2 nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands 227 EXPLOSIVE SPALLING OF CONCRETE MATERIALS UNDER EXTREME ENVIRONMENTS Kaspar Willam (1), Keun K. Lee (2), Yunping Xi (3), G. Xotta (4), and V. Salomoni (4) (1) University of Houston, Texas, USA (2) Jacobs Engineering Group, Inc., Denver, Colorado, USA (3) University of Colorado, Boulder, USA (4) University of Padova, Padova, Italy Abstract This paper describes recent findings of an experimental and computational program to investigate the effect of mismatch when concrete materials are subjected to rapid heating and drying. The main focus are interaction effects in heterogeneous composites when the constituents with different thermal expansion and hygral shrinkage properties are subjected to severe environmental load scenarios. This paper addresses the question, whether spalling in concrete materials is caused (a) by the contrast of constituent material properties, or (b) by thermal-shock-induced stability aspects of subdomains subjected to compression. This discussion reaches beyond the traditional arguments of thermal stress spalling due to restrained thermal expansion, or due to pore pressure spalling caused by the phase change of the free pore water under high temperature. 1. INTRODUCTION Under high temperatures concrete is a composite material that experiences several degradation processes, such as thermal softening, thermal expansion, and drying shrinkage. At the microstructural level, many physical and chemical processes take place under the high temperature including phase transformations, mass transportations, damage development, and internal pore pressure build-up. These degradation processes have come to the forefront in the safety assessment of important concrete structures like tunnels and high rise buildings. And thus, there is an urgent need for a comprehensive understanding of concrete materials exposed to high temperature under fire environment. In addition to the gradual degradation processes, there is a rapid failure process occurring in concrete structures under fast heating known as explosive spalling. The spalling of concrete has been considered to be a result of multi-axial stresses induced by severe temperature gradient as well as internal pore pressure built-up caused by the formation of moisture clog, which is due to multi physics transport of mass and energy. The spalling of concrete results in significant loss of concrete mass over a very short period of time from the structure that may be extremely detrimental to structural integrity. A thorough understanding of the multi-physics transports in the pore system and structural degradation in the solid skeleton of concrete is definitely needed.
Transcript
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
227
EXPLOSIVE SPALLING OF CONCRETE MATERIALS UNDER EXTREME ENVIRONMENTS
Kaspar Willam (1), Keun K. Lee (2), Yunping Xi (3), G. Xotta (4), and V. Salomoni (4)
(1) University of Houston, Texas, USA (2) Jacobs Engineering Group, Inc., Denver, Colorado, USA
(3) University of Colorado, Boulder, USA (4) University of Padova, Padova, Italy Abstract
This paper describes recent findings of an experimental and computational program to investigate the effect of mismatch when concrete materials are subjected to rapid heating and drying. The main focus are interaction effects in heterogeneous composites when the constituents with different thermal expansion and hygral shrinkage properties are subjected to severe environmental load scenarios. This paper addresses the question, whether spalling in concrete materials is caused (a) by the contrast of constituent material properties, or (b) by thermal-shock-induced stability aspects of subdomains subjected to compression. This discussion reaches beyond the traditional arguments of thermal stress spalling due to restrained thermal expansion, or due to pore pressure spalling caused by the phase change of the free pore water under high temperature.
1. INTRODUCTION Under high temperatures concrete is a composite material that experiences several
degradation processes, such as thermal softening, thermal expansion, and drying shrinkage. At the microstructural level, many physical and chemical processes take place under the high temperature including phase transformations, mass transportations, damage development, and internal pore pressure build-up. These degradation processes have come to the forefront in the safety assessment of important concrete structures like tunnels and high rise buildings. And thus, there is an urgent need for a comprehensive understanding of concrete materials exposed to high temperature under fire environment. In addition to the gradual degradation processes, there is a rapid failure process occurring in concrete structures under fast heating known as explosive spalling. The spalling of concrete has been considered to be a result of multi-axial stresses induced by severe temperature gradient as well as internal pore pressure built-up caused by the formation of moisture clog, which is due to multi physics transport of mass and energy. The spalling of concrete results in significant loss of concrete mass over a very short period of time from the structure that may be extremely detrimental to structural integrity. A thorough understanding of the multi-physics transports in the pore system and structural degradation in the solid skeleton of concrete is definitely needed.
