Reduced Scale Modelling Reduced Scale Modelling of geotechnical ...

SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES

1st Workshop Experimental Opportunities O - SERIES S S Project through Transnational Access

Reduced Scale Modelling of geotechnical problems i the in th centrifuge t if Dr. Jean-Louis Chazelas – Laboratoire Central des Ponts et Chaussées – Nantes – FR Dr. Gopal Madabhushi - Schofield Centre – University of Cambridge - UK

SERIES General Committee Meeting - Iasi, July 15th 2009


Introduction Modern day Civil Engineer uses the following methods in design: For simple problems Empirical or Semi-empirical methods Closed form solutions For complex problems Finite Element Analysis y Testing of Physical Models at Small Scale Field Monitoring SERIES General Committee Meeting - Iasi, July 15th 2009


For Geotechnical Problems, when using the FE method, we need to know the constitutive behaviour of soil i.e. the stress strain behaviour of the soil under the type of loading i experiences it i needs d to b be k known. p g this into the FE codes If Yes,, we can program and proceed with the design If No, No ??? Let us look at the stress strain behaviour of soil



Stress – Strain behaviour of soil Let us consider the shear stress Vs shear strain for loose and dense soils

Dense Sand

Shear Stress τ

Loose Sand

Shear S e box bo test es Shear Strain γ

Soil is highly NON-LINEAR and PLASTIC SERIES General Committee Meeting - Iasi, July 15th 2009


Physical Modelling in Geotechnics As soil is non-linear we cannot simply model our problem (say a caisson i subjected bj d to lateral l l lload) d) at small ll scale l

Dense Sand

Shear Stress τ

Loose Sand

Prototype behaviour at large stresses

Prototype behaviour at large stresses and when large strains are mobilised

Model behaviour at small stresses and strains

Shear Strain γ

We need to create prototype stresses and strains in our models !!! SERIES General Committee Meeting - Iasi, July 15th 2009


Centrifuge g Modelling g Technique q Consider, for simplicity, a block structure of dimensions L × B × H sitting on a horizontal soil bed. Principle of Centrifuge Modelling • In a centrifuge a reduced scale model is subjected to centrifugal acceleration so that correct prototype stresses and d strains i are createdd in i the h model. dl Stress under the block is given by Centrifuge C t if Model

Idealised Id li d Field Fi ld Structure 1g

Ng 3

H/N

M

H

M/N

B/N L/N

B L

Mg σ = LB

ε =

δL L

σ =

× Ng M Mg N3 = L × B LB N N

M

ε=

δL / N L/ N

=

δL L



C t if l Acceleration: Centrifugal A l ti The easiest way to create high gravity is by spinning our soil models in a centrifuge. When the centrifuge is rotating with an angular velocity of ‘ω‘, the centrifugal acceleration at any radius ‘r’ is given by centrifugal acceleration = r × ω2 We wish to match this centrifugal acceleration to be the same factor as the one we used to scale down our prototype by ie ‘N’ (geometrical scaling factor). ⇒

N × g = r × ω2 SERIES General Committee Meeting - Iasi, July 15th 2009


For example, if we wish to scale a prototype problem at 100g, Using a centrifuge with working radius of 4.125 m We will be doing;

100 × 9.81 = 4.125 × ω

2

100 × 9.81 = 15.42 rad / s ω= 4.125

⇒ ..RPM ≅ 147 14 .3 SERIES General Committee Meeting - Iasi, July 15th 2009


Scaling laws Dynamic Fundamental Equation Length 1/N Volume 1/N3 Density 1 Stress 1 Stain 1 Acceleration N Velocity 1/N Displacement 1/N Force 1/N2 Time 1/N Frequency N Darcy's law with water 1/N2 Time y law with viscosityy N*water Darcy's Time 1/N SERIES General Committee Meeting - Iasi, July 15th 2009


