Centrifuge modelling of foundations subjected

Transcription

10/24/2013
French Institute
of Science and Technology
for Transport, Development
and Networks
Centrifuge Modelling of
foundations subjected to cyclic
loading
Luc Thorel
ALERT Doctoral school Soil-Structure Interaction
Aussois, 4 oct. 2013
www.ifsttar.fr
French Institute of Science and Technology for Transport, Development and Networks
Outline
• Where do I come from?
• Ifsttar : French institute of science and technology
for transport, development and networks
• Physical Modelling
• Cyclic loading on foundations
www.ifsttar.fr
1
10/24/2013
Nantes
Paris
TGV
2h00
Nantes
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Nantes
• 6th french city
• About 580 000 inhabitants
• Maritime harbour
“Portus Namnetum” during the Roman Empire
• University & Research and higher education cluster L’UNAM
76 000 students including 2 300 PhD students
11 000 personnel including 4 200 researchers and faculty members
9 doctoral schools training more than 400 PhD students per year
124 research units
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2
10/24/2013
Nantes
La folle journée
8 times « champion de France »
3 times winner of the french cup
Carnaval
Gâteau nantais
Prime minister
J.M.
Ayrault
Mayor
since
1989
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Petit beurre LU
Nantes
• Sea-shore 55km
• Saint Nazaire shipyard
Queen Mary 2
• Châteaux de la Loire (2h driving)
Chenonceau
Chambord
Amboise
Blois
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3
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Nantes’ Physical Modelling facilites
climatic wind tunnel
(CSTB)
wave tank (ECN)
semi-anechoic chamber
(IFSTTAR)
laser vibometry bench
(IFSTTAR)
towing tank (ECN)
geo-centrifuge (IFSTTAR)
+ shaker + robot
Pavement fatigue carousel
(IFSTTAR)
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4
10/24/2013
IFSTTAR: one ambition
Produce, disseminate and enhance
knowledge allowing for efficient, sustainable
and fair society
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Areas of research
•
Human and freight mobility, means and uses
•
Systems, transport means and their reliability
•
Our impacts on transport safety and health
•
Urban engineering, housing and networks
•
Civil engineering and building materials
•
Natural hazards
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5
10/24/2013
Organization chart from 2013 on
Materials and
structures
Geotechnical engineering,
earth sciences, natural
hazards
Components and
systems
Transport, health, safety
Planning, travel
practices and the
environment
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Key numbers
In 2011
•
A 120 million Euro budget
•
282 publications in international
reviews
•
160 research contracts
•
110 expert appraisals
•
76 patents
•
74 theses defended
•
61 european projects
• 6 main sites as well as offices
in Belfort, Grenoble, Nice, Le
Grand Quevilly and ClermontFerrand
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Ifsttar : Nantes centre
LCPC, Nantes centre
47°09’24’’N
01°38’21’’W
Centrifuge
building
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Ifsttar geo-centrifuge
Data acquisition
on board
max. acceleration 200×g
Swinging basket
L=1.4m
w=1.15m
H=1.5m
max. mass
2t
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Ifsttar centrifuge scheme
Rotating mass 42t
Asynchroneous
engine 2-speeds
(1000 & 1500 tr/mn)
Power 410 kW
Slip rings :
measurements : 101
power : 5 + 4 (160A)
Fiber optic
6 hydraulic joints
(air, water, oil)
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Centrifuge main activities
Foundations under
horizontal seismic loading
Piles subjected to cyclic loading (V or H)
Ground vibration isolation
Composite foundations
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www.ifsttar.fr
Another way of modelling :
physical modelling on small
scale model
• How to study a physical problem?
• The use of small scale model in civil
engineering
• How to link the (small scale) model to the
(full scale) prototype?
• Physical modelling in geotechnics
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How to study a physical problem?
• Analytically
• Numerically
• Experimentally
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Analytical method
♦ knowledge of each physical phenomenon involved
 knowledge of the boundary conditions
 full equations of the phenomenon
 knowledge of the exact solutions to the equations
e.g. in the field of mechanics :
Equilibrium equations
Boundary conditions
Behaviour
ex : elastic beam
subjected to bending
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Numerical Method
The analytical solution is not necessarily known
Have to find an approximate solution : finite element, finite differences, …
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Experimental method (1)
