PROBABILISTIC MODELLING OF CONCRETE
STRUCTURES DEGRADATION
B. Teplý, P. Rovnaníková, P. Rovnaník, D. Vořechovská
Brno University of Technology, Czech Republic
REC 2012, Brno
•
Outline
Degradation of RC structures
…Time aspect
…Codes and regulations
…Durability limit states
•
•
Software tool
Evaluation of some degradation models
…Carbonation m. vs. in situ measurement on
cooling tower
…Chloride ingress m. vs. in situ measurement on
bridge in Italy
…Corrosion m. vs. numerical m.
•
Conclusions
Degradation mechanisms vs. time
Degradation mechanisms vs. time
carbonation and/or
chloride ingress
Degradation mechanisms vs. time
steel
depassivation
carbonation and/or
chloride ingress
Degradation mechanisms vs. time
steel
depassivation
carbonation and/or
chloride ingress
steel corrosion
Codes and regulations
• ISO 13832 (2008)
General principles on Design of Structures for Durability
• fib Model Code (2010)
Bulletins 55, 56 (First complete draft)
Bulletin 34 Model Code for Service Life Design (2006)
• EN 206-1 (2000)
Concrete – Part 1: Specification, performance,
production and
Conformity
Durability limit states
1. Service life format t PS  t D,where tPS  tini  t prop
1a. Simplified/initiation LS
2. Limit state format
tini  tD
R tD   S tD  ULS
Slim  S tD 
SLS
Durability limit states
Steel depasivation (tini):
Pf (tD )  P a  xc  t D   0  Pd
Pf (tD )  P Ccr  Ca  t D   0  Pd
Steel corrosion (tprop):
Pf (tD )  Pr  ra tD   0  Pd
Pf (tD )  Pwcr  wa tD   0  Pd
Software tool
FReET-D probabilistic modeling of degradation
processes in time
www.freet.cz
(Teplý, Vořechovská, Chromá, Rovnaník – Brno University of Technology)
Utilizes probabilistic platform of FReET
(Vořechovský, Rusina, Novák – Brno University of Technology)
Features: random input variables, MC, LHS,
FORM, statistical parameters of result,
sensitivity analysis, estimation of probability Pf
and reliability index , automatic parametric
studies, Bayess updating, number of
degradation models
FReET-D: implemented models
No. of
models
Carbonation
13
Chloride
ingress
1
2
Frost attack
3
Sulphate attack
Acid attack
1
1
1
1
1
2
1
Reinforcement
corrosion
1
1
Outputs
carbonation depth, time to depassivation (concretes with
Portland and blended cements)
depth of chlorination, time to depassivation
concentration of chlorides
actual degree of saturation, relative dynamic modulus of
elasticity, loosening of concrete at surface
rate of concrete corrosion
depth of concrete corrosion
net rebar diameter (uniform cor.)
pit depth (pitting cor.)
net cross sectional area (pitting cor.)
time to cracking (uniform cor.)
crack width (uniform cor.)
stress intensity factor (prestressed reinforcement, pitting
corrosion, fracture mechanics approach)
strength and ductility of corroded steel
Evaluation of carbonation models
Cooling tower (Keršner et al. 1996)
• height of 206 m
• in-site investigation at the age of 19.1 years
• the depth of carbonation measured at 75
locations (on both the internal and external
surfaces)
Evaluation of carbonation models
Analytical models
a) fib Model Code (Bulletin No. 34)
b) Papadakis et al. (1992), based on mass
conservation
c) Papadakis et al. (1992), R.H. function updated
d) Morinaga (1992), R.H. function updated
(Teplý et al. 2010)
Evaluation of carbonation models
Carbonation depth
(19.1 years)
External surface
(RH = 70%)
Internal surface
(RH = 93%)
Mean [mm]
COV [%]
Mean [mm]
COV [%]
fib Model Code
10.8
48
4.4
60
Papadakis et al. (1992)
8.2
24
1.9
43
Papadakis et al. (1992)
R.H. function updated
12.7
18
8.3
51
Morinaga (1992), R.H.
function updated
11.9
21
7.7
53
In situ measurements
(Keršner et al. 1996)
14.9
56
8.0
29
(Vořechovská et al. 2010)
Evaluation of carbonation models
Carbonation depth
(19.1 years)
External surface
(RH = 70%)
Internal surface
(RH = 93%)
Mean [mm]
COV [%]
Mean [mm]
COV [%]
fib Model Code
10.8
48
4.4
60
Papadakis et al. (1992)
8.2
24
1.9
43
Papadakis et al. (1992)
R.H. function updated
12.7
18
8.3
51
Morinaga (1992), R.H.
function updated
11.9
21
7.7
53
In situ measurements
(Keršner et al. 1996)
14.9
56
8.0
29
(Vořechovská et al. 2010)
Evaluation of chloride ingress models
Bridge in Italy
Wendner, R., Strauss, A., Guggenberger, T., Bergmeister, K.
and Teplý, B., 'Ansatz zur Beurteilung von chloridebelasteten
Stahlbetonbauwerken mit Bewertung der Restlebensdauer',
Beton- und Stahlbetonbau 12/2010
Chloride concentration
measured in the different
distances from the nearest
surface (from 10 to 50 mm)
Evaluation of chloride ingress models
a)
b)
c)
d)
e)
fib Model Code
(Bulletin No. 34)
fib Model Code;
substituted
surface
concentration
Crank´s solution
of Fick´s 2nd
law
Thomas and
Baumfort (1999)
Nilsson and
Carcasses
(2004) and Tang
and Gulikers
(2007)
Evaluation of corrosion model
Analytical model (Li et al. 2006)
vs.
Numerical computation based on nonlinear FE
(Vořechovská and Vořechovský 2010)
Evaluation of corrosion model
Analytical model (Li et al. 2006)
porous zone
rust
steel
concrete
no
corrosion
crack
filling of
porous
zone
crack
crack on
initiation
concrete
Constant geometry: thick-wall cylinder
surface,
(Bažant 1979, Pantazopoulou and Papoulia 2001, Tepfers 1979)
spalling
Evaluation of corrosion model
Numerical model
►ATENA program
(Červenka Consulting)
► constitutive model
based on smeared
crack approach
► used fracture plastic
model NLCEM
► expansion of
corrosion products:
(negative) shrinkage of
reinforcement
Evaluation of corrosion model
Comparison of models
Identical parameters: geometry, E, ft
Extras for numerical model: GF, fc,…
Conclusions
• Durability design of RC structures is now actual
in engineering practice
• Durability/performance based approach to the
specification of concrete durability may be
based on predictive (proven!) models utilization
• FReET-D is a software tool for fully probabilistic
performance based design; the other proves of
the degradation models are needed
• FReET-D can be effectively utilized in
combination with FReET and ATENA software