Introduction

The utilization of timber as a sustainable and carbon-neutral building material has witnessed remarkable growth in recent years, with softwood species predominantly serving as structural timber. However, in view of recent climate changes and global warming, coniferous forests are expected to decline (Diffenbaugh and Field 2013; Boulanger et al. 2015; Reich et al. 2015), while hardwood forests are predicted to become more abundant. For this reason, adaptation strategies are needed in the future to sustain the role of timber as a structural material. One of such strategies involves the increased utilisation of hardwood species for these purposes, both through harvesting and forestation. In Central Europe, the implementation of beech is particularly important, as it is the predominant species in this part of Europe, with around 10–15 % of the total stock (Pramreiter and Grabner 2023).

To effectively utilize beech as a building material, a comprehensive understanding of its properties and phenomena is essential. The most fundamental are undoubtedly the mechanical properties. Recent research has extensively explored this area (Ehrhart et al. 2022; Plos et al. 2022; Rais et al. 2022; Krüger et al. 2023; Fortuna et al. 2020). Furthermore, other knowledge is important as well, such as the hygroscopic and swelling behaviour (Majka and Rogoziński 2022; Hackenberg et al. 2023), the long-term rheological behaviour (Thaler and Humar 2013), the effects of thermal treatment (Czajkowski et al. 2020; Chien et al. 2018), and so on (Schirp et al. 2014; Simon et al. 2014). In addition, the behaviour of beech in the event of fire is also particularly important. Although numerous studies have been carried out in this field to investigate the charring and charring rates of beech specimens (Hugi et al. 2007; Cermák et al. 2019; Liu and Fischer 2024; Machová et al. 2021), some advanced numerical and experimental studies that provide more details of the material behaviour and charring of beech in fire conditions cannot be found. Therefore, this article addresses comprehensive investigation of charring of beech and the temperature when charring occurs, called char-front temperature of beech. This aspect has not been previously explored and holds significant implications for the fire design of structural elements made of beech and for the development of simplified methods. The commonly accepted char-front temperature, according to EN 1995-1-2 (2004), is 300 \(^{\circ }\)C, and is primarily determined for softwood species. American Wood Council (2018) gives a slightly lower value of 550 F (288 \(^{\circ }\) C). This article aims to determine if the 300 \(^{\circ }\)C assumption also applies to beech wood.

Advanced experimental and numerical analyses were used to determine the char front temperature. In the experimental phase, large scale fire tests were conducted on beech specimens that were subjected to the temperatures following standard temperature-time fire curve EN 1991-1-2 (2004). These tests involved monitoring the charring depth over time by removing specimens from the furnace at various intervals. In addition, specimens were equipped with thermocouples (hereinafter referred to as TC) that were installed precisely at the locations were the zone of charring was expected. The char front temperature was then determined based on the measurements of temperature development in the TCs and the charring depth, which was physically measured after the specimens were removed from the furnace. The experimental research was supported by the advanced numerical research. To numerically determine the char front temperature, a recently developed numerical model PYCIF (Pečenko and Hozjan 2021; Pečenko et al. 2023) was used. This model integrates a detailed description of heat and mass transfer in timber, combined with pyrolysis reaction, and enables a precise determination of charring depth and also the char front temperature.

Materials and methods

Test specimens

The test specimens were made of glued laminated beech boards, with dimensions of \(b_{1} \times h_{1} = 100\ \text {mm} \times 18\) mm. In total, 10 boards were glued together, giving the cross-section dimensions of the specimen \(b \times h = 100\ \text {mm} \times 180\) mm. The length of the specimen was 1000 mm. For the fire test, 6 specimens were put in the furnace. The average initial moisture content of each specimen is given in Table 1 and was determined with the Brookhuis FMW moisture meter. Based on these measurements, the average dry densities of the specimens were estimated.

Table 1 Average initial moisture content and dry density of the specimens
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Fire test

The fire test was performed in a horizontal furnace at the Fire laboratory of Slovenian National Building and Civil Engineering Institute. The temperatures in the furnace followed the standard temperature-time curve given in EN 1991-1-2. The furnace is compliant with standard EN 1363-1 (2020), and it has the dimensions of 3 m by 4 m and a height of 2 m. The walls are made of fireproof bricks with a total thickness of 450 mm. The floor is made of fireproof concrete, while the ceiling is made of aerated concrete blocks with a thickness of 200 mm, sealed in-between the blocks. In total, six oil fuelled burners are installed in the furnace. To measure the temperatures in the furnace, 12 plate TCs were installed.

