EERI Technical Seminar Series Impact of Soil-Structure Interaction on Response of Structures Seminar 1: Practical Applications to Shallow Foundations New Tools for Structural and Geotechnical Practitioners on the Horizon Tara C. Hutchinson
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
New Tools for Structural and Geotechnical Practitioners on the Horizon
Tara C. Hutchinson
2
Collaborative Project
UCD (Kutter), UCLA (Stewart), UCSD (Hutchinson), USC (Martin)Graduate Students: Rosebrook, Phalen, Gajan, Raychowdhury, Harden, ChangSupport provided by PEER
3
Modes of Foundation Deformation
L
D
H
Induced earthquake motion
Super structure
θ
Flexible foundation L = length of footing
B = width of footingH = thickness of footingD = depth of embedment
Vertical mode
Sliding mode
Rocking mode
u(t)
θ(t)f
s(t)
Initial position of footing top
f
4
Rocking: Base HingingShear walls fixed and perfectly hinged at the baseHinges at base decrease moment, shear, and drift to wall
Alavi and Krawinkler (2004)Fixed Wall Hinged Wall
5
Reduction in kinetic energy by the impact:
2
0
2
)]2cos1([ α−−=I
mRIr
•Energy dissipated by rocking block = f(amplitude, frequency) of the rocking motion
•In 1963, no known method to design a rocking structure with reliable stability.
Early Work
Housner (1963)
6
Experimental validation of Housner’s workTheoretical “r” in good agreement with average experimental value.
Rocking also generates impact energy that is transferred back to structure Development of simple method to predict maximum displacement due to rocking
Early Work
Priestley et al. (1978)
7
Rocking: Structural Solutions
Filiatrault et al. (1992), Anderson (2003)Kurama et al. (1999), Priestley et al. (1999)Taghdi et al. (2000)Holden et al. (2003)Bonelli and Holmberg (2004)Marko et al. (2004)Ajrab et al. (2004)Toranzo-Dianderas et al. (2004)
8
e.g. Draped Tendons
Wall remains protected from damage while tendons yield
Energy dissipated through tendons
Ajrab et al. (2004)
9
e.g. Mechanical Base Dampers
Steel dampers
Shake table tests on ¼-scale masonry wall modelDampers provided local energy dissipation directly at base ends of wallLittle to no damage observed in wall with base dampers
Toranzo-Dianderas et al. (2004)
10
Key Ideas: Foundations
Soil-foundation interface can provide the key features of:
Rocking can provide valuable dissipation of energy during seismic loading (due to bearing capacity mobilization)Re-centering can reduce deformation demands (due to gap formation and closing)
11
Simulations - Previous WorkSDOF & MDOF systems w/ lumped massesRigid, 2-element, Winkler system of springsLinear-elastic springs
Chopra & Yim; Yim and Chopra (1985)
12
Simulations - Previous WorkElastic Winkler springs below nonlinear (degrading) shear wall structureTwo different GM types (long duration & short impulsive motion)
Nakaki & Hart (1987)
13
Simulations – Previous WorkApplication to Bridge modelingComposite of parallel springsCombined w/ nonlinear
column behavior
Fenves (1997)
14
“Big Picture” Question
Under what conditions should foundation rocking be avoided, allowed, or encouraged in building design?