Test on the real structure
It has to exist: difficulties with an unique structure
(Civ.Engng)
Parametric studies difficult to perform: material, complex
geometry, boundary conditions
In geotechnical engineering: natural variablity of soil
properties
Analogy between 2 phenomena that follow the same
laws
e.g.: electrical analogy of hydraulic diffusion in soils
[Schneebeli, 1966; Lafhaj & Shahrour 2002 -IJPMJ]
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Experimental Method (2)
Test on small scale model
• when the complexity is so high that numerical and
analytical methods are not sufficient
3D problem
Complex and numerous boundary conditions
Material rheology not known very well
• when loading is too high to be duplicated easily (seism)
• when a large number of tests are required (parametric
study)
• when the test duration is too long (soil consolidation)
• when the structure does not yet exists
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The use of physical modelling in
civil engineering
• Aerodynamics
• Hydrodynamics
• Others
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12
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The use of physical modelling in civil engineering
Aerodynamics
Influence of the wind and the storms on structure
Bridges, towers, chimneys, big buildings (stade de France, la
Défense Arch, Millau viaduct,…)
Wind tunnel : CSTB Nantes (Climatic wind tunnel Jules
Verne), ONERA,…
Millau viaduct
Stade de France
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La Défense, Paris
Hydrodynamics (1)
Influence of waves, currents
Erosion, transport Harbours, Near-shore, Offshore.
Mont Saint-Michel
SOGREAH(Grenoble)
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13
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Hydrodynamics (2)
Towing tank, wave tank:
Ecole Centrale de Nantes,
SOGREAH, DGA, UFRJ
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Others
• Noise propagation due to traffic
CSTB Grenoble, IFSTTAR : semi-anechoic room
• Geology et tectonics
fault formation, tectinc plates collision, salt dome
mouvement
IPG (Paris)
• Surface Geophysics
Ultrasonic wave propagation IFSTTAR
• Seism simulation
Structures behaviour
Soil-structure interaciton, liquefaction
CEA, IFSTTAR, French
Japan,
California
Institute of Science and Technology for Transport, Development and Networks
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14
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How to link the model to the
prototype?
•
•
•
•
•
•
Definitions
Similitude
Example : heat propagation
Dimensional Analysis
Dimensionless Variables
Vaschy-Buckingham theorem
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How to link the model to the prototype?
Definitions
• PROTOTYPE = full scale structure
• MODEL = representation at the small scale of
an object which is intended to be realized at
the full scale (or conversely)
Chimical molecule : MODEL > PROTOTYPE
Geotechnical structure : MODELE < PROTOTYPE
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Similitude
From mathematics : geometrical transformation that
includes :
• - homothety (scale 1/N)
• - displacement (translation or rotation)
Ap
Am
PROTOTYPE
Similitude centre
Small scaleMODEL
SIMILAR
To the Prototype
O
Corresponding points Ap from the prototype and Am from the model
are HOMOLOGOUS
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Galileo Galilei (1564-1642)
Susterman, Musée des Offices, 1636
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Geometrical Similitude  Similitude
of the behaviour
Galileo Galilei, 1638 : Discourses and
Mathematical Demonstrations Relating to Two
New Sciences (Discorsi e dimostrazioni
matematiche, intorno à due nuove scienze, 1638):
“A larger machine, built of the same material and
in the same proportion as the smaller,
corresponds with exactness to the smaller in
every respect except that it will not be so
strong or so resistant against violent
treatment; the larger the machine, the greater its
weakness.”
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The Geometrical Similitude may be
an OBSTACLE to the Similitude
concerning the Nature, Structure
and Behaviour
Galileo Galilei, 1638
“If one wishes to maintain
in a great giant the same
proportion of limb as that
found in an ordinary man
he must either find a
harder and stronger
material for making the
bones”
8
WEIGHT
POIDS
(force)
6
4
2
BEARING
CAPACITE
CAPACITY
PORTANTE
0
(force)
0
1
Longueur
Length
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2
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Example : Heat Propagation
Newton 1704 : Proportionally a small globe is cooling off
more rapidly than a bigger one
Buffon 1770 : Experimental verification on iron canonballs => age of the earth~77000 years
Fourier 1822 : Analytical theory of heat
Fourier law

