Bifurcation Analysis in Geomechanics kI*Uk M-
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by #Ws53mT
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I.VARDOULAKIS PDw{R]V+
Department of Engineering Science K6pw8
National Technical University of Athens H`<?<ak6'M
Greece 6 ,N6jaW
and @?2n]n6
J.SULEM &v#`t~
Centre d’Enseignement et de Recherche en Mécanique 6w#nkF
des Sols T!(
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Ecole Nationale des Ponts et Chaussées/LCPC VEh]p5D
France Q5E:|)G
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Published by B.-A $/
Blackie Academic & Professional, an imprint of Chapman & Hall, {-*\w-~G
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ QjukK6#W
This edition published in the Taylor & Francis e-Library, 2005. rB]W,8~%
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? Xt(!
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This question no doubt will be asked by engineers working in this area with generally ^!>.97*
rather practical and application oriented portfolios. Uu2N9.5
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled b!~TAT&8
conditions such as those dealt with in structural engineering of surface ^eTZn[qH>w
facilities? !Q[}s#g
Are subsurface rock conditions with inherent heterogeneity, anisotropy and |Is'-g!
layering not so uncertain that highly sophisticated numerical techniques with very G.VYp6)5
precise determination of failure are out of balance? sX'U|)/pD
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation _Y
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analysis in that way. Until recently there was definitely no strong business pull from w yD%x(
petroleum engineering to develop bifurcation analysis in geomechanics because no Hptq,~_t
operating company was really asking for improved production performance. Application &,uC9$
of bifurcation analysis to petroleum engineering was clearly a technology push; a _O52ai><b
technique that was available and was (and is) waiting for people seeing opportunities to ec?1c&E
apply it. }|He?[TR
Once these opportunities were found, this fine technology appears to be a lot more >Pkdu}xP3
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to A#:8X1w
solve the very important question of scale dependency of our rock mechanical tests, 3bH5C3(u
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ sQ(1/"gb
wellbore. Transition between different borehole failure and stabilisation mechanisms can ??TdrTS
now be understood, which significantly increases the scope for barefoot completions and 4]"w b5%
exclusion or postponement of sand control. `!kL1oUYE
Suddenly a technology that was initially regarded as rather academic contributes to Gm@iV,F%R
millions of dollars savings. U+!UL5k
This book gives an excellent overview and in-depth treatment of all aspects of M'|)dM|
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, B007x{-L
which can be exploited not only in petroleum engineering rock conditions but in many kbq:U8+k
other geomechanical applications. -M`D>
Cor Kenter ;l`X!3
M7U:g}
s*{mT6s+T
This book by Vardoulakis and Sulem is an outstanding contribution to the important (6#M9XL
field of geomechanics and will also be useful to the many branches of engineering and nL\ZId
applied science, particularly those dealing with mechanical behavior. G"f du(.@
Following a self-contained Introduction, chapter 2 introduces the basic concepts from W8uVd zQ
continuum mechanics and thermodynamics before the incremental formulation of '^lUL) R
standard continuum mechanics, particularly useful for stability and bifurcation ;siJ~|6)
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze ):}Fu
in detail buckling and interface instabilities, including multilayered and cracked media gL,"ef+nM
which offer a natural stimulus for introducing the concept of Crosserat continuum. u
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Chapter 5 provides an updated contribution to the mechanics of water-saturated R8{e&nPE
media. It takes Biot’s original contribution to a new level of understanding, including o~}1oN
important physical phenomena such as grain crushing and non-Darcean flow. It uses ._K$0U!
the essentials of mixture formalism but achieves a great economy of postulates and D3]@i&^B
mathematical generalizations with no direct physical interpretation. {*nEKPq(_*
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current iiehrK&T!
plasticity theories and discuss in a systematic and thorough manner the problems of ;:^ Lv
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure |<QI%Y$dr
and grain characteristics are explained. The benchmark problems of the triaxial <!hpfTz*
compression test, the biaxial compression test and the cavity inflation test are analyzed :D^Y?
in detail as examples of loss of material stability and progressive failure. z-)*Q
The stage has now been set for the introduction of higher order continuum models to cCYl$Ms kZ
describe correctly bifurcation and periodic phenomena in granular materials. Standard xrX?ZJ
theories of soil plasticity do not contain an internal length scale, and thus features such J{^n=X9M0J
as thickness and spacing of shear bands, as well as the stress-strain response in the iZu:uMoc
softening regime, cannot be addressed. As a result, finite element calculations do not k{qLkcOg=
converge and related boundary value problems are ill-posed. The authors were among ?V6 %>RU
the first to show that Cosserat and higher order gradient plasticity models can resolve q'fPNQg
these difficulties. HD~jU>}}
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in B{N=0 cSi
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and afV
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the necessity of higher order terms in removing ill-posedeness in the softening regime E.U0qK],
with simultaneous determination of shear-band characteristics (not captured by AAdD\%JZ
standard continuum theory) is documented. 6BR\iZ
The book concludes with an account of stability of undrained deformations. This 8t--#sDy{0
problem is complex and very little understood despite its practical importance. The xf[zE Et
authors demonstrate that fundamental work can intelligibly be applied to solve 5@CpP-W#
outstanding geomechanics problems with extended engineering implications. Careful y 2cL2c$BT
laboratory tests are used to calibrate the theoretical models. \/X{n*Hw?
This well-organized volume is a substantial and valuable reference for civil engineers j&
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and geologists, as well as mechanical engineers and metal physicists. It should be of t{[gKV-b
value to any junior or senior researcher with a keen interest in the stability of #Ul4&QVeg
deformation. `Q+i-y
Elias C.Aifantis
~t$mw,
Center for Mechanics of Materials and Instabilities HUD7{6}4
Michigan Technological University Iy6p>z|
and Aristotle University of Thessaloniki