Cambridge Centrifuge Facility

Turner Beam Centrifuge g - Universityy of Cambridge g



Acceleration fields in the Centrifuge The beam Centrifuge at LCPC Radius 5.50 m 2T in the basket at 100 g

1D D earthqua ake

Centrifuge acceleration = vertical of the model

Y Z



Reducing scales - Limits Size effect Shallow foundation diameter /grain size > 35 Pil di Pile diameter t //grain i size i = 45 or 60

Silo effect

Width = 35 cm σ = 33 kPa in the center σ = 23 kPa against the wall σ = 28 kPa at 5 cm from the wall

Boundaryy effect Neutralized zones

Ratio size/width

IJPMG Vol.7,n°3, 2007 SERIES General Committee Meeting - Iasi, July 15th 2009


Limits Rsurface R

ω

Gc =ω 2 R

Vertical section Vertical stress in the soil 0

100

200

300

400

Depth - m prototype

0 5 10 15 20

Prototype Model at depth *50

25

G is radial Problem in little centrifuges (error on surface 0.7% at 5.1m and box 0.8 m )

G centrifuge function of z G at 1/3 of the total depth: error ~ 2% ?



Limits :

fundamental equation unknown = scaling rules ???

E Example l : iinternal t l erosion i within ithi embankment b k t ⇒ preliminary tests for empirical evaluation of leading parameters



Reference: Non-Cohesive Soil -LCPC LCPC : fine Fontainebleau sand or Hostun Sand - UCAM : Fraction D or E,, (Leighton ( g Buzzard 52/100 or 100/120 sands)) or Hostun Sand (from France) C Cu

Reference: Cohesive Soil LCPC : Speswhite Kaolin

on site

z

In the centrifuge

During spin up the undrained cohesion UCAM : Speswhite S hit K Kaolin li clay l reduces to 0 at surface or E-grade Kaolin clay (higher Permeability, so faster consolidation)



UCAM – Team for earthquake experimenting G Gopal l Madabhushi M d bh hi

R d in Reader i Geotechnical G t h i l Engineering E i i

Stuart Haigh

University Lecturer

Ulas Cilingir Mark Stringer Darren Chian Jenny Haskell Charles Heron

Research Associate Research Student Research Student Research Student Research Student

Technician team John Chandler Kristian Pather Chris McGinnie D id Yates David Y t Anama Lowday

Centrifuge Operator & Mechanical Centrifuge Operator & Mechanical

Electronics Support I t Instrumentation t ti Support S t Schofield Centre Administrator SERIES General Committee Meeting - Iasi, July 15th 2009


Earthquake simulation – Device in Cambridge

• • • • •

Mechanical system y Simple, cheap and robust Tone bursts of desired frequency (0~5 Hz) Earthquakes of desired duration (0 (0~100 100 seconds) Earthquakes of desired intensity (up to 0.4g at bedrock) SERIES General Committee Meeting - Iasi, July 15th 2009


Cambridge – New Servo-Hydraulic Shaker Commissioning in March/April 2010 Will model realisitic earthquake motions such as Kobe motion or Northridge motion PGA of 0.6g 0 6g Max operational g level 100g SERIES General Committee Meeting - Iasi, July 15th 2009


Model Containers for Dynamic Testing

Laminar Box

Dimensions: 1g Æ Depth = 226 mm; Length=560 mm; Width=250 mm 100 Æ Depth 100g D th = 22 22.6 6 m; L Length=56.0 th 56 0 m; Width Width=25.0 25 0 m SERIES General Committee Meeting - Iasi, July 15th 2009



Small ESB Box




Large ESB Box




Window Box



Example Project: Soil-Structure Interaction of Tunnels

Model container and fast camera system on swing ready for centrifuge flight

View of the square tunnel model in model container

Ulas Cilingir & Gopal Madabhushi



Typical Data

Measured accelerations around tunnel

Typical dynamic earth pressure – time history

Ulas Cilingir & Gopal Madabhushi

Normalized lining accelerations at the crown of circular tunnels relative to the invert for tunnels with different flexibility ratiosscale) ratiosscale).

