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8/13/2019 Centrifugal Physical Modeling & Scaling Laws
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Centr i fuge Physical Model ing &
Scaling Laws
Tarek Abdoun
RPI/UCD NEES Centrifuge Research and Training
Workshop 2011
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Geotechnical Centrifuge
Ng
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Ground Centrifuge Modeling
Concept
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Radial g-field
At which radius do you calculate g = w2
r? Pick a point in the model where you are
most concerned about accuratelymodeling the effective stress. Set g
accordingly. For level ground: s = r (gavg overburden)(d)
Document the RPM and the radius to a
reference point on the model container
Might need to account for g variation indeep models
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Why Physical Model Tests?
Complex, nonlinear stress-strain behaviorof soil (made of interacting particles, air,
water)
Difficulty of numerical simulation of soiland soil-structure systems at large strains
and failure
Validate and calibrate numerical methods
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Why Centrifuge Model Tests?
Small-scale models are cost-effective Soil properties are highly stress-dependent
Centrifuge produces equal confining stresses
in model and prototype, therefore same soilproperties
Then, reasonable assumption that strains anddeformations are also equal in model and
prototype
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Application Domain: Systems
Natural or artificial soil deposits, differentsoil types, different geometries, earth
dams and dykes
Soil-foundation and soil-structure systems: foundations of buildings, bridges
buried pipes and tunnels, basements
earth levees with sheetpiles
etc.
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Application Domain : Loadings
Static gravity loads
Earthquake shaking
Blasting Ground deformation
Water waves
Contaminant transport
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Centrifuge Modeling Limitations
Useful only for systems containingsoil or other pressure-dependent
material
Models allow limited detail
Effect of model boundaries
Time scale and strain-rate issues
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Scaling Laws (N = number of gs)
Stress & Pressure * = 1
Density * = 1
Length 1/N
Velocity 1 Acceleration N
Volume 1/N3
Mass 1/N3
Force 1/N2
Time (dynamic) 1/N
Time (diffusion) 1/N2
Scaling Laws
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Catalogue of scaling laws and
similitude questions in
centrifuge modelling
Technical Committee TC2Physical
Modelling in Geotechnics 2007 Covers: dynamics, fluid flow in soils, heat
transfer and ice, particle size effects, rate
effects
About 60 references
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NEES-PipelinesEvaluation of Ground Rupture Effects on Critical Lifelines
Numerical
Model ing
Centr i fuge
Model ingFull scale
Testing
http://localhost/var/www/apps/conversion/tmp/PREFACE%202007/Movies/Strike-Slip%20-%202%20speeds.wmvhttp://localhost/var/www/apps/conversion/tmp/PREFACE%202007/Movies/Full%20scale-30sec.wmv8/13/2019 Centrifugal Physical Modeling & Scaling Laws
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EA vs. EI for Structural Elements
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.02 0.04 0.06 0.08 0.1 0.12
tm/Dm
tp/Dp
EA curve
EI curve
Em/Ep= 0.6
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EA vs. EI for Structural Elements
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.02 0.04 0.06 0.08 0.1 0.12
tm/Dm
tp/Dp
EA curve
EI curve
Em/Ep= 0.6
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EA vs. EI for Structural Elements
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.02 0.04 0.06 0.08 0.1 0.12
tm/Dm
tp/Dp
EA curve
EI curve
Em/Ep= 0.6
tm/Dm = 2 tp/Dp
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Other Factors: Strain Rate
0 1 2 3 4
Axial Strain (%)
0
5
10
15
20
25
AxialStress(MP
a)
HDPE Material Stress-Strain Behavior
0.1%/min
1%/min10%/min
1%/min
0.16%/min
130%/min
300%/min
Hypobolic Fit (Merry & Bray, 1997)
RPI Uniaxial Tension Test
100%/min300%/min
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-63.5oStrike-Slip (Tension)
http://localhost/var/www/apps/conversion/tmp/scratch_4/Strike-Slip%20-%202%20speeds.wmv8/13/2019 Centrifugal Physical Modeling & Scaling Laws
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http://localhost/var/www/apps/conversion/tmp/scratch_4/HDPE2overhead2.wmv8/13/2019 Centrifugal Physical Modeling & Scaling Laws
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Time Scaling Conflict
Dynamic TimeL = 0.5 a t2 L* = a* t*2t* = sqrt(L*/a*)
t*dyn= sqrt(L*/(1/L*)) = L* or 1/N
Diffusion Time, consider time factor, TFor similarity, T* = 1 = cv* t* /L*
2
t*dif
= L*2/ cv
*
If cv* = 1 (same soil in model and prototype) then:
t*dif= L*2 or 1/N2
Conflictt*dif t*dyn
