Overview of Soil-Structure Interaction Principles [PDF]

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Overview of Soil-Structure Interaction Principles

Jonathan P. Stewart University of California, Los Angeles

Overview A. B. C. D.

Introduction General methods of analysis Inertial interaction Kinematic interaction

A. Introduction Response dictated by interactions between: • Structure • Foundation • Underlying soil/rock System analysis evaluates response given freefield motion, ug No SSI when___________

SSI effect =______________

A. Introduction. Three critical aspects of SSI • Inertia → base shear (V) and moment (M)

F=ma

M V

A. Introduction. Three critical aspects of SSI • Inertia → base shear (V) and moment (M) • V → relative foundation/free-field displacement (uf)

V

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

A. Introduction. Three critical aspects of SSI • uf, θf → foundation damping

A. Introduction. Three critical aspects of SSI uf

• uf, θf → foundation damping • Radiation damping – foundation acts as wave source

p

p s θf

s

s p

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

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

A. Introduction. Three critical aspects of SSI 2. Kinematic interaction •

Incoherent ground motions → base slab averaging

u1

u3

u2

Sa

T

A. Introduction. Three critical aspects of SSI 2. Kinematic interaction •

•

Incoherent ground motions → base slab averaging Ground motion reductions with depth

u1

u2

Sa

T

A. Introduction. Three critical aspects of SSI 3. Foundation deformations •

Loads from superstructure inertia

A. Introduction. Three critical aspects of SSI 3. Foundation deformations • •

Loads from superstructure inertia Deformations applied by soil

Beyond scope of current presentation Nikolaou et al. (2001)

B. General Methods of Analysis • Direct approach – Full modeling of soil, foundation, structure – Propagate waves through system

Beyond scope of current presentation

B. General Methods of Analysis • Direct approach • Substructure approach Focus of this seminar

C. Inertial Interaction • Springs used to represent soilfoundation interaction • Complex-valued – Real part represents stiffness – Imaginary part related to damping Combination of real and complex parts comprises “Impedance function”

C. Inertial Interaction • Springs used to represent soilfoundation interaction • Complex-valued • If rigid foundation, simplifies to: – 3 springs for 2D system – 6 springs for 3D system k j = k j (a0 ,υ ) + iωc j (a0 ,υ )

kθ kz

kx

C. Inertial Interaction. Effects on System Behavior • Concepts of period lengthening and foundation damping – System period ~ k fixed k fixed h 2 T = 1+ + T kx kθ

– System damping β β0 = β f + ~ i

uf hθ u

ug

(T T )

3

Foundation damping factor

m

θ

K*fixed, c kx

kθ

h

C. Inertial Interaction. Effects on System Behavior 30

β=0 h/r = 1

12

β~ζ f0 (%)

8 h/r = 2

4 0 0.0

h/r = 4 0.1

0.2

0.3

0.4

h/(vs ×T)

Hysteretic soil damping

Foundation Damping, βf(%)

16

β = 0.1

e/ru = 0 PGA > 0.2g PGA < 0.1g 20

h/rθ = 0.5 1.0

10 2.0 0 1

1.5 Period Lengthening, T/T

∼

20

2

C. Inertial Interaction. Effects on Base Shear

0.6

Spectral Acceleration (g)

• Force-based procedure • SSI affects design spectral ordinate • Usually not considered for design of new buildings

(a) 0.5 0.4 0.3

0

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

T, βi = Fixed-base period, damping ratio (neglects SSI effects) ~ S

a

Sa

Sa ~ S

0.2 0.1

∼ ∼ T, β

T 0

~ T

βi a

T

~ T

1

Period (s)

β0 2

C. Inertial Interaction. Effects on Displacement-Based Pushover Analysis • 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

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

Sa

Performance point Pushover curve

Reduced seismic demand (SFSI + extra str. damping)

Sd

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

SSI Can Affect Retrofit Decisions

SSI Can Affect Retrofit Decisions

Fixed-Base

SSI Can Affect Retrofit Decisions

Flexible-Base

C. Inertial Interaction. Impedance Functions k j = k j (a0 ,υ ) + iωc j (a0 ,υ ) a0 = ωr/Vs j =

ku = α u K u kθ = α θ K θ

ν = Poisson’s ratio

u (translation, x or z) θ (rocking) K u ru cu = β u VS K r cθ = β θ θ θ VS

ru =

Af π

rθ = 4 4 I f π

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

C. Inertial Interaction. Impedance Functions

Static Stiffness (surface foundation) Circle:

