Performance-based Evaluation of the Seismic Response of Bridges with

Foundations Designed to Uplift

Marios Panagiotou Assistant Professor, University of California, Berkeley

Bruce KutterProfessor , University of California, Davis

Acknowledgments

Pacific Earthquake Engineering Research (PEER) Center for funding this work through

the Transportation Research Program

Antonellis GrigoriosGraduate Student Researcher, UC Berkeley

Lu YuanGraduate Student Researcher, UC Berkeley

3 Questions

1. Can foundation rocking be considered as an alternative seismic design method of bridges resulting in reduced: i) post-earthquake damage, ii) required repairs, and iii) loss of function ?

2. What are the ground motion characteristics that can lead to overturn of a pier supported on a rocking foundation?

3. Probabilistic performance-based earthquake evaluation ?

“Fixed” Base Design

flexural plastic hinge

Susceptible to significant post-earthquake damage and permanent lateral deformations that:

• Impair traffic flow

• Necessitate costly and time consuming repairs

Design Using Rocking Shallow FoundationsPier on rocking

shallow foundation“Fixed” base pier

Pier on rocking pile-cap“Fixed” base pier

Design Using Rocking Pile Caps

Design Using Rocking Pile-Caps

Pile-cap with socketsPile-cap simply supported on piles

Mild steel for energy dissipation ?

Rocking Foundations - Nonlinear Behavior

B

Moment, M

Rotation, Θ

Infinitely strong soil

NB 6

M

NElastic soil

NB 2

Θ

Inelastic soil

Nonlinear Behavior Characteristics

Fixed-base orshallow foundation with extensive soil

inelasticity

Rocking pile-cap or shallow foundation

on elastic soil

Shallow foundation with limited soil

inelasticity

Force, F

Displacement, Δ

SDOF Nonlinear Displacement ResponseMean results of 40 near-fault ground motions

0 1 2 30

10

20

30

40R = 2

Sd (i

n)

T (sec)0 1 2 30

10

20

30

40R = 4

T (sec)0 1 2 30

10

20

30

40R = 6

T (sec)

Clough

Flag

NonlinearElastic

0 1 2 30

10

20

30

40R = 2

Sd (i

n)

T (sec)0 1 2 30

10

20

30

40R = 4

T (sec)0 1 2 30

10

20

30

40R = 6

T (sec)

Clough

Flag

NonlinearElastic

Numerical Case Study of a Bridge

An archetype bridge is considered and is designed with:i) fixed base piers ii) with piers supported on rocking foundations

120 ft 150 ft 150 ft 120 ft150 ft

Archetype bridge considered – Tall Overpass

56 ft

Analysis using 40 near-fault ground motions

Computed Response of a Bridge System

120 ft 150 ft 150 ft 120 ft150 ft

Archetype bridge considered – Tall Overpass

56 ft

• 5 Spans • Single column bents• Cast in place box girder

50 ft

6 ft

39 ft

B

D = 6ft• Column axial load ratio N / fc

’Ag = 0.1

• Longitudinal steel ratio ρl = 2%

Designs Using Rocking Foundations

50 ft

6 ft

39 ft

B = 24 ft (4D)

D = 6ft50 ft

6 ft

39 ft

B = 18 ft (3D)

D = 6ft

Soil ultimate stress σu = 0.08 ksi

FSv = Aσu / N = 5.4

Shallow foundation Rocking Pile-Cap

Modeling of BridgeOPENSEES 3-dimensional model

Columns, deck : nonlinear fiber beam element

Abutment , shear keys: nonlinear springs

Soil-foundation : nonlinear Winkler model

Forc

e

Deformation

Bridge Model - Dynamic Characteristics

1st mode, T1 (sec) 2nd mode, T2 (sec)

Fixed - base B = 4D Rocking Pile Cap B=3D

1.10.8

1.91.8

2.11.9

Monotonic Behavior – Individual Pier

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5000

10000

15000

20000

Drift Ratio, / H, (%)

Mom

ent,

(kip

s-ft)

Fixed baseB=5D, FSv=8.4

B=4D, FSv=5.4

Pile cap, B=3D

Ground Motions Considered – Response Spectra , 2% Damping

2 4 6 8 100

1

2

3

4

5

Sa

(g)

0.5 1 1.5 2 2.5 30

1

2

3

4

5

Sa

(g)

2 4 6 8 100

100

200

300

400

T (sec)

Sd

(in)

0.5 1 1.5 2 2.5 30

25

50

75

T (sec)

Sd

(in)

2 4 6 8 100

1

2

3

4

5

Sa

(g)

0.5 1 1.5 2 2.5 30

1

2

3

4

5

Sa

(g)

2 4 6 8 100

100

200

300

400

T (sec)

Sd

(in)

0.5 1 1.5 2 2.5 30

25

50

75

T (sec)

Sd

(in)

Computed Response of BridgeΔ

ΔfΔ: total drift

Δf: drift due to pier bending

z

z: soil settlement at foundation edge

Computed Bridge Response - Total drift, Δ

0 5 10 15 20 25 30 35 400

5

10

15

Drif

t Rat

io

/ H

, (%

)

Ground Motion Number0 5 10 15 20 25 30 35 40

0

5

10

15

Drif

t Rat

io

/ H

, (%

)

Ground Motion Number0 5 10 15 20 25 30 35 40

0

5

10

15

Drif

t Rat

io

/ H

, (%

)

Ground Motion Number

0 5 10 15 20 25 30 35 400

2

4

6

8

Ground Motion Number

Flex

ural

Drif

t Rat

io,

f / H

, (%

)

0 5 10 15 20 25 30 35 400

2

4

6

8

Ground Motion Number

Flex

ural

Drif

t Rat

io,

f / H

, (%

)

0 5 10 15 20 25 30 35 400

2

4

6

8

Ground Motion Number

Flex

ural

Drif

t Rat

io,

f / H

, (%

)

Computed Bridge Response Drift due to pier bending Δf

0 5 10 15 20 25 30 35 400

2

4

6

8

10

Ground Motion Number

Set

tlem

ent Z

, (in

)

Computed Bridge Response

Ground motion characteristics that may lead to overturn ?

