performance-based earthquake resistant design of concrete ... · research in progress at the rcces...

City University London

Civil Engineering Department

Research Centre for Civil Engineering Structures

Research in progress at the

Research Centre for Civil

Engineering Structures

Performance-based

earthquake resistant design of concrete bridges

Konstantinos I. Gkatzogias (PhD student)

Prof. A. J. Kappos (supervisor)

December, 2014

Research in progress at the RCCES

Overview of PBD/DBD methods for bridges

DDBD procedure by Kowalsky (2002), Dwairi, Kowalsky (2006): Applicable to

multi-degree-of-freedom (MDOF) continuous concrete bridges with flexible or

rigid superstructures (target displacement profile based on modal analysis: EMS)

Similar version of the method included in the Priestley et al. book (2007):

Design in longitudinal direction, approximate method for higher mode effects

focusing on deck forces only)

Adhikari, Petrini, Calvi (2010): Long-span bridges with tall piers (approximate

procedure for higher mode effects on flexural strength of hinges)

Suarez-Kowalsky (2007-11): SSI in drilled shaft bents, skewed configurations of

piers and/or abutments, conditions for applying DDBD using predefined

displacement patterns, target displacements that account for P-Δ

Kappos-Gkatzogias-Gidaris (2012-13): Modal DDBD (proper consideration of

higher mode effects + additional design criteria)

Bardakis, Fardis (2011): ‘Indirect’ displacement-based design of bridges based

on calculating inelastic rotations from elastic analysis

Kappos and co-workers (1997-2010): Deformation-based design (Def-BD)

procedure focusing on buildings


Steps of the deformation-based procedure for bridges

Start

Step 1: Flexural design of dissipating zones based on serviceability criteria

Step2: Serviceability/operationality verifications

Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria

Step 4: Design and detailing for shear

Step 5: Detailing for confinement, anchorages and lap splices

End

Selection of seismic actions for PBD

Set-up of the partial inelastic model (PIM)

Type of analysis Earthquake level

Linear

Nonlinear

Nonlinear

<ν0EQII

EQII

EQIII

EQIV

EQIV

Implicitly consid.

Implicitly consid.



Step 1: Flexural design of plastic hinge zones based on operationality criteria

Establishes basic level of strength for the bridge to remain operational during

and after the selected level of earthquake (Τr=40110yrs-ordinary bridges):

yielding zones (pier ends) in PIM have strength determined from an initial

elastic analysis (dynamic or, if permitted, static); pier stiffness (EIefMy/φy)

estimated from simplified procedures (preferably the Caltrans charts)



Step 1: Flexural design of plastic hinge zones based on operationality criteria

Establishes basic level of strength for the bridge to remain operational during

and after the selected level of earthquake (Τr=40110yrs-ordinary bridges):

yielding zones (pier ends) in PIM have strength determined from an initial

elastic analysis (dynamic or, if permitted, static); pier stiffness (EIefMy/φy)

estimated from simplified procedures (preferably the Caltrans charts)

allowable damage expressed explicitly as rotational ductility factor (μθ)

R/C pier design typically based on fcd, fyd, but damage verification typically

based on inelastic analysis using mean values (fcm, fym); also, overstrength

is present in some zones, due to detailing and practical requirements

elastic analysis run for a fraction (ν00.75) of EQII: pier strength

elastic analysis run for EQII: bearing deformations

the goal is to reach the target μθ in the piers and γv in the el. bearings

during the operationality earthquake (not to be much lower than it!)

Elastic

Inelastic

θy

My

θinel θel

Mel



simple approach, assume :

elastic-perfectly-plastic M – θ

Mtot – θtot & ME – θE have identical slope

(typically applies in bridge piers)

β-values from Bardakis & Fardis (2011)

inelastic pier rotations are estimated from elastic ones

Step 1 contnd

Μy from θy (My ≥ MG)

θy = θinel / μθ,ls

θinel ≈ β θel

Mel, θel (analysis)

,

,

31 1

ls y plpl ls

ls

y y eq

L

h



Start






End




Linear

Nonlinear

Nonlinear

<ν0EQII

EQII

EQIII

EQIV

EQIV

Implicitly consid.

Implicitly consid.



