VALIDATION OF SEISMIC
SOIL-FOUNDATION-STRUCTURE INTERACTION ANALYSIS OF
MELOLAND ROAD OVERCROSSING
A Project
Presented to the faculty of the Department of Civil Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Civil Engineering
by
Thomas Albert Mar
SPRING
2013
© 2013
Thomas Albert Mar
ALL RIGHTS RESERVED
ii
VALIDATION OF SEISMIC
SOIL-FOUNDATION-STRUCTURE INTERACTION ANALYSIS OF
MELOLAND ROAD OVERCROSSING
A Project
by
Thomas Albert Mar
Approved by:
__________________________________, Committee Chair
Dr. Benjamin Fell
____________________________
Date
iii
Student: Thomas Albert Mar
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the project.
__________________________, Graduate Coordinator
Dr. Matthew Salveson
Department of Civil Engineering
iv
___________________
Date
Abstract
of
VALIDATION OF SEISMIC
SOIL-FOUNDATION-STRUCTURE INTERACTION ANALYSIS OF
MELOLAND ROAD OVERCROSSING
by
Thomas Albert Mar
The purpose of this project is to investigate the validity of seismic soil-foundationstructure interaction analysis of a typical California highway bridge structure subjected to
near-fault ground motions.
A three-dimensional nonlinear finite element model of Meloland Road
Overcrossing was developed. The model included a combination of elements including
shell elements for the bridge deck. The column and piles were modeled using frame
elements. Abutment-backfill and ground soil were simulated using nonlinear springs.
The complete bridge system was subjected to three-component recorded free-field
earthquake motions. The resulting dynamic response of the bridge model was found to
be in close agreement with motions recorded at various locations on the bridge. This
validates the practical application and methodology of this project and may be used for
evaluating the seismic response of other typical bridges.
__________________________________, Committee Chair
Dr. Benjamin Fell
____________________________
Date
v
ACKNOWLEDGEMENTS
I would like to express my upmost gratitude to Dr. Anoosh Shamsabadi for the
many hours he spent sharing his expertise and advising me on this project. I also feel
very grateful toward my committee members: Professor Benjamin Fell and Professor
Matthew Salveson, whose instruction and insight has prepared me for a future in
engineering. And last but not least, I would like to thank my friends and family for their
love and encouragement that has gotten me to where I am today.
vi
TABLE OF CONTENTS
Page
Acknowledgements .................................................................................................................. vi
List of Tables ........................................................................................................................ viii
List of Figures .......................................................................................................................... ix
Section
1. INTRODUCTION .............................................................................................................. 1
2. BRIDGE DESCRIPTION ................................................................................................... 2
3. SEISMIC INSTRUMENTATION AND INPUT GROUND MOTIONS .......................... 6
4. IDEALIZED SOIL PROFILES AND PROPERTIES ........................................................ 9
5. GLOBAL BRIDGE MODELING .................................................................................... 11
5.1. Soil-Abutment-Structure Interaction ....................................................................... 14
5.2. Soil-Foundation-Structure Interaction..................................................................... 17
5.2.1. Lateral Soil Resistance.................................................................................... 18
5.2.2. Axial Soil Resistance ...................................................................................... 21
5.2.3. Pile Tip Resistance.......................................................................................... 23
6. DYNAMIC ANALYSIS RESULTS ................................................................................ 25
4. CONCLUSION AND OUTLOOK ................................................................................... 31
Appendix................................................................................................................................. 32
References ................................................................................................................................ 39
vii
LIST OF TABLES
Tables
Page
1.
Input motion characteristics .................................... .………………………………. 6
2.
Idealized soil properties.............................................. ……………………………. 10
3.
Element material properties ...............………….…………………………………. 12
4.
MRO probabilistic seismic hazard deaggregation . ………….…………………. 33
5.
Spectral accelerations for T=0.26 sec and scale factors ………….……………. 35
viii
LIST OF FIGURES
Figures
Page
1.
Meloland Road Overcrossing panorama ............... .………………………………. 2
2.
Elevation and plan view of MRO................................ ……………………………. 3
3.
MRO bent cross section .......................………….…………………………………. 4
4.
Bent pile foundation layout .............................................. …………………………. 5
5.
North and south abutment layout .................................... …………………………. 5
6.
Locations of 29 strong motion accelerometers on MRO . ………………………. 7
7.
Input motion in longitudinal, transverse, and vertical directions ..... …………… 8
8.
