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DISCUSSIONSEditor's Note. The model investigated by the authors, which is based on a law of flow associated with the Coulomb or Mises --Schleicher plane of failure, predicts in the plastic region only expansion deformations. In reality the actual behavior of soils, as has been reported repeatedly in the literature, does not correspond to the predictions of this variant of the theory of plastic flow. The recommendations concerning the design of foundations on the basis of allowable displacements obtained by calculation are insufficiently founded within the scope of the investigated model. Still more disputable is the application of the investigated model to a calculation of waterlogged earth dams. It is impossible to draw definite conclusions on the basis of analyzing the stress --strain state of the dam for the Kolyma hydroelectric station, since the calculation scheme does not correspond to reality (the gradual construction of the structure, filling of the reservoir, and core consolidation processes, i.e., the real loading trajectory, are not taken into account).

Ключевые слова: геомеханика; механика грунтов; теория механики зернистых сред Сравнение моделей сплошной и дискретной (зернистой) сред Анализ работ различных авторов показал, что ими были рассмотрены механические явления, возникающие в грунтах при воздействии на них местной нагрузки. При этом были установлены (при давлениях на грунт, больших структурной прочности) две критические нагрузки: Р кр1 и Р кр2. Величину Р кр1 называют начальной критической нагрузкой, еще совершенно безопасной в основаниях сооружений, так как до ее достижения грунт всегда будет находиться в фазе уплотнения. Р кр2-предельная, критическая нагрузка, при которой полностью исчерпывается несущая способность грунта.

In recent years there has been rather wide use of watertight devices (diaphragms, skim) made of bituminous concrete, and attempts have been made to use films of various polymeric materials. The most reliable in service and the simplest to accomplish are vertical diaphragms located in the center of the dam profile [1,2].The main problem in the calculation of diaphragms is the determination of their deformations, particularly horizontal displacements in the plane of the dam cross section. Diaphragms made of bituminous concrete or films have a negligible resistance to bending [2] and in calculations can be regarded as perfectly flexible elements. Coupling of the flexible diaphragm with the foundation can be by various means: free support, hinged, or embedded in the foundation. Diaphragms made of essentially extensible materials (bituminous concrete or film), regardless of the coupling with the foundation, can be regarded with sufficient accuracy in calculations as freely yietding flexible strips completely following the displacements of the inside face of the downstream shoulder. For a diaphragm of low-extensible material, its coupling with the foundation can be taken into account by introducing appropriate corrections into the diagram of displacements calculated for a diaphragm with a conditionally free lower end.Thus, determination of the horizontal displacements of a diaphragm amounts to a determination of such displacements for the inside vertical face of the downstream shoulder due to the action of the load from the upper pool, In a previous work [3] a similar problem was solved for the case of a triangular shoulder of noncohesive soil, where a comparison of experimental data with calculated values is given. We will consider herein an analogous problem for the more general and more frequently encountered case of a trapezoidal downstream shoulder. The solution is carried out for the case of plane strain under the following assumptions: a) within the part of the shoulder being compacted partial surfaces of sliding (upward yielding) are formed which coincide with the outline of the Surfaces of sliding in the presence of upward yielding; b) over the entire length of the partially formed surface of sliding a state of equilibrium occurs which is characterized by the Coulomb relation; c) the surfaces of sliding are taken to be plane. Of the three assumptions the last two have been used repeatedly in the literature and do not cause particular objections. We must add that in the case of the direct action of a distributed load normal to the face of the shoulder, analogous to the interaction of a smooth wall with the soil, the surfaces of sliding will actually be plane or closely so. As is known, in the case of a vertical smooth wall and horizontal backfilI the surfaces of sliding in V. V. Sokolovskii's rigorous theory are plane, coinciding with the plane surfaces of sliding according to Coulomb. The first assumption was advanced by V. A. Florin as a working hypothesis [4]. Later, this hypothesis was used by us when solvi...