Robert Jansson and David Lange
SP Fire Resarch SP Report 2015:33S
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The fire behaviour of an inner lining for
tunnels
Abstract
The fire resistance of a sprayed concrete inner lining for tunnels has been investigated experimentally and theoretically. During the initial first test on a section of nominal size 5 × 3 × 0.12 m3 the specimen maintained the integrity and insulation criteria during 180 minutes fire exposure with the Hydrocarbon fire curve. Also during the second test, where two specimens of half the size were tested, the integrity and insulation criteria’s were maintained but during this test the fire exposure was reduced during a period of the test due to a technical malfunction.
The thermal properties of the sprayed concrete was shown by TPS measurements to be in the span of the values found in the Eurocode. Further on, calculations based on the Eurocode model including temperature dependent stress/strain was shown to give results on the safe side compared with measurements performed during the test. Stresses calculated in the supporting steel bars were 2 to 3 times higher than the measurements which is conservative.
Key words: tunnels, fire, sprayed concrete
SP Sveriges Tekniska Forskningsinstitut
SP Technical Research Institute of Sweden SP Report 2015:33
ISBN 978-91-88001-62-7 ISSN 0284-5172
Contents
1
Introduction
8
2
Test specimens
9
2.1 Material and conditioning 12
2.2 Instrumentation 12
2.2.1 Temperature measurement in specimens 12
2.2.2 Temperature in furnace 13
2.2.3 Strain measurements on rods 13
2.3 Additional measurements 14
2.3.1 Deformation measurements with laser 14
2.3.2 Surface temperatures with thermal camera 14
3
Measurements of mechanical and thermal properties
including moisture content in the concrete
14
4
Results from fire tests
16
4.1 Observations 17
4.2 Temperature measurements 19
4.3 Stresses in rods 22
4.4 Deformation of concrete and supporting system 25
4.5 Measurements of fire spalling 26
5
Modelling of thermal and mechanical behaviour
27
5.1 Background to EN 1992-1-2 model 27 5.2 Modelling approach 30 5.3 Thermal modelling 31 5.4 Mechanical modelling 35 5.4.1 Model 1 36 5.4.2 Model 2 36 5.4.3 Models 3 and 4 37 5.4.4 Model 5 38 5.4.5 Model 6 39 5.4.6 Model 7 41 5.5 Discussion 43
6
Conclusions
44
7
References
45
8
Appendix A - Deviations from nominal thickness
46
9
Appendix B - Positions of thermocouples
48
10
Appendix C – Results from measurement of thermal
properties
49
11
Appendix D – Furnace temperatures
52
12
Appendix E – Degree of refinement in thermal model
55
Preface
This work is part of the “ Stockholm Bypass, tunnel safety studies”, co-funded by EU Trans-European transport network (TEN-T). The sole responsibility of this publication lies with the author. The European Union is not responsible for any use that may be made of the information contained therein.
We wish to thank the following persons for valuable support during the project: Peter Lindqvist and Martin Rabe for their good spirit when measuring the thickness variations of the specimens and transforming the test setup from idea to reality. Joakim Albrektsson that despite a high working load from being in the final stages of thesis writing helped us with running some of the models. Bengt Bogren for being Bengt Bogren and performing the practical work with determination of thermal properties.
The thermal and mechanical modelling in the project have been performed by Dr. David Lange whereas the experimental design and project leading have been the responsibility of Dr. Robert Jansson.
Summary
Two fire resistance tests have been performed on a sprayed concrete inner lining for tunnels. During the first test on a section of nominal size 5 × 3 × 0.12 m3 the specimen maintained the integrity and insulation criteria during 180 minutes fire exposure with the Hydrocarbon fire curve. During the second test on two specimens with half the size both the integrity and the insulating criteria was maintained during the 180 minutes long fire exposure but during this test there was a dip in furnace temperature during a part of the testing time due to a malfunction in the gas delivery system to the furnace.
The thermal properties of the tested concrete was measured with the transient plane source method at temperatures 22, 150, 170 and 300°C. Compared with the Swedish national choice for temperature dependent thermal properties in the Eurocode, EN 1992-1-2:2004, it was found that for the first three temperature levels the investigated sprayed concrete had a slightly higher thermal diffusivity and at the level 300°C the value was as the national choice.
The measured behaviour during the test was modelled using the finite element method, using the simplified temperature dependent stress/strain model in the Eurocode, EN 1992-1-2. Various parameters were investigated, including the way that the supporting frame assembly is accounted for in the modelling, the effect of concrete thickness on the results and the effect of Poisson’s ratio on the numerical results. The thermal calculations showed a reasonable good agreement with experiments, although influenced by the higher diffusivity of the concrete at low temperatures compared with the concrete properties taken from the Eurocode. When investigating the stress development in the supporting rods it was found that in the model gives very large stresses in comparison with the test results by a factor of 4 when the deformation of the steel supporting frame is omitted and a factor of 2 when it is included. The mechanical response appears to be strongly influenced by the asymmetry of the test specimen, caused by uneven spraying, and this may have impacted upon the comparison between the test and the numerical modelling. This needs further investigation, however it appears that for the case modelled the numerical analysis is conservative.
1
Introduction
The main purpose of this study is to investigate the fire resistance of a roof section of an inner lining concept made of sprayed concrete for tunnels. Also the applicability of the thermal and mechanical model defined in the Eurocode EN 1992-1-2:2004 is investigated for this type of cross section. Calculations are compared with measurements of the stress development in the supporting rods.
The nominal thickness of the sprayed inner lining is 120 mm and it is hanging from the tunnel roof in rods as shown in Figure 1.
Figure 1 Supporting system and reinforcement visible before spraying the inner lining. (Photo: Thomas Dalmalm, Trafikverket)
To be able to test the fire resistance of the roof section of the inner lining, special purpose test specimens of a suitable size were manufactured to fit a horizontal fire resistance furnace with an opening of 5 by 3 meters. Two tests were performed, one with an element covering the whole furnace, and one with two test specimens each covering one half of the furnace. During the tests the specimens were hanging from rods anchored to a system of steel beams which were intended to provide a boundary condition which as closely as possible represented the stiff boundary condition of the unlined tunnel wall.
The sprayed concrete used in this study included an addition of 2 kg/m3 of Polypropylene (PP) fibres to reduce the amount of fire spalling. As the test specimens were relatively young, 49 and 51 days respectively, it was concluded that this amount was needed due to the fact that young and moist concrete is known to spall much during fire exposure. As a comparison, during previous tests for the project Norra Länken on 70 days old sprayed concrete tested for a period of 60 minutes with standard fire exposure less fibres were used with acceptable results. i.e. no violent spalling in the early phase of the fire, see Table 1.
