Investigation of the effect of yielding of a foundation on the frequency and mode of natural vibrations of dams by the finite-element method

Abstract

Section 5 "Hydraulic Structures-of SNiP II-A.12-69 "Construction in Seismic Regions. Design Standards" was approved by resolution No. 21 of GosstroiUSSRof February 7, 1972, and put into effect on October I, 1972. The new standard stipulates calculation of hydraulic structures for seismic loads by tlm dynamic (spectral) method, which takes into account the characteristics of the dynamic working of structures and thu~ reflects more correctly their behavior during earthquakes. Within the framework of this standard method it is possible to achieve a considerable economic saving by taking into account the yielding of a foundation, which greatly reduces the seismic loads at the lower vibration tones. The effect of foundation yielding on the dynamic behavior of darns can be determined most completely by the fiulte-element method.The spectral method calls for expanding the external load (seismic action) with respect to the modes of natural vibrations of the structure. For such expansion it is necessary to know the frequency (period) of natural vibrations and the displacements of points of the structure corresponding to a given vibration mode. These parameters are needed for calculating a structure in the case of any form of assignment of the seismic action (seismicity coeffir.tent or analog accelerogram). Their values are decisive when calculating the design dynamic load. Therefore, it is necessary to have at one's disposal modern, effective, and sufficiently accurate methods of determining the frequeaucies (periods) and modes of natural vibrations. In particular, this is important for darns having zones differing in configuration and properties of the materials.A special feature of hydraulic structures which distinguishes them from other types of structures is the large supporting area, which governs the increased effect of foundation yielding on their dynamic characteristics. In addition, these characteristics will be affected also by inhomogeneity of the foundation which is inevitable in view of the considerable length of structures of this type. For example, for the 300-m-high dam of the Nurek hydro development the width at the base exceeds 1.5 kin. It is natural to expect that with such ratios of width to height of the dam the effect of the foundation should be considerable.So far the modes and frequencies of natural vibrations of hydraulic s~uctures have been determined most often according to simplified calculation models in which the structure was divided heightwise into a series of con-cen~ated masses arranged along a vertical Line, each of which had only one degree of freedom-in a direction perpendicular to this line. Here it was usually assumed that during vibrations all points of the dam located at the same level are displaced by the same amount, equal to the deflection of a cantilever, which ignored the difference of displacements of individual points over the width of the structure. In such calculation models the foundation was assumed perfectly rigid, and in individual cases its yielding was taken into acc...

Calculation of the dynamic characteristics of an earth dam together with the foundation by the finite element method

“…It is shown in [7] that in calculating the seismic stability of high rock-fill dams having a comparatively depressed profile and low-head earth structures having a broadly spread profile it is impossible to limit oneself to the use of simplified design models (for example, systems with lumped parameters with a small number of degrees of freedom, models of an overhanging bar with consideration of only shear strain in the structures, etc. ).…”