Copula-EVT-based simulation for optimal rubble-mound breakwater design

Abstract

The aim of this paper is to present a Monte Carlo based procedure to predict the performance of a rubble-mound breakwater under a randomly generated sequence of sea storms. This approach helps to predict potential damage incurred or possible failures involved in the breakwater during the service time in order to calculate the maintenance cost and consequently to select the optimal design which has the lowest construction and maintenance costs. As a result, the optimal design of the breakwater cross-section can be selected. Using copulas, we investigate the dependence structure existing between the significant wave heights and the significant wave periods, and between the maximum significant wave heights in the storms and the storm durations, since these variables are the main factors affecting the economical breakwater design. The tail of the significant wave heights, the corresponding storm durations and corresponding significant wave periods were fitted by a number of generalised extreme value distributions. We have modelled the joint distribution functions using a dependence measure (Kendall's tau) and its relationship with the class of Archimedean copulas, and then we have chosen the best copula that fits the empirical joint distribution function. To avoid overestimating the virtual effect of the storm, the equivalent triangle storm model is used to represent the generated storms. The damage associated with each individual sea state in the storm is quantified using the Melby formula, and accordingly the cost of the damage or failures is evaluated. The computed total costs for 10 different design significant wave heights and the probability of failure for different design significant wave heights and different service times are presented. In this simulation the failure rate together with the cost are simply double safety controls: one is through the failure rate, and the other is through the cost. If the resulting failure rates are not reasonable, either too low or too high, the cost will indicate this clearly through the rational variation in its value (the larger the failure rate, the lower the initial cost and the higher the maintenance cost, and vice versa).

Keywords:

• copula
• POT
• equivalent triangular storm model
• Monte Carlo simulation
• damage and failure

Acknowledgements

The authors would like to thank Professor Juan J. Quesada-Molina and Professor Miguel A. Losada from the University of Granada for their advice and recommendations.