Table 1 Spalling on sprayed concrete for the Norra Länken tested for 60 minutes with ISO 834 exposure. Specimens without load or restrain of nominal size 3400 × 1200 × 100 mm3.
Test specimen Spalling Note
A 1 kg/m3 PP No spalling
B 1.2 kg/m3 PP Spalling of corner in the boundary zone.
The corner was spalled off after 42 minutes of
exposure. C 1.2 kg/m3 PP No spalling
D 1.5 kg/m3 PP Spalling of corner in the boundary zone.
The corner was spalled off after 56 minutes of
exposure.
In the Hallandsås project sprayed concrete for protection of moulded concrete was tested under 2 hours of RWS fire exposure. During these tests concrete slabs with a geometry of 1800 × 1200 × 540 mm3 were protected with sprayed concrete including different types of steel and PP fibre additions. One of the mixes tested was without steel fibres but included 1.5 kg/m3 PP fibres. Nominal thickness of this sprayed system was 90 mm but no detailed mapping of the height of the surface was performed before the fire test. During the fire test slight spalling occurred as surface flaking on almost the whole surface but only on a small part of the surface the thickness of the protection reduced to values under the nominal thickness. The minimum remaining protection after spalling was in one small spot 68 mm. This test indicates that an addition of 1.5 kg/m3 PP fibres does not prevent spalling from occurring during RWS fire exposure but progressive spalling where the whole layer is consumed is avoided during a severe heating scenario.
In a French study sprayed concrete was exposed to the severe modified hydrocarbon curve [7] which is more severe than the standard fire curve and the hydrocarbon curve. Results from this study show that with an addition of 2 kg/m3 PP fibres the spalling in a 160 mm thick slab was zero and in a 200 mm thick slab 15 mm. In the latter case the spalling was evenly distributed over the whole surface.
2
Test specimens
Test specimens for fire testing were manufactured by Byggs Sprutbetong AB in Solna, Sweden. One specimen of size 5 × 3 × 0.12 m3, two specimens of size 2.5 × 3 × 0.12 m3 and three unreinforced specimens of size 1 × 1 × 0.12 m3 were manufactured. The unreinforced specimens were used for determination of compressive strength, moisture content and measurement of thermal properties.
The cross section of the specimens for fire testing can be seen in Figure 2. This figure also includes the support system built with HEB 100 beams that was mounted 28 days after spraying. Spacing between the rods for connecting to the support system was 1.2 meters. The reinforcement consisted of a reinforcement mesh made of 8 mm diameter bars and at square spacing of 100 mm. The reinforcement mounted together with reinforcement crosses attached to the rods for support can be seen in Figure 3. In this figure the rods are sticking out through the back side of the formwork.
Figure 2 Cross section of test specimens including support system. During the test the specimen is hanging in the rods placed 1.2 meter from each other.
Figure 3 Formwork for spraying the large specimen.
When arriving to SP it was clear that the surfaces of the specimens were uneven, as shown in Figure 4, so measurements of the thickness were made on a square grid with 20 cm sides on the whole surface. The large specimen, 5 x 3 m2, was also slightly uneven on the upper side so this also had to be measured in order to determine the actual thickness.
Results from the measurement on the large slab can be seen in Figure 5 and a summary of the deviations can be found in Table 2. More detailed plots of the measured heights of the three tested slabs can be found in Appendix A.
Figure 4 Surface of sprayed concrete.
Figure 5 Deviation from nominal thickness, 120 mm, of the large specimen.
Table 2 Deviation from nominal thinness 120 mm.
Specimen Average [mm] Max [mm] Min [mm]
Test 1 (5 x 3 m2) 31 97 -21
Test 2A (2.5 x 3 m2) 19 77 -18
Test 2B (2.5 x 3 m2) 29 110 -10
During the fire tests the test specimens were hanging from rods attached to a steel beam system as shown in Figure 6. As in the real inner lining system used in tunnels the distance between the rods was 1.2 meters. The whole test setup as placed on the horizontal furnace at SP can be seen in Figure 6.
0 400 800 1200 1600 2000 2400 2800 0 400 800 1200 1600 2000 2400 0028 3200 3600 4000 4400 4800 50-100 0-50 -50-0
Figure 6 Test specimen and support system on top of the fire resistance furnace. The sprayed concrete roof is hanging in rods that is attached to a steel frame made of HEB 100 beams.
2.1
Material and conditioning
The sprayed concrete was a C35/45 mix with maximum aggregate size 8 mm and cement content of 500 kg/m3 manufactured by Betongindustri. The water/cement ratio was 0.43 and 2 kg/m3 of PP-fibres with designation SIKA Crackstop were added to the mix. The diameter of the fibres was 18 µm and the length 6 mm. The fibres were included to reduce the amount of fire spalling. As the test specimens were relatively young, 49 and 51 days, it was concluded that 2 kg/m3 was needed due to the fact that young and moist concrete is known to spall much during fire exposure.
After spraying the specimens in a vertical position Byggs Sprutbetong AB stored the specimens soaked in water for 7 days and then stored them outside. After 28 days the specimens were detached from the formwork and the support system made of steel beams was attached. Thereafter the specimens were sent to SP arriving at the age of 35 days. At SP the specimens were kept in an indoor climate until the days of testing, the large specimen was tested at an age of 49 days and the two smaller specimens were tested at the age 51 days.
2.2
Instrumentation
2.2.1
Temperature measurement in specimens
The specimens were equipped with thermocouples at different depths. Thermocouples were attached to the reinforcement before spraying. Due to the rough mechanical impact during spraying that can change the position of thermocouples, the thermocouples located in the concrete were mounted after spraying at SP by drilling from the cold side of the specimen. The drilled holes were filled with mortar. In test 1, on the large slab, 42
thermocouples were used distributed at a distance of 0, 30 90 and 110 mm from the cold side, on the reinforcement on the nominal depth 48 mm from the cold side and on the rods that the specimens were hanging from. In test 2, the test on the two smaller slabs, 54 thermocouples were used. Due to the unevenness of the sprayed concrete surface all thermocouple depths initially defined from the cold surface had to be recalculated based on the depth in the mapping of the surface.
2.2.2
Temperature in furnace
During both fire tests the temperature in the furnace was measured with 10 plate-thermometers. The fire exposure used was the Hydrocarbon fire curve, EN 1363-2 for 180 minutes.
2.2.3
Strain measurements on rods
To estimate the stresses developed in the rods strain gauges were mounted on the rods at their mid-height, 100 mm from the concrete surface, as seen in Figure 7. The gauges were mounted in three locations around the circumference of the rods at a separation angle of 120 degrees to be able to detect the normal force and if any bending moments were present. Based on these strain measurements and the stiffness of the material in the rods, 210 GPa, the stress and load on the rods during the tests were calculated. During both the tests 6 of the in total 12 rods were equipped with strain gauges.
