+{\displaystyle \frac{\mathrm{\Delta }x}{\mathrm{2}k}}\right]}^{-\mathrm{1}}}},

where,

(9) {\alpha }_i={\displaystyle \frac{{ϵ}_{\mathrm{r}}\sigma }{T_{\mathrm{t}}-T_i}}(T_{\mathrm{t}}^{\mathrm{4}}-T_{\mathrm{t}}^{\mathrm{4}})+\mathrm{0.023},(\mathrm{k}\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}\mathrm{K}),

(10) {ϵ}_{\mathrm{r}}={\left({\displaystyle \frac{\mathrm{1}}{{ϵ}_{\mathrm{f}}}}+{\displaystyle \frac{\mathrm{1}}{{ϵ}_i}}-\mathrm{1}\right)}^{-\mathrm{1}},

\sigma -Stefan-Boltzmann constant (W/m^{\mathrm{2}}{K}^{\mathrm{4}}) ;

(11) {\dot{q}}_L=A_{\mathrm{v}}{ϵ}_{\mathrm{f}}\sigma (T_{\mathrm{t}}^{\mathrm{4}}-T_{\mathrm{0}}^{\mathrm{4}})(\mathrm{k}\mathrm{W}),

(12) {\dot{q}}_c=\mathrm{0.09}{A}_{\mathrm{v}}{H}_v^{\mathrm{1}/\mathrm{2}}{H}_{\mathrm{u}\mathrm{i}}(\mathrm{k}\mathrm{W}),

k -Thermal conductivity of boundaries (kWm^-1K^-1); c_{\mathrm{p}} - Specific heat of boundaries (kJ/kg·K); H_{\mathrm{u}\mathrm{i}} - Calorific value of combustible material (MJ/kg).

The mathematical heat balance model developed was complicated. Hence a series of curves was developed for different ventilation and fuel load values (Fig. 4).

(d) Law’s maximum temperature equations

Law [ 17] derived an empirical equation for the maximum temperature using reported results.

For normal fuel loads:

(13) T_{\max }={\displaystyle \frac{\mathrm{6000}(\mathrm{1}-e^{-\mathrm{0.1}\eta })}{\sqrt{\eta }}},

for low fuel loads:

(14) T=(\mathrm{1}-e^{-\mathrm{0.05}\mathrm{\Psi }})T_{\max },

where,

(15) \eta ={\displaystyle \frac{A_{\mathrm{t}}-A_{\mathrm{v}}}{A_{\mathrm{v}}\sqrt{H_{\mathrm{v}}}}},

(16) \mathrm{\Psi }={\displaystyle \frac{L}{\sqrt{A_{\mathrm{v}}(A_{\mathrm{t}}-A_{\mathrm{V}})}}},

L - Fire load (kg); A_{\mathrm{t}} - Area of walls, ceilings and floor (m²); A_{\mathrm{v}} - Window area (m²) ; H_{\mathrm{v}} - height (m)

(e) Mehaffey’s Japanese parametric curves

Mehaffey [ 18] presented a time-temperature curve based on Eurocode and Japanese parametric post-flashover models.

(17) T-T_{\mathrm{0}}=\beta t^{\mathrm{1}/\mathrm{6}},

where, \beta - Constant (Ks^-1/6); t - Time of ignition (s).

For post-flashover ventilation-controlled fires, \beta is given by:

(18) \beta =\mathrm{3.0}T(\mathrm{0}){\left[{\displaystyle \frac{F_{\mathrm{v}}}{A_{\mathrm{t}}\sqrt{k\rho c_{\mathrm{p}}}}}\right]}^{\mathrm{1}/\mathrm{3}},

\rho - Density of boundaries (kg/m³).

The duration is given by:

(19) t_{\mathrm{b}}={\displaystyle \frac{{M^{″}}_{\mathrm{f}}{A}_{\mathrm{f}}}{\mathrm{0.1}{F}_{\mathrm{v}}}},

where, t_{\mathrm{b}} - Fire duration [s]; {M^{″}}_{\mathrm{f}} - Fire load per unit area (kg/m²); A_{\mathrm{f}} - Floor area (m²).

(f) Ma and Makelainen’s parametric curves

Ma and Makelainen [ 19] developed a parametric time-temperature curve to represent small to medium post-flashover fire temperatures using two key fire severity parameters, namely; maximum gas temperature ( T_{\max } ) and time at maximum temperature in mins ( t_{\mathrm{m}} ), and a shape constant (\delta ) .

