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Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

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Page 1: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Overview of Soil-Structure Interaction Principles

Jonathan P. StewartUniversity of California, Los Angeles

Page 2: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Overview

A. IntroductionB. General methods of analysisC. Inertial interactionD. Kinematic interaction

Page 3: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction

• Structure• Foundation• Underlying soil/rock

Response dictated by interactions between:

System analysis evaluates response given free-field motion, ug

No SSI when___________ SSI effect =______________

Page 4: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• Inertia → base shear (V) and moment (M) F=ma

V

M

Page 5: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• Inertia → base shear (V) and moment (M)

• V → relative foundation/free-field displacement (uf)

V

Page 6: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• Inertia → base shear (V) and moment (M)

• V → relative foundation/free-field displacement (uf)

• M → relative foundation/free-field rotation (θf)

M

Page 7: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• uf, θf → foundation damping

Page 8: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• uf, θf → foundation damping

• Radiation damping –foundation acts as wave source

uf

p

s

p

s

p

s

θf

Page 9: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

• uf, θf → foundation damping

• Radiation damping –foundation acts as wave source

• Hysteretic damping in soil

uf

τ

Δ

τ

Δ

Area ∝ hysteretic damping, βs

Page 10: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

1. Inertial soil structure interaction• Inertia from vibration of structure and

foundation• Causes foundation translation and rotation

(uf and θf)• Directly affects system flexibility and mode

shapes• Introduces foundation damping

Page 11: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

2. Kinematic interaction• Incoherent ground

motions → base slab averaging

u1 u2 u3

Sa

T

Page 12: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

2. Kinematic interaction• Incoherent ground

motions → base slab averaging

• Ground motion reductions with depth

Sa

T

u1u2

Page 13: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

3. Foundation deformations

• Loads from superstructure inertia

Page 14: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

A. Introduction. Three critical aspects of SSI

3. Foundation deformations

• Loads from superstructure inertia

• Deformations applied by soil

Nikolaou et al. (2001)

Beyond scope of current presentation

Page 15: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

B. General Methods of Analysis

• Direct approach– Full modeling of soil,

foundation, structure– Propagate waves

through system

Beyond scope of current presentation

Page 16: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

B. General Methods of Analysis

• Direct approach• Substructure

approach

Focus of this seminar

Page 17: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction

• Springs used to represent soil-foundation interaction

• Complex-valued– Real part represents

stiffness– Imaginary part related

to damping

Combination of real and complex parts comprises

“Impedance function”

Page 18: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction

• Springs used to represent soil-foundation interaction

• Complex-valued• If rigid foundation,

simplifies to:– 3 springs for 2D

system– 6 springs for 3D

system),(),( 00 υωυ aciakk jjj +=

xkzk

θk

Page 19: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction.Effects on System Behavior

• Concepts of period lengthening and foundation damping– System period

– System dampingθkhk

kk

TT fixed

x

fixed2

1~

++=

( )30 ~ TTi

fβββ +=

Foundation damping factor

kxkθ

θ

ug uf hθ u

m

hK*fixed, c

Page 20: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles
Page 21: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction.Effects on System Behavior

Hysteretic soil damping

1 1.5 2Period Lengthening, T/T

0

10

20

30

Foun

datio

n D

ampi

ng, β

f(%)

e/ru = 0PGA > 0.2gPGA < 0.1g

h/rθ = 0.5

1.0

2.0

0.0 0.1 0.2 0.3 0.4

h/(vs ×T)

0

4

8

12

16

20

β = 0.1β = 0

~ζ 0(%)h/r = 1

h/r = 2

h/r = 4

βf

Page 22: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

• Force-based procedure

• SSI affects design spectral ordinate

• Usually not considered for design of new buildings

C. Inertial Interaction.Effects on Base Shear

T

S a

S a

~S a

~S a

T ~T

Flexible-base period, damping ratio(includes SSI effects)

Fixed-base period, damping ratio(neglects SSI effects)

0 1 2Period (s)

0.1

0.2

0.3

0.4

0.5

0.6

Spec

tral A

ccel

erat

ion

(g)

~T

(a)

