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.

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The purpose of this paper is to introduce the geotechnical engineering community to the treatment of uncertainties in site characterization within the framework of the second-generation Eurocodes. To do so, the main uncertainties related to the Ground Model, the ground properties and the groundwater levels are described before discussion of the statistical and modelling involved. This paper also explains the determination of “representative values” of ground properties within the framework of the Second-Generation Eurocode 7, either selecting the value based on engineering judgment and comparable experience, being in this case termed a “nominal value”; or evaluating the value by statistical methods, being in this case termed a “characteristic value”. Additionally, since 2nd-Gen Eurocode 7 allows using reliability-based methods for the verification of limit states, the paper gives some guidance for choosing probability distribution types, and for assessment their parameters like the mean and standard deviation. Finally, two examples are provided to show how to deal with the new elements involved with uncertainty treatment in terms of statistical analysis and probabilistic modelling @en

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.

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The second-generation Eurocodes, in particular EN 1990 and EN 1997, will rely more heavily on reliability and probability approaches for design (and verification) of geotechnical structures and for treating available data. The determination of groundwater levels will be based on concepts like annual probability of exceedance or fraction of time exceeded. When groundwater time series are available, the required groundwater levels can be determined using statistical analysis. In this paper we illustrate assessing the various groundwater levels values using extreme value statistics for real life data sets, highlighting pitfalls and providing practical recommendations for geotechnical practitioners. To that end, we address the selection of probability distributions, processing of the data to obtain annual extreme values and sanity checks of the results.@en

Data-driven site characterization (DDSC) aids geotechnical engineering by inferring and mapping soil parameters of the subsurface domain. In practice, the limited availability of site investigation data may hinder the performance of traditional machine learning methods and implies significant uncertainty in the predictions, which is typically not quantified. In this study, a framework for Bayesian site characterization (BaySiC) is applied on a benchmark example. Adopting Bayesian statistics enables the framework to deal with small training data sets and allows for coherent quantification of uncertainty, which is valuable to engineering practice for assessing the reliability and the determining characteristic values. BaySiC uses site investigation data to infer statistical estimators of cone penetration test (CPT) parameters and their dependence, as well as to learn spatial correlations. Consecutively, it generates a three-dimensional (3D) map of the subsurface by predicting the CPT parameter values and classifying the material type over the soil domain. For the benchmark example, the study formulated two models within the BaySiC framework and demonstrated their conduct in several cases of varying complexity. Eventually, the performance of the models was evaluated and compared in both deterministic and probabilistic terms. One of the models proved highly effective in predicting the material type at new locations of the subsurface domain, whereas the other provided accurate mapping of the CPT parameters even in complex stratigraphic cases. Also, investigating and comparing the results of the models led to insights regarding the effectiveness of their formulation. Moreover, the paper used hypothesis testing as a means of assessing the predictive power of the model independently from the validation data set. Stemming from the benchmark example, the paper draws conclusions that are meaningful to geotechnical engineering and decision-making.@en

Bayesian inference poses as a means for characterizing the uncertainty in geotechnical parameters based on limited site investigation data. In this study, a Hierarchical Bayesian analysis framework is used to analyse a site investigation database in order to derive geotechnical soil parameters for two widely applied strength models. The first one focuses on calibrating the relationship between in-situ CPT measurements and undrained shear strength. The second one is the SHANSEP soil strength model, which is used forevaluating the undrained shear strength using OCR information. The framework operates in a hierarchical fashion, performing inference on separate project sites and at the same time drawing conclusions on a global level. The result is site characterization on a probabilistic level and the derivation of geotechnical parameters together with their probability distributions. The results are assessed by evaluating their influence in the failure probability of a geotechnical structure, demonstrating that the proposed hierarchical approach provides a more complete description of uncertainty than standard practice methods.@en

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.

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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.

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During construction of a dike, slope stability often reaches critical levels, due to the excess pore water pressures in the foundation. The loading condition during construction has similarities with the design conditions during flood loading. Not only in terms of the pore water pressures as the main driving force, but also in terms of criticality of the stability. This paper examines how the information of survival of the construction stage can be used to improve the reliability estimate for a dike in flood conditions, using Bayesian updating. The approach is exemplified for a range of typical dikes and for a case study of a full-scale test embankment. The main result is that the reliability can increase significantly by including the information of construction survival and the uncertainty reduction involved, especially for dikes on soft soil blankets. For the investigated cases, the posterior failure probability was up to several orders of magnitude lower than the prior failure probability. The main factors influencing the degree of reliability update, were the ground conditions and the degree of criticality of the slope stability during construction. In conclusion, using the information of the survived construction leads to improved reliability-based safety assessments of dikes, and consequently to more targeted and cost-effective flood protection.@en

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.

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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.

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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.