(20) {\displaystyle \frac{T-T_{\mathrm{0}}}{T_{\max }-T_{\mathrm{0}}}}={\left({\displaystyle \frac{t}{t_{\mathrm{m}}}}\exp \left(\mathrm{1}-{\displaystyle \frac{t}{t_{\mathrm{m}}}}\right)\right)}^{\delta }.

For ventilation controlled fires:

(21) T_{\max }=\mathrm{1240}-\mathrm{11}\eta ,

where, \eta =A_{\mathrm{t}}/A_{\mathrm{v}}\sqrt{h_{\mathrm{v}}} is the inverse opening factor (m^-1/2).

For fuel controlled fires:

(22) T_{\max }=T_{\mathrm{m}\mathrm{c}\mathrm{r}}\sqrt{{\displaystyle \raisebox{1ex}{$\eta $}\!\left/ \!\raisebox{-1ex}{${\eta }_{\mathrm{c}\mathrm{r}}$}\right.}},

where, {\eta }_{\mathrm{c}\mathrm{r}}=\eta in the critical region; T_{\mathrm{m}\mathrm{c}\mathrm{r}} = Maximum fire temperature in the critical region (value of T_{\max } for \eta ={\eta }_{\mathrm{c}\mathrm{r}} )

(g) Barnett’s BFD curves

Barnett [ 20, 21] developed a new empirical model for compartment fire temperatures. He used a single log-normal equation to represent both the growth and decay phases in his curve, known as “BFD Curve” (Fig. 5). This equation was developed using curve fitting to 142 natural fire tests with a range of fuels and different enclosure materials [ 20]. The “BFD Curve” is a good replacement for the standard time-temperature curve as it takes the shape of the natural fire curve including the decay phase and fits the results of actual fire tests closer than previously known models. Also it requires only three factors; the maximum gas temperature, the time at which it occurred and a shape constant for the curve. “BFD curve” is defined by:

(23) T=T_{\max }{e}^{-\mathit{z}}+T_{\mathrm{0}}(°C),

where,

(24) z={({\log }_{e}t-{\log }_e{t}_{\mathrm{m}})}^{\mathrm{2}}/s_{\mathrm{c}},

s_{\mathrm{c}} - Shape constant for the temperature-time curve.

Barnett and Clifton [ 22] states that the maximum temperature ( T_{\mathrm{m}} ) can be derived from Law’s [ 17] maximum temperature Eqs. (13) and (14). To calculate the time ( t_{\mathrm{m}} ) at which this maximum temperature occurs, they recommend two methods: obtain it from the graph plotted against heat release rate Q (MW) and time or calculate it from the parametric time – temperature curve in Eurocode 1 Part 1.2 [ 11] Annex A and use Eq. (25).

(25) t_{\mathrm{m}}=\mathrm{60}{t}_{\max },

where, t_{\mathrm{m}} - Time for input into BFD curve (minutes); t_{\max } - time from Eurocode 1 Part 1.2 [ 11] (hours).

The shape constant s_{\mathrm{c}} is related to the thermal insulation of enclosure (c) and the pyrolysis coefficient k_p as:

(26) s_{\mathrm{c}}=c{k}_{\mathrm{p}},

where, c - 38 for enclosures with minimum insulation and applies to steel sheet roof and walls sixteen for enclosures with maximum typical insulation and applies to an enclosure with timber floors and plasterboard lined walls and ceiling.

(27) k_{\mathrm{p}}=\mathrm{1}/(\mathrm{148}{F}_{\mathrm{o}\mathrm{2}}+\mathrm{3.8}),

(28) F_{\mathrm{o}\mathrm{2}}=A_{\mathrm{v}}{h}_v^{\mathrm{0.5}}/A_{\mathrm{t}\mathrm{2}}(m^{\mathrm{0.5}}),

(29) A_{\mathrm{t}2}=A_{\mathrm{t}}-A_{\mathrm{v}}({\mathrm{m}}^{\mathrm{2}}),

where, A_{\mathrm{t}} - Total internal surface area of enclosure including openings (m²); A_{\mathrm{v}} , h_{\mathrm{v}} - sum of areas (m²) and Mean height of vertical openings (m)

(h) Eurocode parametric curves

To better represent real fires, Eurocode 1 Part 1.2 [ 11] prescribes a simple mathematical relationship for “Parametric” fires, allowing a Time-Temperature relationship to be obtained for the combinations of fuel load, ventilation openings and the thermal properties of wall lining materials in Annex-A. Figure 6 shows the effects of these parameters on the resulting curves.

