10:39 pm october 9, 1963 - DICA

Centre for Computational Structural and Materials Mechanics
La modellazione del degrado dovuto a
reazione alcali-silice in dighe di
calcestruzzo
Claudia Comi
Dipartimento di Ingegneria Civile e Ambientale
Meccanica dei materiali e delle strutture
http://www.dica.polimi.it/sezioni/materiali/
Politecnico di Milano, 9 ottobre 2013
VAJONT DAM (10:39 p.m. october 9, 1963)
2
1910
deaths
A massive landslide of about 260 million m3 of earth and rock, which fell into
the reservoir at up to 110 km per hour completely filled up the narrow
reservoir in front of the dam. 50 million m3 of water overtop the dam in a 230metre-high wave
1
Contents
•Motivation
•The alkali-silica reaction
•Multi-phase (three-phase vs two-phase) elasto-damage model
for the description of the simultaneous influence of temperature
and humidity on ASR and its structural consequences
•A model founded on a more realistic microscopic scheme and
based on the coupling of two different damage variables:
chemical damage and mechanical damage
•Closing remarks
Acknowledgements
Rossella Pignatelli*, U. Perego*, R. Fedele*, Paulo J. M. Monteiro**
(*) Politecnico di Milano
(**) University of California Berkeley
Durability of concrete structures
Pian Telessio
arch gravity dam (Italy)
Pian Telessio dam, Central Plumbline (concio 4/6)
70
Measuring station 1
Measuring station 2
Measuring station 3
Measuring station 4
Crest Displacement
Crest Displacement Mean 12
Increase of crest
displacement in the upstream
direction 20 years after its
completion due to an alkaliaggregate reaction
Monte (m m)
60
50
40
20
10
0
-10
1999
1990
1980
1970
14/01/1970
08/07/1970
13/01/1971
13/07/1971
19/01/1972
06/07/1972
11/01/1973
03/07/1973
08/01/1974
03/07/1974
14/01/1975
01/07/1975
14/01/1976
15/07/1976
23/02/1977
29/08/1977
07/02/1978
25/08/1978
10/05/1979
26/11/1979
24/07/1980
08/01/1981
07/07/1981
12/01/1982
09/09/1982
12/05/1983
14/11/1983
15/05/1984
06/11/1984
07/05/1985
09/12/1985
13/06/1986
07/01/1987
07/07/1987
25/02/1988
12/10/1988
10/05/1989
06/11/1989
04/05/1990
09/01/1991
04/07/1991
09/01/1992
02/07/1992
09/02/1993
13/09/1993
04/03/1994
17/10/1994
29/05/1995
06/11/1995
02/05/1996
14/11/1996
02/07/1997
07/01/1998
05/08/1998
08/02/1999
Valle (m m )
30
2008, displacement of central
pendolum > 60 mm
rehabilitation works by means
of vertical slot cuttings
2
Key issues – open problems
5
The Alkali-Aggregate-Reaction can have a severe impact on
• Structure (dam) safety
• Structural functioning
What is the safety margin when the reaction will stop?
What are the more appropriate rehabilitation provision or a
replacement is needed?
Study of the AAR, in particular the alkali-silica reaction
(ASR) (how to avoid the reaction in new structures or
mitigate the effect)
Reliable modeling of the consequence of this reaction on
the structural mechanical behavior (what is an appropriate
constitutive description)
Alkali-silica reaction
Silica of aggregates
(SiO2)
+ Alkali in cement mortar
Na+, K+
Alkali-silica gel + Water
AGGREGATES CONCRETE
Alkali-silica gel
Alkali-silica gel swelling
GEL
+ WATER
localized formation of gel
mechanical properties degradation
cement
mortar
aggregate
3
ASR process: mechanical consequences
• Swelling, expansion
• Microcracks formation
• ...
• Tensile strength reduction
Ben Haha, 2006
• Elastic moduli reduction
-32%
mean
ASR process: structural consequences
• Swelling, expansion
• Microcracks formation
• Strength reduction
• Elastic moduli reduction
• ...
Increase of crest displacement in the upstream direction
4
Factors influencing the reaction
•aggregate type and dimensions: fast reacting,
•alkali content ( Na+, K+ )
ASR
•temperature
slow reacting
38°C
higher temperature
faster reaction
FREE EXPANSION
TESTS
23°C
EXPERIMENTAL DATA
(LARIVE 1998)
•humidity
100%
higher humidity
59%
higher expansion
faster reaction
EXPERIMENTAL DATA
(POYET 2006)
Scales of analysis for ASR
microscopic scale
meso-scale
structural scale
 macro

