Durability Assessment of Large Surfaces

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Sykora & Holicky
-

Durability Assessment of Large Surfaces


1

Durability Assessment of Large Surfaces

Using Standard Reliability Methods

M. Sykora & M. Holicky

Czech Technical University in Prague

Introduction

Measurements

Simplified deterioration model

Example

Conclusions

Sykora & Holicky
-

Durability Assessment of Large Surfaces


2

Cooling tower and


its maintenance

Sykora & Holicky
-

Durability Assessment of Large Surfaces


3

Steel retaining walls

Sykora & Holicky
-

Durability Assessment of Large Surfaces


4

Site measurements

Local distribution of a carbonation depth

0
12
24
0
0.1
Relative Frequency
n = 74
m= 11.05 mm
v = 0.31
a = 0.59
Lognormal
Gamma
Normal
Carbonation Depth [mm]
spatial variation (environmental actions,

material properties)?

→ discretisation techniques

→ simplified approach based on “independent”


elementary surfaces

Sykora & Holicky
-

Durability Assessment of Large Surfaces


5

Simplified deterioration model

-

division into
zones

(similar exposures


splash/upper parts of piers)

-

within zones homogeneous
random

fields

W

(material properties,
concrete cover)

+

hyperparameters

X

(single
value for
whole structure)

-
discretization

of the zone into
N

elementary surfaces (random field
variables independent)








fib Bulletin 59
Condition control and assessment of reinforced concrete structures

Sykora & Holicky
-

Durability Assessment of Large Surfaces


6

Simplified deterioration model

P
f
(
t
) = P{
n
deg
(
t
)

/

N


a
lim
}


=
E
X
(
t
)
{1
-

F
binom
[
N
a
lim
,
N
,
p
f
(
W
|
x
(
t
)
)]}

-

For
steel

structures the size of an elementary surface may
correspond to a size of inspected areas (e.g. 3 m)

-

Concrete
, chloride ingress ~ 0,5
-
2 m

The limiting deterioration level

a
lim

= 0,1
-
0,2

a
lim

= 0,15 accepted in the example

p
f
(∙) is the failure probability of an elementary surface

FORM/

SORM

Sykora & Holicky
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Durability Assessment of Large Surfaces


7

Example


carbonation of concrete

fib

Model
Code

for

Service

Life

Design

Type

Variable

Symbol

Distrib.

Unit


X

V
X

Random

Concrete cover

R

Beta

mm


R

0.35

fields

Inverse carbon.

resistance

R
NAC,0
-
1

Gamma

(mm
2
/y.) /

(kg/m
3
)

2e4

0.5


Relative humid.

RH
real

Beta

-

0.71

0.18

Hyper
-

CO
2

concentr.

C
s

normal

kg/m
3

8.2e
-
4

0.12

parameters

Model uncert.

K
S

LN

-

1

0.1


elementary surface:
p
f
(
t
,

R
|
k
S
,
x
)
= P[
R
(

R
) −
k
S

S(
t
,
W
|
x
)
< 0
]

Measurements

no trend?






2
s
1
NAC,0
c
5
.
2
5
ref
5
real
w
s
real
1
NAC,0
w
SR
c
0767
.
0
7
1
1
2
,
,
,
b
tow
p
b
t
c
R
t
rh
rh
t
b
c
rh
t
R
S

























Sykora & Holicky
-

Durability Assessment of Large Surfaces


8

Variation of
P
f
(
t
) with
t


R

= 25

mm,
a
lim

= 0.15

0
20
40
60
80
100
0
0.
1
0.
2
0.
3
0.
4
0.5
time
t
P
f
(
t
)
N
= 10
0
N
= 20
N
= 1
N
= 10
0
no correlation
Sykora & Holicky
-

Durability Assessment of Large Surfaces


9

Probabilistic optimization of the concrete cover


The total cost

C
tot

=
C
0

+
C
1

μ
R

+ E[
C
f
]



Expected consequences




Annual discount rate
q
















t
q
P
P
C
C




d
1
1
E
f
f
f
f
Sykora & Holicky
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Durability Assessment of Large Surfaces


10

Variation of
optimum
reliability index
b
opt

with
N

q

= 0.03,
t

= 40

years, and
C
f

/

C
1

= 100 and 1

000

0
1
2
3
N
b
opt
(

R
,opt
)
100
1000
1
.
10
4
1
.
10
5
10
C
f
/
C
1
=
100
C
f
/
C
1
= 1 000
Sykora & Holicky
-

Durability Assessment of Large Surfaces


11

Conclusions


Structural durability may be affected by
spatial variability
particularly for large surfaces.


Presented model seems to require
lower

computational

demands

compared to random field techniques (to be proved by
upcoming studies).


This model is expected to be an effective tool for
optimisation

studies
.


Numerical

example

of concrete carbonation reveals that the
failure probability somewhat increases with a size of surface.


The
optimum

concrete cover and
reliability

index

can be
considered
independent

of the size of the surface area.

Sykora & Holicky
-

Durability Assessment of Large Surfaces


12

Miroslav

Sykora

and Milan
Holicky


miroslav.sykora@klok.cvut.cz


Durability Assessment of Large Surfaces

Using Standard Reliability Methods

Thank you for your attention.