For the heating phase:

(30) T=\mathrm{20}+\mathrm{1325}(\mathrm{1}-\mathrm{0.324}{e}^{-\mathrm{0.2}t*}-\mathrm{0.204}{e}^{-\mathrm{1.7}t*}-\mathrm{0.472}{e}^{-\mathrm{19}t*}),

where, t^{*} - Fictitious time,

(31) t^{*}=t\times \mathrm{\Gamma }(hr),

\mathrm{\Gamma } - Modification factor “gamma”,

(32) \mathrm{\Gamma }={{[O/b]}^{\mathrm{2}}/(\mathrm{0.04}/\mathrm{1160})}^{\mathrm{2}},

b - Thermal inertia of boundary of enclosure,

(33) b=\sqrt{\rho c\lambda }(J/m^2{s}^{1/2}K);

\rho - density of boundary of enclosure ( \mathrm{k}\mathrm{g}/{\mathrm{m}}^{\mathrm{3}} ); c - Specific heat of boundary of enclosure ( J/kgK ); \lambda - τhermal conductivity of boundary of enclosure ( W/mK );

O- opening factor

(34) O=A_{\mathrm{v}}\sqrt{h_{\mathrm{e}\mathrm{q}}}/A_{\mathrm{t}},(m^{1/\mathrm{2}})

;

A_{\mathrm{v}} - Total area of vertical openings on all walls (m²); h_ep- Weighted average of opening heights on all walls ( m ); A_{\mathrm{t}} - Total area of enclosure (m²).

The above parametric time-temperature relationship is applicable to: Compartments with mainly cellulosic type fuel loads, Compartment floor areas up to 500 m², Thermal inertia: \mathrm{100}\le b\le \mathrm{2200}J/m^{\mathrm{2}}{s}^{\mathrm{1}/\mathrm{2}}K and Opening factor: \mathrm{0.02}\le O\le \mathrm{0.2}{m}^{1/2} .

The maximum temperature T_{\max } in the heating phase occurs when t^{*}=t_{\max }^{*} , where

(35) t_{\max }^{*}=t_{\max }\times \mathrm{\Gamma },

(36) t_{\max }=\max \left[\left(0.2\times {10}^{-3}{q}_{\mathrm{t}\mathrm{d}}/O\right);t_{\lim }\right],

q_{,\mathrm{t}\mathrm{d}} - Design value of the fuel load density related to the total surface area A_{\mathrm{t}} of the enclosure; q_{,\mathrm{t}\mathrm{d}}=q_{,\mathrm{f}\mathrm{d}}{A}_{\mathrm{f}}/A_{\mathrm{t}} (MJ/m²);

(37) \mathrm{50}\le q_{t,d}\le \mathrm{1000};

q_{,\mathrm{f}\mathrm{d}} - Design value of the fuel load density related to the surface area A_{\mathrm{f}} of the floor (MJ/m²); A_{\mathrm{f}} - compartment floor area (m²); t_{\lim } - for slow growth rate, t_{\lim }=\mathrm{25}\min ; for medium fire growth rate, t_{\lim }=\mathrm{20}\min ; and in case of fast fire growth rate, t_{\lim }=\mathrm{15}\min .

For the cooling phase:

(38) T=T_{\max }-\mathrm{625}(t^{*}-t_{\max }^{*})for{t}_{max}^{*}\le \mathrm{0.5},

(39)

(40) T=T_{\max }-\mathrm{250}(t^{*}-t_{\max }^{*})for{t}_{\max }^{*}\ge \mathrm{2.}

Computational modeling

Several computer models have been developed for calculating temperatures in post-flashover room fires. FPEtool, FASTLite, FAST and CFAST are some models capable of simulating fires with the use of t-squared model, but most of them have limitations. They are developed as a sequence of advancement to previous models. COMPF2 is a widely used computer program for calculating temperatures in post-flashover room fires. BRANZFIRE software includes a multi-room zone model with flame spread and fire growth models.

It is apparent that variation exists between these models and the fire time-temperature curve differs according to the method of calculations and their limitations based on many simplifying assumptions to real fire situations. Also reliable and detailed measurement data from large-scale fire tests are needed for validation of these computer models. Therefore there is a need to obtain a simple method to predict the post-flashover time-temperature curve.

Compartment fires

Compartment fire tests were conducted to investigate the fire behavior and record the realistic time-temperature distributions. Jones [ 5] conducted three compartment tests (2.4 m cube) for buildings with modern thermoplastics materials. Using his results in Fig. 7, he questions the adequacy of using standard fire curves to determine the fire performance of structural elements in a building fire.

