Strength Analysis in Geomechanics

The book presents a new approach for the solution of geomechanical problems - it explicitly takes into account deformation and fracture in time, which are neglected in classical methods although these properties create important effects. The method reveals the influence of the form of a structure on its ultimate state. It uses the rheological law which accounts for large strains at a non-linear unsteady creep, an influence of a stress state type, an initial anisotropy and damage. The whole approach takes into account five types of non-linearity (physical as well as geometrical ones) and contains several new ideas. For example, it considers the fracture as a process, the difference between the body and an element of the material which only deforms and fails because it is in the structure, the simplicity of some non-linear computations against the consequent linear ones, the dependence of the maximum strain in dangerous poins of the body only on the material.

Résumé
It is hardly possible to ?nd a single rheological law for all the soils. However, they have mechanical properties (elasticity, plasticity, creep, damage, etc. ) that are met in some special sciences, and basic equations of these disciplines canbeappliedtoearthstructures. Thiswayistakeninthisbook. Itrepresents the results that can be used as a base for computations in many ?elds of the Geomechanics in its wide sense. Deformation and fracture of many objects include a row of important e?ects that must be taken into account. Some of them can be considered in the rheological law that, however, must be simple enough to solve the problems for real objects. On the base of experiments and some theoretical investigations the c- stitutive equations that take into account large strains, a non-linear unsteady creep, an in?uence of a stress state type, an initial anisotropy and a damage are introduced. The test results show that they can be used ?rst of all to ?nding ultimate state of structures for a wide variety of monotonous lo- ings when equivalent strain does not diminish, and include some interrupted, step-wise and even cycling changes of stresses. When the in?uence of time is negligible the basic expressions become the constitutive equations of the plasticity theory generalized here. At limit values of the exponent of a ha- ening law the last ones give the Hooke's and the Prandtl's diagrams.

Contenu
Erratum.- Introduction: Main Ideas.- Main Equations in Media Mechanics.- Some Elastic Solutions.- Elastic-Plastic and Ultimate State of Perfect Plastic Bodies.- Ultimate State of Structures at Small Non-Linear Strains.- Ultimate State of Structures at Finite Strains.