βi

β0

T, β0 =

T, βi =

∼ ∼

Page 23: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

• Initial seismic demand– Should be drawn for

foundation motion, not free-field

– Spectral ordinates should reflect system damping ratio

• Pushover curve– Soil springs in

pushover analysis

C. Inertial Interaction.Effects on Displacement-Based

Pushover Analysis

Initial seismic demand (free-field)Reduced seismic demand (SFSI effects)

Reduced seismic demand(SFSI + extra str. damping)Pushover curve

Performance point

Sa

Sd

Page 24: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Are these effects important?• YES, especially for

short-period structures

• Field data shows:– Foundation damping

ratios up to ~ 10-20%– Period lengthening up

to ~ 1.5– Foundation/ff Sa’s at

low period as low as ~0.5

Page 25: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

SSI Can Affect Retrofit Decisions

Page 26: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

SSI Can Affect Retrofit Decisions

Fixed-Base

Page 27: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

SSI Can Affect Retrofit Decisions

Flexible-Base

Page 28: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance Functions

),(),( 00 υωυ aciakk jjj +=

j = u (translation, x or z)θ (rocking)

uuu Kk α=S

uuuu V

rKc β=

θθθ α Kk =SVrK

c θθθθ β=

a0 = ωr/Vs ν = Poisson’s ratio

πfu Ar =

4 4 πθ fIr =

Two aspects of impedance function analysis: 1) Static stiffness (e.g., Kx)2) Dynamic modifiers (e.g., αx, βx)

Page 29: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance Functions

Static Stiffness (surface foundation)

ux GrKυ−

=2

8

( )3

138

θθ υGrK

−=

uz GrKυ−

=1

4

Circle: Rectangle:

Used in NEHRP Provisions

FEMA-356

Page 30: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance Functions

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎞⎜⎜⎝

⎛+=

θθθ r

eKKreKK Eu

UEU 21321Circle:

Rectangle:

Static Stiffness (embedment modification)

FEMA-356

Page 31: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles
Page 32: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance Functions

• Issue: What is the effective Vs for a non-uniform profile?

• Vs increase with depth– Increases foundation

stiffness– Impedes radiation damping

at large λ (low f) relative to halfspace

Dealing with nonuniform profilesVS

Depth

Page 33: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance Functions

• For stiffness, use

– Ze = 0.75ru or 0.75rθ–

• For damping, use (Vs)0

Dealing with nonuniform profilesVS

Depth

ttZ

V es =

( )∑ Δ=

is

i

Vztt

Δzi

Page 34: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

C. Inertial Interaction. Impedance FunctionsDealing with nonuniform profiles

0 1 2

a0 = ωr/Vs0

0.0

0.5

1.0

β u

0 1 2

a0 = ωr/Vs0

0.00

0.15

0.30

β θ

TRANSLATION ROCKING

Half., β=0.1Half., β=0

α=0.025

α=0.

23n=0.5

n=1

α=0.02

5

α=0.23

Half., β=0.1

Half., β=0

0 2 4 6 8G(z)/G0

6

4

2

0z/

r

α=0.23

α=0.025

0 2 4 6 8G(z)/G0

6

4

2

0

z/r

n=12/31/2

z

G(z) υ, ρ

2r

after Gazetas, 1991

BIAS

Page 35: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

1. Evaluate foundation radii••• Analysis of If must consider shear wall

configuration and potential rotational coupling between walls

2. Evaluate foundation embedment, e3. Evaluate effective height of structure, h4. Initial fixed base damping, βi (usually 5%)

πfu Ar =

4 4 πθ fIr =

C. Inertial Interaction. Typical Application

Page 36: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

5. Evaluate T/T using structure-specific model :

• Fixed-base period T

Displacement

Forc

e

1

k

C. Inertial Interaction. Typical Application

Page 37: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

5. Evaluate T/T using structure-specific model :

• Fixed-base period T• Flexible-base period

T• Calculate ratio T/T• Ductility correction:

