- Email: [email protected]
Procedure for implementing new materials to the component additive method
Fire Safety Journal xxx (2017) 1–12
Contents lists available at ScienceDirect
Fire Safety Journal j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi r e s a f
Procedure for implementing new materials to the component additive method Katrin Nele Ma€ger a, *, Alar Just a, Joachim Schmid b, Norman Werther c, Michael Klippel b, Daniel Brandon d, Andrea Frangi b a
Tallinn University of Technology, Ehitajate Tee 5, 19086 Tallinn, Estonia ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany d RISE Building Technology, 11486 Stockholm, Sweden b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Fire safety design Component additive method Timber structures Fire tests Thermal simulations
The performance of light timber frame wall and floor assemblies in fire depends on their composition. The assemblies' ability to form fire-separations between building compartments (separating function) can be assessed by full-scale fire testing or calculation methods. Calculations are the low cost and more flexible alternative. The component additive method is a commonly used calculation method for fire design of timber structures. The method considers the insulation ability of the material layers present in the assembly. The component additive method described in this article is developed to be flexible to implement different materials and products of different dimensions. However, the amount of different materials currently included in this method is rather limited and there is no generally accepted procedure to implement new materials. This paper presents a common agreement of the procedure to implement new materials which comprises of: (1) the design and execution of model-scale fire tests; (2) determination of the modified thermal properties needed for simulations; (3) thermal simulations of assemblies in fire conditions; (4) development of design equations and; (5) verification by one or more full-scale fire test(s). The abovementioned steps have been clearly presented in this paper and supported by examples.
1. Introduction The component additive method is used for fire resistance design of structures for insulation criteria and for calculating the start time of charring of load-bearing timber elements protected by claddings and other materials, exposed to ISO 834 standard fire [1]. Component additive methods have been developed in the UK [2], Canada [3] and Sweden [4]. The common feature of these methods is that the fire resistance of a structure is determined by the contribution of each layer. The current EN 1995-1-2 [5] details a method based on the Swedish component additive method. The component additive method in the current version of EN 1995-12 [5] includes basic material groups: wood based boards, gypsum boards and mineral wool. It was improved and extended to be applicable to timber structures consisting of multiple layers of gypsum plasterboards, wood panels, mineral wools and their combinations [6], and to permit the implementation of new building materials or products. The improved
component additive method is published in the European technical guideline Fire Safety in Timber Buildings [7] and has been proposed for the revised European design standard EN 1995-1-2 for timber structures exposed to fire. The possibility of adding new materials and products makes this method more comprehensive. The implementation of new materials is based on experimental results and thermal simulations which can be performed using any finite element (FE) software capable of performing a heat transfer analysis. The materials are described by their temperaturedependent thermal properties – thermal conductivity, specific heat and density which shall be known at a large range of temperatures. Test methods (e.g. thermo-gravimetric analysis and transient plane source method) are available for measuring the thermal properties of materials. Due to the complex phenomena occurring in fire and the limitations of material testing, the thermal properties might need to be changed (calibrated) [5] to better describe the real behaviour of the materials under fire exposure. To investigate the behaviour of the material and
* Corresponding author. E-mail address: [email protected] (K.N. M€ager). https://doi.org/10.1016/j.firesaf.2017.09.006 Received 19 April 2017; Received in revised form 8 August 2017; Accepted 18 September 2017 Available online xxxx 0379-7112/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: K.N. M€ager, et al., Procedure for implementing new materials to the component additive method, Fire Safety Journal (2017), https://doi.org/10.1016/j.firesaf.2017.09.006
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
provide a basis for calibration, some model-scale fire tests are needed (see chapter 3.1). The model-scale test configurations were suggested in Ref. [6] and further developed in Refs. [8] and [9]. Recently, an analytical calibration procedure for obtaining the effective thermal properties of the materials was proposed in Refs. [9,10]. It should be noted that the implementation of new materials into the method shall be verified by full-scale fire tests according to [11]. The fire resistance time based on the calculation method should be shorter compared to full-scale test results. Currently, none of the European standards describe the procedure of developing product-specific equations to be used with the improved component additive method. This paper presents a proposal for the implementation procedure of new building materials to be used in combination with the component additive method. The aim is to present a clear and easy-to-use general procedure so that the component additive method would be open for all types of materials that might be of interest. The component additive method is only applicable to assess the fire performance of timber frame assemblies against insulation criteria related to the ISO 834 standard fire. Predictions of integrity failure of elements of the assembly, such as the fall-off of gypsum boards, can only be based on full-scale standard fire tests, because calculations are still very complex (crack-formation, dynamics of hot gases, etc.). For example, premature integrity failure may occur due to sudden failure of claddings or opening of gaps, which often is dependent on the construction details such as fixings. However, extensive experience of fullscale testing of timber frame assemblies permitted to define some rules about detailing of timber frame assemblies that have been included for example in EN 1995-1-2 [4]. Thus, the integrity criterion may be assumed to be satisfied if the insulation criterion has been satisfied and panels remain fixed to the timber structure on the unexposed side [12].
line with the insulation requirements set in the standard EN 13501-2 [14]. The temperature limitation on the fire-unexposed surface of the structure should prevent the ignition of nearby objects. The fire resistance tins of the timber assembly is the sum of the contributions from the different layers as shown in (1) (layer naming according to Fig. 1).
tins ¼
i¼n1 X
tprot;i þ tins;n
(1)
i¼1
where. tins is the total fire resistance of the assembly [min]; tprot;i is the protection time of the layer i [min]; tins;n is the insulation time of the last layer of the assembly on the unexposed side [min]. The protection and insulation times of the material layer can be calculated taking into account the basic values of the layers, the position coefficients and joint coefficients by Equations (2) and (3).
tprot;i ¼ tprot;0;i ⋅kpos;exp;i ⋅kpos;unexp;i þ Δti ⋅kj;i
(2)
tins;n ¼ tins;0;n ⋅kpos;exp;n þ Δtn ⋅kj;n
(3)
where
tprot;i is the protection time of layer i [min]; tins;n is the insulation time of layer n [min]; tprot;0;i is the basic protection time of the layer i [min]; tins;0;n is the basic insulation time of the layer n [min]; kpos;exp is the position coefficient that takes into account the influence of layers preceding the considered layer []; kpos;unexp is the position coefficient that takes into account the influence of layers backing the considered layer []; Δt is the correction time for layers protected by fire improved protective boards (for example gypsum plasterboards, Type F according to EN 520 [15] or gypsum fibreboards according to EN 15283-2 [16]) [min]; kj is the joint coefficient [].
2. Improved component additive method The improved component additive method takes into account the contributions of each layer considering different possible heat transfer paths through the structure. In all known fire tests of timber frame assemblies, for example [13], the heat transfer path through the cavity insulation layer is prevalent. See also Fig. 2. The layers fulfil different functions (Fig. 1). The last layer of the assembly on the fire-unexposed side serves an insulating function (insulation time) while the previous layers have a protective function (protection time). These functions are defined by different temperature criteria on the fire-unexposed side of the considered layer. The protection time tprot,i is the time until the temperature rise on the fire-unexposed side of the considered layer is (1) 250 K on average or (2) 270 K at any point. Ambient conditions are usually 20 C, hence the temperature criteria become 270 C and 290 C, respectively. These criteria are approximations to account for the failure of thermally degraded material layers. They are also close to the charring temperature of timber (300 C) [5]. Therefore, the sum of protection times of the layers preceding the timber elements may be used as a slightly conservative value for starting time of charring. The insulation time tins,n of the last layer of the assembly is the time until the temperature rise on the fire-unexposed side is equal to 140 K on average over the whole area and 180 K at any point. These criteria are in
The coefficients and basic values are dependent on the material of the investigated layer and the influence of the preceding and backing layers. These values are presented in Refs. [7] and [18] based on the work of [6]. A comparison of full-scale fire test results and calculations (of the same configurations) according to the component additive method are shown in Fig. 3 [6,9]. The presented test configurations consisted of a wide variety of combinations of materials. From this it was concluded that the design method is conservative. The calculations tend to be more conservative for longer fires. 3. Procedure for adding new materials The addition of new materials and products to the improved component additive method requires the determination of the previously mentioned coefficients and values. The general steps to be taken are in the following order: 1. Estimation of initial thermal properties at elevated temperatures, e.g. using thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC) and transient plane source (TPS) methods. 2. Model-scale fire tests. 3. Thermal simulations with initial properties and comparison with model-scale fire test data. 4. Determination of the effective thermal properties. 5. Thermal simulations and comparison with model-scale fire test data.
