Risk-based and probabilistic reliability design methods are starting to be integrated into the daily geotechnical engineering practice, as shown by the current draft of EN1997 (Eurocode 7), which explicitly allows Reliability-based verification of limit states. The semi-probabilistic design methods in EN1997 are a compromise between ease of use and accuracy of the achieved reliability levels. In contrast, EN1990 (Eurocode 0) requires accurate full probabilistic design targets. An assessment to investigate if the semi probabilistic methods from EN1997 comply with the EN1990 reliability targets is therefore necessary since the link between the norms is not explicitly established.
In this study, pile foundations serve as an example to assess compatibility between the EN1990 and EN1997. The deterministic Dutch pile design approach by van Mierlo & Koppejan (1956), CPT based design method, is adapted to the semi probabilistic model pile recipe in the EN1997 draft. This thesis assesses what reliability levels are achieved by the model pile design method in draft EN1997 considering the axial bearing capacity and how these compare to the reliability targets in EN1990.
Methodology: To assess the performance of the model pile method from EN1997, the design outcome from the semi-probabilistic model pile method is compared to fully probabilistic quantification methods of the resistances and loads. Two probabilistic quantifications are used in the assessment, a Bayesian and a Student-T model. The achieved reliabilities are assessed with both the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). Additional insight into the influence of different parameters is provided with sensitivity analysis and the calibration of partial factors. The assessment was applied in two case studies located in the Netherlands.
In both case studies, the EN1997 designs resulted in reliability levels in good agreement with the reliability targets stated in EN 1990. This suggests an agreement between the semi-probabilistic and the full probabilistic models if sufficient CPTs are used. In both case studies, EN1997 designs accounted for more model uncertainty than the probabilistic models suggest, thus partial model factor (γRd) in EN1997 may be conservative. EN1997 covers spatial variability and uncertainty due to limited observations with the correlation factor (ζ, a factor that transforms calculated to representative values, and the partial resistance factor (γRc). The coverage of uncertainty with these two factors seems to be rather low, especially for situations with few CPTs available (less than 10), although the results seem to depend strongly on the degree of spatial variability in the CPT field. In the case of homogeneous soil conditions between observations, EN1997 design methods led to over-conservative designs for low numbers of observations. If the variability between limited observations (less than 10 CPTs) was high, designs are assessed to be less reliable than EN1990 requires.
Overall, the results suggest good agreement of the semi-probabilistic design methods from EN1997 with the reliability targets defined in EN1990, for designs based on sufficient observations. The sensitivity analysis and isolation of the resistance uncertainty showed for the two cases that the uncertainty of the resistance has the dominating influence on the reliability of the piles, suggesting a low impact of complex stochastic load models. The latter finding suggests that probabilistic treatment of the resistance may be sufficient for assessing pile reliability in practice, while design values could be used for the loads.

Reliability analysis is a rational method for dealing with uncertainties. It is increasingly used for the design and assessment of (civil) structures. Reliability analysis, possibly in combination with performance data, allows for instance to update (extend) the lifetime of existing quay wall structures. This gives economic advantages when assessing quay walls, figuring there are thousands of kilometres of quay walls worldwide. Soil-structure analysis (e.g. analysis of quay walls) is however complex and in general requires finite element (FE) models. Conventional reliability methods are mostly incapable of dealing with FE models because they have long (infeasible) calculation times e.g. Monte Carlo, or they cannot deal with the typical noisy and incomplete FE model output e.g. FORM. One way of dealing with these challenges is by using a metamodelling approach, i.e. build up and make use of a response surface on a limited number of model evaluations. One specific application which uses metamodelling is ERRAGA, which is an abbreviation for Efficient and Robust Reliability Analysis for Geotechnical Applications. This thesis investigates the potential of ERRAGA/metamodelling for reliability analysis of quay walls in engineering practice.\medskip

