Performance-based Evaluation of the
Seismic Response of Bridges with
Foundations Designed to Uplift
Marios Panagiotou
Assistant Professor, University of California, Berkeley
Bruce Kutter
Professor , University of California, Davis
Acknowledgments
Pacific Earthquake Engineering Research
(PEER) Center for funding this work through
the Transportation Research Program
Antonellis Grigorios
Graduate Student Researcher, UC Berkeley
Lu Yuan
Graduate 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
Susceptible to significant postearthquake damage and
permanent lateral deformations
that:
• Impair traffic flow
flexural plastic
hinge
• Necessitate costly and time
consuming repairs
Design Using Rocking Shallow Foundations
“Fixed” base pier
Pier on rocking
shallow foundation
Design Using Rocking Pile Caps
“Fixed” base pier
Pier on rocking pile-cap
Design Using Rocking Pile-Caps
Pile-cap simply
supported on piles
Pile-cap with sockets
Mild steel for energy
dissipation ?
Rocking Foundations - Nonlinear Behavior
Moment, M
Elastic soil
N
Infinitely strong soil
NB
2
M
Θ
B
Inelastic soil
NB
6
Rotation, Θ
Nonlinear Behavior Characteristics
Force, F
Displacement, Δ
Fixed-base or
shallow foundation
with extensive soil
inelasticity
Shallow foundation
with limited soil
inelasticity
Rocking pile-cap
or
shallow foundation
on elastic soil
Mean results of 40 near-fault ground motions
R=2
R=4
R=6
40
40
40
30
30
30
20
20
20
10
R=2
10
40
0
0 30 1
2
T (sec)
Sd (in)
d
SDOF Nonlinear Displacement Response
10
40
0
0 30
3
20
1
2
T (sec)
3
0
0
Nonlinear
Elastic
R=6
40
1
2
T (sec)
3
Clough
Flag
20
10
1
2
T (sec)
Flag
0
030
3
20
10
0
0
R=4
Clough
Nonlinear
Elastic
10
1
2
T (sec)
3
0
0
1
2
T (sec)
3
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
Analysis using 40 near-fault ground motions
Archetype bridge considered – Tall Overpass
56 ft
120 ft
150 ft
150 ft
150 ft
120 ft
Computed Response of a Bridge System
Archetype bridge considered – Tall Overpass
56 ft
150 ft
120 ft
150 ft
•
•
•
39 ft
6 ft
D = 6ft
50 ft
B
150 ft
120 ft
5 Spans
Single column bents
Cast in place box girder
•
Column axial load ratio N / fc’Ag = 0.1
•
Longitudinal steel ratio ρl = 2%
Designs Using Rocking Foundations
Shallow foundation
Rocking Pile-Cap
39 ft
39 ft
6 ft
6 ft
50 ft
50 ft
D = 6ft
D = 6ft
B = 24 ft (4D)
Soil ultimate stress σu = 0.08 ksi
FSv = Aσu / N = 5.4
B = 18 ft (3D)
Modeling of Bridge
OPENSEES 3-dimensional model
Abutment , shear keys:
nonlinear springs
Columns, deck :
nonlinear fiber beam element
Force
Soil-foundation :
nonlinear Winkler model
Deformation
Bridge Model - Dynamic Characteristics
Fixed - base
1st mode, T1 (sec)
2nd mode, T2 (sec)
1.1
0.8
B = 4D
2.1
1.9
Rocking Pile Cap B=3D
1.9
1.8
Monotonic Behavior – Individual Pier
20000
Moment, (kips-ft)
15000
10000
Fixed base
B=5D, FSv=8.4
5000
B=4D, FSv=5.4
Pile cap, B=3D
0
0
0.5
1
1.5
2
2.5
3
Drift Ratio,  / H, (%)
3.5
4
4.5
5
4
4
3
2
2
1
0.5
1
1.5
2
2.5
0
3
75
2
4
6
8
10
2
4
6
8
10
400
300
50
Sd (in)
Sd (in)
3
25
Sd (in)
0
Sa (g)
5
1
10
10
5
Sa (g)
Sa (g)
Ground Motions Considered – Response
Spectra , 2% Damping
200
100
0
0.5
1
1.5
T (sec)
2
2.5
3
0
T (sec)
Computed Response of Bridge
Δ
Δ: total drift
Δf
Δf: drift due to
pier bending
z: soil settlement
at foundation edge
z
Computed Bridge Response - Total drift, Δ
Drift Ratio  / H, (%)
15
10
5
0
0
5
10
15
20
25
30
Ground Motion Number
35
40
f
Flexural Drift Ratio,  / H, (%)
f
Flexural Drift Ratio,  / H, (%)
Computed Bridge Response
Drift due to pier bending Δf
8
6
4
2
0
0
5
10
15
20
25
Ground Motion Number
Ground Motion Number
30
35
40
Computed Bridge Response
Settlement Z, (in)
10
8
6
4
2
0
0
5
10
15
20
25
30
Ground Motion Number
35
40
Ground motion characteristics that may lead
to overturn ?