Lennon and Moore [ 4] reported eight full scale fire tests conducted in a room of 12m \times 12m \times 3m. These tests were conducted for various combinations of fuel loads, ventilation factors and compartment lining materials (Table 2) and the results are shown in Fig. 8 [ 23]. Test results showed that experimental temperatures exceeded standard curve values and that the use of standard fire curve would severely underestimate the fire severity. Abecassis-Empis et al. [ 24] conducted fire tests in a two-bedroom apartment in a 23-storey high-rise building. Test compartments were furnished with regular living room/office items to develop a realistic design fire scenario. This study highlighted the disparity between the predicted and experimental fires.

The time-temperature curves from compartment tests are based on typical arrangement of that particular compartment relating to the level of fuel load, ventilation conditions, compartment geometry and thermal characteristics of construction materials as evident from Figs. 7 and 8. Therefore they do not reflect the true time-temperature curve for a building fire. A suitable time-temperature curve should be established to represent building fires. Fire has three distinct phases namely; Growth, Fully-developed and Decay phases (Fig. 1). The growth phase is of relatively long duration and gives a very low rise in the compartment temperature depending on fuel type and ignition source, in comparison with fully developed fires. For this reason the growth period is ignored in the standard time-temperature curves and the fire is considered to start from flashover. This has been incorporated into all the standard curves by a time shift included within it. The standard fire curve [ 1] also has a time shift and commences from the flashover point.

Also there is growing concern about analyzing compartments for traveling fires. In large compartments, fires tend to travel along the floor, burning only for a limited time in one place [ 24]. Hence the structure will be exposed to a non-uniform temperature profile with a longer decay period. Therefore the traditional method of assuming homogenous temperature profile for the entire building element cannot be considered to be conservative. However, the traveling fires have considerable impact only on large compartments where long structural elements exist.

This review shows that it is very difficult to envisage the fire time-temperature curve in a compartment. Several time-temperature curves were derived using mass and energy balance equations, heat release rates and curve fitting to temperature profiles from compartment tests. Many researchers used different types of fuels and ventilation conditions to obtain and validate their fire curves. Hence most of these equations have limitations while their application is limited to the conditions used by them.

Development of realistic design fire time-temperature curves

This section presents the realistic design fire curves developed based on Eurocode parametric and Barnett’s BFD curves following the review of fire curves presented in the last section. The Eurocode parametric fire curve [ 11] was considered as it allows a time-temperature relationship to be developed for a set of basic fire parameters, fuel load, ventilation openings and thermal properties of lining materials, with realistic values. They include the two phases of fire development; heating and cooling phases, but the decay rates are linear and very fast. Hence Barnett’s “BFD” curve is considered to be a good alternative to Eurocode parametric curve as it takes the natural shape of a fire curve, and has already shown to agree with the results of compartment tests. Section 3 identified that three basic parameters namely, fuel load, ventilation openings and thermal properties of lining materials, define the time-temperature curve in a compartment. Therefore these parameters are considered next.

Fuel loads in modern buildings

Fuel load is defined as the energy (MJ) released by the combustion of compartment contents. Its value is expressed as Fuel Load Density (FLD), which is the heat energy released per m² of floor area. Fuel load in a compartment is made of permanent (electrical and ventilation fittings) and variable loads (furniture and ornaments). Fuel loads in residential buildings depend on the geographic location, home construction and furnishing styles, and also vary within a building depending on the room usage. They have changed significantly in modern buildings due to the increasing usage of plastic items. Fuel loads have been historically established by surveys of typical buildings. The recent CIB W14 report [ 26] summarizes the extensive surveys of fuel loads conducted in many countries for different occupancies based on their type of usage.

Kumar and Rao [ 27] conducted a fuel load survey of 35 residential buildings in India and produced total (permanent and variable) fuel load values according to the type of houses and room usage. Their results showed that FLD in a one-room house is very much higher than in three and four-room houses since the household equipment is crammed in a small floor area. The mean FLD in store rooms (852.30 MJ/m²) is much higher than in other rooms. Kitchen (672.98 MJ/m²) and bedrooms (495.75 MJ/m²) seize the second and third places, respectively.

Type of houses [ 7]

Bwalya et al. [ 7, 9] conducted a survey for fuel loads in Canadian homes and the values are shown in Table 3. As for previous surveys, kitchen and bedrooms occupy the top most ranks in terms of FLD values. Figure 9 summarizes the mean FLD values for residential dwellings currently available from all the resources.

