Centrifugal Physical Modeling & Scaling Laws

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.wmv


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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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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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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.wmv


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http://localhost/var/www/apps/conversion/tmp/scratch_4/HDPE2overhead2.wmv


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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.mp4


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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.avi


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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



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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


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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Centrifugal Physical Modeling & Scaling Laws