Rectangle:

8 Kx = Gru 2 −υ 8 Kθ = Grθ3 3(1 − υ )

4 Kz = Gru 1−υ Used in NEHRP Provisions FEMA-356

C. Inertial Interaction. Impedance Functions

Static Stiffness (embedment modification) Circle:

Rectangle:

FEMA-356

(K U )E

⎛ 2 e = K U ⎜⎜1 + ⎝ 3 ru

⎞ ⎟⎟ ⎠

(K θ )E

⎛ e = K θ ⎜⎜1 + 2 rθ ⎝

⎞ ⎟⎟ ⎠

C. Inertial Interaction. Impedance Functions

Dealing with nonuniform profiles VS

• Issue: What is the effective Vs for a nonuniform profile? • Vs increase with depth – Increases foundation stiffness – Impedes radiation damping at large λ (low f) relative to halfspace

Depth

C. Inertial Interaction. Impedance Functions

Dealing with nonuniform profiles VS

• For stiffness, use Ze Vs = tt – Ze = 0.75ru or 0.75rθ – Δzi tt = ∑ (Vs )i

• For damping, use (Vs)0

Δzi Depth

C. Inertial Interaction. Impedance Functions

Dealing with nonuniform profiles G(z)/G0 2 4 6

0

8

. , β=

z/r

ROCKING

0. 1

0

02

5

0.15 Ha

0.

1

3

α=

0 .2

α= 0.0

βθ

.5 =0

n=

βu

1

BIAS

25 n

2/3

=0.

α=

0 0.

1/2

0.30

Half., β=0 0.5

n=1

f. , β H al

H a lf

4 6

TRANSLATION

1.0

2

3

6

z

2 0. α=

α=0.025

4

8

0 G(z) υ, ρ

2 z/r

0

2r

0

G(z)/G0 2 4 6

0. α=

1

a0 = ωr/Vs0

2

0.00

0

β lf.,

=0

23

1

2

a0 = ωr/Vs0

after Gazetas, 1991

C. Inertial Interaction. Typical Application 1. Evaluate foundation radii • • •

ru =

Af π

rθ = 4 4 I f π

Analysis of If must consider shear wall configuration and potential rotational coupling between walls

2. Evaluate foundation embedment, e 3. Evaluate effective height of structure, h 4. Initial fixed base damping, βi (usually 5%)

C. Inertial Interaction. Typical Application ∼

5. Evaluate T/T using structure-specific model : Fixed-base period T

Force

•

k 1 Displacement

C. Inertial Interaction. Typical Application ∼

• •

Fixed-base period T Flexible-base period ∼ T ∼ Calculate ratio T/T Ductility correction:

• • ~ Teff Teff

⎧ ⎛ μ ⎞ ⎡⎛ T~ ⎞ 2 ⎤ ⎫ ⎪ ⎪ f ⎜ ⎟ ⎟ ⎜ ⎢ ⎥ −1 ⎬ = ⎨1 + ⎜ ⎟ ⎜ ⎟ ⎥⎦ ⎪ ⎪⎩ ⎝ μ s ⎠ ⎢⎣⎝ T ⎠ ⎭

0 .5

Force

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

keff 1 Displacement

C. Inertial Interaction. Typical application 6. Evaluate foundation damping βf based on ∼ Teff/Teff, h/rθ and e/ru e/r = 0.5 u

PGA > 0.2 g PGA < 0.1g 30 Foundation Damping, βf (%)

e/ru = 0 PGA > 0.2g PGA < 0.1g 20

h/rθ = 0.5 1.0

10 2.0 0 1.5 Period Lengthening, T/T

∼

1

2

h/rθ = 0.5 20

1.0

10

2.0

0 1

1.5 Period Lengthening, T/T

∼

Foundation Damping, βf(%)

30

2

C. Inertial Interaction. Typical application 7. Evaluate flexible-base damping ratio, β0 β0 = β f + ~

(T

eff

βi Teff

)

3

8. Evaluate the effect on spectral ordinates of the change in damping from βi to β0 ⎛ C1 − C2 ln(100β 0 ) ⎞ Eq. 3-7 and 3-8 of FEMA440 ~ ⎟⎟ Sa = Sa ⎜⎜ C3 ⎝ ⎠ (assumes βi = 0.05)

Limitations 160’-0”

100’-0”