Soil and lining deformations from Particle Image Velocimetry (PIV) analysis SERIES General Committee Meeting - Iasi, July 15th 2009


Example Project: Response of Pile Groups during Earthquakes

Schematic layout of the pile group testing

Mark Stringer & Gopal Madabhushi

Pile group driven into the soil before centrifuge flight



Example Project: Response of Pile Groups during Earthquakes Shaft friction

Pore pressure on the tip p of the p pile and settlement of the pile group Change of shaft friction after the earthquake

Post-earthquake pore pressure response Mark Stringer & Gopal Madabhushi



Example Project: Dam-ReservoirFoundation Interaction

(11m)

(5.5m) (19m)

(2 5m) (2.5m)

Cross-section of the model Sadia Saleh & Gopal Madabhushi

Plan view taken in-flight during Earthquake loading SERIES General Committee Meeting - Iasi, July 15th 2009


Typical data 0.5

max= 0.32

g

min= -0.41 -0.5 0.5

0

5

10

15

20

25

g

30

35

ACC 7340

0

max= 0.18 min= -0.23

-0.5 0.5

0

5

10

15

20

25

30

35

max= 0.20

ACC 8888

0

g

Acceleration and pore pressuretime histories were recorded at several locations

ACC 7334

0

min= -0.17

1.2

-0.5 0.5

Concrete dam on rigid foundation (EQ4)

1

5

10

15

20

-0.5

Flexible dam (EQ4)

25

30

35

I Input t Acceleration A l ti

0

g

Concrete dam on flexible foundation (EQ4)

0

m = 0.28 max= 0 28 min= -0.29

0

5

10

15

Time (sec)

20

25

30

35

0.8 200

(kPa)

PPT 11264

Effective Vertical Stress

100

max= 53.82

50

min= -23.9

0 -50 50

04 0.4

0

5

10

15

20

25

30

35

40

200 150

0.2

(kPa)

y/H

150

0.6

Effective Vertical Stress

PPT 11266

100

max= 55.41

50

min= -24.4 24 4

0

0 0

0.02

0.04

0.06

0.08

0.1

Pdyn/wH

0.12

0.14

0.16

0.18

-50

0

5

10

15

20

Time (sec)

25

30

35

40



Example l Project: P j Reluis R l i Project P j - Propped P d Cantilever C il Retaining walls

View of the retaining wall model

Views of the propped retaining wall model

Ricardo Conti, Guilia Viggiani & Gopal Madabhushi



Example Project: Reluis Project -Tunnels

Ricardo Conti, Guilia Viggiani & Gopal Madabhushi



05 0.5

BM9

0

0

0.2

0.4

0.6

0.8

1

1.2

-0.5 1.4

Δ M (N m m /m m )

RELUIS Project - Tunnels

0 01 0.01 HS10 0 0.2

0.4

0.6

0.8

1

1.2

-0.01 1.4 10

HS10 ACC

0

0

0.2

0.4

0.6

0.8

1

1.2

-10 1.4

A c c e le ra tio n (g )

0

Δ N (N /m m )

0.02

(s) Instrumented Tunnel to measureTime hoop stress and bending stresses



Di t ib t d T Distributed Testing ti UK - NEES Project Meeting Bristol

New Zealand

Oxford

O f Oxford

Cambridge

Powerpoint Presentation from NZ



Proof of Concept: Distributed testing Apart p from the simple, p , tele-participation p p tests carried out so far,, the scope for distributed testing is enormous As part of UK-NEES project, University of Cambridge is committed to test a bridge pier foundation Live demonstration of distributed testing to be given at Institution of Civil Engineers, London Centrifuge running at Cambridge Shaking table test at Bristol S b Sub-structure testing i at O Oxford f d



UK-NEES Project: Distributed Testing Prototype structure:

Large-scale test of pier: Bristol Test of piled foundation: Cambridge Interface forces/displacements passed between substructures via internet