q   K grad T
Heat equation
T
 Cp
 div ( K grad T )
t
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Heat Propagation
density
temperature
time
Dimensions?
Thermal Conductivity
Specific Heat
Heat equation
T
 Cp
 div ( K grad T )
t
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Joseph Fourier
(1768-1830)
Dimensionnal Analysis
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Académie des Sciences,
1823
Dimensionnal Homogeneity
Each term of an equation has the same dimension
than the others
Relationships between physical variables do not
depend on the unit system choosen
7 fundamental units
•
Length [m]
•
Mass [kg]
•
Time [s]
•
Electrical intensity [A]
•
Temperature [K]
•
Light Intensity [Candela]
•
Quantity of matter [mole]
[L]
[M]
[T]
[I]
[Q]
[J]
[mole]
Many combined units
•
Force [N = kg.m.s-2]
•
Pressure [Pa = N.m-2]
•
Inertia [m4]
•
Velocity [m/s]
•
Energy [J = N.m]
•
etc...
[MLT-2]
[ML-1T-2]
[L4]
[LT-1]
[ML2T-2]
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Heat propagation on small scale
model
m
2
m
T
 T
km
m
t
 xm
Tm = T*.Tp
tm =
km =
 
t*.tp
k*.kp
2
* *
T * T p
2 T p
p k T
k
2
2
t*  t p
x*  x p
 
m = *.p
2
p
T p
p  T

k
2
t p
 xp
 
T*= scaling factor
Fourier dimensionless Number
k * t*
x
*2
1
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Example : cooling of a volume of
water
km tm

kptp
x  x 
m 2
p 2
same fluide  same diffusivity
km=kp
Coffee cup
SMALL SCALE MODEL
xp
1000
xm
Olympic swimming pool
PROTOTYPE
tp
1.000.000
tm
1mn  2 year
But the boundary conditions are different
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Dimensionless variables
• If X1, …. Xi, …Xn are arbitrary physical variables
• It is possible to build an adimensionless number:
pi = Xi / X1 …X2…. X3
Example : Fourier number
Thermal Diffusivity [L2/T]
Time [T]
Length [L]
p
Fourier

k t
x
2
dim  less 
Reynolds
Mach
Péclet
Euler
Froude …
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Complete series
• It is possible to build m INDEPENDENT dimensionless
numbers p1, …pj,…. pm : it is a COMPLETE SERIES
Example : fluid mechanics without heat exchange
8 variables : F, l, v, , h, g, c, Ts
Complete series of 5 dimensionless numbers : Reynolds (viscosity) Euler
(pressure) Froude (heavy fluid) Mach (compressibility) Weber (surface tension)
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Dimensional Matrix
• Each dimensionless number p based on those variables may
be written:
p = (X1)u1. (Xi)ui . (Xn)un
If Xi depends only on j « units » L, M, T (j = 3):
dimension of Xi : [Xi] = [ Lai Mbi Tci ]
dimension of p: p  [La1Mb1Tc1] u1... [ Lan Mbn Tcn ] un
a1. u1+…. an.un =0
b1. u1+…. bn.un =0
j equations
etc….
c1. u1+…. cn.un = 0
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Dimensional matrix
a1 a 2
b1 b2