Need methods to quantify the benefits (e.g. structural demand reduction, energy available at footing)Need methods to quantify the consequences (e.g. permanent and cyclic settlement, rotations)
15
Research ProgramPhysical Model Testing
1-g experiments (Bartlett, Weissing, Negro)Centrifuge experiments
Wall-foundation; 8 series of tests (Gajan, Rosebrook, Kutter): KRR and SSG seriesBuilding-Foundation; 1 series/two bldg-fnds (Chang, Thomas): JMT series
Numerical ModelingMacro-element modeling (UCD)Winkler-based modeling (UCSD)
16
Centrifuge (UC Davis)
Our tests: N=20Lm= (1/20)*Lp ; σm= σp
Center for Geotechnical Modeling at UC Davis: 9.1-m radius
centrifuge
d σ = ρ. g. d
Prototype
d/N σ = ρ. (N.g). d/N= ρ. g. d
Model (N-g)
Scaling in centrifuge:
17
Wall-Foundation Experiments
LA1 LA2
LB4
LB3
LB1LB2
LC4
LC3
LC1LC2
C2
C2
C2
Station A Station B Station C
beams continue for length of box
Z
y
ACTUATOR
ACTUATOR
200.0Nevada Sand
KRR and SSG Series experimentsRosebrook & Kutter (2002) and Gajan et al. (2003)
18
Tests on clay and sandVarying embedment (0, B, 3B)Model wall-footing systems with various precompression loads(“FSv = 3-15”)
Planar wall-footing model
Two wall-footing models
loaded in parallel
Wall-Foundation Experiments
19
A word about definitions…Classical terminology in Geotech Eng: Factor of Safety
…against …<bearing, overturning, sliding> failuree.g. FSv, FSot, FSsBut…there is little association with “safety” in this definition
Effectively analogous to axial stress in a column: eg 10%f’cAgWe’ll refer to this as a degree of pre-compression eg Qult/Qapplied (Qu/Qa)
Defined for any mode (axial, shear, moment)
20
Physical Observations
21
Findings: Footing ResponseMoment-rotation plots show good energy dissipation but result in settlementKθ and s = f(soil type, soil density, footing size, aspect ratio, Df , Qu/Qa, loading)
-0.08 -0.04 0 0.04 0.08Rotation (rad)
-400
-200
0
200
400
Mom
ent (
KN
m)
-0.08 -0.04 0 0.04 0.08Rotation (rad)
-160
-120
-80
-40
0
40
Settl
emen
t (m
m)
22
Findings: Settlement-Rotation
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Half Amplitude of Cyclic Rotation, θ [rad]
Nor
mal
ized
Set
tlem
ent P
er C
ycle
, Uv/c
ycle
FSv = 2.0, Dr = 45% (TRISEE83)FSv = 2.0, Dr = 93% (Weissing)FSv = 3.4, Dr = 80% (SSG02)FSv = 3.4, Dr = 80% (SSG02)FSv = 4.0, Dr = 80% (SSG03)FSv = 4.1, Dr = 60% (KRR02)FSv = 5.3, Dr = 80% (SSG02~Dynamic)FSv = 6.4, Dr = 80% (SSG03~Dynamic)FSv = 6.8, Dr = 80% (SSG02)FSv = 8.2, Dr = 80% (SSG03)FSv = 9.6, Dr = 80% (SSG02)
2.0 < FSv < 3.5
3.5 < FSv < 7.0
7.0 < FSv
Increasing Dr
23
InelasticBeams w/
Fiber Hinges
Rigid ElasticBeam-Column
Spring Array
G.S.
Prototype(Dashed)
Nonlinear Beam-Column Elements
Elements
(when occurs)
Prototype R/C Structure
(units in meters)Target Tn ~ 0.5s;
(Qu/Qa)govern = 5
Idealized Finite Element Model
Dense dry sand
Building-Foundation Tests2.54 7.62 7.62
2.84 1.00 1.00
G.S.
