Progettazione e Certificazione Antincendio delle Strutture Civili e Industriali Vicenza, 21 Giugno 2006

Transcription

1 Progettazione e Certificazione Antincendio delle Strutture Civili e Industriali Vicenza, 21 Giugno 2006 Incontro Tecnico promosso da Gruppo EFFE2 e Summania Beton Progettazione di Strutture Prefabbricate Civili e Industriali Resistenti al Fuoco Carmelo Majorana Dipartimento di Costruzioni e Trasporti Facoltà di Ingegneria Università degli Studi di Padova & CPR-TRASTEC

2 CONCRETE AT HIGH TEMPERATURE Concrete fire assessment G.Khoury, 2000 G.Khoury et al., FIB 4.3.1, Fire Design of Concrete Structures Materials, structures and modelling Guide to good practice

3 CONCRETE AT HIGH TEMPERATURE Concrete fire assessment G.Khoury, 2000 G.Khoury et al., FIB 4.3.1, Fire Design of Concrete Structures Authors: Gabriel Alexander Khoury (UK), Joris Fellinger (NL), Kees Both (NL), Carmelo Majorana (I), Yngve Anderberg (S), Niels Peter Høj (CH)

4 Progettazione e Certificazione Antincendio delle Strutture Civili e Industriali Vicenza, 21 Giugno 2006 Padua CTHM Model Layout Mathematical model of chemo-thermo-hydro-mechanical behaviour of concrete at high temperature Modelling of thermo-chemo-mechanical degradation of concrete at high temperature Modelling of strains and stresses of concrete at high temperature Spalling phenomena consequent to fire

5 Progettazione e Certificazione Antincendio delle Strutture Civili e Industriali Vicenza, 21 Giugno 2006 Autori della Ricerca C.E. Majorana 1 D. Gawin 2, F.Pesavento 1, B.Schrefler 1, F.Corsi 3 1 Dipartimento di Costruzioni e Trasporti Università degli Studi di Padova (Italy) & CPR-TRASTEC 2 Dept. of Building Physics and Building Materials Technical University of Łódź (Poland) 3 ENEA Casaccia, Rome, (Italy),

6 CONCRETE AT HIGH TEMPERATURE Causes of thermal spalling phenomenon stresses: aggregate - cem. matrix + thermal degradation + chemical degradation moisture clog High pressure of vapour + water from dehydration

7 CONCRETE AT HIGH TEMPERATURE Causes of thermal spalling phenomenon Constraints for thermal dilatation Mechanical stresses stresses: aggregate - cem. matrix + thermal degradation + chemical degradation moisture clog + thermal dilatation of water High pressure of vapour + water from dehydration

8 CONCRETE AT HIGH TEMPERATURE Causes of thermal spalling phenomenon G.Khoury, Spalling Review, UPTUN Project, EC, Mid Term Meeting, Venice, November 2004

9 PHYSICAL MODEL Assumptions Concrete treated as a deformable, multiphase porous material Local thermodynamic equilibrium state Phase changes and chemical reactions (hydration/dehydration) Full coupling: hygro thermo - mechanical (stress strain) chemical (cement hydration / concrete dehydration)

10 PHYSICAL MODEL Assumptions Different mechanisms of moisture and energy transport Evolution of material properties, e.g. porosity, permeability, strength properties Non-linear material properties with respect to temperature, gas pressure, moisture content and material degradation

11 PHYSICAL MODEL Transport mechanisms Capillary water (free water): advective flow (water pressure gradient) Physically adsorbed water: diffusive flow (water concentration gradient) Chemically bound water: no transport Water vapour: Dry air: advective flow (gas pressure gradient) diffusive flow (water vapour concentration gradient) advective flow (gas pressure gradient) diffusive flow (dry air concentration gradient)

12 PHYSICAL MODEL Phase changes and chemical reactions Dehydration: solid matrix + energy chemically adsorbed water Hydration: chemically adsorbed water solid matrix + energy Evaporation: capillary water + energy water vapour Condensation: water vapour capillary water + energy Desorption: physically adsorbed water + energy water vapour Adsorption: water vapour physically adsorbed water + energy

