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

Sivapalan Gajan

Advisor: Bruce Kutter

Seminar – 06. 01. 2005

Overview of Presentation

Background

Experimental Findings

Footing-Soil Interface Modeling

Implementation in OpenSEES

Shallow Foundations Supporting Rocking Shear Walls

Material and geometrical nonlinearities – soil yielding and footing uplift

Nonlinear bearing pressure distribution – Nonlinear moment-rotation behavior

Energy dissipation beneath the footing and associated permanent deformations

Shear wall and frame structure (after ATC, 1997)

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

(ATC 40 – 1997)

Foundation rocking and mobilization of ultimate capacity reduce seismic demands on the structure (FEMA 1997 and ATC 1997)

Issues

•Analytical challenges to reliable modeling of soil-foundation behavior

•Uncertainty in soil properties

•Lack of interaction between Structural and Geotechnical Engineers/Researchers

Purposes of Research

•To further the understanding of footing-soil interface behavior under realistic confining pressures.

•To investigate the effects of static vertical factor of safety (FSV) on energy dissipation and permanent deformations

•To model the nonlinear cyclic load-displacement behavior of footing-soil interface for combined vertical, shear and moment loading - allowing soil yielding and footing uplift.

What Have We Done?

Centrifuge Experiments Macro-Element ModelingUnderstanding Footing-Soil Interface Behavior

Modeling Footing-Soil Interface Behavior

Outcome

Interface Model inOpenSEES

Centrifuge Experiments

Rosebrook (KRR01, KRR02, KRR03)Gajan and Phalen (SSG02, SSG03)Gajan and Thomas (SSG04)Thomas and Gajan (JMT01, JMT02)

Single-Wall

Double-Wall

Frame-Wall

Parameters varied

Soil propertiesSoil type (sand and clay)Dr (80% and 60%)

Structure propertiesShear wall weight (FS = 2 to 15)Footing geometry (rectangular and square)Footing embedment (D = 0 to 3B)

Loading typesPure vertical loadingLateral slow cyclic loading

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

Dynamic base shaking

Forces and Displacements at the Interface

Load-Displacement Behavior at Interface

FS = 5.0, D = 0.0 m, L = 2.8 m, h = 4.9 m

Effect of Soil Type - Clay

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

Load Paths in V-H-M Space

M

V

M

H

Vertical Load Ratio Moment-to-Shear Ratio

VVFS MAX

V = hHM

=

Effect of Vertical Factor of Safety

Effect of Vertical Factor of Safety

same Vult, different V same V, different Vult

Effect of Load Height (M/H = 1.2 m)

FS = 5.0, D = 0.0 m, L = 2.8 m, h = 1.2 m

Dynamic Base Shaking

FS = 5.0, D = 0.0 m, L = 2.8 m, a_max = 0.5 g

Energy Dissipation Vs Permanent Deformation

Half Amplitude Cyclic Rotation (Rad.)

0.001 0.01 0.1

Settl

emen

t per

Cyc

le (m

m)

0

10

20

30

40

FS = 2 ~ 4FS = 5 ~ 8FS = 10 ~ 15

Ener

gy D

issi

patio

n pe

r Cyc

le (k

Nm

)

0

10

20

30

40

A

M

θ

θ

s

Energy Dissipation Vs Permanent Deformation

Half Amplitude Cyclic Rotation (Rad.)

0.001 0.01 0.1

Nor

mal

ized

Set

tlem

ent

0.000

0.005

0.010

0.015

Ener

gy D

issi

patio

n R

atio

0.1

0.2

0.3

0.4

0.5

0.6

FS = 2 ~ 4FS = 5 ~ 8FS = 10 ~ 15

M

θ

A1

A2

EDR = A2 / A1

Uv = s / L

Failure Envelopes in V-H-M Space

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 = 0.42Cremer et al. (2001)

Houlsby and Cassidy (2002)

Nova and Montrasio (1991)