Fig. 1. Numbering and function of the layers in a timber frame structure. 2
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
test methods can be used to develop an understanding of the thermal and physical behaviour of the material under investigation. Among the most widely used material testing methods are the thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC) and transient plane source (TPS) methods. Thermal properties of the materials should be measured at elevated temperatures usually up to 1200 C. The real behaviour of materials in fire should be investigated with fire tests according to [11]. Model-scale tests allow observing the heat transfer through the specimen and, to a limited extent, the physical changes in a material. Full-scale tests give the most complete picture of the behaviour of the material in fire. Performing a variety of tests allows for observing the different reactions of the material to heating, and therefore obtaining a more complete understanding of the material. During fire tests, temperature measurements are recorded at characteristic locations using type K thermocouples. It should be noted that a 19-mm thick wood particleboard as the backing layer of the assembly is recommended in Ref. [6]. However, the board could also be replaced with other wood-based boards with well-known thermal properties. In the following, the model-scale test specimen configurations proposed for cladding and insulation materials are presented. Most materials can be sorted to one of these groups based on common end-use scenarios. In the specimens where insulation is present, the full thickness of the cavity shall be filled with insulation and its proper fixation shall be ensured throughout the whole duration of the test. Available tests shall cover the variety of thicknesses and densities (if relevant) for which the equations will be derived.
Fig. 2. Thermal image taken of the unexposed side of a model-scale test with an unprotected insulation material filling the whole cavity. Lighter areas are cavities with insulation that show higher temperatures than the timber beam in the middle.
3.2. Claddings In order to determine the equations for claddings, a series of tests with claddings directly exposed to fire and at least one test with insulation behind the cladding shall be provided. The number of fire tests depends on the type of the cladding (thickness, density, etc.) to be assessed. The fall-off of the investigated cladding must not occur due to inadequate fixation. An example of the model-scale fire test specimen with the position of the thermocouples (TC) to obtain the necessary temperature measurements is shown inFigs. 4 and 5. The insulation material used in the cavities should meet the following recommendations: Recommended thickness 100 mm or more. Non-combustible, melting temperature 1000 C. Fixed in place during the post-protection phase. Typically, a stone wool insulation with density around 30 kg/m3 should be used. 3.3. Insulation materials In order to determine the equations for insulation materials, a series of tests with insulation materials directly exposed to fire and at least one test with insulation protected by a cladding (e.g. gypsum board) shall be provided. The fixation of the insulation material shall be guaranteed until the end of the fire test. Fall-off of the cladding should occur when the protection time of the cladding is reached (i.e. the temperature rise on the fire-unexposed side of the cladding is 250 K on average or 270 K at any point). The number of fire tests depends on the type of the insulation material (thickness, density, etc.) to be assessed. An extrapolation to other thicknesses is generally not possible. Interpolation between thicknesses and densities assessed is generally possible. An example of the model-scale fire test specimen with the position of the thermocouples (TC) to obtain the necessary temperature measurements is shown in Figs. 4 and 6.
Fig. 3. Comparison of calculated fire resistances and full-scale test results from Ref. [6] with data points added from Ref. [9]. Number of layers is denoted by n.
6. Step-by-step thermal simulations for developing design equations. 7. Validation of equations with full-scale tests. The aforementioned steps are mostly taken one after the other. Therefore, care shall be taken to obtain results as accurate as possible in each step. Otherwise the cumulative error increases. In the following sections, the determination of the background information and input for the simulations is described. 3.1. a. Experiments Adding new materials to the method is based on test data. Different 3
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 4. Plan of model-scale test specimen viewed from the fire exposed side showing thermocouple locations.
Fig. 5. Cross-section of model-scale test specimens for claddings.
Measured thermal properties may not be directly applicable to all thermal simulations. This is due to two main reasons which will be discussed in the following. Firstly, the majority of fire tests are performed following the ISO 834 standard fire curve [1]. Existing material testing equipment is not capable of following the temperature rise of the standard fire curve. Additionally, it has been proven that the way of heating influences the heat transfer through the material and therefore the measured material characteristics as well [17]. This means that in order to accurately simulate the tested configurations, the thermal properties of the materials need to be modified [5]. Secondly, some simplifying assumptions have been made during the development of thermal simulation software used for analysing structures at elevated temperatures. This means, for example, that in the simulations heat is transferred in the structure only by conduction since most construction elements are made of solid materials. Effects like mass transport, cracking etc. shall be considered separately in the simulation
3.4. Thermal simulations Thermal simulations are used for developing the design equations by following a systematic simulation program described in detail in chapter 4. Any FE software which allows the modelling of the thermal heat transfer in building structures subjected to fire can be used to perform the necessary thermal analyses. The thermal simulation software usually require thermal conductivity, specific heat and density at elevated temperatures as input for describing the material. The latter can be shown to have a lesser effect on the results of the simulations. For the use in thermal simulations, the material properties shall be known at different temperatures (usually between 20 and 1200 C). No precise requirements can be made for the specific temperature points where thermal properties shall be determined. The necessity depends on the material and the thermo-chemical reactions it goes through at different temperatures.
4
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 6. Cross-section of test specimens for insulation.
reference for the calibration of thermal material properties. The test data must not include the mechanical fall-off of the investigated material nor be influenced by the excessive thermal degradation of the fixation of the investigated material (e.g. insulation failure due to the charring of timber battens). A few different approaches for finding the thermal properties are possible (as presented in Refs. [8–10]). This paper does not limit the methodology used to obtain the effective thermal properties of materials as long as they are applicable to the standard fire curve. A possible analytical approach for finding (calibrating) the effective thermal properties introduced by Refs. [9,10] corresponding to a relevant temperature range, is based on rather simple principles. The mathematical analysis software changes the input value (e.g. thermal conductivity) at a single temperature by a set percentage. Then, the difference between the simulated and tested time-temperature curves can be calculated (for example, as the residual sum of squares). This is repeated to find the thermal properties at different temperatures that yield temperature predictions that highly correspond with the experimental measurements. As the thermal properties will change as the heat propagates, the properties found are temperature dependent (Fig. 8). Visual evaluation of the fit of the simulated curve should (also) be used. In the context of fire safety engineering of timber structures, the fitting of characteristic temperatures of 160 C and 270 C is most important. It is recommended that the simulation results at these temperatures not differ from the tests by more than a few minutes. This ensures the (effective) thermal properties used to obtain the simulation curve are precise enough to be used as the basis for developing the equations. See also Fig. 7. Finally, the effective thermal properties are used to simulate the different test setups tested in standard fire. A comparison of the results should be made with the thermocouple readings from the fire tests. If all simulations show shorter or equal time to reach the characteristic temperatures (160 C and 270 C), then the thermal properties developed by calibration are declared to be effective. The effective (calibrated) thermal properties of the material can be used in thermal simulations which may be used as an advanced
approach. Therefore, for some materials (e.g. insulation materials and wood) the calculation is an approximation. On the surfaces, heat is exchanged with the environment via convection and radiation. These phenomena are taken into account by specifying the appropriate coefficients (general values for emissivity and convection coefficient are presented in EN 1991-1-2 [5]). Temperature calculations within solid materials are based on the Fourier equation [18]. The Fourier equation describing one-dimensional conduction, which is necessary in this case, is presented in Equation (4).
k
∂2 T ∂T ∂T k ∂T ¼ cρ ⇒ ¼ ⋅ 2 ∂t ∂t cρ ∂ x ∂2 x
(4)
where T is the temperature [K]; xis the coordinate in the direction of heat transfer [m]; k is the thermal conductivity [W/(mK)]; ρis the density [kg/m3]; c is the specific heat [J/(kgK)]; t is time [s]. From Equation (4) it can be seen that the thermal conductivity is divided by the product of specific heat and density. This means that theoretically only one of these values needs to be calibrated to fit test data if there is sufficient certainty in the values of the other components. The limitations of software and testing equipment create a need for modifying the measured thermal properties. The term effective thermal properties refers to the (measured) properties of the material that have been modified (calibrated) to cater to the ISO 834 standard fire curve. A procedure for obtaining these properties is described in the next subchapter. 3.5. Calibration of thermal properties The thermocouple readings from model-scale fire tests are the 5
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 7. a: Comparison of tested and calibrated time-temperature curves for gypsum boards. b: Configuration of the tested and simulated specimen.
suitable equations derived by fitting a trend line to the simulation points, see Fig. 9. The following figure shows an example where the linear fit is most appropriate. The important thing to notice is that the simulation results are conservative compared to fire test data and that the proposed linear function is in good agreement with simulated data points.
calculation tool for fire design of timber structures. Additionally, these effective thermal material properties are used in the subsequent steps to determine the design equations, as presented in the following section. 4. Determination of the design equations The procedure of determining the design equations was developed by Schleifer [6] and further improved in this study. The determination of the design equations is based on thermal FE simulations. Finite element simulation software use the effective thermal properties as the means of describing the material behaviour in fire. Materials can be divided into three general groups: (1) fire rated claddings, (2) combustible claddings, and (3) insulation materials. The simulations needed for those groups differ slightly as presented in Table 1. In the following, the development of these equations (times and coefficients) is described.