In this thesis ERRAGA is tested on two realistic case studies located in the port of Rotterdam. The first case is called the ‘Sleepbootkade’, a quay constructed from a combi wall with anchors. The second case study is called the HHTP-quay, a combi wall with relieving platform and MV-piles. In the first case focus is placed on getting to understand the details and workings of the ERRAGA method. In the second case focus has been put on the creation of the reliability model and the practical applicability of ERRAGA using the experiences of the first case. Two critical limit states are tested within the case studies: wall failure in bending and geotechnical failure. Especially the limit state geotechnical failure is challenging as relevant output parameters are known to be noisy and/or incomplete.\medskip

The main finding of this thesis is that reliability analysis of quay walls using ERRAGA in combination with a numerical model shows good potential. ERRAGA can generate reliable and accurate results within only hundreds of realizations, hereby overcoming the main drawbacks of existing reliability methods. Main drawback of the ERRAGA method seems to be its inherent complexity and ‘black box’ nature. For the user to employ the full potential of the method some more in depth knowledge and especially the user-defined settings are required. Based on the gained experiences in this thesis some first recommendations are presented for the use and application of ERRAGA in projects.

In practice, many structures among which quay walls are designed according the Dutch national guidelines (CUR). Dutch national practical guidelines (NPR), with guidelines for renovation, is still in development for the building industry. These guidelines follow the Dutch Norms (NEN) and Annexes. The guidelines propose procedures in which newly-built or existing quay walls are designed. This study investigates the effects of past performance on the semi-probabilistic level I method for the purpose of design and evaluation of quay walls. This research is performed with a case study considering a CUR class III quay wall from. The objective of this research is gathering insight into the different aspects of past performance, among which degradation and information about survived years, on the reliability level and corresponding influence factors. Firstly, prior analyses including deterministic validation are performed. The output resulting from characteristic values of the cross-section is validated by means of Blum and analyses with the subgrade reaction method. The computed deterministic output appears to be in accordance with the results from the reference study. Afterwards, prior probabilistic analyses were performed in which the reliability, weight factors and corresponding partial safety factors are reconsidered. Failure mechanism ’yielding of front wall’ is a frequent phenomenon and is assessed in this research. Level II FORM is used for the calculation and level III Importance sampling for the validation. The cross-section is adjusted according the reference case and the results are reasonably in compliance with the results found by GeoDelft for CUR class III. The computed 50 year reliability index β = 4.53 and corresponds well to the target reliability level of β_t = 4.5. Additionally, the situation in which random input variables are correlated and model uncertainty is included, is considered as well. These correlations and model uncertainty are determined based on previous researches among which. The cohesion of clay, internal friction angles, wall friction angles and water levels are correlated. The model uncertainty factor is lognormally distributed and applies as multiplication factor on the maximum bending moment. Explicitly, the latter results in a significant influence on the limit state. Effects given the reference period are considered as well. Large numbers of the dominant load variable q are simulated. The (extreme value) distribution converges to a Gumbel distribution with σ = 0.61. The stochastic distribution of the dominant load is transformed from and to different reference periods: 1, 5, 10, 25, 50 and 100 years. Eventually, for posterior analyses the 50 year reference case is translated to an annual situation in which the annual reliability index and sensitivity factors are derived. Including model uncertainty and cross correlated random variables, one finds a reliability index β = 2.33 as assumption for the posterior analyses. The Equivalent Planes method (EPM) has already been applied in the field of flood defences for reliability updating. This method formulates an failure plane equivalent to two or more combined limit states. In this research, the method has been applied in the temporal context. This means that the Equivalent Planes method is considered in the derivation of the reliability given effect(s) of past performance. The annual reliability index and sensitivity factors are used in this reliability updating method. The autocorrelation represents the correlation of the concerned variable in time. Time-dependent variables including uniform load and water levels assume an auto-correlation of 0, other parameters initially assume an auto-correlation equal to 1. The annual reliability index and sensitivity values are iteratively applied in this method for combining limit states. The equivalent failure plane Z uses a simplified expression in the standard normal space. Eventually a time-dependent reliability curve, as presented by the green line in figure 1, is found. Without model uncertainty, the blue curve is obtained. A higher initial annual reliability index results in a relatively smaller increase of the conditional reliability index. Hence, the effect of past performance decreases when a higher start value of the reliability index is used. Due to the reduced cross-correlation between the water levels on both sides, the time-dependent reliability significantly increases. At last, the time-related effects of quay walls are considered. These effects include:

• The irreducible time-dependent uncertainty related to the model uncertainty factor. Randomness or natural variation is included in the model uncertainty factor. This is performed by considering situations with a reduced autocorrelation ρ(Z_i, Z_j) (0.25, 0.50 and 0.75). The reducible time-dependent uncertainty of load variables including q, w_a and w_p. Knowledge uncertainties (epistemic uncertainties) are reducible in time, meaning autocorrelation approaching 1. The autocorrelations of the considered variables distributions are derived by using transformed random distributions.

• Degradation by corrosion of the stiffest elements in the steel front wall. Corrosion is studied by considering the effects of a log normally distributed wall thickness loss according to corrosion curve 3. This corrosion rate affects the primary element characteristics of the equivalent combined wall. The correlation between the water levels on the active and passive is reconsidered and changed from 0.75 to 0.25.


As follows, the below figures show the annual development of the annual reliability as a function of time t. Notice that the annual reliability index increases as the extent to which the uncertainty is epistemic increases. Further, the reliability converges less rapid to larger value(s) in case of auto-correlation approaching 0. In this research, corrosion is considered as an epistemic uncertainty. Two modelling approaches have been considered: an engineering approach, a second order approach. The engineering approach solely considers a reducing section modulus W, whereas the second order approach is additionally including the second moment of inertia I. Corrosion curve 3 results in both approaches to a flattening of the conditional reliability index as time progresses. In addition, the speed in which the influence of time-independent epistemic uncertainties decreases, is less in case of corrosion. Hence, the involvement of stochastic degradation negatively affects the extent to which the uncertainties are reducible. The updated reliability index is also calculated per reference period. This is performed with probabilistic calculation rules. The corresponding sensitivity values, given survival of previous years (see figure(s) 5), can be used in the semi-probabilistic level I method for derivation of the updated partial safety factors. These factors can be applied in the derivation of the design values per random variable considering a service life time t. Hence, the reliability of a quay wall and the transformed sensitivity coefficients can be updated with the Equivalent Planes method. Incorporation of degradation and other time-related effects is seemingly possible. However, further research with finite element modelling is recommended for verification purposes.

The design and reassessment of quays is subject to uncertainties. Examples of these uncertainties are the soil parameters, soil behavior and the current state of the structural parts. Especially in the reassessment of existing structures it is hard to prove a quay to be safe. In this thesis Bayesian updating is used as a method to reduce this uncertainty. Bayesian updating is a technique to probabilistically update the model prediction based on measurement data. One of the solutions to obtaining this data is test loading a quay wall. How to perform a test load and possible other solutions to obtaining the measurement data are not part of this research. The research focusses on how to use the data one obtains from a test loading. The effectiveness of test loading is reviewed by performing Bayesian updates with several fictitious measurement cases. Both Blum and a finite element model are updated based on fictitious strain and displacement measurements. The results show that Bayesian updating successfully reduces the standard deviations in all model predictions. This has a significant impact on the calculated reliability indices. The key benefit of performing a Bayesian update is that a statistically most likely combination of stochastic input parameters is determined. The thesis gives recommendations towards an application of Bayesian updating in practice and as fictitious measurement cases are used, an overall strategy is given for obtaining the required measurement data in practice.

The Dutch flood defences are subjected to the new Dutch safety assessment program (WBI 2017) that incorporates the latest insights and safety regulations. As a consequence of the updated piping assessment model, studies are expected to identify more piping prone areas in the Netherlands, which makes it worthwhile to investigate alternative piping mitigation solutions that could be less expensive. A new potential solution is the Pipingontspanner, which consists of relief wells in combination with a water catchment area. The Pipingontspanner relieves water pressure fromthe aquifer and uses the water as counter pressure against the Uplift mechanism, thereby reducing the likelihood of piping.

The study investigates the technical and economic feasibility of the Pipingontspanner as a piping mitigation measure. A problem analysis was used to identify the components that form challenges in realising the concept and pinpoint the research to the functioning, effectiveness and applicability of the Pipingontspanner concept.