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In this paper we show how to calibrate a site-specific transformation model to measure the undrained shear strength from CPTs. This practically unbiased transformation model can then be used to make a better estimation of the spatial average parameter, such as the depth-average of a soil layer in a homogenous deposit, using less costly indirect measurements. We show that there is a considerable difference in terms of characteristic value and probability density, between the assumptions of entirely random or systematic transformation uncertainty. Ultimately we show what the effect is of making more realistic choices for the random and systematic part in the transformation uncertainty for a case study with actual data.@en

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.

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De Projectoverstijgende Verkenning Kabels & Leidingen (POV K&L) wordt uitgevoerd binnen het landelijke Hoogwaterbeschermingsprogramma (HWBP) met als belangrijkste doelom de risico's van kabels en leidingen bij dijkversterkingsprojecten te minimaliseren. Vanuit de POV K&L is voor Zeeburgereiland een innovatieve faalkansanalyse uitgevoerd bij het dijkontwerp met een parallelle waterleiding.@en

One of the failure mechanisms of dikes is slope instability at the landward side. Often, one instability does not lead to flooding, and several successive instabilities are needed before the dike overtops, and erosion and breaching can occur, especially at lower water levels. In this paper we propose a method to estimate the probability of flooding, taking into account the residual resistance against flooding after the first instability. We base ourselves on basic probabilistic techniques and common slope stability analyses and estimate the probability of flooding by calculating the probability of several successive (conditional) instabilities. Because the geotechnical failure and dike failure is not the same for each water level, we evaluate the probability for different water levels. The case example shows that there is a considerable margin between the probability of geotechnical failure and the probability of flooding, especially at relatively low water levels. It also shows that the current practice of assuming that the probability of flooding is equal to the probability of instability is very conservative.@en

One of the most rapidly emerging measures in infrastructure asset management is Structural Health Monitoring (SHM), which aims at reducing uncertainty in structural performance by using monitoring equipment. As earthen flood defence structures typically have large strength uncertainties, such techniques can be particularly promising. However, insight in the key characteristics for successful SHM for flood defences is lacking, which hampers the practical implementation. In this study, we explore the benefits of pore pressure monitoring, one of the most promising SHM techniques for earthen flood defences. The approach is based on a Bayesian pre-posterior analysis, and results are evaluated based on the Value of Information (VoI) obtained from different monitoring strategies. We specifically investigate the effect on long-term reinforcement decisions. The results show that, next to the relative magnitude of reducible uncertainty, the combination of the probability of having a useful observation and the duration of a SHM effort determine the VoI. As it is likely that increasing loads due to climate change will result in more frequent future reinforcements, the influence of scenarios of different rates of increase in future loads is also investigated. It was found that, in all considered possible scenarios, monitoring yields a positive Value of Information, hence it is an economically efficient measure for flood defence asset management both now and in the future.@en

In risk analysis of riverine flood defence systems, sections of flood defences are often considered separately, herewith ignoring their interdependence, e.g. due to the hydraulic response following dike breaches in the system. In previous studies it has been found that such interdependence can have a significant influence on flood risk estimates and the spatial distribution. In this paper a method is proposed for the economic optimisation of riverine flood defence safety levels from a river system perspective. In order to deal with the computational challenge of integrating the hydraulic interactions in an economic optimisation, a surrogate model was developed. Despite the many simplifications, this model yields reasonably accurate results within acceptable time. The application of the model to a case study in the Netherlands has shown that taking into account interactions between flood defences has significant influence on optimal long term strategies for flood defences. The results suggest that accounting for interdependence in setting safety standards and reinforcement prioritisation yields a significant return on investment both in terms of lower investment cost and in terms of reduced risks.@en

This paper presents a Bayesian model to determine the model uncertainty of a critical horizontal gradient model for piping for dikes, such a Lane and Bligh. A Bayesian model is needed for two reasons. First, there is a large overlap in cases that failed and survived. Second, the evidence of the failed cases is limited .The model consists of a non-informative prior that is combined with likelihood functions for failed and survived cases. This involves modeling the mean and standard deviation of the model uncertainty as random variables. For survived cases we know the limit state function was larger than 0 for the observed water level. For failed cases we know the limit state function was smaller than 0; or Z = 0; which is a less conservative assumption. This information is used to determine the likelihood functions for failed and survived cases. The prior and likelihoods are combined to find the posterior distributions of the mean and standard distribution of the model uncertainty. Using integration, this finally results in the (lognormal) distribution of the model uncertainty. The model is applied to the data of Bligh and Lane and shows both a high mean and high standard deviation of the model uncertainty, where the model of Lane performs better than Bligh. It is recommended to tailor the proposed model to dikes by making a different distinction between horizontal and vertical erosion. Furthermore, it is recommended to apply the model to more dike specific data since the Bligh data mainly consists of dams instead of dikes. @en