The stability of rock engineering projects is tightly related to the mechanical behaviour of rock discontinuities. Although the mechanical behaviour of a discontinuity is often associated with shearing (sliding), experimental data have shown that it can be accompanied by more complex phenomena such as dilation and post-peak strength reduction. Numerous researchers have contributed to the understanding and modelling of discontinuities behaviour. However, many of the constitutive models available in the literature are questionable when applied in practice either because they are highly empirical with parameters that are hardly determined or because they oversimplify the examined behaviour. Moreover, the models are often proposed for a certain range of stresses and specific stress paths, which makes numerical implementation difficult for large-scale engineering applications. This dissertation aims to evaluate the capabilities and the limitations of different constitutive models for rock discontinuity in the context of both numerical implementation and simulation of the mechanical behaviour of rock discontinuity. The first part of the research project investigates the main features of the existing models in the literature. From the investigated models, the two models highly adopted in research and engineering practice, namely the Coulomb’s model and Barton-Bandis’s model, are extensively investigated. Some enhancements and modifications are made to these two models to improve their modelling capabilities and ensure the numerical stability of numerical implementation. Regarding the Coulomb model, the adopted modifications include the reformulation of the model within the framework of strain softening providing a rigorous implemented version that describes the post-peak behaviour of a discontinuity adopting a linear reduction of the strength. Additionally, the employed modifications to the Barton-Bandis model provide a robust version of the model applying reformulations to the original yield surface that increase its validity in the whole range of the τ-σn space. Furthermore, a simplified definition of the post-peak behaviour, which aligns with the original formulation of the model but at the same time allows for a straightforward numerical implementation, is proposed. To validate the implementation of these models in PLAXIS (implementation done by the PLAXIS research team), the models are implemented in Python scripts for Constant Normal Load (CNL) shear test configuration. Concretely the implemented models are calibrated with experimental data to simulate CNL tests using a PLAXIS 2D Finite Element (FE) model and the obtained results are compared with both Python theoretical simulation and experimental results to verify the FE implementation. The results of these simulations validate the numerical implementation in PLAXIS and prove the applicability of the enhanced models to reproduce with adequate accuracy the mechanical behaviour of a rock discontinuity on a lab scale. Finally, the implemented constitutive laws are employed to perform a FE analysis of a large-scale application of a deep underground excavation in a discontinuous rock layer using PLAXIS 2D. To facilitate the creation of this complex geometry, an automatic discontinuity network generator is developed and improved using PLAXIS Python scripting API. The implemented discontinuity laws are then applied to the randomly generated discontinuity sets to simulate the behaviour of the rock mass. Stress and failure analyses are performed for the most critical discontinuities and wedges formed around the excavation to validate the numerical implementation and analyze the applicability of the constitutive models. The analysis of the boundary value problem confirms both the reliability of the numerical implementation and the applicability of the enhanced constitutive laws to simulate the analyzed large-scale problem.

Soil liquefaction is a phenomenon in which an otherwise stiff, loosely packed, cohesionless soil loses its strength and behaves behaves like a viscous liquid in response to a change in stress conditions. This study focuses on liquefaction under monotonic load (i.e. static liquefaction) and not cyclic liquefaction. While the role of state variables such as relative density in liquefaction is well established, the importance of intrinsic soil properties (ISPs) is less clear. ISPs include grain size gradation, mineralogy and grain shape The critical state soil mechanics framework can be used to link these properties to liquefaction susceptibility. One approach to do so is the "Relative Contractiveness" (RC) concept proposed by Verdugo & Ishihara (1996). This thesis investigates the role of ISPs in soil liquefaction and tests the RC concept through a combination of statistical analyses, four case studies and a new experimental study.

The statistical analysis shows that an increasing fines content generally leads to greater relative contractiveness and especially at lower stress levels, indicating increased sensitivity to liquefaction. Particle shape plays a multi-faceted role in liquefaction susceptibility, as increased angularity may increase compressibility but also increase resistance to particle rotation and hence reduce the likelihood of flow behaviour. The mineralogy of soils was difficult to statistically analyse as the information is usually not given, but extra care should be taken when dealing with sands that are not made of quartz, as most index methods are based on quartz.

The case studies exemplified varied applicability and benefit per case. The Ijmuiden case demonstrated the limitations of field tests and critical state determination. It did indicate medium to high relative contractiveness for the tested soils. The Nerlerk berm failure demonstrated the importance of fines content in liquefaction susceptibility, as only the finer of the two soils used for the hydraulic fill liquefied. However, the geometry and differences in deposition method also played a role. For the Hollandsch Diep case environmental factors are ought to play a more important role in liquefaction rather than that the soil is intrinsically exceptionally susceptible to liquefaction. The Bangabandhu bridge case highlighted the limitations of compressive loading based methods as the soil was particularly weak in tensile loading. It also highlighted the importance of mineralogy and grain shape, as the presence of plate-like micaceous particles drastically reduced its strength.

The new experimental study investigated a soil from the Eastern Scheldt estuary in the Netherlands, a region historically notorious for liquefaction flow slides. Surprisingly, the sampled soil was not prone to liquefaction at all, showing strong dilative tendencies under triaxial compression.

