Performance-Based Wildfire CurveContrary to indoor fire, exterior wildfire presents a different behavior; therefore, the authors proposed a performance-based design curve for wildfires, opposing classical nominal curves. Several curves are presented in the literature, which considers three phases of a fire growth, flashover, and cooling. One of these curves is the one presented by Blagojević and Pešić (2011), in which these three phases are well represented for wildfires [Eq. (3)]. This one presents the best fit when comparing other studies’ measured in situ temperature versus time wildfire curves. Therefore, this temperature function is used in this work (Fig. 4):(3) T[∘C]=Tmax[t[s]tmax[s]exp(1−t[s]tmax[s])]cwhere parameter Tmax = maximum peak temperature; tmax = time instant when it happens; and c = dimensionless parameter that measures the growth and decrease of temperature. If c = 1, then the cooling is near-linear degradation, but if c > than 1, then the cooling presents a rapid exponential decrease.Two different curves were generated: the first is for fire in trees with a higher temperature amplitude but a shorter duration; the second is for fire in the bush with a lower temperature amplitude but a longer duration. The authors chose to use a design fire curve instead of an upper-bond of all measured experimental fire temperatures. This is because the results measured by other authors present some variability due to atmospheric and geographic conditions. Therefore, some of these confounders or variables are indirectly accounted in the design wildfire curve.The first two different Tmax were computed using the average maximum temperature Tmmax [Eq. (5)] of all other authors referenced before, for fires in trees and bushes. Second, both curves were assembled using the 95% characteristic values in Annex D “Design Assisted by Testing” in EN1990-1-1 (CEN 2002a) for the maximum temperature Tmmax. The maximum temperature values were tested for normal distribution using the Kolmogorov–Smirnov test. The values of kn (that affects the size of the sample) in Annex D (Table D.1) of EN1990-1-1 (CEN 2002a) were used with standard deviation coefficient sx in Table 1 to calculate Tk,95%max[∘C] [Eq. (4)]. No safety coefficient is used for the maximum temperatures since it is an accidental action:(4) with(5) Tmmax=∑i=1nTmaxinsx2=∑i=1n(Tmaxi−Tmmax)2n−1Table 1. Characteristic 95% temperatures for fire in trees and bushesTable 1. Characteristic 95% temperatures for fire in trees and bushesParametersTmmax[∘C]sx[°C]kn[−]Tk,95%max[∘C]Trees940.81154.371.831,223.30Bushes675.11118.941.72879.69However, for the case of the peak time frame tmax and indirect duration parameter c for the cooling phase, due to the scatter of experimental results of wildfire curves measured in situ, the chosen values are the most severe for design purposes and the ones in the range of an upper-bond curve. Therefore, the adopted values are presented in Table 2, for both fires in trees and bushes.Table 2. Adopted parameters for the design wildfire curves for trees and bushesTable 2. Adopted parameters for the design wildfire curves for trees and bushesParametersTmax[°C]tmax[sec]c[−]Trees1,223501.5Bushes8801501.0Both curves are plotted in Fig. 5, and compared with real measured wildfire curves, in which, as predicted, both are an envelope fire curve. Therefore, it can be concluded by observing Fig. 5 that the tree-fire design fire curve is capable of acquiring the first swift temperature growth, but then the bush-fire design is good for attaining the longer length duration of a wildfire due to burning bushes.When designing the protection of dwelling against wildfire, it is possible to not know in advance if trees or bushes surround it; in that case, it is wise to use the combined input of both fire design fire curves. Also, it is impossible to predict whether the fire has started in bushes or trees during the design phase. Therefore, the design fire curves in Fig. 5 may present some delay that may change the thermal response due to variations of material thermal properties. Therefore, as an alternative a combined envelope wildfire curve is proposed next to solve this problem, using the combined maximum temperature data (Tmax) of fires in trees and bushes.Therefore, this work also studied the possibility of using a single wildfire design curve, with the average values and characteristic values of the maximum temperatures of trees and bushes at the same time. This will provide a new fire curve, with the characteristic parameters given in Table 3.Table 3. Adopted parameters for the design wildfire curve combined envelope for trees and bushes simultaneouslyTable 3. Adopted parameters for the design wildfire curve combined envelope for trees and bushes simultaneouslyParametersTmax[°C]tmax[sec]c[ − ]Trees + bushes1,0501501.0Fig. 6 depicts the new combined envelope wildfire design curve, which captures almost all maximum wildfire temperatures. Some minor values of fires in trees are below the characteristic envelope temperature, but their duration is quite short. Therefore, for a general design, this envelope wildfire curve is still suitable, and this curve will be later compared with the previous ones in the thermal numerical section.

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