13 MATHEMATICAL MODEL Micro - macro - description Balance equations: local formulation (micro- scale) Volume Averaging Theory by Hassanizadeh & Gray, 1979,1980 global formulation (macro- scale) Representative Elementary Volume Model development: Lewis & Schrefler: The FEM in the Static and Dynamic..., Wiley, 1998

14 THEORETICAL MODEL Model equations Dry air & skeleton mass balance Water (liquid & gas) & skeleton mass balance Enthalpy balance for the multiphase medium Linear momentum balance for the multiphase medium (mechanical equilibrium condition) Evolution equations: -dehydration - thermo-chemical & mechanical degradation (isotropic damage theory) ( & enhancement) full developments & details: Gawin D., Majorana C.E., Schrefler, B.A., : Numerical analysis of hygrothermal, MCFM, (1999) Gawin D.: Modelling of coupled heat and (habilitation thesis), Tech. Univ. Lodz (2000) Pesavento F.: Nonlinear modelling of concrete (PhD. thesis), Univ. Padova (2000) Khoury G.A., Majorana C.E., CISM Course, Udine, (2003)

15 THEORETICAL MODEL State and internal variables Gas pressure p g Capillary pressure p c Temperature T Displacements u Mechanical damage d Thermo-chemical damage V Dehydration degree Γ dehydr

16 THEORETICAL MODEL Numerical solution Discretization in space (FEM): p = p ( t) = N p ( t), p = p ( t) = N p ( t), g g p g c c p c T = T( t) = NT( t), u= u( t) = Nu( t). Weak formulation (by Galerkin method): C p& + C p& + C T& + C u& + K p + K p + K T + f = 0, gg g gc c gt gu gg g gc c gt g C p& + C p& + C T& + C u& + K p + K p + K T + f = 0, cg g cc c ct cu cg g cc c ct c Cp& + Cp& + CT& + Cu& + Kp + Kp + KT+ f= 0, tg g tc c tt tu tg g tc c tt t C u & + C p& + C p& + C T& + f& = 0, uu ug g uc c ut u t C ( x) x& + K( x) x+ f( x) = 0 where x T = { p, p, T, u} g c u

17 THEORETICAL MODEL Numerical accuracy with D.E.I. Modified component-wise backward error with different pivoting techniques Univ. of Padua

18 MODELLING OF CONCRETE DEGRADATION Total damage Joint action of the thermo-chemical and mechanical damage ET ( ) ET ( ) Eo( T) D = 1 = 1 = 1 1 d 1 V E ( T ) E ( T) E ( T ) o a o o a ( ) ( ) σ% S = σ = S% σ ( 1 d )( 1 V ) Multiplicative 0 e 0 σ = (1 d)(1 V) Λ : ε = (1 D) Λ : ε e [Majorana, Vitaliani, 1996] [Gerard, Pijaudier-Cabot, Laborderie,1998] [Gawin, Pesavento, Schrefler, 2003] [Giannuzzi, 2003]

19 MODELLING OF CONCRETE DEGRADATION Total damage Stress strain relationship 10 5 C30 0 Stress [MPa] C 100 C 200 C 400 C 600 C C Strain [-]

20 STRESS AND STRAINS OF CONCRETE Phenomenological approach Shrinkage strain dε sh = β dϕ sh e.g: [Bazant ed., Mathematical Modelling of Creep and Shrinkage of Concrete, Wiley, 1988] No physical mechanisms are taken into account Based directly on the experimental data

21 STRESS AND STRAINS OF CONCRETE Effective stress principle Capillary pressure & disjoining pressure Forces: in water capillary disjoining in skeleton capillary disjoining

22 STRESS AND STRAINS OF CONCRETE Effective stress principle σ" = σ + α I s p 3,5E-01 Coefficient x 3,0E-01 p s = p g x ws s p c 2,5E-01 2,0E-01 1,5E-01 [Gray & Schrefler, 2001] 1,0E-01 5,0E-02 p s = p g S p c 0,0E+00 0,0 0,2 0,4 0,6 0,8 1,0 Saturation [-] where ws x s is the solid surface fraction in contact with the wetting film, I - unit, second order tensor, α - Biot s coefficient, p g - pressure in the gas phase, p s - pressure in the solid phase