In conclusion, this study suggests that the relative contractiveness concept could be used as a screening method for assessing liquefaction risk, rather than a deterministic method for designing parameters. However, further studies with extensive and consistent material characterization and critical state determination are needed to verify the validity of the relative contractiveness concept. Discrete element modelling of soils could also provide future opportunities for advancing our comprehension of the role of ISPs in liquefaction susceptibility.

Using an expensive-to-evaluate numerical model, such as a finite element method (FEM) model, is deemed unavoidable in solving modern geotechnical engineering problems. At the same time, the application of reliability analysis in dealing with uncertainties (e.g. soil properties) is increasing rapidly. This could pose a time-wise problem for an FEM model since reliability analysis normally takes much more than only one realization (function call) of the model. It becomes a bigger problem when a design optimization process is taking place. More often than not, design optimization is performed by a ”trial-and-error” method in practice, which the process itself would even take longer just to give engineers the ”sense” of achieving an optimal design (in terms of safety and economy). Therefore, the actual optimality of the design is not systematically proven and quantified. This research proposes a novel reliability-based design optimization (RBDO) method by combining existing theories regarding active-learning Kriging-based Monte Carlo Simulation (AK-MCS) and (1+1)-Covariance Matrix Adaptation evolution scheme ((1+1)-CMA-ES). To achieve accuracy and efficiency, the method consists of four enrichment stages. These enrichment stages ensure the method accurately and efficiently predicts the optimal design combination by considering the reliability constraint. The chosen case study is the reinforcement design of the Starnmeer polder dyke in the Netherlands, which is simulated as an FEM model. Within a limited number of function calls, the proposed RBDO method could accurately predict the optimal dimensions of the dyke that delivers the targeted reliability index. The reliable performance of the proposed method is further demonstrated by solving three analytical optimization problems.

As the construction of sub-aerial and submarine geotechnical structures increase in amount, rate and size, so do their associated risks. Often, with use constitutive models, finite element analyses (FEAs) are performed in order to identify and mitigate these risks. NorSand, which is a consti- tutive model based on critical state soil mechanics for particulate materials (e.g., sand), is one of the first models to integrate the state parameter ψ into its constitutive framework to model dense and loose sands material with the same parameter set. Importantly, it is able to identify the liquefaction potential as it can simulate softening behaviour due to pore pressure increase of loose soils in undrained conditions. Since NorSand has recently been implement into PLAXIS, a geotechnical analysis software capable of performing FEAs, it must be verified, validated and applied with the software, which is done in this report. First, stress-path and parametric analyses were conducted at single stress points. The stress- path analyses show how the state variables evolve for different triaxial conditions. Systematically changing the input parameters to extremes found in literature helped determine their influence on the evolution of stresses and strains. The resulting figures can be used to help future calibrations to experimental lab test data. The PLAXIS implemented NorSand (PLAXIS NorSand) was verified by comparing it with an implementation written in Visual Basic for Applications (VBA NorSand) by the authors of the model Jefferies and Been. Verification in this context means determining if PLAXIS NorSand is able to produce outputs as intended by the authors. Various testing conditions, both triaxial and direct simple shear, showed overlap and agreement between the outputs of both implementations, verifying PLAXIS NorSand. Then, the model was compared to, albeit not in a traditional sense, an ’analytical solution’, which is the relationship between the mobilized friction ratio Mi and state parameter ψ in its simplest form. The mobilized friction ratio and stress ratio at peak strength of PLAXIS NorSand and the ’analytical solution’ were compared. The values between both showed less than 3% difference, further verifying PLAXIS NorSand. The constitutive model was then validated - i.e., established that PLAXIS NorSand is able to approximate soil behaviour as intended. First, by using the soil parameter set that had been derived from lab tests of Erksak sand as a baseline, the input parameters were varied until PLAXIS NorSand was calibrated to individual triaxial tests as best as possible. Then, triaxial tests of Erksak, Nerlerk and Ticino sand were approximated with PLAXIS NorSand without changing the soil parameters determined from lab test data. PLAXIS NorSand is able to follow lab test data decently well with one parameter set. And if one decides to take the time and calibrate individual lab tests, and deviate from soil parameters determined from a set of lab tests, they can be matched even better. Additionally, it showed a consistent need for activation of the softening flag (S = 1) in order to appropriately model loose soils in undrained conditions. Furthermore, NorSand exhibits indefinite hardening in dense soils during undrained loading, which can be avoided by employing a ’cavitation cut-off’. The last part of this report tested PLAXIS NorSand by applying it in FEAs of a simplified submerged landslide, which was subjected to 20 centimeters of displacement at the crest through a rigid slab in undrained conditions. First, the difference in slope behaviour due to change in soil density within NorSand was determined: dense soil resulted in the slope to be able to bear the full 20 centimeter displacement, whereas increasing the void ratio (i.e., increasing the positive value for the state parameter) gave the effect of even quicker slope collapse and a lower bearing capacity. In other words, when using NorSand, the looser soil the further the failure surface moves up and the quicker the structure fails to maintain equilibrium. Lastly, NorSand was compared to Modified Cam-Clay and Mohr-Coulomb to highlight the differences in their ability to model static liquefaction, while being triggered by unrealistic loading conditions. Even though none of the FEAs showed actual liquefaction, since it is accompanied with the fluidization and loss of structure, they still gave in indication of the liquefaction potential. NorSand, contrary to the other constitutive models, showed the expected high sensitivity to forced displacement resulting in clear shear bands resembling Prandtl-type failure mechanism and early onset soil body collapse.