Six glued laminated beech specimens were put in the furnace (Fig. 1a) through the horizontal openings cut in the upper slab (Fig. 1b). In order to physically measure charring depths at different times of fire exposure, the specimens were taken from the furnace after 10, 20 and 30 min of fire exposure. After the specimens were removed from the furnace, the openings were immediately covered with fireproof calcium-silicate boards to prevent the oxygen to enter the test zone.

To statistically evaluate the results, the specimens were installed in pairs as shown in Fig. 1c. They were separated by a 30 mm layer of ceramic wool, thereby exposing them to fire from three sides. To monitor the temperatures during fire exposure, K-type wire TCs with a diameter of 1.5 mm were installed in the specimens. The guaranteed temperature measurement uncertainty for this type of TCs is below 2 K. The TCs were placed in pre-drilled holes (Fig. 1d), parallel to the longer edge of the specimen cross-section. The holes had a length of 50 mm and were oriented parallel to the expected temperature isoline to avoid increased heat flux through the TCs and possible wrong measurement (Fahrni et al. 2018; Terrei et al. 2021). The TCs were led out of the furnace underneath the ceramic wool (Fig. 1b).

Fig. 1
figure 1

a The position of the specimens in the furnace. b The installation of the specimen through the opening in the ceiling. c The fabrication of specimen pairs. d The drilling of the holes for the installation of TCs. Photo: Robert Pečenko

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To investigate the hypothesis of whether the assumption of char front temperature of 300 \(^{\circ }\)C can be applied to beech, the positions of the boreholes (and consequently the TCs) were chosen precisely. The aim was to have TCs located in the zone of the estimated charring. To this end, a preliminary numerical study was conducted, where the development of charring depth was predicted. The study employed on a simple heat transfer analysis based on the theory of heat conduction through solid material, and the assumption of the char front temperature of 300 \(^{\circ }\)C. While this assumption cannot be generally considered, it provided a useful foundation for a rough estimation of charring. For the thermal boundary conditions the coefficient of heat transfer by convection was \(\alpha _{c} = 25\) W/m\(^{2}\)K and the surface emissivity was \(\varepsilon _{m} =\) 0.8. The initial dry density of beech was \(\rho _{0} = 643.9\) kg/m\(^{3}\), which was the mean density of all specimens given in Table 1. The temperature-dependent density reduction factor considered in this study was derived from the relationship given in EN 1995-1-2. The specific heat of timber and thermal conductivity were taken into account according to EN 1995-1-2. Furthermore, the thermal conductivity was additionally varied to simulate the variability of timber properties and to obtain the envelope of possible developments of charring depths. The preliminary study revealed that after 10 min of fire exposure, the expected charring depth ranged from 5 to 15 mm from the exposed edge. This depth increased to between 10 and 20 mm after 20 min of fire exposure and between 15 and 25 mm after 30 min of fire exposure. Based on this information, the drilling distances from side exposed edge were chosen. For the specimens taken from the furnace after 10 min of fire exposure, the boreholes were located 5, 10 and 15 mm from the side exposed edge. Similarly, for the specimens removed after 20 min, hole positions were at 10, 15, and 20 mm from the side exposed edge. In the case of the specimens subjected to 30 min of fire exposure, the drilling was done at distances of 15, 20 and 25 mm from the side exposed edge. Further details about the position and naming of the TCs are given in Fig. 2. For each specimen, there were three main measuring positions: at the bottom (a), in the middle (b) and at the top of the specimen (c). At each position, there were 3 TCs strategically placed 5 to 25 mm away from the side exposed edge, as previously detailed. In total, 54 TCs were utilized, 9 for each specimen.

Fig. 2
figure 2

Location and labelling of TCs

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Determining cross-section dimensions and other geometrical characteristics of specimen after fire

After the specimens were taken out of the furnace, they were extinguished with water. Then, the specimens were left for about a month in a storage room with a constant temperature of 20 \(^{\circ }\)C and a relative humidity of 55 %. After that, the char layer was mechanically removed, leaving the specimens with the pyrolysis layer (approximatively 5–10 mm depth) and sound wood underneath. Next, the specimens were transversely cut to extract dimensions, charring depths and other geometrical characteristic of the cross-section. In total, each specimen was cut into 15 pieces. Some cuts were randomly chosen, others were exactly at the location of the TCs to verify the assumption of 300 \(^{\circ }\)C char front temperature for beech. Each cut piece of the specimen was placed on the support in front of the white glass wall and photographed. The glass wall was lit from behind giving the best possible contrast between the specimen and the background (see Fig. 3). The resolution of all photos taken was 5408 x 3600 pixels. The photos were subsequently cropped (Fig. 4a) and filtered to obtain perfectly white background and dark specimen. Wolfram Mathematica filters Sharpen (Fig. 4b) and Lighter (Fig. 4c) were used in this two-stage filtering procedure.

