ABSTRACT

Basing on the experimental evidence of solids under the ultimate state of loading, the first author proposed a family of new discrete models. These models consist of rigid bodies and two types of connection Springs, one of which resists the dilatational deformation, while the other the shear deformation. Theoretical basis of the models are described first and then application of these models is proposed to soil and rock mechanics. Numerical examples on the limit analysis of a pile on the sloping foundation and a tunnel excavated in the vicinity of the slope of a sloping foundation are shown for verification of the proposed method.

INTRODUCTION

At the present moment the finite element method has become one of indispensable tools for analysis of soil and rock mechanics problems. It is, however, common recognition that the soil and rock foundations are essentially discontinuous structures and the hysteresis is another important characteristic of these materials. Therefore it is definitely needed to develop a new method of analysis in which effects of such discontinuous character- istics are fully taken into account. So far a limited number of work have been carried. Considering the such a status, the present authors proposed a new discrete method of limit analysis recently. In this paper outline of the proposed method will be introduced briefly with some numerical examples conducted to verify the usefulness of' the proposed method.

THEORETICAL BASIS OF NEW DISCRETE MODELS

Generally speaking all materials are composed of very large number of particles and therefore it is obvious that their deformation may be controled not only by the strength of the particles themselves but also by the intergranular strength. From the stand point of the solid mechanics solids are generally considered as continua and their intergranular strength is usually neglected. It is, however, well known from ample experimental evidence that essential feature of plastic deformation is the slip movement and at the ultimate state of loading solids or structures may move like a link mechanism composed of rigid blocks. The first author believed that at this point there exists a limitation in application of structures where relative slip movement among particles play an important role in their plastic deformation. Basing on such consideration he proposed a new discrete model entitled the "Rigid Bodies-Spring Model" as follows: Consider a set of three dimensional rigid bodies of arbitrary shape as shown in Fig. 1.

(Figure in full paper)

They are assumed to be in equilibrium with external loads, and reaction forces are produced by the spring system which is distributed over the contact surface of two adjacent bodies. For further development of new element models, it will be assumed that the contact area is known and fixed. It should be mentioned here that in actual contact problem, the contact surface are not known a priori, and therefore it can be determined only in iterative way. Taking two such rigid bodies under contact, an infinitesimal deformation of the spring system Ls considered (Figure 2).

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