4.3. Position coefficients
4.2. Development of basic protection times
Position coefficients consider the influence of the layers behind (backing layer) and before (preceding layer) the considered layer. For the development of position coefficients, a system of FE simulations and configurations is needed (see Table 1). The position coefficient kpos,exp takes into account the effect of the preceding layer (in the direction of heat flow) on the investigated layer. The effect is depending on the sum of the protection times of all preceding layers. The investigated layer is initially protected by a layer of massive timber (ρ ¼ 450 kg/m3) or stone wool (densities 30 and 90 kg/ m3) with a thickness of 10–50 mm varied in 10 mm increments. To develop the equations for kpos,exp, the simulation results might need to be expressed through different terms to fully investigate the character of the curves and the dependencies of the values on different characteristics (e.g. basic protection times, thickness, etc.). This can be done by plotting the position coefficients against the protection times, thickness and/or density or other factors. See chapter 4.3.2 for an example of the development of the position coefficients. The coefficient kpos, unexp takes into account the effect of the backing layer on the layer under investigation. It is recommended that the developed equations are within 5% of the simulation points at any given thickness or other parameter. This criterion is the required accuracy as the resulting equations shall reflect the simulation results rather closely in order for them to be acceptable altogether.
The basic protection time tprot,0,i is the time from the start of standard fire exposure until the temperature rise on the unexposed side of the material layer reaches 250 K on average. This is taken to be the time when the material has thermally degraded and has lost its protective function. Similarly to the basic insulation times, the available tested thicknesses and densities shall be simulated. The basic protection time of the investigated layer shall be developed based on the FE simulations of configuration 2 shown in Table 1. Then, the times from the start of standard fire exposure until the temperature criterion is reached are plotted against thickness (and/or density) and
4.3.1. Position coefficient kpos,exp,n The position coefficient kpos,exp,n is used when the investigated layer n is the last layer on the fire unexposed side. The temperature rise criterion for the last layer is 140 K on average over the whole area of the unexposed side. The position coefficient kpos,exp,n is developed from simulations of configuration 3 in Table 1. The time when the temperature behind the protection layer reaches 270 C is recorded (t1 ¼ tprot,1) and the simulation is continued without the protection layer which is considered to have fallen off. When the temperature on the unexposed side of the investigated material layer
4.1. Development of basic insulation times The basic insulation time tins,0,n describes the time (from the start of the fire exposure) to reach the temperature rise of 140 K on the unexposed side of the investigated layer. It corresponds to the fire resistance of a single layer without the influence of the adjacent materials. The basic insulation time of the investigated layer is developed based on the FE simulations of configuration 1 shown in Table 1. Simulations shall be conducted for different thicknesses and densities if applicable. Based on the results of the simulations, the times from the start of standard fire exposure until the temperature rise criterion is reached are plotted against thickness (and/or density) and suitable equations derived to approximate the simulation results and fire test results. For the range of thicknesses and densities of interest fire test results shall be available.
6
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 8. Thermal properties (a: thermal conductivity; b: specific heat; c: change in density) used for obtaining results shown in Fig. 7a.
reaches 160 C the simulation is ended and the time recorded as (t2). The position coefficient is calculated as shown in equation (5):
kpos;exp;n ¼
tins;2 tins;0;2
(See analogous procedure shown in the next chapter).
(5)
4.3.2. Position coefficient kpos,exp,i The position coefficient kpos,exp,i can be developed from simulations of configuration 4 shown in Table 1. Initially, the setup shown shall be simulated until the temperature between the preceding layer and the investigated layer reaches 270 C and the time is recorded as t1 (¼tprot,1). After that, the preceding layer is removed and the simulation continued. When the temperature behind the investigated layer reaches 270 C the simulation will be stopped and the time recorded as t2. The formula for calculating the position coefficient is given in Equation (6):
where tins,2 is the insulation time of layer 2, calculated as t2 - t1 [min]; tins,0,2 is the basic insulation time of layer 2 [min]. Due to the different thicknesses of the preceding layer, the fall-off of these layers occurs at different times. The position coefficients can be represented graphically in order to provide a formula for the coefficient. 7
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Table 1 Simulation program.
8
K.N. M€ ager et al.
kpos;exp;i ¼
tprot;2 tprot;0;2
Fire Safety Journal xxx (2017) 1–12
The formula(s) for the calculation of the position coefficient shall be derived by expressing the dependencies through different factors. For example, from Fig. 10 a clear dependency of the position coefficient on the thickness of the investigated material can be seen. Thickness and basic protection time of the investigated material are in correlation with each other. Therefore, the position coefficient values can be expressed through the quotient of the basic protection time of the investigated layer and the sum of protection times of preceding layers (simplified here as one layer of varying thickness of timber or stone wool). The Equation (7) is for the determination of position coefficient kpos,exp,i for the example shown in Fig. 10.
(6)
where tprot,2 is the protection time of layer 2, calculated as t2-t1 [min]; tprot,0,2 is the basic protection time of layer 2 [min]. Fig. 10 shows an example with gypsum plasterboards. The points on the graph are the position coefficients obtained from simulations with different protection times of the preceding layer. A clear dependency on the thickness of the investigated layer can be seen.
9
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 9. Example of a comparison of simulation results (configuration 2 in Table 1) compared with results of model-scale fire tests with the same configurations and the developed formula. Example is based on an insulation material known to the authors.
Fig. 10. Position coefficient values from simulations with an investigated gypsum plasterboard with timber as the preceding layer.
kpos;exp;i
P 8 X tprot;0;i tprot;i1 > > if tprot;i1 < 1 0; 3 ⋅ > < hi 2 ¼ b X > t tprot;0;i > > : a⋅ Pprot;0;i if tprot;i1 2 tprot;i1
4.3.3. Position coefficient kpos,unexp,i In Ref. [6], the value of the position coefficient kpos, unexp,i for different materials backed by cladding materials is given as 1.0. A simulation of configuration 5 presented in Table 1 is needed where the investigated material is backed by 60 mm of stone wool (density 30 kg/m3). The time required for the temperature to reach 270 C between the materials is recorded as tprot,1. The position coefficient kpos, unexp,i is calculated according to Equation (8):
(7)
where a ¼ 0; 5 þ 0; 026 ⋅ b ¼ 0; 8 0; 185
tprot;0;i hi . t g prot;0;i hi .
kpos;unexp;i ¼
hi is the thickness of the investigated board [mm]. The grey curves in Fig. 11 are obtained from Equation (7). The equations describe the simulation points rather well (difference at any point is less than 4%), however, for most applications the equation might be too complex. Simplifications are allowed as long as the equation results are within 5% of the simulation points.
tprot;1 tprot;0;1
(8)
If different densities and/or thicknesses of the investigated material are available, the coefficient shall be expressed as a function of these factors. 4.4. Joint coefficient kjoint The coefficients for the joint configurations consider the detail of the 10
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 11. Position coefficients from Equation (7) compared with simulation results.
layer reaches T2 ¼ 160 C (for Δtn) or T2 ¼ 270 C (for Δti). The time is recorded as tTf,160 or tTf,270. A proposed alternative approach [19] involves the fall-off times instead of fall-off temperatures. The fall-off time tf can be determined by full-scale fire testing according to EN 13381-7 [20]. With this approach, the protective layer is removed from the assembly at time tf. Then the simulation is continued until the temperature behind the protected layer reaches 160 C or 270 C. These times are recorded as ttf,160 or ttf,270. The rest of the procedure is analogous. To develop the formulas the results are plotted on a graph with the axes being the correction time and the basic insulation or protection time of the backing layer. The correction times Δtn and Δti for graphs are calculated as shown in Equations (11) and (12).
joints and their influence on the insulation or protection time. Joint coefficient should be taken into account for layers on the unexposed side with joints or for layers that have a void cavity behind. Joint coefficient shall be determined by fire tests comparing test configurations with and without joints.
kjoint ¼
tins;joint;n tins;n
(9)
kjoint ¼
tprot;joint;i tprot;i
(10)
tins, joint,n is the insulation time of layer n with joints [min]; tprot, joint,i is the protection time of layer i with joints [min]. Currently a simple collection of tabulated values is presented in Ref. [7]. 4.5. Correction time Δt
Δtn ¼ tTf;160 t270;160
(11)
Δti ¼ tTf;270 t270;270
(12)
Correction times should be derived for any material that can be used as a fire improved cladding.