R/C Shear
Isolated R/CStrip Footing
Wall
Isolated R/CSpread Footings
R/C Beam-Column
9.53
1.00
4.76Members
4.76
Ductile Beam-Column Joint
24
Slow cyclic lateral loading (inertial input)Dynamic loading (base excitation)Earthquake loading (base excitation)
Dr=85% dense dry sand
Station A
Station B
Plan view of Soil Box
Continuous out-of-plane guide
Continuous low-friction out-of-plane guide
extension arm for actuator support
Building-Foundation Tests
25
One Bay Model
Square Footing
Shearwall
Strip Footing
Hollow steel columns
Beam-column fuses
Mass-blocks
Beam-wall fuses
Hollow steel beams 4
86 m
m
(9.5
3 m
)
508 mm (10.1 m)
Ductile fuse: full bridge configuration
of 4 strain gages
51 mm0.1 Lbeam
26
Two Bay Model
Instr: load cell, strain gages, accelerometers, linear pots
Shearwall
Strip Footing
Hollow steel columns
Beam-column fuses
Mass-blocks
Beam-wall fuses
Square Footing
Hollow steel beams
486 m
m
(9.5
3 m
)
889 mm (17.8 m)
27
Two Bay in Centrifuge
Actuator arm
Soil thickness = 4 m (prototype)
Loading plane
28
One Bay Testing Summary
396 mm / 4.16 % HSC8
240 mm / 2.52 % HSC7
116 mm / 1.22 % HSC6
55 mm / 0.58 % HSC50.93 g D428 mm / 0.29 % HSC40.65 g D312 mm / 0.13 % HSC30.20 g D2 17 mm / 0.18 % HSC20.09 g D1 19 mm / 0.20 % HSC1
Base acc (g) NameAve Max Disp/Drift Ratio (%)
Name
29
Physical Observations
30
Findings: Global Response
-300 -200 -100 0 100Displacement (mm)
-400-200
0200400
Forc
e (k
N)
-3 -2 -1 0 1Total Drift (%)
-4
0
4
C (g
)
wall side
column side-380 -360 -340 -320 -300Displacement (mm)
0
10
20
30
Forc
e (k
N)
-0.4 -0.2 0 0.2 0.4Total Drift (%)
-0.100.10.20.30.4
C (g
)
wall side
column side
(a) (b)
Test D3PA = 0.65g
Test HSC4γ = 0.3%
One-bay Model
31
Findings: Footing Response -0.4 -0.2 0 0.2 0.4 0.6
Rotation (deg)
-2000
-1500
-1000
-500
0
500
Mom
ent (
kN m
)
-1.6 -1.2 -0.8 -0.4 0Rotation (deg)
-200
0
200
400
600
Mom
ent (
kN m
)
Strip footing Square footing
-160-120 -80 -40 0 40Base Disp (mm)
-200-100
0100200300400
She
ar (k
N)
-160 -80 0Base Disp (mm)
-300
-200
-100
0
100
She
ar (k
N)
0 200 400 600 800Axial force (kN)
-100
-80
-60
-40
-20
0
Set
tlem
ent (
mm
)
0 200 400 600 800Axial force (kN)
-80
-60
-40
-20
0
Set
tlem
ent (
mm
)
columnside
columnside
columnside
columnside
One-bay Model
Test D3PA = 0.65g
32
Findings: Energy DissipationOne Bay Dynamic: Moment-Rotation
% of Moment Rotation Energy
0%
20%
40%
60%
80%
100%
D 1 D 2 D 3 D 4
Test name
Square FootingStrip Footing
Two Bay Dynamic: Moment-Rotation% of Moment-Rotation Energy
0%
20%
40%
60%
80%
100%
D 5 D 6 D 7 D 8 D 9
Test name
Exterior Sq FootingInterior Sq FootingStrip Footing
One-bay Model
Two-bay Model
33
Findings: Energy Dissipation
0 0.5 1 1.5 2 2.5Max Drift (%)
60
70
80
90
100
EΣf
ootin
gs/E
Σtot
al (%
)
One BayTwo Bay
sQvVMfootings EEEE −−− ++=∑ θ (1)
)(∑+∑=∑ −θMjointsfootingstotal EEE (2)
34
Summary of Physical Model Tests
Previous (1g) and recent centrifuge tests substantiate and assist in quantifying the benefits and consequences of rocking shallow foundations; for the subset of structure-foundation modelsProvide a robust set of data for calibration of numerical models
35
Numerical Modeling
Macro-element modeling (UCD)Winkler-based (design-oriented) modeling (UCSD)All modeling conducted in OpenSEES(PEER developed platform)Sensitivity Studies & Model comparisons
36
Macro-element Model
macro-element
Considers foundation and surrounding soil as a single macro-element
