modeling of cyclic load-deformation behavior of footing

Modeling of Cyclic Load-Deformation Behavior of Footing-Soil Interface

Sivapalan Gajan

Advisor: Bruce Kutter

Geotech Seminar

University of California, Davis

11. 10. 2004

Overview

Brief introduction to the project

Centrifuge experiments

Modeling of footing-soil interface

Comparison of model simulations with experiments

Implementation of the model in OpenSEES

Shallow foundations supporting rocking shear wallsRocking of shear wall and foundation

Partial separation of footing (uplift) and soil yielding

Highly nonlinear bearing pressure distribution

Location of footing-soil contact area and the bearing pressure distribution

Base shear loading produces sliding of footing

Shear wall and frame structure (after ATC, 1997)

Forces and displacements acting on the footing-soil interface

s

uθ

M

V

H

s: vertical displacement (settlement)u: horizontal displacement (sliding)θ: rotationV: vertical loadH: horizontal loadM: moment

Purposes of Research

To study the effects of soil-foundation interaction in shallow foundations during cyclic and dynamic loading

To explore the nonlinear load-displacement behavior of shallow foundations under combined (V-H-M) loading

Vertical force – settlementHorizontal force – slidingMoment – rotation

To perform centrifuge experiments with influencing parameters systematically varied

To develop numerical models that can be used in design

Scope of Research

Physical ModelingCentrifuge experiments – model footings attached with shear wall structures tested on both sand and clay

Constitutive ModelingModeling of cyclic load-displacement behavior of footing-soil interface

Numerical ModelingImplementing the footing-soil interface model in OpenSEES finite element framework

Centrifuge experiments

7 series of centrifuge experiments including about 60 shear wall-footing models

(KRR01, 02, 03, SSG02, 03, 04, JMT01)

Parameters varied

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

Structure propertiesShear wall weight (FS = 2 to 10)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

Slow cyclic lateral loading – one actuator

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

Slow cyclic lateral loading – two actuators

θ

u

θ

1h2h2d1h1d2hu

1h2h1d2d

−⋅−⋅

=

−−

=θ

11hu

12hu

1d2d

+⋅

θ

+⋅

θ

=

Slow cyclic lateral loading - Animation

Experimental results

0.08 0.06 0.04 0.02 0 0.02 0.04 0.06400

200

0

200

400

Rotation (rad)

Mom

ent,

M (k

N.m

)

20 0 20 40 60

50

0

50

Horizontal displacement, u (mm)

Hor

izon

tal l

oad,

H (k

N)

0.08 0.06 0.04 0.02 0 0.02 0.04

100

50

0

Rotation (rad)

Settl

emen

t, s (

mm

)

20 0 20 40 60

100

50

0

Horizontal displacement, u (mm)

Settl

emen

t, s (

mm

)

file "U:\Gajan\SSG02\20g-cyclicTests\test3\Test#3a.prt"=

Data from test SSG02, test#3a, FS = 6, embedment = 0.0m, load height = 4.9m, footing length = 2.84m

Modeling of footing-soil interface behaviorBeam on nonlinear Winkler foundation

Collaborative researchTara Hutchinson (UCI)

Macro modeling

Houlsby and Cassidy Cremer et. al

Contact-Element 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 center of the footing

contact-element

Forces at soil-footing interface

O

V

H

)sin(F)cos(RV θ⋅+θ⋅= )sin(R)cos(FH θ⋅−θ⋅=

eR)sin(hcgVhHM ⋅=θ⋅⋅+⋅=

Vinitial positionO

O

displaced position

V

M

F

R

H

R

θ

Eccentricity animation – experiment

θ

θ+

θθ

⋅=θθ

θθ

⋅=θθ

θ⋅=θ

d)(de

d)(deR

d)(dM

d)(deR

d)(dM

)(eR)(M

pressurecontact

Contact lengthFSCurvature (θmax)

Pressure distributionSoil typeContact length

Rounding of soil surface beneath footing

-4 -2 0 2 4 6 8 10Horizontal Distance (inches)

-1.5-1

-0.50

0.51

1.5

Ver

tical

D

ista

nce

(inch

es)