A hydraulic model and a design approach demonstrate the functioning of the concept. The hydraulic model describes the flow underneath the dyke, through the well and towards the basin above it. A critical point for the flow calculation appeared to be the time-dependent interaction between the river and the basin water level, which leaves only numerical calculation methods to describe the problem. The numerical program Modflow was chosen to predict the Pipingontspanner groundwater flow by simulating a flood wave scenario for a green dyke with piping problems and implementing relief wells and a basin. A parametric design approach was followed to create a Pipingontspanner model that could obtain the optimal configuration for a measure that can only be calculated with a groundwater flow model. For the verification of design configurations, relevant failure mechanisms have been included in this model. For the selection of the optimal configuration, a cost-benefit analysis has been used as an evaluation criterion. The Pipingontspanner model creates, calculates, verifies and evaluates the different design configurations.

The effectiveness of the Pipingontspannerwas illustratedwith a sensitivity and a cost analysis. For a variety of subsoil and hydraulic conditions, the sensitivity analysis showed that the safety factor for Uplift increases substantially for higher permeability of the aquifers and slowly growing hydraulic loads. The influence of the cover layer permeability and storage coefficient is negligible on the performance of the Pipingontspanner. On the other hand, the costs analysis showed that well maintenance, well monitoring and basin dyke construction costs are the main cost drivers of the design.
The total cost grows exponentially if the basin width behind the dyke is limited as the number of wells increases for smaller basins.

The applicability of the Pipingontspanner was demonstrated through a case study of a green dyke
in Tiel with piping problems. In addition, the design and costs of the Pipingontspanner in Tiel were compared against a traditional piping berm measure to illustrate the economic feasibility of
the concept. The results showed that the Pipingontspanner is not only able to mitigate the piping problem, but it does so with a smaller footprint and lower total cost than the piping berm. However, the case study also showed that limitations in the current groundwater flow model setup required an adaptation of the case geometry to prevent the drying up of the top layer cells, which would terminate the simulations.

The Pipingontspanner concept has proven to be technically feasible and economically competitive compared to the piping bermunder the conditions of:
1. a permeable aquifer with a minimum transmissivity of 25 m^2/d;
2. a minimum hinterland space of 10 m behind the dyke.

Constitutive models are one of the main building blocks of the Finite Element Analysis that nowadays is used in almost every geotechnical engineering project. Thus, finding realistic stress-strain behaviour models has been one of the main fields of research in Geotechnical Engineering. However, constitutive equations have become increasingly complex featuring 10 or more parameters as inputs with sometimes small correlations to physical properties (Beaty & Byrne, 1998; Bauer, 1996). Thus, a more data driven approach can be determined to account for that issue. In this thesis, that data driven approach will be attempted by using Neural Networks. The main goal of the thesis is to access if Neural Networks can be used to model constitutive soil behaviour. Specifically, two approaches are used to model stress-strain behaviour of soils.
The first approach is classified as a generic approach because the investigation is mostly focused on which techniques of the Neural Network can help with the modelling of stress and strain behaviour. In that way the Network can be thought of as a “black box”. The prediction after the training of the Neural Network is achieved by dataset retrieved inputs and from inputs that are retrieved from the last step of the prediction. The latter has the objective of replicating the prediction as it is achieved from a typical constitutive model. The aim is the minimisation of errors after training. The feedback and the non-feedback predictions do not produce the same results which imply that the network is sensitive towards a certain input. This is further validated by conducting a sensitivity analysis and by looking into the activation of each node for certain loading cases. Dropout and reassessing the inputs and outputs are attempted to resolve this issue but the results remain erroneous.
The second approach is to create a component based Neural Network. In this case a link is created between the function of the neural Network and typical soil behaviour. The linear elastic model is modelled with a linear activation function. In this case the network is successful in reproducing the full linear-elastic matrix. The linear elastic perfectly plastic model is modelled by connected the linear elastic matrix with a ReLU layer as it is seen in continuum mechanics. The Neural Network accurately predicts the stress-strain relationship. And it can be used to also predict the stress path of “noisy” datasets. However, when trained with noise the signal added to the training dataset is recognised as a pattern from the Neural Network. Finally, the work hardening model does not successfully model the stress-strain relationship as it tends to exaggerate the contribution of the stress input versus the strain input. All in all, this is an effort towards the development of a Neural Network constitutive model with the final aim of producing data driven constitutive models.