z1 z2

an 
bn 

zn 
 u1   0 
 u2   0
  
 un   0
   
j lines (j ≤ n)
n columns
(system gally undetermined)
Each solution (u1, u2, …, ui,…, un) gives a p number based on those
variables :
p = (X1)u1. (Xi)ui . (Xn)un
•Vaschy-Buckingham theorem (1914)
A complete series of m INDEPENDENT dimensionless
numbers p1, …pj,…. pm may be formed
With m = n - r
where r is the rank of the dimensional matrix
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In Practice
COMPLETE SIMILITUDE between the model
and the prototype : the m = n - r dimensionless
number pi have simultaneously the same
value for the two systems
INCOMPLETE SIMILITUDE
The most important similitudes are selected for
each particular case
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Physical Modelling in
Geotechnics
•
•
•
•
Similar stress
Centrifuge
Scaling factors
Scale effect & size effect
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Physical modelling in geotechnics
Similar stress
•Soil behaviour is NOT
LINEAR and depends on the
STRESS state
•Many soil parameters depends on  :
Void ratio: e = e0 -log( ’)
Undrained cohesion: Cu = α  ’. OCRβ
Shear strength:  = C ’ +  ’ tg
Young’s modulus: E = a ( ’)2/3
etc...
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Similar stress
Prototype (full scale)
σP = ρP gP zP
Model (small scale)
σm = ρm gm zm
Same stress state between prototype and model
σ* = σm / σP = 1
Same soil
ρ* = ρm / ρP = 1
Reduced scale
z* = zm / zP = 1/N
σ* =1
ε*=1
Increase of g-level, e.g. : MACROGRAVITY
g* = gm / gP = N
Strain : if ξ*=ℓ*=1 => ε* = ξm ℓP / ξP ℓm = 1
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How to change “g”?
• Moving on another planet : Jupiter G=2.5g
• Shock
• Hydraulic gradient : v’=(iw + ’) z
• Base-friction table
• Centrifuge
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Centrifuge : Edouard Phillips (1821-1889)
1869
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Scaling factors
Length, displacement
density
acceleration
stress
Force
Time (dynamics)
Angle
Mass
Surface
Volume
Energy
Bending Moment
*=1/N
*=1
g*=N
*=1
F*=1/N2
t*=1/N
a*=1
m*=1/N3
S*=1/N2
V*=1/N3
E*=1/N3
M*=1/N3
Phillips, 1869
Behaviour independant
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1st tests in geotechnical
centrifuge ~ 1930
• BUCKY, University Columbia,USA
• Stability of mines
• POKROVSKI, Moscou
• Stability of earthworks
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Centrifuges in the world
Ifsttar
• ~ 40 with a radius > 3m
Payload [kg]
Max.
acceleration
[×g]
[Ng, 2013]
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Size and scale effects
Size effect : linked to the size of the geotechnical work
differences in the results obtained for several prototypes tested
e.g; [Ovesen, 1979] bearing capacity coefficient: “the larger the prototype diameter, the
smaller the bearing capacity and the less tendency to peak”
Scale effect (or grain size effect) : for the simulation of the same prototype, the results
at the prototype scale are different.
The comparison of such models is known as the “ modeling of models technique”
[Schofield, 1980], which is specific to centrifuge modelling.
Due to the fact that the same soil is used for both model and prototype.
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Size and scale effects
Log (BM)
Same prototype
Prototypes
with different sizes
[Ovesen, 1979]
Log (N)
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How to avoid scale effects?
Clay
Sand
No scale effect
Bearing capacity of shallow footings (circular or strip)
pile tip, penetrometer
B/d50 35
Response of piles to lateral loads
B/d50 45
or 60
Pull out load of anchor plates (circular or rectangular)
B/d50 48
Stability of tunnel face (B=tunnel diameter)
B/d50 175
Grain size effect on frictional interface
B/d50 50
or 100
[Garnier et al., 2007]
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Cyclic loading on foundations
• Cyclic loading
• Shallow foundation
• Deep foundation
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Cyclic loading on foundations
•
•
•
•
Very few recommandations in the design codes
Typical loads : waves & wind (Windturbines), currents, boat accosting and
mooring to quays, variable overloads or thermal dilatations
A preliminary step before seismic loading investigations
Programme SOLCYP (SOLlicitations CYcliques des Pieux ) 2008-2014
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[Jardine