KRR02, Station AE, West Footing

-10 -8 -6 -4 -2 0 2 4 6Horizontal Distance (inches)

-1-0.5

00.5

1

Ver

tical

D

ista

nce

(inch

es)

KRR02, Station CE, West Footing

-10 -8 -6 -4 -2 0 2 4 6Horizontal Distance (inches)

-1-0.5

00.5

1

Ver

tical

D

ista

nce

(inch

es)

KRR02, Station CE, East Footing

-4 -2 0 2 4 6 8 10Horizontal Distance (inches)-1.5

-1

-0.5

0

0.5

1

Ver

tical

D

ista

nce

(inch

es)

KRR02, Station AE, East Footing

θ1, degree of rounding θ2, degree of rounding

θ=(θ1+θ2)/2=5 degrees

θ=3.5 degrees

θ=4 degrees

θ=10 degrees

Rosebrook (2002)

Factors affecting moment-rotation behavior

Vertical factor of safetycontact length

Type of pressure distributionlocation of eccentricity

Vertical stiffness of soilMaximum rotation experienced by the soil

curvature of soil surfacecontact location

Moment-rotation model formulation

Internal variables

xi

i c db

pressure distribution

V

O

M

footing

soil_min

a

soil_max

∆i

Ri

θ

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

Method of computation

xi

i c db


V

O

M

footing

soil_min

a

soil_max

∆i

Ri

1. The incremental rotation (∆θ) is applied to the contact element

2. The point of rotation of the rigid footing, for that ∆θ, is initially assumed (starts with the footing-soil_max contact point at the back side of the footing)

3. The new location of the footing is updated at every node.


xi

i c db


V

O

M

footing

soil_min

a

soil_max

∆i

Ri

4. The new position of the soil_min surface is located using the rebounding ratio and footing position

5. The new position of the soil_min surface is located using the rebounding ratio and footing position

6. The contact nodes of the footing with soil_min and soil_max surfaces at both sides of the footing is found from the new locations of footing and soil surfaces (nodes a, b, c, and d in Fig.)


xi

i c db


V

O

M

footing

soil_min

a

soil_max

∆i

Ri

7. The new bearing pressure distribution at every node that is in contact with the soil_max surface (between nodes b and c) is calculated first

[ ]VultkvsoilMaxsoilMaxRR 1incr,iincr,i1incr,iincr,i ⋅−+= −−

0.1R0.0 incr,i ≤≤


xi

i c db


V

O

M

footing

soil_min

a

soil_max

∆i

Ri

8. The distribution of R along the contact length is integrated using equation 3 to get the total resisting vertical force, Vr

[ ]∑=

θ⋅∆⋅⋅=d

aiii )cos(R

LVultVr∫ ⋅θ⋅⋅= dx)cos()x(R

LVultVr or

9. For vertical equilibrium,

VVr =


xi

i c db


V

O

M

footing

soil_min

a

soil_max

∆i

Ri

10. If abs(V - Vr) < = tolerance

[ ]∑=

⋅∆⋅⋅=d

aiiii xR

LVultM

Else

Go back to step 2 and change the point of rotation depending onV > Vr or V < Vr

Initial condition

Initially uniform pressure distribution

As M increases,

If (FS > 2){

trapezoidaluplift before yielduplift + yieldultimate

}Else{

trapezoidalyield before upliftyield + upliftultimate

}

Parameters:FSkv

Allotey and Naggar (2003)

Model simulationFS = 5.0M/H = 5.0 mRotation measured in the experiment is applied to the model

Input parameters

Simulation animation

Comparison with experiment

0.06 0.04 0.02 0 0.02 0.04 0.06500

250

0

250

500

Rotation (rad)

Mom

ent (

kN.m

)

0.06 0.04 0.02 0 0.02 0.04 0.0680

60

40

20

0

experimentcontact element model

Rotation (rad)Se

ttlem

ent (

mm

)

Critical contact length (Lc) and ultimate moment (Mu)

LC

L

emax VFooting base

Rounded soil

LC

L

emax VFooting base

Rounded soil

LC – minimum contact length required to maintain a vertical FS = 1

−=LLc1

2L.VMu

vFS1

LLc

=

Theoretical extreme behaviors

M

θ

S

θ

0

0

VL/2

Lθ/2

FS = inf.

