Strength Analysis in Geomechanics ^C ,/T2>
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by [9YlLL@
S. Elsoufiev 886 ('
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Springer, 2007 _{2Fx[m%
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Foundations of Engineering Mechanics 0`g}(}'L
Series Editors: V.I. Babitsky, J. Wittenburg e4>L@7
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It is hardly possible to find a single rheological law for all the soils. However, <{-(\>f!9
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) !}Woo$#ND
that are met in some special sciences, and basic equations of these disciplines hy!'Q>[`
can be applied to earth structures. This way is taken in this book. It represents B
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the results that can be used as a base for computations in many fields of the ]ut-wqb{p
Geomechanics in its wide sense. Deformation and fracture of many objects R:pBbA7E
include a row of important effects that must be taken into account. Some of i 5 >J
them can be considered in the rheological law that, however, must be simple qH {8n`
enough to solve the problems for real objects. E7Gi6w~\
On the base of experiments and some theoretical investigations the constitutive 4z-,M7iP
equations that take into account large strains, a non-linear unsteady %>I?' y^
creep, an influence of a stress state type, an initial anisotropy and a damage @'F8 |I 6
are introduced. The test results show that they can be used first of all to clR?< LO
finding ultimate state of structures – for a wide variety of monotonous loadings s= GOB"G
when equivalent strain does not diminish, and include some interrupted, \>aa8LOe
step-wise and even cycling changes of stresses. When the influence of time Mo/2,DiI5
is negligible the basic expressions become the constitutive equations of the ^2Fs)19R
plasticity theory generalized here. At limit values of the exponent of a hardening
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law the last ones give the Hooke’s and the Prandtl’s diagrams. Together 7YQK@lS
with the basic relations of continuum mechanics they are used to describe the ( > +k 3
deformation of many objects. Any of its stage can be taken as maximum T}b(
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allowable one but it is more convenient to predict a failure according to the '
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criterion of infinite strains rate at the beginning of unstable deformation. The :?&WKW
method reveals the influence of the form and dimensions of the structure on x3Dg%=R
its ultimate state that are not considered by classical approaches. 61s2bt#
Certainly it is hardly possible to solve any real problem without some a@S4IoBg%
assumptions of geometrical type. Here the tasks are distinguished as antiplane R&x7 Iq:=D
(longitudinal shear), plane and axisymmetric problems. This allows Ht=6P)
to consider a fracture of many real structures. The results are represented ]P}K3tN%]
by relations that can be applied directly and a computer is used (if necessary) m_r@t*
on a final stage of calculations. The method can be realized not only in \Z6gXO_
Geomechanics but also in other branches of industry and science. The whole r0hta)x a
approach takes into account five types of non-linearity (three physical and `ykMh>* {
two geometrical) and contains some new ideas, for example, the consideration <x>k 3bD
of the fracture as a process, the difference between the body and the element XEgx#F ;F
of a material which only deforms and fails because it is in a structure, the 5m%baf2_
simplicity of some non-linear computations against linear ones (ideal plasticity Im' :sJ31
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the vP87{J*DE1
independence of maximum critical strain for brittle materials on the types of 2RSHB o
structure and stress state, an advantage of deformation theories before flow 0^)8*O9$
ones and others. 1"4nmw}
All this does not deny the classical methods that are also used in the book E{+c*sz
which is addressed to students, scientists and engineers who are busy with P"~qio-
strength problems.