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
228
In the present study the governing equations for mass and heat transfer will be established for a deformable porous body (concrete), the equations for stress analysis will be summarized, the material models based on microscopic deterioration mechanisms will be introduced, and the solution for the multi-physics governing equations will be presented.
2. GOVERNING EQUATIONS
2.1 Mass balance equation The governing equations for effective mass balance will be used in this study. In concrete
under high temperature the transport of liquid mass is mainly driven by vapor migration [1], so we can define effective mass balance by combining two water species as one, which is a combination of vapor and liquid water. Other simplifications can also be made, for example, the variation of the porosity at the range of temperature, T=100~500°C, is negligibly small; the solid skeleton of concrete experiences very small dilatation before spalling; and the flux of the relative motion between gas and vapor is negligible. The resulting mass balance equation is
� � 0, �� ��
�� seee
se
vt
v - (1)
in which ρe are effective phase-averaged apparent density; vs is solid mass velocity; t is time; ϕ is porosity; and ρe ve.s is the effective flux due to relative motion of phase e with respect to the reference phase, the solid s. Eq.(1) the first term on the left-hand side indicates the effective mass change due to the averaged mechanical response, the second one represents the effective mass change in time, and the third one indicates the effective fluid mass flow by Darcy’s law.
The flux term in Eq. (1), the last term can be interpreted as � � esee Jv ���� , where the effective flux of moisture in concrete, Je (kg/m3s or PCF/s) includes the flux due to the gradient of moisture concentration according to Fick’s law as well as the Soret flux due to the gradient of temperature TDDJ wT
eww
e ���� where Dww designates moisture diffusivity and DwT is the moisture diffusivity due to temperature variation. The effective density ρe is a function of pressure P and temperature T, and thus we have TTPP eeeee ��� ���� and
Substituting Eq. (2) into Eq. (1) yields the effective mass balance equation
0/0
123
4����
����
���
���/0
123
4����
����
���
�����
��
��
��
�� TT
DDPP
DtT
TtP
Pv
e
wwwTe
e
e
ww
ee
e
es
e - (3)
2.2 Energy balance equation The energy balance equation can be written as
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
229
� � ee qtTC
tQ
�����
�� (4)
in which Q is heat, qe is the effective heat flux, and (ρC)e is the effective heat capacity of concrete. In Eq. (4), the energy due to convection is assumed to be negligible.
Similar to the mass transfer flux, the effective heat flux can also be expressed in terms of temperature gradient and moisture gradient (the Dufour flux), TDDq TT
eTw
e ���� where DTT denotes thermal conductivity and DTw is the conductivity due to moisture variation. Again, combining the chain rule for ρe, the heat flux becomes
TDT
DPP
Dq TT
e
Twe
e
e
Twe ���
�
����
�
��
����
� (5)
Substituting Eq. (5) into Eq. (4) yields the effective energy balance equation
� � /0
123
4����
����
�
��
�� /0
123
4����
����
���
���� TD
TDP
PD
tTC TT
e
Twe
e
e
Twe (6)
2.3 Momentum balance equation The instantaneous momentum balance of all phases e.g. fluid and solid skeleton, occupied in
a porous medium reaches
0 � gIPLL eTeT � (7) where is LT the differential operator and I is the unit vector. The effective stress is σe = σ + PeI where σ is the total stress, and Pe is the effective pressure defining fluid pressure in a partially saturated porous medium of concrete.
2.4 The discretized system equations The governing equations can be discretized, compacted and expressed in the matrix form
56
57
8
59
5:
;56
57
8
59
5:
;
///
0
1
222
3
4 56
57
8
59
5:
;
///
0
1
222
3
4 �
T
P
U
TT
PTPPPU
TTTP
PTPP
UTUPUU
FFF
PU
dtd
CCCCP
U
KKKKKKK
<< 00
000
00 (8)
where θ represents the temperature variation from a reference temperature. Each row in Eq. (8) forms a system of ordinary first order differential equation in time. The relationships between mechanical response, pore pressure and temperature variation are included. The first row is the system of equilibrium equations which indicate the mechanical response due to a mechanical loading, the effective fluid pressure and the thermal loading; the second row is the mass continuity which represents the mass flow due to Darcy’s flow and Soret flux, i.e. the pressure change induced by the gradient of temperature; and the third row is the system of energy equations which characterizes the energy flow due to Fourier’s flux and Dufour flux, i.e. the heat energy variation caused by the gradient of pressure.