FS = 1

0.05 0 0.05100

0

100

M50

T500.05 0 0.05

200

0

200

M1_1

T1_1

0.05 0 0.050.02

0

0.02

0.04

0.06

s50

T500.05 0 0.05

1.5

1

0.5

0

s1_1

T1_1

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: local coupling with V

10 p[i]Vult

VFS1Fv ==

VultHFh =

[ ]Fv1Fv21Fh −⋅⋅=

[ ]

−⋅⋅⋅= iii_node p1p21

811local_f

When (p = 0.0 or 1.0)f_local = 0.0

When (p = 0.5)f_local = 1.0

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

Combining local and global coupling factors

[ ]

−⋅⋅⋅= iii_node p1p21

811local_f

Local coupling factor for every node is calculated based on their q/qult and summed up

[ ] ∑⋅=Nodes.no

ii_nodelocal local_fkhekh

Global coupling factor is calculated based on the location of force point in M-H space

−

=din_d

dglobal_f

Final shear stiffness is obtained by combing local and globalcoupling factors

[ ] [ ] global_fkhkh localglobal ⋅=

[ ] dukhdH global ⋅=

Settlement induced by sliding

Fv

contraction

1 < FS < 2

ds

1

FS > 2

0 0.5

dilation

dudu

ds

Fh

Associate flow rule doesn’t work for settlement induced by sliding

Results: shear - sliding

20 0 20 40 60

50

0

50

Sliding (mm)

Shea

r for

ce (k

N)

20 0 20 40 6080

60

40

20

0

experimentSliding (mm)

Settl

emen

t (m

m)

40 20 0 20 40 60

50

0

50

Sliding (mm)

Shea

r for

ce (k

N)

40 20 0 20 40 6080

60

40

20

0

contact element modelSliding (mm)

Settl

emen

t (m

m)

Results – shear - sliding

40 20 0 20 40 60

50

0

50

Sliding (mm)

Shea

r for

ce (k

N)

40 20 0 20 40 6080

60

40

20

0


Sliding (mm)Se

ttlem

ent (

mm

)

Overall comparison

0.06 0.04 0.02 0 0.02 0.04 0.06500

250

0

250

500

Rotation (rad)

Mom

ent (

kN.m

)

40 20 0 20 40 60

50

0

50

Sliding (mm)

Shea

r for

ce (k

N)

0.06 0.04 0.02 0 0.02 0.04 0.0680

60

40

20

0

Rotation (rad)

Settl

emen

t (m

m)

40 20 0 20 40 6080

60

40

20

0


Sliding (mm)

Settl

emen

t (m

m)

Model parametersFooting geometry

width, Blength, Lembedment, D

Soil strength parametersfriction angle, Фunit weight, γ

Soil stiffness parametersvertical stiffness, kvinitial shear stiffness, khrebounding ratio, Rv

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

Implementation in OpenSEES

Need to add a new materialfootingSection2d.hfootingSection2d.cpp

Axial force and moment and corresponding displacements are coupled by

zeroLengthSection - elementsectionForceDeformation – material

There are no materials/elements that couple three forces and displacements (for a 2D problem) in OpenSEES

Implementation in OpenSEESTo implement the footing-soil interface model in OpenSEES:

1. M-V coupling only

Material

FootingSection2d

SectionForceDeformation

ZeroLengthSection

Element

TaggedObject

DomainComponent

2. M-H-V coupling

new-SectionForceDeformation

Material

FootingSection2dnew-ZeroLengthSection

Element

TaggedObject

DomainComponent

Implementation in OpenSEES

V

O

H

Properties of the model

Model is simple and computationally fast

Coupled force-displacement relationships

Only 4 model parameters

No need for external mesh generation

Reproduces the mechanisms observed in the experiments

Acknowledgements

PEERKey RosebrookJustin Phalen

Jeremy ThomasRoss BoulangerBoris JeremicDan WilsonChad JusticeTom Coker

modeling of cyclic load-deformation behavior of footing

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