Bifurcation Analysis in Geomechanics hZ0CnY8 '
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by -];/ *nl
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I.VARDOULAKIS >h0iq
Department of Engineering Science V^P]QQ\
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National Technical University of Athens ,{HxX0
Greece <#s=78
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and 1XAXokxj
J.SULEM XA~Cc<v
Centre d’Enseignement et de Recherche en Mécanique cu4&*{
des Sols TU-4+o%;
Ecole Nationale des Ponts et Chaussées/LCPC +ou
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France P9)E1]Dc$
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Published by >xU$)uE&
Blackie Academic & Professional, an imprint of Chapman & Hall, 2FxrMCC
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ RnN]m!"5
This edition published in the Taylor & Francis e-Library, 2005. ^T[8j/9o^
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? CfguL@tR.
This question no doubt will be asked by engineers working in this area with generally F_9e ju^|
rather practical and application oriented portfolios. oh
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Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled ccc*"_45#
conditions such as those dealt with in structural engineering of surface ad "yo=%1
facilities? R^PPgE6!$
Are subsurface rock conditions with inherent heterogeneity, anisotropy and OS k+l
layering not so uncertain that highly sophisticated numerical techniques with very v2e*mNK5
precise determination of failure are out of balance? S <C'#vj
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation (j^Qa~{mG4
analysis in that way. Until recently there was definitely no strong business pull from W=fw*ro
petroleum engineering to develop bifurcation analysis in geomechanics because no i NX%Zk[
operating company was really asking for improved production performance. Application }Km+5'G'U
of bifurcation analysis to petroleum engineering was clearly a technology push; a E880X<V)>
technique that was available and was (and is) waiting for people seeing opportunities to u%J04vG"D
apply it. $niJw@zC
Once these opportunities were found, this fine technology appears to be a lot more '~HCYE:5
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to tiZ5
:^$b4
solve the very important question of scale dependency of our rock mechanical tests, I%]~]a
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ >+iJ(jqq
wellbore. Transition between different borehole failure and stabilisation mechanisms can :}\w2W E[
now be understood, which significantly increases the scope for barefoot completions and $TON`+lB
exclusion or postponement of sand control. `ZCeuOH
Suddenly a technology that was initially regarded as rather academic contributes to <9JI@\>
millions of dollars savings. q6h'=By
This book gives an excellent overview and in-depth treatment of all aspects of 4l/hh|3@
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, ^gb3DNV~y
which can be exploited not only in petroleum engineering rock conditions but in many UEZnd8
other geomechanical applications. OOzk@j^
Cor Kenter nRYHp7`
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This book by Vardoulakis and Sulem is an outstanding contribution to the important EZy:_xjZ
field of geomechanics and will also be useful to the many branches of engineering and Zl5cHejM
applied science, particularly those dealing with mechanical behavior. g.wp
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Following a self-contained Introduction, chapter 2 introduces the basic concepts from e6E{l
continuum mechanics and thermodynamics before the incremental formulation of uhi(Gny.
standard continuum mechanics, particularly useful for stability and bifurcation k8!|WqfP
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze D00I!D16
in detail buckling and interface instabilities, including multilayered and cracked media dWK;
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which offer a natural stimulus for introducing the concept of Crosserat continuum. <L4.*
Chapter 5 provides an updated contribution to the mechanics of water-saturated )HHG3cvU
media. It takes Biot’s original contribution to a new level of understanding, including BI\ )vr$
important physical phenomena such as grain crushing and non-Darcean flow. It uses C`s
the essentials of mixture formalism but achieves a great economy of postulates and !c}?u_Z/
mathematical generalizations with no direct physical interpretation. L *a:j
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current p"A2N+
plasticity theories and discuss in a systematic and thorough manner the problems of .lclW0*
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure MKqMH,O
and grain characteristics are explained. The benchmark problems of the triaxial ,/?7sHK-0
compression test, the biaxial compression test and the cavity inflation test are analyzed h<)YZ[;x
in detail as examples of loss of material stability and progressive failure. KIyhvY~
The stage has now been set for the introduction of higher order continuum models to O$F<x,
describe correctly bifurcation and periodic phenomena in granular materials. Standard KIY/nu
theories of soil plasticity do not contain an internal length scale, and thus features such
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as thickness and spacing of shear bands, as well as the stress-strain response in the F];"d0O#5
softening regime, cannot be addressed. As a result, finite element calculations do not ZY_aE
converge and related boundary value problems are ill-posed. The authors were among {+`'ZU6C
the first to show that Cosserat and higher order gradient plasticity models can resolve !GB\-(
these difficulties. W7bA#p(
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in n}KF)W=
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and J7Z`wjX1
the necessity of higher order terms in removing ill-posedeness in the softening regime EW$.,%b1
with simultaneous determination of shear-band characteristics (not captured by Z>0a?=1[
standard continuum theory) is documented. :{:R5d(_I
The book concludes with an account of stability of undrained deformations. This v5 |XyN"
problem is complex and very little understood despite its practical importance. The s(~tL-_ K
authors demonstrate that fundamental work can intelligibly be applied to solve F8u;C:^d
outstanding geomechanics problems with extended engineering implications. Careful OVwcjhQ
laboratory tests are used to calibrate the theoretical models. _ELuQ>zM]+
This well-organized volume is a substantial and valuable reference for civil engineers N4]Sp v
and geologists, as well as mechanical engineers and metal physicists. It should be of L#t^:%
value to any junior or senior researcher with a keen interest in the stability of Hz?C9q3BX
deformation. g+g0iS
Elias C.Aifantis ORVFp]gG
Center for Mechanics of Materials and Instabilities $<;!F=%8
Michigan Technological University fN)A`> iP
and Aristotle University of Thessaloniki