Bifurcation Analysis in Geomechanics "GLYyC
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by Z~RdFC
U IQ 6SvM
I.VARDOULAKIS *2#FRA#q
Department of Engineering Science gA"<MI'y
National Technical University of Athens 1<ehV
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Greece zf7rF}
and O,]_ tp
J.SULEM um}N%5GAa
Centre d’Enseignement et de Recherche en Mécanique .h!9wGi`
des Sols X?kPi&ru
Ecole Nationale des Ponts et Chaussées/LCPC (NM6micc
France H8<m9zDvl
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Published by 8L{$v~ +
Blackie Academic & Professional, an imprint of Chapman & Hall, :@WLGK*u.
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ x{2o[dK4}
This edition published in the Taylor & Francis e-Library, 2005. 'XEK&Yi1
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? FSVS4mtiX\
This question no doubt will be asked by engineers working in this area with generally Hz5;Ruw'
rather practical and application oriented portfolios. B%y! aQep
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled i&1U4q
conditions such as those dealt with in structural engineering of surface ?d#Lr*m
facilities? `:R-[>5P8
Are subsurface rock conditions with inherent heterogeneity, anisotropy and 5{HtJ?sKc5
layering not so uncertain that highly sophisticated numerical techniques with very -P*xyI
precise determination of failure are out of balance? F;X"3F.!
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation BM.-X7)
analysis in that way. Until recently there was definitely no strong business pull from rQ
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petroleum engineering to develop bifurcation analysis in geomechanics because no @n>{&^-c
operating company was really asking for improved production performance. Application T[m ~6
of bifurcation analysis to petroleum engineering was clearly a technology push; a .oEFX8
technique that was available and was (and is) waiting for people seeing opportunities to -t%L#1k
apply it. =s6E/K
Once these opportunities were found, this fine technology appears to be a lot more {QW-g
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to TXx'7[
solve the very important question of scale dependency of our rock mechanical tests, U* 4{"
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ |O%:P}6c
wellbore. Transition between different borehole failure and stabilisation mechanisms can |o|gP8
now be understood, which significantly increases the scope for barefoot completions and OM1*Iy
exclusion or postponement of sand control. Sr-|,\/O
Suddenly a technology that was initially regarded as rather academic contributes to U~Xf= f_Q$
millions of dollars savings. \N4d_fPj
This book gives an excellent overview and in-depth treatment of all aspects of `|uoqKv
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, BZ2nDW*%
which can be exploited not only in petroleum engineering rock conditions but in many TJE%
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other geomechanical applications. exsQmbj* %
Cor Kenter k RQ~hRT6
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This book by Vardoulakis and Sulem is an outstanding contribution to the important BQE{
field of geomechanics and will also be useful to the many branches of engineering and m\1VF\
applied science, particularly those dealing with mechanical behavior. zLo;.X[Y
Following a self-contained Introduction, chapter 2 introduces the basic concepts from KQ- ,W8Q5
continuum mechanics and thermodynamics before the incremental formulation of )K8P+zn~
standard continuum mechanics, particularly useful for stability and bifurcation {WIY8B'c
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze w<v1N
in detail buckling and interface instabilities, including multilayered and cracked media ^P]?3U\nj
which offer a natural stimulus for introducing the concept of Crosserat continuum. SHytyd
Chapter 5 provides an updated contribution to the mechanics of water-saturated ^zKt{a
media. It takes Biot’s original contribution to a new level of understanding, including i1tVdbC]
important physical phenomena such as grain crushing and non-Darcean flow. It uses Ck:#1-t8{
the essentials of mixture formalism but achieves a great economy of postulates and 4n#YDZ
mathematical generalizations with no direct physical interpretation. ip<15;Z
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current 4,gol?a
plasticity theories and discuss in a systematic and thorough manner the problems of :EYu 4Y
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure ^}>zYt
and grain characteristics are explained. The benchmark problems of the triaxial ~:2&/MOP?
compression test, the biaxial compression test and the cavity inflation test are analyzed v/]Qq
in detail as examples of loss of material stability and progressive failure. +}kO;\
The stage has now been set for the introduction of higher order continuum models to fFjL pl
describe correctly bifurcation and periodic phenomena in granular materials. Standard h=!M6yap<
theories of soil plasticity do not contain an internal length scale, and thus features such c6f|y_2
as thickness and spacing of shear bands, as well as the stress-strain response in the Ng?apaIi@~
softening regime, cannot be addressed. As a result, finite element calculations do not xq#U4E
converge and related boundary value problems are ill-posed. The authors were among U LV)0SB
the first to show that Cosserat and higher order gradient plasticity models can resolve ?e"Wu+q~L
these difficulties. bcUC4g\9N
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in UwZu:[T6H
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and ~?2rGE
the necessity of higher order terms in removing ill-posedeness in the softening regime vYYS.ve
with simultaneous determination of shear-band characteristics (not captured by <Z2(qZ^Z
standard continuum theory) is documented. N[#iT&@T}/
The book concludes with an account of stability of undrained deformations. This XulaPq
problem is complex and very little understood despite its practical importance. The lv=yz\
authors demonstrate that fundamental work can intelligibly be applied to solve 20$F$YYuk
outstanding geomechanics problems with extended engineering implications. Careful A Z]P+v
laboratory tests are used to calibrate the theoretical models. F_ ,L2J
This well-organized volume is a substantial and valuable reference for civil engineers .WBI%ci
and geologists, as well as mechanical engineers and metal physicists. It should be of hTlnw[I
value to any junior or senior researcher with a keen interest in the stability of Lhl$w'r
deformation. Y')O>C0~
Elias C.Aifantis JmnBq<&,0
Center for Mechanics of Materials and Instabilities <WZ1-
Michigan Technological University i_[^s:*T
and Aristotle University of Thessaloniki