Strength Analysis in Geomechanics rBLcj;,
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by U3 -cH
S. Elsoufiev rFJPeK7
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Springer, 2007 H,Y+n)5
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Foundations of Engineering Mechanics @OB7TI_/
Series Editors: V.I. Babitsky, J. Wittenburg mne?r3d
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It is hardly possible to find a single rheological law for all the soils. However, d EvjB" x
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) 5ltrr(MeD
that are met in some special sciences, and basic equations of these disciplines 8TE2q Pm
can be applied to earth structures. This way is taken in this book. It represents !k}]` z^d
the results that can be used as a base for computations in many fields of the ?TLzOYJp
Geomechanics in its wide sense. Deformation and fracture of many objects K|ZB!oq
include a row of important effects that must be taken into account. Some of qX %oLa
them can be considered in the rheological law that, however, must be simple nf2[hx@=U
enough to solve the problems for real objects. " <=HmE-;
On the base of experiments and some theoretical investigations the constitutive #GVf +8"
equations that take into account large strains, a non-linear unsteady />13?o#
creep, an influence of a stress state type, an initial anisotropy and a damage !zW22M
are introduced. The test results show that they can be used first of all to -~rZ| W~v
finding ultimate state of structures – for a wide variety of monotonous loadings YD@n8?~$$
when equivalent strain does not diminish, and include some interrupted, VUQx"R9-
step-wise and even cycling changes of stresses. When the influence of time -ld1o+'`v!
is negligible the basic expressions become the constitutive equations of the eKv{N\E
plasticity theory generalized here. At limit values of the exponent of a hardening >u0B ~9_E
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together cvk$ I"q+
with the basic relations of continuum mechanics they are used to describe the P2t9RCH
deformation of many objects. Any of its stage can be taken as maximum Ia%S=xU{=
allowable one but it is more convenient to predict a failure according to the >OotgJnhC
criterion of infinite strains rate at the beginning of unstable deformation. The t/KH`
method reveals the influence of the form and dimensions of the structure on L"(k ;Mfe
its ultimate state that are not considered by classical approaches. sWGc1jC?.F
Certainly it is hardly possible to solve any real problem without some " 0sk(kT
assumptions of geometrical type. Here the tasks are distinguished as antiplane ZR*Dl.GWY
(longitudinal shear), plane and axisymmetric problems. This allows 0)0,&@])7
to consider a fracture of many real structures. The results are represented B*AF 8wX|
by relations that can be applied directly and a computer is used (if necessary) ,?KN;~t#vz
on a final stage of calculations. The method can be realized not only in [ +2 iwfD
Geomechanics but also in other branches of industry and science. The whole nv OJY6)$V
approach takes into account five types of non-linearity (three physical and j` 5K7~hv
two geometrical) and contains some new ideas, for example, the consideration sVNM#,
of the fracture as a process, the difference between the body and the element 5<RZ ht$i
of a material which only deforms and fails because it is in a structure, the ;3P~eeQR
simplicity of some non-linear computations against linear ones (ideal plasticity ^!j,d_)b!
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the J9V,U;"\
independence of maximum critical strain for brittle materials on the types of ui!MQk+D9
structure and stress state, an advantage of deformation theories before flow 7O]$2
ones and others. R\MFh!6sn
All this does not deny the classical methods that are also used in the book 0Q)m>oL.
which is addressed to students, scientists and engineers who are busy with gc[BP>tl\
strength problems.
