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

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

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

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

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

Dynamic Soil-Structure Interaction AnalysisStructure Discretization

PileElements

Beam Elements

Legend

Structural Element Node

Rigid Joint

Idealized Soil Profile

Dike

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

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See Next Slide

See Next Slide

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

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.

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

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.

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)

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.”

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.

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

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

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

SSI-Kinematic Interaction AnalysisPseudo Static Slope Stability – Planar Failure Surfaces

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

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)

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)

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

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

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