23 STRESS AND STRAINS OF CONCRETE Effective stress principle Shrinkage Coefficient strain Ratio χ [m/m] [-] χ /S [-] Shrinkage strains 0, High Performance Concrete 0, at experiment at T=20 C theory by Coussy 0, theory by Gray & Schrefler 0,0006 theory by Schrefler & Gray 0.6 theory by Schrefler & Gray 0, theory by Coussy 0.5 theory by Coussy 0, , , , % 0 20% 40% 60% 80% 100% 0% 0 20% 0,2 40% 0,4 60% 0,6 80% 0,8 100% 1 Saturation [%] Saturation Relative humidity [%] [-] [Gray & Schrefler, 2001] σ σ I s " = +α p s g ws c = χs p p p [Coussy, 1995] dσ dσ Idp s " = +α s g c = w dp dp b S dp Experimental data from: [Baroghel-Bouny, Mainguy, Lassabatere, Coussy, Cement Concrete Res. 29, 1999]

24 STRESS AND STRAINS OF CONCRETE Concrete strain at high temperature Load Free Thermal Strain (LFTS) model Linear strain [m/m] Thermal dilatation of C E-03 0,9 1,0E E-03 experimental 0,8 8,0E-03 total 6.0E-03 0,7 therm_dilat 6,0E-03 0,6 shrinkage 5.0E-03 thermo-chem. 4,0E-03 0,5 4.0E-03 0,4 2,0E E-03 0,3 0,0E+00 0,2 2.0E-03-2,0E-03 0,1 1.0E-03-4,0E E+000 0,1 0,2 0,3 0,4-6,0E Dehydration degree [-] ,0E-03 Thermo-chem. strain [m/m] Thermo-chemical damage [-] Thermo-chem. damage [-] Temperature [ o C] dε V dv tchem = βtchem ( ) LFTS - irreversible part of thermal strain V thermo-chemical damage parameter LFTS model according to: [Gawin, Pesavento, Schrefler, Materials and Structures, 2004]

25 STRESS AND STRAINS OF CONCRETE Concrete strain at high temperature Load Induced Thermal Strain (LITS) model 1,00E-02 Transient thermal creep of C-90 dε tr = βtr( V ) Q:σ% f( T ) c a dt Linear strain [m/m] 7,50E-03 5,00E-03 2,50E-03 0,00E+00-2,50E-03-5,00E-03-7,50E-03-1,00E-02 0% load 15% load 30% load 60% load 45% load Temperature [oc] 1 Q = γδ δ γ δ δ + δ δ 2 ( )( ) ijkl ij kl ik jl il jk LITS: [Khoury 1986, Thelandersson, 1987] [Khoury, Majorana, 2001] β tr (V) relation according to: [Gawin, Pesavento, Schrefler, Materials and Structures, 2004]

26 CONCRETE AT HIGH TEMPERATURE Constitutive relationships material properties Dehydration of concrete Dehydration degree [-] 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Dehydration rate [1/s] 0,035 0,03 0,025 0,02 0,015 0,01 0, ,2 0,4 0,6 0,8 1 Temperature [ o C] Dehydration degree [-] Γ = Γ = ( Γ ) a A exp dehydr ( t) [ T ( t) ] dehydr max Γ t Γ E RT T temperature of concrete A Γ chemical affinity

27 CONCRETE AT HIGH TEMPERATURE Constitutive relationships material properties Permeability damage relationship 1.E-13 Water intr. permeability [m 2 ] 1.E-14 1.E-15 1.E-16 1.E-17 C-60 C-60 SF C-70 C-90 1.E Damage parameter [-] k p f ( T) p = ko g p o g A A D D

28 NUMERICAL MODELLING Stages of numerical solution Governing equations of the model Galerkin s (weighted residuum) method Variational (weak) formulation FEM (in space) FDM (in time domain) Discretized form (non-linear set of equations)

29 NUMERICAL MODELLING Stages of numerical solution Discretized form (nonlinear equations) the Newton - Raphson method Solution of the final, linear equation set the frontal method Computer codes (HMTRA, HITECOSP, HITECOSP2)

30 MODEL VALIDATION Temperature-pressure measurement test Experimental facility CSTB Grenoble (France) 2mm 10mm radiant heater 5000W C Tested material: C-100 Fibres content: 0-3 kg/m 3 thermal insulation (ceramic blocks) 50mm specimen 30x30x12 cm 2 Measurements of temperature and gas pressures at 6 depths from the heated surface pressure Validation of the numerical model temperature Balance details about tests: [Kalifa et al.., 2001]