Constitutive model that relates the forces (V, H, M) and displacements (s, u, θ) acting at the base center point of the footing
37
38
Macro-Element Model
39
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 = 0.42
Cremer et al. (2001)
Houlsby and Cassidy (2002)
Nova and Montrasio (1991)
Failure Envelopes
40
Element - ZeroLengthSection
Section - SoilFootingSection
-ndm 2 –ndf 3
Node i (0, 0)
Node j (0, 0)
Fixed
Free
section SoilFootingSection -secID -FS -Vult -L -Kv -Kh -deltaLelement 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 Implementation
41
Experimental-Numerical Comparison
(Qu/Qa = 2.5)
42
• Series of individual uncoupled springs• For applied H-M-V, ensemble of springs calculates:
• Sliding displacement• Rotation• Settlement
• Shear-vertical responses uncoupled• Gap, closure, damping defined by springs in series
y
z
θ
Q-z springs P-y spring
T-y spring
Winkler-based Model
Near-StructurePlastic Response
Far-StructureElastic Response
Drag
ElasticDamper
Closure
Plastic
Beam Nodes
Fixed Nodes
43
Winkler-based Model• Vertical resistance from non-linear Qz springs• Horizontal resistance is a combination of
• Nonlinear Py for passive earth pressures• Nonlinear Ty for base sliding
• Mesh generator implementation• All springs based on Boulanger et al., 2000• Previously calibrated to pile test data
Variable Lateral Springs Spacing
VerticalStiffness
Distribution
qiPressure Distribution
Lend
Soil PropertiesShear Modulus, GPoisson's Ratio, υFriction Angle, φ'
KXkend
Lmid
kmid
x
CL
KX
KZ
Kθ
44
q0= 2. Cr. qultElastic portion:
Plastic portion:
}Qult = ultimate bearing capacity Kel = initial elastic stiffness (vertical)z50 = displacement at 50% of Qultn, c, Cr = parameters defining the shape of the Q-z curve in plastic region - hard-coded in the material model
- User Inputs
q0= load at the start of the plastic loading cycle
Cr = q/qult when plastic yielding first occurs in virgin loading
-0.8 -0.4 0 0.4 0.8Normalized vertical settlement (s/z50)
-1-0.8-0.6-0.4-0.2
00.2
Nor
mal
ized
ver
tical
load
(Q/Q
ult)
Winkler-based Model: q-z
n
opoultult
zzzczcqqqq
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−+⋅
⋅−−=
50
50)(
Vertical nonlinear springs; providing vertical and rocking resistance (aka “q-z” in pile analysis, for tip resistance)
45
Winkler-based Model: p-yHorizontal nonlinear springs; accounting for passive resistance in front of the embedded footing (aka “p-y” in pile analysis, also lateral resistance)
}Pult = ultimate bearing capacity Kel = initial elastic stiffness (vertical)z50 = displacement at 50% of Pultn, c, Cr = parameters defining the shape of the P-y curve in plastic region - hard-coded in the material model
- User Inputs
Cr = p/pult when plastic yielding first occurs in virgin loading
-20 -10 0 10 20Normalized Lateral Displacement, u/y50
-1
-0.5
0
0.5
1
Nor
mal
ized
Lat
eral
Lo
ad, H
/pul
t p0= 2. Cr. pultElastic portion:
Plastic portion:
p0= load at the start of the plastic loading cycle
n
opoultult
yyycycpppp
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−+⋅
⋅−−=
50
50)(
46
-20 -10 0 10 20Normalized Lateral Displacement, u/z50
-1
-0.5
0
0.5
1
Nor
mal
ized
Lat
eral
Lo
ad, H
/t ult
tult = ultimate lateral capacity (friction) Kel = initial elastic stiffness (lateral)y50 = displacement at 50% of tultn, c, Cr = parameters defining the shape of the T-y curve in plastic region - hard-coded in the material model