Step 2: Serviceability/operationality verifications

Set-up of the partially inelastic model

PIM for bridges:

piers modelled as yielding elements (strength from Step 1, stiffness: M-φ

analysis, e.g RCCOLA.net (AUTh))

all other parts of the bridge modelled as elastic members (including common

bearings; but LRBs should be modelled inelastically)

Selection of seismic actions

Pairs of records are required for 3D analysis (or triplets, if vertical motion is

influential)

Recommended selection criteria: M, R (from deaggregation of hazard analysis),

PGA (e.g. 0.1g), similarity of spectra, accepted variability of response

Modern tools (like ISSARS, Sextos-Katsanos (2013)) select sets of e.g. 7 records

based on such ‘multi-criteria’, also including the EC8 procedure

Scaling procedures: EC8-Part 1/2 (based on considered earthq. components)



Step 2 contnd

Serviceability/operationality verifications

PIM analysed for set of records (7) scaled to the seismic action associated

with operationality requirement

verifications include specific limits for pier drifts, ductility factors (μθ) and

plastic hinge rotations (θp); ideally μθ,an μθ,ls=f(εc , εs)

recommended values of μθ and/or θp vary significantly, e.g. proposals by

Eastern (DesRoches et al.) and Western (Priestley et al.) US teams

εc, εy are good basis for estimating damage to R/C piers

damage to bearings (γb<0.51.5) should also be checked, might be critical

joint widths should be such as to prevent damage to backwalls



Start






End




Linear

Nonlinear

Nonlinear

<ν0EQII

EQII

EQIII

EQIV

EQIV

Implicitly consid.

Implicitly consid.



Step 3: Verifications for the ‘life safety’ or ‘damage limitation’ limit state

PIM is now analysed for records scaled to the seismic action associated with

damage limitation or life safety requirement (Tr 5003000yrs)

elastomeric bearings γb1.52.0

verifications of pier drifts, ductility factors (μθ) and plastic hinge rotations

(θp) based on allowable εc , εs

verifications that members assumed elastic do not yield (except for

continuity slabs)



Start






End




Linear

Nonlinear

Nonlinear

<ν0EQII

EQII

EQIII

EQIV

EQIV

Implicitly consid.

Implicitly consid.



Step 4: Design for shear

Less ductile failure mode VE should be calculated for higher seismic actions

(Tr 2500yrs) associated with ‘collapse prevention’

to avoid 3rd set of response-history analyses, VE from Step 3 could be

empirically scaled; recommended γv 1.101.20

no need for code-type conservative capacity design, since inelastic analysis

is used!

Step 5: Detailing of critical members

Detailing of R/C piers for: confinement, anchorages, lap splices

the actual μφ values from Step 3 can be used, implicitly associated with

‘collapse prevention’ (e.g. γω 2.00)

bearings should be verified based on stability considerations

'

'cr r

r

G S rN A

tConstantinou et al. (2011)


Def-BD: Implementation & Verification

Description of the studied bridge (T7 Overpass)

3-span structure (27 - 45 - 27m)





Prestressed concrete box girder section (variable geometry)






Deck monolithically connected to the (circular single-column) piers

Unrestrained transverse displacement at the abutments (elastom. bearings)






Deck monolithically connected to the (circular single-column) piers

Unrestrained transverse displacement at the abutments (elastom. bearings)

Different pier heights (longitudinal deck slope of 7%)

Surface foundations



Analysis of the bridge

Software used: Ruaumoko3D


Performance criteria

EQII: Columns: εc≤3.54.0‰ or εs≤15.0‰, elastom. bearings: γb≤1.0

EQIII: Columns: εc≤18.0‰ or εs≤60.0‰, elastom. bearings: γb≤2.0

EQIV: Columns: εc≤εcc,u or εs≤ εs,u, elastom. bearings: toppling

‘Limit-state’ (ls) deformations: Based on allowable strains and section analysis

e.g.

Limited

service

Disruption of

service

Negligible

damage

Minimal

damage

Moderate

damageSevere damage

50 100 200 No repairMinimal

repair

Feasible

repairReplacement

**

* * * * EQI ●

40.9 65.1 87.8 95 EQII ●

10.0 19.0 34.4 475 EQIII ●

2.0 4.0 7.8 2462 EQIV ●

* Implicit definition according to Step 1

** Partial or complete replacement may be required

PE (%) in

50/100/200 yrsTr (yrs)

Earth-

quake

level

Full service

0

1000

2000

3000

4000

5000

6000

7000

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

M (

kN

m)

φ (m-1)

N=10.4 MN

Bilin.