Ground motions with strong pulses (especially low frequency) that result
in significant nonlinear displacement demand
Accel.
Pulse
PulseAA
Pulse
PulseBB
ap
ap
Tp
Time
Time
Time
Time
Rocking response of rigid block on
rigid base to pulse-type excitation
Zhang and Makris (2001)
Displ.
Vel.
Tp
Near Fault Ground Motions and their representation
using Trigonometric Pulses
Ground acceleration,
ag ( g )
Northridge 1994, Rinaldi (FN)
1
Landers 1999, Lucerne Valley (FN)
1
Tp = 0.8 sec
0.5
0.5
0
0
-0.5
-0.5
Ground velocity
vg ( in / s )
-1
0
ap = 0.7 g
5
10
-1
0
80
80
40
40
0
0
-40
-40
-80
0
5
time (sec)
10
-80
0
Tp = 5.0 sec
ap = 0.13 g
10
20
30
10
20
time ( sec )
30
Conditions that may lead to overturn
39 ft
6 ft
WD = 1350 kips
50 ft
Accel.
Pulse
PulseAA
B = 18 ft
ap
Tp
Tp
Time
Time
Time
Time
Displ.
WF = 300 kips
ap
Vel.
D = 6ft
Pulse
PulseBB
Minimum ap at different Tp that results in overturn ?
Conditions that may lead to overturn
14
12
Pulse A
Pulse B
8
p
a (g)
10
6
4
2
0
0
2
4
Tp (sec)
6
8
Conditions that may lead to overturn
1
Pulse A
Pulse B
ap (g)
0.75
0.5
0.25
0
0
2
4
Tp (sec)
6
8
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)
P[dm>DM LS]
Column
Abutment
1
1
0.8
0.8
0.6
0.6
0.4
0
0
0.4
Cracking
Spalling
Bar Buckling
Failure
0.2
5
10
Onset of Damage
Joint Seal Assembly
BackWall
Approach Slab
0.2
15
0
0
4
P[dm>DM LS]
Shear Key
Bearing
1
1
0.8
0.8
0.6
0.6
Elastic Limit
Concrete Spalling
Failure
0.2
0
0
120
240
Shear force (kips)
12
Long. Displacement (in.)
Drift Ratio (%)
0.4
8
360
0.4
Yield
Failure
0.2
0
0
4
8
12
Displacement (in.)
16
PBEE Evaluation
Foundation Damage Model
Column Foundation
1
P [ dm > DM LS]
0.8
0.6
Elastic
First Yield
Limited Yielding
Extensive Yielding
0.4
0.2
0
0
1
2
Normalized Edge Settlement z / z
3
yield
PBEE – Median Total Repair Cost
Total Repair Cost ( million of $)
1.0
Fixed Base
0.8
B=4D, Fsv=5.4
Pile Cap, B=3D
0.6
0.4
0.2
0
0
0.5
1
Sa ( T = 1 sec ), (g)
1.5
2
PBEE – Disaggregation of Cost
Fixed Base Bridge
Repair Cost (million of $)
0.3
EDGE COLUMNS
MIDDLE COLUMNS
BEARINGS
SHEAR KEYS
0.2
0.1
0
0
0.5
1
Sa (T=1sec), (g)
1.5
2
PBEE – Disaggregation of Cost
Bridge with Shallow Foundations B=4D
Disaggregation
of Cost - B=4D, Fsv=5.4
EDGE COLUMNS
0.3
MIDDLE COLUMNS
BEARINGS
Repair Cost (million of $)
SHEAR KEYS
EDGE COLUMNS FOUNDATIONS
MIDDLE COLUMNS FOUNDATIONS
0.2
0.1
0
0
0.5
1
Sa(T=1sec), (g)
1.5
2
END
Response of Individual Pier on Rocking Pile Cap
Base rotation ( radians )
Northridge, Rinaldi - FN
Landers, Lucerne Valley - FN
0.04
0.04
0.02
0.02
0
0
-0.02
-0.02
-0.04
0
20
time ( sec )
40
-0.04
0
50
time ( sec )
100
Response of Individual Pier on Rocking Pile Cap
1.6
LCN
1.3xLCN
base rotation ( radians )
1.2
0.8
0.4
0
-0.4
-0.8
-1.2
-1.6
0
5
10
15
time ( sec )
20
25
30