While reliability methods have already been widely adopted in civil engineering, the efficiency and robustness of finite element-based reliability assessments of quay walls are still fairly low. In this paper, the reliability indices of structural and geotechnical failure modes of two real-life quay walls are determined by coupling probabilistic methods with finite element models, taking into account a large number of stochastic variables. The reliability indices found are within the range of the targets suggested in the design codes presently in use. Nevertheless, neglecting model uncertainty and correlations between stochastic variables leads to an underestimation of the probability of failure. In addition, low sensitivity factors are found for time-independent variables, such as material properties and model uncertainty. Furthermore, the results are used to reflect on the partial factors used in the original design. Important variables, such as the angle of internal friction, are subjected to a sensitivity analysis in order to illuminate their influence on the reliability index. Port authorities and terminal operators might be able to use the findings of this paper to derive more insight into the reliability of their structures and to optimise their service life and functionality, for example by deepening berths or increasing operational loads.

The assessment of service-proven quay walls subject to corrosion-induced degradation is inherently a time-dependent reliability problem. Two major challenges are the modelling of corrosion and taking into account the decrease of epistemic uncertainty throughout the quay wall's service life. The main objective of this study is to examine the probability of failure, despite successful past performance, when the quay wall is subject to corrosion and randomly imposed variable loads. The development of the annual failure rate is modelled using crude Monte Carlo and by performing a first-order system reliability analysis. The annual failure rates found for service-proven quay walls vary over time. For those with successful service histories and subject to low corrosion rates, the highest reliability indices are observed in the first year of the service life, whereas with higher corrosion rates the final year prevails. In general, it seems more practical to evaluate reliability on an annual basis rather than over longer time periods, since the latter will introduce an iterative procedure to determine the wall's remaining lifetime. The key findings of this study can be crucial for the lifetime extension of existing quay walls, and presumably also for other service-proven geotechnical structures subject to corrosion.

General frameworks for reliability differentiation have evolved over time and are mainly developed for new buildings. However, recommendations for existing quay walls are lacking. In this study target reliability indices for assessing existing quay walls were derived by economic optimisation and by evaluating the Life Quality Index criterion (LQI). In quay wall design, some dominant stochastic design variables are largely time-independent, such as soil and material properties. The influence of time-independent variables on the development of the probability of failure was taken into consideration in this study, because this affects the present value of future failure costs and the associated target reliability indices. The reliability indices obtained in accordance with the LQI acceptance criterion were a little lower than the target reliability indices derived by economic optimization. The target reliability indices obtained for existing quay walls depend on the consequences of failure and the remaining service life. If failure modes of a quay wall are largely time-invariant and already survived the first period of the service life, the residual probability of failure is lower for an existing quay wall compared to a new quay wall. Hence, this should be considered in the determination of target reliability indices. The method of approach to assess the development of reliability over time can also be used for evaluating target reliability indices of other civil and geotechnical structures.

Structures, such as quay walls, have to meet a particular level of safety. Consequently, in the Eurocode standards, three reliability classes are distinguished, each corresponding to a target reliability index and set of partial factors. In this study, more insight is acquired into the relationship between the quay wall's construction costs and the associated reliability index β. It appeared that the marginal costs of safety investments of quay walls are fairly low and in the same order of magnitude of the uncertainty of the estimate of the construction costs. Hence, it seems that the current reliability classes, as defined in the Eurocode standards, are non-efficient for quay walls. In addition, this study investigates the influence of the partial factors and three failure mechanisms on the construction costs and the reliability index. It was concluded that for the considered cases, the soil's angle of internal friction strongly influences the construction costs and the β of the quay wall. Furthermore, it follows that economic optimisation in the probabilistic design of quay walls is possible by increasing the target reliability index of the failure mechanism 'insufficient passive soil resistance' and decrease the target reliability index of 'yielding of sheet pile profile'.

Structural codes rely on generalised target reliability indices, which are mainly derived for buildings. It is unclear, however, whether these indices are applicable to the specific risk-profile of quay walls, jetties, and flexible dolphins. In this study, target reliability indices for marine structures were derived from various risk acceptance criteria, such as economic optimisation, individual risk, societal risk, the life quality index, and the social and environmental repercussion index. This article uses a method to determine reliability targets distinguishing time-dependent and time-independent variables, because some important stochastic design variables in the design of marine structures, such as soil and material properties, are largely time-independent. The assessment framework of ISO 2394, taking into account social, economic, and environmental impact, has proven to be a solid basis for reliability differentiation. The method of approach considered in this paper can also be used for evaluating target reliability indices of other geotechnical structures.

This paper present several cases in the Port of Rotterdam where both in the design and construction phase several different did not marched as expected. These cases are interesting for both the design as well the construction phase of a project. People will make mistakes however the mistakes describes in this paper have to be judged in time as not always everything was understood during the design and construction and the people of that time still these huge structures.

Design codes and standards rely on generalised target reliability indices. It is unclear, however, whether these indices are applicable to the specific risk-profile of marine structures. In this study, target reliability indices for quay walls were derived from various risk acceptance criteria, such as economic optimisation, individual risk (IR), societal risk (SR), the life quality index (LQI) and the social and environmental repercussion index (SERI). Important stochastic design variables in quay wall design, such as retaining height, soil strength and material properties, are largely time-independent, whereas other design variables are time-dependent. The extent to which a reliability problem is time variant affects the present value of future failure costs and the associated reliability optimum. A method was therefore developed to determine the influence of time-independent variables on the development of failure probability over time. This method can also be used to evaluate target reliability indices of other civil and geotechnical structures. The target reliability indices obtained for quay walls depend on failure consequences and marginal costs of safety investments. The results were used to elaborate the reliability framework of ISO 2394, and associated reliability levels are proposed for various consequence classes. The insights acquired were used to evaluate the acceptable probability of failure for different types of quay walls.