2.3
Additional measurements
2.3.1
Deformation measurements with laser
During the fire tests the upper surfaces of the test specimens were scanned with a
HDS7000 terrestrial laser scanner to measure deformations of the concrete upper surfaces and the supporting steel beam system.
2.3.2
Surface temperatures with thermal camera
The temperature development of the upper non exposed surface was monitored with a thermal camera. The exact temperatures from this type of measurement in this
experimental situation is associated with large potential errors but from the relative temperature distribution thermal images can be used to monitor the development of cracks at the surface of the specimens.
3
Measurements of mechanical and thermal
properties including moisture content in the
concrete
Measurement of strength, thermal properties and moisture content were performed on material taken from 1 × 1 × 0.12 m3 slabs that were manufactured and stored together with the larger specimens that were fire tested. Material for the tests was taken from the centre of this slabs to avoid influences from the boundaries.
At the age of 42 days, the week before the fire tests, cores with diameter 100 mm were drilled for the determination of compressive strength and thermal properties. No large cracks or large voids from manufacturing were detected in the cross section. The measured compressive strength of three 100 mm high cylinders was 54, 58 and 59 MPa with an average of 57 MPa. Density of the cores for compressive strength tests were 2260 kg/m3.
At the day of the second fire test two pieces of the material, with an initial weight of 5.351 and 6.029 kg, were put in a drying oven at 105°C. With this method a moisture content of 7.2% of the dry weight was determined.
The thermal properties of the sprayed concrete were measured with the transient plane source (TPS) method [1,6]. With this method both the thermal conductivity and the thermal diffusivity are determined simultaneously. When analysing test results it is important to remember that the thermal diffusivity is related to the thermal conductivity and specific heat in the following way:
𝛼 =𝜌𝐶𝜆 𝑝 α = Thermal diffusivity [m2 /s] λ = Thermal conductivity [W/mK] ρ = Density [kg/m3 ] Cp = Specific heat [J/kgK]
ρCp = Volumetric specific heat [J/m 3
The values of thermal properties for concrete in the Eurocode EN 1992-1-2:2004 are a result of a curve fitting procedure, i.e. these are effective values. In this fitting procedure, the specific heat was defined including a peak that represents the latent heat of
evaporation. A temperature dependent thermal conductivity was then chosen to fit as many test results as possible. As seen in Figure 8 there are a higher and a lower curve for the temperature dependent thermal conductivity in the Eurocode. Inside this span a national choice can be made. In Sweden Boverket have chosen the lower curve of thermal conductivity.
In Figure 8 to Figure 10 the values determined by the TPS method at temperatures 22, 150, 170 and 300°C are compared with the values found in the Eurocode, EN 1992-1-2:2004. Both the thermal conductivity and thermal diffusivity measured are between the high and the low curves defined in Eurocode with the value for thermal diffusivity at the temperature 300°C almost the same as the lower curve. From the ratio of these two values, the volumetric specific heat, we see that it is slightly lower than in Eurocode for the first three temperatures and for the highest temperature, 300°C, the measurement is slightly higher. It is important to remember that the Eurocode values were developed by curve fitting to results from fire tests. Therefore these values include effects from moisture transport which is not included in the determination of thermal properties with the TPS method. Despite this the experimental values found correspond fairly well with the Eurocode.
Figure 8 Thermal conductivity measured with TPS compared with values in the EN 1992-1-2. The lower curve is the national choice made by Boverket for ordinary concrete in Sweden.
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Figure 9 Thermal diffusivity measured with TPS compared with values from the EN 1992-1-2 for a density of 1992-1-21992-1-260 kg/m3 and no moisture effect. The moisture influence by latent heat of evaporation between 100 and 200°C is taken away as this is not a phenomenon covered by the TPS measurement.
Figure 10 Volumetric specific heat measured with TPS compared with values from EN 1992-1-2 for a density of 2260 kg/m3. The peak in the Eurocode is adjusted depending on the moisture content. In the TPS measurement the moisture is not present at temperatures over 100 °C so the measurement shall be compared with an value for concrete without a moisture peak.
4
Results from fire tests
Two fire tests were performed. The first fire test was on a sprayed concrete slab covering the whole furnace, 5 x 3 m2, and the second test was on two slabs of half the size. During both tests the aim was to follow the Hydrocarbon fire curve defined in EN 1363-2 for a period of 180 minutes. Measured temperatures in the furnace during the tests can be found in Appendix D.
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3 % moisture
Eurocode
no moisture
TPS
4.1
Observations
Test 1 was performed December 17, 2014 on the large slab as illustrated in Figure 6. Visual observations from the test are compiled in Table 3.
Table 3 Visual observations from test 1.
Time from start [min:sec] Observations
Specimen orientation on furnace
0:00 Start of test.
3:35 Spalling start in the north east corner of the specimen.
8:00 Spalling events stops.
22:14 Water starts to pour out in cracks on the non-exposed surface of the slab.
80:00
Thermal image indicating the crack development on the upper surface.
78:30 Much water is accumulated on the cold surface as the thermal bending makes the water stay. This water was removed with a vacuum cleaner.
180:00 The heating of the furnace stops but the measurements in the cross-section and in the rods are continuing also during the cooling phase.
236:00 Measurements stops.
Test 2 was performed December 19, 2014 on two slabs as illustrated in Figure 11. Visual observations from the test are compiled in Table 4.
Figure 11 Test 2 including two slabs covering the furnace. Table 4 Visual observations from test 2.
Time from start [min:sec] Observations.
Specimen orientation on furnace:
0:00 Start of test.
2:27 Spalling in close to the south end of specimen A.
6:55 Spalling in south east end of specimen A.
14:40 The heating of the furnace is stopped by an error in the gas supplying system, giving the result that the furnace starts to cool down but all measurement systems still worked. The furnace temperature drop during the malfunction is shown below.
All furnace temperatures can be found in in Appendix D. 0 200 400 600 800 1000 1200 0 60 120 180 Tem per at ur e [ oC] Time [min] Hydrocarbon fire Average temperature in the furnace North
A
B
40:00 After restart the specified temperature level in the hydrocarbon fire curve is reached again.
80:00
Thermal image indicating the crack development on the upper surface.
180:00 The heating of the furnace stops but the measurements of stresses in the rods and temperatures in the cross-sections are continuing also during the cooling phase.
234:00 Measurements stops.
4.2
Temperature measurements
Temperatures were measured inside the cross sections with type K thermocouples. The thermocouples mounted on the reinforcement were included from the beginning during spraying whereas the thermocouples in the cross section were drilled in from the cold side. Due to the uneven shape of the surface a recalculation procedure was performed based on thickness measurements to figure out the real depths.
