Waves resulting from partial dam break with the formation of a breach in the form of a cut to the channel bottom

Abstract

This paper gives experimental data on the propagation speed and height of a dam-break wave arising in the tailwater region during a partial dam break event. These data were used to confirm the Khristianovich calculation method.Key words: partial dam break, breach, discharge coefficient, dam-break wave, propagation speed.As is known, during a dam break event, a smooth level depression wave propagates in the headwater region and a dam-break wave propagates in the tailwater region. The characteristics of these waves depend on the initial depths of the headwater and tailwater regions and on the shape and sizes of the hole (breach) formed. The case of a total dam break, which is characteristic of high-pressure arch dams, has been well studied both theoretically [1, 2], and experimentally [3,4]. An example of such break events is the break of the arch dam 65 m high in Malpasset (France) on December 2, 1959 [5]. However, more often, dams break only partially. A method for calculating partial dam break waves is proposed in [1].The present paper reports the results of an experimental study of the waves resulting from a partial break of a model dam. The flow pattern near the breach was considered in [6,7]. The parameters of dam-break waves were studied in [8]. In those papers, the breach width was significantly smaller than the channel width and the breach crest elevated above channel bottom. In practice, earth dams break more often. In this case, as a rule, the breach has the shape of a narrow cut to the channel bottom. Exactly this breach shape is considered in the present paper.A diagram of the experiment is given in Fig. 1. The experiments were performed in a rectangular channel 16 m long, 0.38 m wide, and 0.5 m high with an even horizontal bottom. At a distance of 6.9 m upstream from the channel exit, there was a dam with a rectangular cut of width b = 0.06 m symmetric about the channel walls. The thickness of the dam along the channel was l = 0.8 m. The initial difference between the headwater depth h − and the tailwater depth h + was produced by a vertical board located near the back side of the dam. At the time t = 0, the board was quickly (in 0.05-0.10 sec) lifted vertically upward.The position of the rectangular coordinate system used further is shown in Fig. 1.The experiments showed that, depending on the ratio of the given parameters in the problem considered, the dam-break wave can have the form of one hydraulic jump or two hydraulic jumps moving one after the other. The same types of dam-break wave occur in the case of a discontinuity decay above a drop of a channel bottom [9][10][11]. Below, a wave with one hydraulic jump will be called a wave of type A and a wave with two jumps will be called a wave of type B. In Fig. 1, the following notation is used: D 2 > 0, 0 D 1 < D 2 , and D 3 < 0 are the speeds of propagation of the first and second jumps and the depression wave, respectively, and h 2 and h 1 are the depth of the first and second jumps, respectively. Transition from a wave of type B to a wave of type...