Fire improved protective boards (e.g. gypsum plasterboard type F acc. to EN 520 [15]) have been observed to stay in place longer than the criteria for protection time (270 C). In order to take this effect into account, the fall-off temperature is assumed to be higher in the simulations. For example, in the case of gypsum boards the failure temperatures are assumed to be Tf ¼ 600 C for wall assemblies and Tf ¼ 400 C for floor assemblies (ceilings) or higher if more precise data from full-scale fire tests for gypsum boards is available. In order to account for the longer protection in the calculation of insulation time of the structure, a correction time Δt is added to the layer preceded by the fire improved protective board. The correction time Δtn for the last layer and Δti for the other layers are derived from simulations of configuration 6 shown in Table 1. Materials behind the investigated fire improved board are generalised and represented by timber (ρ ¼ 450 kg/m3, representing cladding materials) and stone wool (ρ ¼ 30 and 90 kg/m3, representing insulation materials). If correction times are needed for other preceding materials then the same approach shall be taken and the values determined separately. Firstly, the simulation is run until the temperature behind the fire protective layer reaches T1 ¼ 270 C and the protective board is removed. Then, the simulation is continued until the temperature behind the backing layer reaches T2 ¼ 160 C (for Δtn) or T2 ¼ 270 C (for Δti). The time is recorded as t270,160 or t270,270. The next simulation is run with the same initial configuration, but the board is kept in place until the temperature reaches fall-off temperature T1 ¼ Tf. After removing the board, the simulation is continued until the temperature behind the backing
5. Verification by full-scale fire tests It is strongly recommended that the verification of the developed equations is done based on a few full-scale fire tests. The duration of the
Fig. 12. Configuration of the full-scale test specimen used as the verification example. 11
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
paper. With this method the verification of the separating function (insulation and integrity criteria) of timber frame assemblies is nowadays usually performed. The procedure is based on model-scale fire tests and extensive thermal simulations with the effective thermal properties. The equations are derived on the basis of simulation results and verified by full-scale fire tests. Acknowledgements The authors acknowledge the network of COST Action FP1404 for the contribution of the Task Group 5 within the Working Group 2 “Structural Elements made of bio-based building materials and detailing”. This work was supported by the start-up research grant PUT794 “Effect of protective materials on the fire performance of timber structures” (2015-2018) financed by the Estonian Research Council. References [1] International Organization for Standardization, ISO 834-1:1999, Fire-resistance Tests - Elements of Building Construction - Part 1: General Requirements, 1999. [2] BSI, British Standard BS 5268–4, Structural Use of Timber - Section 4.2, Recommendations for calculating fire resistance of timber stud walls and jousted floor constructions, 1990. [3] NRCC, National Building Code of Canada, vol. 2, 2005. [4] J. Noren, Additionsmetoden - Ber€akning Av Brandmotstånd Hos Avskiljande V€aggar, 1994. Stockholm. [5] CEN, EN 1995-1-2:2004 Eurocode 5: Design of Timber Structures - Part 1-2: General - Structural Fire Design, 2004. [6] V. Schleifer, Zum Verhalten von raumabschliessenden mehrschichtigen Holzbauteilen im Brandfall, ETH Zürich, 2009, http://dx.doi.org/10.3929/ethz-a005771863. € [7] B. Ostman, E. Mikkola, R. Stein, A. Frangi, J. K€ onig, D. Dhima, T. Hakkarainen, J. Bregulla, Fire Safety in Timber Buildings, SP Technical Research Institute of Sweden, Stockholm, 2010. [8] R. Breu, Improved Component Additive Method for the Separating Function Development of a Testing and Calculation Procedure, ETH Zürich, 2016. [9] K.N. M€ager, Implementation of New Materials to the Component Additive Method for Fire Design of Timber Structures, Tallinn University of Technology, 2016. [10] K.N. M€ager, D. Brandon, A. Just, Determination of the effective material properties for thermal simulations, in: R. G€ orlacher (Ed.), Int. Netw. Timber Eng. Res. Meet. 49, Graz, Austria, August 2016, Timber Scientific Publishing, Karlsruhe, 2016, pp. 397–400. [11] CEN, EN 1363-1:2012 Fire Resistance Tests. General Requirements, 2012. [12] A. Frangi, V. Schleifer, M. Fontana, Design model for the verification of the separating function of light timber frame assemblies, Eng. Struct. 32 (2010) 1184–1195. [13] A. Just, Full-scale Fire Tests of Timber Frame Walls, Tallinn, 2009. [14] CEN, EN 13501-2:2016 Fire Classification of Construction Products and Building Elements, Classification using data from fire resistance tests, excluding ventilation services, 2016. [15] CEN, EN 520:2004 Gypsum Plasterboards - Definitions, Requirements and Test Methods, 2004. [16] CEN, EN 15283-2:2008 Gypsum Boards with Fibrous Reinforcement, Definitions, requirements and test methods - Part 2: Gypsum fibre boards, 2008. [17] G.K. Semitelos, I.D. Mandilaras, D.A. Kontogeorgos, M.A. Founti, Simplified correlations of gypsum board thermal properties for simulation tools, Fire Mater. 40 (2016) 229–245, http://dx.doi.org/10.1002/fam.2282. [18] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, seventh ed., John Wiley & Sons, 2011. [19] K.N. M€ager, A. Just, A. Frangi, D. Brandon, Protection by fire rated claddings in the component additive method, in: Int. Netw. Timber Eng. Res. Meet. 50, Kyoto, Japan, August 2017, 2017. [20] CEN, EN 13381-7:2002 Test Methods for Determining the Contribution to the Fire Resistance of Structural Members - Part 7: Applied Protection to Timber Members, 2002. [21] K.N. M€ager, Implementation of New Materials to the Component Additive Method for Fire Design of Timber Structures, vol. 71, SP Rapport, 2016, p. 2016.
Fig. 13. Comparison of protection times of each layer from one full-scale fire test and calculations of the same setup of the configuration shown in Fig. 12. Table 2 Comparison of fire resistance times from a full-scale fire test and calculations of the configuration shown in Fig. 12. Layer no
Material
1 2 3 4 5 6
Gypsum 1 Gypsum 1 Glass wool 1 Glass wool 2 Gypsum 1 Gypsum 1
a
Time to reach 270 C (160 C for last layer) behind layer tprot (tins) [min] Calculation
Full-scale test
31,0 67,2 78,5 80,0 89,7 (112,1)
32 68 n.aa 111 n.aa (147)
Was not measured.