Idealized soil profile for bent piles ................................. …………………………. 9
9.
Idealized soil profile for abutment piles ....................... …………………………. 10
10.
Representation of the soil-foundation-structure interaction system . …………. 11
11.
Midas Civil bridge model............................................... …………………………. 12
12.
MRO column cross section and moment-curvature ... …………………………. 13
13.
Soil-abutment force-displacement curve.................................... …………………15
14.
Distributed springs to model soil-abutment interaction .. ……………………….16
15.
Nonlinear springs represent interaction between soil and piles
(Shamsabadi et al. 2010) .............................................................. …………………17
16.
P-y curves generated by LPile ....................................... …………………………. 18
17.
Lateral force-displacement curves at depths x = 0’, 4.7’, 9.4’, 14.1’, 18.8’,
23.5’ ......................................................................................................... …… 20
ix
18.
Lateral force-displacement curves at depths x = 28.2’, 32.9’, 37.6’, 42.3’,
47’ ........................................................................................................ ……… 20
19.
Vertical force-settlement curves at depths x = 0’, 4.7’, 9.4’, 14.1’, 18.8’,
23.5’ .................................................................................................... ………. 22
20.
Vertical force-settlement curves at depths x = 28.2’, 32.9’, 37.6’, 42.3’,
47’ .................................................................................................... ………… 22
21.
Tip force-settlement curve ............................................. …………………………. 24
22.
Mode shape 1, T = 0.264 sec ......................................... …………………………. 25
23.
Mode shape 2, T = 0.259 sec ......................................... …………………………. 25
24.
Mode shape 3, T = 0.195 sec ......................................... …………………………. 26
25.
Mode shape 4, T = 0.156 sec ......................................... …………………………. 26
26.
Mode shape 5, T = 0.111 sec ......................................... …………………………. 27
27.
Mode shape 6, T = 0.103 sec ......................................... …………………………. 27
28.
Channel 13 displacement response ............................... …………………………. 28
29.
Channel 19 displacement response ............................... …………………………. 28
30.
Channel 27 displacement response ............................... …………………………. 29
31.
Channel 1 displacement response ................................. …………………………. 29
32.
Channel 2 displacement response ................................. …………………………. 30
33.
Channel 17 displacement response ............................... …………………………. 30
34.
MRO design Sa versus T ................................................ …………………………. 32
35.
1979 Imperial Valley at MRO Sa versus T.................. …………………………. 33
x
36.
1979 Imperial Valley earthquake motions in longitudinal, transverse,
and vertical directions ..................................................... …………………………. 34
37.
DBE displacement response at abutment channels..... …………………………. 35
38.
MCE displacement response at abutment channels .... …………………………. 36
39.
Hysteretic behavior of abutment soil spring ................ …………………………. 36
40.
Abutment relative displacement during MCE ............. …………………………. 37
41.
Column relative displacement response during MCE …………………………. 38
xi
1
1. Introduction
Modern earthquake records with near-source characteristics, such as those of the
1994 Northridge, California, the 1995 Kobe, Japan, and the 1999 Chi-Chi, Taiwan
earthquakes, have increased the importance of nonlinear seismic analyses employing soilfoundation-structure-interaction (SFSI) on bridge structures. It has been well recognized
from these records that SFSI plays a significant role in the global response of highway
bridges during strong seismic excitation.
This project will investigate the accuracy of a three-dimensional, nonlinear timehistory analysis employing SFSI on a typical California highway bridge structure. The
analysis will use a direct approach in which nonlinear soil foundation properties are
explicitly included in a global finite element model to account for both the geotechnical
and structural responses during a seismic event. Many bridges are supported on deep pile
foundations that penetrate multiple soil layers with varying stiffness and strength
properties. During a strong earthquake, ground motion is expected to produce excitation
along the entire pile length. The effects of depth-varying foundation properties will be
rigorously addressed by including each individual pile (with distributed soil springs along
their lengths) in the global bridge model. Recorded earthquake motions will be applied
to the model and the resulting displacement response will be compared to real earthquake
recordings from the structure to validate this analytical method.
2
2. Bridge Description
Meloland Road Overcrossing (MRO) was chosen for this investigation due to its
relatively simple design and heavy seismic instrumentation. MRO was constructed in
1971 in Imperial County, California. It is located over Interstate 8 approximately 0.31 mi
from the Imperial Valley fault rupture. The structure is a two-span prestressed reinforced
concrete box-girder bridge supported on single column bent and integral abutments, as
shown in Figure 1.