Despite such recommendations of suitable FLD values by many researchers and standards, it is uncertain which mean value and percentile are to be selected in determining a time-temperature curve to represent a more realistic fire scenario in residential buildings. Hence many academics and researchers in the field of fire engineering were asked this question, whose recommendations were to select a realistic value from the available literature that is justifiable to the present building environment than using a value obtained 20 years ago. However for design purposes it is obvious to select the worst case fire scenario, which reflects the actual fire profile in a modern building. Therefore an average value of 780 MJ/m² was selected from Eurocode 1 Part 1.2 [ 11], which is very close to Bwalya et al.’s [ 9] recent fuel load survey results (807 MJ/m²) obtained for Canadian homes. Also for design load, an 80th percentile value of 948 MJ/m² was selected, and by taking into account the factors such as combustion for cellulosic materials (m= 0.8), fire activation risks for compartment area ( {\delta }_{\mathrm{1}} = 1.5), type of occupancy ( {\delta }_{\mathrm{2}} = 1) and active fire fighting measure ( {\delta }_n = 1) as given in Eurocode 1 Part 1.2 [ 11], the design variable fuel load density for residential building was determined as 1138 MJ/m². For permanent fuel load density, a value of 130 MJ/m² is proposed in [ 28]. Hence the design fuel load density for residential buildings is determined as 1268 MJ/m².

Thermal properties of wall lining materials

The compartment boundaries of enclosure materials for this research were chosen as light gauge steel partitions lined with gypsum plasterboards and rock fiber insulations for walls and ceiling, and concrete floor slab to represent a typical single storey residential building. The thermal inertia of the compartment enclosure materials was calculated using Eq. (41).

(41) b=\sqrt{\rho c\lambda }[\mathrm{J}/{\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{1}/\mathrm{2}}\mathrm{K}].

Properties of 16 mm thick Firestop^TM Gypsum plasterboard at ambient temperature (20°C) are as follows based on [ 29].

Density ( \rho ) = 729 \mathrm{k}\mathrm{g}/{\mathrm{m}}^{\mathrm{3}} ; specific heat (c) = 950 J/kgK ; thermal conductivity ( \lambda ) = 0.25 W/mK .

Hence the thermal inertia of gypsum plasterboard, b=\sqrt{\rho c\lambda } = 416.10 \mathrm{J}/{\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{1}/\mathrm{2}}\mathrm{K} .

Similarly the thermal inertia (b) values of cold-formed steel, rock fiber insulation and concrete were also calculated, and are summarized in Table 4. To account for different fire scenarios two different fire compartments having light gauge steel frame walls and ceiling panels with and without rock fiber insulations and concrete floors were selected.

Realistic design fire time-temperature curves – Compartment A

This section presents the details of developing realistic design fire time-temperature curves for a typical compartment (Compartment A) with the following configuration: Walls and Ceiling – LSF walls with two 16 mm thick Firestop^TM gypsum plasterboards and Concrete Floor. Fuel load and thermal property values presented in the last two sections were used for a range of ventilation opening sizes. Table 5 gives the compartment dimensions and the ventilation opening sizes including the calculations leading to opening factors.

Compartment thermal inertial: Thermal inertia of gypsum plasterboard (b_{\mathrm{g}}) = 416.10 \mathrm{J}/{\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{1}/\mathrm{2}}\mathrm{K} ; Thermal inertia of concrete (b_{\mathrm{c}}) = 1899.00 J/m^{\mathrm{2}}{s}^{\mathrm{1}/\mathrm{2}}K .

From Table 5, For an opening factor O = 0.20 m^1/2; Total surface area (A_{\mathrm{t}}) = 46.08 {\mathrm{m}}^{\mathrm{2}} ; Total area of ventilation (A_{\mathrm{v}}) = 7.62 m²; floor area (A_{\mathrm{f}}) (3.6 × 2.4) = 8.64 m²; compartment thermal inertia (b) = {\displaystyle \frac{(A_{\mathrm{t}}-A_{\mathrm{f}}-A_{\mathrm{v}})b_{\mathrm{g}}+A_{\mathrm{f}}{b}_{\mathrm{c}}}{(A_{\mathrm{t}}-A_{\mathrm{v}})}} = 749 \mathrm{J}/{\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{1}/\mathrm{2}}\mathrm{K} .

