The increasing demand for renewable energy sources is driving a significant rise in the adoption of offshore wind energy. Offshore wind turbines are typically supported by large foundation piles driven into the seabed. The primary method of installation is by hydraulic impact hammers. However, this method generates excessive underwater noise among other drawbacks. Consequently, alternative techniques are being explored by both researchers and industry. One promising alternative is vibratory driving, which theoretically produces less underwater noise compared to impact driving. Nevertheless, there remains a substantial amount of energy transmitted into the water column, particularly from the higher harmonics of the driving frequency. While energy at the fundamental frequency is essential for efficient driving, the energy associated with higher harmonics does not contribute to this efficiency and can significantly increase radiated underwater noise. To address this issue, this study proposes a mitigation strategy to block energy transfer at super-harmonic frequencies in the pile-water-soil system. To selectively target these frequencies without affecting the fundamental one, a mitigation approach utilizing locally-resonant metamaterials is proposed. This involves integrating a transition piece between the vibratory hammer and the pile, that incorporates periodically inserted multiple-degrees-of-freedom systems. By manipulating the natural frequencies of these periodic inclusions, the transition piece forms band-gaps at the relevant super-harmonics. Initial findings indicate that this design has the potential to effectively mitigate noise and vibration at targeted frequencies. Nonetheless, further investigations employing more sophisticated models are necessary to confirm these outcomes.@en

Vibratory offshore pile driving offers a potential solution for reducing the underwater noise generated during the installation of foundation piles compared to using impact hammers. Existing noise prediction models are specifically tailored to impact pile driving scenarios. This paper introduces a novel methodology for underwater noise predictions during vibratory pile driving. A non-linear driveability model is utilised to derive realistic non-linear interface friction forces, which are then incorporated into a noise prediction model. The study emphasises the significance of integrating a driveability analysis, revealing substantial differences from traditional models that assume perfect contact between the pile and soil. The authors argue that the proposed model provides more realistic outcomes when considering smooth driving without refusal, in contrast to traditional models designed for impact piling. The results illustrate noticeable deviations in pressure levels and seabed vibrations between the linear and presented methods at the driving frequency and its superharmonics. Furthermore, the research demonstrates that the noise field is highly sensitive to variations in system dynamics and excitation spectrum during driving, using both small- and large-diameter monopiles as examples. This research contributes to developing more effective driving techniques to reduce underwater noise pollution and facilitate sustainable offshore wind turbine installations.

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Periodic fluid-solid layered media exhibit distinctive features that can be utilized in various engineering disciplines, such as selective transmission of guided waves, omnidirectional band-gaps and Fano resonances, depending on the spatial configuration and the material properties of the fluid and solid layers involved. This work utilizes the Thin-Layer Method (TLM) in the study of layered fluid-solid media, by extending the original normal modes-based method to acousto-elastic problems. By means of this development, the band-gap structure of these periodic systems can be analysed and their effect when incorporated in fluid or solid full-/half-spaces can be investigated seamlessly for different periodic arrangements. Conclusively, this study presents a framework to analyse these systems, serving as a basis for non-local continuum theories, as well as unveiling desirable dispersion characteristics for the design of metamaterials.

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This paper presents a new shaker design for the Gentle Driving of Piles method. Specifically, a lab-scale vibratory device has been developed that can simultaneously apply axial and torsional vibrations, both possessing frequency-amplitude decoupling. This design was implemented and tested in a lab-scale experimental campaign, where both pile and soil were extensively instrumented. The monitoring of the dynamic pile and soil behaviours during driving with various installation settings is of utmost importance to comprehend the governing mechanisms of the process. In that manner, the optimization of pile installation may be realized both for axial vibratory driving and GDP. In this work, the frequency-amplitude decoupling is pivotal, as it is showcased that both enhanced installation performance and reduced power consumption can be attained with proper selection of the installation settings and exploitation of high-frequency torsion.