The system for naming the thermocouples is as follows:
• “A”, a letter saying in what area the thermocouple is located.
• “33”, depth from exposed surface in millimetres. This value is calculated from the drilling depths from the unexposed surface combined with the height map of the sprayed surface.
• “re”, thermocouple mounted on the reinforcement.
• “surf”, standardized thermocouple with pad mounted on the cold surface. The different thermocouple areas in test 1 can be seen in Figure 12. Coordinates for position of individual thermocouples can be found in Appendix B. The temperatures measured during test 1 can be seen in Figure 13 to Figure 17. Note that the surface temperatures shown in Figure 17 did never exceed 180 degrees of temperature rise during the test and the average temperature rise were under 140 degrees which means that the insulation criterion for fire resistance was never broken. Also the integrity criterion was fulfilled during the whole testing time as no holes through the specimen were developed.
Figure 12 Different areas, A-E, with thermocouples in test 1.
Figure 13 Test 1, temperatures measured with thermocouples placed on depths between 27 and 38 mm from the fire exposed surface.
0 100 200 300 400 500 600 700 0 50 100 150 200 250 300
Tem
per
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Time [min]
27-38 mm
A 33 B 27 C 32 E 38 a E 35Figure 14 Test 1, temperatures measured with thermocouples placed on depths between 52 and 68 mm from the fire exposed surface.
Figure 15 Test 1, temperatures measured with thermocouples placed on depths between 77 and 99 mm from the fire exposed surface.
0 100 200 300 400 500 0 50 100 150 200 250 300
Tem
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Time [min]
52-68 mm
A 52 B 55 C 58 F 68 0 100 200 300 400 500 0 50 100 150 200 250 300Tem
per
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Time [min]
77-99 mm
A re 99 A 94 A 96 B 91 C re 93 D 82 E re 87 F 91 F 77Figure 16 Test 1, temperatures measured with thermocouples placed on depths between 106 and 153 mm from the fire exposed surface.
Figure 17 Test 1, temperatures measured with thermocouples placed on the unexposed surface.
4.3
Stresses in rods
During the first test six of the twelve rods that the specimen was hanging from were equipped with strain gauges. Based on the measured strains the force and the moment in the rods was then calculated. Results on force and moment during the first test can be seen in Figure 18 andFigure 19. It is evident that the rods in the outer corners of the specimens are in compression caused by the thermal bowing of the specimen during fire exposure. The other rods are mainly in tension although rod A is changed to compression after about 100 minutes. When comparing nominally symmetrical pairs A - C and D - F there is a substantial scatter in the results. This is mainly caused by the very uneven surface of the specimen making the specimen un-symmetric, see Appendix A.
0 50 100 150 200 250 300 0 50 100 150 200 250 300
Tem
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Time [min]
106-153 mm
A 114 B re 115 B 128 C 111 E 106 F re 135 F 153 0 20 40 60 80 100 120 140 160 180 0 50 100 150 200 250 300Tem
per
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Time [min]
Cold surface 131-184 mm
A surf 148 B surf 167 C surf 145 C surf 141 D surf 177 E E surf 131 F surf 184Figure 18 Test 1, change in axial force in the rods during the test. Compressive force is negative in the diagram.
Figure 19 Test 1, bending moment and angle of moment in measurement point in rod. Zero degrees is north.
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Ang
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x
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x
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A B C
During the second test one of the two slabs was instrumented with strain gauges on all six rods. When analysing the results in Figure 20 and Figure 21 a very large spread in results is present. This is probably caused by the very uneven surface.
Figure 20 Test 2, change in axial force in the rods during the test. Compressive force is negative in the diagram.
Figure 21 Test 2, bending moment and angel angle of moment in measurement point in rod. Zero degrees is north.
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4.4
Deformation of concrete and supporting system
A 3D scan of the concrete slab and the supporting system was made at different times with a laser system. From these 3D scans the deformation of the concrete and the supporting system was calculated. In Figure 22 and Figure 23 deformations of the supporting system are shown. These deformations measured were not expected when the experiment was designed, ideally the system wold not be deformed by the stresses from the expanding concrete.
Figure 22 Deformation of the supporting system at the positions of the six rods in the centre of the specimen during test 1.
Figure 23 Deformation of the supporting system at the positions of the six rods closest to the short edges of the specimen during test 1.
-0.035
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De
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Time [min]
A
B
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x4
x5
x6
x1 x2 x3
D E F
x4 x5 x6
A B C
x1 x2 x3
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x4 x5 x6
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4.5
Measurements of fire spalling
After the fire tests the amount of fire spalling was estimated. During test 1 spalling was detected in 5 locations of the heated surface, see Figure 24 and Table 5. In test 2 spalling occurred on one location with an estimated depth of 10-20 mm, see Figure 25.
Figure 24 Spalling during test 1. Estimated amount can be seen in Table 5.
Table 5 Estimated depth and dimensions on spalled area during test 1.
Spalling depth [mm] Size, X [mm] Size,Y [mm]
A 10-30 800 1200 B 10 300 400 C 10-30 100 100 D 10-30 500 1200
A
B
C
D
Figure 25 Spalling during test 2. Estimated depth 10-20 mm. X and Y dimensions of spalled area 1000 x 700 mm2.
5
Modelling of thermal and mechanical
behaviour
The applicability of the simplified Eurocode model for concrete at high temperatures was investigated by comparing results from calculations with measurements from the tests.
5.1
Background to EN 1992-1-2 model
In EN 1992-1-2 chapter 3.2.2.1 a temperature dependent stress strain relationship is stated for concrete in compression. Together with tabulated values in the Eurocode the
mathematical formulation in Figure 26 gives a temperature dependent stress strain relationship.
Figure 26 Mathematical model according to EN 1992-1-2 for stress/strain relationship of concrete under compression at elevated temperatures. In the figure fc,θ is the temperature dependent compressive strength, εc1,θ is the strain at peak stress and εcu,1 is the ultimate
strain. Temperature dependent values of this parameters to be used in the model can be found in the Eurocode.
The function adopted for this description was developed in the 70-ties by Popovics in a model for describing the room temperature behaviour [2]. This model was in 1985 suggested by the RILEM1 Committee PHT 44 [3] as a way of describing high
temperature behaviour. In the RILEM suggestion the effect of transient state strain2 was included in an effective way in the same manner that was previously done by Schneider [4]. The reason for introducing it was to facilitate simple calculations and according to the committee the model had been used with success in fire investigations. But, more
importantly, the model implicitly including transient state strain, is not suitable for more complex calculations according to the committee [3], but it was included in the Eurocode despite this limitation. For more complex calculations the explicit Schneider or
Anderberg/Thelandersson models was recommended by the committee.
