Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials
In most engineering problems related to determination of limit capacity of soil foundation and its interaction with a structure, only static field was considered. Starting from the Coulomb yield condition, the stress field was determined in a more or less
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LIMIT AN ALYSIS AND RHEOLOGICAL APPROACH IN
SOIL MECHANICS
EDITED BY v
W. OLSZAK AND L. SUKLJE
SPRINGER-VERLAG WIEN GMBH
This work is Slbject to copyright.
Ali rights are reserved. whether the whole or part of the material il concerned specifucally those of translation, reprinting. re-u se of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. ©1978 by Springer-Verlag Wien Originally publisbed by Springer-Verlag Wien-New York in 1978
ISBN 978-3-211-81511-3 DOI 10.1007/978-3-7091-4352-0
ISBN 978-3-7091-4352-0 (eBook)
PREFACE
The formal analogy which exists between the basic relationships of the mathematical theory of plasticity and those of soil mechanics, stems for transferring the methods of the first to the wide fields of the second. Of course, the essential physical differences have to be appropriately taken into account. This primarily refers to the notion of the yield criterion as well as to that of the plastic potential which may, in certain cases, be adopted. The above approach is generally being used when investigating problems of limit equilibrium conditions. However, experimental evidence clearly shows that the elastic-plastic approach can constitute the first approximation to reality only and that soils often exhibit rheological properties. Thus, in order to be able to adequately represent their response to various types of loading programmes, we have to consider both the irreversible and time-dependent character. These facts are well reflected in the papers of the present volume. It contains Jour series of lectures on some soil mechanics problems, presented at the International Centre for Mechanical Sciences within the scope of the Summer Session in 1976. Three series are related to the theory of plasticity as applied to limit equilibrium problems, while the fourth deals with the influence o{non-linear viscous response onto the development of stresses and strains in solids. The classical limit equilibrium analysis is based on the system of differential equations obtained by combining the appropriate yield criterion with the equilibrium conditions. Using Alohr-Coulomb's failure law, the joint differential equations were first deduced, jor plane wedge-shaped plastic domains, by Boussinesq (1885), and irl a more general form by Kotter (1903). The use of these equations was l'ery limited until appropriate rzumerical procedures facilitated their wide application to bearing capacity and earth pressure problems (Caqllot 1943. Sak%tlskij 1954, and others).
II
Preface
The adaptation of the theory of plasticity to strain-hardening and strain-softening media, with the stress-strain and strain-displacement relationships incorporated in the analysis, resulted in the use of the plasticity theory in the wide domain from the "at rest" up to the failure stress-states. On the other hand, the consideration of the flow rule and of the kinematic relations has permitted to construct the velocity fields corresponding to the limit stress fields of soils
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