Probabilistic Design of a Rubble Mound Breakwater

All over the world rubble mound breakwaters are built to protect harbours, shorelines, and other vulnerable coastal areas against wave action and currents. Most of the designs for these structures use so called deterministic or semi-probabilistic design methods (level I). With these methods insight in the uncertainties, and consequently the actual failure probability and behaviour of the structure, is lacking. Moreover, less is known about the physical and mathematical relation between the variables and design formulas. The uncertainties in the variables and design formulae in a semi-probabilistic method are taken into account by partial safety factors. This could lead to an overly conservative design. By applying a probabilistic calculation (level II and III) insight is obtained in the relations between variables, the failure behaviour and the probability of failure of the structure. This information can explain why certain structures, which are designed with a semi-probabilistic method, fail even though the design conditions are not reached or in most cases survive above the design conditions. Information on the actual failure behaviour and probability is desired to make a more reliability design and economic optimization. Despite these benefits probabilistic design methods offer, it is not often applied in daily engineering practice. Multiple studies show the feasibility of designing a rubble mound breakwaters with a probabilistic design method in theory. However in practice only few rubble mound breakwaters are designed with a probabilistic design method. This research investigates how a probabilistic design of a rubble mound breakwater can be made in practice and provides some guidelines when a probabilistic design can be considered. The project Taman is used as a case and from this project a rubble mound breakwater is selected for the fully probabilistic calculation. Simplifications are made regarding the applied mathematical models1 and only four failure mechanisms related to the Ultimate Limit State (ULS) are examined. The four main failure mechanisms are: seaside and rear-side armour stability, toe stability and macro stability. With these simplifications a clear and thoroughly insight is gained in the probabilistic design process of a rubble mound breakwater without loosing track of the actual objective of this study. The fully probabilistic calculation is made with a level III probabilistic design method by applying a Monte Carlo simulation. The results show that this method is a good way to take into account the occurring statistical and physical correlation. Furthermore the Monte Carlo analysis gives a good insight in the most dominant failure mechanisms and in the governing failure situations for each mechanism. The results of the fully probabilistic calculation show that making a semi-probabilistic design based on the design rules in The Rock Manual [2007] results in a conservative design (Pf ,sys,tL = 0.5%). One optimization step is made for the simplified case in this research by applying lower stone classes for the four considered failure mechanisms. This results in failure probability (Pf ,sys,tL = 11.25%) which is still lower than the in general allowable probability of failure (Pf ,sys,tL = 15%). Although not all failure mechanisms for the ULS are taken into account, this study proves that a fully probabilistic calculation results in a more optimized design compared to a semi-probabilistic design method for the examined case. In conclusion a fully probabilistic calculation for a rubble mound breakwater is possible in practise. The results show that it is certainly beneficial to apply a fully probabilistic calculation (Level III) compared to a semi-probabilistic (level I) calculation. However, not in all cases it is possible to apply a fully probabilistic calculation and a couple of aspects should be checked before starting the calculation: • Statistical and physical correlation of the main variables have to be known • Sufficient reliable data for boundary conditions should be available • Applied mathematical models should be incorporated in the fully probabilistic calculation • Design requirements don’t follow directly from the standards and therefore must be agreed with the client This research shows that neglecting the statistical and part of the physical correlation results in an over dimensioned design for a rubble mound breakwater. A fully probabilistic (level III) design method with a Monte Carlo simulation proves to be a good way to include these correlations in the fully probabilistic design process. Sufficient reliable data for the boundary conditions should be available at the project location to make a fully probabilistic design method feasible. Large uncertainties in the boundary conditions result in a high failure probability of the rubble mound breakwater. To determine for which boundary conditions sufficient reliable data has to be known, a FORM analysis (level II) could be applied. This analysis gives ®-values which indicates the influence of each input variable on the failure probability of the rubble mound breakwater. For example in the examined case the uncertainties in the significant wave height have a large contribution to the variation in the probability of failure. The results show that a fully probabilistic calculation is not feasible in this case when the uncertainties in Hs have a standard deviation (σ) of 25% or more. In the semi-probabilistic design the hydraulic boundary conditions are determined via the models SWAN and Delft3D. Additionally the model D-Geo Stability is used for the semi-probabilistic design to check the geotechnical failure mechanisms. In this research is concluded that all hydraulic, geotechnical and geometric conditions need to be carried out in fully probabilistic way. For the fully probabilistic calculation of the simplified case simplifications are made for the mathematical models. These simplifications give a good approximation of the models in this study. However, the mathematical models have to be (in some way) integrated in the statistical analysis to make a fully probabilistic design.