Buckling

Hoop fracture

Bar fracture

Ultimate

M-φ for column section

,

,

31 1

ls y plpl ls

ls

y y eq

L

h



Implementation: Selection of input motions (ISSARS) No. Name Region Date Station Magnitude Distance (km) PGA(g) Hor. Component 1 (HC1) Hor. Component 2 (HC2)

1 Imperial Valley-02 USA 19.05.1940 El Centro Array #9 6.95 12.99 0.258 IMPVALL_I-ELC180 IMPVALL_I-ELC270

3 Imperial Valley-06 USA 15.10.1979 Chihuahua 6.53 18.88 0.270 IMPVALL_H-CHI012 IMPVALL_H-CHI282

5 Imperial Valley-06 USA 15.10.1979 Holtville Post Office 6.53 19.81 0.248 IMPVALL_H-HVP225 IMPVALL_H-HVP315

6 Imperial Valley-06 USA 15.10.1979 SAHOP Casa Flores 6.53 12.43 0.357 IMPVALL_H-SHP000 IMPVALL_H-SHP270

8 Corinth, Greece Greece 24.02.1981 Corinth 6.60 19.92 0.264 CORINTH_COR--L CORINTH_COR--T

10 Northridge-01 USA 17.01.1994 Arleta - Nordhoff Fire St. 6.69 11.10 0.330 NORTHR_ARL090 NORTHR_ARL360

12 Northridge-01 USA 17.01.1994 LA - Hollywood Stor FF 6.69 23.61 0.335 NORTHR_PEL090 NORTHR_PEL360

13 Northridge-01 USA 17.01.1994 LA - N Faring Rd 6.69 16.99 0.246 NORTHR_FAR000 NORTHR_FAR090

16 Kobe, Japan Japan 16.01.1995 Kakogawa 6.90 24.20 0.267 KOBE_KAK000 KOBE_KAK090

Zone Scaling factor (SF) Spectral deviation δ P1 SEE (%) P2 SEE (%)

II 1 3 5 6 12 13 16 1.18 0.1651 13.17 13.51

III 1 5 6 8 10 13 16 1.81 0.1956 12.33 14.74

Suite of records

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

Sa

(g)

T (sec)

IMPVALL_I-ELC270.AT2

IMPVALL_H-CHI282.AT2

IMPVALL_H-HVP315.AT2

IMPVALL_H-SHP270.AT2

NORTHR_PEL360.AT2

NORTHR_FAR090.AT2

KOBE_KAK090.AT2

Average-T Sc.

EC8-2 (T =4.0s) (Unsc.)D

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

Sa

(g)

T (sec)

IMPVALL_I-ELC270.AT2

IMPVALL_H-HVP315.AT2

IMPVALL_H-SHP270.AT2

CORINTH_COR--T.AT2

NORTHR_ARL360.AT2

NORTHR_FAR090.AT2

KOBE_KAK090.AT2

Average-T Sc.

EC8-2 (T =4.0s) (Unsc.)D



Assessment using inelastic response-history analysis (RHA)

Refined ‘limit-states’: Analysis of column sections based on final detailing

Inelastic modelling of all yielding members, using standard point-hinge

approach (with Takeda model)

Verification of design for Ζone ΙΙ & ΙΙΙ

Use of spectrum-compatible synthetic records (ASING code), i.e. a different

set from that used in the Def-BD procedure

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 0.5 1.0 1.5 2.0 2.5

Sa

(g)

T (sec)

SIM1

SIM2

SIM3

SIM4

SIM5

Average

EC8-2 (T =4.0s)D

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0 2.5

Sd

(cm

)

T (sec)

SIM1

SIM2

SIM3

SIM4

SIM5

Average

EC8-2 (T =4.0s)D


Verification


EQII: Excellent agreement of design and assessment (for critical

performance level), despite the different input motions used in each case

EQIII & EQIV: Differences in the area of Abt1 and Pier1 (differences could be

attributed to the fact that the ‘structure-specific’ ground motion selection was

based on linear analysis and was different from assessment set

P-D effects are not critical

(EQIII-A-NL and MDDBD-A(EIass) result in similar displacements and drifts)


0.000.020.040.060.080.100.120.140.160.180.200.220.240.260.280.300.320.340.360.380.40

