Читать книгу Earthquake Engineering for Concrete Dams - Anil K. Chopra - Страница 19

As mentioned in Section 1.3.3 in the context of gravity dams, the seismic coefficient of 0.1 is much smaller than the ordinates of the pseudo‐acceleration response spectra for intense ground motions (Figure 1.3.2). Thus the earthquake forces for arch dams also were greatly underestimated in traditional analysis procedures.

The effective earthquake forces on a dam due to horizontal ground motion may be expressed as the product of a seismic coefficient, which varies over the dam surface, and the weight of the dam per unit surface area. The seismic coefficient associated with earthquake forces in the first two modes of vibration of the dam (fundamental symmetric and anti‐symmetric modes of a symmetric dam) varies, as shown in Figure 1.4.1. In contrast, traditional design procedures ignore the vibration properties of the dam and adopt a uniform distribution for the seismic coefficient, resulting in erroneous distribution of lateral forces and hence of stresses in the dam. A dynamic analysis procedure that eliminates such errors is developed in Chapter 8. Including dam–water–foundation interaction, this procedure is shown in Chapter 10 to produce seismic response results that are consistent with the motions of two arch dams recorded during earthquakes.

As mentioned in Section 1.3.3, the additional water pressures included in traditional design procedures for gravity dams are unrealistically small and have little influence on the computed stresses and hence on the geometry of the dam that satisfies the design criteria. This observation is equally valid for arch dams because the additional water pressures considered for arch dams are similar to those for gravity dams.

Demonstrated in Chapter 9 is the importance of two interaction mechanisms – which are ignored in traditional design – in the dynamics of arch dams. When dam–water interaction and water compressibility are properly considered, hydrodynamic effects result in significant increases in the earthquake‐induced stresses in arch dams, more so than for gravity dams. Similarly, when dam–foundation interaction including foundation mass and radiation damping are properly considered, this interaction mechanism generally has a profound influence on the earthquake‐induced stresses in arch dams just as in the case of gravity dams.

Figure 1.4.1 Distribution of seismic coefficients over the dam surface in the first two vibration modes of an arch dam.

Source: Adapted from Bureau of Reclamation (1977).