test is required to cover the validity of the derived equations in standard fire. The calculated fire resistance times of each layer shall be equal or shorter than the same times obtained from full-scale fire tests. An example of a full-scale fire test (see section 7.3. in Ref. [21]) used for the verification of equations derived for a fire resistant gypsum plasterboard product (type F according to [15]) is shown in Fig. 12. The examples in Fig. 13 and Table 2 show comparisons of test results and calculated values. The design equations used for the gypsum layers are developed from calibrated effective thermal properties. The biggest differences between experimental and calculated results can be found to originate from insulation layers (3 and 4) which are considered more conservatively. 6. Conclusions A common procedure for the implementation of new materials to use with the component additive method is proposed by authors of this
12
Contents lists available at ScienceDirect
Fire Safety Journal j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi r e s a f
Procedure for implementing new materials to the component additive method Katrin Nele Ma€ger a, *, Alar Just a, Joachim Schmid b, Norman Werther c, Michael Klippel b, Daniel Brandon d, Andrea Frangi b a
Tallinn University of Technology, Ehitajate Tee 5, 19086 Tallinn, Estonia ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany d RISE Building Technology, 11486 Stockholm, Sweden b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Fire safety design Component additive method Timber structures Fire tests Thermal simulations
The performance of light timber frame wall and floor assemblies in fire depends on their composition. The assemblies' ability to form fire-separations between building compartments (separating function) can be assessed by full-scale fire testing or calculation methods. Calculations are the low cost and more flexible alternative. The component additive method is a commonly used calculation method for fire design of timber structures. The method considers the insulation ability of the material layers present in the assembly. The component additive method described in this article is developed to be flexible to implement different materials and products of different dimensions. However, the amount of different materials currently included in this method is rather limited and there is no generally accepted procedure to implement new materials. This paper presents a common agreement of the procedure to implement new materials which comprises of: (1) the design and execution of model-scale fire tests; (2) determination of the modified thermal properties needed for simulations; (3) thermal simulations of assemblies in fire conditions; (4) development of design equations and; (5) verification by one or more full-scale fire test(s). The abovementioned steps have been clearly presented in this paper and supported by examples.
1. Introduction The component additive method is used for fire resistance design of structures for insulation criteria and for calculating the start time of charring of load-bearing timber elements protected by claddings and other materials, exposed to ISO 834 standard fire [1]. Component additive methods have been developed in the UK [2], Canada [3] and Sweden [4]. The common feature of these methods is that the fire resistance of a structure is determined by the contribution of each layer. The current EN 1995-1-2 [5] details a method based on the Swedish component additive method. The component additive method in the current version of EN 1995-12 [5] includes basic material groups: wood based boards, gypsum boards and mineral wool. It was improved and extended to be applicable to timber structures consisting of multiple layers of gypsum plasterboards, wood panels, mineral wools and their combinations [6], and to permit the implementation of new building materials or products. The improved
component additive method is published in the European technical guideline Fire Safety in Timber Buildings [7] and has been proposed for the revised European design standard EN 1995-1-2 for timber structures exposed to fire. The possibility of adding new materials and products makes this method more comprehensive. The implementation of new materials is based on experimental results and thermal simulations which can be performed using any finite element (FE) software capable of performing a heat transfer analysis. The materials are described by their temperaturedependent thermal properties – thermal conductivity, specific heat and density which shall be known at a large range of temperatures. Test methods (e.g. thermo-gravimetric analysis and transient plane source method) are available for measuring the thermal properties of materials. Due to the complex phenomena occurring in fire and the limitations of material testing, the thermal properties might need to be changed (calibrated) [5] to better describe the real behaviour of the materials under fire exposure. To investigate the behaviour of the material and
* Corresponding author. E-mail address: [email protected] (K.N. M€ager). https://doi.org/10.1016/j.firesaf.2017.09.006 Received 19 April 2017; Received in revised form 8 August 2017; Accepted 18 September 2017 Available online xxxx 0379-7112/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: K.N. M€ager, et al., Procedure for implementing new materials to the component additive method, Fire Safety Journal (2017), https://doi.org/10.1016/j.firesaf.2017.09.006
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
provide a basis for calibration, some model-scale fire tests are needed (see chapter 3.1). The model-scale test configurations were suggested in Ref. [6] and further developed in Refs. [8] and [9]. Recently, an analytical calibration procedure for obtaining the effective thermal properties of the materials was proposed in Refs. [9,10]. It should be noted that the implementation of new materials into the method shall be verified by full-scale fire tests according to [11]. The fire resistance time based on the calculation method should be shorter compared to full-scale test results. Currently, none of the European standards describe the procedure of developing product-specific equations to be used with the improved component additive method. This paper presents a proposal for the implementation procedure of new building materials to be used in combination with the component additive method. The aim is to present a clear and easy-to-use general procedure so that the component additive method would be open for all types of materials that might be of interest. The component additive method is only applicable to assess the fire performance of timber frame assemblies against insulation criteria related to the ISO 834 standard fire. Predictions of integrity failure of elements of the assembly, such as the fall-off of gypsum boards, can only be based on full-scale standard fire tests, because calculations are still very complex (crack-formation, dynamics of hot gases, etc.). For example, premature integrity failure may occur due to sudden failure of claddings or opening of gaps, which often is dependent on the construction details such as fixings. However, extensive experience of fullscale testing of timber frame assemblies permitted to define some rules about detailing of timber frame assemblies that have been included for example in EN 1995-1-2 [4]. Thus, the integrity criterion may be assumed to be satisfied if the insulation criterion has been satisfied and panels remain fixed to the timber structure on the unexposed side [12].
line with the insulation requirements set in the standard EN 13501-2 [14]. The temperature limitation on the fire-unexposed surface of the structure should prevent the ignition of nearby objects. The fire resistance tins of the timber assembly is the sum of the contributions from the different layers as shown in (1) (layer naming according to Fig. 1).
tins ¼
i¼n1 X
tprot;i þ tins;n
(1)
i¼1
where. tins is the total fire resistance of the assembly [min]; tprot;i is the protection time of the layer i [min]; tins;n is the insulation time of the last layer of the assembly on the unexposed side [min]. The protection and insulation times of the material layer can be calculated taking into account the basic values of the layers, the position coefficients and joint coefficients by Equations (2) and (3).
tprot;i ¼ tprot;0;i ⋅kpos;exp;i ⋅kpos;unexp;i þ Δti ⋅kj;i
(2)
tins;n ¼ tins;0;n ⋅kpos;exp;n þ Δtn ⋅kj;n
(3)
where
tprot;i is the protection time of layer i [min]; tins;n is the insulation time of layer n [min]; tprot;0;i is the basic protection time of the layer i [min]; tins;0;n is the basic insulation time of the layer n [min]; kpos;exp is the position coefficient that takes into account the influence of layers preceding the considered layer []; kpos;unexp is the position coefficient that takes into account the influence of layers backing the considered layer []; Δt is the correction time for layers protected by fire improved protective boards (for example gypsum plasterboards, Type F according to EN 520 [15] or gypsum fibreboards according to EN 15283-2 [16]) [min]; kj is the joint coefficient [].
2. Improved component additive method The improved component additive method takes into account the contributions of each layer considering different possible heat transfer paths through the structure. In all known fire tests of timber frame assemblies, for example [13], the heat transfer path through the cavity insulation layer is prevalent. See also Fig. 2. The layers fulfil different functions (Fig. 1). The last layer of the assembly on the fire-unexposed side serves an insulating function (insulation time) while the previous layers have a protective function (protection time). These functions are defined by different temperature criteria on the fire-unexposed side of the considered layer. The protection time tprot,i is the time until the temperature rise on the fire-unexposed side of the considered layer is (1) 250 K on average or (2) 270 K at any point. Ambient conditions are usually 20 C, hence the temperature criteria become 270 C and 290 C, respectively. These criteria are approximations to account for the failure of thermally degraded material layers. They are also close to the charring temperature of timber (300 C) [5]. Therefore, the sum of protection times of the layers preceding the timber elements may be used as a slightly conservative value for starting time of charring. The insulation time tins,n of the last layer of the assembly is the time until the temperature rise on the fire-unexposed side is equal to 140 K on average over the whole area and 180 K at any point. These criteria are in
The coefficients and basic values are dependent on the material of the investigated layer and the influence of the preceding and backing layers. These values are presented in Refs. [7] and [18] based on the work of [6]. A comparison of full-scale fire test results and calculations (of the same configurations) according to the component additive method are shown in Fig. 3 [6,9]. The presented test configurations consisted of a wide variety of combinations of materials. From this it was concluded that the design method is conservative. The calculations tend to be more conservative for longer fires. 3. Procedure for adding new materials The addition of new materials and products to the improved component additive method requires the determination of the previously mentioned coefficients and values. The general steps to be taken are in the following order: 1. Estimation of initial thermal properties at elevated temperatures, e.g. using thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC) and transient plane source (TPS) methods. 2. Model-scale fire tests. 3. Thermal simulations with initial properties and comparison with model-scale fire test data. 4. Determination of the effective thermal properties. 5. Thermal simulations and comparison with model-scale fire test data.