Soil properties are spatially variable due to the natural deposition process. Because of this inherent spatial variability, a slope can actually fail along any potential slip surface. A single value of Factor of safety cannot account for this variation dominated the slope stability problem. Probabilistic analysis considering the spatial variability is a reasonable method to quantify the risk of the slope stability problem. Thus, in order to better simulate this variation, the theory of random field has been widely used in the slope stability problem. However, statistical outcomes derived from the probabilistic analysis will be influenced by how the random fields are generated and how the random field values are assigned to each potential slip surface. In order to investigate the extent of this influence, this study proposed a new probabilistic slope stability analysis method and compared it with the other two methods in terms of accuracy and efficiency. In this report, three different probabilistic slope stability analysis methods are presented. These methods combined the traditional limit equilibrium method of slices with random fields, which can account for the inherent spatial variability of soil properties. An exponential decaying function is used to describe the correlation structure of this spatial variation. This correlation structure is further expressed by the form of covariance matrix. Since the covariance matrix is a symmetric positive definite matrix, Cholesky decomposition is used to decompose it into the product of two triangular matrices. Because the triangular matrix is more computationally efficient, the two-dimensional random field is generated by multiplying a normal random number vector with the lower triangular matrix derived from Cholesky decomposition.

The stability of breakwaters in seismically active areas is not always guaranteed. A new approach to model a breakwater subjected to an earthquake is with PM4Sand. The goal of this research is to find if breakwaters subjected to earthquakes can be correctly modelled with PM4Sand.
To investigate PM4Sand a breakwater subjected to an earthquake on centrifuge scale is modelled in Plaxis. The soils of the centrifuge test are modelled with PM4Sand and UBCSand. After calibrating the soil parameters and incorporating the proper earthquake signal results are generated and compared. The investigated results focus on the settlements of the caisson, deformations of the breakwater and generated Excess Pore Water Pressures underneath the breakwater due to the earthquake. Comparing the results from the numerical models with the centrifuge test result show that both the UBCSand model and PM4Sand can give comparable results for the settlements and deformations. However, both UBCSand and PM4Sand were not able to give the correct EPWP development underneath the breakwater.
Due to the incorrect behaviour of the EPWP underneath the breakwater resulting from the numerical models, this research is not able to conclude that PM4Sand can be used for modelling breakwaters subjected to earthquakes. Further research is needed to investigate the development of EPWP underneath the breakwater during an earthquake. Focus points of future research can be: the influence of the amplitude of an earthquake signal on the EPWP, the influence of modelling a centrifuge test on the behaviour of the EPWP and the influence of the initial static shear stress on the EPWP development.

Recent development have caused that the policy regarding the installation of onshore wind turbines on embankments has changed to 'Yes, provided that ...' in the Netherlands. (Simplified) approaches are available within professional practice to analyse the risk of liquefaction, but are considered to be conservative. In this thesis, a methodology is formulated to model the key aspects of liquefaction of a soil layer underneath a dike system subjected to cyclic loading by an onshore wind turbine. The key aspects are defined as: cyclic loading, soil-structure interaction and consolidation behaviour. A modification to the model of Seed and Rahman (1978) is implemented in this thesis.
The applicable modelling conditions (quasi-static or dynamic) are investigated for the current situation. The analysis is performed using analytic and numerical models (Plaxis 2D). Both models conclude that the loads induced by the wind turbine can be modelled as quasi-static as the loads are sufficiently slow to neglect inertia effects. The influence of the cyclic loads by the wind turbine on the liquefiable soil layer is determined by the Cyclic Stress Ratio (CSR). The influence due to the soil-structure interaction is determined using a Finite Element Analysis (Plaxis 2D). The Hardening Soil small strain model gives a more accurate prediction of the CSR in the soil, as the soil response is stiffer during un/re-loading. The presence of the embankment results in various modes of shearing in the soil, e.g. triaxial compression, triaxial extension and direct simple shear. The CSR does not include the effect of static shear stresses and various modes of shearing in the soil. This effect should rather be accounted by the Cyclic Resistance Ratio (CRR). The consolidation behaviour modelled using the model of Seed and Rahman (1978) which applies the consolidation equation with generation term. The model is able to model partial consolidation, which is defined as a state where excess pore pressures can be generated and dissipate simultaneously. The generation term is based on an empirical relationship of the development of pore pressures. The model is implemented using a Finite Difference Method in a cylindrical coordinate system to represent the dissipation behaviour of a granular soil. The method allows to model the consolidation characteristics in radial and vertical direction, a layered soil, the load intensity and the loading frequency. As a result, the maximum pore pressure ratio in the soil reduces. A limitation of the model is its uncoupled nature. Therefore, no strains are determined. The constitutive behaviour inherent to the liquefaction phenomena, such as plastic deformations, is lacking. Oostpolderdijk is used as a case study to compare the modified method of Seed and Rahman (1978) to the reference engineering method and the method of Boulanger and Idriss (2014). The comparison with Boulanger and Idriss (2014) suggests that the modified model gives reasonable results. The application of the modified method results in a more favourable result compared to the reference engineering method. However, a sensitivity analysis shows that liquefaction can’t be ruled out because the sensitivity to permeability is high.