Figure 1: Meloland Road Overcrossing panorama
The As Built bridge plans indicate the bridge deck to be 208 ft long and 34 ft
wide with each span measuring 104 ft, as shown in Figure 2. The depth of the deck is 5.5
ft. The height of the 5 ft diameter column is approximately 21 ft and is supported on 25
timber piles with a square concrete cap, as shown in Figure 3 and Figure 4. The
3
monolithic abutment backwalls have a height of the approximately 13 ft. Each abutment
is supported on a single row of 7 timber piles, as shown in Figure 5.
Figure 2: Elevation and plan view of MRO
4
Figure 3: MRO bent cross section
5
Figure 4: Bent pile foundation layout
Figure 5: North and south abutment layout
6
3. Seismic Instrumentation and Input Ground Motions
MRO is seismically instrumented with 29 strong-motion accelerometers.
Recorded time-histories from these instruments are available for several earthquakes,
including the 7.2 magnitude 2010 Baja California earthquake. An additional 3
accelerometers are located at a free-field site 30 ft from the bridge column. The location
of the instruments that measure free-field motions (Channels 14, 15 and 24) and structure
accelerations (all other channels) are shown in Figure 6.
Displacements time histories developed from the recorded free-field accelerations
from the 2010 Baja California earthquake were used as the input motions for this project.
Each record lasts approximately 88 seconds. The strongest component of the ground
motion is in the longitudinal (N-S) direction. The acceleration time histories are shown
in Figure 7. Peak ground accelerations, velocities, and displacements of the three input
motions are summarized in Table 1.
Table 1: Input motion characteristics
Peak Acceleration Peak Velocity Peak Displacement
(g)
(in/sec)
(in)
Longitudinal (N-S)
0.21
7.15
5.22
Transverse (E-W)
0.16
6.72
4.14
Vertical
0.12
2.53
1.39
Bridge Direction
25
Figure 6: Locations of 29 strong motion accelerometers on MRO
26
N
23
32
8
29
4
9
20
22
14
24
(b) Plan View
15
21
30
1
2
(a) Eleva on View
7
13
30
17
26.5
6
104
5
16
18
104
31 28
27
19
3
12
11
10
7
18
34
Acceleration (g)
8
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
(a) Longitudinal (Channel 15)
0
10
0.2
30
40
50
Time (sec)
60
70
80
90
60
70
80
90
60
70
80
90
(b) Transverse (Channel 24)
0.15
Acceleration (g)
20
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
0
10
20
Acceleration (g)
0.15
30
40
50
Time (sec)
(c) Vertical (Channel 14)
0.1
0.05
0
-0.05
-0.1
-0.15
0
10
20
30
40
50
Time (sec)
Figure 7: Input motion in longitudinal, transverse, and vertical directions
9
4. Idealized Soil Profiles and Properties
A Log of Test Boring sheet provided with the As Built bridge plans shows the
type and strength description of each layer of soil. Idealized soil profiles were developed
for this investigation to simplify calculations. The idealized soil profile at the bent is
shown in Figure 8.
Figure 8: Idealized soil profile for bent piles
The piles penetrate a combination of sandy and clay soil layers. The water table
is located roughly 9 ft below the ground surface. The soil parameters relevant to this
project, including effective unit weight, friction angle, and cohesion, are summarized in
Table 2.
10
Table 2: Idealized soil properties
Soil Properties
γ' (pcf)
ϕ (deg)
c (psf)
1
Sand
120
32
-2
Sand
57.6
32
-3
Clay
55.6
-1500
4
Sand
57.6
32
-5
Clay
55.6
-1500
Notes: γ' = Effective Unit Weight, ϕ = Friction Angle, c = Cohesion
Layer
Soil Type
The pile foundations of the abutments penetrate to approximately the same depth
as those of the bent. Therefore, the soil at the abutments features a very similar profile as
shown in Figure 9.
Figure 9: Idealized soil profile for abutment piles
11
5. Global Bridge Modeling
The approach for modeling MRO was to split the complete SFSI system into two
groups connected by a foundation interface. The first group included the superstructure
and column. The second group included the pile foundations and surrounding soil. The
abutment backwalls and pile cap acted as an interface for the two groups. Figure 10
represents how the complete SFSI system was modeled.