2012]
Soil-footing interaction : building
subjected to lateral cyclic loading
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Cyclic loading : shallow foundations
Objectives
Rotation of buildings on shallow
footings (cyclic overturning
moments)
Cyclic
loads
Izmit (Turkey), 17th august 1999
[AFPS picture]
Determine the relationship
between horizontal load &
rotation of the foundation
under static and cyclic
horizontal loading
Saturated clay
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Centrifuge test programme
Heavy building
V/Vmax = 60%
Building
•
Square footing (B = 10 m)
•
Vertical load = Dead weight
Two buildings (100×g tests)
Light building
V/Vmax = 26%
Soil
•
Soft saturated clay : Undrained shear strength increasing linearly with depth (CPT tests)
Loading programmes
•
•
•
Vertical monotonic loading to failure
( Determination of vertical bearing capacity)
Horizontal monotonic loading to failure (with constant vertical dead weights M1 or M2)
Cyclic horizontal loading under self weight (with and without a sand layer below the footing)
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Experimental set-up : lateral loading device
Cyclic loading device
Model M2 after the test
Servo-jack
LVDTs
Load cell
LVDTs
Loading
direction
Load cell
Building model
PPTs
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Results : Horizontal cyclic loading (1)
f=0.16 Hz , H=± 3, ± 6, ± 8 & ± 10 daN
(Failure :HR ~ 1MN prototype scale)
2a
4
30
2b
1b
0
IP 121
10
0
1a
-10
1b
2a
2b
3a
-20
3b
4
IP 119
-30
0
2
2
4
6
8
10
Time (minute)
12
14
16
18
Load vs. Time
-10
0
2
4
6
8
10
Time (minute)
12
14
16
18
20
s & yG (mm)
20
-40
yG
15
Horizontal displacement vs. time
10
3a
5
1a
0
2a
1b
30
3a
20
2a
10
1a
IP 113
3b
2b
IP 112
1b
IP 105
0
IP 115
0
2
2b
4
6
8
10
Time (minute)
12
14
16
18
Pore pressure accumulation
(model scale)
S
-5
4
40
-10
4
3b
at depth B/4
50
Pressure variation
at depth B/4 (kPa)
H (daN)
1a
at the interface
3b
Pressure variation
at soil interface (kPa)
3a
10
Settlement vs. Time
-10
0
2
4
6
8
10
12
14
16
18
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TimeInstitute
(minute)
French
of Science and Technology for Transport, Development and Networks
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Results : Horizontal cyclic loading (2)
0.000
Overturning moment prototype (MN x m)
4 sets of cycles (prototype scale)
0.00
-0.001
-0.01
-0.003
-0.004
-0.02
-0.005
-0.006
-0.03
-0.007
-0.008
-0.04
-0.009
A
-0.010
-0.05
0.0
Settlement prototype (m)
B
0.1
Rotation (degree)
0.1
0.0
0.00
0.0
-0.02
-0.1
0.2
Rotation (degree)
-0.3
-0.06
-0.4
-0.08
-0.5
-0.10
-0.6
-0.12
-0.7
C
D
-0.8
-0.14
0
1
Rotation (degree)
2
0
5
5
0
0
-5
-5
A
-10
2
4
6
Rotation (degree)
B
-10
0.4
-0.2
-0.04
10
0.0
Overturning moment prototype (MN x m)
Sellement prototype (m)
-0.002
10
0.1
Rotation (degree)
0.2
0.0
10
10
5
5
0
0
-5
-5
C
0.2
Rotation (degree)
0.4
D
-10
-10
0
8
1
Rotation (degree)
Settlement-rotation
2
0
2
4
6
Rotation (degree)
8
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Moment-rotation
Results : Effect of cyclic sequences
on lateral resistance
M (MN.m)
2 5 .0
Test T9 (after cycles)
3
M (MN.m)
Test T10 (after cycles)
2 0 .0
1 5 .0
Test T7
15
Test T9
1 0 .0
M [MN x m]
O v e rt u r n i n g m o m e n t (M N x m )
20
Test T14
5 .0
Tests on Building M1
10
2
5
0 .0
Before cycles
After cycles
1
0
-5 .0
0
5
10
15
20
25
1 - r e m o v i n g t h e b u i l d in g in t h e in it i a l p o s it io n
V [MN]
2 - s h i ft d u e to c y c l ic s e q u e n c e s
-1 0 .0
3 - la s t h o r iz o n ta l s ta tic s e q u e n c e
-3 .0
-2 .0
V (MN)
q (°)
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-1 .0
0 .0
Rotation(degree)
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Conclusions & prospects
for shallow foundation
• Non-linear load-displacement behaviour
• Strain accumulation : settlement & rotation
• Large amount of work being dissipated in the foundation (M-q
curve)
• Effect of two vertical weight => failure envelope
• Drained interface
• Comparison with numerical analysis (collaboration with
University of Athens)
• Soil reinforcement below the foundation (e.g. piled
embankment)
• Seismic loading (e.g. with the Centrifuge earthquake
simulator)
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Deep foundations
Piles subjected to :
vertical loading
horizontal loading