This MSc thesis was initiated as part of an interdisciplinary project researching post-disaster coastal reconstruction in the Tohoku region of Japan. On March 11, 2011, a highly destructive earthquake induced tsunami hit the north-eastern part of Honshu island, causing enormous damage to numerous small towns along the coast. Since 2011 various studies have been completed to better understand this historical event and explain the nature of tsunamis. However, some researchers have noted the inability of tsunami models, using only an earthquake as a source, to reproduce the timing, frequency and wave heights recorded along the Tohoku coast in March 2011. The differences are especially striking for the Sanriku coast – a relatively small area north of Sendai plain characterised by a ria-type coastline. D. R. Tappin et al. (2014) suggested that a secondary source is required to explain the deviating model results and locally higher tsunami waves, such as a submarine landslide. In low-lying coastal areas, tsunamis are an unavoidable hazard to human lives. A common way of addressing natural disasters of this scale is with timely warning and evacuation, which in turn requires appropriate techniques for prediction of an upcoming disaster. While earthquake induced tsunamis provide a sort of a warning signal, tsunamis generated by a submarine landslide can be much more difficult to predict. Landslide tsunamis are usually concentrated in local areas and do not propagate far, as they are more dispersive than earthquake tsunamis. However, the source of landslide tsunamis is often located on a continental slope near the coastal line. As a result, waves reach the shore in a very short period of time and run-up heights can reach extremely high levels (Harbitz et al., 2006). Thus, landslide generated tsunamis pose a serious hazard to densely populated coastal areas. Within the scope of this thesis, a number of experimental simulations on submarine slope failures were conducted in a so-called static liquefaction tank – a unique testing facility for large scale experiments at the Geo-Engineering Laboratory of TU Delft. To improve the understanding of tsunami generation, this study focuses on the moment of onset of a submarine slope failure and wave generation, linking the processes within failing soil mass to initial characteristics of waves. This study illustrates the connection between these two processes that are usually only considered individually from either a geotechnical or hydraulic perspective.

In seismically active areas, liquefaction hazards have always been a complicated aspect to evaluate as part of the seismic design of a project. In the case of the design of critical facilities, this becomes crucial, as beyond design basis conditions may elevate the seismic loads significantly and create a considerable liquefaction risk in areas of deep alluvial deposits. Furthermore, traditional semi-empirical methods lose their applicability at depths larger than 15 m, which becomes problematic if one wishes to analyse the liquefaction hazard of deep Holocene deposits. Given this shortcoming and the rapid growth of numerical tools available for geotechnical earthquake engineering, the use of liquefaction-predicting constitutive models, like PM4Sand, provides the opportunity to obtain more accurate and physically-consistent results. For this purpose, this research is divided in three main parts. The first part covers the study of the onset of liquefaction with the use of two cyclic undrained direct simple shear test databases and the identification of liquefaction-triggering criteria, in terms of pore pressures and shear strains which can consistently define a liquefied state in sands. The second part includes the thorough analysis of the capabilities of the PM4Sand model, in Plaxis, through a benchmark calibration study using one of the previously mentioned laboratory test databases, concluding in the proposal of a modified calibration methodology based on pore pressure ratio (ru) and shear strain (γ) liquefaction-triggering criteria. The third and last part covered a practical case study oriented towards the design of a critical facility, where a beyond design liquefaction hazard analysis of a hypothetical site was evaluated incorporating the findings from the previous parts. A one-dimensional liquefaction hazard analysis was performed using a single earthquake signal and soil profile, where the consistency of the PM4Sand model in terms of liquefaction-triggering was evaluated and the numerically-obtained results were compared to those calculated through one semi-empirical method. Additionally, the one-dimensional model was extended and a two-dimensional liquefaction hazard analysis, including the presence of a simplified structure, was performed with the aim of evaluating the effects of soil-structure interaction and structural load variation on the liquefaction hazard of the soil profile over distance.

In this report, an experimental investigation of the influence of currents on submarine slope stability is presented for the Eastern Scheldt storm surge barrier case. Slope instabilities, including liquefaction failures, have been observed in the scour hole slopes near this barrier. The currents above the sloping bed are expected to initiate the liquefaction slope failures. The effects of the excess pore water pressure increase, that is generated by the currents, on the soil response are investigated by triaxial tests. Multiple excess pore water pressure rates are applied on a loose soil sample. The triaxial tests show that higher excess pore water pressure rates result in earlier developments of strains at lower stress ratios. This research is intended as a step towards a better understanding of the initiation mechanism of the liquefaction slope failures near the barrier.

