NUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE DAMAGE AND EXPLOSIVE SPALLING

Transcription

1 NUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE DAMAGE AND EXPLOSIVE SPALLING Prof. Joško Ožbolt 1 Josipa Bošnjak 1, Goran Periškić 1, Akanshu Sharma 2 1 Institute of Construction Materials, University of Stuttgart, Germany 2 Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai, India Sponsored by DFG 1

2 Contents Introduction Thermo-mechanical (TM) model Thermo-hygro-mechanical (THM) model Applications of the thermo-mechanical model Plain concrete beams in fire Reinforced concrete beams in fire Applications of the thermo-hygro-mechanical model Macro vs. meso scale FE analysis Average vs. Local properties (porosity, permeability,..) Influence of inhomogeneities on explosive spalling Influence of external loading, permeability and rel. humidity on explosive spalling Permeability tests at elevated temperatures Summary and Conclusions 2

3 Introduction Concrete does not burn, however, when exposed to fire there are: Large degradation of mechanical properties Large thermal (non-elastic) strains Thermal induced damage and explosive spalling Limited number of experiments on relatively small structures Difficulties in experimental measurements Alternative & support realistic numerical models Multi scale modeling (explosive spalling) 3

4 Explosive spalling of concrete cover Experimental evidence (high strength concrete): Explosive spalling is a local phenomenon: Relatively small volume of the material on concrete surface fails - potential energy is transformed into kinetic energy + dynamic fracture of concrete Main reasons: Pore pressure & thermally induced stresses Influencing parameters: permeability, humidity, heating rate, external load, boundary conditions & geometry Addition of polypropylene prevents explosive spalling; Reasons: Increase of porosity, permeability, additional microcracking Large scatter of measured data 4

5 Theoretical framework macro & meso FE analysis Continuum mechanics Quasi-static loading conditions Green-Lagrange strain tensor Co-rotational stress tensor Irreversible thermodynamics Mechanical model - temperature sensitive microplane model for concrete Discretization method - standard finite elements Smeared crack concept with crack band method as a localization limiter 5

6 Processes to be modeled Non-mechanical processes: Transport of capillary water Transport of heat Pore pressure Mechanical processes: Damage and cracking of concrete Dynamic fracture of concrete (explosive spalling) Interaction between mechanical and non-mechanical processes 6

7 Temperature dependent microplane model (mechanical strain) Finite strains: co-rotational stress & GL strain tensor Kinematic constraint : from ij V, D, Tr 0 V F V ( V ) 0 D F D ( D,eff ) 0 Tr F Tr ( Tr,eff, V ) Weak form of equlibrium: 0 ij 0 V ij 3 2 S 0 (n D i n j ij 3 )ds 3 2 S 0 Tr 2 (n n ) ds i rj j ri Macroscopic temperature dependent concrete properties Uniaxial tensile strength f t (T,t) Uniaxial compressive strength f c (T,t) Tensile fracture energy G F (T,t) Compressive fracture energy G C (T,t) = 100G F (T,t) Poisson s number = constant Calculated temperature and time dependent properties of the microplane model 7

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9 Hygro-thermal part of the model (THM model) (single phase model) 9

10 Hygro-thermo-mechanical coupling (permeabilty & porosity) 10

11 Application of the TM model macro analysis Plain concrete beams exposed to ISO 834 fire Specimen geometry and loading setup (4 point bending) heating all in mm V1 L1 C1 FE discretization Z F23 Y X F3 11

12 Relative strength Relative strength Plain concrete beam (4-point bending) Ultimate load reduction due to fire exposure (comparision of experimental and numerical results) C25 (experimental) C25 (hot strength) C25 (residual strength) C45 (experimental) C45 (hot strength) C45 (residual strength) Temperature [ C] Temperature [ C] 12

13 RC beams exposed to ISO 834 fire (three-sided exposure) Specimen geometry and loading setup (4 point bending) Reinforcement Measured air temperatures X Y Z Concrete X Y Z FE discretization 13

14 Relative ultimate load Relative stiffness RC beams exposed to ISO 834 fire (three-sided exposure) Ultimate load reduction due to fire exposure (comparision of experimental and numerical results) (a) (b) k 1 _FE Analysis k 1 _Experiment k 2 _FE Analysis k 2 _Experiment FE Analysis Experiment Duration of heating [h] Duration of heating [h] 14

15 RC beams exposed to ISO 834 fire (three-sided exposure) Failure mode for the reference beam (without fire exposure) Failure mode and temperature distribution after 60 minutes of fire 15

16 Application of the THM model macro scale Geometry Reasons & mechanism temperature induced stresses pore pressure geometrical instability... Plane strain FE mesh sym. Investigated parameters: permeability humidity heating rate strength of concrete the role of geometrical non-linearity 16

17 Stress normal to surface [MPa] Stress parallel to surface [MPa] Thermal-strain induced stresses (macro analysis) 17

18 Explosive spalling macro scale Time evolution of relevant quantities at the position of initialization of crack (spalling) 18

19 Summary based on numerical studies (macro analysis) Stresses due to thermal strain alone cause no explosive spalling Pore pressure, mainly controlled by permeability, has dominant influence on explosive spalling Geometrical instability due to compressive stresses increases the risk of explosive spalling Expected level of local pore pressure (simple engineering model): n = porosity n= 0 p= n= 1 p= 0 n= 0.5 p= ft n= 0.1 p= 9ft 19

