EERI TechnicalSeminar Series

Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations

New Tools for Structural and Geotechnical Practitioners on the Horizon

Tara C. Hutchinson

2

Collaborative Project

UCD (Kutter), UCLA (Stewart), UCSD (Hutchinson), USC (Martin)Graduate Students: Rosebrook, Phalen, Gajan, Raychowdhury, Harden, ChangSupport provided by PEER

3

Modes of Foundation Deformation

L

D

H

Induced earthquake motion

Super structure

θ

Flexible foundation L = length of footing

B = width of footingH = thickness of footingD = depth of embedment

Vertical mode

Sliding mode

Rocking mode

u(t)

θ(t)f

s(t)

Initial position of footing top

f

4

Rocking: Base HingingShear walls fixed and perfectly hinged at the baseHinges at base decrease moment, shear, and drift to wall

Alavi and Krawinkler (2004)Fixed Wall Hinged Wall

5

Reduction in kinetic energy by the impact:

2

0

2

)]2cos1([ α−−=I

mRIr

•Energy dissipated by rocking block = f(amplitude, frequency) of the rocking motion

•In 1963, no known method to design a rocking structure with reliable stability.

Early Work

Housner (1963)

6

Experimental validation of Housner’s workTheoretical “r” in good agreement with average experimental value.

Rocking also generates impact energy that is transferred back to structure Development of simple method to predict maximum displacement due to rocking

Early Work

Priestley et al. (1978)

7

Rocking: Structural Solutions

Filiatrault et al. (1992), Anderson (2003)Kurama et al. (1999), Priestley et al. (1999)Taghdi et al. (2000)Holden et al. (2003)Bonelli and Holmberg (2004)Marko et al. (2004)Ajrab et al. (2004)Toranzo-Dianderas et al. (2004)

8

e.g. Draped Tendons

Wall remains protected from damage while tendons yield

Energy dissipated through tendons

Ajrab et al. (2004)

9

e.g. Mechanical Base Dampers

Steel dampers

Shake table tests on ¼-scale masonry wall modelDampers provided local energy dissipation directly at base ends of wallLittle to no damage observed in wall with base dampers

Toranzo-Dianderas et al. (2004)

10

Key Ideas: Foundations

Soil-foundation interface can provide the key features of:

Rocking can provide valuable dissipation of energy during seismic loading (due to bearing capacity mobilization)Re-centering can reduce deformation demands (due to gap formation and closing)

11

Simulations - Previous WorkSDOF & MDOF systems w/ lumped massesRigid, 2-element, Winkler system of springsLinear-elastic springs

Chopra & Yim; Yim and Chopra (1985)

12

Simulations - Previous WorkElastic Winkler springs below nonlinear (degrading) shear wall structureTwo different GM types (long duration & short impulsive motion)

Nakaki & Hart (1987)

13

Simulations – Previous WorkApplication to Bridge modelingComposite of parallel springsCombined w/ nonlinear

column behavior

Fenves (1997)

14

“Big Picture” Question

Under what conditions should foundation rocking be avoided, allowed, or encouraged in building design?

Need methods to quantify the benefits (e.g. structural demand reduction, energy available at footing)Need methods to quantify the consequences (e.g. permanent and cyclic settlement, rotations)

15

Research ProgramPhysical Model Testing

1-g experiments (Bartlett, Weissing, Negro)Centrifuge experiments

Wall-foundation; 8 series of tests (Gajan, Rosebrook, Kutter): KRR and SSG seriesBuilding-Foundation; 1 series/two bldg-fnds (Chang, Thomas): JMT series

Numerical ModelingMacro-element modeling (UCD)Winkler-based modeling (UCSD)

16

Centrifuge (UC Davis)

Our tests: N=20Lm= (1/20)*Lp ; σm= σp

Center for Geotechnical Modeling at UC Davis: 9.1-m radius

centrifuge

d σ = ρ. g. d

Prototype

d/N σ = ρ. (N.g). d/N= ρ. g. d

Model (N-g)

