The historic canal walls of Amsterdam, stretching 200 km in total, are constructed as a masonry wall on a timber deck supported by vertical timber piles. Understanding the resistance against lateral failure of these quays has been challenging due to uncertainties in their working principles, geometry, soil and structural properties. This paper proposes a Bayesian approach to include evidence from past loading situations and corresponding deformations into the reliability assessment. This approach enables refinement of the reliability predictions and parameter distribution uncertainties, leading to a more accurate prediction of the resistance against the lateral failure of historic quay wall. Depending on the type of evidence, an a-priori reliability prediction for a quay wall that fails to meet safety standards can be updated to any of the three consequence classes outlined in NEN8700. In a case study, a quay wall with an a-priori reliability of β = 1.5 has been increased to β = 3.2 by including evidence of an extreme survived load of 10 kN/m² that resulted in displacements of less than 4 mm. This is a decrease in failure probability by two orders of magnitude, showing the potential impact of using observational information in combination with Bayesian updating.

Complex probabilistic approaches for the analysis of structures have been increasing in interest and application both in the area of research and in practice in order to provide a more uniform level of reliability. Also, the design codes, such as the Eurocodes, are developing provisions to address reliability-based design methods in more detail. Moreover, FEM is very popular nowadays using advanced constitutive laws and modelling staged construction. This is especially important for geotechnical structures, such as retaining walls for deep excavations, for which soil-structure interaction is a complex mechanism. The paper will present a full probabilistic analysis performed for a real case temporary retaining wall of a deep excavation. The probabilistic analysis was combined with FEM using advanced constitutive models. The objective is to demonstrate the feasibility of a full probabilistic analysis, using the current advanced design methods, and to assess the reliability produced by Eurocode designs. The main uncertainties were modelled as random variables and the limit state verification was expressed in terms of reliability index or, equivalently, the probability of failure for SLS and ULS verification. The procedure of coupling probabilistic analysis using Probabilistic Toolkit reliability software with FEM Plaxis 2D commercial software for geotechnical analysis is given in detail while emphasizing some critical aspects in relation with these types of combined analyses and reliability concepts. At last, some issues related to the provisions of the current design codes are presented and discussed in order to facilitate the implementation of reliability-based design, either through probabilistic methods or by partial factors.

Ground anchors are crucial components in various construction and engineering applications. They play a critical role in retaining structures and, therefore, design guidelines have established the necessity of comprehensive testing campaigns to derive the anchors characteristic resistance. The latter is a specified percentile within a presumed statistical distribution. In principle, a limited number of investigation tests cannot be used to estimate the characteristic values. To overcome this limitation, in a simplified way, the design codes suggest reducing the resistance found in experimental results by a factor to estimate the anchor characteristic resistance to be used in the design. In this paper, the authors propose a new approach for interpreting ground anchor test results and determining the statistical distribution of ground anchor resistance. The approach is based on the use of Bayesian updating, formulated as a structural reliability problem, and on the definition of a simplified phenomenological model relating the imposed load and the measured anchor (creep) displacements. This distribution can be used to determine a “proven” anchor characteristic resistance, which can then be used to update the anchor design.

A kriging-based metamodelling approach for analysing the structural reliability of a sheetpile wall in a dyke is formulated. This specific problem is characterised by high target reliabilities ((Formula presented.)) in combination with a noisy and incomplete numerical model response. Starting from the original formulation of active learning kriging-based Monte Carlo simulation (AK-MCS), a robust two-stage metamodel framework is formulated in combination with adaptive multiple importance sampling, Gaussian process classification and kernel enhancements. Learning functions and convergence criteria are revised to maintain consistency with the metamodel enhancements. The developed metamodel is applied in the reliability analysis of a soil-structure interaction problem involving a sheetpile wall in a dyke body, which is representative of a class of problems encountered in engineering practice. Low dimensional example studies demonstrate the workings of the model and give insight into the model response. Full probabilistic analyses are then performed to estimate the probabilities of structural failure in a reliability updating context. The results show that after several necessary enhancements of the classical formulations, metamodelling approaches can be used successfully in combination with noisy and incomplete computational models as are often encountered in geotechnical engineering practice.

Common practice for design of retaining walls for deep excavations is by using characteristic values for geotechnical parameters—as a cautious estimate—for Serviceability Limit State (SLS) and combined with partial factors for Ultimate Limit State (ULS), as indicated in the current design codes such as the Eurocodes. However, more complex probabilistic approaches are increasing in application in order to provide a more uniform level of reliability, thus reducing the cost of the investment or the risk, or both. Also, in terms of tools and methods for performing the calculations, the Finite Element Method (FEM) is very popular nowadays due accessible computers power and user-friendly specialized software which can provide more realistic model, with affordable calculation effort. The present paper presents a case study of applied full probabilistic analysis of a retaining wall for real project deep excavation in Bucharest city, Romania, by FEM calculation in Plaxis 2D software coupled with Probabilistic Toolkit (PTK) software for reliability calculation. The limit function is set on a target value for the displacements of the retaining wall to allow to design for the SLS, since this is in many cases the governing state for deep excavations in urban areas. Different probability distributions are used for assessing the statistics of the geotechnical parameters and the reliability results obtained through these are discussed. Also, a discussion is made on the necessity of including more specific target reliability values for SLS verification and especially for temporary structures in the design codes.

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.

Spatial variability and limited measurements often result in low reliability estimates of geotechnical failure modes of dikes (i.e., earthen flood defences). Required dike reinforcements are usually not executed within a few years after inception, which enables efforts to improve reliability estimates by reducing uncertainty. Often decision makers are unclear on whether uncertainty reduction is worth investing, and which (combination of) methods yields the highest Value of Information (VoI). This paper presents a framework to assess the VoI of two uncertainty reduction methods (proof loading and pore pressure monitoring) for a case study of a typical river dike with an insufficiently stable inner slope, using a decision tree. In all cases, a positive VoI was found for at least one strategy consisting of a proof load test, monitoring or both. The optimal strategy of proof loading and monitoring has a VoI of 4.0 M€, being a reduction in total cost of 25% compared to a conventional dike reinforcement. It was also found that sometimes proof loading enhances the VoI of pore pressure monitoring, which demonstrates the benefits of jointly considering different methods in a single decision tree. The decision framework yields insight in total cost and VoI of risk reduction strategies, which enables decision makers to determine where proof loading and/or pore pressure monitoring are efficient, leading to more efficient flood defence asset management.

The design of new and assessment of existing quay walls is subject to large uncertainties. Dealing with these uncertainties is a crucial part of the engineering process. The way uncertainties are addressed has a large impact on construction and maintenance costs and on the reliability ultimately obtained. Especially in the assessment of existing structures the uncertainties can be large. An existing structure allows us to use actual performance information in the assessment, such as the structural response to loading. One way to obtain the structural response is test loading assisted by monitoring. In this research Bayesian updating is used to reduce uncertainties and to more effectively use the obtained measurement data. We present a case study of an existing quay structure along with fictitious measurement data to demonstrate the potential effects of test loading on the reliability of the structure. The results show that Bayesian updating successfully reduces the uncertainty (i.e. standard deviation) of the model prediction. Using monitoring data and Bayesian updating provides a more realistic model of the capacity of the existing quay structure and thus a more accurate reliability assessment. Which may lead to extension of the structure's lifetime or that higher loads can be accepted.