Performance-based Evaluation of the Seismic Response of Bridges with
Foundations Designed to Uplift
Marios PanagiotouAssistant Professor, University of California, Berkeley
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 Questions3 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 deformationsthat:
• Impair traffic flow
• Necessitate costly and time consuming repairs
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,
Infinitely strong soil
NB6
M
NElastic soil
NB2
Inelastic soil
Nonlinear Behavior Characteristics
Fixed-base or
shallow foundation with extensive soil
inelasticity
Rocking pile-cap or
shallow foundation on elastic soil
Shallow foundation with limited soil
inelasticity
Force, F
Displacement,
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
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 l = 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 u = 0.08 ksi
FSv = A u / N = 5.4
Shallow foundation Rocking Pile-Cap
Modeling of Bridge
OPENSEES 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=5.4Pile cap, B=3D
Ground Motions Considered – Response Spectra , 2% Damping
0.5 1 1.5 2 2.5 30
1
2
3
4
5
Sa
(g)
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)
2 4 6 8 100
100
200
300
400
T (sec)
Sd
(in)
Computed Response of Bridge
f: total drift
f: drift due to pier bending
z
z: soil settlement at foundation edge
Computed Bridge Response Computed Bridge Response -- Total drift, Total drift,
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
Computed Bridge Response Drift due to pier bending f
0 5 10 15 20 25 30 35 400
2
4
6
8
10
Ground Motion Number
Settl
emen
t Z, (
in)
Computed Bridge Response
Ground motion characteristics that may lead to overturn ?
Acc
el.
Pulse A
Vel.
Time
Dis
pl.
Pulse B
Time
Tp
ap
Tp
ap
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.
Time
Dis
pl.
Pulse B
Time
Tp
ap
Tp
ap
Pulse A Pulse B
Time Time
WD = 1350 kips
WF = 300 kips
Minimum ap at different Tp that results in overturn ?
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[dm
>DM
LS]
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 (
milli
on o
f $)
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 COLUMNSMIDDLE COLUMNSBEARINGSSHEAR KEYSEDGE COLUMNS FOUNDATIONSMIDDLE COLUMNS FOUNDATIONS