Fig. 3
figure 3

Original photo of the sample after fire

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Fig. 4
figure 4

a Cropped photo b Sharpened photo c Photo modified by filter Lighter d The contour of the cross section with centroid (blue dot) (color figure online)

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Figure 4c was then transformed into number array in which every pixel was described by three binary numbers, e.g. white pixel is \(\left\{ 1,1,1 \right\}\), black or almost black pixel is \(\left\{ 0,0,0 \right\}\), etc. Based on this, in each line of pixels, the first and the last non-white pixels were determined, describing the left and right border of the cross-section, which eventually gave the contour (Fig. 4d). Once the contour was identified, the area, the coordinates of the cross-section centroid, the moment of inertia and other geometric quantities could be easily evaluated. Finally, to obtain the actual dimensions of the cross-section, the scale had to be determined by the size of the pixel. In our case, the pixel dimension was 0.1334 mm. The geometric quantities extracted for further analyses were the section modulus of the residual cross-section \(W_{y,\text {r}}\), the width of the residual cross-section \(b_{r}\), avoiding the rounding effect of charring and the height of the residual cross-section \(h_{r}\), determined as the difference between maximum and minimum coordinates of the cross-section in the vertical direction. The lateral and bottom charring depths were then determined as:

$$\begin{aligned} d_{\text {ch,l}}= & {} \frac{b- b_{\text {r}}}{2}, \end{aligned}$$
(1)
$$\begin{aligned} d_{\text {ch,b}}= & {} h- h_{\text {r}}. \end{aligned}$$
(2)

Note that the lateral and bottom charring depths are not the same. In general, when the cross-section width is smaller compared to its height, the bottom charring depth is greater due to the rounding effect of charring. However, standard EN 1995-1-2 simplifies this by introducing a notional charring depth \(d_{\text {ch,n}}\), which is assumed to be constant around the cross-section perimeter, meaning that there is no difference between lateral and bottom charring depths. This simplification is well-suited for quickly estimating the residual cross-section, although it is not physically completely accurate. For comparison with the standard, the notional charring depth was calculated in this study as well. It was determined from the section modulus of the residual cross-section:

$$\begin{aligned} W_{y,\text {r}}=\frac{\left( b-2d_{\text {ch,n}}\right) \left( h-d_{\text {ch,n}}\right) ^2}{6}. \end{aligned}$$
(3)

The section modulus is chosen based on the fact that the specimens were exposed to fire from three sides, which usually applies for elements subjected to bending. For this reason, the section modulus is a more appropriate quantity for determining the notional charring depth.

Numerical model of charring - PYCIF

The model PYCIF (PYrolysis Charring In Fire) is an advanced numerical model developed to predict the charring of timber elements exposed to fire conditions (Pečenko and Hozjan 2021). It couples the phenomena of heat and mass transfer and pyrolysis reaction. The empirical value of the char front temperature in the PYCIF model is not needed, because the charring criterion is physically based (for more details see Pečenko and Hozjan 2021; Pečenko et al. 2023). The equations describing these coupled heat-mass-pyrolysis phenomena consist of three continuity equations describing the conservation of bound water, water vapour and the residual gas mixture (air and pyrolytic gases), energy conservation equations and five equations describing the process of pyrolysis. Mass conservation equations are:

$$\begin{aligned} \begin{array}{ll} \dfrac{\partial c_{b}}{\partial t}=\nabla \cdot {{\textbf {J}}}_{b}+\dot{c},\\ \dfrac{\partial \left( \varepsilon _{g} \tilde{\rho }_{v}\right) }{\partial t}=\nabla \cdot {{\textbf {J}}}_{v}-\dot{c},\\ \dfrac{\partial \left( \varepsilon _{g} \tilde{\rho }_{g}^{*}\right) }{\partial t}=\nabla \cdot {{\textbf {J}}}_{g^{*}}, \end{array} \end{aligned}$$
(4)