Structure
Interface
Soil Springs
Founda on & Soil
Figure 10: Representation of the soil-foundation-structure interaction system
In this direct approach for modeling, all structural components, foundation components
and soil support springs are explicitly included in the bridge model.
Midas Civil was used to build the finite element model of MRO. Figure 11 shows
12
the complete global model with pile foundations. The bridge deck, abutment backwalls,
and pile cap were modeled using shell elements with applicable structural properties.
Frame elements were used for the column and piles. In addition, the column elements
were modified for cracked sectional properties. The typical material properties used for
this project are listed in Table 3.
Figure 11: Midas Civil bridge model
The cracked moment of inertia for the column was determined from momentcurvature analysis. This analysis was performed using the software’s section designer.
By indicating the column’s material properties, geometry, and loading, the idealized
moment-curvature was calculated as shown in Figure 12.
Table 3: Element material properties
Material
Concrete
Timber
Bridge Components
Deck, Backwalls,
Column, Pile Cap
Piles
Unit Weight
(pcf)
Material Properties
Modulus of Elasticty Yeild Strength
(ksi)
(ksi)
150
3645
5
50
1500
1.25
13
MRO Column Moment-Curvature
140000
(Φy, Mp)
120000
Moment (kip-in)
100000
80000
Actual
60000
Idealized
40000
20000
0
0
0.0001
0.0002
0.0003
0.0004
Curvature (rad/in)
0.0005
0.0006
Figure 12: MRO column cross section and moment-curvature
Plastic Moment, Mp, was calculated to be 114311 kip-in. The idealized yield
curvature, Φy, was calculated to be 0.00009 rad/in. The cracked moment of inertia, Icr,
was then solved for using the following relationship:
Icr =
=
Mp
Eϕy
(1)
114311
3645(0.00009)
= 348456 in4 ≈ 0.5Ig
The cracked moment of inertia was roughly half of the gross moment of inertia.
Therefore, a section modifier of 0.5 was used for the moment of inertia in each direction
of the column.
14
5.1. Soil-Abutment-Structure Interaction
The interaction between the bridge deck, abutment wall and embankment soil has
a hyperbolic relationship that has been experimentally observed and verified with finite
element analysis. However, including abutment backfills in a global bridge model would
be laborious and computationally expensive. As such, Shamsabadi, Khalili-Tehrani,
Stewart, and Taciroglu (2010) proposed the use of a simplified relationship between the
lateral load per unit with of abutment backwall, F, and the lateral displacement, y. The
proposed Hyperbolic Force Displacement (HFD) relationship is given by:
F(y) =
Cy
1 + Dy
C = 2K 50 −
D = 2(
(2)
Fult
ymax
K 50
1
−
)
Fult ymax
where Fult is the maximum abutment force per unit width of backwall developed at
displacement ymax. K50 is the average abutment stiffness at half the maximum abutment
force.
The dynamic soil-abutment-structure interaction in the direction perpendicular to
the abutment wall was modeled using a nonlinear, inelastic spring. The spring represents
the near-field load-deformation behavior at the longitudinal abutment-embankment soil
interface. To develop the backbone curve of the spring, the following simplified HFD
relationship proposed by Shamsabadi et al. (2010) was used:
15
F(y) =
8y
H1.5
1 + 3y
(3)
H is the height of the backwall in feet and y is the lateral displacement in inches.
Given an abutment height of 13 ft and width of 34 ft, the backbone curve for the
nonlinear spring is shown in Figure 13.
Soil-Abutment Interaction
4500
4000
Lateral Force (kip)
3500
3000
2500
2000
1500
1000
500
0
0
1
2
3
Displacement (in)
4
5
Figure 13: Soil-abutment force-displacement curve
For modeling purposes, the nonlinear spring representing the abutment-soil
interaction was divided into 16 smaller springs in parallel and uniformly applied across
the abutment face as shown in Figure 14. Each spring was also connected to a
completely fixed ground node. It should be noted that these springs only work in
compression and do not provide support in tension.
16
Figure 14: Distributed springs to model soil-abutment interaction
For skewed bridges a uniformly distributed pattern of springs may not accurately
represent the soil-abutment interaction. However, because MRO is straight, the
abutments are expected to “purely push” into the embankment soil during an earthquake,
therefore making the model sufficient.
