Discussion on constructional norms

Abstract

The current SNiP [Construction Specifications and Regulations] II-A. 12-62 [i] envisage that the seismic resistance of a dam made of local materials should be calculated, for example, by the method of circular-cylindrical slip surfaces. The seismic loads are regarded as inertial forces acting at the centers of gravity of the mathematical elements into which the cross section of the dam is divided. However, the norms do not envisage calculation of the stability of the embankment slopes; planning organizations usually use Mononobe's formula or one of its variants. In these formulas, the stability of an embankment slope is assessed from the stability of an individual stone at rest on the surface of the slope. As the coefficient of friction in static equilibrium they take the tangent of the angle of internal friction of the stony material, measured by shear instruments or devices involving triaxial compression. We shall show that this approach is physically unsound. In particular, this is revealed by the fact that the formulas lead to imaginary values if the angle of internal friction is equal to the angle of repose. However, the angle of internal friction cannot be replaced by any coefficient of surface friction without changing the mathematical structure of Mononobe's formula and its variants. Thus we have to develop a new, physically sounder method of calculating the seismic stability of an embankment slope made of local (coarse detrital) materials. Such a method might be based on d'Alembert's principle. In this we do not consider static equilibrium (rest), but motion of single stones, or of a short, thin layer of material down the slope; account is taken of the residual deformation of the material composing the dam slope. As we see from Ambraseis's report to the Second International Conference on Seismic Construction [2], we can classify such residual deformations as weak signs of seismic action, not endangering the structures of a whole. Such damage can be repaired during routine maintenance. Here we must mention that the principle of considering residual deformations in assessing the strength of a structure is not new; in particular, for dams made of local materials it was apparently first used by Prof. G. I. Pokrovskii at the VODGEO Institute in 1941 in his studies of the seismic stability of the Ortotok gravel dam. In the recently published method of Prof. A. P. Sinitsyn [3], residual deformation is already the main factor considered in designing the dam profile.In practice, the nature of the motion of individual stones (or layers) on the surface of a slope made of stones of a given rock with given mechanical properties is determined by the acting forces and the forces of friction in the plane of motion. In our case, on the basis of d'Alembert's principle [4], for the action of gravity, friction, and seismic acceleration, with allowance for inertial forces (but disregarding air resistance), we can write down an equation for the motion at any time (see Fig. i):where F = P sin O is the component of the body's ...