Scaling in centrifuge:

17

Wall-Foundation Experiments

LA1 LA2

LB4

LB3

LB1LB2

LC4

LC3

LC1LC2

C2

C2

C2

Station A Station B Station C

beams continue for length of box

Z

y

ACTUATOR

ACTUATOR

200.0Nevada Sand

KRR and SSG Series experimentsRosebrook & Kutter (2002) and Gajan et al. (2003)

18

Tests on clay and sandVarying embedment (0, B, 3B)Model wall-footing systems with various precompression loads(“FSv = 3-15”)

Planar wall-footing model

Two wall-footing models

loaded in parallel

Wall-Foundation Experiments

19

A word about definitions…Classical terminology in Geotech Eng: Factor of Safety

…against …<bearing, overturning, sliding> failuree.g. FSv, FSot, FSsBut…there is little association with “safety” in this definition

Effectively analogous to axial stress in a column: eg 10%f’cAgWe’ll refer to this as a degree of pre-compression eg Qult/Qapplied (Qu/Qa)

Defined for any mode (axial, shear, moment)

20

Physical Observations

21

Findings: Footing ResponseMoment-rotation plots show good energy dissipation but result in settlementKθ and s = f(soil type, soil density, footing size, aspect ratio, Df , Qu/Qa, loading)

-0.08 -0.04 0 0.04 0.08Rotation (rad)

-400

-200

0

200

400

Mom

ent (

KN

m)

-0.08 -0.04 0 0.04 0.08Rotation (rad)

-160

-120

-80

-40

0

40

Settl

emen

t (m

m)

22

Findings: Settlement-Rotation

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Half Amplitude of Cyclic Rotation, θ [rad]

Nor

mal

ized

Set

tlem

ent P

er C

ycle

, Uv/c

ycle

FSv = 2.0, Dr = 45% (TRISEE83)FSv = 2.0, Dr = 93% (Weissing)FSv = 3.4, Dr = 80% (SSG02)FSv = 3.4, Dr = 80% (SSG02)FSv = 4.0, Dr = 80% (SSG03)FSv = 4.1, Dr = 60% (KRR02)FSv = 5.3, Dr = 80% (SSG02~Dynamic)FSv = 6.4, Dr = 80% (SSG03~Dynamic)FSv = 6.8, Dr = 80% (SSG02)FSv = 8.2, Dr = 80% (SSG03)FSv = 9.6, Dr = 80% (SSG02)

2.0 < FSv < 3.5

3.5 < FSv < 7.0

7.0 < FSv

Increasing Dr

23

InelasticBeams w/

Fiber Hinges

Rigid ElasticBeam-Column

Spring Array

G.S.

Prototype(Dashed)

Nonlinear Beam-Column Elements

Elements

(when occurs)

Prototype R/C Structure

(units in meters)Target Tn ~ 0.5s;

(Qu/Qa)govern = 5

Idealized Finite Element Model

Dense dry sand

Building-Foundation Tests2.54 7.62 7.62

2.84 1.00 1.00

G.S.

R/C Shear

Isolated R/CStrip Footing

Wall

Isolated R/CSpread Footings

R/C Beam-Column

9.53

1.00

4.76Members

4.76

Ductile Beam-Column Joint

24

Slow cyclic lateral loading (inertial input)Dynamic loading (base excitation)Earthquake loading (base excitation)

Dr=85% dense dry sand

Station A

Station B

Plan view of Soil Box

Continuous out-of-plane guide

Continuous low-friction out-of-plane guide

extension arm for actuator support

Building-Foundation Tests

25

One Bay Model

Square Footing

Shearwall

Strip Footing

Hollow steel columns

Beam-column fuses

Mass-blocks

Beam-wall fuses

Hollow steel beams 4

86 m

m

(9.5

3 m

)

508 mm (10.1 m)