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The increasing demand for renewable energy sources is driving a significant rise in the adoption of offshore wind energy. Offshore wind turbines are typically supported by large foundation piles driven into the seabed. The primary method of installation is by hydraulic impact hammers. However, this method generates excessive underwater noise among other drawbacks. Consequently, alternative techniques are being explored by both researchers and industry. One promising alternative is vibratory driving, which theoretically produces less underwater noise compared to impact driving. Nevertheless, there remains a substantial amount of energy transmitted into the water column, particularly from the higher harmonics of the driving frequency. While energy at the fundamental frequency is essential for efficient driving, energy associated with higher harmonics does not contribute to this efficiency and can significantly increase radiated underwater noise. To address this issue, this study proposes a mitigation strategy to block energy transfer at super-harmonic frequencies in the pile-water-soil system. To selectively target these frequencies without affecting the fundamental one, a mitigation approach utilizing locally-resonant metamaterials is proposed. This involves integrating a transition piece between the vibratory hammer and the pile, that incorporates periodically inserted multiple-degrees-of-freedom systems. By manipulating the natural frequencies of these periodic inclusions, the transition piece forms band-gaps at the relevant super-harmonics. Initial findings indicate that this design has the potential to effectively mitigate noise and vibration at targeted frequencies. Nonetheless, further investigations employing more sophisticated models are necessary to validate these outcomes.@en

The Gentle Driving of Piles (GDP) is a new technology for vibratory (mono)pile installation that is based on simultaneous application of low-frequency/axial and high-frequency/torsional vibrations. In this paper, a numerical modelling framework, that has been developed and successfully applied to axial vibratory driving, is employed to study GDP. In that manner, the major driving mechanism of this method is comprehended on the basis of field observations and numerical analyses. As regards the numerical model, the pile is described as a thin cylindrical shell and the soil medium is treated as a linear elastic layered half-space. The pile-soil coupling is realized via a history-dependent frictional interface, that accounts for friction force degradation due to the accumulation of loading cycles at the soil material points. The redirection of the friction force vector due to the high-frequency torsion manifests as the main driving mechanism of GDP. Finally, the soil disturbance during installation is compared for the cases of GDP and axial vibratory driving, showcasing the dissimilar characteristics of the induced soil motion.

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The installation of foundation piles for offshore wind turbines using traditional hydraulic impact hammers raises concerns about the impact of underwater noise on marine life. To address this issue, the offshore wind industry investigates the use of alternative driving techniques, such as vibratory pile installation, to reduce sound levels and expedite installation. This paper discusses a method for modelling underwater sound generated in vibratory piling and presents sound maps of broadband sound levels. The complete model comprises sub-models, including the generation of the source field and the propagation of the sound in range-dependent shallow water environments. The sound source model utilizes a non-linear three-dimensional pile–soil-water modelling framework tailored for vibratory pile installation in layered media, capturing the coupled pile-soil-water interaction at the source. The sound propagation model employed for generating sound maps is a normal mode model, designed to simulate propagation loss in range-dependent acousto-elastic half-spaces of varying bathymetry. The paper concludes with the theoretical case study of underwater noise emission from vibratory pile installation in the North Sea. Numerical simulations with the adopted modelling framework can be used by marine biologists to assess the environmental impact of underwater sound on marine species.@en

This paper studies the mechanism that leads to the reduction of frictional soil reaction forces during pile driving, termed friction fatigue. We focus on axial vibratory driving, an environmentally friendly monopile installation method, and examine two friction fatigue formulations, i.e. a penetration-based and a cyclic memory mechanism. Friction fatigue plays a pivotal role in pile drivability and post-installation bearing capacity for piles installed via axial vibratory driving. Through numerical analyses and validation against field data from onshore experiments, the efficacy of these memory mechanisms is assessed. The results reveal that the proposed cyclic memory mechanism provides consistently more accurate predictions than the corresponding penetration-based approach, offering a promising option for modelling friction fatigue in vibratory driving. This study advances our understanding of friction fatigue in the context of vibratory driving for offshore monopile installation, emphasizing the need for further numerical and experimental works in this topic.