The starting point of this thesis lies in the area on Groningen, Netherlands. More specifically, induced earthquake activity is observed in this area due to gas extraction activities, which reduce underground gas pressure. In combination with the location’s geomorphology, liquefaction can occur due to earthquake excitations. Furthermore, the area of Groningen is a location with urban activity and infrastructure, such as pipelines, present. The post-liquefaction effect of these pipelines is their uplift, which can lead to failure, along with all its negative consequences. Furthermore, the creation of two different models, capable of describing the soil-structure interaction of pipelines and post-liquefied soil was the main objective of this thesis. The means by which these models were created was the implementation of the spring and dashpot method. More specifically, Kelvin-Voigt models were used for the ground’s behaviour to be modelled. These models required two main parameters to be specified in each case, the spring coefficient (k) and the dashpot coefficient (c). In order for the spring coefficient to be determined, the creation and usage of post-liquefaction p-y curves was deemed necessary while the problem specific dashpot coefficients used, had previously been determined by means of physical modelling. The ground profile consisted of fully saturated loose sand and the pipes investigated had diameters of 110, 160 and 200mm. The first model was a single degree of freedom one, with that being the vertical. As for the second one, it was a multi degree of freedom one. More specifically, it consisted on two degrees of freedom, the vertical and horizontal ones. The results of these models were validated by comparison to previous studies and further investigation of affecting parameters was carried out. More specifically, the way and the degree up to which several parameters of both ground and structure characteristics affect their interaction were investigated. More specifically, the first parameters considered were the pipelines’ diameter as well as their weight, resulting from their geometry and transported material. Next, the effect of the pipelines’ burial depth was considered and then, the effect of the soil’s initial stiffness. Finally, the effect of the dashpot coefficient was investigated for the multi degree of freedom models. A comparison between single and multi-degree of freedom solution results was also carried out. The results of this study were validated by comparison to previous research findings. Most results and conclusions were in complete agreement with the so far existing bibliography. However, what was found to be inaccurate was the previously determined dashpot coefficient for 110mm diameter pipelines and hence, these were left out of scope of study.

One of the most severe deteriorations in reinforced concrete structures is associated with reinforcement corrosion, where the corrosion distribution shows considerable spatial variability. In the existing investigations of spatial variability of corrosion on the reliability of reinforced concrete structures, symbolic expressions are used for the structural performance. However, structural behaviors like stress redistribution and plasticity spread are not captured. In this research, a computational framework is designed to couple the probabilistic analysis with the nonlinear finite element analysis. Random fields is used with the computational framework to represent the spatial variability of corrosion.A 60 m girder of a reinforced concrete bridge is taken as the case study to explore the effect of spatial variability of corrosion on reliability of static indeterminate reinforced concrete structures. The reliability analysis is target on ultimate capacity of the beam to carry the traffic load. The girder is modeled as a 3 span continuous beam. The modelling of corrosion damages on reinforcement (area of cross section and physical properties) is based on assumption of pure pitting corrosion. In the axial direction of the beam, spatial variability is modeled with random field. In order to study the effect of different level of spatial variability, the correlation length of the random field is set from infinite large to 125 mm. Between adjacent bars, extreme cases of fully spatial correlated and totally spatial independent are studied.The case study shows:i) when corrosion develops, pitting corrosion can severely reduce resistance of the structure and localized damage may lead to a brittle structural response.ii) spatial variability of pitting corrosion in the axial direction of the beam leads to higher failure probability of the structure.iii) spatial variability of pitting corrosion between adjacent bars leads to lower failure probability of the structure.iv) the effect of spatial variability of corrosion on reliability of static indeterminate reinforced concrete structure is a collective effect of probabilistic and physical characteristic.In order to facilitate the reliability assessment of corroded reinforced concrete structures, additional efforts are also contributed to: quantification of uncertainty for the bond model of corroded reinforcement; comparison of various reliability methods with the probabilistic nonlinear finite element analysis framework.The thesis fills the knowledge gap of probabilistic nonlinear finite element analysis of reinforced concrete structures with spatial varied corrosion and quantifies the effects of spatial variability of corrosion on the reliability of a static indeterminate reinforced concrete structure. The analysis framework designed in this thesis is also applicable for other reliability assessment of corroded reinforced concrete structures.

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.

In the northern part of the Netherlands, the exploitation of gas fields has been inducing small earthquakes, causing damage to existing buildings.
With the aim of preventing consequences to people and structures, the VIIA Groningen project deals with CC2 and CC3 buildings retrofit and provides reinforcement measures when necessary.
As part of the structural response assessment, after the NPR 9998 (2015), and eventual special cases from the latest NPR 9998 (2017), non-linear time history analyses (NLTH) are executed, comprising seismic ground response analysis (SRA).
The propagation of seismic waves through a 1D soil column is highly dependent on the characteristics of the materials constituting the soil deposits. Hence, it is essential to correctly interpret the soil properties, in order to achieve realistic representations of the in-situ conditions.