Fig. 1. Numbering and function of the layers in a timber frame structure. 2
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
test methods can be used to develop an understanding of the thermal and physical behaviour of the material under investigation. Among the most widely used material testing methods are the thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC) and transient plane source (TPS) methods. Thermal properties of the materials should be measured at elevated temperatures usually up to 1200 C. The real behaviour of materials in fire should be investigated with fire tests according to [11]. Model-scale tests allow observing the heat transfer through the specimen and, to a limited extent, the physical changes in a material. Full-scale tests give the most complete picture of the behaviour of the material in fire. Performing a variety of tests allows for observing the different reactions of the material to heating, and therefore obtaining a more complete understanding of the material. During fire tests, temperature measurements are recorded at characteristic locations using type K thermocouples. It should be noted that a 19-mm thick wood particleboard as the backing layer of the assembly is recommended in Ref. [6]. However, the board could also be replaced with other wood-based boards with well-known thermal properties. In the following, the model-scale test specimen configurations proposed for cladding and insulation materials are presented. Most materials can be sorted to one of these groups based on common end-use scenarios. In the specimens where insulation is present, the full thickness of the cavity shall be filled with insulation and its proper fixation shall be ensured throughout the whole duration of the test. Available tests shall cover the variety of thicknesses and densities (if relevant) for which the equations will be derived.
Fig. 2. Thermal image taken of the unexposed side of a model-scale test with an unprotected insulation material filling the whole cavity. Lighter areas are cavities with insulation that show higher temperatures than the timber beam in the middle.
3.2. Claddings In order to determine the equations for claddings, a series of tests with claddings directly exposed to fire and at least one test with insulation behind the cladding shall be provided. The number of fire tests depends on the type of the cladding (thickness, density, etc.) to be assessed. The fall-off of the investigated cladding must not occur due to inadequate fixation. An example of the model-scale fire test specimen with the position of the thermocouples (TC) to obtain the necessary temperature measurements is shown inFigs. 4 and 5. The insulation material used in the cavities should meet the following recommendations: Recommended thickness 100 mm or more. Non-combustible, melting temperature 1000 C. Fixed in place during the post-protection phase. Typically, a stone wool insulation with density around 30 kg/m3 should be used. 3.3. Insulation materials In order to determine the equations for insulation materials, a series of tests with insulation materials directly exposed to fire and at least one test with insulation protected by a cladding (e.g. gypsum board) shall be provided. The fixation of the insulation material shall be guaranteed until the end of the fire test. Fall-off of the cladding should occur when the protection time of the cladding is reached (i.e. the temperature rise on the fire-unexposed side of the cladding is 250 K on average or 270 K at any point). The number of fire tests depends on the type of the insulation material (thickness, density, etc.) to be assessed. An extrapolation to other thicknesses is generally not possible. Interpolation between thicknesses and densities assessed is generally possible. An example of the model-scale fire test specimen with the position of the thermocouples (TC) to obtain the necessary temperature measurements is shown in Figs. 4 and 6.
Fig. 3. Comparison of calculated fire resistances and full-scale test results from Ref. [6] with data points added from Ref. [9]. Number of layers is denoted by n.
6. Step-by-step thermal simulations for developing design equations. 7. Validation of equations with full-scale tests. The aforementioned steps are mostly taken one after the other. Therefore, care shall be taken to obtain results as accurate as possible in each step. Otherwise the cumulative error increases. In the following sections, the determination of the background information and input for the simulations is described. 3.1. a. Experiments Adding new materials to the method is based on test data. Different 3
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 4. Plan of model-scale test specimen viewed from the fire exposed side showing thermocouple locations.
Fig. 5. Cross-section of model-scale test specimens for claddings.
Measured thermal properties may not be directly applicable to all thermal simulations. This is due to two main reasons which will be discussed in the following. Firstly, the majority of fire tests are performed following the ISO 834 standard fire curve [1]. Existing material testing equipment is not capable of following the temperature rise of the standard fire curve. Additionally, it has been proven that the way of heating influences the heat transfer through the material and therefore the measured material characteristics as well [17]. This means that in order to accurately simulate the tested configurations, the thermal properties of the materials need to be modified [5]. Secondly, some simplifying assumptions have been made during the development of thermal simulation software used for analysing structures at elevated temperatures. This means, for example, that in the simulations heat is transferred in the structure only by conduction since most construction elements are made of solid materials. Effects like mass transport, cracking etc. shall be considered separately in the simulation
3.4. Thermal simulations Thermal simulations are used for developing the design equations by following a systematic simulation program described in detail in chapter 4. Any FE software which allows the modelling of the thermal heat transfer in building structures subjected to fire can be used to perform the necessary thermal analyses. The thermal simulation software usually require thermal conductivity, specific heat and density at elevated temperatures as input for describing the material. The latter can be shown to have a lesser effect on the results of the simulations. For the use in thermal simulations, the material properties shall be known at different temperatures (usually between 20 and 1200 C). No precise requirements can be made for the specific temperature points where thermal properties shall be determined. The necessity depends on the material and the thermo-chemical reactions it goes through at different temperatures.
4
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 6. Cross-section of test specimens for insulation.
reference for the calibration of thermal material properties. The test data must not include the mechanical fall-off of the investigated material nor be influenced by the excessive thermal degradation of the fixation of the investigated material (e.g. insulation failure due to the charring of timber battens). A few different approaches for finding the thermal properties are possible (as presented in Refs. [8–10]). This paper does not limit the methodology used to obtain the effective thermal properties of materials as long as they are applicable to the standard fire curve. A possible analytical approach for finding (calibrating) the effective thermal properties introduced by Refs. [9,10] corresponding to a relevant temperature range, is based on rather simple principles. The mathematical analysis software changes the input value (e.g. thermal conductivity) at a single temperature by a set percentage. Then, the difference between the simulated and tested time-temperature curves can be calculated (for example, as the residual sum of squares). This is repeated to find the thermal properties at different temperatures that yield temperature predictions that highly correspond with the experimental measurements. As the thermal properties will change as the heat propagates, the properties found are temperature dependent (Fig. 8). Visual evaluation of the fit of the simulated curve should (also) be used. In the context of fire safety engineering of timber structures, the fitting of characteristic temperatures of 160 C and 270 C is most important. It is recommended that the simulation results at these temperatures not differ from the tests by more than a few minutes. This ensures the (effective) thermal properties used to obtain the simulation curve are precise enough to be used as the basis for developing the equations. See also Fig. 7. Finally, the effective thermal properties are used to simulate the different test setups tested in standard fire. A comparison of the results should be made with the thermocouple readings from the fire tests. If all simulations show shorter or equal time to reach the characteristic temperatures (160 C and 270 C), then the thermal properties developed by calibration are declared to be effective. The effective (calibrated) thermal properties of the material can be used in thermal simulations which may be used as an advanced
approach. Therefore, for some materials (e.g. insulation materials and wood) the calculation is an approximation. On the surfaces, heat is exchanged with the environment via convection and radiation. These phenomena are taken into account by specifying the appropriate coefficients (general values for emissivity and convection coefficient are presented in EN 1991-1-2 [5]). Temperature calculations within solid materials are based on the Fourier equation [18]. The Fourier equation describing one-dimensional conduction, which is necessary in this case, is presented in Equation (4).
k
∂2 T ∂T ∂T k ∂T ¼ cρ ⇒ ¼ ⋅ 2 ∂t ∂t cρ ∂ x ∂2 x
(4)
where T is the temperature [K]; xis the coordinate in the direction of heat transfer [m]; k is the thermal conductivity [W/(mK)]; ρis the density [kg/m3]; c is the specific heat [J/(kgK)]; t is time [s]. From Equation (4) it can be seen that the thermal conductivity is divided by the product of specific heat and density. This means that theoretically only one of these values needs to be calibrated to fit test data if there is sufficient certainty in the values of the other components. The limitations of software and testing equipment create a need for modifying the measured thermal properties. The term effective thermal properties refers to the (measured) properties of the material that have been modified (calibrated) to cater to the ISO 834 standard fire curve. A procedure for obtaining these properties is described in the next subchapter. 3.5. Calibration of thermal properties The thermocouple readings from model-scale fire tests are the 5
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 7. a: Comparison of tested and calibrated time-temperature curves for gypsum boards. b: Configuration of the tested and simulated specimen.
suitable equations derived by fitting a trend line to the simulation points, see Fig. 9. The following figure shows an example where the linear fit is most appropriate. The important thing to notice is that the simulation results are conservative compared to fire test data and that the proposed linear function is in good agreement with simulated data points.
calculation tool for fire design of timber structures. Additionally, these effective thermal material properties are used in the subsequent steps to determine the design equations, as presented in the following section. 4. Determination of the design equations The procedure of determining the design equations was developed by Schleifer [6] and further improved in this study. The determination of the design equations is based on thermal FE simulations. Finite element simulation software use the effective thermal properties as the means of describing the material behaviour in fire. Materials can be divided into three general groups: (1) fire rated claddings, (2) combustible claddings, and (3) insulation materials. The simulations needed for those groups differ slightly as presented in Table 1. In the following, the development of these equations (times and coefficients) is described.
