Thermal Response of Timber Slabs Exposed to Travelling Fires and Traditional Design Fires

In this study, we used a multi-scale model of charring of timber integrated into Gpyro [29], that solves the physical and chemical changes of wood in the solid phase. The gas-phase was not simulated and only approximated by design fires as explained in Sect. 3.2. The model itself was developed by extending the across scale approach of Rogaume [30] by introducing uncertainty quantification as well as testing the appropriateness of the complexity of the model. The idea behind this approach is to study different chemical and physical processes in isolation across scales [31]. The assumption is that by studying them in isolation, the final model will be more robust and valid in extrapolation as it is common in engineering science [32]. The latter part is key for this study, as we will use the model to simulate the charring response of a wood sample to a design fire for which no experimental data exist. The complete development and validation of the model can be found in [33‐35] and will be summarised here. The model consists of a physical and chemical sub-model. The chemical kinetic model was developed at the microscale [34], following a literature review that found that no appropriate heterogenous kinetic model of charring existed in the literature [34, 35]. At the microscale, the model was validated against a range of experiments with mg-samples of wood from the literature under a wide range of heating conditions, oxygen concentrations, and heating intensities. These experiments were selected according to the thresholds in [36]. Following this validation, the kinetic model was incorporated into Gpyro, which is a generalised pyrolysis solver [29], by Richter and Rein [33]. The mathematical formulation of the model can be found in [33] with the material properties described in the next section. All material properties were taken from the literature. The model itself predicts well several experiments at the mesoscale (g-samples) from the literature, as well as compares well to several other computational models of various complexities available in literature. In fact, the model reproduces the mass loss rate and in-depth temperatures of wood in different grain orientations, of different moisture content, under different oxygen concentrations, and different heat fluxes in experiments conducted by different authors. One can therefore conclude that the model is valid at both the micro-and mesoscale, and that the model can predict experiments under different heating regimes and boundary conditions. In this study, we will assess the performance of the model against macroscale experiments (> kg-samples) before using the model in extrapolation to simulate previously unstudied design fires. The results in extrapolation will be deemed valid if the model compares well at all scales as such agreement indicates that the model captures all major physical and chemical processes.

In this study, we simulate the response of one-dimensional wood samples to different design fires in furnace like conditions (thermal and oxygen boundary conditions), as shown in Figure 3. The wooden sample is assumed to behave as a solid block, and its depth of char can be estimated by the 300 °C isotherm. The former assumption holds for all Cross-Laminated Timber and Glulam as long as they do not delaminate. This set-up and choice of isotherm represents the experiment and choice of Konig and Wallij [21], who studied spruce under the standard (90 min) and several parametric fires. In our simulations, we will extend the heating conditions to include travelling fires. Konig and Wallij studied the charring rates of spruce using samples of 95 mm thickness by measuring the temperatures at 0,6,18, 30, 42, and 54 mm deep. All simulations assumed that each sample is 95 mm thick. In the simulations, the samples were discretised with a mesh size of 0.3 mm and a timestep of 0.09 s was used. These values were found to yield equivalent results to a mesh of 0.1 mm and 0.01 s, which was previously identified as the optimum mesh size for experiments at the mesoscale (experiments with g-samples) [37]. The material properties of spruce were assumed equal to generic wood [33], shown in Table 1, with only the density adjusted to the measured value of 430 kg/m³ [21] and the moisture content to 12%. The latter was estimated based on the experimental drying procedure [21, 38], but all simulations were also run at 5% moisture content for comparison. Our underlying assumptions and Table 1 shows that the model assumes that the thin layer of ash stays on the surface of the wood, thus creating a small resistance to mass and heat transfer. This assumes that the ash is not removed by either flow or gravity.

The boundary conditions at the front (Eq. 1) and back surface (Eq. 2) are modelled as follows:where T is the temperature, z is the spatial coordinate, h_c the heat transfer coefficient,\(\bar{\varepsilon }\) the emissivity, \(\bar{\psi }\) the porosity, \(\rho_{g}\) the gas-phase density, D the diffusivity, Y the gas-phase mass fraction, P is the pressure, and \(h_{m}\) the mass transfer coefficient. A convection coefficient of 9 W/m²-K [39] was assumed at z = 0 and the emissivity is defined in [33]. We estimated the average heat transfer coefficient as \(h_{c} = 9\frac{W}{{m^{2} - K}}\) [39] for \(z = 0\) and \(h_{c} = 0\frac{W}{{m^{2} - K}}\) for \(z = L\) due to the insulation. The emissivity of wood was estimated as 0.7 [40], while the emissivity of char and ash are estimated to be 0.95 [41]. From the heat-mass transfer analogy [42], we estimated \(h_{m0} \approx \frac{{h_{c} }}{{c_{g} }} = 9\frac{g}{{m^{2} - s}}\) for z = 0 and \(h_{m0} = 0 \frac{g}{{m^{2} - s}}\) for z = L with \(c_{g} = 1000\frac{J}{kg - K}\). No in-depth radiation is considered as it is negligible for wood [43]. The temperature \(T_{\infty }\) was assumed to follow the employed design fire at z = 0 and the ambient condition at z = L. The oxygen concentration within the furnace was assumed to be 8% as report by Schmid et al. [10]. Future research should explore the appropriate oxygen concentration and boundary conditions for realistic fires in large compartments and their impact on the charring of timber. For this work the same boundary conditions are adopted for all the design fires due to the lack of experimental evidence and understanding of fire dynamics in timber framed compartments.