Conflict Resolution By increasing viscosity of the fluid (m* = 1/L* or N)
Decreasing the particle size of the soil (k* = C (D10*)2 )
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Time Scaling Conflict
Sometimes, conflict can be neglected without
changing cv both model and prototype are undrained during dynamic
event
both model and prototype are drained during dynamic event
we may want to systematically vary viscosity to coveran interesting range. (Reviewers may have difficulty
with this concept)
It takes time to saturate a large model with viscous
pore fluid. For practical purposes, we may knowinglyviolate time scale factor similarity, and then account
for the different cvby analysis
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Modeling of Shear Bands
J. DeJong, U. Mass Amherst web page
The shear band thickness
depends on particle size, not
on L* (N)
http://localhost/var/www/apps/conversion/Videos/pile1.mp48/13/2019 Centrifugal Physical Modeling & Scaling Laws
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Modeling of Shear Bands
P ti l Si R d ti
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Particle Size Reduction
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1Particle size, mm
%S
oilpassing
Scaled Sand
Ottawa Sand F#55
Centr i fuge
Model ing
Full Scale Testing
http://localhost/var/www/apps/conversion/tmp/scratch_4/half%20small%20final.avi8/13/2019 Centrifugal Physical Modeling & Scaling Laws
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Particle Size effect
Most basic requirement is that there are a
sufficient number of particles across thedimensions of a model so that we can model thesoil as a continuum. Required Dmodel/Dparticle depends on the problem.
Footings: Dfooting/Dparticle > 30 (minimizesparticle size effect)
To model contact stress and capillary rise most
accurately, need to use same particle size (poresize) and fluid. The Ability to model capillary riseis an advantage of centrifuge high g modeling.
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Explosions are Volumetric
Explosions Scale as N
3
1 gram of explosive tested at
100g is equivalent to one million
(106) grams of prototype
explosive, or one metric ton
(2200 lb)
Scale effects also include
particle size effects and
differences in radial acceleration
Application of High Speed
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Application of High Speed
Camera to Blasting Tests
1.E-02
1.E-01
1.E+00
1.E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Scaled Charge Mass (kg)
ScaledDepth(m)
S&H su-ho bu-ve su-ve Pow er (S&H)
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Blast Modeling
Groun
dwater/Contaminant
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Time Scales as g2 E.G., 24 Hour test @ 105g = 30 years prototype time
Advection (Hydraulic flow)No theoretical
problems
Dispersivity (Diffusion, Dispersion)morecomplicated, but can be done
Groundwater/Contaminant
Transport
Groundwater/Contaminant
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General: Single contaminant, conservativecontaminantmodels acceptable
The robot gives us a unique opportunity to
determine the transport and concentration with
time of multiple contaminants
Groundwater/Contaminant
Transport (cont.)
B d /C t i ff t
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Boundary/Container effects
Flexible Containers
Hinged plate, Laminar boxes
Ideal for gently sloping
or level ground
Complementary Shear issue
B d /C t i ff t
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Boundary/Container effects
Rigid containers P-waves from
ends of the container
Side frictionAvoid narrow containers (width < height)
Reduce sides friction
Move structures e.g., away from boundaries
Lateral stiffness (maintaining Ko)
Ground motion selection
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Ground motion selection
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Fi l Th ht
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Final Thoughts Centrifuge Modeling is a tool that makes model tests more
accurate because it reproduces prototype stress levels in
a small scale model but be mindful of its limitations Centrifuge Modelingis useful to:
Test the validity of a numerical model
Perform systematic parameter studies
Discover mechanisms of behavior Model testing is valuable for problems where field
data is insufficientcan obtain data that isimpossible to obtain in other ways.
Advanced instruments of NEES (robotics,shakers, instrumentation) enable more accurateand more detailed models than was possible inthe past.
NEES t if h
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NEES centrifuge research
Complementary NEES Centrifuges
UCD: larger container, V&H shaker, more sensorsper test, multiple tests per container
RPI: medium size, H&H shaker, more tests permonth, Robot, split box.
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hank You
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