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Piles – vertical loading
• Objective : to build the cyclic stability
diagramme
• Centrifuge tests
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Cyclic stability diagramme
Tension failure
Compression failure
Identification of the number of cycles to
reach « failure » :
Displacement = (pile diamater)/10
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10/24/2013
example for suction piles
Cyclic Load Ratio, +/- Qcyc / Qu [%]
Static Offset , Qm/Qu [%] [Clukey et al. 1995]
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Small scale model
G-level= 23
Model pile
Embdmnt = 560
mm
Ø = 18 mm
Prototype pile
(Merville)
13 m
Ø = 0,41 m
Rough
Rn ~ 0,5
Sand grain
Cast in placewww.ifsttar.fr
piles
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10/24/2013
Pluviation
 Fontainebleau Sand NE34
d50 = 0.2 mm; ρdmax= 1736 kg/m3; ρdmin = 1417 kN/m3
 Sand raining or pluviation
8 piles in the strongbox
Strongbox
 (kN/m3)
ID (%)
C02
16,72
91,8
C03
16,72
91,6
C04
16,75
92,6
C05
16,76
92,8
C06
16,55
87
C07
16,77
93,2
C08
16,77
93,2
Moyen
16,72
91 ,7
Strongbox
ρ (kN/m3)
ID (%)
C09
16,1
74,3
C10
16,1
74,3
2 distinct density index (ID)
~ 90%
~75%
Sand mass reconstitution by pluviaiton
technique
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Experimental setup
Model strongbox in the
centrifuge swinging basket
Swinging basket
Ifsttar geotechnical
Centrifuge
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37
10/24/2013
Experimental setup
Electric jack
Electric jack
Laser Displacement
sensor
Beam
pile
Strongbox
pile
Loading device
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Experimental setup
Small bar
Force sensor
Pile
Ball-joint connection
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10/24/2013
Experimental Programme
- Monotonic test (tension & compression)
Determine Qrc et Qrt (displacement controlled @ 1mm/min)
Failure criteria :
Tension : Force peak
Compression : Intersection of linear slopes
- Cyclic tests (Force controlled)
Failure criterion : Displacement = 10% Øpile
Qrc : Monotonic resistance in compression
Qrt : Monotonic resistance in tension
Qm : mean cyclic amplitude
Qc : amplitude de la composante cyclique
4 daN/s (modèle )
21 kN/s (prototype)
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Experimental Programme
Types of tests
Qm = 0
Qm ≠ Qc
Qm ≠ Qc
3
5
3
5
Qm = Qc
Qm = Qc
3
2
6
Pure tension
Pure compression
Nbr tests : 64 ( ID ~ 90% & 75%)
Cyclic = 40, Monotonic = 16
Two-ways
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10/24/2013
From the records to the results
Monotonic Compression
Référence : C05 – T01
Recorded data
Prototype load-displacement curve
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Density effect
Fontainebleau sand ID 91% & 74%
Qrt / Qrc ~ 70%
Monotonic compression tests
Monotonic tension tests
Resistance reduced by ~ 50%
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Reproducibility
Cyclic tension :
C02-T08 : failure after 24 cycles
Same trends
C07-T04 : failure after 15 cycles
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Cyclic tension
Failure : 460 cycles
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41
10/24/2013
Two ways
Failure : 7 cycles
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Two ways : influence of Vm
1) Downward movement
2) Upward Failure =f(Vm)
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10/24/2013
Tension : influence of Vc
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Unstable : ncycles < 100
Meta-stable : 100<n<1000
Stable : n>1000
or
rate of displacement
< 1mm/1000 cycles
[Tsuha et al. 2012]
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10/24/2013
In field tests on bored piles
Centrifuge tests on cast in place piles
[Puech et al., 2013]
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Piles – horizontal loading
•
•
•
•
•
Theoretical background : beam theory
Instrumentation
Model device
Bending moments
P-y curves
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Theoretical background : beam theory
Winkler model
• soil reaction P(z), at a depth z, depends on the modulus of soil
reaction Es, and on the lateral displacement Y(z)
Pz   Es z  Y z 
• quasi-static equilibrium
n
x
x
 M z 
 P z   0
z 2
2
 2 Yz 
z 2
y
M
T
Section
droite
de surface a
• Behaviour
Mz   E p I p
y
ny
t
N
z
z
• equilibrium equation re-written in displacements
 4 Yz 
z
4