In the RILEM document [3] the procedure for creating a stress strain relationship implicitly including transient state strain is also described. The type of curves implicitly including transient strain effects can be distilled from total deformation curves created under different load levels with some complementary information on ultimate stress. In Figure 27 the principle is shown.
1 RILEM is an International Union of Laboratories and Experts in Construction, Materials,
Systems and Structures.
2 Transient state strain is an experimental determined strain component in the opposite direction of
Figure 27 Total deformation (ε) under different load levels (α) for creating a stress strain relationship implicitly including transient state strain. When, as an example, analysing the stress strain behaviour at 400 degrees you start with the deformation for free thermal strain, X0 as zero. Then X1 gives the deformation at a load 10% of the room temperature
compressive strength, and X2 gives the deformation at 30% load, and so on. This is then done for different temperatures, see Y0-Y3 for temperature 600 degrees.
Further on it can be of interest to know that the tabulated stress strain data in Table 3 in the present EN 1992-1-2 that includes an implicit transient strain compensation was in an earlier version , ENV 1992-1-2:1995, formulated as in the figure below:
X
0
X
1
X
2
X
3
Y
0
Y
1
Y
2
Y
3
Figure 28 Formulation of εc1,θ, strain at peak stress, in a previous version of the Eurocode ENV1992-1-2:1995. The values under the green frame is values without implicitly including transient state strain and the values under the red frame is including the transient state strain effect.
5.2
Modelling approach
The EN 1992-1-2:2004 material data described in section 5.1 was implemented in a finite element model of the first fire test described above using the Abaqus finite element program, version 6.14-1 [5]. Several different versions of the model were created, some including the action of the HEB 100 steel beams from which the hangers were suspended and some which did not. Both versions of the model were run in uncoupled temperature displacement analyses – i.e. the thermal analysis was run first and then the structural analysis was run, reading the results of the thermal analysis as a field variable into the model. In the thermal analyses all of the hangers and the steel supporting frame were omitted.
Symmetry was taken into account during all modelling, with one half of the concrete shell, and steel frame when this was included, being modelled. The concrete shell was
modelled using 4-noded shell elements with reduced integration (S4R), with a layer of rebar included in the shell section definition, at the same height as it was in the test specimen – 12 mm above the centre of the nominal design thickness. The mesh of the shell was sized in such a way that the location of the ends of the hangers corresponded with the location of the nodes on some of the elements. The ends of the hangers were then tied in both rotation and displacement to the nodes of the slab.
The hangers themselves were modelled as 2-noded linear beam elements, as were the HEB 100 beams where present. The longitudinal and transverse beams were positioned in model space, accounting for the fact that the longitudinal beams were welded below the transverse beams, and then were tied at the connection to the hanger by means of tying rotational and translational displacements to a reference point which was created and located at the top of the hangers. The complete model geometry, including hangers and the HEB 100 beams and rendered with the beam profiles and shell thickness visible, is shown in Figure 29. The symmetry boundary condition which is applied to the model is located at the right hand edge as seen in the figure.
Figure 29 Finite element model geometry including HEB 100 beams and hangers.
5.3
Thermal modelling
Thermal modelling was carried out on the concrete only. The lower surface of the
concrete was exposed to both convection and surface radiation to represent the conditions inside of the fire resistance furnace. The convective heat transfer coefficient was 50 W/m2K. Emissivity of the surface for the radiation boundary condition was assumed to be 0.7. The temperature amplitude of both the radiative and convective boundary conditions was set to follow the hydrocarbon fire curve. The unexposed surface of the shell was exposed to the same types of boundary condition, however the convective heat transfer coefficient was set to 4 W/m2K; and the temperature of the source in both cases was set to an ambient room temperature of 293 K.
The material properties are taken from the Eurocode, choosing the lower curve for thermal conductivity shown in Figure 8, as this is the present national choice in Sweden. The specific heat capacity has been modified to account for the 7% moisture content in the concrete.
As shown in Figure 5, the sprayed concrete varied in thickness considerably. In fact, the real average thickness of the specimen was 151 mm as opposed to the nominal thickness 120 mm. The initial finite element modelling, carried out as a pre study, was based on the nominal thickness. 13 points were used through the shell thickness for the heat transfer analysis. A more detailed discussion of the effect of this resolution can be found in appendix E.
A comparison between the measured temperatures at different depths and the calculated temperatures around those depths is shown in figures 30 to 34. Dashed lines indicate the measured temperatures from the tests and solid lines indicate the calculated temperatures from the finite element analysis. In Figures 30 to 32 the predicted temperatures are shown at 10 mm intervals from the nearest points both above and below the measured data, e.g. in Figure 30, the measured data is shown from thermocouples with a depth from the exposed surface to the thermocouples of between 27 and 38 mm and the calculated values are shown at depths of 20, 30 and 40 mm. Because of the deviation in thickness between the designed specimen and the as-built specimen a number of thermocouples had a depth from the exposed surface which was greater than the designed cover and a number of surface thermocouples were mounted in portions of the shell structure which were thicker than the numerical model. This is reflected in Figures 33 and 34, where calculated
temperatures are reported only up to the thickness of the numerical model, although measured temperatures are reported with greater depth to the thermocouples.
Figure 30 Test 1, comparison between temperatures measured with thermocouples and temperatures calculated using heat transfer analysis between 27 and 38 mm
Figure 31 Test 1, comparison between temperatures measured with thermocouples and temperatures calculated using heat transfer analysis between 52 and 68 mm
Figure 32 Test 1, comparison between temperatures measured with thermocouples and temperatures calculated using heat transfer analysis between 77 and 99 mm
Figure 33 Test 1, comparison between temperatures measured with thermocouples and temperatures calculated using heat transfer analysis between 106 and 153 mm
Figure 34 Test 1, comparison between temperatures measured with thermocouples and temperatures calculated using heat transfer analysis at the unexposed surface level
A comparison between the predicted and the measured temperatures in Figures 30 to 34 shows fair agreement between the experiments and the calculations. The calculations have a slower heat penetration than the tests, and this is likely influenced by the higher diffusivity of the concrete at temperatures less than 300°C in the tests in comparison with the Eurocode material properties. It can be seen in Figure 30 that the predicted
temperatures at 20 and 40 mm bound the measured temperatures. However in Figure 31 it can be seen that at 50 and 70 mm depth from the exposed surface in the calculation the predicted temperatures no longer bound the measured temperatures, with the measured temperatures being higher. This trend continues, with a worse fit in the calculated temperatures as the depth to the thermocouples increases, i.e. a region with lower temperatures where the TPS measurement shows that the thermal diffusivity is higher than the thermal conductivity prescribed in the national choice in Sweden.