UK-NEES Project: Distributed Testing

h, v and θ sent from Cambridge to Bristol

V H

M

H,V,M demands from Bristol to Cambridge

Centrifuge model in flight at Cambridge



UK-NEES Project



UK-NEES Project - Typical data



Earthquake Simulator at LCPC

Actidyn QS80 Shaker Electro-hydraulic system Tone burst from 20Hz – 200 Hz model « real earthquakes » 20-300 Hz model Pga = 0,5g prototype

In the centrifuge g basket SERIES General Committee Meeting - Iasi, July 15th 2009


Earthquake Simulator at LCPC

Dynamic Equilibrium

1D earthquake

The payload and the counteweight as a moving set de-coupled from the basket

Control Closed loop below 120 Hz on LVDT Open loop over 120 Hz up to 400 Hz SERIES General Committee Meeting - Iasi, July 15th 2009


LCPC – Shaker Specifications Specifications for full load sine tone burst

Specifications for full load real reference earthquakes



LCPC -Shaker Sh k performances f Control over harmonics in sine ~ 10% of reference Control over spurious movements ~ 10% of reference 6.00

10.0

¤ 5.00

Y table X table Z table

M a g n itu d e , g

Real, g

4.00

0

2 00 2.00

-5.00 Y table X table Z table R f Y1 Ref

0

-10.0 357m

450m s

50.0

100

150

200

250

300

350

400

Hz

X - yawing i Y – direction of shake Shaking table Top view

Z – Rocking - Lifting



LCPC -Shaker Shaker performances Typical simulation of a « real earthquake - Northridge 1994 - LCPC

Control over spurious movements Kobe – 70 gc – 3.2 dB below reference

Repeatability



LCPC – Team for earthquake experimenting Jean-Louis Chazelas

Senior Researcher

Sandra Escoffier

Reseacher

Gérard Rault

Research Engineer

Technical team Patrick Gaudicheau Alain Néel Claude Favraud Philippe Audrain X

C.O. - mechanics, hydraulics support C.O. - electronics, hard & software, network support C O - mechanical design of model and devices C.O. C.O. - electroméchanics, hydraulics support Metrology - Dynamics

C.O. : Centrifuge Operator SERIES General Committee Meeting - Iasi, July 15th 2009


LCPC – other devices ESB Box Electromagnetic impact generator

0,80 x 0,35 x 0.41 m model Prototype dimensions : 40 gc : 32 x 14 x 16 m 60 gc : 48 x 21 x 24 m

Data Acquisition System

: LMS – 72 channels

Fs = 100 Hz to 25 kHz 72 Channels Voltage or ICP accelerometers 48 Channels Strain Gauge, Voltage, ICP accelerometers

Saturation S t ti Device D i …......................................…………end 2009 Laminar Box for liquefaction tests.................... end 2009 SERIES General Committee Meeting - Iasi, July 15th 2009


LCPC recent studies Soil – Pile Interactions : Isolating inertial and kinematics

Bending moment kNm

kinematic

Bending moment kNm

De epth(m)

inertial Impact

Deptth (m)

Deptth (m)

Bending moment profiles

Combined

Bending moment kNm

Dynamic PY loops

(PhD M. H. Bonab – LCPC – Univ Rouen 2002 PhD Chenaf – LCPC – Univ Nantes 2007) SERIES General Committee Meeting - Iasi, July 15th 2009