Winkler-based Model: t-y
t0= 2. Cr. tultElastic portion:
Plastic portion:
t0= load at the start of the plastic loading cycle
n
opoultult
yyycyctttt
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−+⋅
⋅−−=
50
50)(
Horizontal nonlinear springs; accounting for frictional resistance between footing and soil (aka “t-z” in pile analysis, skin resistance)
47
0 4 8 12Normalized settlement (z/z50)
0
0.4
0.8
1.2
Nor
mal
ized
load
(Q/Q
ult)
Strip FootingRegressed Qz curveKRR01 # S2KRR01 # S25KRR01 # S28KRR01 # S31Regressed Qz curve (m+/ - s)
General footing condition
Strip SquareCentrifuge tests Full-scale testsL/B = 3.5-6.6 B = 1-3mDf = 0-0.3m Df = 0.7-0.9mFSv = 2-3.8 FSv = 2-2.3
General soil condition Medium to dense sand (Dr = 55-80%) phi= 33-400
Water content = 0-5%
Mechanistic Calibration; eg q-z
48
Experimental-Numerical Comparison
-4 -2 0 2 4Rotation θ (degrees)
-400
-200
0
200
400
Mom
ent M
(kN
-m)
-4 -2 0 2 4Rotation θ (degrees)
400
300
200
100
0
Settl
emen
t s (m
m)
Experimental SimulationBNWF Mesh Simulation(a) (b)
Sand, Qu/Qa=3.0, φ’ = 38, Dr = 60%
49
Comparison of Models
1.29
0.40
0.84
Tn (flex base/no sliding)(sec)
2.61
4.79
3.13
Factor of safety (FSv)
2.72
6.46
3.75
Mass @ floor
x 105 (kg)
6.94
3.78
5.78
Total weight on the footing(MN)
1.420.765233
0.580.2116.42
0.980.44 414.41
Tn (flex base/ sliding)(sec)
Tn (fixed base)(sec)
StoriesHeight (m)
Model
3 different wall-footing prototypesRange of EQ motions & static cyclic inputResting on OC clayTn (fixed-base) ~ 0.2-0.8 secTn (flexible-base) ~ 0.4-1.3 sec
50
Physical parameters used in the studyBasic and Given parameters
cu = 52.67 kPa, φ = 00
ν = 0.5, Gmax = 26.33 MN/m2
Rayleigh damping = 5% (first two modes)
Radiation damping = 5%
Derived parameters
Bearing capacity, Qult = 18.11 MN (from Terzaghi, 1943)
Shear Capacity, Vult = 3.32 MN (Vult=c*Lf*Bf)
Vertical stiffness, Kv = 814 MN/m (from Gazetas, 1991)
Horizontal stiffness, kx = 750 MN/m (from Gazetas, 1991)
Comparison of Models
51
M-θ (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion-0.03 -0.02 -0.01 0 0.01 0.02 0.03Rotation (radian)
-40
-20
0
20
40
Mom
ent (
MN
.m)
Model1 - Motion CUCDUCI
Moment-Rotation
UCDUCSD
52
S-θ (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion-0.03 -0.02 -0.01 0 0.01 0.02 0.03
Rotation (radian)
-120
-80
-40
0
40
Set
tlem
ent (
mm
)
Model1 - Motion CUCDUCI
Settlement Vs Rotation
UCDUCSD
53
V-v (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion-100 0 100 200 300Sliding (mm)
-4
-2
0
2
4
She
ar F
orce
(MN
)
Model1 - Motion CUCDUCI
Shear Force Vs. Sliding
UCDUCSD
54
Revisit Shear Resistance Modeling
Vu (old)= 3.32 MN; Vu (new)= 26 MNKx (old)= 750 MN/m; Kx (new)= 1815 MN/mTn (model1)= 0.98s; Tn (model1)= 0.95sTn (model2)= 0.58s; Tn (model2)= 0.54sTn (model3)= 1.42s; Tn (model3)= 1.35s
55
V-v (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion
UCDUCSD
-2 -1 0 1 2Sliding (mm)
-4
-2
0
2
4
She
ar fo
rce
(MN
)
56
M-θ (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion
UCDUCSD
-0.02 0 0.02Rotation (rad)
-40
-20
0
20
40
Mom
ent (
MN
-m)
57
S-θ (Model 1: Tn(fb) = .44s)
2% in 50 Year Motion
UCDUCSD
02 -0.02 0 0.02Rotation (rad)
-160-120
-80-40
040
Set
tlem
ent (
mm
)
( )
58
DiscussionPositive comparative points
Initial stiffnesses and general shape of M-θ response reasonably comparableInitial settlement response and shape of settlement response, particularly in higher amplitude earlier cycles reasonably comparable
