Strength Analysis in Geomechanics -7&?@M,u
6`1k
^
by f0OgK<.>T
S. Elsoufiev HX yFj
KA?v.s
Springer, 2007 Y!F!@`%G
uO"y`$C$_
Foundations of Engineering Mechanics Gj)uy jct
Series Editors: V.I. Babitsky, J. Wittenburg `6UtxJSx
[Q|M/|mnR1
It is hardly possible to find a single rheological law for all the soils. However, ve6x / PD
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) zqY)dk
that are met in some special sciences, and basic equations of these disciplines b 1 H7
can be applied to earth structures. This way is taken in this book. It represents sx:Hv1 d
the results that can be used as a base for computations in many fields of the 7pz\ScS e
Geomechanics in its wide sense. Deformation and fracture of many objects w?*j dwh,'
include a row of important effects that must be taken into account. Some of 9?$RO[vo
them can be considered in the rheological law that, however, must be simple vsc&Ju%k
enough to solve the problems for real objects. wz h. $?~
On the base of experiments and some theoretical investigations the constitutive ;KL9oV!<f
equations that take into account large strains, a non-linear unsteady zx7#)*
creep, an influence of a stress state type, an initial anisotropy and a damage 0_L m#fE U
are introduced. The test results show that they can be used first of all to t|< FA#
finding ultimate state of structures – for a wide variety of monotonous loadings ZOC#i i`:
when equivalent strain does not diminish, and include some interrupted, V\"1wV~E
step-wise and even cycling changes of stresses. When the influence of time ^g[J*{+!W
is negligible the basic expressions become the constitutive equations of the %Sul4: D#
plasticity theory generalized here. At limit values of the exponent of a hardening k},> ^qE
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together Y| :YrZSC
with the basic relations of continuum mechanics they are used to describe the ,&[7u9@
deformation of many objects. Any of its stage can be taken as maximum $M39 #a
allowable one but it is more convenient to predict a failure according to the H@ Q`
criterion of infinite strains rate at the beginning of unstable deformation. The h mds(lv7
method reveals the influence of the form and dimensions of the structure on ?|lI X z
its ultimate state that are not considered by classical approaches. Ox~ 9_d
Certainly it is hardly possible to solve any real problem without some Fav^^vf*1
assumptions of geometrical type. Here the tasks are distinguished as antiplane _Ds@l VY
(longitudinal shear), plane and axisymmetric problems. This allows l^
Rm0t_
to consider a fracture of many real structures. The results are represented %EWq2'/5
by relations that can be applied directly and a computer is used (if necessary) X% X$Y6
on a final stage of calculations. The method can be realized not only in 8?kP* tmcZ
Geomechanics but also in other branches of industry and science. The whole +v!v[qn
approach takes into account five types of non-linearity (three physical and g#|oi f9o
two geometrical) and contains some new ideas, for example, the consideration _F^$aZt?e
of the fracture as a process, the difference between the body and the element bs
BZ E
of a material which only deforms and fails because it is in a structure, the gJK KR]4*
simplicity of some non-linear computations against linear ones (ideal plasticity Ch7Egz l7?
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the >J@egIKzP
independence of maximum critical strain for brittle materials on the types of [g`, AmR\!
structure and stress state, an advantage of deformation theories before flow c_Tzyh7l4
ones and others. 8""mp]o9
All this does not deny the classical methods that are also used in the book wA631kr
which is addressed to students, scientists and engineers who are busy with {\L|s 5=yr
strength problems.
