Influence d'une fissure sur la répartition des pressions sous le radier d'un barrage

The effect of a crack in the ground upstream from a dam on pressure distribution underneath the apron

Diplômé d'études supérieures, Assistant à l'I.N.S.A. de Lyon, France.

Résumé

The article describes a study of pressures underneath the apron of a dam with a crack in the ground at its upstream end. Steady flow is assumed, taking place with the boundary conditions shown on Fig. 1, also with the following assumptions : - (i) An infinitely deep layer of pervious ground underneath the dam ; (ii) The crack BC being considered as a straight line segment, but neglecting loss of head between B and C. 1. Case of crack of infinite length L = ∞). The problem has a single parameter : the angle 0 of the crack to the ground upstream. Application of the Schwarz-Christoffel transformation gives the following : - (i) Formulae (1) and (1 bis) for the pressure p along the apron, i.e. depending on x/l (values of the function F [0, (x/l)] are given by the curves on Figure 3 for single values of 0; (ii) Formulae (2) and (2 bis) giving the module P of the pressure resultant for various values of 0 (values of G (0) are given by the curve on Fig. 4) ; (iii) Formula (3) giving the abscissa X of the point of application of the pressure resultant for various values of 0 (values of x0/l are given by the curve on Fig. 6). II. Case of a crack of finite length. There are two parameters to this problem : 0 and the ratio between crack and apron length L/l. The above method ther gives the following : - (i) Formulae (1) and (6), which play the same part as formulae (1) and (1 bis) and lead to two following types of curve : Curves giving variations of F, i.e. of the pressure along the apron in terms of x/l, for given values of L/l and 0 (Fig. 8) ; Curves giving the variation of pressure p at a definite point of the apron in terms of L/l , for given values of x/l and 0 ; (ii) The formulae in section 3, which are identical to those given for L = ∞. Figs 10 and 11 give the variations of G and x0/l.