Centrifugal Model Tests(Updated) new presentation

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Geotechnical Centrifuge Modelling is a technique utilized to carryout model
tests in order to study geotechnical issues
PART I - INTRODUCTION
CENTRIFUGE MODEL TESTS

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TUNNEL
STABILITY

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FOUNDATIONS OF BRIDGES
AND BUILDINGS

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SETTLEMENT OF
EMBANKMENTS

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STABILITY OF SLOPES

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EARTH RETAINING
STRUCTURES

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SEAWALLS

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Centrifuge creates prototype stress levels in a reduced-scale model and one-to-one
scaling of stress enhances the similarity of geotechnical models to get accurate data to
assist solve complex problems related to geotechnical materials
Seismic Performance evaluation of Embankment Dams : K-Water Institute , S.Korea
Provides data to improve understanding of basic mechanisms of deformation
and failure

PART II – HISTORICAL BACKGROUND
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Earliest idea of using a centrifuge to increase self-weight of a small scale
model was developed by Edouard Phillips in Paris in 1896 who suggested
using a centrifuge to solve bridge engineering problems, but no actual test was
carried out at that time
Craig, W.H (1995) : Geotechnical Centrifuge : Past , Present and Future

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Philip B. Bucky in 1931 conducted centrifuge model tests at Columbia
University in the USA to study the integrity of mine roof structures in rock
Bucky, P.B. (1931). Use of models for the study of mining problems

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Pokrovsky and Davidenkov from USSR used a centrifuge to investigate
problems associated with embankment and slope instability
A number of geotechnical centrifuges were built in the USSR to tackle various
problems in soils and rocks alongside a few research projects undertaken in
the USA by Panek in 1949 and Clark (late 1950s and early 1960s)
Hoek in South Africa in mining engineering
Prof. Schofield developed first geotechnical centrifuge in U.K in Cambridge
University
Romberg in Sweden to study gravity tectonics
Ramberg (1968) - Simulation of geophysical events and processes
Schmidt (1976) - Craters formed by near-surface nuclear explosions and
planetary impact of large bodies
Scott (1979) - Cyclic and Dynamic testing of piles
1933
1940-60
1965
1966
1968
1970-80
Joseph, H.H , R.V (1988) : A Literature Review Of Geotechnical Centrifuge Modelling With Particular Emphasis on Rock Mechanics

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PART-II HISTORICAL BACKGROUND
BRITISH GEOTECHNICAL SOCIETY SURVEY(1999)
CENTRIFUGE
MODELLING
The great and the good of 50 years of geotechnics : Ground Engineering (July 1999)

PART III – PRINCIPLES OF CENTRIFUGE
MODELLING
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PART-III PRINCILPLES OF CENTRIFUGE MODELLING
Bucky in 1931 suggested that “to produce at corresponding points in a small
scale model, the same unit stresses that exist in a full scale structure, the
weight of material of the model must be increased in the same ratio that the
scale of the model is decreased with respect to the full scale structure. The
effect of increase in weight may be obtained by the use of centrifugal force, the
model being placed in a suitable revolving apparatus”
Joseph, H.H , R.V (1988) : A Literature Review Of Geotechnical Centrifuge Modelling With Particular Emphasis on Rock Mechanics

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PART - III PRINCILPLES OF CENTRIFUGE MODELLING
Test is conducted on a 1/N scale model of a prototype in the enhanced gravity field of a
geotechnical centrifuge
The gravity is increased by the same geometric factor N relative to the normal earth’s
gravity field (referred to as 1 g)
Average Vertical stress
exerted by block on soil
Vertical strain induced in the
soil for characteristic length ᾳ
Average Vertical stress
exerted by scale model
block on soil
Vertical strain induced in
the soil for characteristic
length ᾳ
BLOCK
STRUCTURE
BLOCK
STRUCTURE
(SCALE MODEL)
Centrifuge Modelling for Civil Engineers : Gopal Madabhhushi

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“Gravity” acting on the scaled model is increased by placing it in a
geotechnical centrifuge, the centrifugal acceleration will give us the “Ng”
environment in which the scaled model will behave in an identical fashion to
the prototype in the field
When the centrifuge is rotating with an angular velocity of θ, the centrifugal
acceleration at any radius r is given by:
ᾱ = r θ2
This centrifugal acceleration is required to be the matched with same
geometric scale factor as the one used to scale down our prototype by N.
N g = r θ2

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The centrifugal acceleration changes with the radial distance from the axis of
rotation of the centrifuge as indicated by above equation. The speed of the
centrifuge will be adjusted such that the model at the desired radius (e.g., a
typical point in the model such as its centroid) will experience the desired
centrifugal acceleration Ng. This will give us the angular velocity θ which we
have to rotate our centrifuge.
N g = r θ2
Characteristic features of a typical geotechnical centrifuge Centrifuge acceleration
John Atkinson (1993) : An Introduction to Mechanics of Soils and Foundations
θ

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FIELD STRUCTURE PROTOTYPE AND CENTRIFUGE MODEL
Conceptual ,
theoretical and
mathematical models
, practical realities ,
accumulating
experience
Scaling Laws
Same soils
Same stresses
Same strains
Scaling Laws
Same soils
Same stresses
Same strains
Similar sizes with
some simplifications
Similar sizes with
additional simplifications
Application
Measurement
Full size field
structure in
earth’s gravity
Exact 1/N th scale
Replica in ideal
Ng gravity
Centrifuge
prototype in
earth’s 1g gravity
1/N th size targeted
model in Ng
centrifuge gravities
A B
C
D
CENTRIFUGE
MODEL
PROTOTYPE

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Scaling laws are relationships that relate the behavior of the centrifuge model and the
prototype. These are required to relate the observed behavior of the scale model in the
centrifuge experiment to the behavior of a prototype
SCALING LAWS
For centrifuge model tests, model laws are generally derived through dimensional
analysis, from the governing equations for a phenomenon, or from the principles of
mechanical similarity between a model and a prototype
By observing the settlement of a structure in the centrifuge model we would like to
predict the settlement of the prototype. As we have scaled down all the length
dimensions of the prototype by a factor of N in the centrifuge model, the scaling law for
settlement would be N, i.e settlements in the centrifuge model are N times smaller than
in the prototype. Similarly area and volume in the centrifuge model will be related to the
prototype by factors of N2 and N3, respectively.

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