Reliability analysis of penstocks
Client: Grand Dixence S.A.
The consequences of a failure event of a penstock in a hydroelectric power station can be enormous. Direct consequences such as property damages and casualties as well as indirect consequences such as a loss of production over many years contribute to the total consequences. A consistent quantitative risk and reliability assessment is crucial for such facilities and has a real monetary benefit for the owner. The risk assessment serves as a basis to identify the most feasible design concepts for penstocks and finally serves to assess the acceptability of the risks for different design concepts together with the efficiency of possible risk reducing measures.
The aim of this project was to develop a probabilistic model for the penstock and calculate the annual failure probability as a basis for risk analysis. In the preliminary study, it was shown that a simplistic model, which only considers the steel lining, was not appropriate to describe the physical behavior of the penstock. As a result, a more realistic model, which explicitly considers, besides the steel lining, the backfilling of the concrete and the straticulated surrounding rocks, was developed.
Additionally, a probabilistic model for the water pressure in the penstock was developed. The extreme value distribution was calculated by taking into account water hammer simulations for different emergency scenarios as well as extreme events in the normal operation.
To model the entire penstock, a spatial hierarchical model was developed to take into account the dependencies, e.g. caused by the water pressure. In total, the system performance was modeled with 78 dependent limit state functions. The annual probabilities of failures for the entire penstock as well as for the relevant cross sections have been calculated and the acceptability of the failure probabilities was confirmed. It was shown that the dependencies have a large influence on the results and should not be neglected in the analysis.