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Nonlinear Modeling of Dynamic Soil-Structure Interaction: A Practitioner’s Viewpoint
By(Arul) K. ArulmoliEarth Mechanics, Inc.Fountain Valley, California
Workshop on Nonlinear Modeling of Geotechnical Problems: From Theory to Practice
Johns Hopkins University, Baltimore, MarylandNovember 3 & 4, 2005
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Factors Affecting Industry Use of Advanced Computer Programs for Dynamic Soil-Structure Interaction Problems
Too complex
Complex model parameters
Verification lacking
Limitations on structural elements and soil-structure interfacesLack in-house expertise
More $ and time to projects
Difficult to sell to client (structural) and/or owner
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Uncertainties in Ground Motion Response Spectra (Input from Geologists/Seismologists)
ACCELERATIONRESPONSE SPECTRA FOR THE PORT OF LOS ANGELES
BASED ON DETERMINISTIC EVALUATION USING DIFFERENT MEAN SOIL ATTENUATION RELATIONSHIPS
Average +42%
Average +47%Average -27%
Average -32%
TYPICAL PERIOD RANGE FOR POLA CONTAINER WHARVES
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Dynamic Soil-Structure Interaction AnalysisAnalysis Cross Section – Container Wharf Problem(Port of Los Angeles, Berth 147)
MLLW = El. 0'
24-inch octagonal prestressed concrete piles
Wharf Deck
-50
-100
0-100
Ele
vatio
n (ft
)
Distance (ft)
0
-200-300-400 100
-150
200 300
Loose to med. dense silty SAND
Soft to stiff CLAY and SILT
Soft to med. stiff lean CLAY
Stiff lean CLAY
Dense to very dense SAND
DikeCutoff Wall
Backfill
Row G F D C B Row A
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Dynamic Soil-Structure Interaction AnalysisFLAC Model (Port of Los Angeles, Berth 147)
-50
-100
0-100
Ele
vatio
n (ft
)
Distance (ft)
0
-200-300-400 100
-150
200 300
Design Water Level = El. +5'
Beam Elements
Pile Elements(minimum discretization length = 2.5')
Soil Grid
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Dynamic Soil-Structure Interaction AnalysisStructure Discretization
PileElements
Beam Elements
Legend
Structural Element Node
Rigid Joint
Idealized Soil Profile
Dike
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Dynamic Soil-Structure Interaction AnalysisSoil Model Parameters
-50
-100
0-100
Ele
vatio
n (ft
)
Distance (ft)
0
-200-300-400 100
-150
200 300
Dense to very dense SAND (SP)
MaterialLayer Material Description
CohesiveStrength, c
(psf)
Total UnitWeight(pcf)
InternalAngle of
Friction, φ'(degrees)
DesignPoisson's
Ratio
DesignShear
Modulus(ksf)
125
115
110
115
120
120
120
135
0
400
See Next Slide
0
0
200
32
0
0
0
0
38
32
45
0.35
0.45
0.45
0.45
0.45
0.35
0.35
0.25
790
652
1280
2940
Stiff lean CLAY (CL)
Backfill (SP)
Quarry Run
Soft to medium stiff lean CLAY (CL)
Soft to stiff CLAY and SILT (CL/ML)
Loose to medium dense silty SAND (SM) below G.W.T. (Liquefied)
Loose to medium dense silty SAND (SM) above G.W.T.
Elevation(ft)
+15 to +5
+5 to -15
-15 to -30
-30 to -60
-60 to -85
-85 to -180
+15 to -6.4
+8 to -65
See Next Slide
See Next Slide
See Next Slide
See Next Slide
See Next Slide
See Next Slide
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Dynamic Soil-Structure Interaction AnalysisModeling Profiles
-50
-100
Ele
vatio
n (ft
)
POLA Station Number
0
48+00
-150
47+00 46+00 45+00 44+00 43+00 42+00
Loose to medium dense SAND above GWT (SM)Loose to medium dense SAND below GWT (SM)
Soft to stiff CLAY and SILT (CL/ML)
Soft to med. stiff lean CLAY (CL)
Stiff lean CLAY (CL)
Idealized Soil Profile2000 4000 6000 8000 100000Shear Strength (psf)
8000 6000 4000 2000 010000Shear Stiffness (ksf)
Vertical discretization of soil profile at wharf location
Dense to very dense SAND (SP)
Proposed Berth 147 Facility
Idealized Section Profile
Strength and Stiffness Variation for Modeling Purposes
Strength Variation
Stiffness Variation
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Dynamic Soil-Structure Interaction AnalysisSurcharges and Dynamic Boundary Conditions
Horizontal Input Motion(applied to base of model)
Refer Note 3
Slaved boundary (refer Note 1)
Refer Note 2
Slaved boundary (refer Note 1)
Refer Note 2
75'
Static Conditions = 1000 psfSeismic Conditions = 600 psf
Container Handling Surcharge = 250 psf(static and seismic condtions)
Notes:1. A slaved boundary is defined by neighboring gridpoints (at the same elevation) forced to move as one in the horizontal and vertical directions.2. Horizontal static forces mobilized from static analysis applied at boundaries.3. Wharf deck constrained to move in horizontal direction only.
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Dynamic Soil-Structure Interaction AnalysisDeconvolution of Surface Motion using SHAKE91
-0.6-0.4-0.20.00.20.40.6
Acc
. (g)
-4-3-2-101234
Vel
. (ft/
s)
-20
-10
0
10
20
0 5 10 15 20 25 30 35Time (second)
Dis
pl. (
in)
Within Motion at El. -180'
Surface Motion
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Dynamic Soil-Structure Interaction AnalysisDeformed Shape at End of Shaking
-50
-100
0-100
Elev
atio
n (ft
)
Distance (ft)
0
-200-300-400 100
-150
200 300
Maximumdisplacement= 11.1 inches
Undeformed structures
Deformed shape
Notes:1. Undeformed soil grid not shown for clarity.2. Magnification factor for plotted displacement = 10.