17
5.2. Soil-Foundation-Structure Interaction
The interaction between pile foundations and their surrounding soil has threedimensional complexity. Nonlinear, inelastic springs along the length of the piles were
used to represent this interaction. Figure 15 shows how support springs are used for
corresponding pile reactions. Three soil reactions were approximated for this project
with the use of support springs: lateral, axial and tip resistance. Due to the geometry of
the bridge structure, significant twisting of the column and foundations was not expected.
Thus, torsional resistance springs were neglected for brevity.
Figure 15: Nonlinear springs represent interaction between soil and piles (Shamsabadi et al. 2010)
The following three sections discuss the development of the nonlinear springs that model
the soil-foundation-structure interaction of MRO.
18
5.2.1. Lateral Soil Resistance
Using the computer program Ensoft LPile, lateral pile-soil support curves (called
p-y curves) were generated using the parameters given in Table 2 and depths shown in
Figure 8. LPile utilizes the following equation to develop a backbone curve that
represents the relationship between lateral soil resistance and lateral deflection:
kxy
P = APu′ tanh ( ′ )
APu
(4)
0.9
For Cyclic Loading
A = {(3.0 − 0.8 x ) ≥ 0.9
For Static Loading
b
Pu′ = Ultimate Soil Resistance
k = Coefficient of variation of subgrade modulus
x = Depth below ground level
y = Lateral deflection
b = Pile diameter
For the bent piles, p-y curves were calculated at 11 depths at equal increments of
4.7 ft from pile top to the pile tip at 47 ft, shown in Figure 16.
P-y Curves
Soil Resistance, p (lbs/in)
14000
12000
10000
8000
6000
4000
2000
0
0
0 ft
0.5
4.7 ft
1
1.5
Lateral Deformation, y (in)
28.2 ft
32.9 ft
37.6 ft
2
2.5
9.4 ft, 14.1 ft, 18.8 ft, 23.5 ft, 42.3 ft, 47 ft
Figure 16: P-y curves generated by LPile
19
Soil resistance of sand is dependent on the overburden pressure due to the weight
of overlying material. Hence, the p-y curves corresponding to nodal depths in sand layers
increase with depth. Soil resistance of clay, on the other hand, is more heavily
dependent on its cohesions. The p-y curves corresponding to nodes in clay layers are
therefore the same because they are calculated using the same cohesion factor for this
project. This trend will be visible in the subsequent figures.
In order to implement the p-y curves as soil springs for the finite element model,
the data must be converted from resistance-displacement to force-displacement. This is
done by simply multiplying the resistance values by the tributary pile length of each
node. The resulting curve is then mirrored about its axes so that the spring will behave
the same in tension and compression. The resulting force-displacement curves are shown
in Figure 17 and Figure 18.
20
Lateral Soil-Pile Interaction
200
Lateral Force, F (kip)
150
100
50
0
-2
-1.5
-1
-0.5
-50
0
0.5
1
1.5
2
-100
-150
-200
Lateral Deflection, Y (in)
0 ft
4.7 ft
9.4 ft, 14.1 ft, 18.8 ft, 23.5 ft
Figure 17: Lateral force-displacement curves at depths x = 0’, 4.7’, 9.4’, 14.1’, 18.8’, 23.5’
Lateral Soil-Pile Interaction
800
Lateral Force, F (kip)
600
400
200
0
-2.5
-2
-1.5
-1
-0.5
-200
0
0.5
1
1.5
2
-400
-600
-800
Lateral Deflection, Y (in)
28.2 ft
32.9 ft
37.6 ft
42.3 ft
47 ft
Figure 18: Lateral force-displacement curves at depths x = 28.2’, 32.9’, 37.6’, 42.3’, 47’
2.5
21
5.2.2. Axial Soil Resistance
Axial skin resistance support curves (called t-z curves) were developed using
hyperbolic functions similar to the HFD model. The following function fits the trend
observed in experimental data for cohesionless soil:
Q=
5S
1 + 4S
(5)
Q=
11S
1 + 10S
(6)
And for cohesive soil:
Here, S is the pile settlement ratio and Q is the side load transfer ratio where
z
S = ( ) ∗ 100
b
Q=
t
fmax
fmax = {
βγ′ x for sand
βc
for clay
β = 1.5 − 0.135√x
(7)
(8)
(9)
(10)
z = Settlement of pile
b = Diameter of pile
t = Side load transfer
fmax = Ultimate side load transfer
x = Depth below ground in feet
The resulting t-z curves using the properties of Table 2 were multiplied by the tributary
surface area of each corresponding node to produce the force-settlement curves shown in
Figure 19 and Figure 20. Theses curves were used for the vertical soil springs in the
finite element model.
