ARCH DAM ANALYSIS 159
and the volume of the arch will be functions of the entry angle selected.
The optimum value of is determined from careful assessment of the geo-
logical structure and associated design parameters. In a perfectly symmet-
rical valley the minimum dam volume would theoretically occur with
2 133° at all elevations. Considerations of abutment entry angle pre-
clude this, and in practice the central angle at crest level is generally
limited to 270°–110°.
Arch and cupola profiles are based on a number of geometrical
forms, the more important of which are introduced below.
(a) Constant-radius profile
The constant-radius profile has the simplest geometry, combining a verti-
cal upstream face of constant radius with a uniform radial downstream
slope. The downstream face radius therefore varies with elevation. The
profile is shown schematically in Fig. 3.14(a), and it is apparent that the
central angle, 2, reaches a maximum at crest level. A constant-radius
profile is not the most economical in volume, but has the merit of analyti-
cal and constructional simplicity. The profile is suited to relatively sym-
metrical U-shaped valleys.
(b) Constant-angle profile
The concept of the constant-angle profile follows logically as a develop-
ment of the constant-radius profile of minimum volume. Constant-angle
geometry is more complex, however, since, as demonstrated by Fig.
3.14(b), it leads to a considerable upstream overhang as the abutments are
approached. Excessive overhang is undesirable, as the resulting local
cross-section can prove unstable under construction or for the reservoir
Fig. 3.13 Abutment entry angle geometry for arch dams