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This paper presents a computationally efficient model for vibratory pile installation. A semi-analytical finite element (SAFE) model for thin cylindrical shells is derived to represent the pile. The linear dynamic response of the soil medium is described by means of Green's functions via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) to account for the underlying elastic half-space. Furthermore, the non-linear pile–soil interaction is addressed through a history-dependent frictional interface and a visco-elasto-plastic tip reaction model that can be characterized on the basis of standard geotechnical in-situ measurements. The solution to the non-linear dynamic pile–soil interaction problem is based on the sequential application of the Harmonic Balance Method (HBM). The constituent components of the model are first benchmarked against established numerical schemes. Subsequently, model predictions are compared with experimental data collected from field tests. It is demonstrated that the proposed model amalgamates rigorous theoretical elements and promising prediction capabilities in a computationally efficient framework, applicable to engineering practice.

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Gentle Driving of Piles (GDP) is a new vibratory installation technology for tubular (mono)piles. It is characterized by the simultaneous application of low-frequency axial and high-frequency torsional vibrations, envisaged to achieve both high installation performance and reduced underwater noise emissions. The concept of GDP has been demonstrated experimentally in a medium-scale onshore field campaign, showcasing the potential of the method in terms of installation and post-installation performances. To further comprehend the mechanics of the GDP method, the driving process is studied by means of a novel pile–soil model; this framework has been recently developed and successfully applied to the problem of axial vibratory driving. In particular, the pile is treated as a thin cylindrical shell via a Semi-analytical Finite Element (SAFE) approach and a linear elastic layered soil half-space is considered via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs). The pile–soil coupling is realized through a hereditary frictional interface and an elasto-plastic tip formulation, both characterized by standard geotechnical in-situ measurements. The comparison of numerical results with field data is favourable for drivability purposes, showcasing the potential of the numerical framework for the analysis of GDP. Conclusively, the mechanics of the installation process are deciphered and the redirection of the friction force vector – induced by high-frequency torsion – is identified as the main driving mechanism of GDP.

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For offshore wind turbines (OWTs), the monopile comprises the most common type of foundation and vibratory driving is one of the main techniques for monopile installation (and decommissioning). In practice, prior to pile installation, a pile driving analysis is performed to select the appropriate installation device and the relevant settings. However, pile penetration results from a complicated vibrator-pile-soil interaction and better understanding of the latter is necessary for an efficient installation process. During the course of installation, the interface and boundary conditions of the pile continuously alter due to the soil layering and the non-linearity of the soil reaction. In this paper, a set of experimental data from an onshore experimental campaign are employed in a numerical scheme to identify the pile strain field based on in vacuo modes of simpler yet related systems. By mapping the pile strain field onto physically-based shape functions, the evolution of the soil reaction during pile installation can be studied, in order to facilitate the back-analysis of driving records and, by extension, improve pile drivability and vibro-acoustics predictions.

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Gentle Driving of Piles (GDP) is a new technology for the vibratory installation of tubular (mono)piles. Its founding principle is that both efficient installation and low noise emission can be achieved by applying to the pile a combination of axial and torsional vibrations. Preliminary development and demonstration of the proposed technology are the main objectives of the GDP research programme. To this end, onshore medium-scale tests in sand have been performed on piles installed using both impact and vibratory driving methods (including GDP). After presenting the development of a purpose-built GDP driving device and the geotechnical characterisation of the site, this paper covers the execution of GDP installation tests. Focus is on the installation performance of GDP-driven piles, which is discussed with the aid of structural and ground monitoring data. The comparison between piling data associated with GDP and standard axial vibro-driving points out the potential of the proposed installation technology, particularly with regard to the beneficial effect of the torsional vibration component. The findings of this study encourage further development of the GDP method and its future extension to offshore full-scale conditions.