31 MODEL VALIDATION Experimental vs numerical test results Température (C ) M C Temps (heures) Distance à la face chauffée Temperature [ C] 2mm 10mm 20mm 30mm 40mm 50mm mm 10 mm 20 mm 30 mm 40 mm 50 mm time [hours]

32 MODEL VALIDATION Experimental vs numerical test results Pression (bars) C 233 C 239 C 240 C 243 C M C Temps (heures) Distance à la face chauffée 10mm 20mm 30mm 40mm 50mm Pressure [bar] mm 20 mm 30 mm 40 mm 50 mm time [hours]

33 MODEL VALIDATION 2 nd Experimental Test Initial conditions : gas pressure: Pa saturation degree 50 % surrounding temperature 25 C Boundary conditions : gas pressure: Pa p vap = 1000 Pa con β c = 0.05 m/s heating rate according to experimental test (5K/min) [Phan L.T., Lawson J.R., Davis F.L., Effects of elevated temperature exposure on heating characteristics, spalling, and residual properties of high performance concrete, Materials and Structures, 34, 83-91, 2001]

34 MODEL VALIDATION 2 nd Experimental Test Rendering of the fracture formation The first layer (2 cm thick) is particularly affected from the explosive spalling phenomenon TOTAL DAMAGE [-] min. 90 min. 100 min. 110 min. 115 min. 120 min. 300 min DISTANCE [cm] t increasing

35 NUMERICAL MODELLING Simulation of a heated column section

36 PADUA CTHM MODEL The model has been / is being implemented by: TNO, Delft, The Netherlands Technical School Prague, Czech Republic Dalian University, China CEA, Paris, France Marne La Vallée, France

37 MODELLING OF FIRE IN TUNNEL Tunnel fires Tauern Tunnel Fire Gotthard Tunnel Fire

38 MODELLING OF FIRE IN TUNNEL Boundary Conditions Experimental & standard curves of temperature history Air Temperature at 6.50 m height Temperature [ C] :00 0:05 0:10 0:15 0:20 0:25 0:30 0:35 0:40 0:45 0:50 0:55 1:00 Time [h] m m 00.0 m m m TEMPERATURA [ o C] Temperature [ o C] ISO 834 HYDRO-CARBON RWS RABT/ZTV CZAS [min.] Time [min]

39 MODELLING OF FIRE IN TUNNEL Heat exchange in tunnel during fire w q c s q w = q c + q r + q m + q s q m q r where: q w = conductive heat flux; q c = convective heat flux; q c = α c A w (T s T w ) j q r = radiation of fire flames; q r = Q r F f->w q m = mutual radiation of walls; q m =σ A w Σ j F w->j (T j4 T w4 ) q s = smoke radiation; q s =σ A w Σ F w-s (T s4 T w4 )

40 MODELLING OF FIRE IN TUNNEL Proposed iterative procedure of computations Simplified model of fire Heat generation in smoke [ Assumed temperature distribution ] Temperature of tunnel lining 3-D Computer Fluid Dynamics (CFD) Model Temperature of gasses Velocity field of gasses 3-D model of radiative heat exchange Convective fluxes Radiative heat fluxes 2D or 3D CTHM model

41 Temperature results (fluid)

42 Structural behaviour

43 MODELLING OF FIRE IN TUNNEL Application of Computational Fluid Dynamics Temperature field in the tunnel (longitudinal section)

44 MODELLING OF FIRE IN TUNNEL Application of Computational Fluid Dynamics Temperature field in the tunnel (cross section)

45 MODELLING OF FIRE IN TUNNEL Application of Computational Fluid Dynamics Gas velocity field in the tunnel (longitudinal section & cross section)

46 MODELLING OF FIRE IN TUNNEL Application of Computational Fluid Dynamics Values of the convective heat exchange coefficient h c = [W/(m 2 K)] Long. section, Section A Cell: x = 1; y = 83; x = 0,375 m; y = 5,993 m l z = [m]