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
230
3. MATERIAL PROPERTIES
3.1 Sorption isotherm and permeability of concrete The following semi-empirical sorption based on capillarity theory was developed by Bažant
[1] for concrete.
e cem RH L0 cem� �� �1 m(T ) if RH = 0.96 (a)
� � )(04.1)04.1(12.010 bRHifRHLe >� (9)
)(04.196.008.0
96.004.1)96.0(96.0 cRHifRH LLL
e ==�
�
where ρcem and ρL
0 are density of cement and water. Relative humidity, RH=Pe ⁄ Psat gw(T), is sensitive to the temperature and pressure, and the empirical expression, m(T), is used
2
0 1010'
'34.22'04.1)( ��
�
����
�
�TTT
TTTm (10)
According to the assumption that at low temperature, below 100°C, the mechanism of humidity transfer is governed by molecule migration along the adsorbed layers as well as flow of capillary water [2], the relationship between relative humidity and temperature was presented by Bazant [1], which is used in this study.
3.1 Yield function: Parabolic Drucker-Prager Model The parabolic Drucker-Prager model is used to investigate spalling failure mechanism under rapid heating. The yield function and flow potential which are temperature-dependent are defined as
)()( 12 TITJF Feff
Feff �� � (11)
The strength parameters αF (T) and βF (T) may be expressed in terms of the uniaxial tensile and compressive strengths of concrete, which are assumed to be temperature-dependent,
3)(')(')(
3)(')(')( TfTfTTfTfT tc
Ftc
F �
�� (12)
I1
eff and J2eff are the first and the second invariant of the effective deviatoric stresses,
respectively.
4. EXPERIMENTAL OBSERVATIONS Experiments were performed to study spalling damage of concrete by Lee et al. [3]. The
concrete specimens were cylinders of 50.8mm (2 in.) in diameter and 100.16mm (4 in.) high. Test specimens with two different initial humidity conditions were placed in a furnace. When the temperature on the surface of specimen reached the target temperatures of 250°C, 400°C, 550 °C the furnace was shut off so that the hot specimens cooled down naturally. Two heating rates of 22°C/min and 1°C/min were used. The four testing conditions are: WF – Water saturated and Fast heating (22°C/min); OF – Oven dried and Fast heating (22°C/min);
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
231
and WS – Water saturated and Slow heating (1°C/min). During heating and cooling no mechanical loads and no mechanical restraints were applied on the specimens.
Figure 1. Spalling failure under surface temperature 550 C: WF550
Spalling failures were observed near the cylinder surface for series WF400 and WF550 (wet and fast heating rate) when target temperatures on the surface are T=400°C and T=550°C. At that time the surface temperatures reached T=350°C. At the depth of 20.4mm (0.81in.) from the surface the measured internal temperature was T=193°C at spalling. It is noted that no spalling failure occurred in the specimen series WS (wet and slow heating rate) and OF (oven dried and fast heating). This indicates that the spalling mechanism is closely related to the interaction of moisture migration and the steep thermal gradient developed by rapid heating and initial moisture conditions. The spalled specimens are shown in Figure 1.
5. NUMERICAL RESULTS
5.1 Internal temperature and pore pressure under high temperatures A 2-D finite element analysis code was developed, which provides solution for the
coupled system equations of mechanical, pressure, and temperature variables. To compare with the tested concrete cylinders, one strip of the specimen was modeled and subjected to mechanical boundary conditions and transport boundary conditions shown in Figure 2 where 4-node axisymmetric finite elements are used and thermal expansion in the axial and radial directions are unconstrained. Elevated temperatures are prescribed on the nodes of the surface and the top surface is subjected to zero flux boundary conditions. The temperature-dependent elastic modulus, E(T), is used [4]. A constant coefficient of thermal expansion is adopted because it does not dramatically change in the temperature range, 20°C ≤ T ≤ 350°C.