Similarly compartment thermal inertia values for a range of opening factors from 0.02 to 0.20 m^1/2 were calculated and the corresponding values are shown in Table 6. Fire curves in Fig. 10 were then drawn for opening factors ranging from 0.02 to 0.20 m^1/2 using Eurocode parametric equations (Eq. (30)). Detailed calculations for an opening factor 0.02 m^1/2 in obtaining the time-temperature fire curve coordinates are shown in Appendix A. Fire curve EU-1 (0.20) represents a rapid fire and EU-8 (0.02) is a long-drawn-out fire which lasts for more than five hours. From the experimental point of view to study the behavior of LSF walls under realistic design fire scenarios, EU-4 (0.08) and EU-7 (0.03) fire curves were considered the most appropriate as they envelope a rapid fire (EU-4) and a prolonged development fire (EU-7) for the extreme opening factor conditions. Also it is assumed that EU-1(0.20) fire which lasts only for about 20 min will not generate a significant impact even on load bearing structural elements. Considering the above it is evident that the curves representing the opening factors 0.03 m^1/2 (EU-7) and 0.08 m^1/2 (EU-4) are considered to be the most suitable curves for the experimental study of LSF wall behavior as they cover the entire range of fire scenarios within the acceptable fire durations of about 4.5 h and 60 min, respectively.

The curves shown in Fig. 10 represent the modern residential building fires in terms of temperature and fire duration. But the only concern in the Eurocode parametric curve [ 11] is the shape of the curve, i.e., the linear decay rate is unrealistic and cannot be justified. Pope and Bailey [ 31] states that Eurocode [ 11] under-predicts the temperatures in the decay phase and the linear time-temperature relationship in the decay phase is not acceptable. To overcome this situation and to have a natural fire time-temperature curve, Barnett’s [ 20] ‘BFD’ curve was also considered. As mentioned earlier, Barnett’s [ 20] “BFD” curve was a good alternative to Eurocode parametric curve as it takes the natural shape of a fire curve, matches the results of actual fire profiles and uses only a single equation compared to the multiple equations of Eurocode Parametric curves [ 11].

The “BFD” curves were drawn for the same parameters as for the Eurocode parametric curves and the relevant detailed calculations in obtaining the time-temperature fire curve coordinates for an opening factor of 0.02 m^1/2 are given in Appendix A. Figure 11 shows the “BFD” curves for opening factors of 0.03 m^1/2 (BFD-7) and 0.08 m^1/2 (BFD-4) together with the Eurocode parametric curves [ 11]. In comparison to the Eurocode parametric curves, the peak temperature values of Barnett’s [ 20] “BFD” curve are less (see Fig. 11), but the shape of the curve fits well with the natural fire curve. The “BFD” curve calculates the maximum temperature from Law’s Eqs. (13)-(16) [ 17]. It is questionable whether they incorporate the effects of modern materials such as thermoplastic, polyurethane and synthetic foams. Therefore it was decided to use the maximum temperature of the Eurocode parametric curve for the “BFD” curve. The “modified BFD” curves and the corresponding Eurocode parametric curves are shown in Fig. 12.

As described earlier, “BFD” time-temperature coordinates are calculated based on three parameters, namely, the maximum temperature (T_max), time to reach the maximum temperature (t_m) and the shape constant (s_c). In developing the “BFD” curves for opening factors 0.03 and 0.08 m^1/2 the time to reach the maximum temperature (t_m) was obtained from Eurocode 1 Part 1.2 [ 11] parametric curve equations as recommended in [ 22]. Eurocode parametric curve [ 11] does not include the pre-flashover phase and hence the time to reach the maximum temperature in Eurocode (t_max) excludes the pre-flashover phase. However, Barnett’s “BFD” curve [ 20] is a natural fire curve, which incorporates both pre-flashover and post-flashover phases. This is clearly evident in Fig. 5. Hence the time to flashover point (i.e., pre-flashover duration) has to be added to t_max (Eurocode) [ 11] to obtain t_m (BFD) [ 20].

Analysis of large experimental fires has shown that the flashover occurs when the heat output of the fire reaches a critical value. The critical value of heat release rate in relation to compartment and ventilation opening sizes is given by Eq. (42) [ 12].

(42) Q_{\mathrm{c}\mathrm{r}}=\mathrm{0.0078}{A}_{\mathrm{t}}+\mathrm{0.378}{A}_{\mathrm{v}}\sqrt{H_{\mathrm{v}}},

where, Q_{\mathrm{c}\mathrm{r}} -Critical value of heat release rate (MW); A_{\mathrm{t}} -Total internal surface area (m²); A_{\mathrm{v}} -Total area of openings on all walls (m²); H_{\mathrm{v}} - height of opening (m).

