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www.fugro.com Soil-Structure Interaction (SSI) by Shahriar Vahdani, Ph.D., P.E. Senior Vice President May, 2011
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Soil-Structure Interaction (SSI)
by
Shahriar Vahdani, Ph.D., P.E.
Senior Vice President
May, 2011
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Soil-Structure Interaction
Kinematic Interaction
Inertial Interaction
Free-Field
Total SSI
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Traditional Approach
Free-Field
Ground Motion
K
C
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Analysis Methods
Complete Method Substructuring Method
Scattered Ground Motion
Massless Structure
K
C
Scattered Ground Motion
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Soil-Structure Interaction (SSI) Analyses
Transbay Terminal Center (TTC)
San Francisco, CA
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Project Team
Transbay Joint Powers Authority (TJPA) - Client
Pelli Clarke Pelli - Architect
Thornton Tomasetti - Structural ARUP - Geotechnical
Fugro – Soil-Structure Interaction AMEC – Ground Motions
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TTC
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TTC Structure
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TTC Structure
55
ft
• 3 superstructure pods
on below-grade Box
• 55 feet of basement
• Buoyant structure
• Held down by tiedowns
• Flexible basement
• Heavy roof level –
behaves like SDOF
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Project Location and Challenges
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TTC and Adjacent Structures
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Soil Profile along TTC
Horizontal Distance (ft)
Ele
vati
on
(ft
)
East West
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Key Technical Issues
Structure - Soil - Structure Interaction
Varying Soil Conditions
Variations within Structure
Buoyancy and Tiedown Modeling
Similar periods of soil column and structure 1st mode
Traveling Waves – 2.5 km/s, 0.2 s delay
Surface Waves – Effect limited by soil capacity
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Approach and Assumptions
2D SSI analysis using SASSI
Explicitly model selected adjacent structures
Address soil variability in conjunction with averaging
effect of structure
Address variability of structure through 4 different 2D
structural sections
Buoyancy implies no friction along base
Tiedowns imply no (or little) rocking
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Zone 1
Zone 2
Zone 3
Sections 1 2 3 4 5
Variation in Soil Profiles:
Soil Sections and Zones
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Dynamic Soil Properties:
Strain Compatible Shear Wave Velocity Ground Motions: GSL-2
Statistical analysis of 84 profiles (7 X 2 X 3 X 2) in each of 3 zones
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Dynamic Soil Properties:
Strain Compatible Damping Ratio Ground Motions: GSL-2
Statistical analysis of 84 profiles (7 X 2 X 3 X 2) in each of 3 zones
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Orientation of Motions
4 Maximum Direction and 3 Minimum Direction (Geomean) ground
motions in Longitudinal Direction
3 Maximum Direction and 4 Minimum Direction (Geomean) ground
motions in Transverse Direction
Vertical Direction – Use Bedrock Motion
Max
Min
Max
Min
Max M
in
Min
Ma
x
Min
Ma
x
Min
Ma
x
Longitudinal
Max
Min
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Ground Motions:
GSL-2, Transverse Sections
Earthquake Station Name Component Velocity Pulse
1999 Duzce, Turkey Lamont 1061 161 MX N/A
1999 Kocaeli, Turkey Arcelik ARC MN 6.7 s
1979 Imperial Valley Cerro Prieto HCP MX N/A
1999 Hector Mine Hector HEC MN N/A
1995 Kobe Nishi-Akashi NIS MX N/A
1992 Erzincan Erzincan ERZ MN 2.2 s
1999 Chi-Chi, Taiwan TCU076 T76 MN N/A
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Ground Motions:
GSL-3, Transverse Sections
Earthquake Station Name Component Velocity Pulse
1992 Erzincan Erzincan ERZ MN 2.2 s
2002 Denali, Alaska Carlo 559 MX N/A
1999 Kocaeli, Turkey Arcelik ARC MN 6.7 s
1999 Hector Mine Hector HEC MN N/A
1999 Kocaeli, Turkey Izmit IZT MX N/A
1999 Chi-Chi, Taiwan TCU076 T76 MN N/A
1999 Chi-Chi, Taiwan TCU089 T89 MX N/A
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Variation within Structure:
2D Structural Sections
GL - 6 GL - 15 GL - 21 GL - 31
Longitudinal
- GL - GL - GL -
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Interaction with Adjacent Buildings
10
0
1s
t S
tre
et
10
1
2n
d S
tre
et
20
1
Mis
sio
n
55
5
Mis
sio
n
40
0
Ho
ward
50
0
Ho
ward
301
Mission
Lowrise
19
9
Fre
mo
nt
301
Mission
Highrise Buttress GL15
GL31
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Direct Method
Time History at Ground Level
Trainbox Racking
Analysis Approach
Scattered motion
Substructuring Method
Transbay Terminal Center (with mass) Transbay Terminal Center (massless)
K
C
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Soil-Structure Interaction Approach
Direct SASSI Analysis
• Full solution in SASSI
• Incorporate both inertial and kinematic effects (models with TTC mass)
• Capable of linear solution only using secant structural properties
Substructuring Analysis
• Develop springs and dashpots from SASSI
• Develop kinematic “scatter motions” (massless model)
Structural Analysis
• Structure on springs and dashpots driven by scatter motions
• Validate response of linear structure with SASSI direct analysis
• Conduct nonlinear structural evaluation for design
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SASSI Models
Section GL-6
Linear, secant
stiffness
properties
Springs model
end wall effect
Soft soil at
base to model
no friction
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SASSI Models
Section GL-15
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100 First St
TTC
SASSI Models
Section GL-15 with Typical Adjacent Bldg.