One of the main challenges in dike design in the Netherlands is to guarantee a sufficient safety level against the development of macro-instabilities in a dike. A case study was performed on a dike section at Herrewijnen-Opijnen, which is part of the Heesseltse Uiterwaarden in the Dutch province of Gelderland. The dike located at this site no longer fulfils the required safety standards, and therefore dike reinforcement is required. This thesis focuses on reinforcing this dike with the new technique of dike pins. Dike pins are grouted steel anchors, that are installed in the dike crest to improve macro-stability. The case study shows that the governing geometrical parameter in design is the centre-to-centre distance of
the dike pins. The cohesion of the clay slope was the governing geotechnical parameter for the determination of the slope safety factor. Arching occurred for high values of the friction angle or the cohesion of the sand layer. A large decrease in the bending moment of the dike pin results from arching. In this parametric study, correspondence was found between the 2D and 3D Plaxis models in terms of slope safety factor and in terms of the development of internal moments in the dike pin. A design scheme was suggested, which shows that in most cases a 2D design method may be chosen. The proposed design scheme simplifies the design method for dike pins.

This Thesis studies the safety assessment method for macro-stability of dikes with high foreshores. Currently, this method is a semi-probabilistic method, which does not take the presence of a foreshore into account. The research concludes that the presence of a foreshore has a significant influence on the failure probability with respect to macro-stability of dikes. The semi-probabilistic assessment method therefore overestimates the failure probability of dikes, which can lead to unnecessary expenses for dike reinforcements. Possible improvements for the safety assessment method are discussed.

Soil properties used to determine the stability of soil structures are variable in nature. Uncertainty in soil can be attributed to its inherent variability, as well as sources of error encountered while estimating the magnitude of its properties. The modelling of these uncertainties will produce more meaningful solutions when evaluating stability. This is especially relevant when quantifying the probability and risk associated with a rare event of failure.

An uncertainty framework is implemented in this report to evaluate improbable slope failure. A slope stability program using a modified subset simulation approach is expanded to account for cross-correlation between cohesion, friction angle and unit weight of soil. The mean of the three soil properties and their correlation coefficients are treated as random variables in the analysis. A parametric study is performed to evaluate the influence of the mean and correlation coefficients of these properties on the probability of failure. The influence of randomising these properties is also evaluated in the analysis. The implemented method is applied for a practical slope example, based on values reported in literature for the expected variability in the mentioned soil properties.

Results demonstrate that modelling the mean of C, phi and gamma as a random variable leads to a significant increase in the probability of failure for a slope. While treating the correlation coefficients as random in the analysis will lead to very little changes in the outcome, some generated correlation matrices may lead to a notable decrease in probability of failure. The stability of the slope is heavily influenced by the input parameters used in the analysis. Furthermore, a proper choice for coefficient of variation of each property and the horizontal and vertical scales of fluctuation is necessary to avoid inaccurate results in the analysis. Other inputs investigated include the type of distribution for each soil property and the range of possible values for their means. Different distribution types are tested in the analysis to identify which of these properly model the variability in the parameter.

By evaluating generated samples within each subset level, it is evident that a combination of low mean values for C and positive correlation between phi and gamma is required for failure at low probability of failure levels. Although the influence of set means of C, phi and gamma on the calculated probability of failure is similar, the same conclusion cannot be made when the means of the properties are random. At low probability of failure levels, the outcome is very sensitive to changes in the minimum possible value for C and less to changes in phi and gamma. Furthermore, it is demonstrated that the mode of failure may be overestimated when analysing stability by reducing the strength of the slope. Shallow failures are encountered when slope is failing under a strength reduction factor of 1, which is a more likely mode of failure in spatially variable soil.