0 10 20 30 40 50 60 70 80 90 100

Dis

pla

cem

ent

(m)

Position (m)

EQII-D-L

EQII-D-NL

EQII-A-NL

EQIII-D-NL

EQIII-A-NL

EQIV-D-NL

EQIV-A-NL

MDDBD-D

MDDBD-A

0.000.020.040.060.080.100.120.140.160.180.200.220.240.260.280.300.320.340.360.380.40

0 10 20 30 40 50 60 70 80 90 100

Dis

pla

cem

ent

(m)

Position (m)

EQII-D-L

EQII-D-NL

EQII-A-NL

EQIII-D-NL

EQIII-A-NL

EQIV-D-NL

EQIV-A-NL

MDDBD-D

MDDBD-A


EQII

EQII: Controls the design

SA (section analysis): refers to the ‘limit-state’ deformations (design values)

Slight exceedance of P1 ‘limit-state’ deformation

Ζone ΙΙ, D =1.20m → ρl,req,Col1 =ρl,req,Col2 = 10.4‰

Zone III, D =1.20m → ρl,req,Col1 =12.5‰, ρl,req,Col2 = 9.5‰

Design was found to be safe during assessment

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 1 2 3 4 5 6 7 8 9 10

Mo

men

t (k

Nm

)

Chord rotation (103rad)

ΖΙΙ

ΖΙΙI

EQII

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 1 2 3 4 5 6 7 8 9 10

Mo

men

t (k

Nm

)


ΖΙΙI

ΖΙΙ



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25 30 35 40

Mo

men

t (k

Nm

)


ΖΙΙI

ΖΙΙ

EQIII

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25 30 35 40

Mo

men

t (k

Nm

)


ΖΙΙI

ΖΙΙ

EQIII

EQIII: Not critical (although bearing strains were close to the def. limits)

All pier ‘limit-state’ deformations were easily satisfied

Pier deformation demand were close to deformation limits corresponding to

minimum transverse reinf. ratio.



EQIV

EQIV: Implicitly checked (also checked explicitly for verification reasons)

Critical for the transverse reinforcement (based on curvature ductility

demand)

D-SA shown is based on transverse steel ρw,min

Ζone ΙΙ: ρw,req,Col1 =12.4‰, ρw,req,Col2 = 10.6‰

Zone III: ρw,req,Col1 =13.2‰, ρw,req,Col2 = 10.4‰

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25 30 35 40

Mo

men

t (k

Nm

)


D-L

D-NL-SA

D-NL-RHA

A-NL-SA

A-NL-RHA

ΖΙΙI

ΖΙΙ

EQIV

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25 30 35 40

Mo

men

t (k

Nm

)


ΖΙΙI

ΖΙΙ



Conclusions

‘Operationality’ PL: governs the design

‘Damage-limitation’ PL: not critical

‘Collapse-prevention’ PL: critical (with respect to stability) for bearings

deformations

Very good prediction of structural response while resulting in safe design

Applicable to most common concrete bridge configurations without practical

limitations related to the irregularity of the structural system considered

Increased adaptability: Different performance objectives accounting for the

importance of the bridge can be met (inclusion in future codes)

Further research is required with investigate the effectiveness of the

suggested procedure for complex bridge configurations (e.g. curved in plan

bridges) and /or under challenging loading conditions (e.g. asynchronous pier

excitation)


Relevant publications

Kappos AJ, Gidaris IG, Gkatzogias KI (2012) "Problems

associated with direct displacement-based design of concrete

bridges with single-column piers, and some suggested

improvements“, Bulletin of Earthquake Engineering,

10(4):1237-1266

Kappos AJ, Gkatzogias KI, Gidaris IG (2013) "Extension of

direct displacement-based design methodology for bridges to

account for higher mode effects“, Earthquake Engineering and Structural Dynamics, 42(4), 581–602

Kappos AJ (2014) Performance-based seismic design and

assessment of bridges, in Ansal, A. (ed.) Perspectives on European Earthquake Engineering and Seismology (Vol.2),

Springer, (in press)

Gkatzogias KI, Kappos AJ (2015) “Deformation-based seismic

design of concrete bridges” Earthquakes and Structures, (submitted)

performance-based earthquake resistant design of concrete ... · research in progress at the rcces...

Documents