ABSTRACT
Unlined canals are very demanding with respect to their cross sections, because the shape affects the magnitude of the current’s erosive force. In Chapter 11 we shall see that, in weak ground, unlined canals require wide, shallow sections, together with gentle slopes. The same does not apply to lined canals because their high resistance
to erosion makes it possible to practically forget any influence that this phenomenon may have with respect to the cross section, except in specific cases, such as chutes. This obviously means that economics govern the decision concerning the canal’s cross section. A similar situation occurs with asphalt concrete linings (except with high speed currents). On the other hand, the problems associated with canals employing a membrane lining with a granular protective covering is the same as unlined canals with respect to their cross sections. When sufficient technical means are not available for the selection of a
determined section for a concrete-or asphalt concrete-lined canal, it would be logical to go for the more economical. Since the cross area of the canal is the decisive element with regard to
the water transport capacity and, on the other hand, the lined perimeter is something that notably increases the costs of the solution. From a purely geometrical point of view, the problem should be tackled by defining the optimum canal section as that which has minimum perimeter for a given cross-sectional area necessary to allow the desired water flow to pass. The actual geometry itself has resolved the problem for us, showing that
the required curve is a half circle. If, as generally occurs, it is not possible to accept a vertical extrados because of slope stability, the necessary solution (also demonstrable) is an arc of circle, the half-angle of which, located at the centre, is the stability limit slope for the ground. This is the form of the which can be seen in Figure 10.1.