4.3. Position coefficients
4.2. Development of basic protection times
Position coefficients consider the influence of the layers behind (backing layer) and before (preceding layer) the considered layer. For the development of position coefficients, a system of FE simulations and configurations is needed (see Table 1). The position coefficient kpos,exp takes into account the effect of the preceding layer (in the direction of heat flow) on the investigated layer. The effect is depending on the sum of the protection times of all preceding layers. The investigated layer is initially protected by a layer of massive timber (ρ ¼ 450 kg/m3) or stone wool (densities 30 and 90 kg/ m3) with a thickness of 10–50 mm varied in 10 mm increments. To develop the equations for kpos,exp, the simulation results might need to be expressed through different terms to fully investigate the character of the curves and the dependencies of the values on different characteristics (e.g. basic protection times, thickness, etc.). This can be done by plotting the position coefficients against the protection times, thickness and/or density or other factors. See chapter 4.3.2 for an example of the development of the position coefficients. The coefficient kpos, unexp takes into account the effect of the backing layer on the layer under investigation. It is recommended that the developed equations are within 5% of the simulation points at any given thickness or other parameter. This criterion is the required accuracy as the resulting equations shall reflect the simulation results rather closely in order for them to be acceptable altogether.
The basic protection time tprot,0,i is the time from the start of standard fire exposure until the temperature rise on the unexposed side of the material layer reaches 250 K on average. This is taken to be the time when the material has thermally degraded and has lost its protective function. Similarly to the basic insulation times, the available tested thicknesses and densities shall be simulated. The basic protection time of the investigated layer shall be developed based on the FE simulations of configuration 2 shown in Table 1. Then, the times from the start of standard fire exposure until the temperature criterion is reached are plotted against thickness (and/or density) and
4.3.1. Position coefficient kpos,exp,n The position coefficient kpos,exp,n is used when the investigated layer n is the last layer on the fire unexposed side. The temperature rise criterion for the last layer is 140 K on average over the whole area of the unexposed side. The position coefficient kpos,exp,n is developed from simulations of configuration 3 in Table 1. The time when the temperature behind the protection layer reaches 270 C is recorded (t1 ¼ tprot,1) and the simulation is continued without the protection layer which is considered to have fallen off. When the temperature on the unexposed side of the investigated material layer
4.1. Development of basic insulation times The basic insulation time tins,0,n describes the time (from the start of the fire exposure) to reach the temperature rise of 140 K on the unexposed side of the investigated layer. It corresponds to the fire resistance of a single layer without the influence of the adjacent materials. The basic insulation time of the investigated layer is developed based on the FE simulations of configuration 1 shown in Table 1. Simulations shall be conducted for different thicknesses and densities if applicable. Based on the results of the simulations, the times from the start of standard fire exposure until the temperature rise criterion is reached are plotted against thickness (and/or density) and suitable equations derived to approximate the simulation results and fire test results. For the range of thicknesses and densities of interest fire test results shall be available.
6
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 8. Thermal properties (a: thermal conductivity; b: specific heat; c: change in density) used for obtaining results shown in Fig. 7a.
reaches 160 C the simulation is ended and the time recorded as (t2). The position coefficient is calculated as shown in equation (5):
kpos;exp;n ¼
tins;2 tins;0;2
(See analogous procedure shown in the next chapter).
(5)
4.3.2. Position coefficient kpos,exp,i The position coefficient kpos,exp,i can be developed from simulations of configuration 4 shown in Table 1. Initially, the setup shown shall be simulated until the temperature between the preceding layer and the investigated layer reaches 270 C and the time is recorded as t1 (¼tprot,1). After that, the preceding layer is removed and the simulation continued. When the temperature behind the investigated layer reaches 270 C the simulation will be stopped and the time recorded as t2. The formula for calculating the position coefficient is given in Equation (6):
where tins,2 is the insulation time of layer 2, calculated as t2 - t1 [min]; tins,0,2 is the basic insulation time of layer 2 [min]. Due to the different thicknesses of the preceding layer, the fall-off of these layers occurs at different times. The position coefficients can be represented graphically in order to provide a formula for the coefficient. 7
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Table 1 Simulation program.
8
K.N. M€ ager et al.
kpos;exp;i ¼
tprot;2 tprot;0;2
Fire Safety Journal xxx (2017) 1–12
The formula(s) for the calculation of the position coefficient shall be derived by expressing the dependencies through different factors. For example, from Fig. 10 a clear dependency of the position coefficient on the thickness of the investigated material can be seen. Thickness and basic protection time of the investigated material are in correlation with each other. Therefore, the position coefficient values can be expressed through the quotient of the basic protection time of the investigated layer and the sum of protection times of preceding layers (simplified here as one layer of varying thickness of timber or stone wool). The Equation (7) is for the determination of position coefficient kpos,exp,i for the example shown in Fig. 10.
(6)
where tprot,2 is the protection time of layer 2, calculated as t2-t1 [min]; tprot,0,2 is the basic protection time of layer 2 [min]. Fig. 10 shows an example with gypsum plasterboards. The points on the graph are the position coefficients obtained from simulations with different protection times of the preceding layer. A clear dependency on the thickness of the investigated layer can be seen.
9
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 9. Example of a comparison of simulation results (configuration 2 in Table 1) compared with results of model-scale fire tests with the same configurations and the developed formula. Example is based on an insulation material known to the authors.
Fig. 10. Position coefficient values from simulations with an investigated gypsum plasterboard with timber as the preceding layer.
kpos;exp;i
P 8 X tprot;0;i tprot;i1 > > if tprot;i1 < 1 0; 3 ⋅ > < hi 2 ¼ b X > t tprot;0;i > > : a⋅ Pprot;0;i if tprot;i1 2 tprot;i1
4.3.3. Position coefficient kpos,unexp,i In Ref. [6], the value of the position coefficient kpos, unexp,i for different materials backed by cladding materials is given as 1.0. A simulation of configuration 5 presented in Table 1 is needed where the investigated material is backed by 60 mm of stone wool (density 30 kg/m3). The time required for the temperature to reach 270 C between the materials is recorded as tprot,1. The position coefficient kpos, unexp,i is calculated according to Equation (8):
(7)
where a ¼ 0; 5 þ 0; 026 ⋅ b ¼ 0; 8 0; 185
tprot;0;i hi . t g prot;0;i hi .
kpos;unexp;i ¼
hi is the thickness of the investigated board [mm]. The grey curves in Fig. 11 are obtained from Equation (7). The equations describe the simulation points rather well (difference at any point is less than 4%), however, for most applications the equation might be too complex. Simplifications are allowed as long as the equation results are within 5% of the simulation points.
tprot;1 tprot;0;1
(8)
If different densities and/or thicknesses of the investigated material are available, the coefficient shall be expressed as a function of these factors. 4.4. Joint coefficient kjoint The coefficients for the joint configurations consider the detail of the 10
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
Fig. 11. Position coefficients from Equation (7) compared with simulation results.
layer reaches T2 ¼ 160 C (for Δtn) or T2 ¼ 270 C (for Δti). The time is recorded as tTf,160 or tTf,270. A proposed alternative approach [19] involves the fall-off times instead of fall-off temperatures. The fall-off time tf can be determined by full-scale fire testing according to EN 13381-7 [20]. With this approach, the protective layer is removed from the assembly at time tf. Then the simulation is continued until the temperature behind the protected layer reaches 160 C or 270 C. These times are recorded as ttf,160 or ttf,270. The rest of the procedure is analogous. To develop the formulas the results are plotted on a graph with the axes being the correction time and the basic insulation or protection time of the backing layer. The correction times Δtn and Δti for graphs are calculated as shown in Equations (11) and (12).
joints and their influence on the insulation or protection time. Joint coefficient should be taken into account for layers on the unexposed side with joints or for layers that have a void cavity behind. Joint coefficient shall be determined by fire tests comparing test configurations with and without joints.
kjoint ¼
tins;joint;n tins;n
(9)
kjoint ¼
tprot;joint;i tprot;i
(10)
tins, joint,n is the insulation time of layer n with joints [min]; tprot, joint,i is the protection time of layer i with joints [min]. Currently a simple collection of tabulated values is presented in Ref. [7]. 4.5. Correction time Δt
Δtn ¼ tTf;160 t270;160
(11)
Δti ¼ tTf;270 t270;270
(12)
Correction times should be derived for any material that can be used as a fire improved cladding.
