Bifurcation Analysis in Geomechanics Dh8'og)7
MuOKauYa
by +Mijio
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I.VARDOULAKIS Z[IM\# "
Department of Engineering Science 4zS0kk;+
National Technical University of Athens R`c[?U
Greece <skqq+
and 2%fIe
J.SULEM g=4^u*
Centre d’Enseignement et de Recherche en Mécanique }ww/e\|Nt=
des Sols l~;>KjZg
Ecole Nationale des Ponts et Chaussées/LCPC t}_ #N'`
France uEJ8Lmi
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Published by ~C%I'z'
Blackie Academic & Professional, an imprint of Chapman & Hall, <$e|'}>A
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ HQ-++;Q
This edition published in the Taylor & Francis e-Library, 2005. b*?u+tWP_
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? ]w6Q? %'9
This question no doubt will be asked by engineers working in this area with generally 1`7zYW&L
rather practical and application oriented portfolios. @p*)^D6E\
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled <v0`r2^S{-
conditions such as those dealt with in structural engineering of surface =|P
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facilities? iv$YUM+
Are subsurface rock conditions with inherent heterogeneity, anisotropy and ia'z9
layering not so uncertain that highly sophisticated numerical techniques with very qMJJB l
precise determination of failure are out of balance? #_35bg4h{
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation ~)ys,Q
analysis in that way. Until recently there was definitely no strong business pull from sRD
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petroleum engineering to develop bifurcation analysis in geomechanics because no aq$ hE-{28
operating company was really asking for improved production performance. Application t>cGfA
of bifurcation analysis to petroleum engineering was clearly a technology push; a ;Z{D@g+
technique that was available and was (and is) waiting for people seeing opportunities to S/5QK(XLC)
apply it. 2g{tzR_j
Once these opportunities were found, this fine technology appears to be a lot more ac l<dY6
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to 5&n{QE?Um
solve the very important question of scale dependency of our rock mechanical tests, !}TsFa
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ Y'|,vG
wellbore. Transition between different borehole failure and stabilisation mechanisms can EB*sd S
now be understood, which significantly increases the scope for barefoot completions and \Vf:/9^
exclusion or postponement of sand control. d>hv-nD
Suddenly a technology that was initially regarded as rather academic contributes to =Hd yra
millions of dollars savings. Y}c/wF7o
This book gives an excellent overview and in-depth treatment of all aspects of <R$ 2x_
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, 7l69SQo]?
which can be exploited not only in petroleum engineering rock conditions but in many ~'_cBJ
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other geomechanical applications. w95M
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Cor Kenter YGyv)\
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This book by Vardoulakis and Sulem is an outstanding contribution to the important O6;"cUv
field of geomechanics and will also be useful to the many branches of engineering and Eu?z!
applied science, particularly those dealing with mechanical behavior. ls@]%pz.1d
Following a self-contained Introduction, chapter 2 introduces the basic concepts from H\S)a FY[
continuum mechanics and thermodynamics before the incremental formulation of LQR2T5S/Q,
standard continuum mechanics, particularly useful for stability and bifurcation ~(d
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problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze kMQ
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in detail buckling and interface instabilities, including multilayered and cracked media yU
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which offer a natural stimulus for introducing the concept of Crosserat continuum. >Wr%usNxc
Chapter 5 provides an updated contribution to the mechanics of water-saturated sP(+Z^/
media. It takes Biot’s original contribution to a new level of understanding, including 2 kDsIEA
important physical phenomena such as grain crushing and non-Darcean flow. It uses G|g^yaq>
the essentials of mixture formalism but achieves a great economy of postulates and u;_~{VJ-
mathematical generalizations with no direct physical interpretation. }sXTZX
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current y>a?<*Y+e
plasticity theories and discuss in a systematic and thorough manner the problems of ]P?<2,
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure -@#w)
and grain characteristics are explained. The benchmark problems of the triaxial WBE>0L
compression test, the biaxial compression test and the cavity inflation test are analyzed "@UQSf,
in detail as examples of loss of material stability and progressive failure. jn2=)KBa_
The stage has now been set for the introduction of higher order continuum models to @z@%vr=vX
describe correctly bifurcation and periodic phenomena in granular materials. Standard ~ skp}g]
theories of soil plasticity do not contain an internal length scale, and thus features such hN-@_XSw<I
as thickness and spacing of shear bands, as well as the stress-strain response in the *HKw;I
softening regime, cannot be addressed. As a result, finite element calculations do not W" 5nS =d%
converge and related boundary value problems are ill-posed. The authors were among 7<yc:}9nx
the first to show that Cosserat and higher order gradient plasticity models can resolve "bo0O7InOV
these difficulties. j<<d A[X
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in |H5.2P&9-5
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and o
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the necessity of higher order terms in removing ill-posedeness in the softening regime )dT@0Ys%
with simultaneous determination of shear-band characteristics (not captured by J$3g3%t
standard continuum theory) is documented. ,S-h~x
The book concludes with an account of stability of undrained deformations. This rpT.n-H>%A
problem is complex and very little understood despite its practical importance. The ^LMgOA(7
authors demonstrate that fundamental work can intelligibly be applied to solve ,'X"(tpu@
outstanding geomechanics problems with extended engineering implications. Careful n"(!v7YNp
laboratory tests are used to calibrate the theoretical models. mOE *[S)
This well-organized volume is a substantial and valuable reference for civil engineers .;?!I_`
and geologists, as well as mechanical engineers and metal physicists. It should be of bHwEd%f
value to any junior or senior researcher with a keen interest in the stability of $m 4-^=
deformation. PXb$]HV
Elias C.Aifantis W$c@C02<
Center for Mechanics of Materials and Instabilities 1-_r\sb
Michigan Technological University LIZB!S@V \
and Aristotle University of Thessaloniki