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In this paper, the characteristics of the induced ground motion are studied for two pile installation methods. Specifically, the classical axial vibratory driving is compared with the Gentle Driving of Piles (GDP) method, to investigate the effect of high-frequency torsional excitation in the soil response. For that purpose, a non-linear 3-D axisymmetric pile-soil interaction model - benchmarked against field data for both methods - is used to perform the numerical study. The friction redirection mechanism, that is mobilized due to the torsional excitation in GDP, leads to a different wavefield in the soil medium compared to axial vibro-driving. In the latter only SV-P wave motions are elicited, whereas torsion introduces SH wave motions as well. For the numerical study, the model is comprised by a thin cylindrical shell coupled with a linear elastic layered half-space through a history-dependent frictional interface. The Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) is employed to accurately describe the wave motion in the soil medium. Comparisons in terms of the peak particle velocities (PPVs) and soil particle trajectories showcase significant motion reduction due to redirection of the soil friction forces, which elicits high-frequency SH waves and reduces the SV-P wave motion.

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Gentle driving of piles (GDP) is a new technology for the vibratory installation of tubular (mono) piles that aims to achieve both efficient installation and low noise emission by combining axial and torsional vibrations. To provide a preliminary demonstration of the GDP concept, onshore medium-scale tests in sand were performed in late 2019 at the Maasvlakte II site in Rotterdam (Netherlands). Several piles were installed using both impact and vibratory driving methods (including GDP), with the twofold aim of comparatively assessing (1) the effectiveness of GDP; and (2) the presence of installation effects in the pile response to lateral loading. This work focuses on the latter aspect and presents a quantitative analysis of the installation effects observed in the pile loading test data recorded in the field. Due to soil inhomogeneity across the field, a purely data-based analysis would have not supported objective conclusions, which led to adoption of an alternative approach based on one-dimensional (1D) numerical modeling. To this end, an advanced cyclic p-y model was calibrated for the simulation of the reference pile loading tests, and the values of key parameters were compared to infer quantitative information about relevant installation effects. The results presented herein inform about the promising performance of the GDP method, particularly in comparison to traditional impact hammering. Although the cyclic lateral pile behavior proves affected by the installation process, certain important aspects of installation effects gradually diminish as more loading cycles are applied.

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The ambitious goals towards the decarbonization of the global energy sector have amplified the demand for renewable energy resources. Amongst the renewables, offshore wind possesses a pivotal role in this endeavour, showcasing remarkable growth in recent years. However, this rapid expansion has been accompanied by a series of technical challenges. Foundation installation comprises one of the most critical phases in the construction of an offshore wind farm and engineering advancements in this topic are vital to accommodate this developmental pace. Bottom-fixed foundations are primarily used to support offshore wind turbines and amongst the available concepts, the monopile is the foremost one. The installation of these substructures is most commonly performed via impact hammering. Notwithstanding the robustness and efficacy of this technique, major environmental concerns have been raised due to the significant levels of underwater noise pollution during driving. In view of this alarming issue, alternative and sustainable pile installation techniques have been progressively drawing attention during the last decade and an increasing number of research projects focus on their investigation and development. At present, the offshore wind industry is increasingly adopting vibratory pile driving. The previous method has been successfully employed in onshore projects for decades, albeit its wider use in the offshore environment is hindered due to the incompleteness of available field observations. To boost the improvement of vibratory installation methods, a new technology has been recently proposed by the Delft University of Technology, namely the Gentle Driving of Piles (GDP). The preceding method aims to enhance the installation performance of vibratory driving for tubular (mono)piles and to reduce the associated noise emissions, via the simultaneous application of low-frequency/axial and high-frequency/torsional vibrations. Naturally, the shift to these technologies is accompanied by emerging research questions pertaining to pile installation, vibro-acoustic and post-installation performances. In this thesis, the development of an engineering-oriented modelling framework for axial vibratory driving and GDP is the primary objective, thereby focusing on the topic of sustainable monopile installation.@en

