Inertia forces associated with the mass of a dam structure are then
expressed in terms of the horizontal and vertical seismic acceleration coef-
ficients,handvrespectively, and gravitational acceleration, g, thus:
horizontal forces: h. (static mass)
vertical forces: v. (static mass)The reversible character of these forces will be noted: for initial analysis
they may be assumed to operate through the centroid of the mass to which
they are considered to apply.
It may be considered unrealistic to assume that peak downward ver-
tical acceleration will be coincident with peak upstream horizontal acceler-
ation, hypothetically the most adverse combination of seismic loads. Three
load cases may then be defined as being more appropriate:
i) peak horizontalground acceleration with zero verticalground accel-
eration,
ii) peak verticalground acceleration with zero horizontalground accel-
eration, and
iii) an appropriate combination of peak horizontal and vertical ground
accelerations, e.g. one component (normally the horizontal) at its
peak value with the other at some 40–50% of its peak.
The application of pseudo-static analysis, together with the associated
determination of inertia forces attributable to the reservoir water, is
addressed in Section 3.1.1 with respect to concrete gravity dam analysis.
For initial seismic assessment of embankment dams, a rapid para-
metric study of the influence of different values of pseudostatic coefficient
can be carried out using stability charts and considering the seismic effect
as approximating to tilting the slope through angle tan^1 h. The factor of
safety of a flatter slope will be much more affected by varying the assumed
value of hthan will that of a steeper slope.
More complex variants of pseudostatic analyses may, inter alia,
employ a non-uniform value of h, increasing towards the crest, derived
from a more rigorous analysis of the anticipated seismic event.
DYNAMIC RESPONSE ANALYSIS
The simplifications inherent in pseudostatic analysis are considerable.
Complex problems of dam-foundation and dam-reservoir interaction are
not addressed, and the load response of the dam itself is neglected. The
interactions referred to are of great importance, as they collectively modify
the dynamic properties of the dam and consequently may significantlyaffect
its load response. They are accounted for in dynamic response analysis,