energy conservation equation is:

$$\begin{aligned} \rho C \frac{\partial T}{\partial t}=\nabla \cdot (\textbf{k} \nabla T)-\left( \rho C {{\textbf {v}}}\right) \nabla T-\Delta H_{s} \dot{c}-Q, \end{aligned}$$
(5)

and the equations describing pyrolysis reaction are:

$$\begin{aligned} \begin{array}{cc} \dfrac{d \rho _{c}}{d t}=-k_{1} \rho _{c},\\ \dfrac{d \rho _{a c}}{d t}=k_{1} \rho _{c}-\left( k_{2}+k_{3}\right) \rho _{a c}, \\ \dfrac{d \rho _{c h}}{d t}=0.35 k_{2} \rho _{a c},\\ \ \dfrac{d \tilde{\rho }_{g, p}}{d t}=0.65 k_{2} \rho _{a c},\\ \ \dfrac{d \rho _{t}}{d t}=k_{3} \rho _{a c}. \end{array} \end{aligned}$$
(6)

In the system of equations (4), the notations \(c_{b},\ \tilde{\rho }_{v}\) and \(\tilde{\rho }_{g}^{*}\) represent the concentrations of bound water, water vapour and residual gas mixture, respectively. \(\varepsilon _{g}\) is porosity of timber, t is time, J\(^{i} (i=b,v,g^{*})\) are mass fluxes of each moving medium (bound water, water vapour and residual gas mixture) and \(\dot{c}\) is the sorption rate. In Eq. (5), T is temperature (in Kelvins), \(\rho C\) is the heat capacity of timber, k is the diagonal matrix containing thermal conductivities in different directions, \({\textbf {v}}\) is the velocity of gaseous mixture which follows Darcy’s law, \(\Delta H_{s}\) is the latent heat of sorption and Q is the energy sink or release due to the pyrolysis reaction. The system (6) that describes the pyrolysis reaction is based on the Broido-Shafizadeh pyrolysis model (Broido and Nelson 1975; Bradbury et al. 1979), where \(\rho _{c}\), \(\rho _{ac}\), \(\rho _{t}\) and \(\rho _{ch}\) are the densities of cellulose, active cellulose, tar and char, respectively, while \(\tilde{\rho }_{g, p}\) is the concentration of gases formed during pyrolysis reaction. The reaction rates \(k_{i},\ i=1,2,3\) follow the Arrhenius law: \(k_{i} = A_{i}\text {exp}\left( \dfrac{-E_{i}}{R T}\right)\), and govern the production rate of active cellulose (\(i=1\)), char with gasses (\(i=2\)) and volatiles (\(i=3\)). The main parameters describing the reaction rates are scale factors \(A_{i}\) and activation energies \(E_{i}\) (\(i = 1, 2, 3\)).

The boundary conditions prescribed at the contact between the timber body and the surroundings are the following:

$$\begin{aligned} \hspace{0.2 cm} h_{cr}=k\frac{\partial T}{\partial n}, \hspace{0.2 cm} {\textbf {n}}\cdot {\textbf {J}}_{v}=\beta \left( \widetilde{\rho }_{v,\infty }-\widetilde{\rho }_{v}\right) , \hspace{0.2 cm} {\textbf {n}}\cdot {\textbf {J}}_{b}=0, P_{g} = P_{g,\infty }, \end{aligned}$$
(7)

where \(h_{cr}\) is the heat flux due to convection and radiation, \(\widetilde{\rho }_{v,\infty }\) and \(P_{g,\infty }\) are the vapour concentration and the gas pressure in the ambient, respectively, \(\beta\) is the mass transfer coefficient and n is the unit vector normal to the outer surface of timber volume. The initial conditions are:

$$\begin{aligned} T(t=0)=T_{0},\widetilde{\rho }_{v}(t=0)=\widetilde{\rho }_{v,0},c_{b}(t=0)=c_{b,0}, P_{g}(t=0)=P_{g,0}. \end{aligned}$$
(8)

The solution to Eqs. (4–6) together with the boundary conditions and the initial conditions is obtained numerically. The Galerkin type finite element method is utilized and implemented in own developed software in the Matlab environment. Further details about the PYCIF model and the solution procedure can be found in Pečenko and Hozjan (2021).

