Bifurcation Analysis in Geomechanics V9/2y9u
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by WS6Qp`c )e
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I.VARDOULAKIS ;a|%W4 "
Department of Engineering Science LawE 3CD
National Technical University of Athens qbQ dx Kk
Greece Y*b$^C%2
and ~_0XG 0oA
J.SULEM i~E0p
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Centre d’Enseignement et de Recherche en Mécanique BZv:E?1z
des Sols gb!0%*
Ecole Nationale des Ponts et Chaussées/LCPC @u$NB3
France !'!\>x$
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Published by #e =E
Blackie Academic & Professional, an imprint of Chapman & Hall, !pj& h0CR
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ #-b}QhxH
This edition published in the Taylor & Francis e-Library, 2005. -p0* R<t
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? oNYFbZw
This question no doubt will be asked by engineers working in this area with generally ;TC]<N.YJT
rather practical and application oriented portfolios. f/z]kfgw
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled 4h?@D_{k
conditions such as those dealt with in structural engineering of surface @-0mE_$[
facilities? H/*slqL
Are subsurface rock conditions with inherent heterogeneity, anisotropy and hKh ad8
layering not so uncertain that highly sophisticated numerical techniques with very N`d%4)|{
precise determination of failure are out of balance? 6J- /%
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation v6wg,,T
analysis in that way. Until recently there was definitely no strong business pull from mz x$(u
petroleum engineering to develop bifurcation analysis in geomechanics because no %<8?$- [
operating company was really asking for improved production performance. Application ,Y|
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of bifurcation analysis to petroleum engineering was clearly a technology push; a A.yIl`'UP#
technique that was available and was (and is) waiting for people seeing opportunities to fg , vTpBk
apply it. bz 7?F!
Once these opportunities were found, this fine technology appears to be a lot more Y_C6*T%
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to Z6M
qcAJ3j
solve the very important question of scale dependency of our rock mechanical tests, GB Vqc!d
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ {|0YcL
wellbore. Transition between different borehole failure and stabilisation mechanisms can "PS ) "t
now be understood, which significantly increases the scope for barefoot completions and |F\fdB}?S:
exclusion or postponement of sand control. g`Q!5WK*
Suddenly a technology that was initially regarded as rather academic contributes to #zgO _ H
millions of dollars savings. nxEC6Vh'
This book gives an excellent overview and in-depth treatment of all aspects of )b%zYD9p
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, B^]Gv7-
which can be exploited not only in petroleum engineering rock conditions but in many H >D?
other geomechanical applications. 3=?,D v0P
Cor Kenter ./zzuKO8XK
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This book by Vardoulakis and Sulem is an outstanding contribution to the important }!r
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field of geomechanics and will also be useful to the many branches of engineering and 9Y:.v@:}0
applied science, particularly those dealing with mechanical behavior. `tuGy}S2
Following a self-contained Introduction, chapter 2 introduces the basic concepts from F( /Ka@
continuum mechanics and thermodynamics before the incremental formulation of H}&JrT95
standard continuum mechanics, particularly useful for stability and bifurcation ~-G_c=E?
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze sEK F
in detail buckling and interface instabilities, including multilayered and cracked media FWp ?l
which offer a natural stimulus for introducing the concept of Crosserat continuum. !]fSS)\H
Chapter 5 provides an updated contribution to the mechanics of water-saturated Piw i
media. It takes Biot’s original contribution to a new level of understanding, including B bCW3 !(
important physical phenomena such as grain crushing and non-Darcean flow. It uses ?b}e0C-a
the essentials of mixture formalism but achieves a great economy of postulates and oV9{{
mathematical generalizations with no direct physical interpretation. * >:<
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current [ns ==gDD
plasticity theories and discuss in a systematic and thorough manner the problems of T t Wzjt
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure *Jt+ -ZM
and grain characteristics are explained. The benchmark problems of the triaxial xFIzq
compression test, the biaxial compression test and the cavity inflation test are analyzed (+xT5 2
in detail as examples of loss of material stability and progressive failure. s^.tj41Gx}
The stage has now been set for the introduction of higher order continuum models to RkTYvAk|kY
describe correctly bifurcation and periodic phenomena in granular materials. Standard . qf~t/o
theories of soil plasticity do not contain an internal length scale, and thus features such a*&&6Fo
as thickness and spacing of shear bands, as well as the stress-strain response in the uT=5zu
softening regime, cannot be addressed. As a result, finite element calculations do not ZP@NV|B
converge and related boundary value problems are ill-posed. The authors were among Chad}zU`
the first to show that Cosserat and higher order gradient plasticity models can resolve ; bHS^
these difficulties. 4MzPm ~Ct
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in k}qCkm27
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and f)Y~F/[$P
the necessity of higher order terms in removing ill-posedeness in the softening regime ~> _UTI
with simultaneous determination of shear-band characteristics (not captured by Vo.~1^
standard continuum theory) is documented. o xUBlye
The book concludes with an account of stability of undrained deformations. This %h, &N D
problem is complex and very little understood despite its practical importance. The X(.[rC>
authors demonstrate that fundamental work can intelligibly be applied to solve o9C# 5%9
outstanding geomechanics problems with extended engineering implications. Careful \"L0d1DK)
laboratory tests are used to calibrate the theoretical models. bVa?yWb.
This well-organized volume is a substantial and valuable reference for civil engineers &s Yxe:H
and geologists, as well as mechanical engineers and metal physicists. It should be of @w(|d<5l:L
value to any junior or senior researcher with a keen interest in the stability of !&.-{ _$
deformation. ^B}q@/KV
Elias C.Aifantis jS8B:>
Center for Mechanics of Materials and Instabilities U 9Ea }aN
Michigan Technological University W1LR ,:$
and Aristotle University of Thessaloniki