Physical DifferencesShear-moment coupling
Results in reduction of shear capacity at given moment; which isnot captured in a Winkler-based modelDifferences more pronounced for lower M/V ratio wall-foundation model
Settlement estimations under low amplitude shaking are challenging to capture accurately; variations in s between models can be on the order of 2-3x
59
Outcomes We hope to propagate this new knowledge and these new tools into practice as they are refined and become more readily available:
All data reports available on-line: cgm.engr.ucdavis.eduOpenSEES implementation and examples of various foundation elements use will be complete by Fall 2007
Findings from this work will help us:Improve nonlinear static proceduresImprove accuracy of our nonlinear dynamic analyses capabilitiesProvide improved confidence in the use of the foundation as an energy dissipative system
60
References (1/5)Ajrab, J. J., Pekcan, G., and Mander, J. B. (2004). “Rocking wall-frame structures with supplemental tendon systems.” Journal of Structural Engineering, ASCE, 130(6), 895–903.Alavi, B. and Krawinkler, H. (2002). “Strengthening of frame structures subjected to near-fault ground motions.” 12th European Conference on Earthquake Engineering. London, U.K., Elsevier Science Ltd., London, U.K.Barlett, P. E. (1976). “Foundation rocking on a clay soil.” M.E. Thesis, University of Auckland, New Zealand.Chang, B., Raychowdhury, P., Hutchinson, T., Thomas, J., Gajan, S., and Kutter, B. (2007). “Evaluation of the seismic performance of combined frame-wall-foundation structural systems through centrifuge testing.” 4th International Conference on Earthquake Geotechnical Engineering. Thessaloniki, Greece, June 25-28.Faccioli, E., Paolucci, R., and Vivero, G. (2001). “Investigation of seismic soil-footing interaction by large scale cyclic tests and analytical models.”4th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. San Diego, California.Gajan, S. (2006). “Physical and numerical modeling of nonlinear cyclic load-deformation behavior of shallow foundations supporting rocking shear walls,” PhD thesis, University of California, Davis.
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References (2/5)Gajan, S. and Kutter, B. L. (2007). “A contact interface model for nonlinear cyclic moment-rotation behavior of shallow foundations.” 4th International Conference on Earthquake Geotechnical Engineering.Thessaloniki, Greece, June 25-28.Gajan, S., Kutter, B. L., and Thomas, J. M. (2005). “Physical and numerical modeling of cyclic moment-rotation behavior of shallow foundations.” 16th International Conference on Soil Mechanics and Geotechnical Engineering.Gajan, S., Phalen, J., and Kutter, B. (2003a). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the SSG02 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-03/01.Gajan, S., Phalen, J., and Kutter, B. (2003b). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the SSG03 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-03/02.Gajan, S., Phalen, J., Kutter, B., Hutchinson, T., and Martin, G. (2004). “Centrifuge modeling of nonlinear cyclic load-deformation behavior of shallow foundations.” 11th International Conference on Soil Dynamics and Earthquake Engineering, and the 3rd International Conference on Earthquake Geotechnical Engineering.
