Bifurcation Analysis in Geomechanics 77=y!SDP
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by }RP 9%n^
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I.VARDOULAKIS ]@<3 6ByM
Department of Engineering Science |Nx!g fU
National Technical University of Athens K&a]pL6D
Greece {]_{BcK+
and *mhw5Z=!
J.SULEM Uub%s`O
Centre d’Enseignement et de Recherche en Mécanique gJ[q
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des Sols &fNE9peQFa
Ecole Nationale des Ponts et Chaussées/LCPC lt(-,md
France p~zTRnm
a518N*]j
Published by o!_; H}pq
Blackie Academic & Professional, an imprint of Chapman & Hall, Q j~W-^/ -
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ `\u),$
This edition published in the Taylor & Francis e-Library, 2005. [{!j9E?(
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What is the use of bifurcation analysis in petroleum engineering rock mechanics? u{lDof>
This question no doubt will be asked by engineers working in this area with generally /*p?UW<*4
rather practical and application oriented portfolios. *$Wx*Jo
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled Kd[`mkmS
conditions such as those dealt with in structural engineering of surface ,DUQto
facilities? 2Z9gOd<M~
Are subsurface rock conditions with inherent heterogeneity, anisotropy and G|Yp<W%o
layering not so uncertain that highly sophisticated numerical techniques with very n~>CE"q
precise determination of failure are out of balance? ~aq?Kk
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation +nyN+X34B
analysis in that way. Until recently there was definitely no strong business pull from y8WXp_\
petroleum engineering to develop bifurcation analysis in geomechanics because no `::(jW.KO
operating company was really asking for improved production performance. Application UeiJhH,u
of bifurcation analysis to petroleum engineering was clearly a technology push; a iKEKk\j-w
technique that was available and was (and is) waiting for people seeing opportunities to L"vG:Mq@D
apply it. cS ;=_%~
Once these opportunities were found, this fine technology appears to be a lot more &/#Tk>:
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to i^V4N4ux]
solve the very important question of scale dependency of our rock mechanical tests, '*{Rn7B5
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ u9~V2>r\
wellbore. Transition between different borehole failure and stabilisation mechanisms can s1b\I6&:J
now be understood, which significantly increases the scope for barefoot completions and $8 ww]}K
exclusion or postponement of sand control. A5H8+gATK
Suddenly a technology that was initially regarded as rather academic contributes to VS@W.0/
millions of dollars savings. xA1pDrfC/
This book gives an excellent overview and in-depth treatment of all aspects of q}24U3ow
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, ]=XL9MI
which can be exploited not only in petroleum engineering rock conditions but in many J3}C T
other geomechanical applications. m_ONsZHy
Cor Kenter jE5
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This book by Vardoulakis and Sulem is an outstanding contribution to the important C]cT*B^
field of geomechanics and will also be useful to the many branches of engineering and L5|;VH
applied science, particularly those dealing with mechanical behavior. UU~;B
Following a self-contained Introduction, chapter 2 introduces the basic concepts from D@1^:'$V
continuum mechanics and thermodynamics before the incremental formulation of ScmzbDu
standard continuum mechanics, particularly useful for stability and bifurcation yW,#&>]# |
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze &IPK5o,
in detail buckling and interface instabilities, including multilayered and cracked media 73Zs/
which offer a natural stimulus for introducing the concept of Crosserat continuum. yT9RNo/w
Chapter 5 provides an updated contribution to the mechanics of water-saturated -EIMh^
media. It takes Biot’s original contribution to a new level of understanding, including hnLgsz
important physical phenomena such as grain crushing and non-Darcean flow. It uses Hw. @Le>
the essentials of mixture formalism but achieves a great economy of postulates and hr"+0KeX
mathematical generalizations with no direct physical interpretation. 4)Wzj4qW
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current 3K]0sr
plasticity theories and discuss in a systematic and thorough manner the problems of P*=3$-`
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure <yaw9k+P
and grain characteristics are explained. The benchmark problems of the triaxial _I"<?sh3
compression test, the biaxial compression test and the cavity inflation test are analyzed r\- k/ 0
in detail as examples of loss of material stability and progressive failure. .8xacVyK2
The stage has now been set for the introduction of higher order continuum models to :qKY@-t7H
describe correctly bifurcation and periodic phenomena in granular materials. Standard RpXG gw
theories of soil plasticity do not contain an internal length scale, and thus features such ?BZ`mrH^
as thickness and spacing of shear bands, as well as the stress-strain response in the [?o vJ
softening regime, cannot be addressed. As a result, finite element calculations do not @9P9U`ZP
converge and related boundary value problems are ill-posed. The authors were among c] 9CN
the first to show that Cosserat and higher order gradient plasticity models can resolve ]Lft^,7
these difficulties. ill' KPy
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in >l*9DaZ
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and y(BLin!O.
the necessity of higher order terms in removing ill-posedeness in the softening regime >N"PLSY1
with simultaneous determination of shear-band characteristics (not captured by QF6JZQh<
standard continuum theory) is documented. "JGig!9
The book concludes with an account of stability of undrained deformations. This B9Tztg
problem is complex and very little understood despite its practical importance. The BJ2W}R
authors demonstrate that fundamental work can intelligibly be applied to solve &IY_z0=
outstanding geomechanics problems with extended engineering implications. Careful '"p*FN
laboratory tests are used to calibrate the theoretical models. D_kzR
This well-organized volume is a substantial and valuable reference for civil engineers mP+yjRw
and geologists, as well as mechanical engineers and metal physicists. It should be of d'nuk#r
value to any junior or senior researcher with a keen interest in the stability of ,'DrFlI
deformation. siZ_JJW
Elias C.Aifantis fszeJS}Dw
Center for Mechanics of Materials and Instabilities H LGy"P
Michigan Technological University 4T\/wyq0
and Aristotle University of Thessaloniki