To interpret the soil layering at a particular site, the Cone Penetration Test (CPT) is commonly used in Groningen. It offers a quick, economical and reliable measurement of ground conditions. However, the CPT-based correlations used to estimate soil properties can constitute a source of uncertainty if not coupled with full-scale testing and laboratory measurements.
The present thesis, thus, deals with the verification and the improvement of two CPT-based correlations used for soil interpretation in Gronigen specifically. The research study focuses on the mathematical models related to the plasticity index (PI) and the undrained shear strength (Su) of soft soils present in Groningen.

A comprehensive database of factual data was compiled in order to group various test types and provide a best-estimate of soil properties for different soil types using geotechnical and stratigraphic considerations. Secondly, a statistical characterisation of data-sets was performed to obtain insight on the correlations performance in relation to the in-situ and laboratory measurements. Based on the outcomes of the statistical comparison, analytical and regression analyses were carried out with the scope of improving the correlation that was deemed to be inadequate. Additionally, a sensitivity analysis was executed to investigate the influence of three relevant soil properties on the seismic ground response from a typical soil profile from Groningen. The parameters assessed are: plasticity index (PI), undrained shear strength (Su), and shear wave velocity (Vs).

Results indicate that, among the considered CPT-based correlations, the equation for PI from Cetin and Ozan (2009) is adequate in some cases. The geotechnical units sandy Clay and Loam show good correspondence with the factual data. On the other hand, the PI predicted with such relation tends to be lower than the laboratory measurements for the remaining soil units (e.g. clean Clay, silty Clay, OC Clay). Conversely, the PI behind the models implemented in the NPR 9998 (Bommer et al., 2017a) are in closer agreement to the factual data, however, the
PI from some soil units can be further improved with the findings from the present research.

For the interpretation of Su, the SHANSEP model from Ladd and Foott (1974) is frequently used. The available factual data showed a poor correspondence with the predicted Su values. Therefore, the SHANSEP model was further studied to calibrate its parameters for different soil types. From the available triaxial consolidated undrained laboratory tests, best-estimate of SHANSEP coefficients were obtained for the main soil types (clean, sandy, and silty Clay). New Su values were validated with the in-situ and laboratory measurements. In this context, it is confirmed that the dependency of Su on the overconsolidation ratio (OCR) is crucial. Moreover, the estimation of OCR from CPT measurements (following the Mayne, 2014, procedure) is found to be partially inaccurate within the SHANSEP framework and needs to be studied in more detail.

Engineering aspects related to the topics of the research are discussed and considerations regarding the applicability of the new correlations are provided. Furthermore, the present study gives indications about the usefulness of a number of test types, suggesting direction for future soil investigations. In addition, look-uptables for PI and Su, based on the outcomes of the present research, are provided as part of the recommendations for implementation in the soil parameter interpretation for the Groningen region.

As soil behaviour is stress-dependent, a centrifuge model with tilting sample box was developed to generate liquefaction flow slides at higher confining stresses. The design and experimental set-up were based on the large liquefaction tank (de Jager et al., 2017). Fluidisation was used as sample preparation technique to produce a saturated, loose and uniform sand bed. The performance of the fluidisation system was evaluated by experimental investigation of the sample by considering the relative density, uniformity, degree of saturation and the influence of viscous pore fluid. The reproducibility of the initial sample was considered acceptable. A series of centrifuge experiments was conducted where the fluidised sand bed was accelerated to varying gravity levels and inclined to a slope with constant tilting rate. In most tests the soil response was characterised by a rapid liquefaction flow slide and a sudden increase in pore pressures. The moment of failure was consistently influenced by a variation in fluid viscosity and tilting rate, regardless of the gravity level; these effects indicated that instability was caused by the restricted seepage rate during loading. It is believed that the liquefaction potential is governed by the extremely loose and highly contractive top layer, which yields a sudden loss of strength under limited drainage conditions. The pore pressure measurements, which showed no excess pore pressures building up prior to failure, can lead to a misunderstanding of the failure mechanism and false assumption of fully drained conditions. Monitoring the pore pressures is therefore not suitable to predict liquefaction flow slides in submarine slopes. Mitigation of liquefaction should be focussed on densification of the looser part of the sandy slope, which is usually the top layer.

The Particle Finite Element Method is a numerical tool that has been introduced more than a decade ago for the solution of engineering problems involving large deformations.
The method falls under the category of mesh-based particle methods, meaning that all information is stored on moving particles that represent the domain under analysis and a computational mesh is used for the solution of the governing equations.
Although the method was initially developed for simulating fluid\hyp{}structure interaction problems, owing to its versatility in handling large deformation and constant changes in domain boundaries and contact interfaces, it has been recently employed for solid mechanics applications. However, the lack of a consistent framework for this kind of problems has lead to different implementations of the method presented in the literature, each with its own special features.
The main objective of this thesis is to implement a variation of the Particle Finite Element Method and investigate the efficiency of the different features available in literature.