multi-phase modelling
basic idea by Ulm, Coussy, Kefei,
Larive (2000)


psw
5
MULTI-PHASE DAMAGE MODEL accounting for the
simultaneous effect of temperature and humidity on ASR
Comi, Pignatelli (2011)

skeleton

pw
pg
water pressure
gel pressure
effective stress
 ij   ij  bw pw ij  bg p g  ij
macro stress
Biot’s coefficients
Multi-phase model
•Equilibrium
•Energy balace
•Mass balance in partially saturated reacting media
liquid
gel forms and swells without flowing with
vapour
respect to the solid skeleton (very low
air
permeability)
no transport equation for gel
solid
weakly permeable materials
gel
[Mainguy, Coussy, Baroghel-Bouny 2001]
•Transport laws
transport of moisture
Darcy
in its liquid form
Fick
Fourier
•State equations
•Evolution laws (water and gel contents, damage)
6
Multi-phase model
STATE EQUATIONS
reaction extent
gel volumetric variation  g  c
temperature
water volumetric variation
damage
FREE ENERGY
chemical potentials
STRESS
gel
water
Damage evolution
ISOTROPIC DAMAGE
LOADING-UNLOADING
CONDITIONS
D  1  (1  Dt )(1  Dc )
f i ( , D)  0
“INELASTIC” EFFECTIVE STRESS
material parameters
"
"
"
[Comi-Perego, 2001]
EXPERIMENTAL DATA: YOUNG’S MODULUS REDUCTION
FOR THE CALIBRATION OF DAMAGE PARAMETERS
7
Evolution of the gel content
REACTION
EXTENT
influence of degree of saturation
on the final expansion
ASR
characteristic time (T, Sw)
latency time (T, Sw)
FREE EXPANSION
TESTS