The boundary conditions used within this study for the furnace are uncertain, and we assess the influence of their uncertainty with Monte-Carlo simulations [44]. In the first step, we found the plausible range for each parameter of the boundary conditions as shown in Table 2. We then created an ensemble of sets of these input parameters by drawing them from a uniform distribution and combing them at random. Using a Monte-Carlo approach, we then did one simulation of the standard fire, Konig’s parametric fire C3, and Konig’s parametric fire C4 for each set of input parameters in our ensemble. These simulations gave us an ensemble of predictions which we used to derive the uncertainty of our simulations. Further details can be found in [44]. In total, we conducted 250 simulations for each design fire.

The developed model predicts in-depth temperatures and charring rates of timber slabs under several design fires well (Figures 4, 5, 6). The depth of char was here evaluated by the 300 °C isotherm, which in turn allowed us to calculate the charring rate. However, we focus on the final depth of char of different design fires as that value quantifies the final strength loss after a fire (the key variable). In a furnace, the boundary conditions of a sample are transient and uncertain. For example, Schmidt et al. [22] investigated the oxygen concentrations in a furnace during fire tests. They found the oxygen concentration to vary between 0 and 10%. We accounted for this uncertainty through Monte-Carlo simulations (Sect. 3.3), which are shown as the shadow region around the simulations. Regardless of the boundary conditions (standard deviation: 2.6 mm), the model predicts the experiments with an average error in the char depth of 2.1 mm in the standard fire (Figure 4), 1 mm in the parametric fire C3 (Figure 5), and 3.8 mm in the parametric fire C4 (Figure 6). The parametric fires C3 and C4 and their name are taken from [21]. Noteable, König and Walleij [21] derived his parametric fires from the works of Magnusson and Thelandersoon [21, 45].

The predictions of the charring rates are always better than the predictions of the temperature. For example, the average error in the temperatures in a standard fire is 14% (Figure 4 left), while the average error in the charring rate is 7%, excluding the first 2 min (Figure 4 right with t > 2 min). This result is unexpected as charring rates are taken as the position of the 300 °C isotherm. In other words, the char depth in the experiments and predictions are derived from the temperature profiles. The reason for this contradiction is that the predictions at low temperatures (roughly < 400 °C) are very good, but greater discrepancies are observed for higher temperatures (see Figure 6). Two discrepancies are particularly large. One is the discrepancy in predicting the temperature at 6 mm in standard fire past 50 min (Figure 4). The other is the discrepancy in predicting the temperature at 30 mm past 40 min (Figure 6). The discrepancy in Figure 4 likely stems from a discrepancy in predicting the char oxidation, which is likely caused by the transient and varying oxygen concentration in a furnace. This can be deduced from the fact that the predictions work well up until 40–50 min. Afterwards (40–45 min) the model diverges from the experiments, as the model predicts that the char oxidation front reaches 6 mm and exposes the thermocouple (heat and mass transport is only slightly limited by ash). In the experiments, however, it seems some char remained, causing the experimental temperature at 6 mm to plateau. This discrepancy is of low concern as we predict in-depth temperatures well. The discrepancy in Figure 6 is likely caused by cracking. In the experiment, the thermocouples are offset from each other. If a crack forms in the wood, it shortens the distance between one thermocouple and the surface while leaving all other thermocouple readings unaffected. For the parametric fire C4 (Figure 6), we predict the temperature readings at 6 mm and 54 mm well, so that it is unphysical to observe a discrepancy at 30 mm. Hence, a crack must have been formed to cause an unexpected rise in temperature at 30 mm. As cracking is not incorporated in the model yet, this discrepancy is of low concern. Hence, we can judge the prediction of charring rates as well, and the predictions of temperature as good despite some discrepancies.