Displacement

Forc

e

1keff

5.02

1~

1~

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎢⎢⎣

⎡−⎟⎟

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

TT

TT

s

f

eff

eff

μμ

C. Inertial Interaction. Typical Application

Page 38: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

6. Evaluate foundation damping βf based on Teff/Teff, h/rθ and e/ru∼

1 1.5 2Period Lengthening, T/T

0

10

20

30

Foun

datio

n D

ampi

ng, β

f(%)

e/ru = 0PGA > 0.2gPGA < 0.1g

h/rθ = 0.5

1.0

2.0

∼ 1 1.5 2Period Lengthening, T/T

0

10

20

30

Foun

datio

n D

ampi

ng, β

f (%

)

e/ru = 0.5PGA > 0.2 gPGA < 0.1g

h/rθ = 0.5

1.0

2.0

∼C. Inertial Interaction. Typical

application

Page 39: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

7. Evaluate flexible-base damping ratio, β0

8. Evaluate the effect on spectral ordinates of the change in damping from βi to β0

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

3

021 )100ln(~C

CCSS aaβ Eq. 3-7 and 3-8 of FEMA440

(assumes βi = 0.05)

( )30 ~effeff

if

TT

βββ +=

C. Inertial Interaction. Typical application

Page 40: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

160’-0”

100’

-0”

Plan

Elevation @ wall Section @ wall

Roof

2nd

1st

20’-0”

Footing 26’L x 3’B x 1.5’t

3’D

10’-0”typical

8” R/C wall – 20’Ltypical

Page 41: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

h uug uf

m

k,c h

kukθ

θ

θ

~TT

kk

khku

= + +12

θ

• Evaluate k• Evaluate ku• Derive kθ• Derive rθ from kθ

Page 42: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

• Analysis is conservative for:– High foundation aspect

ratios (a/b > 2)0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

c rx =

cθ,

x(β=0

)/(ρV

LaI x)

0.0 0.5 1.0 1.50.0

0.2

0.4

0.6

0.8

1.0

c ry =

cθ,

y(β=0

)/(ρV

LaI y)

(a) rocking around x-axis

(b) rocking around y-axis

L/B > 10

L/B = 5

range for L/B = 1 - 2and circles

L/B = 4-5

L/B = 3L/B = 2

range for L/B = 1and circles

Footing

2L

2B

L/B → ∞

y

x

( )V

VLa

s=−

3 41.

π υ

a BVS

0 =ω

Modified from: Dobry and Gazetas, 1986

Page 43: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

• Analysis is conservative for:– High foundation aspect

ratios (a/b > 2)– Deeply embedded

foundations (e/ru > 0.5)

a0

βu βθ

0 2 4 60

1

2

3

0 2 4 60

1

2

3

e/r = 1

1/2

0

1

1/2

e/r = 1

1

1/2

0

**

a rVS0 = ω

Modified from: Apsel and Luco, 1987

s

uuuu V

rKc β=sVrKc θθ

θθ β=

Page 44: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

• Analysis is conservative for:– High foundation aspect

ratios (a/b > 2)– Deeply embedded

foundations (e/ru > 0.5)

• Analysis unconservativefor:– nonuniform profiles, a0<1

0 1 2

a0 = ωr/Vs0

0.0

0.5

1.0

β u

0 1 2

a0 = ωr/Vs0

0.00

0.15

0.30

β θ

TRANSLATION ROCKING

Half., β=0.1Half., β=0

α=0.025

α=0.

23n=0.5

n=1

α=0.02

5

α=0.23

Half., β=0.1

Half., β=0

0 2 4 6 8G(z)/G0

6

4

2

0

z/r

α=0.23

α=0.025

0 2 4 6 8G(z)/G0

6

4

2

0

z/r

n=12/31/2

z

G(z) υ, ρ

2r

BIAS

after Gazetas, 1991

0 2 4 6 8G(z)/G0

6

4

2

0

z/r

α=0.23

α=0.025

0 2 4 6 8G(z)/G0

6

4

2

0

z/r

n=12/31/2

z

G(z) υ, ρ

2r

Page 45: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations• If distributed shear walls,

must consider coupling of wall rotations

• Analysis is conservative for:– High foundation aspect

ratios (a/b > 2)– Deeply embedded

foundations (e/ru > 0.5)• Analysis unconservative

for:– nonuniform profiles, a0<1– large impedance contrast at

depth; Vs2 ≥ 2 × Vs1

a

DS

vs1

vs2

ρ1

ρ2

Page 46: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction

• Contributions from: – Base-slab averaging– Foundation

embedment

after Veletsos et al., 1997

Page 47: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction.Base Slab Averaging