47 MODELLING OF FIRE IN TUNNEL Application of Computational Fluid Dynamics Fluid temperature evolution Fluid velocity evolution (B.A.Schrefler et al., 2005)

48 MODELLING OF FIRE IN TUNNEL Numerical example Assumptions for simulations Radiative heat power of flames: Q r = 2.5 (5, 14) MW Smoke characteristics: CO 2 = 20% H 2 O = 15% Values of radiation reflection coefficient: lining: ρ=0.2 (short wave rad.); ρ=0 (long wave rad.) road: ρ=0.1 (short wave rad.); ρ=0 (long wave rad.) Convective heat exchange coefficient: α c =27 W/m 2 K Initial temperature of rocks: 20 C Initial temperature of concrete: 20 C

49 MODELLING OF FIRE IN TUNNEL Thermo-mechanical simulations Mesh for the 3-D thermo-mechanical simulations Number of elements: 4743 Element type: brick Number of cross sections: 31 Cross sections length: 2m

50 MODELLING OF FIRE IN TUNNEL Hygro-thermo-chemo-mechanical simulations Mesh for the 2-D HITECOSP simulations S6 S4 Number of elements: 470 Number of nodes: 1513 Number of DOFs: 7565 S1

51 SIMULATION RESULTS Fire of various thermal power in tunnel Temperature temperatura (K) [K] 1573, , , , , ,15 973,15 873,15 773,15 673,15 573,15 473,15 373,15 273,15 Section sekcja66 5MW 10MW 40MW czas (s) Time [s] Temperature changes Temperature temperatura (K) [K] 1573, , , , , ,15 973,15 873,15 773,15 673,15 573,15 473,15 373,15 273,15 Section sekcja4 44 5MW 10MW 40MW czas (s) Time [s] Temperature temperatura (K) [K] 1573, , , , , ,15 973,15 873,15 773,15 673,15 573,15 473,15 373,15 273,15 Section sekcja11 5MW 10MW 40MW czas (s) Time [s]

52 SIMULATION RESULTS Fire of various thermal power in tunnel ciśnienie pary wodnej (MPa) Vapour pressure [MPa] 0,6 0,5 0,4 0,3 0,2 0,1 Section sekcja6 6 5MW 10MW 40MW Vapour pressure changes czas (s) Time [s] Vapour pressure [MPa] ciśnienie pary wodnej (MPa) 0,6 0,5 0,4 0,3 0,2 0,1 Section sekcja44 5MW 10MW 40MW ciśnienie pary wodnej (MPa) Vapour pressure [MPa] 0,6 0,5 0,4 0,3 0,2 0,1 Section sekcja11 5MW 10MW 40MW czas (s) Time [s] czas (s) Time [s]

53 SIMULATION RESULTS Fire of various thermal power in tunnel Total damage [-] param. zniszczenia całkowitego (-) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Section sekcja6 6 5MW 10MW 40MW czas (s) Time [s] Total damage parameter changes Total damage [-] param. zniszczenia całkowitego (-) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Section sekcja44 5MW 10MW 40MW czas (s) Time [s] Total damage [-] param. zniszczenia całkowitego (-) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Section sekcja czas (s) 5MW 10MW 40MW Time [s]

54 PROTECTION AGAINST SPALLING Thermal-shielding of tunnel linning Convective flux: Q ( ) c = αc T T Radiative flux: Q = εσ T T r ( 4 4 ) 0 strum Heat ien flux ciep [W/m ła ( kw 2 K] /m 2 ) Convection konwekcja Radiation radiacja ε=0.9 Radiation radiacja E=0.15 ε=0.15 Radiation radiacja E=0.30 ε= temperatura ( o C) Temperature [ o C]

55 PROTECTION AGAINST SPALLING Thermal-shielding of tunnel surface Thermo-shielding (TS) layer with ceramic void spheres Physical properties: - decrease of the heat exchange coef. : - decrease of the mass exchange coef. : BC without TS-layer: W/(m K) decrease of the absorption coef. : ε=0.15 ε=

