Strength Analysis in Geomechanics MOIMW+n
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by FGu#Pa
S. Elsoufiev s E0ldN"
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Springer, 2007 OHK]=DH:M
NzG] nsw
Foundations of Engineering Mechanics 6'ia^om
Series Editors: V.I. Babitsky, J. Wittenburg fB`7f
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It is hardly possible to find a single rheological law for all the soils. However, \KkA U 6
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) *s (L!+
that are met in some special sciences, and basic equations of these disciplines O[\obi"}
can be applied to earth structures. This way is taken in this book. It represents 3$h yV{
the results that can be used as a base for computations in many fields of the e)2w&2i`(F
Geomechanics in its wide sense. Deformation and fracture of many objects N5Ih+8 zT
include a row of important effects that must be taken into account. Some of D |9ItxYu
them can be considered in the rheological law that, however, must be simple (<ngdf`,
enough to solve the problems for real objects. Mo0pN\A}h
On the base of experiments and some theoretical investigations the constitutive (x/xqDpmBS
equations that take into account large strains, a non-linear unsteady ]C5/-J,F
creep, an influence of a stress state type, an initial anisotropy and a damage O"m(C[+ [
are introduced. The test results show that they can be used first of all to cnR18NK
finding ultimate state of structures – for a wide variety of monotonous loadings uM@ve(8\
when equivalent strain does not diminish, and include some interrupted, IpKpj"eoLy
step-wise and even cycling changes of stresses. When the influence of time Oi, :q&
is negligible the basic expressions become the constitutive equations of the |\J! x|xy
plasticity theory generalized here. At limit values of the exponent of a hardening Gp}}M Gk
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together 7|^5E*8/
with the basic relations of continuum mechanics they are used to describe the m!^z{S
deformation of many objects. Any of its stage can be taken as maximum DRmN+2I
allowable one but it is more convenient to predict a failure according to the 1LonYAHF
criterion of infinite strains rate at the beginning of unstable deformation. The 2sYOO>
method reveals the influence of the form and dimensions of the structure on
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its ultimate state that are not considered by classical approaches. ,&0iFUwN_
Certainly it is hardly possible to solve any real problem without some 3mH(@ -OA
assumptions of geometrical type. Here the tasks are distinguished as antiplane T}y@ a^#
(longitudinal shear), plane and axisymmetric problems. This allows ZGC*BP/
to consider a fracture of many real structures. The results are represented 3#~w#Q0%
by relations that can be applied directly and a computer is used (if necessary) 'h{| ]
on a final stage of calculations. The method can be realized not only in W'f)W4D$6
Geomechanics but also in other branches of industry and science. The whole _>(qQ-P x
approach takes into account five types of non-linearity (three physical and k8 O%gO
two geometrical) and contains some new ideas, for example, the consideration H@V+Q}
of the fracture as a process, the difference between the body and the element M }qrF~
of a material which only deforms and fails because it is in a structure, the NG\^>.8
simplicity of some non-linear computations against linear ones (ideal plasticity ibv.M=
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the ),& tF_z:
independence of maximum critical strain for brittle materials on the types of m$ 80D,3
structure and stress state, an advantage of deformation theories before flow d>}R3T
ones and others. ?/FCq6o
All this does not deny the classical methods that are also used in the book IT0 [;eqR
which is addressed to students, scientists and engineers who are busy with K&UTs$_cI
strength problems.