Fire improved protective boards (e.g. gypsum plasterboard type F acc. to EN 520 [15]) have been observed to stay in place longer than the criteria for protection time (270 C). In order to take this effect into account, the fall-off temperature is assumed to be higher in the simulations. For example, in the case of gypsum boards the failure temperatures are assumed to be Tf ¼ 600 C for wall assemblies and Tf ¼ 400 C for floor assemblies (ceilings) or higher if more precise data from full-scale fire tests for gypsum boards is available. In order to account for the longer protection in the calculation of insulation time of the structure, a correction time Δt is added to the layer preceded by the fire improved protective board. The correction time Δtn for the last layer and Δti for the other layers are derived from simulations of configuration 6 shown in Table 1. Materials behind the investigated fire improved board are generalised and represented by timber (ρ ¼ 450 kg/m3, representing cladding materials) and stone wool (ρ ¼ 30 and 90 kg/m3, representing insulation materials). If correction times are needed for other preceding materials then the same approach shall be taken and the values determined separately. Firstly, the simulation is run until the temperature behind the fire protective layer reaches T1 ¼ 270 C and the protective board is removed. Then, the simulation is continued until the temperature behind the backing layer reaches T2 ¼ 160 C (for Δtn) or T2 ¼ 270 C (for Δti). The time is recorded as t270,160 or t270,270. The next simulation is run with the same initial configuration, but the board is kept in place until the temperature reaches fall-off temperature T1 ¼ Tf. After removing the board, the simulation is continued until the temperature behind the backing
5. Verification by full-scale fire tests It is strongly recommended that the verification of the developed equations is done based on a few full-scale fire tests. The duration of the
Fig. 12. Configuration of the full-scale test specimen used as the verification example. 11
K.N. M€ ager et al.
Fire Safety Journal xxx (2017) 1–12
paper. With this method the verification of the separating function (insulation and integrity criteria) of timber frame assemblies is nowadays usually performed. The procedure is based on model-scale fire tests and extensive thermal simulations with the effective thermal properties. The equations are derived on the basis of simulation results and verified by full-scale fire tests. Acknowledgements The authors acknowledge the network of COST Action FP1404 for the contribution of the Task Group 5 within the Working Group 2 “Structural Elements made of bio-based building materials and detailing”. This work was supported by the start-up research grant PUT794 “Effect of protective materials on the fire performance of timber structures” (2015-2018) financed by the Estonian Research Council. References [1] International Organization for Standardization, ISO 834-1:1999, Fire-resistance Tests - Elements of Building Construction - Part 1: General Requirements, 1999. [2] BSI, British Standard BS 5268–4, Structural Use of Timber - Section 4.2, Recommendations for calculating fire resistance of timber stud walls and jousted floor constructions, 1990. [3] NRCC, National Building Code of Canada, vol. 2, 2005. [4] J. Noren, Additionsmetoden - Ber€akning Av Brandmotstånd Hos Avskiljande V€aggar, 1994. Stockholm. [5] CEN, EN 1995-1-2:2004 Eurocode 5: Design of Timber Structures - Part 1-2: General - Structural Fire Design, 2004. [6] V. Schleifer, Zum Verhalten von raumabschliessenden mehrschichtigen Holzbauteilen im Brandfall, ETH Zürich, 2009, http://dx.doi.org/10.3929/ethz-a005771863. € [7] B. Ostman, E. Mikkola, R. Stein, A. Frangi, J. K€ onig, D. Dhima, T. Hakkarainen, J. Bregulla, Fire Safety in Timber Buildings, SP Technical Research Institute of Sweden, Stockholm, 2010. [8] R. Breu, Improved Component Additive Method for the Separating Function Development of a Testing and Calculation Procedure, ETH Zürich, 2016. [9] K.N. M€ager, Implementation of New Materials to the Component Additive Method for Fire Design of Timber Structures, Tallinn University of Technology, 2016. [10] K.N. M€ager, D. Brandon, A. Just, Determination of the effective material properties for thermal simulations, in: R. G€ orlacher (Ed.), Int. Netw. Timber Eng. Res. Meet. 49, Graz, Austria, August 2016, Timber Scientific Publishing, Karlsruhe, 2016, pp. 397–400. [11] CEN, EN 1363-1:2012 Fire Resistance Tests. General Requirements, 2012. [12] A. Frangi, V. Schleifer, M. Fontana, Design model for the verification of the separating function of light timber frame assemblies, Eng. Struct. 32 (2010) 1184–1195. [13] A. Just, Full-scale Fire Tests of Timber Frame Walls, Tallinn, 2009. [14] CEN, EN 13501-2:2016 Fire Classification of Construction Products and Building Elements, Classification using data from fire resistance tests, excluding ventilation services, 2016. [15] CEN, EN 520:2004 Gypsum Plasterboards - Definitions, Requirements and Test Methods, 2004. [16] CEN, EN 15283-2:2008 Gypsum Boards with Fibrous Reinforcement, Definitions, requirements and test methods - Part 2: Gypsum fibre boards, 2008. [17] G.K. Semitelos, I.D. Mandilaras, D.A. Kontogeorgos, M.A. Founti, Simplified correlations of gypsum board thermal properties for simulation tools, Fire Mater. 40 (2016) 229–245, http://dx.doi.org/10.1002/fam.2282. [18] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, seventh ed., John Wiley & Sons, 2011. [19] K.N. M€ager, A. Just, A. Frangi, D. Brandon, Protection by fire rated claddings in the component additive method, in: Int. Netw. Timber Eng. Res. Meet. 50, Kyoto, Japan, August 2017, 2017. [20] CEN, EN 13381-7:2002 Test Methods for Determining the Contribution to the Fire Resistance of Structural Members - Part 7: Applied Protection to Timber Members, 2002. [21] K.N. M€ager, Implementation of New Materials to the Component Additive Method for Fire Design of Timber Structures, vol. 71, SP Rapport, 2016, p. 2016.
Fig. 13. Comparison of protection times of each layer from one full-scale fire test and calculations of the same setup of the configuration shown in Fig. 12. Table 2 Comparison of fire resistance times from a full-scale fire test and calculations of the configuration shown in Fig. 12. Layer no
Material
1 2 3 4 5 6
Gypsum 1 Gypsum 1 Glass wool 1 Glass wool 2 Gypsum 1 Gypsum 1
a
Time to reach 270 C (160 C for last layer) behind layer tprot (tins) [min] Calculation
Full-scale test
31,0 67,2 78,5 80,0 89,7 (112,1)
32 68 n.aa 111 n.aa (147)
Was not measured.
test is required to cover the validity of the derived equations in standard fire. The calculated fire resistance times of each layer shall be equal or shorter than the same times obtained from full-scale fire tests. An example of a full-scale fire test (see section 7.3. in Ref. [21]) used for the verification of equations derived for a fire resistant gypsum plasterboard product (type F according to [15]) is shown in Fig. 12. The examples in Fig. 13 and Table 2 show comparisons of test results and calculated values. The design equations used for the gypsum layers are developed from calibrated effective thermal properties. The biggest differences between experimental and calculated results can be found to originate from insulation layers (3 and 4) which are considered more conservatively. 6. Conclusions A common procedure for the implementation of new materials to use with the component additive method is proposed by authors of this
12