Optimal inspection decisions for the block mats of the Eastern-Scheldt barrier
Introduction
In this article, we consider the problem of inspecting the block mats of the Eastern-Scheldt storm-surge barrier. These mats are part of the barrier’s sea-bed protection and they must be inspected to detect possible scour holes that might endanger the stability of the barrier. Therefore, one is interested in obtaining optimal rates of inspection for which the expected maintenance cost is minimal and the probability of failure of the block mats is safe. For this purpose, mathematical expressions were obtained for the probability of failure of one scour hole (the probability that a scour hole is deeper than a certain failure level) and for the probability of failure of the block mats (the probability that at least one scour hole is deeper than the failure level).
A large number of articles were published on the subject of optimising maintenance through mathematical models (see e.g., [3]). Most maintenance optimisation models are based on lifetime distributions or Markovian deterioration models. As it is often hard to gather data for estimating either the parameters of a lifetime distribution or the transition probabilities of a Markov chain, few of these models were applied (see [3]). Moreover, in the case of well-planned preventive maintenance, complete lifetimes will rarely be observed. Therefore, we propose to model maintenance on the basis of the main uncertainties involved: the rate of scour-hole initiation and the rate of scour-hole development.
The inspection problem is a result of Jorissen and De Leeuw van Weenen [8] and van Noortwijk et al. [16]. Our model differs from the model in Ref. [8] in the sense that, among other things, we regard scour erosion as being a stochastic process rather than a deterministic process. It differs from the model in Ref. [16] in the sense that we assume the rate of scour erosion to be decreasing rather than being a constant. The stochastic processes of scour-hole initiation and scour-hole development was regarded as a Poisson process and a gamma process, respectively. The rate of scour erosion was determined by using an empirical law. Moran [11] used gamma processes in his theory of water storage in dam reservoirs. In The Netherlands, gamma processes have also been used to model decision problems for optimising maintenance of dykes, beaches, and berm breakwaters (see [14], [17], [18]).
The article is set out as follows. A brief description on the Eastern-Scheldt barrier is given in Section 2. In Section 3, we present the inspection model for the block mats of the barrier. Conclusions can be found in Section 4.
Section snippets
The Eastern-Scheldt barrier
With storm-induced tides of some 4 m above average sea level, the flood of February 1, 1953, caused a severe catastrophe in Zeeland, The Netherlands. Almost 200 000 ha of polderland flooded, resulting in huge losses of life and property. In the southwest of The Netherlands, 1835 people and tens of thousands of animals drowned. To avoid future losses caused by floods like the one in 1953, the Dutch parliament adopted the so-called Delta Plan. The greater part of this plan called for raising the
Maintenance of the block mats
The block mats consist of synthetic material to which small concrete-blocks (with a height of 17 cm) are attached in a regular pattern. The purpose of this section is to obtain safe and cost-optimal rates of inspection for these mats.
Conclusions
In this article, we have presented a maintenance model that enables optimal inspection and repair decision to be determined for the block mats of the Eastern-Scheldt barrier. The model is based on the stochastic processes of scour-hole initiation and scour-hole development. They were regarded as a Poisson process and a gamma process, respectively. A physics-based approach was used to estimate the decreasing rate of current-induced scour-hole development and a case study has shown the usefulness
Acknowledgements
The authors would like to thank Roger Cooke, Matthijs Kok, and the referees for their helpful suggestions and comments.
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