Bifurcation Analysis in Geomechanics 'L0 2lM
"Rs^0iT7>
by K=Fcy#,f
sbNCviKP
I.VARDOULAKIS 1p9f& w
Department of Engineering Science '(u [
National Technical University of Athens Mk[_yqoCO
Greece E9226
and I[<C)IG
J.SULEM o *I-~k
Centre d’Enseignement et de Recherche en Mécanique ]Wv\$JXI
des Sols u 8N+ht@
Ecole Nationale des Ponts et Chaussées/LCPC fX} dh9
France XX}RbE#4
7,jh44(\=
Published by [>?B`1;@
Blackie Academic & Professional, an imprint of Chapman & Hall, |TEf? <"c
Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ \kWceu}H,
This edition published in the Taylor & Francis e-Library, 2005. Gz~P
0Z^w}
+\.gd L)
What is the use of bifurcation analysis in petroleum engineering rock mechanics? rMf& HX
This question no doubt will be asked by engineers working in this area with generally 4U>
rather practical and application oriented portfolios. jPA?0h
Is there any use at all, is it not just an academic subject, at best useful for wellcontrolled NY1olnI
conditions such as those dealt with in structural engineering of surface +69sG9BA
facilities? zc,fJM
Are subsurface rock conditions with inherent heterogeneity, anisotropy and &sWq SS
layering not so uncertain that highly sophisticated numerical techniques with very Fv5@-&y$W
precise determination of failure are out of balance? Dw6Q2Gnv
Many sceptics, amongst whom I have found myself for some time, look upon bifurcation xp>ra2A
analysis in that way. Until recently there was definitely no strong business pull from UO<%|{W+
petroleum engineering to develop bifurcation analysis in geomechanics because no -@L*i|A
operating company was really asking for improved production performance. Application N9:xtrJ]_J
of bifurcation analysis to petroleum engineering was clearly a technology push; a <(@m913|
technique that was available and was (and is) waiting for people seeing opportunities to )BS./zD*[<
apply it. 5oWR}qqFK
Once these opportunities were found, this fine technology appears to be a lot more ^i#q{@g
beneficial for our ‘rough’ business than initially anticipated. For instance, it allows us to &Cdk%@Tj]B
solve the very important question of scale dependency of our rock mechanical tests, 1"~@UcJ
such as whether a hollow cylinder with a 8 mm hole can be representative for an 8½′′ [al$7R&
wellbore. Transition between different borehole failure and stabilisation mechanisms can 3Xf}vdgdM$
now be understood, which significantly increases the scope for barefoot completions and q^goi1
exclusion or postponement of sand control. PGu6hV{
Suddenly a technology that was initially regarded as rather academic contributes to =}U`q3k
millions of dollars savings. Alp9]
0(
This book gives an excellent overview and in-depth treatment of all aspects of /o![%&-l
bifurcation analysis in geomechanics. This is sophisticated and powerful technology, o& $Fc8bH
which can be exploited not only in petroleum engineering rock conditions but in many 0ltq~K
other geomechanical applications. Scs \nF2
Cor Kenter C8@SuJ
L&'2
.azdAq'r&\
This book by Vardoulakis and Sulem is an outstanding contribution to the important i+T$&$b
field of geomechanics and will also be useful to the many branches of engineering and J0lTp /
applied science, particularly those dealing with mechanical behavior. g;eMsoJG
Following a self-contained Introduction, chapter 2 introduces the basic concepts from OZLU>LU
continuum mechanics and thermodynamics before the incremental formulation of 1|n,s-
standard continuum mechanics, particularly useful for stability and bifurcation ShHm7+fV
problems, is presented in chapter 3. This formalism is employed in chapter 4 to analyze n>Q/XQXB
in detail buckling and interface instabilities, including multilayered and cracked media SH5GW3\h
which offer a natural stimulus for introducing the concept of Crosserat continuum. hq$:62NYg
Chapter 5 provides an updated contribution to the mechanics of water-saturated vQ26U(7\>
media. It takes Biot’s original contribution to a new level of understanding, including HRje4=:
important physical phenomena such as grain crushing and non-Darcean flow. It uses Ry[VEn>C1
the essentials of mixture formalism but achieves a great economy of postulates and 0D:J d6\
mathematical generalizations with no direct physical interpretation. O^4:4tRpt
In the same spirit, chapters 6 to 8 provide self-contained reviews of the current #ra:^9;Es:
plasticity theories and discuss in a systematic and thorough manner the problems of Sep}{`u
bifurcation and shear-band formation. The effects of non-coaxiality, confining pressure 4 K{4=uU
and grain characteristics are explained. The benchmark problems of the triaxial *V3 }L
Z
compression test, the biaxial compression test and the cavity inflation test are analyzed K
)1K ]
in detail as examples of loss of material stability and progressive failure. i@Q)`>4
The stage has now been set for the introduction of higher order continuum models to 4wMKl6mL
describe correctly bifurcation and periodic phenomena in granular materials. Standard -&D~TL#
theories of soil plasticity do not contain an internal length scale, and thus features such "F}anPY
as thickness and spacing of shear bands, as well as the stress-strain response in the x:"_B
softening regime, cannot be addressed. As a result, finite element calculations do not ~%k<N/B
converge and related boundary value problems are ill-posed. The authors were among VGA?B@
the first to show that Cosserat and higher order gradient plasticity models can resolve 70a7}C\/o
these difficulties. N
0&h5
Self-contained accounts of Cosserat plasticity and second-grade plasticity are given in Yep(,J~'
chapters 9 and 10, respectively. Bifurcation and shear-band analyses are performed and !YsLx[+
the necessity of higher order terms in removing ill-posedeness in the softening regime u0#q)L8
with simultaneous determination of shear-band characteristics (not captured by yo") G!BN
standard continuum theory) is documented. P0DvZV8
The book concludes with an account of stability of undrained deformations. This I%b,
H`
problem is complex and very little understood despite its practical importance. The \ d+&&ns
authors demonstrate that fundamental work can intelligibly be applied to solve :_i1)4[!
outstanding geomechanics problems with extended engineering implications. Careful GmPNzHDb
laboratory tests are used to calibrate the theoretical models. r2qxi'
This well-organized volume is a substantial and valuable reference for civil engineers Pc`d@q
and geologists, as well as mechanical engineers and metal physicists. It should be of tlQ3BKp
value to any junior or senior researcher with a keen interest in the stability of kdITh9nx<r
deformation. AnfJyltS
Elias C.Aifantis W(1p0|WQ:
Center for Mechanics of Materials and Instabilities )#9/vIQ
Michigan Technological University b,$H!V*
and Aristotle University of Thessaloniki