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