Dynamic foundation loading from a concrete dam can be determined from finite element analyses utilizing initial forces, nodal displacements, and stiffness matrices. Dynamic three-dimensional analyses of potentially unstable foundation rock masses can then be performed by including static and time-varying dam and inertia forces. Permanent cumulative displacements can be estimated by double integration of the relative acceleration when the factor of safety against sliding for a rock mass drops below 1.0. Recent research indicates that the dynamic behavior of rock discontinuities may also be an important consideration.


La charge dynamique que representent les fondations d'un barrage en beton peut se determiner à partir d'analyses d'elements finis, utilisant les forces initiales, les deplacements nodaux, et les matrices de raideur. En incluant les forces - à la fois statiques et variables dans le temps - du barrage et de l'inertie, il serait alors possible de realiser des analyses dynamiques à trois dimensions des roches de fondation potentiellement instables. Les deplacements cumulatifs permanents peuvent être calcules au cas où le facteur de securite du massif baisserait au moins de 1,0. De recentes recherches indiquent que le comportement dynamique des discontinuites des roches pourrait aussi figurer comme une consideration importante.


Die dynamische Belastung der Gruendung einer Betonstaumauer kann durch Erfassung der Initialkrafte, Nodalverschiebungen und Steifigkeitsmatrizen mit Hilfe eines Finite-Elemente-Verfahrens ermittelt werden. Unter Beruecksichtigung der statischen und zeitabhangigen Staudamm- und Tragheitswerte ist es sodann möglich, dynamische dreidimensionale Analysen von potentiell labilen Gebirgsmassivgruendungen durchzufuehren. Bleibende kumulative Verschiebungen können berechnet werden, wenn der Sicherheitsfaktor der Gesteinsmassen unter 1,0 abfallt. Neuere Forschungsergebnisse lassen darauf schließen, daß das dynamische Verha1ten von Gesteinsdiskontinuitaten auch ein wichtiger Faktor sein kann.


The application of three-dimensional finite element analyses to determine the response of major concrete dams to various static and dynamic loads,is relatively common. Response history finite element analyses of concrete dams are generally accepted as being necessary to adequately assess safety for significant earthquakes. However, comparable analyses to estimate foundation behavior during earthquakes are usually not performed. Foundation stability is often determined by pseudo-static assessments whereby the inertial effect of peak or effective ground acceleration is simply added to the maximum loading from the dam. This approach is deficient because the maximum loads resulting from the dynamic response of the dam rarely occur at the same instant in time as the peak or effective, ground acceleration. Although the simple superposition of-maximum loads results in conservative estimates of the magnitude of foundation loading, more realistic assessments could result in savings of foundation treatment. Additionally, a more critical condition may occur when all loads are not at their maximum. This paper describes techniques for computation of three-dimensional, time-varying foundation loads from dynamic analyses, and for performance of stability analyses of potentially unstable rock masses. The techniques account for time-varying ground accelerations as well as the time-varying magnitude and direction of foundation loads from the dam.


A common means of analytically modeling the foundation of a concrete dam is by assuming a two-dimensional elastic half-space under each abutment section where loading from the dam is applied. Unfortunately, this assumes that foundation deformations are independent of the shape of the foundation surface and that movements at a particular abutment section are due only to loads applied directly at that section. A related approach is to place spring elements at abutment sections. The stiffness of the elements is usually based on elastic half-space considerations, and the coupling effects between the abutment sections are again ignored. Occasionally, the abutments are assumed to be fixed and the foundation loads are obtained from integration of stresses over some portion of the abutment. Integration of stresses may not result in an adequate estimate of the directions of resultant loads. In addition, not providing for abutment deformations does not allow for appropriate load distributions, particularly in the case of arch dams. A more realistic approach is to model the foundation with the same continuum finite elements used to model the dam. Concentrated nodal forces applied at the dam-foundation juncture are not accounted for by equation (1) and must be added separately. However, this type of loading is seldom encountered in concrete dam analysis. The vector of initial element forces is required for temperature, gravity, and pressure-loading. For example, zero displacement associated with temperature loading results in large stresses and therefore large loads. If for this case the initial element forces are neglected in equation (1), the resulting forces would be incorrectly calculated as zero since the displacements are zero. The accuracy of the calculated loads may be checked by setting the stiffness and loading of the dam structure to zero and applying the calculated loads directly to the foundation. The resulting foundation deformation-should be identical to that from the original analysis.

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