• If distributed shear walls, must consider coupling of wall rotations

8” R/C wall – 20’L typical

Plan 20’-0” Roof 10’-0” typical 2nd 1st

3’D Footing 26’L x 3’B x 1.5’t

Elevation @ wall

Section @ wall

Limitations • If distributed shear walls, must consider coupling of wall rotations

• Evaluate k • Evaluate ku • Derive kθ • Derive rθ from kθ uf h θ

ug

~ T k kh2 = 1+ + T ku kθ

u m

θ k,c

ku

kθ

h

Limitations x y

1.0

crx = cθ,x(β=0)/(ρVLaIx)

– High foundation aspect ratios (a/b > 2)

Footing

2B

0.8

VLa =

3.4Vs π(1 − υ) L/B > 10 L/B = 5

0.6

0.4

range for L/B = 1 - 2 and circles 0.2

(a) rocking around x-axis 0.0 0.0

0.5

1.0

1.5

1.0

cry = cθ,y(β=0)/(ρVLaIy)

• If distributed shear walls, must consider coupling of wall rotations • Analysis is conservative for:

2L

0.8

L/B = 4-5

L/B→ ∞

L/B = 3 L/B = 2 0.6

0.4

range for L/B = 1 and circles

0.2

(b) rocking around y-axis 0.0 0.0

0.5

ωB a0 = VS

1.0

1.5

Modified from: Dobry and Gazetas, 1986

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)

3

3

2

*

βu

1/2

e/r = 1

2

e/r = 1

*

βθ

1

1

1/2

1

1 1/2

0

0

0

0

2

4

6

a 0 = ωr V

S

K u ru cu = β u Vs

0

0

2

a0

4

Kθ rθ cθ = βθ Vs

Modified from: Apsel and Luco, 1987

6

Limitations 8

2r

0

z/r

6

z

BIAS

., β=

n=1 1/2

2/3

ROCKING

0. 1

=0. 1

0.15

α=

0 .2 3 n= 1

0. 02

5

βθ

5 02 0. 0.5 = α n=

α=

βu

4

0.30

Half., β=0 0.5

0 α=

0.0

0

8

f., β

Half

G(z)/G0 4 6

2

6

TRANSLATION

1.0

2

0 G(z) υ, ρ

2 4

0

Ha l

– nonuniform profiles, a0 2) – Deeply embedded foundations (e/ru > 0.5)

0

z/r

• If distributed shear walls, must consider coupling of wall rotations • Analysis is conservative for:

1

2

a0 = ωr/Vs0

0.00

0

β=

0

3 .2

1

a0 = ωr/Vs0

after Gazetas, 1991

lf., Ha

2

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 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)

D. Kinematic Interaction. Transfer Function to RRS Recorded Filtered

Acceleration (g)

Acceleration (g)

0.4 0.2 0 -0.2

0.4 0 -0.4 -0.8

-0.4 2

4

6 8 Time (s)

10

2

12

Tranfer Function Amplitude, RRS

1 0.8 0.6 CAP_fn (Tm = 0.51s) Transfer Function RRS, 2% damping RRS, 5% RRS, 10% RRS, 20%

0.4 0.2 0 0.01

4

6 8 Time (s)

10

12

1.2

1.2 Tranfer Function Amplitude, RRS

Recorded Filtered

0.8

0.1

Period (s)

1

10

1 0.8 0.6 NWH_fn (Tm = 0.70s) Transfer Function RRS, 2% damping RRS, 5% RRS, 10% RRS, 20%

0.4 0.2 0 0.01

0.1

Period (s)

1

10

Procedure for KI • Evaluate effective foundation size, be = √ab

a

b

• Evaluate embedment depth, e

e

Procedure for KI Foundation/Free-Field RRS

• Evaluate RRS from base slab averaging, RRSbsa

1 0.9 0.8 0.7

Simplified Model be = 65 ft

0.6

be = 130 ft be = 200 ft

0.5

be = 330 ft

0.4 0

0.2

0.4 0.6 0.8 Period, T (s)

1

1.2

Procedure for KI

• RRS = RRSbsa × RRSe

Foundation/Free-Field RRS

• Evaluate RRS from embedment: RRSe

1.2 C

1 0.8

D

0.6

Site Classes C and D e = 10 ft e = 20 ft e = 30 ft

0.4 0.2 0 0

0.4

0.8 1.2 Period, T (s)

1.6

2

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 (overestimates RRS)

• Base slab averaging model not applicable for – Flexible foundations (non-interconnected) – Pile-supported foundations with slab-soil gap

References Apsel, 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.