20 Motivation Explosive spalling meso scale analysis Average properties of concrete are not relevant Heterogeneity Local material properties strongly influence explosive spalling Inhomogeneity of heating field influences explosive spalling Large scatter of measured data (average pore pressure, average permeability,..)can be explained by the fact that explosive spalling is local and not global (macroscopic) phenomena To realistically study explosive spalling analysis at meso scale is required 20

21 Influence of inhomogeneity on explosive spalling Non-homogeneity of heat flux Material homogeneity Permeability of concrete a 0 = 6 x m/s macro scale, homogeneous heat flux explosive failure after t= 13,2 min macro scale, non-homogeneous heat flux explosive failure after t= 12,0 min homogeneity of temperature field non-homogeneity of temperature field - heat flux over the width varied by 25% 21

22 Influence of inhomogeneity on explosive spalling Homogeneity of heat flux Influence of different distribution of permeability Random variation of permeability (a 0 = 6 x 10-14, a 01 =1 x ) meso scale, constant permeability explosive failure after t= 15,4 min meso scale, spatial variation of permeability explosive failure after t= 14,9 min 22

23 Influence of inhomogeneity on explosive spalling Homogeneity of heat flux Influence of different aggregate configuration (meso scale) Max. aggregate size d = 8mm (realistic ratio of coarse aggregates in concrete) Permeability of concrete a 0 = 6 x m/s meso scale, spatial distribution of aggregate A explosive failure after t= 10,7 min meso scale, spatial distribution of aggregate B explosive failure after t= 9,33 min 23

24 Influence of inhomogeneity on explosive spalling Homogeneity of heat flux Macro and meso scale model 50 x 50 x 50 mm macro scale, explosive failure after t= 8,1 min meso scale explosive failure after t= 6,9 min Section A Section A 24

25 Influence of external load on explosive spalling Influence of external compressive load Comparison between macro- and meso-scale Experimental evidence: External compressive loads enhance explosive spalling!! 25

26 Time to spalling [min] Time to spalling [min] Influence of permeability and humidity on explosive spalling Meso scale Influence of permeability and relative humidity on explosive spalling Time of spalling vs. humidity VarA_ETK Relative humidity [%] Time of spalling vs. mortar permeability VarA_ETK 5.E-16 5.E-15 5.E-14 Permeability [m2] Spalling does not occur at very low humidity level as well as in case of very permeable concrete. 26

27 Explosive spalling - meso scale Time evolution of pore and volumetric pressure at the position of initialization of crack (spalling) 27

28 Permeability at high temperatures - General PDE-Pressure decay experiment Darcy s law: Q k A dp dx Q [m 3 ] - the volumetric flux k [m 2 ] - the permeability factor (apparent) A [m 2 ] - the cross-sectional area η [Pa s] -the dynamic viscosity of the transported fluid dp /dx [Pa/m] - the pressure gradient Slip flow phenomenon (compressible fluids): k kint 1 b p Apparent permeability: ln( r2 / r1 ) Qp 2 H ( p p ) k p [Pa] - the pressure (average) k int [m 2 ] - the permeability factor (intrinsic) b [Pa] - the Klinkenberg slip flow coefficient 28

29 Permeability at high temperatures - Verification RILEM Permeability experiment Permeability test at 20 C: RILEM Permeability experiment K = 2,6 x m 2 Pressure decay experiment K= 2,0 x m 2 29

30 Permeability at high temperatures - Setup Test setup Concrete specimen 30

31 Permeability at high temperatures - Setup Nitrogen inlet Nitrogen outlet 31

32 Relative permeability [ki/k(80 C)] Permeability at high temperatures - Results Comparison with experimental data obtained from literature Schneider Kalifa et al 2001 (Cembureau method) Kalifa et al 2001 (Hassler method) Experiment C50/ Temperature [ C] Experimental results obtained from the literature - Specimens were not dried prior testing (Schneider), residual permeability (Kalifa et al.) Experiments C50/60 Specimens kept at 60 C until steady mass state prior to testing 32

33 lntrinsic permeability [m 2 ] Permeability at high temperatures - Results Test results with concrete C80/95 with and without addition of polypropylene fibres 1E-14 1E-15 1E-16 1E-17 1E-18 Loss of thermal stability (120 C) Melting point (160 C) Temperature [ C] PP 0%-1 PP 0%-2 PP 0%-3 PP 1%-1 PP 1%-2 PP 1%-3 Experiment - Specimens kept at 60 C until steady mass state prior to testing 33

34 Virgin concrete Microscopic investigation PP Fibers 20 min of exposure to 200 C 2 days of exposure to 200 C 34

35 2 days of exposure to 200 C Microscopic investigation Empty space in polypropylene microcracks 35

36 Summary & conclusions Thermo-mechanical phenomena - macro scale For explosive spalling thermo-hygro-mechanical model is required Explosive spalling is a local phenomenon - local properties are relevant Macroscale modelling cannot capture all the aspects of explosive spalling Explosive spalling can be properly modeled only at meso scale Large scatter of measured data show that the phenomenon is local and not global Experimental results = PP fibres mitigate explosive spalling A new experimental setup for measurement of permeability at high temperature Experiments confirmed that the permeability is the key parameter governing the explosive spalling. These findings correspond well to the results of the numerical analysis. The designed equipment for measurement of permeability of concrete at hot conditions is simple and reliable. 36

37 Thank you! 37