Ductile fuse: full bridge configuration

of 4 strain gages

51 mm0.1 Lbeam

26

Two Bay Model

Instr: load cell, strain gages, accelerometers, linear pots

Shearwall

Strip Footing

Hollow steel columns

Beam-column fuses

Mass-blocks

Beam-wall fuses

Square Footing

Hollow steel beams

486 m

m

(9.5

3 m

)

889 mm (17.8 m)

27

Two Bay in Centrifuge

Actuator arm

Soil thickness = 4 m (prototype)

Loading plane

28

One Bay Testing Summary

396 mm / 4.16 % HSC8

240 mm / 2.52 % HSC7

116 mm / 1.22 % HSC6

55 mm / 0.58 % HSC50.93 g D428 mm / 0.29 % HSC40.65 g D312 mm / 0.13 % HSC30.20 g D2 17 mm / 0.18 % HSC20.09 g D1 19 mm / 0.20 % HSC1

Base acc (g) NameAve Max Disp/Drift Ratio (%)

Name

29

Physical Observations

30

Findings: Global Response

-300 -200 -100 0 100Displacement (mm)

-400-200

0200400

Forc

e (k

N)

-3 -2 -1 0 1Total Drift (%)

-4

0

4

C (g

)

wall side

column side-380 -360 -340 -320 -300Displacement (mm)

0

10

20

30

Forc

e (k

N)

-0.4 -0.2 0 0.2 0.4Total Drift (%)

-0.100.10.20.30.4

C (g

)

wall side

column side

(a) (b)

Test D3PA = 0.65g

Test HSC4γ = 0.3%

One-bay Model

31

Findings: Footing Response -0.4 -0.2 0 0.2 0.4 0.6

Rotation (deg)

-2000

-1500

-1000

-500

0

500

Mom

ent (

kN m

)

-1.6 -1.2 -0.8 -0.4 0Rotation (deg)

-200

0

200

400

600

Mom

ent (

kN m

)

Strip footing Square footing

-160-120 -80 -40 0 40Base Disp (mm)

-200-100

0100200300400

She

ar (k

N)

-160 -80 0Base Disp (mm)

-300

-200

-100

0

100

She

ar (k

N)

0 200 400 600 800Axial force (kN)

-100

-80

-60

-40

-20

0

Set

tlem

ent (

mm

)

0 200 400 600 800Axial force (kN)

-80

-60

-40

-20

0

Set

tlem

ent (

mm

)

columnside

columnside

columnside

columnside

One-bay Model

Test D3PA = 0.65g

32

Findings: Energy DissipationOne Bay Dynamic: Moment-Rotation

% of Moment Rotation Energy

0%

20%

40%

60%

80%

100%

D 1 D 2 D 3 D 4

Test name

Square FootingStrip Footing

Two Bay Dynamic: Moment-Rotation% of Moment-Rotation Energy

0%

20%

40%

60%

80%

100%

D 5 D 6 D 7 D 8 D 9

Test name

Exterior Sq FootingInterior Sq FootingStrip Footing

One-bay Model

Two-bay Model

33

Findings: Energy Dissipation

0 0.5 1 1.5 2 2.5Max Drift (%)

60

70

80

90

100

EΣf

ootin

gs/E

Σtot

al (%

)

One BayTwo Bay

sQvVMfootings EEEE −−− ++=∑ θ (1)

)(∑+∑=∑ −θMjointsfootingstotal EEE (2)

34

Summary of Physical Model Tests

Previous (1g) and recent centrifuge tests substantiate and assist in quantifying the benefits and consequences of rocking shallow foundations; for the subset of structure-foundation modelsProvide a robust set of data for calibration of numerical models

35

Numerical Modeling

Macro-element modeling (UCD)Winkler-based (design-oriented) modeling (UCSD)All modeling conducted in OpenSEES(PEER developed platform)Sensitivity Studies & Model comparisons

36

Macro-element Model

macro-element

Considers foundation and surrounding soil as a single macro-element

Constitutive model that relates the forces (V, H, M) and displacements (s, u, θ) acting at the base center point of the footing

37

38

Macro-Element Model

39

Nor

mal

ized

Mom

ent [

F M =

M/(V

ULT

.L)]

