Bifurcation Analysis in Geomechanics f"j9C%'*
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by Q
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I.VARDOULAKIS 0KgP'oWvY
Department of Engineering Science sK+uwt
National Technical University of Athens }}]Lf 3;
Greece FI?J8a
and _Y&.Nw
J.SULEM c;X,-Q9
Centre d’Enseignement et de Recherche en Mécanique W3>9GY90R
des Sols V~/-e- 9u
Ecole Nationale des Ponts et Chaussées/LCPC xl,%
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France ~!PWJ~U
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Published by lGR0-Gh2
Blackie Academic & Professional, an imprint of Chapman & Hall, 1`L.$T,1!
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ u=v-,Tw
This edition published in the Taylor & Francis e-Library, 2005. h~9P34m
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? 9m2FH~
This question no doubt will be asked by engineers working in this area with generally g&F$hm
rather practical and application oriented portfolios. '5$@I{z
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled %}zkmEY.e
conditions such as those dealt with in structural engineering of surface k]r4b`x`
facilities? 4D<C;>*/b
Are subsurface rock conditions with inherent heterogeneity, anisotropy and e<9 ^h)G
layering not so uncertain that highly sophisticated numerical techniques with very pQ0*)}l,
precise determination of failure are out of balance? I2i'
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation yUo8-O aL7
analysis in that way. Until recently there was definitely no strong business pull from =d ;#Nu-
petroleum engineering to develop bifurcation analysis in geomechanics because no {'M/wT)FeC
operating company was really asking for improved production performance. Application [fT$# '6
of bifurcation analysis to petroleum engineering was clearly a technology push; a p2rT0gu!
technique that was available and was (and is) waiting for people seeing opportunities to JZxA:dg
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apply it. tl!dRV92
Once these opportunities were found, this fine technology appears to be a lot more 0%L:jq{5
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to #9[>
solve the very important question of scale dependency of our rock mechanical tests, x X3I`
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ +3-5\t`
wellbore. Transition between different borehole failure and stabilisation mechanisms can Q[NoFZ
V!
now be understood, which significantly increases the scope for barefoot completions and \rxjvV4fcZ
exclusion or postponement of sand control. Wj|W B*B
Suddenly a technology that was initially regarded as rather academic contributes to z{w %pUn}
millions of dollars savings. =0EKrG
This book gives an excellent overview and in-depth treatment of all aspects of G]k[A=dg
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, O9By5j 4
which can be exploited not only in petroleum engineering rock conditions but in many LkzA_|8:D
other geomechanical applications. VPT?z
Cor Kenter e>e${\=,
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This book by Vardoulakis and Sulem is an outstanding contribution to the important ^VMCs/g6
field of geomechanics and will also be useful to the many branches of engineering and IaSPwsvt'
applied science, particularly those dealing with mechanical behavior. j][&o-Ev
Following a self-contained Introduction, chapter 2 introduces the basic concepts from "PRHQW
continuum mechanics and thermodynamics before the incremental formulation of XPMUhozV
standard continuum mechanics, particularly useful for stability and bifurcation 8M,o)oH
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze %Y;^$%X%_
in detail buckling and interface instabilities, including multilayered and cracked media 1irSI,j%z
which offer a natural stimulus for introducing the concept of Crosserat continuum. =Jw*T[ E
Chapter 5 provides an updated contribution to the mechanics of water-saturated >5kz#|@P
media. It takes Biot’s original contribution to a new level of understanding, including Fs4shrt
important physical phenomena such as grain crushing and non-Darcean flow. It uses >%92,hg
the essentials of mixture formalism but achieves a great economy of postulates and P,)D0i
mathematical generalizations with no direct physical interpretation. @Z'i7Z
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current ey[Z<i1
plasticity theories and discuss in a systematic and thorough manner the problems of )mOM!I7D@
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure >M{98NH
and grain characteristics are explained. The benchmark problems of the triaxial weu+$Kr
compression test, the biaxial compression test and the cavity inflation test are analyzed 59j`Z^e
in detail as examples of loss of material stability and progressive failure. `{>/'o
The stage has now been set for the introduction of higher order continuum models to ibQ
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describe correctly bifurcation and periodic phenomena in granular materials. Standard -o"b$[sf=Z
theories of soil plasticity do not contain an internal length scale, and thus features such %RtL4"M2j
as thickness and spacing of shear bands, as well as the stress-strain response in the w{[^
softening regime, cannot be addressed. As a result, finite element calculations do not zo"L9&Hzo
converge and related boundary value problems are ill-posed. The authors were among FqbGT(QB0
the first to show that Cosserat and higher order gradient plasticity models can resolve gvWgw7z
these difficulties. srN7
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in Yq|_6zbYf
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and =,N"% }
the necessity of higher order terms in removing ill-posedeness in the softening regime S{&%tj~U
with simultaneous determination of shear-band characteristics (not captured by Ekq(
standard continuum theory) is documented. +VW8{=$
The book concludes with an account of stability of undrained deformations. This "k @[7
7
problem is complex and very little understood despite its practical importance. The ,T
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authors demonstrate that fundamental work can intelligibly be applied to solve b,+KXx
outstanding geomechanics problems with extended engineering implications. Careful 8VQ!&^9!U#
laboratory tests are used to calibrate the theoretical models. zT&"rcT">
This well-organized volume is a substantial and valuable reference for civil engineers 5;/q[oXI
and geologists, as well as mechanical engineers and metal physicists. It should be of +3zQ"lLD^
value to any junior or senior researcher with a keen interest in the stability of }2RbX,0l9
deformation. [DeDU:
Elias C.Aifantis E+XS7':I
Center for Mechanics of Materials and Instabilities Ty{
SZUJ
Michigan Technological University *`w>\},su
and Aristotle University of Thessaloniki