• Existing theoretical models– User-specified

incoherence parameter, κ

– Rigid foundation, soil is uniform halfspace

• Result is foundation / free-field transfer function, not RRS 2

22

,0 sin~

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ev

rs

e

bb

Vb

a ακω

after Veletsos and Prasad, 1989; Veletsos et al., 1997

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

Tran

sfer

Fun

ctio

n A

mpl

itude

Disk

a/b=1

a/b=1/4, 4

αv = 0

0a~

Page 48: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Calibration against field data

κ = -0.037 + 7.4E-04 Vs (m/s)

0 200 400 600Vs (m/s)

0.00

0.20

0.40

0.60

κa

Surface foundationsShallowly emb.

σ = 0.55

90% confidence intervals

0

1

2

3

4

Ampl

itude

(|H

3|)

1

κ = 0.11

0 5 10 15 20 25Frequency (Hz)

Kim and Stewart, 2003

Page 49: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Calibration against field data

κ = -0.037 + 7.4E-04 Vs (m/s)

0 200 400 600Vs (m/s)

0.00

0.20

0.40

0.60

κa

Surface foundationsShallowly emb.

σ = 0.55

90% confidence intervals

Kim and Stewart, 2003

222

,0 sin~

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ev

rs

e

bb

Vb

a ακω

rs

eo V

ba,2

~ κω=

2

1

2

1

,0 222

~nnb

VnVnb

Vb

a e

s

se

rs

e ωωκω=≈=

Site Class 0.1 0.4 0.8A 1.00 1.00 1.00B 1.00 0.97 0.95C 0.97 0.87 0.77D 0.95 0.71 0.32E 0.77 0.22 *F * * *

Peak Ground Acceleration, PGA (g)

Note: Use straight line interpolation for intermediate values of PGA* = should be estimated from site-specific analysis

Shear Wave Velocity Reduction Factor, n2

Page 50: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction.Embedment Effects

Elsabee and Morray (1977) and Day (1978):• Evaluated transfer functions for vertically incident,

coherent waves• Developed simple model

,

0 2 4 6a0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

rθFI

M/u

g

0 2 4 6a0=ωr/Vs

0.0

0.2

0.4

0.6

0.8

1.0

1.2

u FIM

/ug

ApproximationHalfspaceFinite soil layer

e/r = 0.5

Translation Rocking

Page 51: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction.Embedment Effects

Elsabee and Morray (1977) and Day (1978):• Evaluated transfer functions for vertically incident,

coherent waves• Developed simple model

,

0 2 4 6a0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

rθFI

M/u

g

0 2 4 6a0=ωr/Vs

0.0

0.2

0.4

0.6

0.8

1.0

1.2

u FIM

/ug

ApproximationHalfspaceFinite soil layer

e/r = 1

Translation Rocking

Page 52: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction.Transfer Function to RRS

Veletsos and Prasad (1989):• Evaluated RRS at 2%

damping for conditions where transfer function amplitude (TFA) known

• Result:– RRS ≈ TFA for T > 0.2 s– RRS ≈ TFA @ T = 0.2 s for

T < 0.2 s

• Result valid for free-field spectrum shown to right Power spectral density of ff motion

Source: Veletsos and Prasad (1989)

Page 53: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

D. Kinematic Interaction.Transfer Function to RRS

0.01 0.1 1 10 Period (s)

0

0.2

0.4

0.6

0.8

1

1.2

Tran

fer F

unct

ion

Am

plitu

de, R

RS

CAP_fn (Tm = 0.51s)Transfer FunctionRRS, 2% dampingRRS, 5%RRS, 10%RRS, 20%

2 4 6 8 10 12Time (s)

-0.4

-0.2

0

0.2

0.4

Acc

eler

atio

n (g

)

RecordedFiltered

0.01 0.1 1 10 Period (s)

