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When calculating various effects of arch dams the well-known Vogt method is used widely for taking into account yielding of the rock foundation, the basic principles of which are [i]: the foundation is regarded as elastic, homogeneous, and isotropic; b) the displacements of the rock foundation regardless of the shape of the canyon are determined on the assumption of the effect of reactive loads on a semiinfinite solid; c) Vogt's formulas in combination with the procedure developed by the U. S. Bureau of Reclamation are used for determining displacements of the rock foundation.The first two principles have a clear physical significance and the area of their use can be determined rather distinctly. As for the procedure of using Vogt's formulas, it contains a certain degree of arbitrariness and its additional evaluation from the standpoint of a more perfect calculation scheme is useful.Vogt examined such a problem: a semiinfinite elastic solid is loaded on a rectangular area with sides a and b. The load is uniformly distributed in the direction of side b and can vary linearly in the other direction. The effect of three types of load was examined: a load normal to the boundary surface of the semiinfinite solid and loads tangential to it. If the concept of generalized forces is used, then the effect of five generalized forces (Pj) was examined and the value of the corresponding five generalized displacements (~Pj) of the rectangular area was determined where ~Px, ~Pu, ~Ps are generalized linear displacements; ~P~, ~P~, generalized angular displacements of the loaded area; the Kj, constant coefficients dependent on the ratio ~ --b/a, Poisson's number, and E, the modulus of elasticity of rock.The procedure of using these formulas for determining the displacements of a rock foundation caused by forces transmitted to it by an arch dam was developed by the U. S. Bureau of Reclamation and consists in the following. The surface of contact of the dam with the rock is developed on the plane bounding the semiinflnite solid, which produces some irregular figure. It is replaced by an equivalent rectangle with sides a and b and is determined by the ratio ~ = b/a, by means of which the constant coefficients Kj figuring in expression (i) are calculated. The generalized displacements of an arbitrary area of rock caused by the contact forces acting on it are determined by means of formulas (i). In this case the same values of Kj are taken for all contact areas, and the real thickness of the dam at that place where the displacement of the rock foundation is being determined is substituted in place of a.This procedure has a formal character and it is insufficiently argued in the technical literature.The calculation model described in [2] examines the joint behavior of an arch dam and foundation according to a scheme in which yielding of the foundation is taken into account under the same assumptions as in the Vogt method, but without the use of the arbitrary procedure described above. This makes it possible to analyze the traditional Vo...

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