LOADING: CONCEPTS AND CRITERIA 129
effective, or field, modulus of elasticity Eeff14 GN m^2 can be approxi-
mated as
fn 600 T/H^2 (Hz). (3.12)An alternative approximate relationship is
fnE1/eff^2 /0.012H(Hz). (3.13)Investigation of equations (3.12) and (3.13) indicates that resonance is
unlikely to occur except in large dams. As examples, the natural frequency
of vibration of monolithic gravity profiles with nominal heights of 20 m and
50 m are shown to be of the order of 15–25 Hz and 6–9 Hz respectively
compared to major seismic shock frequencies of the order of 1–10 Hz.
While resonance of an entire dam is unlikely, it should be noted that
vulnerable portions of a dam may be at risk due to inertia effects. High
local stresses may be generated at sudden discontinuities in the profile, e.g.
at a change of downstream slope to accommodate the width of a crest
roadway. Careful detailing is required to minimize the risk of local over-
stress and cracking, as illustrated in Fig. 3.3. Similar care is necessary in
the design of potentially vulnerable crest structures, e.g. gate or valve
towers.
Seismic loads can be approximated using the simplistic approach of
pseudostatic or seismic coefficient analysis. Inertia forces are calculated in
terms of the acceleration maxima selected for design and considered as
equivalent to additional static loads. This approach, sometimes referred to
as the equivalent static load method, is generally conservative. It is there-
Fig. 3.3 Seismic effects and crest profiles