0

0.2

0.4

0.6

0.8

1

1.2

Tran

fer F

unct

ion

Am

plitu

de, R

RS

NWH_fn (Tm = 0.70s)Transfer FunctionRRS, 2% dampingRRS, 5%RRS, 10%RRS, 20%

2 4 6 8 10 12Time (s)

-0.8

-0.4

0

0.4

0.8

Acc

eler

atio

n (g

)

RecordedFiltered

Page 54: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Procedure for KI

• Evaluate effective foundation size, be = √ab

• Evaluate embedment depth, e

e

a

b

Page 55: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Procedure for KI

• Evaluate RRS from base slab averaging, RRSbsa

0 0.2 0.4 0.6 0.8 1 1.2Period, T (s)

0.4

0.5

0.6

0.7

0.8

0.9

1

Foun

datio

n/Fr

ee-F

ield

RR

SSimplified Model

be = 65 ftbe = 130 ftbe = 200 ftbe = 330 ft

Page 56: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Procedure for KI

• Evaluate RRS from embedment: RRSe

• RRS = RRSbsa× RRSe

0 0.4 0.8 1.2 1.6 2Period, T (s)

0

0.2

0.4

0.6

0.8

1

1.2

Foun

datio

n/Fr

ee-F

ield

RR

SSite Classes C and D

e = 10 fte = 20 fte = 30 ft

C

D

Page 57: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

Limitations of KI Procedure

• Neglect KI effects for soft clay sites (NEHRP E)• Firm rock sites (i.e., NEHRP A and B):

– Neglect embedment effects– Based slab averaging model conservative (over-

estimates RRS)• Base slab averaging model not applicable for

– Flexible foundations (non-interconnected)– Pile-supported foundations with slab-soil gap

Page 58: Overview of Soil-Structure Interaction Principles · Overview of Soil-Structure Interaction Principles Jonathan P. Stewart University of California, Los Angeles

ReferencesApsel, R.J. and Luco, J.E. (1987). “Impedance functions for foundations embedded in a layered

medium: an integral equation approach,” J. Earthquake Engrg. Struct. Dynamics, 15(2), 213-231.Day, S.M. (1978). “Seismic response of embedded foundations,” Proc. ASCE Convention, Chicago,

IL, October, Preprint No. 3450.Dobry, R. and Gazetas, G (1986). “Dynamic response of arbitrarily shaped foundations,” J. Geotech.

Engrg., ASCE, 112(2), 109-135.Elsabee, F. and Morray, J.P. (1977). “Dynamic behavior of embedded foundations,” Rpt. No. R77-33,

Dept. of Civil Engrg., MIT, Cambridge, Mass.FEMA-356: Prestandard and commentary for the seismic rehabilitation of buildings, Federal

Emergency Management Agency, Washington, D.C., 2000. FEMA-440: Improvement of Nonlinear Static Seismic Analysis Procedures, Department of Homeland

Security, Federal Emergency Management Agency, June, 2005. Gazetas, G. (1991). Chapter 15: Foundation Vibrations, Foundation Engineering Handbook, H.-Y.

Fang, ed., 2nd Edition, Chapman and Hall, New York, NY.Kim, S. and Stewart, J.P. (2003)."Kinematic soil-structure interaction from strong motion recordings,"J.

Geotech.. & Geoenv. Engrg., ASCE, 129 (4), 323-335.Nikolaou, S., Mylonakis, G., Gazetas, G., and Tazoh, T. (2001). “Kinematic pile bending during

earthquakes: analysis and field measurements,” Geotechnique, 51(5), 425-440. Veletsos, A.S. and Verbic, B. (1973). “Vibration of viscoelastic foundations,” J. Earthquake Engrg.

Struct. Dynamics, 2(1), 87-102.Veletsos, A.S., Prasad, A.M., and Wu, W.H. (1997). “Transfer functions for rigid rectangular

foundations,” J. Earthquake Engrg. Struct. Dynamics, 26 (1), 5-17.Veletsos, A.S. and Prasad, A.M. (1989). “Seismic interaction of structures and soils: stochastic

approach,” J. Struct. Engrg., ASCE, 115(4), 935-956.