This paper presents a computationally efficient mode-matching method to predict the relative axial motion of two elastic rods in frictional contact. The motion is of the stick-slip type and is non-uniform along the rods. The proposed method utilizes the piecewise linearity of the problem in time and space. The original set of nonlinear partial differential equations describing the dynamics of the coupled system is first reduced to a system of linear, per time interval, ordinary differential equations by means of modal decomposition. The global modes are used for one of the two rods, while for the other rod, different modes are identified per time interval based on the regions in stick or slip phase. Subsequently, the system response is obtained by combining the piecewise linear solutions. A comparison of the solution method proposed with standard numerical techniques shows its advantage both in terms of computational time and accuracy. Numerical examples demonstrate the capability of the method to analyse cases involving either harmonic- or impact-type forces that drive the relative motion. Although the discussion in this paper is limited to the one-dimensional configuration, the approach is generic and can be extended to problems in more dimensions.

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The Alternating Frequency-Time (AFT) Harmonic Balance method has been widely applied in the analysis of non-linear mechanical systems under periodic excitation. Customarily, a periodic displacement is considered as ansatz in a harmonic balance analysis. In the present work, a deviation from the latter ansatz is realized and the periodicity is assumed in the velocity, leading to a linear term in the displacement of the system. The latter approach aims to facilitate the analysis of a certain class of systems, which are characterized by a fast periodic motion and a slow non-periodic motion. The motivation of this study originates in the area of offshore engineering and more specifically in the topic of monopile installation. During vibratory pile installation, the pile is forced into the soil under the combined action of a periodic excitation at the pile top and the self-weight of the pile and the vibratory device. As a result, the pile simultaneously penetrates into the soil as a rigid body (slow motion) and vibrates in the driving frequency and its super-harmonics both as a rigid and a flexible body (fast motion). In this study, the AFT harmonic balance with the ansatz of periodic velocity is implemented in different problem cases. A set of non-linear mechanical systems are analysed, ranging from a single-degree-of-freedom to a continuum, to showcase the potential application of the method and to verify its accuracy.@en

In the original publication, Eqs. (11) and (17) are published incorrectly, and this has been corrected as follows: (Formula presented.) The original article has been revised.

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In this paper, the energy flux in a pile modeled as an elastic shell, is studied theoretically and experimentally. Based on this analysis, a new procedure is proposed to quantify the pile installation efficiency. This procedure is of importance for vibratory installation of the foundations of offshore wind turbines and it is believed to be the first procedure that relies directly on the energy propagating down the pile rather than the energy supplied by the vibratory shaker. The proposed approach is tested on piles installed by two distinct vibratory techniques, i.e. the axial vibratory driving and the recently developed Gentle Driving of Pile (GDP) method. The field data obtained during an experimental campaign were analyzed with the proposed energy flux approach. The cumulative energy flux in the pile normalized by the energy input of the shaker is found to be the best measure for quantification of the installation efficiency. Correspondingly, the main proposition of this paper is that the installation efficiency will be maximized provided that the normalized cumulative energy flux is at its maximum.

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During the last decade the offshore wind industry grew ceaselessly and engineering challenges continuously arose in that area. Installation of foundation piles, known as monopiles, is one of the most critical phases in the construction of offshore wind farms. Prior to installation a drivability study is performed, by means of pile driving models. Since the latter have been developed for small-diameter piles, their applicability for the analysis of large-diameter monopiles is questionable. In this paper, a three-dimensional axisymmetric pile driving model with non-local soil reaction is presented. This new model aims to capture properly the propagation of elastic waves excited by impact piling and address non-local soil reaction. These effects are not addressed in the available approaches to predict drivability and are deemed critical for large-diameter monopiles. Predictions of the new model are compared to those of a one-dimensional model typically used nowadays. A numerical study is performed to showcase the disparities between the two models, stemming from the effect of wave dispersion and non-local soil reaction. The findings of this numerical study affirmed the significance of both mechanisms and the need for further developments in drivability modeling, notably for large-diameter monopiles.

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