modeling of cyclic load-deformation behavior of footing
TRANSCRIPT
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Modeling of Cyclic Load-Deformation Behavior of Footing-Soil Interface
Sivapalan Gajan
Advisor: Bruce Kutter
Geotech Seminar
University of California, Davis
11. 10. 2004
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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
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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)
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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
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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
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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
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Centrifuge experiments
7 series of centrifuge experiments including about 60 shear wall-footing models
(KRR01, 02, 03, SSG02, 03, 04, JMT01)
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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
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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
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Slow cyclic lateral loading – two actuators
θ
u
θ
1h2h2d1h1d2hu
1h2h1d2d
−⋅−⋅
=
−−
=θ
11hu
12hu
1d2d
+⋅
θ
+⋅
θ
=
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Slow cyclic lateral loading - Animation
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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
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Modeling of footing-soil interface behaviorBeam on nonlinear Winkler foundation
Collaborative researchTara Hutchinson (UCI)
Macro modeling
Houlsby and Cassidy Cremer et. al
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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
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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
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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
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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)
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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
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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
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Method of computation
xi
i c db
pressure distribution
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.
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Method of computation
xi
i c db
pressure distribution
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.)
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Method of computation
xi
i c db
pressure distribution
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 ≤≤
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Method of computation
xi
i c db
pressure distribution
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 =
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Method of computation
xi
i c db
pressure distribution
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
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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)
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Model simulationFS = 5.0M/H = 5.0 mRotation measured in the experiment is applied to the model
Input parameters
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Simulation animation
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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
)
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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
=
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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
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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 −⋅⋅=
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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
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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
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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 ⋅=
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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
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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)
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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
experimentcontact element model
Sliding (mm)Se
ttlem
ent (
mm
)
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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
experimentcontact element model
Sliding (mm)
Settl
emen
t (m
m)
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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)
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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
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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
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Implementation in OpenSEES
V
O
H
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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
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Acknowledgements
PEERKey RosebrookJustin Phalen
Jeremy ThomasRoss BoulangerBoris JeremicDan WilsonChad JusticeTom Coker