F Pesavento* - WIT Press · Damage and spalling in HP and UHP concrete at high temperature C.E....

$: F Pesavento* - WIT Press · Damage and spalling in HP and UHP concrete at high temperature C.E. Majorana\ F Pesavento* ' Dipartimento di Costruzioni e Trasporti, Universitd di Padova,$
Damage and spalling in HP and UHP concrete

at high temperature

C.E. Majorana\ F Pesavento*' Dipartimento di Costruzioni e Trasporti,Universitd di Padova, Italy

Abstract

The present work deals with a new model to analyse the behaviour of concrete athigh temperature. For the safety evaluation of concrete structures exposed toelevated temperature, for instance during a fire or in the case of nuclear accident,prediction of concrete performance is of great practical importance. In suchconditions concrete, especially high performance and ultra high performanceconcrete, may be subject to spalling phenomena which jeopardizes the integrityof the construction. Spalling involves thermal, hygral and mechanical processes.

Such complex phenomena require a numerical simulation implementing newmathematical models.

In the model here presented concrete is considered as a multiphase materialconsisting of a solid phase, two gas phases and three water phases. The effect ofdamage on permeability and non-linearities due to temperature and pressures areincluded and phase changes such as hydration-dehydration, evaporation-condensation, adsorption-desorption, are considered.

Based on the mathematical model, the computer code HITECOSP wasdeveloped.

Some results of computer simulations behaviour of HPC and UHPCstructures are presented and discussed. They show the robustness of thecomputer code HITECOSP, as well as its usefulness for a better understanding ofphysical phenomena and for a more accurate evaluation of possibility of spallingoccurrence in concrete structures during fire.

Damage & Fracture Mechanics VI, C.A. Brebbia, A.P.S. Selvadurai, (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-812-0

106 Damage and Fracture Mechanics VI

1 Introduction

At ambient temperature High and Ultra High Performance concrete present muchbetter features than a normal concrete because of their lower permeability, lowerporosity and higher compactness. This means greater mechanical strength, inparticular as far as the compression strength is concerned, and an improveddurability.

At low temperatures, in fact, the cement matrix increases the strength of highperformance concrete, because of its higher density and homogeneity, involvinga better distribution of the stresses than a traditional concrete. At highertemperature just this matrix becomes the weak point of the materials showinglow mechanical strength.

With the temperature increase the aggregates progressively expand as long asthey are not chemically altered, while the cement matrix, after an initiallyexpansion, is subject (over 150°C) to a progressive shrinkage. These twoopposite phenomena involve a micro-cracking process which deals with asubsequent damaging of the material microstructure.

Moreover low permeability inhibits water mass transfer causing high gaspressure values, crack-opening and a further increase of intrinsic permeability.

This process, resulting in a reduction of Young's modulus, a decrease of finalstrength and a different slope in the softening part of stress-strain curve, maylead to a collapse of the structure known as spalling.

A phenomenological approach, Bazant et al. [1-5], is usually applied fordescription of changes of concrete physical properties during complex hygro-thermal and mechanical phenomena at high temperature. It means that all thesechanges are expressed as a function of temperature, moisture content and gaspressure, i.e. physical quantities measured directly during experimental tests.However results of such tests are strongly dependent upon form and dimensionsof a test sample, as well as physical conditions during experiment. Henceapplication of the results of these tests for prediction of concrete behaviour inconditions that differ significantly from the experimental ones is veryquestionable.

Consequently a new mechanistic mathematical model was developed.Concrete is considered as a multiphase material consisting of a solid phase, twogas phases and three water phases. Refinements such as non-linearities due totemperature and pressures, hydration-dehydration, evaporation-condensation,adsorption-desortpion, phenomena are considered, Schrefler et al. [11-17].

Different physical mechanisms governing the liquid and gas transport in thepores of partially saturated concrete are clearly distinguished, i.e. capillary waterand gas flows driven by their pressure gradients, adsorbed water surfacediffusion caused by saturation gradients, as well as air and vapour diffusiondriven by vapour density gradients, Schrefler et al. [11-17].

Concrete damaging effects arising from coupled hygro-thermal andmechanical interaction were considered by use of the isotropic non-local damagetheory and besides a further coupling between intrinsic permeability and


Damage and Fracture Mechanics VI 107

mechanical damage has been introduced to take into account the changes ofmaterial microstructure.

2 Mathematical model

The model consists of the four balance equations: mass of dry air, mass of waterspecies (both in liquid and gaseous state, taking phase changes, i.e. evaporation -condensation, adsorption - desorption and hydration - dehydration process, intoaccount), enthalpy of the whole medium (latent heat of phase changes and heateffects of hydration or dehydration processes are considered) and linear andangular momentum of the multiphase system obtained using a procedure ofspace averaging of the conservation equations for heat and mass transfer writtenfor the individual constituents of the medium , Whitaker et al. [6-10]. They arecompleted by an appropriate set of constitutive and state equations, as well assome thermodynamic relationships, Schrefler et al. [11,12].

