Acceptance Criteria for Deteriorating Structural Systems

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

Deterioration in Structural/Engineering 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