5.4
Mechanical modelling
A number of different cases were studied for the mechanical model, these are summarised in table 6 below.
Table 6 Summary of models and modelling approach undertaken Model Summary
Model 1 120 mm shell structure thickness Hangers restrained at the top Supporting steel frame omitted Model 2 120 mm shell structure thickness
Displacement of hangers prescribed to follow measured results Supporting steel frame omitted
Model 3 120 mm shell structure thickness
Displacement of hangers prescribed to follow measured results Supporting steel frame omitted
Poissons ratio of concrete 0.125 Model 4 120 mm shell structure thickness
Displacement of hangers prescribed to follow measured results Supporting steel frame omitted
Poissons ratio of concrete 0.5 Model 5 120 mm shell structure thickness
Hangers attached to supporting steel structure which is explicitly included Model 6 151 mm shell structure thickness
Hangers attached to supporting steel structure which is explicitly included Model 7 No shell structure
Hangers attached to supporting steel structure
Ends of hangers loaded according to load measured in the experiment In all cases, the concrete model chosen reflected the designed mix, with a concrete compressive strength of 40 MPa. Unless otherwise specified Poisons ratio of the concrete was assumed to be 0.25. The compressive stress vs strain curve is based on the Eurocode model described in section 5.1, above. The tensile behaviour is strain based and the peak tensile strength is assumed to be 10% of the compressive strength. The behaviour was implemented in Abaqus using the concrete damaged plasticity material model. The sprayed concrete in the test had variations in thickness over the whole surface, something which is difficult to model using the chosen approach. Therefore the numerical model cannot be expected to follow the test results exactly. Nevertheless, the general trends and magnitudes of the forces should be comparable.
5.4.1
Model 1
The results of model 1 in terms of the load which results on the hangers is shown in figure 35. First of all, comparing the load history in the test with the load history of the simulation, it can be seen that the non-uniformity of the thickness of the specimen causes a strong asymmetry in the experimental load history. This asymmetry is not reflected in the model in which uniformity of the concrete thickness is assumed.
In this model the hangers are restrained at the top, representing a totally rigid supporting frame. Initial curvature of the specimen under thermal loading results in a tensile force being applied at hangers B and E and a compressive force being applied at hangers A, C, D and F, as in the test. Continued heating leads to the loads on hangers A and C
becoming tensile.
The magnitude of the loads which are measured compared with those observed in the model are not similar, with the calculated load on the hangers at B and E being nearly four times that of the load measured in the experiment. As well as the thermal curvature induced in the concrete shell, this may be influenced by the inability of the hangers to deflect downwards in this model.
Figure 35 Load history in the hangers from the analysis of model 1.
5.4.2
Model 2
For model 2, the tops of the hangers had a prescribed displacement which was equal to that measured during the fire test. The resulting load history is shown in Figure 36. Once more, the initial curvature leads to a tensile load in hangers B and E and a compressive load in hangers A, C, D and F. The magnitude of these forces is only marginally lower than the magnitude of the forces calculated in Model 1.
Accounting for the deflection of the supporting frame by applying the measured deflections therefore has minimal impact on the results of the calculation.
Figure 36 Load history in the hangers from the analysis of model 2.
5.4.3
Models 3 and 4
The objectives of models 3 and 4 was to explore the impact of changing Poisons ratio of the concrete on the results. For model 3, Poisons ratio was set to 0.125, one half of that for models 1 and 2; and for model 4 the ratio was set to 0.5, double that for models 1 and 2. The tops of the hangers were forced to follow the measured displacement of the supporting frame, as in model 2. The results of the analyses are shown in figures 37 and 38.
Comparison of these figures with one another as well as with figure 36 shows that the Poisons ratio of the concrete has a very small influence on the load history in the hangers. Overall the behaviour is very similar, with only minor differences in the magnitudes at different times observed.
Figure 38 Load history in the hangers from the analysis of model 4.
5.4.4
Model 5
All of the models from 1 to 4 assumed either fixed boundary conditions for the tops of the hangers or prescribed a displacement equal to the measured displacement. It is clear from the load histories which are plotted that this approach is overestimating the magnitude of the loads on the hangers in the analysis by a factor of as much as 4.
Model 5 includes the supporting frame modelled explicitly, without prescribed load or displacement on the hangers. The frame is able to deflect downwards according to the load which results from thermal displacement of the concrete shell. All other aspects of the model are identical to Models 1 and 2. The resulting load history is shown in Figure 39. It can be seen that the overall trends of load history in model 5 agree well with those observed before. And while the overall loads are again higher than those which are reported in the test results, this is by a factor of only a little more than 2 in this model.
Figure 39 Load history in the hangers from the analysis of model 5.
The deflection history of the frame above the hangers in model 5 is shown in figures 40 and 41. Each figure shows the deflection along a different transverse beam on the supporting frame, with Figure 40 showing the deflections along the beam which is above hangers A, B and C; and Figure 41 showing the deflections along the beam which is above hangers D, E and F. Surprisingly, the calculated deflections show remarkably good agreement with the measured deflections; which is not consistent with the calculated forces in the hangers being a factor of up to 2 higher in the calculation than the test.
Figure 40 Deflection history above the hangers A, B and C from the analysis of model 5.
Figure 41 Deflection history above the hangers D, E and F from the analysis of model 5.
5.4.5
Model 6
Model 6 is identical to model 5, with the exception of the fact that the thickness of the concrete is increased to reflect the average thickness of the concrete shell in the test; i.e. from 120 to 151 mm. As can be seen in Figure 42 which shows the load history, this has some impact on the load in the model, with a slower increase in the tensile load on hangers B and E, although the magnitude of the forces in the hangers is still up to 3 times higher than that measured in the test when the peak forces are compared. Comparing the deflection history of model 6, Figures 42 and 43, with that of model 5, Figures 40 and 41, the magnitude of the deflections can be seen to be only slightly larger when the concrete shell thickness is increased.
Figure 42 Load history in the hangers from the analysis of model 6.
Figure 43 Deflection history above the hangers A, B and C from the analysis of model 6.
5.4.6
Model 7
At this stage it is clear that the modelling approach which is being used results in larger loads on the hangers, in the case of all models; but a similar deflection in the supporting frame in models 5 and 6.
