Читать книгу Earthquake Engineering for Concrete Dams - Anil K. Chopra - Страница 41

Comparing the response of the dam to horizontal and vertical ground motions (Figures 2.5.5 and 2.5.6) it is apparent – consistent with common view – that without impounded water the response to vertical ground motion is relatively small because the excitation term in Eq. (2.4.10) is much smaller for vertical ground motion (l = y) than for horizontal ground motion (l = x). With impounded water in the reservoir, the response is affected by the added hydrodynamic mass, damping, and force terms in Eq. (2.4.10). Because the added hydrodynamic mass and damping are independent of the excitation direction, the response functions due to horizontal and vertical ground motions display the same resonant frequency and effective damping. However, the added force is associated with hydrodynamic pressures acting in the horizontal direction on the vertical upstream face of a rigid dam, whether the ground motion is horizontal or vertical. In the latter case, is much larger than the small . As a result, hydrodynamic effects (including water compressibility) cause a larger increase in response to vertical ground motion than in response to horizontal ground motion. This is apparent by comparing the response curves for the dam without water and with water associated with the two excitations (Figures 2.5.1 versus 2.5.2 and Figures 2.5.3 versus 2.5.4).

Putting this issue in historical context, the response of concrete gravity dams to the vertical component of ground motion was overestimated in the earliest studies based on the assumption of non‐absorptive reservoir bottom (Chopra and Chakarabarti 1973, 1974). An absorptive reservoir bottom gives a more plausible estimate of the response to vertical ground motion and its smaller contribution to the total earthquake response of the dam (Fenves and Chopra 1983). Although not negligible, this contribution is of secondary importance. Thus, the response to only the horizontal component of ground motion is considered in developing the procedure for simplified analysis of two‐dimensional dam–water–foundation systems (Sections 2.6, 3.4, and 3.5); this procedure is intended for preliminary analysis and design of dams.