Footing-Soil Interface ModelingConsiders foundation and surrounding soil as a single

macro-elementConstitutive model that relates the forces (V, H, M) and

displacements (s, u, θ) acting at the base center point of the footing

macro-element

Lateral Cyclic Loading - Animation

Forces and Displacements at the Interface

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

Cyclic Moment-Rotation Model

Model Simulations - Animation

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 −⋅⋅=

Effect of Moment-to-Shear Ratio on Ultimate Capacities

Normalized Shear [H/VULT]

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Nor

mal

ized

Mom

ent [

M/(V

ULT

.L)]

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15h/L = 1.75 h/L = 1.25

h/L = 0.42

15

5

FSV = 2

10

FM/FH = h/L

FSV = 2 ~ 5

FSV = 5 ~ 10

FSV = 10 ~ 15

Moment-Shear Coupling

Normalized Shear (FH = H/VULT)

0.00 0.05 0.10 0.15 0.20

Nor

mal

ized

Mom

ent [

F M =

M/(V

ULT

.L)]

0.00

0.05

0.10

0.15

FSV = 20

FSV = 2.5

13

765

43.5

FM/FH = 1.75

FM/FH = 1.25

FM/FH = 0.42

Gradient

Flow Direction

Shear-Sliding Modeling: Global Coupling with M

−

=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

1BFh

AFm

2

2

2

2=+

LVultMFm⋅

=

VultHFh =

du

dθ

Model Parameters

Footing geometrywidth, Blength, L

Strength parametersultimate-to-applied vertical load ratio (FSV)moment-to-shear ratio

Stiffness parametersunloading-reloading vertical stiffness, kvinitial shear stiffness, khrebounding ratio, Rv

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

Model Simulations - (FS = 5)

Simulation and Experiment (FS = 5)

Model Simulations - (FS = 2.5)

Simulation and Experiment (FS = 2.5)

Model Simulations - (FS = 7.5)

Simulation and Experiment (FS = 7.5)

OpenSEES

NodeElementMaterialLoad patternConstraintsEtc….

Nodal displacementsElement forcesEtc….

System of equationsSolution algorithmIntegratorEtc….

Recorder

AnalysisDomain

Builds the model

Performs analysisin Domain

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

Model Builder

Records everything thathappens in Domain

Interface Model in OpenSEES

Macro-Element ModelWinkler Model

Class Hierarchy in OpenSEES

OpenSEES

DomainComponent Material Analysis Classes

Node Element LoadUniaxial Section

SectionForceDeformationFiberSection

Integrator

BeamColumn

ZeroLengthSection

8-node Brick

ConvergenceTest

SoilFootingSection

Accessing the model in OpenSEES

Element - ZeroLengthSection

Section - SoilFootingSection

-ndm 2 –ndf 3

Node i (0, 0)

Node j (0, 0)

Fixed

Free

section SoilFootingSection -secID -Vult -V -L -Kv -Kh <-noSubNodes -tol>

element 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 Simulations

Frame – Shear Wall – Foundation System

Modifications in OpenSEES Model

V is NOT a ConstantV is a Constant(Original Model) (Improved Model in OpenSEES)

Dynamic Analysis in OpenSEES

Summary

Footing-soil interface behavior depends onStatic vertical factor of safety (FSV)Applied moment-to-shear ratio

Larger FSVIncreases the moment capacity Decreases the permanent deformation

Larger FSV + Rocking allowedConsiderable amount of energy can still be

dissipated without degradation in moment capacity

Footing-Soil “Interface-Element”

Model is based on the physics, geometry and mechanism of the problem and reproduces the load-displacement behavior observed in the experiments

Captures the coupled force-displacement relationships in (V-H-M) space with only 4 major model parameters

No need for external mesh generation and the model is computationally fast

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

Further Work

Dynamic finite element analysis in OpenSEES with structural, soil and interface elements

Uncertainty analysis – Effect of uncertainties in soil properties on model predictions

Model simulations for I-shape foundations ?

Make the model work better !