Acc

el.

Pulse A

Vel.

Time

Displ

.

Pulse B

Time

Pulse C

Time

Tp

ap

Tp

ap

Acc

eler

atio

nVe

loci

tyD

ispl

acem

ent

Pulse A Pulse B

Time Time

Ground motions with strong pulses (especially low frequency) that result in significant nonlinear displacement demand

Rocking response of rigid block on rigid base to pulse-type excitation

Zhang and Makris (2001)

Near Fault Ground Motions and their representation using Trigonometric Pulses

0 5 10-1

-0.5

0

0.5

1G

roun

d ac

cele

ratio

n,

a g ( g

) Northridge 1994, Rinaldi (FN)

0 10 20 30-1

-0.5

0

0.5

1 Landers 1999, Lucerne Valley (FN)

0 5 10-80

-40

0

40

80

time (sec)

Gro

und

velo

city

v g (

in /

s )

0 10 20 30-80

-40

0

40

80

time ( sec )

Tp = 0.8 sec

ap = 0.7 g

Tp = 5.0 sec

ap = 0.13 g

Conditions that may lead to overturn

50 ft

6 ft

39 ft

B = 18 ft

D = 6ft

Acc

el.

Pulse A

Vel.

TimeDispl

.

Pulse B

Time

Pulse C

Time

Tp

ap

Tp

ap

Acc

eler

atio

nVe

loci

tyD

ispl

acem

ent

Pulse A Pulse B

Time Time

WD = 1350 kips

WF = 300 kips

Minimum ap at different Tp that results in overturn ?

Conditions that may lead to overturn

0 2 4 6 80

2

4

6

8

10

12

14

a p (g)

Tp (sec)

Pulse APulse B

Conditions that may lead to overturn

0 2 4 6 80

0.25

0.5

0.75

1

a p (g)

Tp (sec)

Pulse APulse B

Probabilistic Performance Based Earthquake Evaluation (PBEE)

The PEER methodology and the framework of Mackie et al. (2008) was used for the PBEE comparison of the fixed base and the rocking designs.

• Ground Motion Intensity Measures [Sa ( T1 )]• Engineering Demand Parameters (e.g. Pier Drift )• Damage in Bridge Components• Repair Cost of Bridge System

PBEE Evaluation – Damage Models (Mackie et al. 2008)

0 5 10 150

0.2

0.4

0.6

0.8

1

Drift Ratio (%)

P[d

m>D

M L

S]

Column

CrackingSpallingBar BucklingFailure

0 4 8 120

0.2

0.4

0.6

0.8

1

Long. Displacement (in.)

Abutment

Onset of DamageJoint Seal AssemblyBackWallApproach Slab

0 4 8 12 160

0.2

0.4

0.6

0.8

1

Displacement (in.)

Bearing

YieldFailure

0 120 240 3600

0.2

0.4

0.6

0.8

1

Shear force (kips)

P[d

m>D

M L

S]

Shear Key

Elastic LimitConcrete Spalling Failure

PBEE Evaluation Foundation Damage Model

0 1 2 30

0.2

0.4

0.6

0.8

1

Normalized Edge Settlement z / zyield

P [

dm >

DM

LS

]

Column Foundation

ElasticFirst YieldLimited YieldingExtensive Yielding

PBEE – Median Total Repair Cost

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1.0

Sa ( T = 1 sec ), (g)

Tota

l Rep

air C

ost (

mill

ion

of $

)

Fixed Base

B=4D, Fsv=5.4

Pile Cap, B=3D

Fixed Base Bridge

PBEE – Disaggregation of Cost

0 0.5 1 1.5 20

0.1

0.2

0.3

Sa (T=1sec), (g)

Rep

air C

ost (

mill

ion

of $

)

EDGE COLUMNSMIDDLE COLUMNSBEARINGSSHEAR KEYS

Bridge with Shallow Foundations B=4D

PBEE – Disaggregation of Cost

0 0.5 1 1.5 20

0.1

0.2

0.3

Sa(T=1sec), (g)

Rep

air C

ost (

mill

ion

of $

)

Disaggregation of Cost - B=4D, Fsv=5.4

EDGE COLUMNS

MIDDLE COLUMNSBEARINGS

SHEAR KEYSEDGE COLUMNS FOUNDATIONS

MIDDLE COLUMNS FOUNDATIONS

END

0 20 40-0.04

-0.02

0

0.02

0.04 Northridge, Rinaldi - FN

Bas

e ro

tatio

n ( r

adia

ns )

time ( sec )0 50 100-0.04

-0.02

0

0.02

0.04 Landers, Lucerne Valley - FN

time ( sec )

Response of Individual Pier on Rocking Pile Cap

0 5 10 15 20 25 30-1.6

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

time ( sec )

base

rota

tion

( rad

ians

)

LCN1.3xLCN

Response of Individual Pier on Rocking Pile Cap