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in which λL, λL ,a ndλρ are scale factors respectively related to the geometry, the elastic moduli, and the densities. We simulated the strain state due to static and dynamic loads in the natural gravitational field, but there are great difficulties in satisfying (1) in the field of the Earth’s gravity, since the model requires special equivalent materials with elevated density and low elastic modulus, while having the shear characteristics of natural soils. There are considerable difficulties in selecting such materials even for simulating concrete structures, and the difficulties increase greatly for earth structures. One approach is to use models made of natural soils in an artificial acceleration field, e.g., centrifuge. This greatly complicates the measurements, and also the reproduction of the seismic loads and boundary conditions. We used a mixed simulation: strain pattern from static loads reproduced in a model made from natural soil by means of anchors installed at many points and thin ties attached to them. Forces were applied to the ties equivalent to the weight of the soil acting in an elementary volume, with the anchor in each case at the center of gravity. The hydrostatic water pressure at the upstream face was reproduced by a system of rigid plungers loaded by presses. The static loads could be varied widely up to the failure stage, and the measurements and observations were quite simple and reliable. The seismic (inertial) loads were reproduced on the assumption that the material is linearly elastic in accordance with the Cauchy criterion. In that situation (model made from natural soil), λE = λρ =1 ; if we take the strain scale as λe = 1, then the scales for the accelerations and vibration periods λa and λT are respectively λa =1 /λL and λT = λL. (2)

1. For relative lengths of piles up to 30–40 their interaction with sand soils obeys Coulomb's law and can be described by dependences (7)–(9) of the present work. 2. Modeling the behavior of rigid piles under a vertical load, we can limit ourselves to a simple similarity, reproducing on the model the angle of internal friction of the soil and pile-driving technology for a geometrical modeling scale of not more than 10 with conversion of the data obtained by the proposed method. 3. Investigation of piles under an inclined or horizontal load requires reproduction of four physical and mechanical characteristics of the soil simultaneously on the model: modulus of deformation, density, angle of internal friction, and lateral earth pressure coefficient, as well as the angle of internal friction. However, in the range of angles of internal friction 30–45° and in rough piles we can limit ourselves to modeling the first three of the indicated parameters. 4. The proposed scheme of behavior of rigid piles and the modeling method based on it permit predicting the behavior of single piles under a vertical load on the basis of existing analogs or tests of small piles.

1. The diagram of the intensity of the seismic pressure of cohesionless soil on a rigid retaining wall has the form of a triangle with a vertex at the base of the wall. 2. The seismic pressure of cohesionless soil on a rigid wall depends more on the elastic characteristics of the soil medium and considerably less on its angle of internal friction. 3. The standard method of determining loads from seismic earth pressure noticeably understates their extent and requires reexamination.

1. The developed model material and method of investigation make it possible to solve successfully problems of the nonlinear behavior of structures under dynamic and static loads on relatively small models. 2. The most “dangerous” zone in a seismic respect is the zone of the upper quarter of the dam within which failure of both the monolithic and block models occurred. 3. For the investigated compressed profile of dams with a limited number of horizontal joints their presence substantially reduces the bearing capacity of the dam. In the present investigations the safety factor decreased by a factor of about 2.8. 4. Strengthening of the upper third of the dam by reinforcement or stressed anchors makes it possible to double the bearing capacity of the structure.

1. The presence of water in the reservoir has little effect on the dynamic characteristics of massive-buttress dams under vibration of the buttresses along the dam axis and its effect shows no increase in analyses for seismic action in the direction across the canyon. 2. In analyses of the earthquake resistance of such dams it is necessary to take into account the interaction through the foundation of the adjacent sections, which have common bearing areas and which, in the case of a homogeneous foundation, lead to a substantial increase in the seismic stresses in the zone of the contact with the grout curtain. 3. For the Kirovsk dam, the foundation stratification led to favorable redistribution of the seismic stresses in the structure in comparison with the case of a homogeneous foundation having a greater deformability. 4. The presence of vertical cracks in the lower zone of the dam propagated to a height of 12 m did not cause substantial changes in the earthquake resistance of the structure. 5. Partial consolidation of all the intersectional joints ensures reliable operation of dams of similar types in narrow sites (L/h=3–4) for earthquakes of magnitude 8–9 across the canyon.

1. Yielding of a foundation has a considerable effect on the seismic stability of roundhead buttress dams. The experimental data presented in the article are not complete but can be used in design for taking into account the indicated factor. 2. When a structure is subjected to a seismic load of the traveling-wave type directed along the canyon, the magnitudes of the stresses in the buttress near the base of the dam can prove to be considerably greater than those obtained by calculation or experiment without consideration of this factor. 3. The local stress concentrations arising in the lower part of the dam in the zone of interlocking side planes of the roundhead buttress can be eliminated in the case of a lateral earthquake by means of joints-notches on the side planes of the roundheads or by constructing under each section a yielding interlayer having an increased tensile strength. 4. Sealing of all the intersectional joints of the dam is an effective method of increasing its seismic stability. This method is especially effective under conditions of narrow sites.