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Normalized Vertical Load [FV = V/VULT]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Nor

mal

ized

She

ar [F

H =

H/V

ULT

]

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

FM/FH = 1.75

FM/FH = 0.42

FM/FH = 1.25

FM/FH = 1.75

FM/FH = 1.25

FM/FH = 0.42

Cremer et al. (2001)

Houlsby and Cassidy (2002)

Nova and Montrasio (1991)

Failure Envelopes

40

Element - ZeroLengthSection

Section - SoilFootingSection

-ndm 2 –ndf 3

Node i (0, 0)

Node j (0, 0)

Fixed

Free

section SoilFootingSection -secID -FS -Vult -L -Kv -Kh -deltaLelement ZeroLengthSection -eleID -iNode -jNode -secID <-orientation>

i

j

Vult – Ultimate vertical loadV – Self weight of the structureL – Length of the footingKv – Initial vertical stiffnessKh – Initial horizontal stiffness

OpenSEES Implementation

41

Experimental-Numerical Comparison

(Qu/Qa = 2.5)

42

• Series of individual uncoupled springs• For applied H-M-V, ensemble of springs calculates:

• Sliding displacement• Rotation• Settlement

• Shear-vertical responses uncoupled• Gap, closure, damping defined by springs in series

y

z

θ

Q-z springs P-y spring

T-y spring

Winkler-based Model

Near-StructurePlastic Response

Far-StructureElastic Response

Drag

ElasticDamper

Closure

Plastic

Beam Nodes

Fixed Nodes

43

Winkler-based Model• Vertical resistance from non-linear Qz springs• Horizontal resistance is a combination of

• Nonlinear Py for passive earth pressures• Nonlinear Ty for base sliding

• Mesh generator implementation• All springs based on Boulanger et al., 2000• Previously calibrated to pile test data

Variable Lateral Springs Spacing

VerticalStiffness

Distribution

qiPressure Distribution

Lend

Soil PropertiesShear Modulus, GPoisson's Ratio, υFriction Angle, φ'

KXkend

Lmid

kmid

x

CL

KX

KZ

Kθ

44

q0= 2. Cr. qultElastic portion:

Plastic portion:

}Qult = ultimate bearing capacity Kel = initial elastic stiffness (vertical)z50 = displacement at 50% of Qultn, c, Cr = parameters defining the shape of the Q-z curve in plastic region - hard-coded in the material model

- User Inputs

q0= load at the start of the plastic loading cycle

Cr = q/qult when plastic yielding first occurs in virgin loading

-0.8 -0.4 0 0.4 0.8Normalized vertical settlement (s/z50)

-1-0.8-0.6-0.4-0.2

00.2

Nor

mal

ized

ver

tical

load

(Q/Q

ult)

Winkler-based Model: q-z

n

opoultult

zzzczcqqqq

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−+⋅

⋅−−=

50

50)(

Vertical nonlinear springs; providing vertical and rocking resistance (aka “q-z” in pile analysis, for tip resistance)

45

Winkler-based Model: p-yHorizontal nonlinear springs; accounting for passive resistance in front of the embedded footing (aka “p-y” in pile analysis, also lateral resistance)

}Pult = ultimate bearing capacity Kel = initial elastic stiffness (vertical)z50 = displacement at 50% of Pultn, c, Cr = parameters defining the shape of the P-y curve in plastic region - hard-coded in the material model

- User Inputs

Cr = p/pult when plastic yielding first occurs in virgin loading

-20 -10 0 10 20Normalized Lateral Displacement, u/y50

-1

-0.5

0

0.5

1

Nor

mal

ized

Lat

eral

Lo

ad, H

/pul

t p0= 2. Cr. pultElastic portion:

Plastic portion:

p0= load at the start of the plastic loading cycle

n

opoultult

yyycycpppp

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−+⋅

⋅−−=

50

50)(

46

-20 -10 0 10 20Normalized Lateral Displacement, u/z50

-1

-0.5

0

0.5

1

Nor

mal

ized

Lat

eral

Lo

ad, H

/t ult

tult = ultimate lateral capacity (friction) Kel = initial elastic stiffness (lateral)y50 = displacement at 50% of tultn, c, Cr = parameters defining the shape of the T-y curve in plastic region - hard-coded in the material model

Winkler-based Model: t-y

t0= 2. Cr. tultElastic portion:

Plastic portion:

t0= load at the start of the plastic loading cycle

n

opoultult

yyycyctttt

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−+⋅

⋅−−=

50

50)(

Horizontal nonlinear springs; accounting for frictional resistance between footing and soil (aka “t-z” in pile analysis, skin resistance)

47

0 4 8 12Normalized settlement (z/z50)

0

0.4

0.8

1.2

Nor

mal

ized

load

(Q/Q

ult)

Strip FootingRegressed Qz curveKRR01 # S2KRR01 # S25KRR01 # S28KRR01 # S31Regressed Qz curve (m+/ - s)

General footing condition

Strip SquareCentrifuge tests Full-scale testsL/B = 3.5-6.6 B = 1-3mDf = 0-0.3m Df = 0.7-0.9mFSv = 2-3.8 FSv = 2-2.3

General soil condition Medium to dense sand (Dr = 55-80%) phi= 33-400

Water content = 0-5%

Mechanistic Calibration; eg q-z

48

Experimental-Numerical Comparison

-4 -2 0 2 4Rotation θ (degrees)

-400

-200

0

200

400

Mom

ent M

(kN

-m)

-4 -2 0 2 4Rotation θ (degrees)

400

300

200

100

0

Settl

emen

t s (m

m)

Experimental SimulationBNWF Mesh Simulation(a) (b)

Sand, Qu/Qa=3.0, φ’ = 38, Dr = 60%

49

Comparison of Models

1.29

0.40

0.84

Tn (flex base/no sliding)(sec)

2.61

4.79

3.13

Factor of safety (FSv)

2.72

6.46

3.75

Mass @ floor

x 105 (kg)

6.94

3.78

5.78

Total weight on the footing(MN)

1.420.765233

0.580.2116.42

0.980.44 414.41

Tn (flex base/ sliding)(sec)

Tn (fixed base)(sec)

StoriesHeight (m)

Model

3 different wall-footing prototypesRange of EQ motions & static cyclic inputResting on OC clayTn (fixed-base) ~ 0.2-0.8 secTn (flexible-base) ~ 0.4-1.3 sec

50

Physical parameters used in the studyBasic and Given parameters

cu = 52.67 kPa, φ = 00

ν = 0.5, Gmax = 26.33 MN/m2

Rayleigh damping = 5% (first two modes)

Radiation damping = 5%

Derived parameters

Bearing capacity, Qult = 18.11 MN (from Terzaghi, 1943)

Shear Capacity, Vult = 3.32 MN (Vult=c*Lf*Bf)

Vertical stiffness, Kv = 814 MN/m (from Gazetas, 1991)

Horizontal stiffness, kx = 750 MN/m (from Gazetas, 1991)

Comparison of Models

51

M-θ (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion-0.03 -0.02 -0.01 0 0.01 0.02 0.03Rotation (radian)

-40

-20

0

20

40

Mom

ent (

MN

.m)

Model1 - Motion CUCDUCI

Moment-Rotation

UCDUCSD

52

S-θ (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Rotation (radian)

-120

-80

-40

0

40

Set

tlem

ent (

mm

)

Model1 - Motion CUCDUCI

Settlement Vs Rotation

UCDUCSD

53

V-v (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion-100 0 100 200 300Sliding (mm)

-4

-2

0

2

4

She

ar F

orce

(MN

)

Model1 - Motion CUCDUCI

Shear Force Vs. Sliding

UCDUCSD

54

Revisit Shear Resistance Modeling

Vu (old)= 3.32 MN; Vu (new)= 26 MNKx (old)= 750 MN/m; Kx (new)= 1815 MN/mTn (model1)= 0.98s; Tn (model1)= 0.95sTn (model2)= 0.58s; Tn (model2)= 0.54sTn (model3)= 1.42s; Tn (model3)= 1.35s