Initially, the meshing procedure of the method was developed, which consists of a Delaunay triangulation for assessing the connectivity of the particles and the ${\alpha}$-shape method for detection of the boundaries of the different domains. This was followed by an investigation on the influence of the related parameter ${\alpha_{lim}}$ on the outcome of the analysis; it appears that this choice has an impact on the results, in terms of the recovered domain volumes and the simulation response; this parameter has to be selected with care, with respect to the nature of the examined problem. Volume variations are also observed, caused by element deletion and/or addition during remeshing, which, eventually, lead to mass oscillations. These effects can be mitigated by either adjusting the value of the ${\alpha_{lim}}$ parameter, refining the particle distribution or prescribing the boundary surface during remeshing, by using a constrained Delaunay triangulation.

Another important feature of the PFEM is the treatment of contact, which is, typically, done in literature via employment of an interface mesh. This mesh is generated during remeshing, using the same scheme as for the regular domain meshes, i.e. a Delaunay triangulation and the ${\alpha}$-shape method, and the generated contact elements are then used to enforce the contact constraints, with a variety of methods. In this work, a simple algorithm that disallows inter-penetration and allows free separation and free movement perpendicular to the contact surfaces was formulated and validated against benchmark solid mechanics problems. The automatic contact detection and interface mesh generation allows for the incorporation of more advanced contact treatment schemes.

Transference of information between successive meshes is important in PFEM for solid mechanics, especially when the history of elemental variables, e.g. stresses, is required for capturing the solid material behavior accurately. The most popular technique is the nodal smoothing technique, where the values are mapped back and forth between the integration points and the particles at each time step; other schemes have been also presented in literature. This scheme has been shown to introduce some smoothing of information, which can be reduced by refining the particle distribution and, in general, does not seem to affect the overall system response significantly.

The developed method was, finally, compared with the available in-house implicit Material Point Method code, which shares the same formulation, on some benchmark quasi-static and dynamic solid mechanics problems. The PFEM demonstrates a more stable behavior in terms of capturing the evolution of stresses and kinematic variables, despite some inaccuracies caused by the smoothing of information and the use of simple, constant-strain triangles. On the other hand, the MPM -in its standard form- exhibits some instabilities in the assembly of equations and stress recovery, which is intensified when cell-crossing occurs, i.e. jumping of material points between elements.
Regarding the computational cost of the two methods, the MPM seems to be faster and require less computer memory for the same number of information points, i.e. particles, with the simulation times, however, increasing exponentially with the number of degrees of freedom.

The phenomenon of earthquake-induced soil liquefaction has been a major issue among geotechnical engineers mainly due to the dramatic consequences this could have on civil structures. Basically, earthquakes propagate shear waves generating excess pore pressures and thus weakening the effective shear resistance of granular soils to their minimum until they liquefy behaving like a viscous fluid. This occurs because the soil experiences undrained behaviour against these rapid cyclic loads. In practice, the cyclic shear resistance of the soil against earthquakes is assessed by means of empirical correlations from in-situ penetration tests and cyclic laboratory tests. However, the liquefaction phenomena analysis is still a topic under research in which soil constitutive models play an important role.
The PM4Sand is an advanced soil constitutive model that has been developed to simulate soil liquefaction behaviour of granular soils by defining mainly three model parameters being an easy calibration model and therefore very attractive for the industry. The current project aims, firstly, to verify the PM4Sand model response at soil element level and secondly, to validate its use for quay wall structures design using the finite element methods software, PLAXIS 2D.
During the first phase of the project, a comparison between the PM4Sand model response and documented cyclic DSS tests documented by Sriskandakumar (2004) is performed. In this, a parametric assessment identifies the influence of the model parameters on the model response, allowing also to evaluate the original calibration methodology proposed by Boulanger and Ziotopoulou (2017). Consequently, initial state conditions are evaluated. It was observed that a proper calibration of the PM4Sand model provides satisfactory response both in terms of stress paths and generation of excess pore pressure, even though the model tends to overestimate the cyclic resistance of the soil at higher cyclic stress levels and to underestimate this at lower levels with respect to a target ‘CRR vs Nc’ relation. Moreover, static shear stress effect is not well captured by the model but this is still under discussion as this effect is not fully understood yet.
In the next phase, modelling of the case study is developed based on research carried out by Iai and Kameoka (1993). The PM4Sand model is calibrated based on the representative SPT tests at the site to then be implemented on the upper liquefiable soil layers. The dynamic analysis of the collapsed quay wall was applied using different approaches: dynamic analysis with and with consolidation effect, and using free-field and tied-degree of freedom lateral boundaries. The results showed that the PM4Sand model is able to properly simulate the onset of liquefaction even though the displacements obtained were much lower than those documented.
Finally, an initial evaluation of the post liquefaction effect of the model was performed that could be considered as a starting point for future research.

