Open granular filter layers are widely applied in bed, bank, and shore protections to reduce hydraulic loads on underlying materials and geotextiles. While traditional design approaches primarily focus on mechanical stability, the transmission and damping of turbulent pressure fluctuations within these filters remain insufficiently understood. This is particularly relevant for the application of natural geotextiles, which are more permeable and mechanically weaker than synthetic alternatives and are therefore more sensitive to fluctuating hydraulic gradients.
This thesis experimentally investigates the propagation and attenuation of turbulent- and wave-induced pressure fluctuations through open granular filter layers, with the objective of validating and extending the spectral framework proposed by Thomas (2023). Physical experiments were conducted in the Hydraulic Engineering flume at Delft University of Technology using filters with thicknesses of 4, 6, and 8 cm. Two vertically aligned pressure sensor arrays were embedded at the top and base of the filter layer, enabling direct measurement of internal pressure fluctuations under both current-driven and wave-induced conditions across a range of flow velocities and water depths.

Pressure time-series were processed using advanced filtering techniques and transformed into power spectral densities. Temporal spectra were converted to spatial (wavenumber) spectra using a convection-velocity-based approach, allowing the damping of pressure fluctuations and the resulting hydraulic gradients to be analysed both per wavenumber and through integrated variance.
The results show broad agreement with the theoretical spectral shape predicted by Thomas (2023), particularly under highly turbulent flow conditions. Damping is found to be primarily governed by geometric parameters, notably the filter thickness and the ratio between water depth and filter thickness (h/D_f). Thicker filters and shallower water depths lead to significantly stronger attenuation of turbulent fluctuations. Flow velocity mainly influences the absolute magnitude of the hydraulic load but does not affect damping efficiency. In contrast, wave-induced pressure fluctuations, characterised by low wavenumbers, experience only limited damping within the filter layer.

By quantifying both spectral damping and transmitted hydraulic loads, this study provides a physical basis for incorporating load-type dependency and geometric scaling into filter design. The findings support more reliable and sustainable design approaches for granular filters and contribute to the safe application of natural geotextiles in hydraulic engineering.

Geotextiles are permeable fabrics used in various civil engineering and construction applications for the protection against erosion and scour. Geotextiles have predominantly been manufactured using synthetic materials due to their durability and precise design pore sizes. However, the environmental concerns associated with synthetic geotextiles have led to the exploration of sustainable alternatives, including natural fibers and biodegradable thermoplastic polymers.

This study addresses the problem of designing stable geotextile filters. The problem statement resolves around the assumption that geotextiles of natural fibers are considered "open" filters. Existing design criteria for open filters do not directly account for load conditions or the use of fibers in the fabric. Instead, they rely on the relationship of the geometrical properties of the base and filter material. To address this gap, a new approach is proposed based on hydraulic pressure gradients. This approach considers the actual gradient and critical gradient at the geotextile interface. To achieve this, the geotextile will be evaluated within the context of an open channel with uniform flow conditions.

The main research objective is to formulate a design method for geotextiles based on the principles of an open filter structures under a single granular filter layer. A comprehensive literature review has been conducted to investigate the hydrodynamic processes that define the actual gradient at the filter/base interface where the geotextile is positioned. The framework of linear wave theory proved to be a valuable tool for investigating and modeling these hydrodynamic processes. To define the actual gradient, the following hypothesis is proposed:

The actual gradient can be defined by adding the average gradient to a turbulent component derived from measured turbulent wall pressure spectra at the top of the filter layer. Based on spectral approach and linear damping, it is hypothesized that these turbulent components undergo damping within the filter layer, resulting in a diminished turbulent component at the filter/base interface.

