Bifurcation Analysis in Geomechanics PeqW+Q.
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by wF% RM$
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I.VARDOULAKIS qnWM %k
Department of Engineering Science $U9]v5
National Technical University of Athens t6mv
Greece GRkN0|ovfj
and /BQqg08@L
J.SULEM Is<XMR|{
Centre d’Enseignement et de Recherche en Mécanique UA2KY}pz5
des Sols ePJ_O~c
Ecole Nationale des Ponts et Chaussées/LCPC OgC,oj,!/
France (S+/e5c)
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Published by 4KR`
Blackie Academic & Professional, an imprint of Chapman & Hall, ISK 8t
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ 3#dz6+
This edition published in the Taylor & Francis e-Library, 2005. 2Vf242z_
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? yFb"2
This question no doubt will be asked by engineers working in this area with generally E"S#d&9
rather practical and application oriented portfolios. i '*!c
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled (s&]V49
conditions such as those dealt with in structural engineering of surface :#?_4D!r
facilities? W}3%BWn
Are subsurface rock conditions with inherent heterogeneity, anisotropy and
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layering not so uncertain that highly sophisticated numerical techniques with very "M[&4'OM
precise determination of failure are out of balance? %,HUn`
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation T`Up%5Dk
analysis in that way. Until recently there was definitely no strong business pull from Do\j _
petroleum engineering to develop bifurcation analysis in geomechanics because no S1Od&v[R
operating company was really asking for improved production performance. Application FJCORa@?_
of bifurcation analysis to petroleum engineering was clearly a technology push; a 3c,4 wyn
technique that was available and was (and is) waiting for people seeing opportunities to (Sgsy^|N
apply it. %g@\SR.
Once these opportunities were found, this fine technology appears to be a lot more m;>G]Sbe
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to esBv,b?*
solve the very important question of scale dependency of our rock mechanical tests, "Ueq
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ G6W|l2P!
wellbore. Transition between different borehole failure and stabilisation mechanisms can AH/o-$C&
now be understood, which significantly increases the scope for barefoot completions and r63l(
exclusion or postponement of sand control. +75"Q:I
Suddenly a technology that was initially regarded as rather academic contributes to PlS)Zv3
millions of dollars savings. 00dY?d{[D
This book gives an excellent overview and in-depth treatment of all aspects of RN[x\" ,
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, a:UkVK]MP
which can be exploited not only in petroleum engineering rock conditions but in many =p=/@ FN
other geomechanical applications. h^Yh~84T
Cor Kenter N wNxO
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This book by Vardoulakis and Sulem is an outstanding contribution to the important 9{j`eAUZl
field of geomechanics and will also be useful to the many branches of engineering and '/6f2[%Y"
applied science, particularly those dealing with mechanical behavior. ~?fl8RF\
Following a self-contained Introduction, chapter 2 introduces the basic concepts from h4 9q(085V
continuum mechanics and thermodynamics before the incremental formulation of 6fI2y4yEz
standard continuum mechanics, particularly useful for stability and bifurcation -.MJ3
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze quaRVD>s +
in detail buckling and interface instabilities, including multilayered and cracked media >Ovz;
which offer a natural stimulus for introducing the concept of Crosserat continuum. 0uW)&>W
Chapter 5 provides an updated contribution to the mechanics of water-saturated '/ Hoq
media. It takes Biot’s original contribution to a new level of understanding, including [f lK
important physical phenomena such as grain crushing and non-Darcean flow. It uses G/},lUzLg
the essentials of mixture formalism but achieves a great economy of postulates and J(/J;PW
mathematical generalizations with no direct physical interpretation. RHNAHw9
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current LiQH!yHW
plasticity theories and discuss in a systematic and thorough manner the problems of XXA'B{@Y)
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure |;)_-=L0P
and grain characteristics are explained. The benchmark problems of the triaxial - ry
compression test, the biaxial compression test and the cavity inflation test are analyzed p=> +3
in detail as examples of loss of material stability and progressive failure. fS|e{!iI"
The stage has now been set for the introduction of higher order continuum models to 5WRqeSGh
describe correctly bifurcation and periodic phenomena in granular materials. Standard GBRiU&D
theories of soil plasticity do not contain an internal length scale, and thus features such o&@ y^<UQ
as thickness and spacing of shear bands, as well as the stress-strain response in the ~Y*.cGA
softening regime, cannot be addressed. As a result, finite element calculations do not =LK`mNA
converge and related boundary value problems are ill-posed. The authors were among @jMo/kO/A
the first to show that Cosserat and higher order gradient plasticity models can resolve Pp69|lxV=k
these difficulties. }wvR s5;o
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in OGJrwl
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and G9QvIXRi
the necessity of higher order terms in removing ill-posedeness in the softening regime O NcLhwH
with simultaneous determination of shear-band characteristics (not captured by z(^dwMw}
standard continuum theory) is documented. Y:m8UnT
The book concludes with an account of stability of undrained deformations. This ;'V[8`Z@
problem is complex and very little understood despite its practical importance. The 0Qvr
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authors demonstrate that fundamental work can intelligibly be applied to solve Je9Z:s[
outstanding geomechanics problems with extended engineering implications. Careful R_GA`U\ {
laboratory tests are used to calibrate the theoretical models. K,|3?CjS
This well-organized volume is a substantial and valuable reference for civil engineers Lk#)VGk:
and geologists, as well as mechanical engineers and metal physicists. It should be of b`S9#`
value to any junior or senior researcher with a keen interest in the stability of UukY9n];]
deformation. u^E0u^
Elias C.Aifantis ,Fkq/h
Center for Mechanics of Materials and Instabilities <[}zw!z
Michigan Technological University 4h--x~ @
and Aristotle University of Thessaloniki