- rotation and overturning,
- translation and sliding and
- overstress and material failure.
Criteria 1 and 2 control overall structural stability. Both must be satisfied
with respect to the profile above all horizontal planes within the dam and
the foundation. The overstress criterion, 3, must be satisfied for the dam
concrete and for the rock foundation.
The sliding stability criterion, 2, is generally the most critical of the
three, notably when applied to the natural rock foundation. The reasons
for this are associated with the influence of geological factors and are dis-
cussed in Section 3.2.3.
Assumptions inherent in preliminary analyses using the gravity
method (Section 3.2.4; USBR (1976, 1987)) are as follows.
- The concrete (or masonry) is homogeneous, isotropic and uniformly
elastic.
- All loads are carried by gravity action of vertical parallel-sided can-
tilevers with no mutual support between adjacent cantilevers (mono-
liths).
- No differential movements affecting the dam or foundation occur as
a result of the water load from the reservoir.
Stability and stress analyses are customarily conducted on the
assumption that conditions of plane strain apply. Gravity analysis is there-
fore carried out on a two-dimensional basis, considering a transverse
section of the structure having unit width parallel to the longitudinal axis
of the dam, i.e. a vertical cantilever of unit width. Internal stresses are
generally determined by the application of standard elastic theories. (It
will be appreciated that two-dimensional analysis is inherently conserva-
tive, particularly in narrower steep-sided valleys, where the three-
dimensional effects afford an additional but not readily determinate
margin of safety.)
More sophisticated techniques, including finite element analysis
(FEA), are applied to stress determination for larger or more complex
structures, or to the investigation of specific problems (see Section 3.2.8).
Attention must be drawn to the importance of maintaining a consis-
tent sign convention for all forces and moments considered in analysis.
The convention employed throughout this chapter is illustrated in Fig. 3.4.
It may be summarized as specifying all forces, loads and moments which
operate in the sense of maintaining equilibrium, e.g. self-weight and self-
weight moment, to be positive.
134 CONCRETE DAM ENGINEERING