Hence an approximate method to determine the flashover time is by substituting the critical value of heat release rate obtained from Eq. (42) to the pre-flashover heat release rate-time relationship of Eq. (4). Pre-flashover time durations were calculated for the “Modified BFD” curves and are shown in Table 7. Hence the flashover times of 4.68 and 4.36 min were added to the Eurocode parametric time t_max to obtain t_m (BFD), and the corresponding BFD curve time-temperature coordinates for opening factors of 0.03 and 0.08 m^1/2 were then calculated accordingly. The effect of adding pre-flashover time to the ‘Modified BFD’ curves is shown in Fig. 13.

From Fig. 13, it is evident that the BFD curves include both pre-flashover and post-flashover profiles resulting in a more realistic natural fire growth. The standard and the Eurocode parametric [ 11] curves also consider only the post-flashover profiles by including an inbuilt time shift. Hence the resulting FRR will be less than that from the “BFD” curve, and is conservative. Therefore it was decided to use the “BFD” curve in the post-flashover condition only, i.e., neglect the pre-flashover phase. For this purpose, the corresponding flashover points were found as shown in Fig. 14 for the “BFD” curves in the case of 0.03 and 0.08 m^1/2 opening factors. They were found to be less than 1 and 2 min, respectively.

This way of modifying the original “BFD” curves appears to be a reasonable solution to derive more realistic design time-temperature curves for design purposes and the method has been suggested by previous researchers for different fire curves [ 19]. The co-author of ‘BFD’ curve was consulted [ 22], who also supported the above modifications including starting the curve from flashover point. Hence to incorporate this change, the “BFD” curves have to be moved toward the temperature axis (y-axis) in order to eliminate the pre-flashover phase. But pre-flashover time periods obtained from the curves are not significant in comparison to the fire durations of 270 and 60 min for 0.03 and 0.08 m^1/2 opening factors, respectively. Also it can be argued that the fire transitions from growth to fully burning phase need not always be rapid as in flashover. It may also be slower and depends on the compartment area, fuel load, heat release rate and ventilation conditions. Therefore considering the above it was decided to ignore this effect and to have the ‘BFD’ curve as a natural fire.

In summary, four curves were selected for this research, EU-4(0.08), EU-7(0.03), “modified BFD-4(0.08) with 4.36 min time increment” and “modified BFD-7(0.03) with 4.68 min time increment”. The first two curves represent the rapid and prolonged Eurocode parametric fire curves while the last two curves represent the natural fire time-temperature curves drawn using the same parameters. In Fig. 15, “EU-4(0.08)”, “EU-7(0.03) ”, “modified BFD-4(0.08) with 4.36 min time increment” and “modified BFD-7(0.03) with 4.68 min time increment” curves were referred to as EU-1(0.08)–Comp A, EU-2(0.03)–Comp A, BFD-1(0.08)–Comp A and BFD-2(0.03)–Comp A, respectively.

Realistic design fire time-temperature curves-Compartment B

This section presents the details of developing realistic design fire time-temperature curves for another typical compartment (Compartment B) with the following configuration: Walls and Ceiling – LSF walls with 25 mm rock fiber insulation sandwiched between two 16 mm thick Firestop^TM gypsum plasterboards (Fig. 16) and concrete floor.

(43)

Else calculate

(44) s_{\lim }=\sqrt{{\displaystyle \frac{\mathrm{3600}{t}_{\max }{\lambda }_{\mathrm{1}}}{c_{\mathrm{1}}{\rho }_{\mathrm{1}}}}}.

(45) If{s}_{\mathrm{1}}>s_{\lim },b=b_{\mathrm{1}}.

(46) Elseb={\displaystyle \frac{s_{\mathrm{1}}}{s_{\lim }}}{b}_{\mathrm{1}}+\left(\mathrm{1}-{\displaystyle \frac{s_{\mathrm{1}}}{s_{\lim }}}\right)b_{\mathrm{2}},

where, b - thermal inertia; b_{\mathrm{1}} , b_{\mathrm{2}} - thermal inertia values of fire exposed layer (layer 1), and the inner layer (layer 2); s_{\mathrm{1}} - layer 1 thickness (fire exposed side); s_{\lim } - fire exposed layer thickness limit; thermal inertia of wall/ceiling configuration; thermal inertia of gypsum plasterboard (b_{\mathrm{g}}) - 416.10 \mathrm{J}/m^{\mathrm{2}}{s}^{\mathrm{1}/\mathrm{2}}K ; thermal inertia of rock fiber (b_{\mathrm{r}}) - 145.00 \mathrm{J}/{\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{1}/\mathrm{2}}\mathrm{K} .