fS
 ASR
w
DEGREE OF SATURATION
Latency and characteristic times
INFLUENCE OF TEMPERATURE AND HUMIDITY
DEGREE OF SATURATION
TEMPERATURE
(ARRHENIUS)
8
MODEL VALIDATION
INFLUENCE OF THE DEGREE OF SATURATION
ON THE REACTION KINETIC AND THE FINAL EXPANSION
FREE EXPANSION TESTS IN DIFFERENT HUMIDITY CONDITIONS
FREE EXPANSION
TESTS
EXPERIMENTAL DATA (LARIVE 1998)
MODEL VALIDATION
FREE EXPANSION TESTS WITH DELAYED IMMERSION IN WATER
Immersion in water
after 28 days
RH 100% for 676 days and
then immersion in water
FREE EXPANSION TESTS
BY (MULTON, 2010)
SHRINKAGE OF SPECIMENS EXPOSED TO DRYING AIR AFTER IMMERSION
two phase model
FREE EXPANSION TESTS
EXPERIMENTAL DATA (MULTON-TOUTLEMONDE 2010)
9
A particular case: two-phase formulation
The gel swelling is the overriding phenomenon, especially for high humidity
environmental conditions
homogenized
concrete
skeleton
concrete with expanding gel
fluidpressurised
pressurised
(water, wet gel
gel
vapor,air)
bi-phase material
gel pressure
effective stress
macro stress
Biot’s coefficient
BEAUHARNOIS DAM (CANADA)
PERIODIC BOUNDARY CONDITIONS
10
SOLUTION STRATEGY
Heat diffusion analysis
 periodic temperature field
Moisture diffusion analysis
periodic degree of saturation field
reaction extent
Mechanical analysis – chemoelastic damage model
 displacements, stress, damage
structural analysis
REACTION EXTENT
INFLUENCE OF TEMPERATURE AND DEGREE OF SATURATION ON REACTION EXTENT
11
Damage patterns
3 years
structural analysis
Horizontal
6 years
60 years
crest displacement
0
-20
-40
eps_0.0020
eps_0.0018
-60
eps_0.0015
-80
-100
0
400
800
1200
1600
2000
2400
2800
Time [weeks]
0
-10
Horizontal displacement [mm]
Horizontal displacement [mm]
20
-20
-30
-40
u x  0.5 mm/year
-50
EXPERIMENTAL
RANGE
-60
-70
u x  0.8 mm/year
-80
12
HEAT AND HUMIDITY CHARACTERISTIC LENGTHS
characteristic lengths for concrete
differ by two orders of magnitude
the moisture diffusion analysis can
be avoided for bulky structures
FONTANA DAM (USA)
Left abutment:
views of cracked
surface from
downstream face
and inside the
inspection
gallery
cracked trajectory
inside a damaged
monolith, sketch of
the post-tensioning
anchor system and
the expansion slot
with indication of fill
soil level variation
[Ingraffea, 1990]
13
Fontana dam
[Comi, Fedele, Perego, 2009]
FONTANA DAM – comparison between the observed crack
pattern and the simulation after 25 years
[Comi, Fedele, Perego, 2009]
14
Chemical damage due to gel swelling
double-porosity poromechanical approach
IN POROMECHANICAL MODELS THE GEL PRESSURE
IS HIGHER THAN THE EXPERIMENTAL VALUE
X-ray image from Kawamura and Iwahori (2004)
THE DAMAGE DUE TO ASR IS LOCALIZED
AROUND THE REACTIVE SITES
Scales of analysis for ASR
microscopic scale
meso-scale
structural scale
15
DIFFUSE DOUBLE-LAYER THEORY
The electrical DDL theory has been used to interpret the ASR gel swelling and to estimate the
pressure that it exerts on the concrete matrix surrounding the reactive sites.
amorphous silica
pore solution
Hydration of a
dissolved
amorphous silica
particle
Diffuse double-layer
of cations around a
charged silica
particle
double layer of counterions leading to alkali silica gel
Gouy-Chapman model
Si-O- Na+
EQUILIBRIUM
between electric force and pressure
gradient
BOLTZMANN EQUATION
between potential, distance from the
particle and charge density
POISSON EQUATION
between concentration and potential
pressure
layerparticles
thicknessof the gel
repulsive force between thedouble
charged
q surface charge
density
swelling pressure
16
fenomeno
Swelling pressure (ASR)
DOUBLE-LAYER THEORY
Gouy-Chapman model
q surface charge density
pressure
tests on gel samples from
Furnas dam (Brazil)
- saturated conditions -
DOUBLE-POROSITY MODEL
34
 macro
Concrete porosity
Porosity due to
chemical damage

(1)