22
Vertical Soil-Pile Interaction
25
20
15
Side Force, F (kip)
10
5
0
-0.2
-0.15
-0.1
-0.05
-5 0
0.05
0.1
0.15
0.2
-10
-15
-20
-25
Settlment, Z (in)
0 ft
4.7 ft
9.4 ft, 14.1 ft, 18.8 ft, 23.5 ft
Figure 19: Vertical force-settlement curves at depths x = 0’, 4.7’, 9.4’, 14.1’, 18.8’, 23.5’
Vertical Soil-Pile Interaction
40
30
20
Side Force, F (kip)
10
0
-0.2
-0.15
-0.1
-0.05
-10
0
0.05
0.1
0.15
-20
-30
-40
Settlement, Z (in)
28.2 ft
32.9 ft
37.6 ft
42.3 ft
47 ft
Figure 20: Vertical force-settlement curves at depths x = 28.2’, 32.9’, 37.6’, 42.3’, 47’
0.2
23
5.2.3. Pile Tip Resistance
Finally, a tip resistance curve (called a q-w curve) for the piles was developed.
The q-w curve was also developed using a hyperbolic function developed from empirical
data. Since the pile tip is embedded in a clay soil layer, the following equation was
calibrated for cohesive soils:
Q=
0.9S
1 + 0.7S
(11)
S is now the Base Settlement Ratio and Q is the End Bearing ratio where
S=
w
∗ 100
b
(12)
Q=
qb
qu
(13)
w = settlement of base
b = diameter of base
q b = End Bearing
q u = Ultimate End Bearing = Nc c
(14)
The End Bearing Factor, Nc, of Equation 14 is approximately 9 for cohesive soils
provided the pile has been driven at least 5 times the diameter of the pile into the strata.
Therefore, the Ultimate end bearing for the piles, given the cohesion in Table 2, is 13500
psf. The End Bearing values are multiplied by the area of the tip resulting in the tip
force-settlement curve shown in Figure 21.
24
Tip Force-Settlement Curve
30
20
Tip Force (kip)
10
0
-1
-0.5
0
0.5
1
-10
-20
-30
Settlement (in)
Figure 21: Tip force-settlement curve
Since each pile penetrates to approximately the same depth and same soil, one qw curve was adequate for each pile. Furthermore, all of the support springs developed
for the bent piles were also used for the abutment piles at the appropriate depths.
Although the bent piles have a slightly different soil profile, this simplification was
considered acceptable when dealing with idealized soil.
25
6. Dynamic Analysis Results
The mode shape shown in Figure 22 displays the primary vertical mode. This
mode has a period of 0.264 seconds. Subsequent mode shapes are shown in Figures 23 to
27, with Figure 23 showing the primary transverse mode and Figure 27 showing the
primary longitudinal mode.
Figure 22: Mode shape 1, T = 0.264 sec
Figure 23: Mode shape 2, T = 0.259 sec
26
Figure 24: Mode shape 3, T = 0.195 sec
Figure 25: Mode shape 4, T = 0.156 sec
27
Figure 26: Mode shape 5, T = 0.111 sec
Figure 27: Mode shape 6, T = 0.103 sec
The earthquake motions were applied to the completed bridge model. Figures 28
through 33 show comparisons of the calculated displacement responses with the
instrument-recorded responses for major points on the bridge. The results of the model
match the records very well at each location. The small discrepancies are most likely due
to the idealization of the model, but are insignificant to the global response. Further
investigation into the behavior of the bridge model with design basis earthquake and
28
maximum credible earthquake level input motions can be found in the appendix section.
