Читать книгу Earthquake Engineering for Concrete Dams - Anil K. Chopra - Страница 46

Because the equivalent SDF system accurately predicts the response of dam–water system to horizontal ground motion over a complete range of excitation frequencies and for a wide range of parameters characterizing the properties of the dam, water, and reservoir bottom materials, it is applicable to the analysis of dam response to arbitrary ground motion. In particular, the peak displacements of the dam and equivalent static lateral forces can be expressed by appropriately modifying Eqs. (2.2.12) and (2.2.14), specialized for horizontal ground motion:

(2.6.14)

(2.6.15)

In these equations, ; and are the ordinates of the deformation and pseudo‐acceleration response spectra at the natural vibration period and damping ratio of the equivalent SDF system, and with defined by Eqs. (2.6.5a) and (2.6.6). Substituting these equations in Eq. (2.6.15) gives the final expression for the equivalent static lateral forces (Chopra 1978):

(2.6.16)

Comparing Eq. (2.6.16) with Eq. (2.2.12), we note that dam–water interaction introduces hydrodynamic pressures at the upstream face, increases Γ₁, and modifies the period and damping ratio where the spectral ordinate is determined.