The response of the steel supporting frame in the numerical model is verified by using superposition of the deflected shape from one of the transverse beams, in this case the transverse section which is located above hangers A, B and C. Each of these beams has 3 hangers from it, one at midspan and one at 100 mm from each of the supports. The deflection at the midspan of this beam as a result of a load on a hanger at midspan is given by
𝛿2,𝑃2 = 𝑃2𝐿 3
48𝐸𝐸
Where δ2,P2 denotes a deflection at location 2 (the midspan, where hanger B is located) caused by a load P at location 2 (P2); L denotes the distance between the supports E is the modulus of elasticity and I is the second moment of area. The deflection at midspan from a load acting at a distance a from the supports is:
𝛿2,𝑃1 =6𝐸𝐸𝐸𝑃1𝑎��𝐸2� 3 − 3𝐿 �𝐸2�2+ (𝑎2+ 2𝐿2)𝐸 2− 𝑎2𝐿�, and 𝛿2,𝑃3 =6𝐸𝐸𝐿 ��𝑃3𝑎 𝐿2� 3 − 3𝐿 �𝐿2�2+ (𝑎2+ 2𝐿2)𝐿 2 − 𝑎2𝐿�
Where δ2,P1 denotes a deflection at location 2 (the midspan) caused by a load P at location 1 (P1); δ2,P3 denotes a deflection at location 2 (the midspan) caused by a load P at location 3 (P3); and a denotes the distance between the supports and the point of load application, which in this case is the distance between the supports and hangers A and C.
The total deflection at the midspan, δ2, as a result of all three of these loads is simply given by:
𝛿2= 𝛿2,𝑃1+ 𝛿2,𝑃2+ 𝛿2,𝑃3
This expression may be used to verify the response of the finite element model of the supporting structure by comparing the deflections which are calculated in the numerical analysis with the deflection which is calculated at the midspan using the equations given above.
Removing the concrete slab from the model and applying the measured loads on the hangers from the experiments to the hangers in the numerical model results in the displacements shown in figure 45. The series labelled ‘measured’ is the measured deflection from the tests; the series labelled ‘abaqus’ shows the deflections which are calculated using the finite element method applying the measured loads as described; and the series labelled ‘calculated’ shows the deflection at hanger B when all 3 of the loads measured at A, B and C are used to calculate the deflections using the equations given above. As would be expected, the lack of longitudinal beams in the simple analytical model results in a slightly higher deflection than the abaqus model, nevertheless these two models do correlate very well. Conversely the measured deflection from the test does not agree well with the finite element model or the analytical model.
The same comparison of deflections calculated using the finite element model with the analytical model described above and with the test results is shown in Figure 46 for the supporting frame above hanger E. This comparison shows better agreement between the analytical and the finite element model; and a far better agreement between the two models and the magnitude of deflections observed in the test at this location. Because the load on the hangers was measured only at locations A to F, symmetry was assumed in the model, although this was clearly not the case in the test as a result of non-uniformity of the concrete thickness. The fact that hangers D, E and F are further away from the assumed line of symmetry may help to reduce the influence of this assumption.
Based on the results of model 7 and the comparison between the analytical, numerical and test results it can be concluded that the behaviour of the steel frame in the numerical model is good; and that this approach is reasonable. It can also be concluded that the effect of the assumption of symmetry above may well have been significant. However no measurements of the force in the hangers on the other half of the system were taken during the test which can be used for comparison. This should certainly be considered for future validation exercises.
Figure 45 Deflection history above hanger B from the analysis of model 7.
5.5
Discussion
The results of the modelling can be summarised as follows:
• A very small change is seen in the results of model 2 in comparison with model 1 by including the deflections which were measured on the supporting frame above the hangers than when the tops of the hangers are restrained in the vertical direction. Explicitly including the supporting frame in the numerical model leads to better agreement between the modelling results and the test.
• Changing the concrete poisons ratio is not seen to have a significant effect on the results of the calculations.
• The model did not initially account for the variations in the concrete shell thickness, however comparing models 5 and 6, this seems to make very little difference in the calculated load and displacement of the hangers.
• There remain questions about the overall behaviour of the system during the test. Comparing the abaqus model (models 5 and 6) including the supporting frame with the test results suggest that for the measured deflections to have occurred the stress in the hangers must have been higher than that measured. However,
comparison with simple analytical approximations and model 7 suggests that the assumption of symmetry may have had an effect on this. This deviation is an unresolved question in need of further investigation. Uncertainties in the mechanical boundary conditions which arise because of the way that the specimens were placed on the furnace may also make it very difficult to model the test; and this may have contributed to this discrepancy.
• One of the purposes of this investigation was to determine if finite element calculations could be used as an alternative to fire testing for this type of spray applied tunnel lining. The loads and deflections which are calculated using the numerical model are larger by a factor of up to 4 than the loads and deflections which were measured during the test unless the steel supporting frame is explicitly included, in which case the loads on the hangers are larger by a factor of about 2. Considering the impact of the assumption of symmetry on the modelling, as shown in the results from model 7, this may account for much of the differences between the overall behaviour of the model and the experiment. The modelling approach proposed is therefore very conservative, and this may justify the use of modelling as opposed to testing. It is possible that the testing methodology could be better designed in order to further validate the modelling approach.
6
Conclusions
Two fire resistance tests have been performed on a sprayed concrete inner lining for tunnels. As the test specimens were relatively young, 49 and 51 days, it was concluded that 2 kg/m3 was needed due to the fact that young and moist concrete is known to spall much during fire exposure. During the first test on a section of nominal size 5 × 3 × 0.12 m3 the specimen maintained the integrity and insulation criteria for fire resistance during 180 minutes fire exposure with the Hydrocarbon fire curve. During the second test on two specimens with half the size both the integrity and the insulating criteria was maintained during the 180 minutes long fire exposure but during this test there was a dip in furnace temperature during a part of the testing time.
The thermal properties of the tested concrete was measured with the transient plane source method at temperatures 22, 150, 170 and 300°C. Compared with the Swedish national choice for temperature dependent thermal properties in the Eurocode, EN 1992-1-2:2004, it was found that for the first three temperature levels the this sprayed concrete had a slightly higher thermal diffusivity and at the level 300°C the value was as the national choice.
