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Daniel Straub & Armen Der Kiureghian
UC Berkeley, Civil and Environmental Engineering Department
JCSS Workshop on Risk Communication and AcceptanceStanford, March 2007
Acceptance Criteria for Deteriorating Structural Systems
Acceptance criteria for deterioration failures
– Goal: Determining acceptance criteria for elements of deteriorating structural systems
– Acceptance criteria should be formulated in terms of a target reliability index βT
or probability of failure for the elements
– Based on the recommendations by the JCSS (Joint Committee on Structural Safety) probabilistic model code:
– These describe acceptance for failure of the system C
Determine the acceptance for deterioration failures F of elements in the system
Classification of structural elements
Four categories according to the structural redundancy:
Name Description Redundancy (Structural importance)
Examples Acceptance criteria
Immediately critical elements
Failure of the element will cause immediate damages to the structural system with a high probability.
None (determining)
Elements of a minimal structure subjected mainly to dead and live load; elements of a statically determinate system; support of a facade element; containment.
According to JCSS target reliability indexes for ultimate limit states – under consideration of the total number of such elements
Critical elements with delayed failure
Failure of the element is likely to cause collapse of the structural system once an extreme live load (e.g., environmental/accidental loads) occurs
Little (critical)
Elements of a minimal structure or primary structural elements of a structure subjected to environmental loads; containment under varying conditions (pressure etc.).
To be defined later.
Criteria must be formulated in terms of accumulated failure probability
Redundant structural elements
Failure of a single element has little bearing on the system capacity, but failure of a group of elements can cause system failure.
Large (minor importance)
Most elements of typical structural systems; joint in a ship hull or redundant offshore structure, reinforcement in concrete slab, foundation pile.
To be defined later.
Criteria must be formulated in terms of accumulated failure probability
Servicability elements (limit states)
Failures has no bearing on the structural capacity and consequences are limited to reduced serviceability
Fully (no importance)
Spalling of concrete elements (when no physical damage is caused by the spalled pieces); non-critical deformations.
According to JCSS target reliability indexes for serviceability limit states or by economical optimization
Elements for which deterioration failures do not immediately lead to system failure
Quantifying structural importance
– In the past (single element importance measure):
then
– Can be computed for general structural systems
– Neglects the effect of more than one simultaneous deterioration failures F
( ) ( )Pr Pri i iSEI C F F C F¬= ∩ −
1i
TT CF
i
PP
N SEI=
Quantifying structural importance
– Assume that the element can be considered as being part of a Daniels system
– The system is designed such that the reliability index for the ultimate limit state without deterioration is equal to the corresponding acceptable value
EI = ∞
R1 R2 RN
Ls
R
E
Ri
. . .R2 s
R
E
Ri
Case a)
Case b)
( ) ( )Pr TsysC F β= Φ − 4.4T
sysβ =in the following:
Factors influencing the system reliability
Compare the simple indicator
with the system reliability related to deterioration failure
More realistic importance measures require computation of systemreliability for all combinations of deterioration failures
( ) ( )Pr Pri i iSEI C F F C F¬= ∩ −
Pr( )C F∩
0 0.2 0.4 0.6 0.8 110
-7
10-6
10-5
10-4
10-3
ρM
0 10 20 30 4010
-8
10-7
10-6
10-5
10-4
10-3
10-2
Number of elements
SEI
Pr(C∩F)
SEIPr(C∩F)
Acceptance criteria for the element from an idealized system
EI = ∞
R1 R2 R5
L
R3 R4
The "real" structural system
μR3= 4μR1= 4μR2= 4μR4= 4μR5
EI = ∞
L
R3RA
EI = ∞
RB
L
RC RDRAR2 R4 R5R1
The idealized system forelements 1,2,4,5
The idealized system forelement 3
Resulting acceptance criteria
0 5 10 15 20 25 30 35 401.5
2
2.5
3
3.5
4
Equivalent number of elements N
Tar
get
relia
bilit
y in
dex β
FT
Brittle elements, βsys
= 4.4
ρM
= 0.0
ρM
= 0.3
ρM
= 0.6
( ) 3.97Tsys Fβ =
Acceptance criteria from simple indicator
– The number of element represents the structural importance of the element
– It is possible to derive the equivalent number of elements that corresponds to the simple indicator
( ) ( )Pr Pri i iSEI C F F C F¬= ∩ −
10-5
10-4
10-3
10-2
10-1
1
1.5
2
2.5
3
3.5
SEI
βFT
SEIDaniels system (ρ
M = 0)
Daniels system (ρM
= 0.3)
Daniels system (ρM
= 0.6)
Acceptance criterion from:
Effect of detectability
Detectability: The ability to detect a deterioration failure (and to repair it)
1) Detectability influences the reference period for the target reliability index
0 5 10 15 20 25 301
2
3
4
5
6
7
8
9
10
Time t [yr]
Rel
iabi
lity
inde
x β
F
TD = 1yr
TD = inf.
Effect of detectability
Detectability: The ability to detect a deterioration failure (and to repair it)
2) Detectability influences the statistical dependence among deterioration failures
0 5 10 15 20 25 30-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
t [yr]
ρF (T
D = inf.)
ρM
(TD = inf.)
ρF (T
D = 1yr)
ρM
' (TD = 1yr)
ρM (TD = inf)
ρM (TD = 1yr)
ρM : Correlation coefficient among the normal distributed safety margins of two elements
Conclusion
– Acceptance criteria for deterioration limit states require consideration of
– Structural redundancy with respect to element failures
– Correlation structure among deterioration failures
– Detectability / persistence of deterioration failures
– For elements in redundant systems, it is proposed to represent the structural importance of elements by simple idealized systems
– For elements with a medium to low structural importance,
– statistical dependence among deterioration failures has a stronginfluence on the required target reliability index
– the number of elements (representing structural importance) has little influence
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