Es
Yz   0
EpIp
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45
10/24/2013
n
x
x
Instrumentation
y
ny
Section
droite
de surface a
Long instrumented pile (12m long @ scale 1/40 )
20 pairs of strain gages => strains
displacement vector :
t
z
X
Y 

x, y, z    Z  x
y
 t  Xn x  Yn y
z
z 

Strain1 :
 zz 
 
2
T

 z 
Z
 2X
 2Y
x 2 y 2
z
z
z
On the skin of the pile : 2
Z B  Y

z 2 z 2
 zz x  0, y  B / 2, z  
half difference of strains measured respectively at the intrados
and extrados => pile curvature :
 2Y  z  M  z 

z 2
EpI p
=> Bending moment profiles (after calibration)
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From the bending moment profile…
P
d 2M
dz 2
y  
(F )k
k FH n
M
dz
EI
M
z
(FH)k
(FH)k
k=1àn
k=1àn
P
1
zi
2
3
2
3
k
y
Fit of the
moment
profile
k
Calculation
of reaction
profile
zi
Calculation of
displacement Y
profile
z
p
z
1
Construction &
validation of P-Y
curves
zi
z
y
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10/24/2013
Experimental device
Pluviation
Pile installation @ 1×g
Horizontal loading with hydraulic servo-jack
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Pile head displacement
DF
F
=
Hc
Hm
Hc
1+
Hm
2
[Thèse Rosquoët, 2004]

 DF 

y n  y1 1  0.08


 Fmax 

0.35
and
Hc
Hm
=
DF
F
DF
2−
F
[Thèse Rakotonindriana, 2009]

lnn 


[Rosquoët F., Thorel L., Garnier J., Canépa Y., 2007. Soils and Foundations]
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10/24/2013
Bending moments
[Ph.D. Rakotonindriana, 2009]
[Ph.D. Rosquoët, 2004]
Variation of the Maximum bending moment < 20%
The altitude of the Maximum bending moment moves downward
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P-Y curves
[Ph.D. Rosquoët, 2004]
[Ph.D. Rakotonindriana, 2009]
Degradation of the p-y curves close to the surface
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10/24/2013
P-Y curves : degradation
Depth
z (m)
rAPI
(.)
r (for DF/Fmax = 1)
(.)
0,6
0,38
0,75
1,2
0,6
0,75
1,8
0,9
0,87
2,4
1
0,87
[Rosquoët et al., 2007. Soils & Foundations]
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Conclusions
•
A non-usual challenge for geotechnical engineers.
•
Centrifuge modelling technique is versatile : several types of
foundations, different natures of soil and a large range of cyclic
loading conditions.
•
Most of the phenomena starts during the first cycles for the shallow
foundation and the pile subjected to lateral loading.
•
For pile axially loaded pile, the loss of friction may be dramatic in
some cases of two-ways loading, conducting to failure.
•
The tools for numerical modelling are still under development, and
may be validated with physical modelling.
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49
10/24/2013
Contacts :
www.ifsttar.fr
Luc.Thorel@ifsttar.fr
tel : (33) (0)24084 5816
fax : (33) (0)24084 5997
Thank you for your attention
www.ifsttar.fr
Thank you for your attention
IFSTTAR
14-20 Bld. Newton
Cité Descartes
Champs sur Marne
77447 Marne-la-Vallée Cedex 2
France
Ph +33 (0)1 81 66 80 00
www.ifsttar.fr
communication@ifsttar.fr
Photos Offices de tourisme Nantes, Guérande, Ville de Nantes, annuaire châteaux de la Loire, LUNAM, Luc Thorel
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50

Centrifuge modelling of foundations subjected

Transcription

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