A considerable thickness variation was present in the sprayed sections. In the large test specimen the average thickness was 31 mm higher than the nominal thickness 0.12 m and the highest thickness measured deviated as much as 97 mm from the nominal thickness. The measured behaviour during the test was modelled using the finite element method, using the prescribed thermal properties and the simplified temperature dependent
stress/strain model in the Eurocode, EN 1992-1-2. Various parameters were investigated, including the way that the supporting frame assembly is accounted for in the modelling, the effect of concrete thickness on the results and the effect of poisons ratio on the numerical results. The thermal calculations showed a reasonably good agreement with experiments close to the exposed surface, but further into the cross section the
temperature development was under estimated when using the Swedish national choice for thermal properties. This results was in line with the results from the determination of the real thermal properties with the TPS method. When investigating the stress
development in the supporting rods it was found that this model gives conservative results in comparison with the test results by a factor of as much as 4 unless the steel frame is included in which case the level of conservativeness reduces. There may be a
considerable impact on the magnitude of the deflections and forces in the hangers of the assumption of symmetry which was taken when designing both the test and the
7
References
[1] Jansson R. “Measurement of concrete thermal properties at high temperature” Proceedings from the fib Task group 4.3 Workshop “Fire Design of Concrete Structures: What now? What Next?”, Milan, Italy, December 2-3, 2004
[2] Popovics “Strenght and Related properties of concrete – A quantitative approach” Book printed 1998
[3] RILEM COMMITTEE 44- PHT “Behaviour of concrete at high temperature” edited by Schneider, 1985
[4] Schneider and Haksever (1976) “Bestimung der äkvivalenten Branddauer von static bestimt gelagarten Stalbetonbalken bei natürlichen bränden” Braunshweig, Germany, 1976
[5] Abaqus version 6.14-1; Dassault systems 2014
[6] ISO 22007-2:2008 Plastics -Determination of thermal conductivity and thermal diffusivity - Part 2: Transient plane heat source (hot disc) method
[7] Feron C., Larive C. and Chatenoud G.“Spalling of sprayed concrete under tunnels fire conditions” Proceedings of Concrete Repair, Rehabilitation and Retrofitting II, 2nd International Conference on Concrete Repair, Rehabilitation and Retrofitting, ICCRRR-2, Cape Town, South Africa, 24-26 November, 2008
8
Appendix A - Deviations from nominal
thickness
Figure 47 Specimen 1, large slab. Deviation from nominal thickness 120 mm.
Figure 48 Specimen 2A, small slab. Deviation from nominal thickness 120 mm. 0 1200 2400 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 0 600 12 00 18 00 24 00 30 00 36 00 42 00 48 00 80-100 60-80 40-60 20-40 0-20 -20-0 -40--20 -60--40 -80--60 -100--80 -120--100 0 600 1200 1800 2400 3000 -120 -100-80 -60 -40 -200 20 40 60 80 100 120 100-120 80-100 60-80 40-60 20-40 0-20 -20-0 -40--20 -60--40 -80--60 -100--80 -120--100
Figure 49 Specimen 2B, small slab. Deviation from nominal thickness 120 mm. 0 600 1200 1800 2400 3000 -120 -100-80 -60 -40 -200 20 40 60 80 60-80 40-60 20-40 0-20 -20-0 -40--20 -60--40 -80--60 -100--80 -120--100
9
Appendix B - Positions of thermocouples
Table 7 Position of individual thermocouples and local deviation from nominal thickness during test 1.
TC x [cm] y [cm] Deviation from nominal thickness
A Ar 75 370 27 A 0 70 375 28 A 30 80 375 24 A 90a 90 385 22 A 90b 75 460 64 A90c 125 407 66 A 110 100 395 23 B Ar 225 370 43 B 0 230 375 47 B 30 220 375 38 B 90a 210 385 25 B90b 225 460 61 B 110 200 395 17 C Ar 65 250 21 C 0a 140 250 25 C 0b 65 250 21 C 30 138 240 21 C 90a 138 260 28 C 90b 75 250 23 C 110 135 250 22 D0 230 250 57 D 90 225 250 52 E Ar 75 130 15 E 0 75 120 11 E 30 78 134 16 E 90a 85 120 8 E 90b 75 40 8 E 110 90 145 25 F Ar 225 130 63 F 0 230 125 64 F 30 220 125 63 F 90a 210 115 61 F 90b 225 40 47 F 90c 175 90 50 F 110 200 105 58
10
Appendix C – Results from measurement of
thermal properties
22C, 0.45W, 80 sec, sensor Kapton 4921
Temperature Th.Conductivity Th.Diffusivity Spec.Heat
22 1.68 0.88 1.91 22 1.68 0.88 1.92 22 1.68 0.88 1.92 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.92 22 1.68 0.87 1.92 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.93 22 1.68 0.87 1.92 22 1.68 0.87 1.92 22 1.68 0.87 1.92 22 1.68 0.87 1.92 22 1.68 0.88 1.92 stdev 0.00 0.00 0.00 average 1.68 0.87 1.92 stdev % 0.04 0.23 0.20
150C, 0.45W, 80 sec, sensor Kapton 4921
Temperature Th.Conductivity Th.Diffusivity Spec.Heat
150 1.29 0.69 1.88 150 1.29 0.69 1.87 150 1.30 0.71 1.83 150 1.30 0.71 1.82 150 1.30 0.71 1.82 150 1.30 0.72 1.82 150 1.30 0.72 1.81 150 1.30 0.72 1.81 stdev 0.00 0.01 0.03 average 1.30 0.71 1.83 stdev % 0.26 1.69 1.45
Temperature Th.Conductivity Th.Diffusivity Spec.Heat 170 1.33 0.69 1.91 170 1.37 0.76 1.80 170 1.26 0.57 2.21 170 1.26 0.59 2.14 170 1.34 0.77 1.75 170 1.30 0.63 2.07 170 1.26 0.59 2.11 170 1.31 0.71 1.84 170 1.34 0.79 1.71 170 1.34 0.76 1.77 170 1.31 0.66 1.99 170 1.25 0.58 2.17 170 1.23 0.56 2.19 170 1.25 0.61 2.06 170 1.28 0.67 1.90 170 1.32 0.76 1.74 170 1.33 0.78 1.70 170 1.32 0.70 1.87 170 1.25 0.59 2.13 170 1.24 0.59 2.09 170 1.27 0.67 1.89 170 1.30 0.73 1.79 170 1.33 0.76 1.75 170 1.30 0.66 1.96 170 1.23 0.57 2.14 170 1.27 0.68 1.87 170 1.32 0.75 1.77 170 1.23 0.57 2.14 170 1.27 0.68 1.87 170 1.31 0.74 1.75 stdev 0.04 0.08 0.17 average 1.29 0.67 1.94 stdev % 3.08 11.25 8.69 300C, 0.45W, 80 sec
Temperature Th.Conductivity Th.Diffusivity Spec.Heat
300 1.15 0.47 2.46 300 1.15 0.47 2.45 300 1.15 0.47 2.46 300 1.15 0.47 2.46 300 1.15 0.47 2.46 300 1.15 0.47 2.46 300 1.15 0.46 2.47
300 1.15 0.47 2.46 300 1.15 0.47 2.45 300 1.15 0.47 2.45 300 1.15 0.47 2.45 300 1.15 0.47 2.46 300 1.15 0.47 2.46 300 1.15 0.47 2.45 stdev 0.00 0.00 0.01 average 1.15 0.47 2.46 stdev % 0.12 0.28 0.23