0.5 Impacted building

0.5 0 -0.5 -1 0

5

10

15

20 25 30 Time - s

35

40

45

acceleration - m/s2

Earthquake

1

d = 7,50 m

0 -0.5 0

5

10 15 20 25 30 35 40 45

0.5

1 Impacted building 0.5 0 -0.5 -1

Passive building

Time - s

0

5

10

15

20

25

Time - s

30

35

40

45

acce eleration - m/s2

Free Field

acceleration - m/s2 a

S-s-S-I

accelera ation - m/s2

ACI CAT' NAT' – Show evidence of Structure – Soil – Structure Interactions

d = 2,50 m 0 Passive building -0.5

0

5

10 15 20 25 30 35 40 45 Time - s



impact

2 B1 12 m from B2

-

d

Longitudinal g //

m/s

2

1 0

-1 0.25

0

0 05 0.05

01 0.1

0 15 0.15

02 0.2

0 25 0.25

03 0.3

0.35 0 35 t-s

04 0.4

0 45 0.45

–

B2 12 m from B1

0.4

0.15

Longitudinal // 2

B2 12 m from B1 angle-

0.2

d=12 m

2

m/s

B1 embedded

0.2

0

m/s

-2

0.1 0.05

-0.2 02 0

-0.4

2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4 t-s

2

m/s

3.5

0

0.15 2

d=23 m

0.1 0.05

-0.1

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2.5

3

Hz

3.5

B1 embedded

0.1

-

0.15

- Longitudinal //

0.05 2

d=38 m

0

m/s2

M2 38 m from M1 angle

2

02 0.2

t-s

m/s

Hz

B1 embedded angle – B2 23 m from B1

Longitudinal //

01 0.1

m/s

B2 23 m from B1

-

3

0.25 0.2

0.2

-0.2

2.5

0.45

B2 38 m from B1

0.1 0 05 0.05

-0.05 -0.1

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2

2.5

3

Hz

3.5

t-s



LCPC recent studies FP6 - QUAKER – Inclined piles under horizontal dynamic load

Elastic layer Eresin = 44*E Esand

End bearing piles - Frequency response behavior : more complex translation – rocking mode of vibration : stiffer

- Pile cap movement reduction of the horizontal dynamic displacement (2 – 3)

- Bending moment below soil surface : decreased at the pile/cap connection : increased in back pile

- Axial load both piles : increased (X 2) Sandra Escoffier · Jean-Louis Chazelas Jacques Garnier, Centrifuge modelling of raked piles, Bull Earthquake Eng, 2008



LCPC recent studies LVDT

LVDT

LVDT

LVDT

Bearing Capacity of shallow foundations on clay (PhD Chadzigogos – LMS X - GDS - 2008)

accelerometers Pore Pressure Transducer



Description of TNA Service Orienting proposals Ma s

se

M2

B&K83 – Voie 15

S-s-S-I B&K91 – Voie 19

Free Field Earthquake

B&K93 sur la fondation – Voie 21

• Begining by the simplest situation

B&K90 – Voie 18 Ma s

se

M1

B&K80 – Voie 16 B&K89 – Voie 17 B&K92 sur la fondation– Voie 20

• Openning the range of possibilities

• Co- defining the process of demonstration

• Influence of the process on the modelling



Description of TNA Service Experimental design

Ma s

se

M2

B&K83 – Voie 15

B&K91 – Voie 19

B&K90 – Voie 18 Ma s

se

M1

Design of model Reduction scale, Soil characteristics – Saturation liquid Computation : FEM, Modal tuning, Soil Characterisation Process of setting up the model Design of intrumentation Sensors Position Reference e e e ce

B&K80 – Voie 16 B&K89 – Voie 17 B&K92 sur la fondation– Voie 20

Free field response Soil acceleration, amplification, starting of liquefaction Boarder effect characterisation (sensors) Input signal design Filtering, tuning amplitude Sequence & Cumulative effect of repeated earthquakes SERIES General Committee Meeting - Iasi, July 15th 2009


Description of TNA Service Performing the experiment Soil Preparation Choice and calibration of sensors Setting up of the model Setting up the instrumentation Consolidation process Shaker Drives tuning Driving the centrifuge the shaker the data recorders Data examination Experiment reporting SERIES General Committee Meeting - Iasi, July 15th 2009

Reduced Scale Modelling Reduced Scale Modelling of geotechnical ...

Reduced Scale Modelling Reduced Scale Modelling of geotechnical ...

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