From the literature review, it can be inferred that the dimensionless turbulent rough wall pressure spectra developed by Blake (1970) offer the most appropriate representation for the relevant hydraulic conditions (rough horizontal bed, uniform open channel flow). In a turbulent wall pressure spectrum, outer scaling variables and inner variables relate to different length scales within the flow, representing large-scale and small-scale fluctuations, respectively. In this hypothesis, it is assumed that the low-frequency region is scaled by the average velocity and water depth, while the scaling variables for the high-frequency region are presented in terms of the shear velocity and nominal diameter of the filter material. By combining both spectra, converting the pressure spectrum to the gradient spectrum, and transforming the spectral domain to the spatial record, the fluctuating gradient can be determined.

The hypothesis was verified using measured data from experiments conducted by Van de Sande (2012) and Wolters & Van Gent (2012). By incorporating Van de Sande's measured dataset into the scaling parameters of the dimensionless pressure spectra and determining the stability parameter for open filters, it was concluded that qualitatively the results align with Van de Sande's findings, indicating stability or instability of the filter layer. However, in some test cases, the hypothesis suggested instability while the experiments indicated stability.

This discrepancy may be due to the fact that while the stability parameter may indicate an unstable filter, it does not necessarily correlate with significant base material transport through the filter layer. In a quantitative analysis, the amount of dimensionless transport of base material was compared to the stability parameter. According to the data presented in figure 4.12, it can be observed that the stability parameter exhibits a value that is three times larger then the stability parameter defined by Schiereck (2012), while not inducing any significant transport of base material. This finding aligns with previous experimental investigations, such as the study conducted by Wolters & Van Gent (2012), which similarly demonstrated that the stability parameter could reach values that are two to three times larger, while still not resulting in notable base material transport.

A direct quantitative comparison was conducted between the measured dataset of Wolters & Van Gent (2012) and the calculated gradients obtained from the hypothesis. The results revealed that the calculated gradients exhibited a comparable magnitude, ranging from 0.25 smaller to 1.50 larger in comparison to the measured gradients reported by Wolters & Van Gent (2012). This indicates a reasonably close agreement between the calculated and measured gradients.

In conclusion, the research objective in this study was to formulate a design method for open geotextiles under a single granular filter layer. To achieve this, it was necessary to take some steps back and define the actual gradients, as well as identifying a suitable method for calculating these gradients. The actual gradient is calculated with the sum of the average gradient and the fluctuating gradient. The fluctuating gradient can be characterized by the turbulent wall pressures, which are derived from the pressure spectrum measured at the top of the filter layer, as described in Blake (1970). Assuming linear damping of the pressures within the filter layer, the actual gradient can be computed at the interface of the geotextile. Consequently, the assessment of stability entails a comparison between this calculated actual gradient and the critical gradient measured by Lemmens (1996).

With a clearer understanding of how to calculate the actual gradients at the geotextile interface, the same approach employed in the hypothesis is applied to address the design of a stable open geotextile under a single granular filter layer. This has been demonstrated through a case study, where the thickness of the filter layer was determined to create a stable filter structure.

Several recommendations can be made to improve the understanding and design methodologies in relation to the hypothesis. Firstly, there is a need for a better understanding of the spectral density of wall pressure fluctuations in open channel flow. This understanding will enable more accurate estimations of fluctuating gradients. Secondly, further research is necessary to incorporate the distribution of pressure at the filter/base interface for non-linear damping. Thirdly, it is advised to conduct tests using modern natural geotextile materials to refine the critical gradient determination and explore alternative approaches, such as considering critical filter velocities. Lastly, it is recommended to extend the design method to encompass wave conditions. Verifying the effectiveness of the design approach under wave conditions through comparison with measured data will ensure its applicability and reliability in practical scenarios.

While further investigations are needed, it still offers a fresh perspective on evaluating the stability of open filter structures. If successfully refined, the design method could become a valuable tool in geotextile design and potentially find applications in other contexts involving "open" structures.

