Page - 972 - in Book of Full Papers - Symposium Hydro Engineering

be done either by applying site specific flood statistics or simplified statistical approaches based on typical statistical characteristics (e.g. HQ50, HQ100, HQ1000). The reciprocal values of these return periods lead to the related probabilities p(Qn), p(Qn-1) etc.. By merging these expressions and relations with the event tree it becomes possible to formulate a simple but long equation for the determination of the ´failure probability´ pD (Eq. 4). 𝑝 𝐷 = (1 − 𝑝 𝐵 ) ∙ (1 −𝑝 𝐹 ) 𝑛 ∙ 𝑝 (𝑄 𝑛 ) [4] + [𝑝 𝐵 ∙ (1 −𝑝 𝐹 ) (𝑛 −1) + (1 − 𝑝 𝐵 ) ∙ 𝑛 ∙ 𝑝 𝐹 ∙ (1 − 𝑝 𝐹 ) (𝑛 −1)] ∙ 𝑝 (𝑄 𝑛 −1) + [𝑝 𝐵 ∙ (𝑛 − 1) ∙ 𝑝 𝐹 ∙ (1 − 𝑝 𝐹 ) (𝑛 −2) +(1 − 𝑝 𝐵 ) ∙ ( 𝑛 2 ) ∙ 𝑝 𝐹 2 ∙ (1 −𝑝 𝐹 ) (𝑛 −2)] ∙ 𝑝 (𝑄 𝑛 −2) + [𝑝 𝐵 ∙ ( 𝑛 −1 2 ) ∙ 𝑝 𝐹 2 ∙ (1 − 𝑝 𝐹 ) (𝑛 −3) +(1 −𝑝 𝐵 ) ∙ ( 𝑛 3 ) ∙ 𝑝 𝐹 3 ∙ (1 − 𝑝 𝐹 ) (𝑛 −3)] ∙ 𝑝 (𝑄 𝑛 −3) [−] 3. OUTLOOK By referring the above introduced failure probability pD to the required safety level in the specific load case (e.g. a return period of 100 years for passing the design flood through a weir) it will become possible to determine the required capacity of the weir respectively the spillway. Hereby the site specific conditions (duration of the critical works and the probability of the malfunction of a gate) have to be taken into consideration. This procedure based on the event tree concept enables an adequate determination of the safety level at different sites under very different conditions (e.g. number and type of gates). The biggest challenge for their successful application will be the appropriate determination of suitable input parameters on the safe side. REFERENCES [1] Deutsches Institut für Normung. Normenausschuss Wasserwesen. DIN 19700-13 2004. [2] DVWK. DVWK Merkblatt 216, Betrachtungen zur (n-1)-Bedingung an Wehren 1990. KEYWORDS SAFETY OF DAMS, GATES 972