Strength Analysis in Geomechanics G JlkEWs
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by > Y7nq\
S. Elsoufiev gcLwQ-
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Springer, 2007 l !Bc0
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Foundations of Engineering Mechanics ziFg+i%s
Series Editors: V.I. Babitsky, J. Wittenburg cW+6Emh
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It is hardly possible to find a single rheological law for all the soils. However, jpND" `Q
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) H8^U!"~E
that are met in some special sciences, and basic equations of these disciplines 3&*_5<t\X
can be applied to earth structures. This way is taken in this book. It represents ^A9D;e6!-
the results that can be used as a base for computations in many fields of the B(}u:[
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Geomechanics in its wide sense. Deformation and fracture of many objects R <kh3T
include a row of important effects that must be taken into account. Some of Vs>/q:I
them can be considered in the rheological law that, however, must be simple }jj @A !N
enough to solve the problems for real objects. EBF608nWfW
On the base of experiments and some theoretical investigations the constitutive f<!3vAh
equations that take into account large strains, a non-linear unsteady uc6;%=%+
creep, an influence of a stress state type, an initial anisotropy and a damage V 0'T )
are introduced. The test results show that they can be used first of all to ( e> .hfrs
finding ultimate state of structures – for a wide variety of monotonous loadings 'G3;!xk$
when equivalent strain does not diminish, and include some interrupted, "S$4pj`<
step-wise and even cycling changes of stresses. When the influence of time 8;'fWV?
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is negligible the basic expressions become the constitutive equations of the z$'_ =9yZ
plasticity theory generalized here. At limit values of the exponent of a hardening ^1d"Rqtv
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together [8Zq
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with the basic relations of continuum mechanics they are used to describe the k_A. aYe
deformation of many objects. Any of its stage can be taken as maximum &[]0yNG
allowable one but it is more convenient to predict a failure according to the eUiJl6^x
criterion of infinite strains rate at the beginning of unstable deformation. The ts2;?`~
method reveals the influence of the form and dimensions of the structure on %m8;Lh- X
its ultimate state that are not considered by classical approaches. VUfV=&D-*g
Certainly it is hardly possible to solve any real problem without some h-"c
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assumptions of geometrical type. Here the tasks are distinguished as antiplane 3$YgGum
(longitudinal shear), plane and axisymmetric problems. This allows L,I 5/ K6
to consider a fracture of many real structures. The results are represented W'2a1E
by relations that can be applied directly and a computer is used (if necessary) YuO-a$BP
on a final stage of calculations. The method can be realized not only in GWs[a$|
Geomechanics but also in other branches of industry and science. The whole D@[Mk"f
approach takes into account five types of non-linearity (three physical and ;d"F'd
two geometrical) and contains some new ideas, for example, the consideration MGUzvSf
of the fracture as a process, the difference between the body and the element rh;@|/<l
of a material which only deforms and fails because it is in a structure, the NL}) _.Og
simplicity of some non-linear computations against linear ones (ideal plasticity ~ b}@*fq
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the zE" ME*ou
independence of maximum critical strain for brittle materials on the types of }m6zu'CV
structure and stress state, an advantage of deformation theories before flow (h8M
ones and others. }P[x Z_S1
All this does not deny the classical methods that are also used in the book @=KuoIV
which is addressed to students, scientists and engineers who are busy with X2
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strength problems.