56 SIMULATION RESULTS Thermal-shielding of tunnel surface History of the temperature changes : On the heated surface: 18 mm from the heated surface: Temperature tem p eratura [K] ( K ) 1373, , , ,15 973,15 873,15 773,15 673,15 573,15 473,15 373,15 273, min 10MWnorm 10MW e=0.15 b=8 10MW e=0.15 b=30 10MW e=0.30 b= Time czas [s] (s) Temperature tem p eratura [K] ( K ) 1373, , , ,15 973,15 873,15 773,15 673,15 573,15 473,15 373,15 273,15 10MWnorm 10MW e=0.15 b=8 10MW e=0.15 b=30 10MW e=0.30 b= min Time czas [s] (s)

57 SIMULATION RESULTS Thermal-shielding of tunnel surface History of the vapour pressure : On the heated surface: 18 mm from the heated surface: ciś nienie Vapour pary pressure wodnej [Pa] (MPa) 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 10MWnorm 10MW e=0.15 b=8 10MW e=0.15 b=30 10MW e=0.30 b= Time czas [s] (s) ciś nienie Vapour p ary pressure wodnej [Pa] ( MPa) 0,7 0,6 0,5 0,4 0,3 0,2 0, min 10MWnorm 10MW e=0.15 b=8 10MW e= czas Time (s)[s]

58 SIMULATION RESULTS Thermal-shielding of tunnel surface History of the total damage parameter : Total param damage. zniszczenia parameter [-] całkowiteg o ( - ) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 On the heated surface: 10MWnorm 10MW e=0.15 b=8 10MW e=0.15 b=30 10MW e=0.30 b= Time czas [s] (s) param. zniszczenia Total damage całkowiteg parameter o (-) [-] 18 mm from the heated surface: 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 1min 0.5min 10MWnorm 10MW e=0.15 b=8 10MW e=0.15 b=30 10MW e=0.30 b= Time czas [s] (s)

59 PROTECTION AGAINST SPALLING Application of PP fibres Method Method Effectiveness Effectiveness Comments Comments Moisture Moisture Content Content Control Control Reduces Reduces vapour vapour Moisture Moisture content content usually usually pressure pressure above above no no spall spall limit limit Compressive Compressive Stress Stress Reduces Reduces Control Control susceptibility susceptibility Not Not economical economical Choice Choice of of Aggregate Aggregate Small Small size size & low low Lightweight Lightweight Double Double expansion expansion edged edged Supplementary Supplementary Reduces Reduces spalling spalling Difficult Difficult in in small small narrow narrow Reinforcement Reinforcement damage damage sections sections Choice Choice of of Section Section Shape Shape Thicker Thicker sections sections Important Important for for I-beams I-beams & reduce reduce spall spall damage damage ribbed ribbed sections sections Thermal Thermal Barrier Barrier Very Very effective effective Use Use in in existing existing structures structures P.P. P.P. Fibres Fibres Effective Effective Use Use in in new new designs designs Air Air entrainment entrainment Can Can be be effective effective Reduces Reduces strength strength Khoury, 2000

60 PROTECTION AGAINST SPALLING Application of PP fibres Granite Granite - SF - 0 Granite - SF - PPF

61 PROTECTION AGAINST SPALLING Application of PP fibres Fibre dimensions : 50μm x 150μm x 19mm 98μm Capillary pores : 0.005μm - 10μm DTA results [Kalifa et al. 2000] melting

62 PROTECTION AGAINST SPALLING Application of PP fibres Aggregate Cement Matrix Percolation theory Percolation threshold Interfacial Transition Zone (ITZ) pores +cracks +ITZ PP fibres pores +cracks +ITZ pores +cracks +ITZ PP fibres pores +cracks +ITZ

63 PROTECTION AGAINST SPALLING Application of PP fibres 1E-10 0,25 1E-11 przepuszczalność Permeability [m 2 ] (m 2 ) 1E-12 1E-13 1E-14 1E-15 1E-16 k k (3kg) k (1.75kg) k (0.9kg) Porosity porowatość [-] ( - ) 0,2 0,15 0,1 0,05 n n (0.9kg) n (1.75kg) n (3kg) 1E-17 1E Temperature temperatura ( o C) [ o C] Temperature temperatura ( o C) [ o C] A p p k = k0 m T f ( T) g AD D β pp ( pp, ) p0 n = n + A ( T T ) + n ( m, T) 0 n 0 pp pp

