Single-stage design is based upon definition of a suitable and uniform
downstream slope. The apex of the theoretical triangular profile is set at or
just above maximum retention level (or DFL) and an initial required base
thickness,T, determined for each loading combination in terms of a satis-
factory factor of safety against overturning, FO. The critical value of Tis
then checked for sliding stability and modified if necessary before check-
ing heel and toe stresses at base level.
An approximate definition of the downstream slope in terms of its
angle to the vertical, d, required for no tension to occur at a vertical
upstream face is given bytand (^1)
1/2
. (3.39)
3.2.8 Advanced analytical methodsThe simplifying assumptions on which gravity method analysis is based
become progressively less acceptable as the height of the dam increases,
particularly in narrower steep-sided valleys. Cantilever height changes
rapidly along the axis of the dam, and interaction between adjacent mono-
liths results in load transfer and a correspondingly more complex structural
response. This interaction is further compounded by the influence of differ-
ential foundation deformations. Where it is necessary to take account of such
complexities, two alternative rigorous analytical approaches are appropriate.(a) Trial load twist analysis
This approach is suited to situations in which, as a consequence of valley
shape, significant twisting action can develop in the vertical cantilevers or
monoliths. Torsional moments are generated as a result of cantilever inter-
action, and some water load is transferred to the steep abutments, resulting
in stress redistribution. The applied loads are thus carried by a combination
of cantilever action, horizontal beam action and twisting or torsion.
Trial load analysis (TLA) is conducted by subdividing the dam into a
series of vertical cantilever and horizontal beam elements, each of unit
thickness and intersecting at defined node points. A trial distribution of
the loading is then made, with a proportion of the nodal load assigned to
each mode of structural behaviour, i.e. cantilever, horizontal beam,
torsion, etc. The relevant node point deflections for each response mode
are then determined. An iterative solution of the resulting complex array
of equations is necessary in order to make the mode deflections, , all
match, i.e., for a correct load distribution,(^) cantilever (^) beam (^) torsion
(^) c
(^) w