The governing equations of the model are expressed in terms of the chosenstate variables: gas pressure pg, capillary pressure p%, temperature T anddisplacement vector of the solid matrix u, Schrefler et al. [11,12]:

Dry air conservation equation:

Water species (liquid-vapour) conservation equation:

(2)

Energy conservation (enthalpy balance) equation:

(3)



Linear momentum balance equation:

(4)

where p is the averaged density of the multi-phase medium.The time derivative of porosity has been eliminated from eqns (l)-(3) by

summing the mass conservation equation of the solid phase with the massconservation equations for dry air, water vapour, capillary water and adsorbedwater.

The model is closed by a set of constitutive and thermodynamic relationshipsfor description of hygro-thermal state of concrete.

2.1 Constitutive equations for description of mechanical behaviour ofconcrete

The effective stresses principle in the Bishop's form is given by Schrefler et al.[16,17]:

a' =a + a/? I, (5)

where the stress a' is the stress effectively responsible for all deformations inthe material and where a is the total stress tensor, I is the unit tensor, a=

jsI -- — is the Biot's constant and p is an average pressure of the mixture of

^fluids filling the voids, positive for compression,

(6)

where /?„ = Pg- P^ and the limit value Sssp (e.g. solid saturation point) and theterm (S-S,̂ ) appears in equations (6) as a consequence of the chosen

saturation definition, including both the adsorbed and capillary water. Besides,the last term in equation (6) has been added because we use here absolutepressure: pure atmospheric pressure does not cause any deformation of themedium, Schrefler et al. [16,17].

The constitutive relationship for the solid skeleton is assumed in the form:

^ = KT(dE-ok^-^) (7)



where KT is a tangent matrix, d£ =l^-dT is the strain increment caused

by thermo-elastic expansion, pg means the cubic thermal expansion coefficient

of the solid and dz° represents the autogeneous strain increments and theirreversible part of the thermal strains.

2.2 Effect of damage and spalling phenomena

Damage of concrete is considered following the scalar isotropic model by

Mazars [18-20]. This theory defines a "modified effective stress" 5 and takesinto account the damage D (0 < D < 1) as a parameter measuring the reduction ofresistant area due to micro-crack beginning and spreading as

^ 1-D

where A is the resistant area of the uncracked material, whereas A is theresistant area of the damaged material. Note that here the meaning of modifiedeffective stress is different from that of equation (5). The effective stress in (5)has to be introduced in equation (8).

During heating of concrete at high temperature complex physical andchemical processes take place, resulting in changes of inner structure, micro-cracks development and porosity increase Bazant et al. [1-5]. All them causingan increase of intrinsic permeability. One can expect that a joint effect oftemperature, gas pressure and material damaging (micro-crack development) onthe intrinsic material permeability, K, may be described as

(9)

where AT, A? and AD are material constants. Parameters At and Ap in (9)have a clear physical interpretation, because they describe effects on the materialpermeability increase of crack opening caused by temperature and pressure rise,respectively. A value of parameter AD in (9) is dependent on the type anddimensions of the cracks developed in concrete matrix.

These coexisting coupled processes: thermal (heat transfer), chemical(dehydration of cement paste), hygral (transfer of water mass, in liquid andvapour form) and mechanical may lead to spalling. The main factors influencingthis destructive phenomena are the heating rate and profile, the section size andshape, the moisture content, the permeability of concrete and mean pore radiusand finally the concrete strength. Further the vapour pressure may play animportant role because of its values reached during heating which may produce akind of explosive spalling, especially in high density materials like high and ultra



high performance concrete. Spalling may result in a loss of load-bearing capacitythrough a loss of section and/or protection the concrete cover provides to thesteel reinforcements with a possible collapse of the structure.

3 A numerical comparison HP - UHP concrete

The numerical examples here reported, deal with a comparison between a highperformance and a ultra high performance concrete wall (10 cm thickness)exposed to fire. The environmental temperature increases following the ISO-Firestandard curve, while the relative humidity is practically zero, except at the firstfew seconds of simulation. The boundary conditions are mixed, convective-radiative for heat exchange on the heated side and convective on the cold side,while purely convective conditions has been used for mass exchange on bothheated and not heated side. The related coefficients are shown in Table 1.

Table 1. Boundary conditions for the wall

SIDE

12

PgInit. Value

[Pa]10132510132S

Coeff.[m/s]0.00.0

RHInit. Value

[-]0.00.0

Coeff.[m/s]0.090.09

TInit. Value

[K]298.2529825

Coeff[W/nfK],

1818

side 1side3

side 2

side 4

Figure 1: Geometry of the wall

At the beginning of the phenomena, in the case of HPC, two damagedzones appear, close to the heated surface and in the inner part of the wall.During the heating the peak value of the damage, localised near the hot side,increases reaching the value 1 for a thickness of 0.5 cm. The values ofdamage in the inner part of the structure are ever behind 0.3, Fig. 3a).