Figure 2. Geometry and meshes extracted from the cylinder specimen
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
232
Transient stresses develop due to temperature gradient and pressure built-up when the
solid cylinder is subjected to surface heating. Internal temperature profiles are compared with the experimental results, and they agreed very well. Pressure variations under different temperatures were computed numerically in the temperature range T=20°C to 350°C, and are shown in Figure 3. The maximum pressure from current numerical study reaches 3.5MPa (507psi) at the location 10mm (0.39in.) from the surface when the temperature on the surface is T=350°C.
Figure 3. Radial pressure vs. temperature profiles
5.2 Stresses and strains under high temperatures The stress and strain analyses were performed in form of thermoelastic and thermoelasto-
plastic analysis studies for oven-dried specimens; thermoporoelastic analysis for water saturated specimens; and thermoporoelasto-plastic analysis for spalling damage of water saturated specimens under rapid heating. The internal stress developments significantly vary with increasing temperature using different analysis methods, which were also shown by the experimental results. Taking the results obtained from thermoporoelasto-plastic analysis as an example, the state of stresses is close to equi-biaxial tension and compression and the radial stress and axial stress exceed the ultimate uniaxial tensile strength. In this case the circumferential stress in compression, σθθ tends to accelerate brittle and sudden failure leading to surface spalling or ablation in the radial and axial directions. Such a failure was obtained from the experimental observation as shown in Figure 1.
The radial displacement results and the difference of radial displacements of thermoelasto-
plastic and thermoporoelasto-plastic analyses indicate that the most critical spalling locations develop near the surface of saturated concrete when the surface temperature reaches T = 350°C. The peak difference of displacements from thermoporoelasto-plastic analysis is 15%~17% higher than the ones from thermoelasto-plastic analysis around r = 42mm (1.65in.)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50 60
Distance [mm]
Pre
ssur
e [M
Pa]
0
50
100
150
200
250
300
350
400
Tem
pera
ture
[°C
]
P @T=350 °C
P @T=200 °C
P @T=100 °C
Tsurf = 350 °C
Tsurf = 210 °C
Tsurf = 100 °C
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
233
Figure 4. Volumetric total strains from the thermoporoelasto-plastic analysis
The spalling features near the surface of concrete cylinders are related to the evolution of
the volumetric strain fields in thermporoelasto-plastic analysis: thermal strains; volumetric-total strains; and volumetric-plastic strains. Thermal strains at different surface temperatures, T=86°C, 100°C, 200°C and 350°C are basically governed by the heating temperature profiles. The volumetric-total strains represent the overall combined responses due to temperature and internal pore pressure transports. At the temperature below T=100°C, the volumetric-total strains follow thermal strains because the internal pore pressures are relatively small. However, the internal pressures near the concrete surface increase as the temperature increases. When the temperature on the surface reaches T= 200°C and T=350°C, the volumetric-total strains at the near surface, r = 20~42mm (0.79~1.65in.) do not follow thermal strains but show the combined effect by T and internal pore pressures. The volumetric-plastic strains showed similar trends as the total strains. Cracking of concrete starts at the axis-region when the temperature on the surface reaches T = 86°C. Then, as temperatures increase, the plastic behavior expands outward to the surface. It can be observed that the incremental rate of the volumetric-plastic strains is followed by the rate of pore pressure development. This suggests that spalling of concrete near the surface is due to the combined effect of thermal as well as hygral loadings.
6. SHAPE EFFECT The experimental study described in Section 4 is for cylindrical specimens representative
of circular columns subjected to fire exposure. For the sake of comparison with the fire performance of rectangular columns, progressive temperature damage in square concrete specimens was studied numerically. The major difference of the two specimens is the sharp corner in the square specimens, which may cause high stress concentration and thus high rate of damage, the so-called “corner effect”. To this end, the F.E. CODE NEWCON 3D [5] was used, in which the basic formulation is different from those described in Section 2 in that the concrete is treated as a multiphase system and the voids are partly filled with liquid and partly with a gas phase. The liquid phase consists of bound water and capillary water and the gas phase is a mixture of dry air and water vapour and is assumed to behave as an ideal gas.