One of the failure mechanisms for water retaining structures is piping. Piping is an internal erosion
mechanism creating hollow spaces (pipes) underneath, for example, a dike as a result of the transport
of soil particles due to seepage. The formation of pipes can cause collapse of the structure once the
erosion process reaches the outside of the dike. This study focusses specifically on the possibility of
the occurrence of this failure mechanism in the Maasvallei area. The Maasvallei covers the area of the
Maas roughly between the Dutch towns Roermond and Mook. The early signs of piping in the form of sand boils are frequently observed during periods of high water levels in the Dutch rivers. Although the total collapse of a dike in the Netherlands due to piping has
not occurred in the past decades, the frequent observation of the early signs of the piping process
has resulted in the inclusion of the piping failure mechanism in the Dutch legal safety assessment
regulations for water retaining structures. During recent high-water periods in 2011 and 2012 sand boils
were observed along several Dutch rivers except at the dikes along the Maas. The striking absence of
sand boils in the Maasvallei area raised the question if the failure mechanism piping is relevant for this
specific area. In the recent assessment of the Dutch dikes, many of the dikes along the Maas in Limburg were found
to be insufficiently safe against piping. The dilemma then becomes clear: the lack of early signs of
piping contradicts the outcome of the safety assessment. Resources could be saved if the dikes do
not need to be reinforced for piping, however, the safety should not be compromised. Within the thesis this dilemma is studied. The main question that is answered is: Is dike-failure due to piping realistic in the Maasvallei?

Geotechnical design problems may be characterized by a certain degree of uncertainty, due to insufficient soil data and transformation of test results in soil parameters. In common practice, engineers perform deterministic analyses according to design standards as Eurocode 7, where the uncertainties are taken into account through partial factors for loads and soil properties to attain certain specified target reliabilities. Forcomplexsoilstructureinteractionproblems, partialfactormethodis difficult to adopt, as the design standards consider geotechnical standards with singlefailuremechanism. ThisisespeciallyproblematicforUltimateLimitstatedesigns where both stiffness and strength properties are dominant. With the advent of limit state design philosophy in Eurocodes, the use of reliability methods in Finite Element Analysis for complex situations has become more and more of interest. Reliability analyses allow to explicitly define the single uncertainties in the model by using an appropriate probabilistic distribution for each source of uncertainty. The reliability index and the probability of failure with respect to a predefined condition are calculated. The problem with using reliability based probabilistic design is the absence of simple computational approaches that can be easily implemented. MonteCarlosimulationsarecommonly usedto solvesoil structureinteraction problems. For a large and complex soil-structure interaction problem, it is computationally intensive to complete even a single run. This practical disadvantage can be solved only by a computationally efficient method. A special purpose application to perform probabilistic analysis in PLAXIS 2D, called PROBANA has been recently developed at Plaxis B.V. PROBANA performs direct probabilistic calculations in the finite element framework, using First Order Reliability Method or Monte Carlo Method. In this thesis, PROBANA (FORM) is used to perform reliability analysis for three benchmarks, and the results from PROBANA – FORM are compared with Point Estimate Method (PEM) and other stochastic Methods. The results from FORM are found to be comparable with that of PEM. It is concludedthatPEMislessaccurateduetoassumptionsmadebyPEMintheunderlying output distribution and FORM is more accurate and practical as it is computationally less intensive compared to other stochastic methods such as the Monte Carlo analysis. An extensive comparison of the reliability based method with Eurocode design method shows possibilities to implement reliability methods with EC7. One such approach is proposed, and demonstrated with the benchmarks.

A new technique is developed in this thesis, which applies boundary conditions to moving boundaries in the Material Point Method (MPM). While MPM has been proven to be useful in slope stability, foundation and seabed ploughing modelling, the application of boundary conditions is still a challenge,
because the location of the boundary is unknown in MPM.

Boundary conditions have currently been applied to fixed boundaries with a known location. These conditions can be applied directly onto the background grid. In this thesis the concept of applying boundary conditions to the background grid has been expanded to boundaries, which do not coincide with the background grid. This technique can thus also be used for moving boundary conditions. Therefore, the research question of this thesis is: Can boundary conditions on moving boundaries be appropriately applied to the background mesh of an MPM in slope stability problems?

The location of the boundary is not defined by current versions of MPM. Thus an edge detection method was constructed to locate the boundary based on the information provided by MPM. The Volume of Fluid method (VOF) and the Surface Marker Method (SMM), two edge detection methods used in fluid dynamics, have been tested. Moreover, a new implementation of the Level Set Method has been developed in this thesis, which uses a composite Bézier curve to define the boundary. The method has been called the Proximity Field Method (PFM). PFM locates the boundary based on the distance towards a material point, VOF uses the volume of material at a location to determine the location of boundaries and SMM places fake material points at the initial boundary to track it.

The accuracy of VOF proved to be too small for the application of boundary conditions. SMM gave a better representation of the boundary at small strains in comparison to PFM. However, the main advantage of MPM is the possibility of large strain modelling, which SMM could not handle. PFM was able to handle these larger strains and was therefore chosen as the basis for the application of boundary conditions.

PFM’s representation of the boundary was improved to be useful in the application of boundary conditions. Smoothing of the surface together with an equal spacing of the material points in the initial condition have improved the representation of the boundary. Moreover, the computation cost had to be reduced, because it was too high after the initial implementation.

Finally, PFM has been used to apply a surface traction to MPM. The surface traction must be distributed from the boundary to the nodes of the background grid. This technique has been tested by applying a load to the top of a soil slope. As intended, the load is transferred to the background grid and changes according to the location of the boundary. As expected, the deformation of the slope is increased due to the application of the load. So, the concept of applying boundary conditions on moving boundaries to the background grid has been proven to work.