64 SIMULATIONS RESULTS Application of PP fibres History of the temperature changes : ISO-834 fire : 10 MW fire in tunnel : K tem p eratura (K ) Temperature [K] min 8min 14min Distance odl. from od pow. surface (m) [m] te m p eratura ( K ) Temperature [K] min 2min 8min Distance odl. from od pow. surface (m) [m]

65 SIMULATIONS RESULTS Application of PP fibres History of the vapour pressure : ISO-834 fire : 10 MW fire in tunnel : ciś n. p ary wodnej ( MPa) Vapour pressure [MPa] % 14min 8min 2min Distance odl. from od pow. surface (m) [m] ciś n. p ary wodnej (M Pa) Vapour pressure [MPa] % 2min 8min 14min Distance odl. from od pow. surface (m) [m]

66 SIMULATIONS RESULTS Application of PP fibres History of the relative humidity : ISO-834 fire : 10 MW fire in tunnel : wilg otność wzg l. ( - ) Relative humidity [-] min 8min 14min wilg otność wzg l. ( - ) Relative humidity [-] min 8min 14min Distance odl. od from pow. (m) surface [m] Distance odl. od from pow. (m) surface [m]

67 SIMULATIONS RESULTS Application of PP fibres History of the total damage parameter : ISO-834 fire : 10 MW fire in tunnel : p Total aram. damage zniszcz. cał [-] k. ( - ) min 8min 14min p Total aram. damage zniszcz. całk [-]. ( - ) min 8min 14min Distance odl. od pow. from (m) surface [m] Distance odl. od pow. from (m) surface [m]

68 SIMULATIONS RESULTS Molecular Structure of PP fibres From crude oil to the polymer Ethylene Monomers used for Polyolefins From crude oil to the polymer Polymerisation - Ethylene Propylene KEY Hydrogen Carbon Oxygen Activation 1-Butene Vinylacetate (VA) Opening of the double bond 1-Hexene 1-Octene n-butylacrylate (nba) Polymerisation Polypropylene Polymers - HOMO PP Propylene Monomer (C3) With Catalyst Propylene Monomer (C3) Polypropylene HOMO Current developments on pp fibres Newcon Project, 2006

69 SIMULATION RESULTS Spalling: energetic considerations Assessment of explosive nature of spalling Knowing a possible thickness of the rupture layer of concrete we get: 1. The volume for integrating the elastic strain energy 2. The area, A fr, to obtain the energy dispersed by fracturing from the specific fracture energy G f 3. The volumes of gas for the evaluation of the work performed by gas itself Δ E = ΔU ΔE + W k fr W = p V p V k k ( ) = ( ) p V p V Adiabatic expansion k Δ E = kinetic energy of spalled concrete ; V = volume of concrete (initial value) k Δ U = elastic strain energy (released) ; V = volume of concrete (final value) Δ E = fracture energy (consumed for fracture) ; = pressures of gas (1=initial, 2=final) fr W = work performed by gas ; k = specific heat ratio for gas 1 2 p i

70 SIMULATION RESULTS Spalling: energetic considerations Assessment of explosive nature of spalling From the previous relationships we have an upper estimation of the velocity of pieces of spalled concrete: v 2 = 2 Δ ( E + W ) k Δm Example HPC (C60) wall subjected to ISO-Fire conditions From simulation with Padua Model we have: Δx=2 cm, T spall =200 C, p 1 =0.1 MPa, p 2 =0.95 MPa and supposing 0.02 x0.02x0.02 m average size of spalled pieces of concrete, Δ E = 550 J/m k Δ U = 1150J/m Δ E = 600 J/m fr W = J/m 2 Total energy of concrete pieces 2 = 1120 J/m v 2 = 6.7 m/s For C90 concrete with p 2 =4 MPa (Kalifa test) we have v 2 =12.4 m/s

71 SIMULATIONS RESULTS Spalling Spalling nomogram

72 SIMULATIONS RESULTS Spalling Spalling abacus (3D)

73 CONCLUSIONS Numerical model of hygro-thermo-chemo-mechanical performance of concrete at high temperature is presented. Energy and mass transport mechanisms typical for different phases of concrete, as well as phase changes and chemical reactions are taken into account. Full coupling between hygral-, thermal-, chemical- and mechanical processes is considered. Evaluation of risk of spalling phenomenon at high temperature.