1 Introduction
2 Deterioration Model
2.1 Corrosion Initiation and Pit Nucleation
Physical problem |
\( \psi \)
|
\( \zeta \)
|
\( J \)
|
\( J' \)
|
\( q_{\psi }^{s} \)
|
---|---|---|---|---|---|
Chloride ingress |
C
fc
| 1 |
\( D_{c}^{*} \vec{\nabla }C_{fc} \)
|
\( C_{fc} D_{h}^{*} \vec{\nabla }h \)
|
\( q_{h}^{s} \)
|
Moisture diffusion |
h
| ∂w
e
/∂h |
\( D_{h}^{*} \vec{\nabla }h \)
| 0 | 0 |
Heat transfer |
T
|
ρ
c
c
q
|
\( \lambda \vec{\nabla }T \)
| 0 | 0 |
2.2 Pit-to-Crack Transition
2.3 Crack Growth
3 Modeling Weather Including Climate Change Effects
3.1 Basic Considerations and Model Description
-
influence of global warming,
-
seasonal variation of weather parameters, and
-
random nature of weather.
3.2 Selected Scenarios
-
carbon dioxide, methane and nitrous oxide emissions;
-
global population growth;
-
introduction of new and clean technologies leading to the reduction of the impact of global change; and
-
use of fossil sources of energy.
-
the difference between the annual means of temperature for the initial year T(t 0 ) and the year of the end of the forecast T(t a ), ΔT,
-
the difference between the annual mean of relative humidity for h(t 0 ) and h(t a ), Δh, and
-
the difference between the normalized durations of cold seasons for R(t 0 ) and R(t a ), ΔR.
Scenario | ΔT (°C) | Δh | ΔR |
---|---|---|---|
Without climate change is neglected | 0 | 0 | 0 |
Expected Use of alternative and fossil sources of energy, birthrates follow the current patterns and there is no extensive employ of clean technologies (equivalent to scenarios RCP2.6–RCP4.5 depending on the location) | 2.5 | 0.05 | − 0.1 |
Pessimistic Vast utilization of fossil sources of energy, appreciable growth of population and there are no policies to develop and extend the use of clean technologies (equivalent to scenarios RCP6–RCP8.5 depending on the location) | 6.5 | 0.1 | 0.2 |
4 Probabilistic Approach
4.1 Modeling Weather Uncertainties
4.2 Probability of Failure
5 Numerical Example
5.1 Problem Description
Variable | Value |
---|---|
Characteristic punctual design load, P
k
| 150 kN |
Elastic modulus of steel, E
st
| 200 GPa |
Characteristic concrete compression strength, f’
ck
| 30 MPa |
Characteristic steel strength, f
yk
| 500 MPa |
Concrete Poisson ratio, ν
c
| 0.2 |
Water to cement ratio, w/c | 0.5 |
Curing period, t
e
| 28 days |
Variable | Units | Distribution | Mean | COV |
---|---|---|---|---|
D
c,ref
| m2/s | Log-normal | 3 × 10−11 | 0.20 |
C
th
| wt % cem. | Normala | 0.5 | 0.20 |
c
t
| mm | Normalb | 50 | 0.25 |
D
h,ref
| m2/s | Log-normal | 3 × 10−10 | 0.20 |
λ
| W/(m °C) | Beta on (1.4; 3.6) | 2.5 | 0.20 |
c
q
| J/(kg °C) | Beta on (840; 1170) | 1000 | 0.10 |
ρ
c
| kg/m3 | Normala | 2400 | 0.05 |
P
| kN | Log-normal | 115 | 0.20 |
f’
c
| MPa | Normala | 40 | 0.15 |
f
y
| MPa | Normala | 600 | 0.10 |
5.2 Results
5.2.1 Influence of Weather Model
5.2.2 Failure Probabilities for Different Levels of Aggressiveness
5.2.3 Influence of Climate Change
Environmental aggressiveness | Tropical | Oceanic | ||
---|---|---|---|---|
Without (%) | Pessimist (%) | Without (%) | Pessimist (%) | |
High | 58.2 (15) | 57.9 (15) | 62.2 (15) | 60.8 (15) |
Moderate | 120.5 (16) | 119.6 (16) | 124.8 (16) | 123 (16) |
Low | 409.4 (18) | 407.7 (18) | 411.2 (18) | 405.2 (19) |
Frequency (cycles/day) | High aggressiveness | Moderate aggressiveness | Low aggressiveness | |||
---|---|---|---|---|---|---|
Without (%) | Pessimist (%) | Without (%) | Pessimist (%) | Without (%) | Pessimist (%) | |
50 | 50.2 (15) | 49.8 (15) | 82.9 (21) | 81.8 (21) | 157.7 (36) | 153.8 (35) |
500 | 32.6 (22) | 32.2 (22) | 49.5 (27) | 48.4 (28) | 103.9 (43) | 101.3 (42) |
1000 | 30 (23) | 29.5 (22) | 45.8 (28) | 45.1 (28) | 97.1 (43) | 94.7 (42) |
2000 | 28.3 (23) | 27.7 (23) | 43.5 (28) | 42.5 (27) | 91.7 (42) | 88.8 (42) |
Frequency (cycles/day) | High aggressiveness | Moderate aggressiveness | Low aggressiveness | |||
---|---|---|---|---|---|---|
Without (%) | Pessimist (%) | Without (%) | Pessimist (%) | Without (%) | Pessimist (%) | |
50 | 54.1 (16) | 52.7 (15) | 86.9 (21) | 85 (21) | 159.3 (35) | 153.1 (36) |
500 | 36.4 (22) | 35.1 (22) | 53.7 (27) | 51.3 (27) | 105.8 (41) | 99.4 (42) |
1000 | 33.8 (23) | 32.6 (22) | 50.3 (27) | 47.9 (27) | 99.3 (41) | 92.5 (42) |
2000 | 32.3 (24) | 30.8 (23) | 48.1 (27) | 45.8 (27) | 93.2 (40) | 86.7 (40) |