The charring in the PYCIF model is identified when the final char yield is reached. This charring criterion, which was introduced, described and validated by Pečenko and Hozjan (2021), serves to determine lateral and bottom charring depths. Furthermore, the section modulus of the residual cross-section is calculated to determine the notional charring depth, following the same procedures as outlined in Eq. (3). This time, however, \(W_{y,\text {r}}\) is calculated numerically.

Model parameters

For the numerical analysis, half of the cross-section (symmetry is considered, see Fig. 5) is discretized by 810 finite elements, with a size of 3.3 \(\times\) 3.3 mm\(^{2}\).

Fig. 5
figure 5

Discretization of the cross-section and model parameters for the initial and boundary conditions

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The basic values for initial and boundary conditions are given in Fig. 5. The initial moisture content and the dry density of timber are considered as the average values from the measurements given in Table 1. The specific heat of timber at room temperature is considered according to Czajkowski et al. (2020), while its temperature variation follows the proposal given in EN 1995-1-2. The thermal conductivity of beech (as a function of temperature) is based on the measurements by Kol and Sefil (2011). Other model input data such as the parameters of pyrolysis reaction \(E_{i}\) and \(A_{i}\), specific heat of active cellulose, tar and pyrolytic gases, porosity of timber, relative permeability of gas, permeability of timber, dynamic viscosity of gas, activation energy, universal gas constant, heat of sorption, diffusion coefficients and others can be found in Pečenko et al. (2015) and Pečenko and Hozjan (2021).

Results and discussion

The development of temperatures

The development of temperatures in all TCs installed in the samples is provided individually for samples taken from the furnace after 10 min (Fig. 6), 20 min (Fig. 7) and 30 min (Fig. 8) of fire exposure and is compared against numerically determined temperatures. Firstly, a significant scatter of the experimentally measured temperatures can be observed, a common phenomenon when TCs are installed in pre-drilled boreholes, since it is very difficult to ensure that the boreholes are aligned parallel to the exposed edge. Consequently, it is difficult to precisely position the TC tip, with deviations of 2 mm or more from the intended distance being possible.

Fig. 6
figure 6

Development of temperatures in specimens exposed to fire for 10 min in points a 5 mm b 10 mm and c 15 mm away from the side exposed edge

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Fig. 7
figure 7

Development of temperatures in specimens exposed to fire for 20 min in points a 10 mm b 15 mm and c 20 mm away from the side exposed edge

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Fig. 8
figure 8

Development of temperatures in specimens exposed to fire for 30 min in points a 15 mm b 20 mm and c 25 mm away from the side exposed edge

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In Figs. 6–8 thick black solid lines represent numerically determined temperatures at the anticipated TCs distances from the exposed edge (5, 10, 15 mm etc.). Additionally, temperature developments at positions deviating by \(\pm\) 2 mm from the expected locations are given as light grey shaded areas. For the majority of the measuring positions, numerically determined temperature areas (light grey shaded areas) fit well with the experimentally measured temperatures. However, another notable phenomenon can be observed in the measured temperatures, namely the temperature locking (plateau) at 100 \(^{\circ }\)C. Although this phenomenon has already been observed in the past (Suzuki et al. 2016), and, as described, is a consequence of moisture evaporation, there is no detailed explanation about the real phenomenon that actually takes place. In the case of TCs installed in boreholes, the moisture front that progresses into timber (for a detailed explanation of this phenomenon see Pečenko et al. 2015) causes the accumulation of moisture in the borehole. When the temperature in the borehole reaches 100 \(^{\circ }\)C, moisture starts to evaporate and causes the temperature to plateau during this phase. However, while this temperature locking occurs locally within the borehole, the surrounding solid timber may already exhibit higher temperatures. Although there is no direct evidence for this, the latest experimental studies (Terrei et al. 2021; Fahrni et al. 2018) show, that when the TCs were installed during the gluing procedure of timber samples (and not in boreholes), the temperature locking did not occur. The occurrence of temperature plateau causes some discrepancies between numerically and experimentally determined temperatures. The biggest discrepancies are observed in Figs. 6c, 7c and 8c, specifically at the measuring positions furthest from the exposed edge. Here, temperatures rise more gradually compared to other positions within the same sample. As described above, temperature plateau is a localised phenomenon that cannot explicitly be modelled in the PYCIF model. The PYCIF model describes the heat transfer with a single conservation equation, that simultaneously accounts for both conductive heat transfer within the solid timber volume and convective heat transfer within the pores. Therefore, the “average”temperature of this subsystem (solid and porous) is considered, which is the basis of macro models. In the PYCIF model the effect of moisture evaporation has a global effect on the development of temperatures within the sample, since the energy of evaporation gradually follows the desorption of bound water above the boiling point (Eq. (5)).