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SASSI Models
301 Mission St.
199 Fremont St.
TTC
Section GL-31
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Adjacent Building Foundation Modeling
301 Mission
Pile Group Foundation
TTC
Mat Foundation
Upper Equivalent Shear Block (Gupper)
TTC
301 Mission
Mat Foundation
Lower Equivalent Shear Block (Glower)
Foundation System
920-14” square
precast Concrete
Piles
Pile spacing:
3’- 6” to 4’- 8”
Pile length:
60’ below slab
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Methodology: Adjacent Building Foundations
Build PLAXIS model with foundation of adjacent buildings explicitly modeled.
Build similar model with the foundation replaced by equivalent shear blocks.
To calculate the equivalent shear modulus:
– Step 1
• Mobilize pile foundation’s lateral resistance by pushing laterally.
• Mobilize shear block’s lateral resistance by pushing laterally.
• Adjust Gupper until lateral resistances from both models are the same.
– Step 2
• Mobilize TTC laterally and record the lateral resistances from both models.
• Calibrate the lower block shear modulus (Glower) until resistances become the same.
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Adjacent Building Foundation Modeling:
301 Mission St. Step 1 - Deformation
Step 2 - Deformation
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Soil Buttress Modeling
Equivalent Buttress Properties
E = 2.2 X 105 ksf
g = 0.139 kcf
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0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Period (s)
Tra
nsfe
r F
un
ctio
n
Free-Field
Direct Method: Transfer Functions at GL-15
Rock
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0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Period (s)
Tra
nsfe
r F
un
ctio
n
Free-Field
Ground Level - Massless Structure
Direct Method: Transfer Functions at GL-15
Rock
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0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Period (s)
Tra
nsfe
r F
un
ctio
n
Free-Field
Ground Level - Massless Structure
Ground Level - Box Mass Only
Direct Method: Transfer Functions at GL-15
Rock
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Direct Method: Transfer Functions at GL-15
0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Period (s)
Tra
nsfe
r F
un
ctio
n
Free-Field
Ground Level - Massless Structure
Ground Level - Box Mass Only
Ground Level - With Mass
Rock
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Displacement Amplification Function
GL15 Model with Mass
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Period (sec)
Dis
pla
ce
me
nt
Am
plifi
ca
tio
n F
un
cti
on
Base
Ground Surface
Top of Structure
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Frequency-Dependent Stiffness and Damping
0 0.5 1 1.5 2500
1000
1500
2000
2500
3000
Frequency (Hz)
C
(k
ips
/ft)
Cglobal
K and C
0 0.5 1 1.5 20
500
1000
1500
2000
Frequency (Hz)
K (
kip
s/f
t)
Kglobal
global global
k c i i
K global = S k i i
C global = S c i i
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GL-6 Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
Base of Trainbox Top of Trainbox
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
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GL-15 Model
Base of Trainbox Top of Trainbox
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
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GL-31 Model TTC Only
Base of Trainbox Top of Trainbox
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
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GL-31 Model with Adjacent Structures
Base of Trainbox Top of Trainbox
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
Scattered Motion
Total Motion
FF Motion
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GL6
GL15
GL21
GL31 TTC Only
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GL6
GL15
GL21
GL31 TTC Only
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GL6
GL15
GL21
GL31 TTC Only
GL31 with Adjacent
Structures
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GL6
GL15
GL21
GL31 TTC Only
GL31 with Adjacent
Structures
Summary at Ground Surface Level
Scattered Motions Total Motions
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SASSI vs. Perform3D Spectra
Section GL-15
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Racking: GL-15 Model with Mass
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 5 10 15 20 25 30 35
Time (s)
Ra
ckin
g (
in.)