For the UHPC wall the situation is completely different. At the beginningonly a small zone close to the heated surface presents a damage, but alreadyafter 3 minutes an extended damaged zone appears (about 2 cm size) and itsdepth enlarges up to 4-5 cm until 9 minutes. At this time station the damageis almost uniformly distributed along the thickness of the wall, Fig. 3b), evenif its maximum value does not exceed 0.5. An immediate consequence ofthese damage profiles is clearly visible in the water content distribution of thewalls, Fig. 6. In the second, UHPC, analysed problem the desaturation of thematerial is faster and deeper than in the first one (HPC), taking into account



the different initial value of water content at 25 °C. In both cases animportant thing to note is the decrease of the vapour pressure, Fig. 5, between7 and 9 minutes, which means a cracking of the material with a subsequentmodification of its structure and therefore an increment of the absolutepermeability. In UHPC case a second peak of vapour pressure is building upat 9 minutes because the strong dehydration of the cement paste whichreleases a considerable amount of chemically bound water. The maximumpeak of vapour pressure is moving towards the inner part of the walls and itsvalue is greater in the second case than in the first one because of a highercompactness and lower permeability of the material. Also the temperatureprofiles, Fig. 4 reflect the different desaturation processes of the concrete. Upto 5 minutes the situation is the same in both the walls, but after this timeinstant the first one presents higher temperature in the zone close to theheated surface because of the stronger evaporation phenomena. A so differentbehaviour of the two materials is due to their different thermo-mechanicalproperties. In fact UHPC presents a higher compactness and a lower intrinsicpermeability than a high performance concrete. This involves higher strength,Young modulus and thermal conductivity and lower porosity, Fig. 2. Inparticular the higher thermal conductivity of ultra high performance concreteis responsible for the deeper penetration of thermal front inside the wall, Fig.4, and of the consequent damage distribution, Fig. 3, while the higherstrength and Young's modulus are the cause of the lower damage values.

3 -r-r-r-

-O- HPC - Therm. Cond._G_ UHPC - Therm. Cond_a_ HPC- Porosity-4&-UHPC - Porosity

Temperature [°C]

Figure 2: Porosity and thermal conductivity of HPC and UHPC [21]



HPC

; ;

i ii ''

— 1 min-6-3 min-*-5 min-e-7 min— 9 min

0,01 0,02 0,03 0,04Distance from heated surface [m]

a)

0,05 0,06

UHPC

0,01 0,050,02 0,03 0,04

Distance from heated surface [m]

b)

Figure 3: Damage distributiona) High Performance Concrete; b) Ultra High Performance Concrete

0,06


350


HPC

0,02 0,04 0,06


a)

0,08 0,1

UHPC

0,02 0,080,04 0,06


b)

Figure 4: Temperature distribution:a) High Performance Concrete; b) Ultra High Performance Concrete

0,1



HPC

2,50E+05 -

0,OOE+000,01 0,02 0,03 0,04


a)

UHPC

0,05 0,06

0,02 0,03 0,04 0,05


b)

Figure 5: Vapour pressure distribution:a) High Performance Concrete; b) Ultra High Performance Concrete

0,06



HPC

0,02 0,04 0,06 0,08Distance from heated surface [m]

a)

0,1

UHPC

EB)

Io -*-

I

1 min3 min5 min7 min9 min

'

i

0,02 0,04 0,06


0,08 0,1

b)

Figure 6: Water content distribution:a) High Performance Concrete; b) Ultra High Performance Concrete



4 Conclusions

An application of a new model to analyse heat and mass transfer in concrete athigh temperatures and related mechanical effects has been presented. Inparticular mechanical behaviour of high and ultra high performance concretestructures subject to fire has been pointed out presenting a comparison betweentwo thin walls.

In the above kind of structures the resistance to fire is of great importancebecause of the features of these materials: high strength, low permeability andconsequently good durability which may allow to classify concrete as a highperformance material at low temperature, but very dangerous when thetemperature increases, because of the increased susceptibility to spalling. Thisphenomena may be a simple separation of surface layers of concrete, orexplosive when the vapour pressure values are particularly high.

For these reasons it is really important to apply a software tool a where amodel able to give a good description of all coupled phenomena interesting theinner structure of the material is implemented.

Acknowledgements

This research was carried out within Brite Euram III BRPR-CT95-0065"HITECO", "Understanding and industrial application of High PerformanceConcretes in High Temperature Environment" and partially funded by MURST40% n° 9908188987_N3, 1999.

References

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[4] Bazant Z.P., and Thonguthai W., Pore pressure and drying of concrete athigh temperature, J. Engng. Mech. Div. ASCE. 104, pp. 1059-1079, 1978.

[5] Bazant Z.P., and Thonguthai W., Pore pressure in heated concrete walls:theoretical prediction, Mag, of Conor. Res. 31(107), pp. 67-76, 1979.

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[18] Mazars J., Application de la mecanique de /' endommagement ancomportament non lineaire et la rupture du beton de structure (in French),Thesy de Doctorat d' Etat, L.M.T., Universite de Paris, 1984.

[19] Mazars J., Description of the behaviour of composite concretes undercomplex loadings through continuum damage mechanics, Proceedings ofthe 10*** U.S. National Congress of Applied Mechanics, Lamb, J.P. (ed.),Publ. oftheASME, 1986.

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[21] Brite Euram III BRPR-CT95-0065 "HITECO", "Understanding andindustrial application of High Performance Concrete in High TemperatureEnvironment" - Final Report.


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