For the two different sections the discretization is represented in Figure 5 and the initial
conditions correspond to a saturation of 90% and a temperature of 25°C. The two samples are heated externally with a thermal ramp of 100°C/min reaching a temperature of 345°C. The material data are reported in Table 1.
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0 10 20 30 40 50 60
Radial distance [mm]
Vol
umet
ric to
tal s
trai
n, ε
tota
l_vo
l
0
0.5
1
1.5
2
2.5
3
3.5
4
Por
e pr
essu
re [M
Pa]
Tsurf=350C
Tsurf=200C
Tsurf=100C
Tsurf=86C
Pore pressure
Pore pressure
Pore pressure
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
234
Figure 5. Finite element meshes for the two sections ( ¼ per symmetry)
Table 6. Input data.
Elastic modulus [MPa] 35000Poisson’s ratio 0.18
Refrence diffusivity along x/y/z directions [mm2/d] 10 Heat conductivity along x/y/z directions [W/m�K] 1.67
Coefficient At for damage in tension 0.9 Coefficient Bt for damage in tension 2000
Coefficient Ac for damage in compression 2.0 Coefficient Bc for damage in compression 2500
The numerical results showed that there is no significant difference in the distributions of
relative humidity in the two different specimens. Comparing the evolution of the total displacements in Figure 6 shows that the displacements in the square specimen change more radically than that in the cylinder from 125°C to 145°C. Figure 7 shows the damage evolution in the two different specimen demonstrating clearly that the rate and extent of damage is much faster and wide spread in the square specimen than in the circular specimen.
Figure 6. Displacement evolutions in the two sections
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
235
Figure 7. Damage evolution in the two different sections
7. CONCLUSIONS � The numerical results show that temperature profiles predicted by the models are
comparable with the experimental tests. � Mechanical response from the thermoporoelasto-plastic analysis shows 15~17% higher
displacements than those from the thermoelasto-plastic analysis, and the difference of radial displacements reaches a maximum near the surface.
� Displacements and stress states near the surface from thermoporoelasto-plastic analysis can be used to explain surface spalling observed in the experimental study.
� The initial humidity condition is an important factor for hygral spalling since higher levels of relative humidity in concrete are necessary for the observed spalling damage.
� Spalling near the concrete surface originated at mid height of the cylinder due to a combination of thermal stresses by fast heating and internal pore pressure. This was verified by the numerical results of total strains and plastic strains.
� The “corner effect” is a very significant phenomenon when the difference of damage is compared in square vs. circular specimens under rapid heating. One may conclude that the evolution of damage in square or rectangular columns proceeds much faster than in circular columns.
ACKNOWLEDGEMENTS The authors wish to acknowledge partial support by the US National Science Foundation
under grant CMS-0409747 to University of Colorado at Boulder. Opinions expressed in this paper are those of the authors and do not necessarily reflect t hose of the sponsor.
REFERENCES [1] Bažant, Z., and Thonguthai W., "Pore pressure and drying of concrete at high
temperature." Magazine of Concrete Research, 31(107) (1979) 67-75. [2] Powers, T. C. and Brownyard, T. L., "Studies of the physical properties of hardened
cement pastes." Research Department Bulletin / Portland Cement Association, 22 (1948).
[3] Lee, J., “Experimental studies and theoretical modelling of concrete subjected to high temperatures, University of Colorado at Boulder. PhD Thesis (2006).
[4] Lee, J.S., Xi, Y., Willam, K., and Jung, Y., “A Multiscale Model for Modulus of Elasticity of Concrete at High Temperatures”, Cement and Concrete Research, 39 (2009) 754–762.
2nd International RILEM Workshop on Concrete Spalling due to Fire Exposure 5-7 October 2011, Delft, The Netherlands
236
[5] Salomoni V., Majorana C.E., Mazzucco G., Xotta G. and Khoury G.A., “ Multiscale modelling of Concrete as a Fully Coupled Porous Medium”, Concrete Materials: Properties, Performance and Applications, Ch. 3, NOVA Science Publishers, (2009) 171-231.