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References (3/5)Gajan, S., Phalen, J. D., Kutter, B. L., Hutchinson, T. C., and Martin, G. (2005). “Centrifuge modeling of the load deformation behavior of rocking shallow foundations.” Journal of Soil Dynamics and Earthquake Engineering, 25, 773–783.Harden, C. W. (2003). “Numerical modeling of the non-linear cyclic response of shallow foundations.” M.S. Thesis, University of California, Irvine.Harden, C. W., Hutchinson, T. C., and Moore, M. (2004). “Investigation into the effects of foundation uplift on simplified seismic design procedures.” Structural Engineers Association of California (SEAOC) 75th Anniversary Convention. 91–111.Harden, C. W., Hutchinson, T. C., and Moore, M. (2006). “Investigation into the effects of foundation uplift on simplified seismic design procedures.” Earthquake Spectra, 22(3), 663–692.Houlsby, G. and Cassidy, M. (2002). “A plasticity model for the behavior of footings on sand under combined loading.” Geotechnique, 52(2), 117–129.Kutter, B., Martin, G., Hutchinson, T., Harden, C., Gajan, S., and Phalen, J. (2003). “Workshop on modeling of nonlinear cyclic load-deformation behavior of shallow foundations.” Pacific Earthquake Engineering Research Center Report, University of California, Davis; PEER report number 2005/14.
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References (4/5)Nova, R. and Montrasio, L. (1991). “Settlements of shallow foundations on sand.” Geotechnique, 41(2), 243–256.PEER (2006). “Open System for Earthquake Engineering - OpenSEESversion 1.7.3”. Retrieved August 25, 2006, from http://opensees.berkeley.edu/.Phalen, J. D. (2003). “Physical modeling of the soil-foundation interaction of spread footings subjected to lateral cyclic loading.” M.S. Thesis, University of California Davis.Rosebrook, K. and Kutter, B. (2001a). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR01 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/09.Rosebrook, K. and Kutter, B. (2001b). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR02 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/10.Rosebrook, K. and Kutter, B. (2001c). “Soil-foundation structure interaction: Shallow foundations: Centrifuge data report for the KRR03 test series.” Center for Geotechnical Modeling Data Report UCD/CGMDR-01/11.
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References (5/5)Rosebrook, K. R. (2001). “Moment loading on shallow foundations: Centrifuge test data archives.” M.S. Thesis, University of California Davis.Taylor, P. W., Bartlett, P. E., and Weissing, P. R. (1981). “Foundation rocking under earthquake loading.” 10th International Conference on Soil Mechanics and Foundation Engineering, Vol. 3. 313– 322.Toranzo-Dianderas, L. A., Restrepo, J. I., Carr, A. J., and Mander, J. B. (2004). “Rocking confined masonry walls with hysteretic energy dissipators and shake table validation.” 13th World Conference on Earthquake Engineering. Paper no. 248.Wiessing, P. R. (1979). “Foundation rocking on sand.” School of Engineering Report No. 203, University of Auckland, New Zealand.
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Small footing
Large footing
Wall-Foundation Experiments
66
Footing locationCurrent soil surface location (soil_min)Maximum past settlement (soil_max)Current bearing pressureMaximum past pressure experienced
Internal variables
Macro-Element Model
67
Shearwall specimen
Lateral Loading Apparatus
Wall-Foundation Experiments
68
Experimental-Numerical Comparison
(Qu/Qa = 7.5)
69
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
Mom
ent M
(kN
-m)
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
Mom
ent M
(kN
-m)
(a) Experiment (b) Numerical Simulation
Type A Footings: Strong Axis Rocking
One-g, Clay, cu = 49 kPa, φ’ = 0
Experimental-Numerical ComparisonTaylor et al (1980); 1-g tests
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-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)
4
3
2
1
0
Settl
emen
t s (m
m)
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Rotation θ (degrees)
4
3
2
1
0
Settl
emen
t s (m
m)
Experimental DataBNWF Mesh Simulation
One-g, Clay, cu = 49 kPa, φ’ = 0
Experimental-Numerical ComparisonType A Footings: Strong Axis Rocking
Taylor et al (1980); 1-g tests