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Dynamic Soil-Structure Interaction AnalysisRow G (Landside) Pile Structural Profiles
HorizontalDisplacement
(inches)
-120
-100
-80
-60
-40
-20
0
-5 0 5 10 15
Ele
vatio
n (ft
)
t = Seismic Surcharge
t = 5 sec
t = 10 sec
t = 15 sec
t = 20 sec
t = 25 sec
t = 25.3 sec
-300 -150 0 150 300
Shear Force(kips)
-600 -300 0 300 600
Bending Moment(kip-ft)
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Dynamic Soil-Structure Interaction AnalysisA Consultant’s Disclaimer!
“Accuracy of FLAC Analysis Results:”
“The results of FLAC should be used as a guide in estimating the overall performance of the embankment-wharf system. In evaluating the FLAC results, one should keep in mind the program limitations, modeling assumptions and other uncertainties inherent in any nonlinear deformation analysis and in estimation of ground motion time histories.”
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Dynamic Soil-Structure Interaction AnalysisWhat is a Reasonable Approach for the Practitioner?
A simplified geotechnical approach, with some built-in conservatism, would be reasonable to provide structural engineers with the necessary design Input.
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Soil-Pile-Structure InteractionContainer Wharf
potential plastic hinge locationssoft clay or liquefaction zone
kinematic Loading - lateral spread displacement demand
rock fill
inertial interaction displacement demand from structural analysis
The two loading conditions induce maximum moments in separated upper and lower regions of pileThe two loading conditions also tend to induce maximum moments at different times during the earthquake
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SSI - Inertial Loading - Three Dimensional Effects
e=49 ftCenter of Rigidity (CR)
Center of Mass (CM)
• Center of Mass (CM) and Center of Rigidity (CR) do not coincide
• Two orthogonal earthquake components
• Non-symmetrical in the longitudinal direction
Seismic Piles
Non-seismic Piles
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SSI-Kinematic Interaction AnalysisSimplified Newmark Time History Analyses
Widely Used to Evaluate Seismic Stability of SlopesDisplacement Based Performance CriteriaAssumes a Rigid Sliding Block on Critical Failure SurfaceYield Acceleration from Stability AnalysisAcceleration-Time History at Base of Sliding Block is Used
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SSI-Kinematic Interaction AnalysisPseudo Static Slope Stability – Planar Failure Surfaces
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SSI-Kinematic Interaction AnalysisNewmark Sliding Block Analysis Results for CLE Motion (ky=0.11g)
0 5 10 15 20 25-20
-10
0
10
20
NE
WM
AR
K D
ISP
. (IN
)Max= 13.1 in
Min= 0.0 in
0 5 10 15 20 25-40
-20
0
20
40
NE
WM
AR
K V
EL.
(IN
/S)
Max= 25.9 in/s
Min= 0.0 in/s
0 5 10 15 20 25-0.5
0
0.5
INP
UT
AC
C. (
g)
TIME (SECOND)
Max= 0.48 g
Min= -0.38 g
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SSI-Kinematic Interaction AnalysisCLE: Newmark Displacement vs. Yield Acceleration
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.00 0.10 0.20 0.30
Yield Acceleration, ky (g)
Dis
plac
emen
t (ft)
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4 ft.Sliding layer
Plastic hinge
Plastic hinge
Assumed fixity for displacements
Assumed fixity for displacements
5D
2D
2D
5D
Pile Pinning: Simplified Structural Calculations
Plastic Hinge (PH) length: ≈ 36 in.Yield curvature: ≈ 200E-6/inPH curvature: ≈ 800E-6/in
0 0.001 0.002 0.003
CURVATURE (1/in)
0
2000
4000
6000
8000
10000
MO
ME
NT
(ki
p.in
)
P=0P=100 kips
P=300 kips
P=500 kipsP=700 kips
CLECurvature
24 in. PILE; PRESTRESSED SECTION; 16X0.6in STRANDS
Results for maximum sliding layerdisplacement:Yield: 2.8 inPH: 5.9 in
(Courtesy, Dr. Nigel Priestley)
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SSI-Kinematic Interaction AnalysisFLAC Liquefaction Example – Pile Pinning Effect
Horizontal Displacements at Row A(Thin Liquefied Layer Case)
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
-0.8 -0.6 -0.4 -0.2 0.0Horizontal Displacement (ft)
Elev
atio
n (f
t)
Pile
Soil with Piles
Soil withoutPiles
-Liquefied Layer
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H ft.
Plastic hinge
Plastic hinge
Assumed fixity for displacements
Assumed fixity for displacements
X=2D
X=2D
Weak Soil layer
My
Fy
MyFy
SSI, Simplified Kinematic Interaction AnalysisPile Pinning: Geotechnical Calculations
(H+2X)2MyFy =
Additional Shear Strength due to Pile Pinning Effects:
APT
FySpp =
APT – Pile Tributary Area
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Dynamic Soil-Structure Interaction EvaluationSummary and Conclusions
Use of advanced computer program for dynamic SSI problem in the industry is limitedSimplified approaches, supported by complex analyses, provide reasonable solutions to dynamic SSI problemsCollaboration between geotechnical and structural engineers is critical for improving the use of computer programs in the industryCollaboration in the industry as well as academia (research) is vitalStructural based computer programs, with geotechnical capabilities, appear to be more viable for dynamic SSI problems