d

CHEMICAL DAMAGE
psw
17
Double-porosity model: state equations
BI-PHASE MODEL poroelasticity
35
macroscopic bulk modulus
Biot’s parameters
HOMOGENIZED POROSITY
concrete porosity
 gw 
mgw
 gw
porosity due to chemical damage
WET GEL VOLUME CONTENT
relative change in fluid mass
fluid mass density
Chemical and mechanical damage model
STRESS
gel pressure
MECHANICAL DAMAGE
CHEMICAL DAMAGE
ft
D  1  (1  Dt )(1  Dc )
fc
[Comi-Perego, 2001]
18
EVOLUTION OF THE CHEMICAL DAMAGE
1. Maximum value of the gel pressure (GouyChapman model): 11 MPa
2. Macroscopic chemical damage: Dch =1-K/K0
damaged solid
skeleton d
total damage Dch
Free expansion and tests on loaded or confined specimens
(Multon 2003)
ASR
free
expansion
20 MPa
loaded
confined
19
model
validation
MODEL
VALIDATION: coupled chemical and mechanical damage
COMPRESSION TESTS (GIACCIO ET AL 2008)
reactive concrete considered
ordinary concrete
chemical damage
Structural analyses
HEAT TRANSPORT
T(x,t)
MOISTURE TRANSPORT
Sw(x,t)
ξ(x,t) d(x,t)
Reaction extent,
Chemical damage
ε (x,t) σ(x,t) D(x,t)
MECHANICAL
ANALYSIS
BEAMS EXPOSED TO MOISTURE GRADIENT
(MULTON-TOUTLEMONDE 2010)
FIRST PHASE
DRYING
14 MONTHS
SECOND PHASE
RE-WETTING
9 MONTHS
20
degree of saturation
chemical damage
reaction extent
Experimental results and model prediction
Evolution of
horizontal strain
Evolution of
vertical strain
21
Three point bending tests
Experimental results(Giaccio et al. 2008)
Model simulation
Closing remarks
oBoth models allows for a good qualitative description of the influence of
temperature and humidity on the structural behavior of concrete affected by ASR
oThe second model combines the phenomenological approach (theory of porous
media) with the experimental information at the micro-scale (through the GouyChapman model)
o The coupling of a chemical damage and a mechanical damage allows to correctly
reproduce the experimental response in terms of strains, degradation of mechanical
properties and gel pressure
o Dependence of the tensile strength of chemical damage
o Anisotropic damage
o Other long-term effects (creep)
o Nonlocal regularization (instead of the fracture energy pseudo regularization)
o Combining numerical analyses with monitoring data
22
45
MS thesis Alessio Datteo
Monitoraggio e analisi numeriche della diga di Monte Lerno (SS)
Livio Pinto
Monitoring
system
pendulum
collimators
46
Monitoring data vs numerical
prediction
10,00
8,00
Crest displacement [ mm ]
6,00
FEM
4,00
Pendolo
2,00
0,00
0
50
100
150
200
250
‐2,00
‐4,00
‐6,00
‐8,00
‐10,00
time [months]
23
Thank you
Key references
48
Journals
C. Comi, R. Fedele, U. Perego - A chemo-thermo-damage model for the analysis of concrete dams
affected by alkali-silica reaction, Mechanics of Materials, 41, pp. 210-230 (2009).
C. Comi, U. Perego – Anisotropic damage model for concrete affected by alkali-aggregate reaction. Int.
J. Damage Mech. 20, 598-617, ISSN:1056-7895 (2011).
C. Comi, B. Kirchmayr; R. Pignatelli - Two-phase damage modeling of concrete affected by alkali-silica
reaction under variable temperature and humidity conditions, International Journal of Solids and
Structures, 49, 3367-3380, (2012).
R. Pignatelli C. Comi, P. Monteiro, A coupled mechanical and chemical damage model for concrete
affected by alkali-silica reaction Cement and Concrete Research, 53 (2013).
Proceedings
C. Comi, R. Pignatelli – On damage modeling of concrete affected by alkali silica reaction in the
presence of humidity gradients. Proc. GIMC2010 September 22-24, 2010, Siracusa (Italy), 4pp CD.
ISBN: 978-88-905217-0-6.
C. Comi, R. Pignatelli – A three-phase model for damage induced by ASR in concrete structures Proc IV
Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering COUPLED
PROBLEMS 2011 M. Papadrakakis, E. Oñate and B. Schrefler (Eds), 20-22 June, 2011, Kos,
Greece, 12pp., ISBN: 978-84-87867-59-0
C. Comi, R. Pignatelli - Modeling of temperature and humidity effects in concrete subjected to alkali silica
reaction, Proc. XX Congresso dell'Associazione Italiana di Meccanica Teorica e Applicata,
Francesco Ubertini, Erasmo Viola, Stefano de Miranda, Giovanni Castellazzi (Eds), Bologna 12-15
September 2011, 10pp, ISBN 978-88-906340-1-7 (online).
C. Comi, P. Monteiro, R. Pignatelli – Chemical and mechanical damage in concrete due to swelling of
alkali-silica gel., Proc. 10th World Congress on Computational Mechanics, P.M. Pimenta and E.M.B.
Campello (Eds), 8-13 July, São Paulo, Brazil, ISBN 978-85-86686-70-2, n°16820, 12pp (2012).
24