Page - 970 - in Book of Full Papers - Symposium Hydro Engineering

2.2. EVENT TREE The key of the event tree concept is the consequent presentation of the events, which can happen if a flood approaches a weir or a spillway (Fig. 1). In a first differentiation it has to be checked whether the gate or weir field is blocked due to critical works. The variable dC,G describes the number of days of ´critical works´ per year for one gate. Critical works are definied as works during which an ad hoc opening of a gate would not be possible. Hereby any kind of inspection, revision and replacement works have to be taken into account. The value  C,G (Eq. 1) shows the probability that one specific gate is being blocked by critical works at any time. If n is the number of gates, consequently pB describes the probability that one of the n existing gates is being blocked by critical works at any time (Eq. 2.). It can be ruled out that more than one gate is being blocked by critical works at the same time. 𝛼 𝐶 ,𝐺 = 𝑑 𝐶 ,𝐺 [𝑑 ] 365,24 [𝑑 ] [−] [1] 𝑝 𝐵 = 𝑛 ∙ 𝛼 𝐶 ,𝐺 [−] [2] Within the scope of a second and much more comprehensive differentiation it has to be checked whether it is possible to open every single gate during a flood event. In order to enable this evaluation the probablity of a malfunction of one gate has to be defined. Consequently the related statistical parameter pF describes the fundamental probability that it is not possible to open one gate at any time. In order to allow a much better understanding of this parameter its reciprocal value ‘f’ shall be used (Eq. 3). This means that in an estimate, which has to be very much on the safe side, one specific gate has to be considered as not properly working within the scope of each fth gate opening. Gates, where little or no external forces are needed for opening (e.g. flap gates oder rubber dams), will show much higher values of ‘f’ compared to other gates like radial gates or even slide gates, where the function of mechanical steering units and a power supply are mandatory for a successful opening. 𝑝 𝐹 = 1 𝑓 [−] [3] By using the two newly introduced paramters pB and pF a complete event tree in the case of an approaching flood can be set up (Fig. 1). Typically the probabilities of the occurance of two of even three gates not working properly will be very little. Anyhow, for the purpose of a universally applicable approach these very unlikely scenarios shall be kept at that time. The event tree can be set up for an optional number of gates (greater than 1). The example shown below (Fig. 1) shows the potential szenarios for a weir with four gates. 970