Channel 13 - Transverse
5
4
Displacement (in)
3
2
1
0
-10
-1
10
30
50
70
90
70
90
-2
-3
-4
Recorded CH 13
MIDAS Model
-5
Time (sec)
Figure 28: Channel 13 displacement response
Channel 19 - Vertical
2
Displacement (in)
1.5
1
0.5
0
-10
-0.5
-1
-1.5
-2
10
30
50
Recorded CH 19
MIDAS Model
Time (sec)
Figure 29: Channel 19 displacement response
29
Channel 27 - Longitudinal
8
Displacement (in)
6
4
2
0
-10
-2
10
30
50
70
90
70
90
-4
-6
Recorded CH 27
MIDAS Model
-8
Time (sec)
Figure 30: Channel 27 displacement response
Channel 1 - Vertical
2
Displacement (in)
1.5
1
0.5
0
-10
-0.5
-1
-1.5
-2
10
30
50
Recorded CH 1
MIDAS Model
Time (sec)
Figure 31: Channel 1 displacement response
30
Channel 2 - Transverse
5
4
Displacement (in)
3
2
1
0
-10
-1
10
30
50
70
90
70
90
-2
-3
-4
Recorded CH 2
MIDAS Model
-5
Time (sec)
Figure 32: Channel 2 displacement response
Channel 17 - Vertical
2
Displacement (in)
1.5
1
0.5
0
-10
-0.5
-1
-1.5
-2
10
30
50
Recorded CH 17
MIDAS Model
Time (sec)
Figure 33: Channel 17 displacement response
31
7. Conclusion and Outlook
A global, three-dimensional finite-element structural model of Meloland Road
Overcrossing, which is seismically instrumented, was developed to investigate the
validity of soil-foundation-structure interaction analysis. The displacement response of
the finite element model given an actual earthquake excitation was in very close
agreement with recorded displacements. This remarkable match achieved between the
model and recorded motions is due to the additional steps taken to realistically estimate
passive soil capacities of the abutments and foundation. The results suggest that
employing SFSI is an effective technique in achieving accurate seismic analyses. The
methodology and procedures performed in this project may be applicable to any ordinary
highway bridge structure.
While detailed structural bridge models consisting of complete SFSI systems can
be used in high profile projects where plenty of resources are available, this kind of
bridge model becomes economically impractical for many ordinary bridges where
resources are limited. An alternate SFSI sub-structuring technique, in which foundation
and soil capacities are kinematically condensed into a single support, can reduce
computational requirements and provide reasonably accurate results.
32
Appendix
The MRO finite element model was exercised with stronger ground motions to
further investigate its behavior. Two additional three-component sets of ground motions
were implemented into the model including a design basis earthquake (DBE) level set
and a maximum credible earthquake (MCE) level set. The acceleration spectra assuming
5% damping are shown in Figure 34.
MRO Spectral Acceleration
5% Damping
2.5
2
Sa (g)
Design Spectrum
1.5
MCE Spectrum
1
0.5
0
0
0.5
1
1.5
2
2.5
T (sec)
Figure 34: MRO design Sa versus T
The design and MCE spectra were calculated based on the bridge’s location at 32.773°
latitude and -115.448° longitude. The spectra were also calibrated for a Site Class D soil.
Probabilistic seismic hazard deaggregation was performed in order to determine
the location’s average hazard. Given the bridge’s location, spectral acceleration period of
0.26 sec, and an average shear wave velocity of 630 ft/sec in the first 100 ft of soil, the
33
mean magnitude, M, and mean site-to-source, R, for a DBE and MCE are shown in Table
4.
Table 4: MRO probabilistic seismic hazard deaggregation
Event Level
DBE
MCE
Mean Return
Time
(yrs)
475
2475
Mean SiteTo-Source
(mi)
1.93
1.18
Mean
Magnitude
6.76
6.8
Ground motions were selected from the PEER Ground Motion Database that
closest matched the parameters developed from deaggregation. Probably not
coincidentally, the motions chosen were from MRO during the 1979 Imperial Valley
earthquake. The acceleration spectra of the three-component motions are shown in
Figure 35. The three-component recorded motions are shown in Figure 36.
1979 Imperial Valley-06
EC Meloland Overpass FF
Sa (g)
1
0.1
0.01
0.001
0.01
0.1
1
10
T (sec)
Fault Normal
Fault Parallel
Vertical
Figure 35: 1979 Imperial Valley at MRO Sa versus T
34
0.3
1979 IMPERIAL VALLEY, EC MELOLAND OVERP FF, 000
Acceleration (g)
0.2
0.1
0
-0.1
0
5
10
15
20
25
30
35
40
35
40
35
40
-0.2
-0.3
-0.4
Time (sec)
0.4
1979 IMPERIAL VALLEY, EC MELOLAND OVERP FF, 270
Acceleration (g)
0.3
0.2
0.1
0
-0.1
0
5
10
15
20
25
30
-0.2
-0.3
-0.4
Time (sec)
0.3
1979 IMPERIAL VALLEY, EC MELOLAND OVERP FF, UP
Acceleration (g)
0.2
0.1
0
-0.1
0
5
10
15
20
25
30
-0.2
-0.3
Time (sec)
Figure 36: 1979 Imperial Valley earthquake motions in longitudinal, transverse, and vertical directions
35
The maximum spectral acceleration for a period of 0.26 sec is 0.56g. Therefore,
the three-component motions were scaled up to reach DBE and MCE levels. Scale
factors of 2.4 to reach a Sa of 1.35g and 3.6 to reach a Sa of 2.03g were used for DBE
and MCE respectively.