From Eq. (43), since b_{\mathrm{g}}>b_{\mathrm{r}} (thermal inertia of layer 1–fire side>thermal inertia of layer 2) wall / ceiling thermal inertia is based on Eqs. (44) to 46.

From Table 5, for an opening factor of 0.20 m^1/2, total surface area (A_{\mathrm{t}}) = 46.08 m²; total area of ventilation (A_{\mathrm{v}}) = 7.62 m²; floor area (A_{\mathrm{f}}) (3.6 × 2.4) = 8.64 m².

From Eq. (36) t_{\max }=\left(0.2\times {10}^3{q}_{\mathrm{t}\mathrm{d}}/O\right) ; from Eq. (37) q_{\mathrm{t}\mathrm{d}}=q_{\mathrm{f}\mathrm{d}}{A}_{\mathrm{f}}/A_{\mathrm{t}} .

For residential buildings, q_{,\mathrm{f}\mathrm{d}}=1268 MJ/m², therefore q_{,\mathrm{t}\mathrm{d}}=\mathrm{1268}\times \mathrm{8.64}/\mathrm{46.08}=\mathrm{237.75} MJ/m²; t_{\max }=(\mathrm{0.2}\times {\mathrm{10}}^{-\mathrm{3}}\times \mathrm{237.75}/\mathrm{0.20})=\mathrm{0.24}\mathrm{h}\mathrm{r} ; s_{\lim }=\sqrt{{\displaystyle \frac{\mathrm{3600}\times \mathrm{0.24}\times \mathrm{0.25}}{\mathrm{950}\times \mathrm{729}}}}\times \mathrm{1000}=\mathrm{17.66}\mathrm{m}\mathrm{m} (for gypsum plasterboard \rho =\mathrm{729} kg/m³, c=950 J/kgK and \lambda =0.25 W/mK).

From Eqs. (45) and (46), s_g>s_{\lim } , (thickness of gypsum plasterboard – 16 mm<s_lim – 17.66 mm). Therefore wall / ceiling thermal inertia b_{\mathrm{w}}=\left[{\displaystyle \frac{\mathrm{16}}{\mathrm{17.66}}}\times \mathrm{416.10}\right]+\left([\mathrm{1}-{\displaystyle \frac{\mathrm{16}}{\mathrm{17.66}}}]\right)\times \mathrm{145} = \mathrm{391.08} , compartment thermal inertia (b) = {\displaystyle \frac{(A_{\mathrm{t}}-A_{\mathrm{f}}-A_{\mathrm{v}})b_{\mathrm{g}}+A_{\mathrm{f}}{b}_{\mathrm{c}}}{(A_{\mathrm{t}}-A_{\mathrm{v}})}} = \mathrm{730} .

Eurocode parametric curve EU-7(0.03) was selected to represent the realistic fire scenario and the corresponding BFD curve was also drawn (Fig. 17). The BFD curve was then modified to represent the modern compartment characteristics in terms of the maximum temperature and pre-flashover duration as before. The sequence of modifying the BFD curve is shown in Fig. 18. As before the time-temperature curves in Fig. 18(b) “EU-7(0.03)” and “modified BFD-7(0.03) with 4.68 min time increment” are now referred to as EU-2(0.03) Comp B and BFD-2(0.03)–Comp B, respectively and are shown in Fig. 18(c). Figure 19 shows the Eurocode parametric curves and the modified “BFD” curves drawn for the realistic design parameters that can be used in the full scale fire tests of LSF walls.

Conclusions

This paper has presented the details of an investigation aimed at developing suitable realistic design fire time-temperature curves for the testing of LSF walls used in modern buildings. It included a detailed review of typical building fires, previously developed fire time-temperature curves, computer models and available parametric equations. It has shown that standard fire curve is not suitable in obtaining the fire resistance of construction elements used in modern buildings. The paper has highlighted that real building fire time-temperature curves depend on the fuel load representing the combustible building contents, ventilation openings and thermal properties of wall lining materials, and provided suitable values of the many required parameters including the fuel loads in residential buildings. It has then developed a series of suitable realistic design time-temperature curves based on Eurocode 1 Part 1.2 [ 11] parametric and Barnett’s ‘BFD’ [ 20] curves. Two compartments with LSF wall panels and a concrete floor were considered with two opening factors simulating both rapid and prolonged fire curves. These fire curves can be used in full scale fire tests to investigate the fire performance of LSF wall panels exposed to modern building fires. Similarly, suitable fire curves can be developed and used to simulate other fire scenarios for practical engineering applications.

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