Bifurcation Analysis in Geomechanics *.~M#M 9c
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by duwZe+
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I.VARDOULAKIS 2j_L
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Department of Engineering Science 4ci
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National Technical University of Athens US
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Greece &d~6MSk
and \9 ^wM>U
J.SULEM pRYt.}/K
Centre d’Enseignement et de Recherche en Mécanique 2p'qp/
des Sols KWd]?e)
Ecole Nationale des Ponts et Chaussées/LCPC wRWN]Vo
France vmk
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Published by Ejn19{
Blackie Academic & Professional, an imprint of Chapman & Hall, XLOk + Fn
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ 7j@TW%FmV\
This edition published in the Taylor & Francis e-Library, 2005. o 0fsM;K
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? RJSNniYr7
This question no doubt will be asked by engineers working in this area with generally L]9*^al
rather practical and application oriented portfolios. 9v/1>rziE
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled $@DXS~UQA
conditions such as those dealt with in structural engineering of surface 'Z;R!@Dm
facilities? `+i<:,z-gs
Are subsurface rock conditions with inherent heterogeneity, anisotropy and 1tfm\/V}ho
layering not so uncertain that highly sophisticated numerical techniques with very 1k;X*r#
precise determination of failure are out of balance? "|&SC0*
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation fkYa
analysis in that way. Until recently there was definitely no strong business pull from ! 5 ]/2
petroleum engineering to develop bifurcation analysis in geomechanics because no ,.DU)Wi?}
operating company was really asking for improved production performance. Application ;[%AeN5W
of bifurcation analysis to petroleum engineering was clearly a technology push; a $ABW|r
technique that was available and was (and is) waiting for people seeing opportunities to J/
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apply it. iao_w'tJ
Once these opportunities were found, this fine technology appears to be a lot more UXe @c@3
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to .,feRK>3
solve the very important question of scale dependency of our rock mechanical tests, bY]aADv\
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ 5J1,Usm
wellbore. Transition between different borehole failure and stabilisation mechanisms can 0~"{z>s '
now be understood, which significantly increases the scope for barefoot completions and EK[~lIXg
exclusion or postponement of sand control. 6J-tcL*4"%
Suddenly a technology that was initially regarded as rather academic contributes to .p <!2
millions of dollars savings. @0+@.&Z
This book gives an excellent overview and in-depth treatment of all aspects of OBu$T&
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, ,@(lYeD"
which can be exploited not only in petroleum engineering rock conditions but in many z${DW@o3
other geomechanical applications. !.kj-==s{7
Cor Kenter &Q 3!ty
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NouT~K`'
This book by Vardoulakis and Sulem is an outstanding contribution to the important &@nI(PXv
field of geomechanics and will also be useful to the many branches of engineering and ~
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applied science, particularly those dealing with mechanical behavior. .y|*
Following a self-contained Introduction, chapter 2 introduces the basic concepts from [N.4i"
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continuum mechanics and thermodynamics before the incremental formulation of T&cf6soo
standard continuum mechanics, particularly useful for stability and bifurcation KN_3]-+B
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze X8y&|uH
in detail buckling and interface instabilities, including multilayered and cracked media O*T(aM3r
which offer a natural stimulus for introducing the concept of Crosserat continuum. Un@d Wf6'
Chapter 5 provides an updated contribution to the mechanics of water-saturated P;][i| x
media. It takes Biot’s original contribution to a new level of understanding, including }eSaF@.
important physical phenomena such as grain crushing and non-Darcean flow. It uses kwWDGA?zFB
the essentials of mixture formalism but achieves a great economy of postulates and !-p5j3 A4L
mathematical generalizations with no direct physical interpretation. 4Bs '5@
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current :[,-wZiT~6
plasticity theories and discuss in a systematic and thorough manner the problems of +<&_1%5+
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure }cEcoi<v!
and grain characteristics are explained. The benchmark problems of the triaxial =J<3B
H^m
compression test, the biaxial compression test and the cavity inflation test are analyzed z'j4^Xz?%$
in detail as examples of loss of material stability and progressive failure. $CRu?WUS]'
The stage has now been set for the introduction of higher order continuum models to 7S}NV7
describe correctly bifurcation and periodic phenomena in granular materials. Standard |!,;IoZ
theories of soil plasticity do not contain an internal length scale, and thus features such F7x]BeTM
as thickness and spacing of shear bands, as well as the stress-strain response in the Qw}uB$S>
softening regime, cannot be addressed. As a result, finite element calculations do not Y'mtMLfMc
converge and related boundary value problems are ill-posed. The authors were among u{o3
the first to show that Cosserat and higher order gradient plasticity models can resolve Y2W|b5
these difficulties. k`_sKr]9
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in VMXccT9i!
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and nD{o8;
the necessity of higher order terms in removing ill-posedeness in the softening regime +d>?aqI\A
with simultaneous determination of shear-band characteristics (not captured by YZMSiDv[e
standard continuum theory) is documented. 58V`I5_
The book concludes with an account of stability of undrained deformations. This n#|ljC
problem is complex and very little understood despite its practical importance. The `1{Y9JdQ
authors demonstrate that fundamental work can intelligibly be applied to solve d)1 d0ES
outstanding geomechanics problems with extended engineering implications. Careful 9$$dSN\&
laboratory tests are used to calibrate the theoretical models. oIrO%v:'!
This well-organized volume is a substantial and valuable reference for civil engineers kNR -eG
and geologists, as well as mechanical engineers and metal physicists. It should be of <Z5-?wgf9
value to any junior or senior researcher with a keen interest in the stability of x+EkL3{
deformation. J;|a)Nw
Elias C.Aifantis ose(#n4 0
Center for Mechanics of Materials and Instabilities ;G.5.q[A
Michigan Technological University k{d]
and Aristotle University of Thessaloniki