ground
concourse
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Results: Racking Summary from SASSI
Section
Average Free-Field
Racking
DFF (in.)
Average Racking at
Ground Level
DBox (in.)
Average Racking
at Concourse
Level
DConc (in.)
GL-15 2.6 2.5 0.8
GL-21 2.6 2.4 0.9
GL-6 2.0 0.3 0.2
GL-31
(TTC Only) 3.4 2.3 1.1
GL-31
(Full Model) 3.4 2.0 1.0
Longitudinal 2.0 – 3.4 0.02 0.02
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Parametric Studies
Considered Mean Strain Compatible Profile as well as
± 1 Std. Dev. Profiles for Each Transverse Section
Effect of Typical Highrise Building
Explicitly Modeled Varying Soil Properties along
Longitudinal Section
Evaluated Full Friction and No Friction Cases for
Longitudinal and Transverse Directions
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Parametric Study: Effect of Variation in Soil Properties at GL-15
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.5
1
1.5
2
2.5
3
3.5
Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
GL15 - Mean Profile
GL15 - High Profile
GL15 - Low Profile
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.5
1
1.5
2
2.5
3
3.5
Period (sec)
Sp
ectr
al A
ccele
rati
on
(g
)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
GL15 - Mean Profile
GL15 - High Profile
GL15 - Low Profile
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100 First St
TTC
Parametric Study: Effect of Typical Highrise
Section GL-15 with Typical Adjacent Bldg.
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.5
1
1.5
2
2.5
Period (sec)
Sp
ec
tra
l A
cc
ele
rati
on
(g
)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
GL15
GL15 + Typical Highrise
Parametric Study: Effect of Typical Highrise
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Parametric Study: Effect of Variation in Soil Properties (Longitudinal)
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Parametric Study: Effect of Variation in Soil Properties (Longitudinal)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Period (sec)
Sp
ec
tra
l A
ccele
rati
on
(g
)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
Longitudinal
Longitudinal + Soil Variations
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Period (sec)
Sp
ec
tra
l A
ccele
rati
on
(g
)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
Longitudinal
Longitudinal + Soil Variations
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Parametric Study: Effect of Friction at Base
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.5
1
1.5
2
2.5
Period (sec)
Sp
ec
tra
l A
cce
lera
tio
n (
g)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
GL15 - No Friction at Base
GL15 - Friction at Base
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.5
1
1.5
2
2.5
Period (sec)
Sp
ec
tra
l A
cce
lera
tio
n (
g)
GSL-2 Ground Motions
Ground Surface - Mean Spectra
GL15 - No Friction at Base
GL15 - Friction at Base
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Summary
Key SSI Issues Addressed:
– Structure-Soil-Structure Interaction
– Variations in soil and structure
Key Findings
– Adjacent structures located less than 25 ft from TTC have significant
impact
– Structural variation affects scatter motions
– “Resonance” of structure and soil response at period of 1.5 sec.
– Translational mode observed at ~ 0.7 sec. – does not govern
superstructure response
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Soil-Structure Interaction (SSI)
by
Shahriar (Shah) Vahdani, Ph.D., P.E.
Senior Vice President
May, 2011
www.fugro.com
Comparison of Free-Field Ground Motions
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Period (sec)
Sp
ec
tra
l A
cce
lera
tio
n (
g)
GSL-2 Ground Motions
Ground Surface
AMEC FF - Section 2 (Mean)
AMEC FF - Section 3 (Mean)
AMEC FF - Section 4 (Mean)
Fugro FF - Zone 2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Period (sec)
Sp
ec
tra
l A
cce
lera
tio
n (
g)
GSL-2 Ground Motions
Ground Surface
AMEC FF - Section 2 (Mean)
AMEC FF - Section 3 (Mean)
AMEC FF - Section 4 (Mean)
Fugro FF - Zone 2
All Ground Motions