55

V-v (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion

UCDUCSD

-2 -1 0 1 2Sliding (mm)

-4

-2

0

2

4

She

ar fo

rce

(MN

)

56

M-θ (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion

UCDUCSD

-0.02 0 0.02Rotation (rad)

-40

-20

0

20

40

Mom

ent (

MN

-m)

57

S-θ (Model 1: Tn(fb) = .44s)

2% in 50 Year Motion

UCDUCSD

02 -0.02 0 0.02Rotation (rad)

-160-120

-80-40

040

Set

tlem

ent (

mm

)

( )

58

DiscussionPositive comparative points

Initial stiffnesses and general shape of M-θ response reasonably comparableInitial settlement response and shape of settlement response, particularly in higher amplitude earlier cycles reasonably comparable

Physical DifferencesShear-moment coupling

Results in reduction of shear capacity at given moment; which isnot captured in a Winkler-based modelDifferences more pronounced for lower M/V ratio wall-foundation model

Settlement estimations under low amplitude shaking are challenging to capture accurately; variations in s between models can be on the order of 2-3x

59

Outcomes We hope to propagate this new knowledge and these new tools into practice as they are refined and become more readily available:

All data reports available on-line: cgm.engr.ucdavis.eduOpenSEES implementation and examples of various foundation elements use will be complete by Fall 2007

Findings from this work will help us:Improve nonlinear static proceduresImprove accuracy of our nonlinear dynamic analyses capabilitiesProvide improved confidence in the use of the foundation as an energy dissipative system

60

References (1/5)Ajrab, J. J., Pekcan, G., and Mander, J. B. (2004). “Rocking wall-frame structures with supplemental tendon systems.” Journal of Structural Engineering, ASCE, 130(6), 895–903.Alavi, B. and Krawinkler, H. (2002). “Strengthening of frame structures subjected to near-fault ground motions.” 12th European Conference on Earthquake Engineering. London, U.K., Elsevier Science Ltd., London, U.K.Barlett, P. E. (1976). “Foundation rocking on a clay soil.” M.E. Thesis, University of Auckland, New Zealand.Chang, B., Raychowdhury, P., Hutchinson, T., Thomas, J., Gajan, S., and Kutter, B. (2007). “Evaluation of the seismic performance of combined frame-wall-foundation structural systems through centrifuge testing.” 4th International Conference on Earthquake Geotechnical Engineering. Thessaloniki, Greece, June 25-28.Faccioli, E., Paolucci, R., and Vivero, G. (2001). “Investigation of seismic soil-footing interaction by large scale cyclic tests and analytical models.”4th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. San Diego, California.Gajan, S. (2006). “Physical and numerical modeling of nonlinear cyclic load-deformation behavior of shallow foundations supporting rocking shear walls,” PhD thesis, University of California, Davis.

61

References (2/5)Gajan, S. and Kutter, B. L. (2007). “A contact interface model for nonlinear cyclic moment-rotation behavior of shallow foundations.” 4th International Conference on Earthquake Geotechnical Engineering.Thessaloniki, Greece, June 25-28.Gajan, S., Kutter, B. L., and Thomas, J. M. (2005). “Physical and numerical modeling of cyclic moment-rotation behavior of shallow foundations.” 16th International Conference on Soil Mechanics and Geotechnical Engineering.Gajan, S., Phalen, J., and Kutter, B. (2003a). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the SSG02 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-03/01.Gajan, S., Phalen, J., and Kutter, B. (2003b). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the SSG03 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-03/02.Gajan, S., Phalen, J., Kutter, B., Hutchinson, T., and Martin, G. (2004). “Centrifuge modeling of nonlinear cyclic load-deformation behavior of shallow foundations.” 11th International Conference on Soil Dynamics and Earthquake Engineering, and the 3rd International Conference on Earthquake Geotechnical Engineering.

