Modeling of Cyclic Load-Deformation Behavior of Shallow Foundations Supporting Rocking Shear Walls

Sivapalan GajanUniversity of California, Davis

Presentation

University of Missouri, Rolla

03. 22. 2005

Overview

IntroductionGeotechnical Earthquake EngineeringSoil-Foundation-Structure Interaction

Physical ModelingCentrifuge Experiments

Constitutive ModelingFooting-Soil Interface Behavior

Numerical ModelingImplementing the Model in Finite Element Analysis

Collapse of Engineered Structures

Niigata Earthquake, 1964

Kobe Earthquake, 1995

San Fernando Earthquake, 1971

Geotechnical Earthquake Engineering

Soil Deformation

Structural Failure

Soil-Structure Interaction

SettlementLateral spreadingLiquefactionEtc.

Beam/column failureStory driftCollapseEtc.

Kinematic/Inertial interactionSoil-Structure interface behaviorEtc.

Physical Modeling

Constitutive Modeling

Numerical Modeling

Shaking tableCentrifuge modelingDynamic field testingEtc.

Element level (micro) behaviorMacro level behaviorEtc.

Finite element analysisEtc.

Problems Research Tools

Soil-Foundation-Structure Interaction

∆, small

Stiff and Strong Foundation

High forcescause shearwall damage ∆, large

Flexible and Weak Foundation

Foundationyielding androcking protectsshear wall

Largedisplacementscause frame

damage

Small displacementsprotect framefrom damage

∆, small∆, small

Stiff and Strong Foundation

High forcescause shearwall damage

High forcescause shearwall damage ∆, large∆, large

Flexible and Weak Foundation

Foundationyielding androcking protectsshear wall

Largedisplacementscause frame

damage

Largedisplacementscause frame

damage

Small displacementsprotect framefrom damage

Kinematic Interaction – Soil Disturbs StructureInertial Interaction – Structure Disturbs Soil

Shallow foundations supporting rocking shear wallsPartial separation of footing (uplift) and soil yielding – depend on each other

Location of footing-soil contact area and highly nonlinear bearing pressure distribution changes rapidly

Base shear loading produces sliding of footing

Shear wall and frame structure

(after ATC, 1997)

NEES Geotechnical Centrifuge at UC Davis

Centrifuge Experimental Set Up

Six series of tests including about 50 shear wall-footing models

Parameters VariedSoil properties

Soil type (dry sand and saturated clay)Dr = 80% and 60% and Cu = 100 kPa

Structure propertiesShear wall weight (FSV = 2 to 10)Height of center of gravity and moment of inertiaFooting geometry (rectangular and square)Footing embedment (D = 0 to 3B)

Loading typesPure vertical loadingLateral cyclic loading

Controlling moment to shear ratio (one actuator)Controlling rotation and sliding (two actuators)

Dynamic base shaking

Vertical cyclic loading

Horizontal cyclic loading

Dynamic Shaking

Types of Loading

Lateral Cyclic Loading – Load Paths

1.23 1.1

0.43

M=H.h

H

h/L = 1.8

M=H.h

V/Vmax

V/Vmax = 0.1 ~ 0.5

1.23 1.1

0.43

M=H.h

H

h/L = 1.8

1.23 1.1

0.43

M=H.h

H

h/L = 1.8

M=H.h

V/Vmax

V/Vmax = 0.1 ~ 0.5

M=H.h

V/Vmax

V/Vmax = 0.1 ~ 0.5

s

uθ

M

V

H

FS = 6.0, D = 0.0 m, L = 2.8 m, h = 4.9 m

Experimental Results: (V, H, M – s, u, θ) - Sand

FS = 3.0, D = 0.0 m, L = 2.7 m, h = 4.6 m

Experimental Results: (V, H, M – s, u, θ) - Clay

FS = 5.0, D = 0.0 m, L = 2.8 m

Dynamic Test Results

Comparison of dynamic back-bone curve with lateral cyclic push test results

Footing-Soil Interface Behavior - Animation

Eccentricity Animation – Experiment

Contact lengthFSCurvature (θmax)