During berthing operations vessels use their bow thruster(s) to improve their manoeuvrability, making them less dependent on the assistance of tugboats. The jet from a bow thruster reflects on the quay wall. It is directed towards the bottom where it reflects, causing high flow velocities over the bed. This may scour the nearby bed when it is left unprotected, leading to instability of the quay wall. Over the years, the shipping industry has been developing continuously, characterized primarily by the upscaling in size of inland- and sea-going vessels. As a result, vessels have more power and larger thruster diameters leading to higher hydraulic loads on quay walls and bed protections of berthing facilities. The most common type of bed protection is rip-rap (partially) penetrated with concrete. However, due to the complex flow field of the reflected jet, the decay profile of the near-bed flow velocities is unknown. This results in uncertainties in the design of bed protections and the required width of these protections that must be penetrated with concrete. In this research, the decay of the near-bed flow velocity in perpendicular direction to the quay wall induced by a 4-channel bow thruster is researched. The eventual goal is to provide a better indication to what extent the bed protection must be penetrated with concrete. Field measurements have been conducted in the North Sea Port of Gent with the Somtrans XXV, one of the largest inland vessels in the Netherlands. The flow velocities near the bed, induced by the bow thruster, have been measured with Acoustic Doppler Velocimeters (ADV), Acoustic Doppler Current Profilers (ADCP) and Ott meters (Ott). The results from the flow velocity measurements have been analysed on three main parameters: influence of the applied bow thruster power, the distance between the measurement instrument frame and the bow thruster and quay wall clearance. The highest flow velocities are measured near the quay wall in the order of 1 m/s reaching up to a maximum of 1.8 m/s. Further away from the quay, the flow rapidly declines towards a more constant level of approximately 0.3-0.4 m/s. To define the maximum load on the bed, the mean flow velocity plus three times the standard deviation is used resulting in a maximum load ranging between 1.6-2.8 times the mean horizontal flow velocity. The Dutch and German guidelines for determining the near-bed flow velocities generally overestimate the measurement results. In addition, the dependency of the Dutch method on the total travelled distance by the jet, based on the sum of the quay wall clearance, the height of the bow thruster above the bed and the distance x from the quay wall, are not reflected in the measurement results. It is recommended that this extensive and unique data set acquired through the field measurements in Gent is further used to analyse the flow field of a reflected jet on a vertical quay wall by validating numerical and scale models. Combining these three different methodologies will contribute to a better understanding of this phenomenon with the eventual goal of optimizing the design of bed protections.

In this thesis, a general method to predict the notional permeability for various structure lay-outs is developed. A numerical model is used to find a characteristic value for different structure lay-outs: the three structures for which Van der Meer determined the P-value, and a fourth structure of which the P-value has to be predicted. The P-value of the fourth structure is predicted by interpolation of the characteristic value of this structure between the characteristic values found for the structures of Van der Meer. The numerical model used is the RANS-VOF model OpenFoam. The developed prediction method uses the total wave induced water pressure over the armour layer as characteristic value. The prediction method is validated for a structure lay-out for which (Kik, 2011) found a P-value of 0.37 by means of physical model testing. A P-value of 0.38 was found by (Kluwen, 2012) for the same structure lay-out by means of more physical model testing. The prediction method predicts a P-value in line with the P-value found by (Kik, 2011) and (Kluwen, 2012). The predicted P-value is 0.35 with this prediction method. A sensitivity assessment has been performed by varying the wave conditions, the porosity of the porous layers of the structure and the Forchheimer parameters applied in the numerical simulations. Results show that the prediction is not very sensitive to changes in the wave conditions or changes in the Forchheimer parameters. And although not confirmed by tests, it seems that the prediction method is not very sensitive for changes in the applied porosities of the porous layers of the structure with unknown P-value. Therefore, the method seems to be a robust method and can be practically used in engineering projects. With this new prediction method for the notional permeability of a breakwater, it is possible to make a more accurate estimate on the notional permeability for more complex rubble mound structures. A more accurate estimate of the notional permeability will improve the accuracy of the initial design of the armour layer in early stages of a project. A next step to further improve the predictions of the notional permeability and to gain a better understanding of the damage of the armour layer of a rubble mound breakwater, is to research the correlation between the wave induced water pressure over the armour layer, the discharge through the armour layer and the flow velocity on top of the armour stones and to research how the combination of these three parameters has influence on the armour layer stability.