Table 5: Spectral accelerations for T=0.26 sec and scale factors
1979 Imperial
Valley
Sa (g)
0.56
SF
--
DBE
MCE
1.35
2.4
2.03
3.6
The scaled recorded motions were implemented into the model. The
displacement response at the abutments for the DBE is shown in Figure 37 and for the
MCE in Figure 38.
40
DBE Time-History Response
Displacement (in)
30
20
10
0
-10
0
5
10
15
20
25
30
CH 27
-20
CH 19
-30
-40
35
CH 13
Time (sec)
Figure 37: DBE displacement response at abutment channels
40
36
50
MCE Time-History Response
40
Displacement (in)
30
20
10
0
-10
0
5
10
15
20
25
30
35
-20
40
45
CH 13
-30
CH 19
-40
CH 27
-50
Time (sec)
Figure 38: MCE displacement response at abutment channels
From Figures 37 and 38, it appears the global system does not undergo significant
inelastic deformations. That is not to say there are none, but they are very minor as
shown in Figure 39.
Force (kip)
Abutment Spring Force-Displacement
200
180
160
140
120
100
80
60
40
20
0
0.9
0.95
1
1.05
Displacement (in)
Figure 39: Hysteretic behavior of abutment soil spring
1.1
1.15
37
To get a better understanding of the bridge response, its relative displacement
during the MCE was plotted, as shown in Figure 40.
2
MRO Relative Displacement
Displacement (in)
1.5
1
0.5
0
0
5
10
15
20
25
30
35
-0.5
CH 13
-1
-1.5
40
CH 19
CH 27
Time(sec)
Figure 40: Abutment relative displacement during MCE
It is clear that there is very little relative displacement of the bridge during the
earthquake. Therefore, large inelastic deformations would not be expected. This is a
characteristic of many bridges with integral abutments. With this configuration, the
bridge is essentially fixed to the surrounding soil. Therefore, during a seismic event, the
bridge will move along with the surrounding soil. This is further illustrated by plotting
the relative displacement at the top and bottom of the column during the MCE.
38
1.5
Column Relative Displacement Response
Displacment (in)
1
0.5
0
0
5
10
15
20
25
30
35
40
-0.5
Top
-1
Bottom
-1.5
Time (sec)
Figure 41: Column relative displacement response during MCE
It can be seen in Figure 41 that the bottom of the column basically moves with the
ground. Although the top of the column does have noticeable relative displacement, it is
very small compared to the global system.
39
References
ASCE (2005). Minimum Design Loads for Buildings and Other Structures, Standards
ASCE/SEI 7-05. ASCE, Washington D.C.
Caltrans (1968). As-Built Drawings, Meloland Road Overcrossing. California
Department of Transportation, Sacramento, CA.
Caltrans (2010). Seismic Design Criteria (v1.6). California Department of
Transportation, Sacramento, CA.
CSMIP (2013). California Strong Motion Instrumentation Program.
http://www.conservation.ca.gov/cgs/smip.
Ensoft (2013). LPile: A Program for the Analysis of Piles and Drilled Shafts Under
Lateral Loads (v6.0). Ensoft, Inc. (www.ensoftinc.com)
MIDASoft (2013). Midas Civil: Integrated Solution System for Bridge and Civil
Engineering. MIDAS Information Technology Co., Ltd. (www.midasuser.com)
PEER (2010). PEER Ground Motion Database (Beta). Pacific Earthquake Engineering
Research Center, University of California, Berkeley.
(http://peer.berkeley.edu/peer_ground_motion_database)
Reese, L., Isenhower, W., Wang, S.T. (2006). Analysis and design of shallow and deep
foundations. Hoboken, NJ: John Wiley & Sons, Inc.
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Journal of Bridge Engineering, ASCE, 15(3), 302-311.
40
USGS (2008). 2008 Interactive Deaggregations (Beta). U.S. Geological Survey.
(http://geohazards.usgs.gov/deaggint/2008/)