Aseismic Design of Shallow (rocking) Foundations · Aseismic Design of Shallow (rocking)...
Transcript of Aseismic Design of Shallow (rocking) Foundations · Aseismic Design of Shallow (rocking)...
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Aseismic Design of Shallow (rocking) Foundations
November 28 2012
Michael Pender
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MJP starting point 1
Structure and foundation form a single entity
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MJP starting point 2
Foundation behaviour is nonlinear
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MJP starting point 3
Elastic soil-structure interaction doesn’t work hence the terminology SFSI (soil-foundation-
structure-interaction)
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Elastic SSI diagram
uhhe
heus
Me
u = us + uh + he
Ks
KhK
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Elastic SSI for a water tower
0 1 20
5
10
15
Frequency ratio
Res
pons
e ra
tio
Fixed base
Elastic soil
su 50 kPa Vs 118 m/s M 50 tonnes h 20 m D 9 m (LRFD)
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MJP starting point 4
Priestley et al 2007: Displacement-based seismic design of structures
use of replacement structure Paper by Trevor Kelly in Bull. NZSEE 2009
many buildings not heavy enough to prevent rocking need better understanding of soil response
Paper by Priestley, Evison & Carr Bull. NZSEE 1978 related NZS4203 (1976) based on Housner BSSA 1963 (a famous paper)
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Nonlinear SFSI
Need a “design” method for modelling foundation moment-rotation curves hands-on approach – quick check on software output or a peer-review tool
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Shibata and Sozen - 1976
Mom
ent
Rotation
M - for substitute(ductile) structure
M - cracked section
M - uncracked section
For a structural component – beam or column
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Priestley replacement structure
Set of equations for elastic pile head stiffness of long piles Extension to include nonlinear behaviour Provides a “spreadsheetable” design environment (or design checking) Could be applied to the Substitute Structure idea of Sozen (1976) and Priestley et al (2007)
Displacement
Shea
rfor
ceSDOF simulationFoundation: shallow or pile
F
he ks
me
Ke
Horizontal & rotationalstiffness
ks
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MJP starting point 5
Nonlinear foundation moment-rotation relation neglect horizontal deformation at foundation level
linear structural behaviour
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Nonlinear foundation response
Experimental data – Tom Algie’s PhD thesis
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Shallow foundation pull-back
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Shallow foundation pull-back
0 5 10 15 20 25 300
20
40
60
80
100
Rotation (millirads)
Mom
ent (
kNm
)
Snap 1Snap 2Snap 3Snap 4Snap 5Snap 6Snap 7Snap 8Snap 9
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Shallow foundation snap-back
0 0.02 0.04 0.06 0.08 0.1 0.12 0.140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Normalised Rotation - θ0/α
Hal
f Per
iod
(sec
s)
Housner's equationTest 6Test 7Test 9
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Shallow foundation snap-back
10-1
100
101
102
0
10
20
30
40
50
60
Half Amplitude Rotation (millirads)
Dam
ping
Rat
io (%
)
Test 5 eastTest 6 eastTest 6 westTest 7 eastTest 7 westTest 9 eastTest 9 west
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Tom’s Abaqus modelling
0 5 10 15 20 25 300
20
40
60
80
100
Rotation (millirads)
Mom
ent
(kN
m)
ExperimentsAbaqus
(Hence not dependent on spring bed modelling.)
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Tom Algie’s finite element work
0 2 4 6 8 100
20
40
60
80
100
120
140
Rotation (millirads)
Mom
ent (
kNm
)
Gezatas formulaAbaqusOpenSEES - constant elasticRuaumoko - constant elasticOpenSees - FEMA elastic
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Hyperbolic M-θ curve fit
0 0.05 0.1 0.15 0.2 0.25 0.30
0.2
0.4
0.6
0.8
1
1.2
Normalised foundation rotation
Norm
alise
dm
omen
tcap
acity Normalised moment capacity at applied vertical load
Best fit curve through measured moment-rotation data
Measured moment-rotation data
a
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Hyperbolic curve as a secant modulus
0 0.05 0.1 0.15 0.2 0.25 0.30
0.2
0.4
0.6
0.8
1
1.2
Normalised foundation rotation
Norm
ailse
dse
cant
rota
tiona
lstif
fnes
s
Foundation rotational stiffness based on Gmaxb
Rotation
Mom
ent
1
K _secant
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Secant modulus on a log rotation scale
10-5 10-4 0.001 0.01 0.1 10
0.2
0.4
0.6
0.8
1
1.2
Normalised foundation rotation (log 10 scale)
Norm
alise
dse
cant
rota
tiona
lstif
fnes
s
Foundation rotational stiffness based on Gmax
Measured data
c
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What about damping?
Important for forced-based and displacement-based design hysteretic damping rather than radiation
not frequency dependent
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Nonlinear finite element damping using PLAXIS 3D
4− 10 3−× 0 4 10 3−×
1− 104×
5− 103×
5 103×
1 104×
Rotation (radians)
Foun
datio
n m
omen
t (kN
m)
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Shallow foundation example
0 0.02 0.04 0.06 0.08 0.10
5 104×
1 105×
1.5 105×
2 105×
Rotation (radians)
Mom
ent (
kNm
)
Hyperbolic moment- rotation curve
stiffness for second iteration
elastic stiffness for first iteration
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Shallow foundation iteration
0 2 4 6 80
1 105×
2 105×
3 105×
Iteration
Foun
datio
n m
omen
t (kN
m)
Mult
FMult ΦMult
Mult
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Pile foundation nonlinear
0 20 40 60 800
50
100
150
Pile head horizontal displacement (mm)
Pile
head
horiz
onta
lshe
ar(k
N)
OpenSeesPL
Davies & Budhu
Field load-unload curve
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Conclusions
An approach to incorporating nonlinear foundation moment-rotation curves into modelling the rocking of shallow foundations reduced foundation actions when compared with classical SSI
nonlinearity at the “middle” of the moment-rotation curve important
based on field test data and 3D nonlinear finite element modelling with foundation loss of contact
not dependent on spring-bed modelling relatively simple hands-on calculation as a design aid or peer review tool.