The development of charring and charring rates

The development of lateral and bottom charring depths (experimental and numerical) is presented in Fig. 9a and b, respectively. The blue crosses (Exp. single av.) in both figures represent the average charring depths of a single specimen (2 results at 10, 20 and 30 min), obtained based on the 15 cut pieces of each specimen as described in section "Determining cross‑section dimensions and other geometrical characteristics of specimen after fire". For the lateral charring depth, the maximum difference between two measurements occurs for samples taken from the furnace after 30 min of fire exposure, while for the bottom charring depth, this occurs for samples taken out after 10 min of fire exposure. In both cases, the scatter is very small, not exceeding 10 %. The blue line (Exp. tot. av.) in Fig. 9 connects a total average charring depth of two specimens (the average of two blue crosses) at different times (10, 20 and 30 min). During the test it was impossible to visually monitor the time of the onset of charring. It is therefore assumed, that it started immediately after the exposure to fire (at t = 0 min). It is common practice to make this assumption in order to compare the charring rates with those given in EN 1995-1-2, although it is generally acknowledged that the onset of charring is initially delayed (Xu et al. 2015). A nearly perfect alignment is evident when comparing the experimental and numerical development of charring. The only difference arises at the beginning of the fire exposure, where the initial delay in charring occurs in the case of numerical simulation. For both, lateral and bottom side, charring starts around 2.5 min after fire exposure.

Fig. 9
figure 9

Development of a lateral \(d_{\text {ch,l}}\). b bottom \(d_{\text {ch,b}}\) charring depth

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Figure 10 shows the development of notional charring depth, as defined in EN 1995-1-2. The notional charring depth is assumed to be constant around the cross-section perimeter and is determined from the section modulus of the residual cross-section, as described in sections Determining cross‑section dimensions and other geometrical characteristics of specimen after fires and "Numerical model of charring ‑ PYCIF". The rounding effect of charring is taken into account. Consequently, slightly larger values of notional charring depth are found (both experimentally and numerically), compared to the lateral and bottom charring depths, as anticipated. In terms of the comparisons between the experimental and the numerical notional charring depths, a strong agreement is observed. Similar to the lateral and bottom charring, the only discrepancies occur at the beginning of the fire exposure, due to the assumption that charring starts immediately in case of the experimental results. On the other hand, with the PYCIF model, charring begins approximately 2.5 min after fire exposure.

Fig. 10
figure 10

The development of notional charring depth \(d_{\text {ch,n}}\)

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Table 2 gives the charring rates for lateral, bottom, and notional charring. These rates are computed at the same time intervals as when the samples were removed from the furnace, namely 10, 20, and 30 min. Additionally, the mean values of all three charring rates at different times are given.

Table 2 Lateral, bottom and notional charring rates
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For the comparison with the experiment, average (linear) numerical charring rates are given in Table 2, additionally assuming that charring starts at the beginning of fire exposure (t=0). In general, a very accurate agreement between experimental and numerically determined charring rates is discovered. Comparing the mean values, the difference is smaller than 3 % for all cases. Standard EN 1995-1-2 proposes the value of notional charring rate of 0.8 mm/min, a value that closely aligns with both the experimental and the numerically determined average charring rates.

The char front temperature

The char front temperature is determined both experimentally and numerically. Experimentally, it is based on the measured temperatures and charring depth. This procedure is illustrated in Fig. 11 for a sample taken from the furnace after 10 min of fire exposure.

Fig. 11
figure 11

Determination of char front temperature based on the experimental measurement of the temperatures and the charring depth

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The lateral charring depth for this sample (sample no. 1 and measuring position a, see Fig. 2 for labelling) was 6.25 mm. The nearest measured temperatures were from TCs positioned 5 and 10 mm away from the exposed edge (TC10-5(1,a) and TC10-10(1,a)). By using linear interpolation of the temperatures between these two points it was possible to estimate the temperature development at the location of the final charring depth, specifically at a point 6.25 mm away from the exposed edge. The char front temperature was then evaluated as shown in Fig. 11. For this sample and these specific measuring positions, the char front temperature was 347 \(^{\circ }\)C. In the same manner, the char front temperatures for other samples and other measuring positions were assessed and are shown in Fig. 12. In total, there were 18 measuring positions. As observed, significant scatter of the results is identified, with the char front temperatures ranging from approximately 220 \(^{\circ }\)C up to 400 \(^{\circ }\)C. However, these extreme values can be considered outliers, given that the majority of the measurements is condensed between 320 \(^{\circ }\)C and 370 \(^{\circ }\)C.