The charring behaviour of timber slabs depends on the fire scenario (assuming all boundary conditions are the same between the scenarios). When comparing all uniform (Figure 7) and non-uniform (Figure 8) fires, one can conclude that char depths differ when the fire scenario differs. In a standard fire, charring only has one stage: a relative constant increase in char depth (fast growth). This is observed both numerically and experimentally (Figure 4). However, for intermediate size compartments (< 500 m²) parametric fires (Figure 7 b & c) are better suited which show a two stage charring behaviour: increase during heating (fast growth) and a plateau during the decay phase (steady-state). This finding is further supported by the experimentally measured char depths in Figures 5 and  6. For travelling fires in large-scale compartments (> 500 m², Figure 8), one observes four stages: no-charring during the far field (T < 200–300 °C), slow increase during the arrival of the near field (T = 300–1200 °C, slow growth), fast charring during burning (T = 1200 °C, fast growth), and plateau during the decay phase (steady state). These qualitative differences in charring behaviour also result in quantitative difference with the largest char depth being observed in the SFPE (Society of Fire Protection Engineers constant temperature fire), ISO (standard fire), and EC-LC (Eurocode fire—long & cool) respectively. Hence, char depths under different fire scenarios differ significantly quantitatively and qualitatively.

While we said previously that charring plateau’s during the decay phase, it actually slowly continues a little into the decay phase (Figure. 7d). Wiesner and Bisby [49] found this previously experimentally. Charring continues post-heating, and sometimes even post-extinction, for three reasons. Firstly, the temperatures in the surrounding environment are still high enough to cause heating (T > 300 °C). Secondly, charring contributes to the gaseous fuel load and, therefore, potential heat release. As explained in Sect. 2, in our simulation the fire dynamics and charring are decoupled as we are using the current fire resistance framework. Secondly, the residual heat in the char will continue to advance the char front for a while. This outcome is important, as the Eurocode [15] —leading regulation in Europe to design timber buildings—offers a set of material properties to calculate charring rates in advanced heat transfer models. These parameters are only valid for heating but could benefit from extension to capture the decay phase. In our simulations charring during the decay phase is small (< 6 mm) while Wiesner and Bisby [49] observed significant charring (~ 20 mm). We attribute this discrepancy to the difference in set-up (column vs. slab, and enclosed vs. open furnace), the cooling time (2–3 min vs. 33 min), and different oxygen flow conditions (8 vs. 21% Oxygen). The above will lead to a different ratio of heat lost to heat transmitted into the solid, heat flux during the decay phase, and additional heat from char or volatile oxidation. The observed difference between the predictions and literature experiments is therefore reasonable.

Another distinction between uniform and non-uniform fires is that the latter dependent on location of the fire (or near field) in the compartment and fire size (Figure. 9). We found that independent of the fire location the maximum char depth is found after 90% (after roughly 40 m) of the fire path (Figures. 9 and 10), with the 2.5% travelling fire being the most severe. This point is unsurprising as the 2.5% travelling fire has the longest pre-heating time before the onset of charring. Hence, the sample can heat up more uniformly towards the temperature range at which pyrolysis starts, without any heating being lost due to pyrolysis. One therefore expects the smallest fire to be the most severe one. Surprisingly, the smallest fire is not the most severe one at the beginning and end of the compartment. At the beginning of the compartment (x = 0 m) there is no preheating time. The burning times of all fires in one location are relatively similar. Therefore, the fire with the highest temperature would be most severe, which is the 47% fire (Figure. 2). At the end of the compartment (x = 45.5 m), we assume the fire is extinguished instantaneously and cools within minutes to ambient temperatures. Hence, the most severe fire is the one that strikes a balance between preheating time (increases as fire size decreases) and peak temperature (decreases as fire size decreases). The fire sizes 2.5–10% strike this balance. In other words, it is important to study an ensemble of fires sizes of non-uniform fires at different location to evaluate their charring behaviour as it depends on location and fire size.

Despite the quantitative and qualitative difference between all fire scenarios, the standard fire represents the most severe heating in terms of charring after the SFPE fire. The char depth after a 90 min fire exceeds the char depth of all other fire scenarios at the end of fire exposure other than the SFPE fire. The latter is unsurprising, as the SFPE fire represents the case of a constant flame burning above the solid for an indefinite time. The char depth after a 90 min standard fire is 53.2 mm (as predicted by the computational model, which is slightly lower than the 58.5 mm given by EN 1995-1-2), while the char depths of parametric and travelling fires at the end of fire exposure are up to 46 to 42 mm respectively. In other words, travelling fires and parametric fires produce equivalent char depth up to 78 to 71 min in a standard fire (based on computational predictions). However, we assumed a fuel load of 540 MJ/m², which in turn assumes that the timber does not contribute to the fuel load in the compartment. Taking the additional fuel load of timber into account would raise the char depth in parametric and non-uniform fires above 53 mm. In other words, a 90 min standard fire would no longer represent the most severe heating in terms of charring. However, evaluating the contribution of timber to the fire is beyond the scope of this study and we focus here on a fuel load of 540 MJ/m². For this fuel load, the 90 min standard fire is representing the most severe heating in terms of char depth. Nevertheless, these findings suggest that the use of the standard fire adjusted for an increased duration to account for the increase in fuel load due to timber charring results in conservative calculation of the charring rate within the assumptions of the standard fire-furnace.