Pressure distributionSoil typeContact length

θ

θ+

θθ

⋅=θθ

θθ

⋅=θθ

θ⋅=θ

d)(de

d)(deR

d)(dM

d)(deR

d)(dM

)(eR)(M

pressurecontact

Footing-Soil Interface Modeling

contact-element

Considers foundation and surrounding soil as a single macro-element

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

Modeling of Moment-Rotation Behavior

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

Internal variables

Moment-Rotation Model

Model Simulations (FS = 6) - Animation

Comparison with experiment

Moment Capacity

Rotational Stiffness

Energy Dissipation

Settlement-Uplift Behavior

Permanent Settlement

Shear–Sliding Modeling: Coupling with V

1

0

p[i]

i_nodeFS1

qult]i[q]i[p

==

10 p[i]Vult

VFS1Fv ==

VultHFh = [ ]Fv1Fv

21Fh −⋅⋅=

Shear-Sliding Modeling: Coupling with M

1BFh

AFm

2

2

2

2=+

LVultMFm⋅

=

VultHFh =

du

dθ

−

=din_d

dglobal_f

When (d d_in)f_global infinite

When (d 0)f_global 0

2

2

2

2

AB

Lh

AB

FhFm

dud

⋅=⋅=θ

Overall comparison: Model Vs Experiment

Model parametersFooting geometry

width, Blength, Lembedment, D

Soil strength parametersBearing Capacity of the Foundations (FS)

Soil stiffness parameters vertical stiffness, kvinitial shear stiffness, khrebounding ratio, Rv

Soil parameters can be specified as a function of depth (settlement)

Implementation in OpenSEESWhat is OpenSEES ?

Open System for Earthquake Engineering SimulationsA finite element framework (open source) that is being

developed by PEER

What is PEER ?Pacific Earthquake Engineering Research CenterOne of the NSF funded Earthquake Engineering Research

centers in USADevelops tools for Performance Based Earthquake

Engineering (PBEE) design

What is PBEE ?Design, evaluation and construction of engineered

structures whose seismic performance meets the diverse economic and safety needs of owners and society

OpenSEES FE Framework

NodeElementMaterialLoad patternConstraintsEtc….

Nodal displacementsElement forcesEtc….

System of equationsSolution algorithmIntegratorEtc….

Model Builder

Recorder

AnalysisDomain

Builds the model

Records everything thathappens in Domain

Performs analysisin Domain

Model Builder stores everythingAnalysis performs analysisRecorder gets the force – disp. info.

Class Hierarchy of OpenSEESOpenSEES_Object

DomainComponent Material Analysis Classes

Node Element LoadUniaxial Section

SoilFootingSectionFiberSection

Integrator

BeamColumn

ZeroLengthSection

8-node Brick

SoilFootingSection.hSoilFootingSection.cpp

NewtonRaphsonAlgo.

A Simple OpenSEES Analysis

V

O

H

A Simple OpenSEES Analysis

OpenSEES Analysis (George Hu)

Beam-Column Frame – Shear Wall - Foundation

Hemi-Spherical Footing

Hemi-spherical footing –Can dissipate energy beneath thefooting without causing permanentdeformations at foundation level

Experimental FindingsMoment-rotation and shear-sliding relationships

Depends on initial vertical static factor of safety (FSV)Controlled by material (soil yielding) and geometrical (footing uplift)

nonlinearitiesMoment capacity does not degrade with cycling, but rotational stiffness

does degrade (due to rounding of the interface and uplift of footing)

Settlement, sliding and rotationSettlement and sliding continue to accumulate with the number of cycles

of rotation, though the rate decreases as the footing embeds itselfApplied moment to shear ratio (height of center of gravity of the

structure) controls the ratio of rotation to sliding at the interface

The results show that yielding of soil beneath the footing causes a large amount of energy dissipation

Reduces shaking demands on the super structureCauses undesired permanent deformations at the foundation

Footing-Soil “Interface-Element”

Model is based on the physics, geometry and mechanism of the problem and is computationally fast

Coupled force-displacement relationships in (V-H-M) space

Only 4 major model parameters

No need for external mesh generation

Reproduces the load-displacement behavior observed in the experiments

Can be used independently as well as with other structural models to analyse soil-foundation-structure interaction problems