Fig. 12
figure 12

All measured char front temperatures, the median of all measured char front temperatures, MAD and estimated standard deviation

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A median is used as a robust estimate of the mean char front temperature to eliminate the influence of outliers. The median char front temperature is 353.6 \(^{\circ }\)C, with a median absolute deviation (MAD) of 26.5 \(^{\circ }\)C. Assuming normal distribution of the char front temperature, then the standard deviation determined from the MAD is 39.4 \(^{\circ }\)C. In case of fire design according to the Eurocode standard EN 1995-1-2, the design value of material properties (strength and stiffness) is determined using the 20\(^{\text {th}}\) percentile. If the same principle is applied to the char front temperature, the 20\(^{\text {th}}\) percentile is calculated to be 320 \(^{\circ }\)C. It is worth noting that for beech, both the median and the 20\(^{\text {th}}\) percentile of char front temperature are higher compared to the char front temperature of 300 \(^{\circ }\)C proposed in EN 1995-1-2.

The procedure to determine char front temperature with the PYCIF model is presented in Fig. 13a. This figure represents the decomposition of solids (cellulose and active cellulose) and the formation of char over time of fire exposure at a point 15 mm away from the exposed edge, along with the corresponding temperature at this location. The char front temperature is calculated based on the charring criterion, specifically at the temperature at which the final char yield is reached.

Fig. 13
figure 13

a Procedure to determine the char front temperature based on the results from the PYCIF model b the numerically determined char front temperatures

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In Fig. 13b the char front temperature as a function of distance from the exposed edge is plotted. As outlined in Pečenko and Hozjan (2021), the char front temperature decreases with increasing distance from the exposed edge as a result of a slower temperature increase deeper within the specimen. The median char front temperature, is somewhat lower (313 \(^{\circ }\)C) than the experimental median value, but still exceeds the 300 \(^{\circ }\)C value specified by Eurocode 5.

Based on the experimental and numerical results it was evident, that the char front temperature for beech exceeds the generally proposed value of 300 \(^{\circ }\)C.

Conclusion

The article presents an experimental and numerical analysis of beech samples exposed to a standard temperature-time fire curve. The main emphasis was to examine the hypothesis if the assumption of 300 \(^{\circ }\)C char front temperature is valid for beech. Additionally, various other quantities were explored, including the development of temperatures in beech samples, the development of charring depths and the charring rates. Several conclusions can be drawn from the findings:

  • A considerable scatter of the experimentally measured temperatures in beech samples was observed, a phenomenon often encountered when employing TCs installed in boreholes. This discrepancy arises due to the difficulty in controlling the exact position of the TC tips, which can deviate by as much as 2 mm or more from the intended location. Utilizing the numerical model PYCIF enabled a relatively accurate temperature determination in beech samples compared to the experimental data, taking into account potential deviations in measuring position (up to 2 mm) from the intended location.

  • A temperature plateau at 100 \(^{\circ }\)C was experimentally measured, attributed to the localized moisture evaporation in the borehole. This phenomenon causes some discrepancies between the numerically and experimentally determined temperatures, as the current PYCIF model does not account for this localized effect.

  • Excellent agreement is found between the experimentally and numerically determined lateral, bottom and notional charring depths, as well as charring rates. In addition, both experimentally and numerically determined notional charring rates closely align with the value of notional charring rate proposed in EN 1995-1-2.

  • As for the key findings of the article, the median of the experimentally measured char front temperature was 353.6 \(^{\circ }\)C, with 20\(^{\text {th}}\) percentile of 320 \(^{\circ }\)C. Meanwhile, median for the numerically determined char front temperature was 313 \(^{\circ }\)C. These results indicate that both experimental and numerical investigations yielded char front temperatures exceeding the proposed value of 300 \(^\circ\)C specified in EN 1995-1-2.

  • Future improvements and refinements of the model should incorporate the localized effects of moisture evaporation to achieve more accurate estimations of temperature plateaus in boreholes.