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References (3/5)Gajan, S., Phalen, J. D., Kutter, B. L., Hutchinson, T. C., and Martin, G. (2005). “Centrifuge modeling of the load deformation behavior of rocking shallow foundations.” Journal of Soil Dynamics and Earthquake Engineering, 25, 773–783.Harden, C. W. (2003). “Numerical modeling of the non-linear cyclic response of shallow foundations.” M.S. Thesis, University of California, Irvine.Harden, C. W., Hutchinson, T. C., and Moore, M. (2004). “Investigation into the effects of foundation uplift on simplified seismic design procedures.” Structural Engineers Association of California (SEAOC) 75th Anniversary Convention. 91–111.Harden, C. W., Hutchinson, T. C., and Moore, M. (2006). “Investigation into the effects of foundation uplift on simplified seismic design procedures.” Earthquake Spectra, 22(3), 663–692.Houlsby, G. and Cassidy, M. (2002). “A plasticity model for the behavior of footings on sand under combined loading.” Geotechnique, 52(2), 117–129.Kutter, B., Martin, G., Hutchinson, T., Harden, C., Gajan, S., and Phalen, J. (2003). “Workshop on modeling of nonlinear cyclic load-deformation behavior of shallow foundations.” Pacific Earthquake Engineering Research Center Report, University of California, Davis; PEER report number 2005/14.

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References (4/5)Nova, R. and Montrasio, L. (1991). “Settlements of shallow foundations on sand.” Geotechnique, 41(2), 243–256.PEER (2006). “Open System for Earthquake Engineering - OpenSEESversion 1.7.3”. Retrieved August 25, 2006, from http://opensees.berkeley.edu/.Phalen, J. D. (2003). “Physical modeling of the soil-foundation interaction of spread footings subjected to lateral cyclic loading.” M.S. Thesis, University of California Davis.Rosebrook, K. and Kutter, B. (2001a). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR01 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/09.Rosebrook, K. and Kutter, B. (2001b). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR02 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/10.Rosebrook, K. and Kutter, B. (2001c). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR03 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/11.

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References (5/5)Rosebrook, K. R. (2001). “Moment loading on shallow foundations: Centrifuge test data archives.” M.S. Thesis, University of California Davis.Taylor, P. W., Bartlett, P. E., and Weissing, P. R. (1981). “Foundation rocking under earthquake loading.” 10th International Conference on Soil Mechanics and Foundation Engineering, Vol. 3. 313– 322.Toranzo-Dianderas, L. A., Restrepo, J. I., Carr, A. J., and Mander, J. B. (2004). “Rocking confined masonry walls with hysteretic energy dissipators and shake table validation.” 13th World Conference on Earthquake Engineering. Paper no. 248.Wiessing, P. R. (1979). “Foundation rocking on sand.” School of Engineering Report No. 203, University of Auckland, New Zealand.

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Small footing

Large footing

Wall-Foundation Experiments

66

Footing locationCurrent soil surface location (soil_min)Maximum past settlement (soil_max)Current bearing pressureMaximum past pressure experienced

Internal variables

Macro-Element Model

67

Shearwall specimen

Lateral Loading Apparatus

Wall-Foundation Experiments

68

Experimental-Numerical Comparison

(Qu/Qa = 7.5)

69

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Mom

ent M

(kN

-m)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Mom

ent M

(kN

-m)

(a) Experiment (b) Numerical Simulation

Type A Footings: Strong Axis Rocking

One-g, Clay, cu = 49 kPa, φ’ = 0

Experimental-Numerical ComparisonTaylor et al (1980); 1-g tests

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-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)

4

3

2

1

0

Settl

emen

t s (m

m)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)

4

3

2

1

0

Settl

emen

t s (m

m)

Experimental DataBNWF Mesh Simulation

One-g, Clay, cu = 49 kPa, φ’ = 0

Experimental-Numerical ComparisonType A Footings: Strong Axis Rocking

Taylor et al (1980); 1-g tests