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Monopiles supporting offshore wind turbines experience combined moment and horizontal loading which is both cyclic and complex – continuously varying in amplitude, direction and frequency. The accumulation of rotation with cyclic loading (ratcheting) is a key concern for monopile designers and has been explored in previous experimental studies, where constant-amplitude cyclic tests have shown rotation to accumulate as a power-law with cycle number. This paper presents results from laboratory tests in dry sand, which explore the rotation response to constant and variable amplitude, unidirectional and multidirectional cyclic loading. The tests are designed to inform model development and provide insight into key issues relevant to monopile design. Unidirectional tests show behaviour consistent with previous studies and provide a basis for interpreting more complex tests; multidirectional tests provide new insight into the monopile response to multidirectional cyclic loading; and multi-amplitude storm tests highlight salient features of the response to realistic loading. Tests are conducted in both very loose and dense sand, where the behaviour is found to be qualitatively similar.

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... All tests experienced ratcheting and the modelled results are compared by plotting the accumulated displacement or rotation against the cycle number. Richards et al. (2019) performed a series of small-scale long term cyclic loading tests in sand. The pile was tested in both dense and loose sand samples and under both one-way and partial two-way loading. ...

... A ratcheting parameter of = 0.75 fit the experimental results well. This is the same that used for the Richards et al. (2019) study, and so suggests that it gives a good estimate of the accumulation of rotation in sand for scale model loads at 1 g. The results show good agreement of total ratcheting, with a slight overestimation of ratcheting for very large numbers of load cycles. ...

... The long term test of Richards et al. (2019) was also used as a sensitivity analysis under long term loading. 10,000 loading cycles with = 0.2 and = 0 was used with values of 0.65, 0.75 and 0.85. ...

Offshore wind turbines (OWTs) experience a range of two-way and partial one-way cyclic load conditions during their operational lifetime. Cyclic loading with a non-zero mean can lead to ratcheting in the soil, which causes the structure to accumulate displacement and rotation over repeated loading, which can compromise the design limit requirements. In this paper a novel ratcheting model is proposed using a Winkler approach with Masing rules and controlled with just one parameter. The model is validated against 5 experimental setups and 17 long term load tests up to 10 5 cycles, and predicts very well the experimental response, performing comparably with other existing ratcheting models. An OWT from North Hoyle wind farm is also modelled and it is found that the closer the driving frequency is to the resonant frequency, the greater the ratcheting response. This means that for soft-stiff type OWTs, where there is little tolerance between the resonant frequency and driving frequencies, it is crucial to consider the potential of ratcheting during the design phase. The model presented here provides a simple and effective method of predicting future ratcheting with a focus on ease of calibration and implementation into existing numerical analysis tools.

... Model tests to investigate the influence of alternating loading directions can be found in [320,318,316,319]. In many of these experimental studies, the aim was to model the installation of the pile prior to cyclic lateral loading as realistically as possible (e.g. ...

... Even though important findings regarding the influence of installation on the bearing behaviour of piles were obtained from the model tests, their transferability to real-scale piles is not unconditional. In particular, this concerns the installation process itself: while in situ tens of thousands blows are often needed during impact pile driving to bring the pile to its final depth (in particular for monopile foundations for OWT), in the laboratory a few hundred blows are usually sufficient to drive the pile to its final embedment depth [206,316]. ...

... et al., the tests by Richards et al.[316], where almost the same test set-up has been used, are simulated. In contrast to the tests byLeblanc et al., ...

This work presents contributions to the numerical modelling of the installation process and subsequent high-cyclic loading of piles, such as relevant for pile foundations for offshore wind turbines (OWTs). The developed numerical tools are implemented in the finite element code numgeo (www.numgeo.de), which is available for download.
The influence of relative acceleration between soil grains and pore fluid, neglected by the most common hydro-mechanically coupled finite element formulation (u-p formulation) but relevant for pile driving processes with high frequencies, is investigated by a novel analytical solution and various finite elements discretising the fluid displacements in addition to the fluid pressures. It is found that only for very large frequencies (> 50 Hz) with simultaneously high values of hydraulic conductivity (>10-³ m/s) the relative acceleration is of importance. Therefore, the u-p formulation is found to be applicable for the analysis of vibratory pile driving.
Constitutive models for the prediction of the mechanical response of soils to millions of load cycles (so-called high-cycle accumulation (HCA) models) are extended to be applicable for partially drained conditions by incorporation of a so-called adaptive strain amplitude, taking into account changes in soil stiffness during the high-cyclic loading. A HCA model for clay is implemented and applied to the analysis of monopiles for OWTs subjected to cyclic lateral loading with numerous load cycles.
Two different mortar contact discretisation techniques are developed and implemented in the finite element code numgeo. It is demonstrated that a segment-based mortar contact discretisation technique can be superior to an element-based technique in terms of numerical stability for vibratory pile driving in water-saturated soil. A general framework for the formulation of constitutive interface models based on constitutive continuum models is presented. Interface models based on Hypoplasticity with intergranular strain extension, the Sanisand model and the HCA model are formulated. In contrast to existing formulations, the boundary conditions are not only satisfied for the continuum but also for the interface zone, considering all stress and strain components in the interface. The simulation of large-scale cyclic interface shear tests shows that only the novel interface formulations allows to correctly consider the stress conditions in the interface zone.
The simulation of the pile installation process using a (hydro-mechanically coupled) Coupled Eulerian-Lagrangian method, which is extended to dynamic analyses, shows that for dry sand the installation-induced changes in the soil state result in a stiffer response of the pile to subsequent loading compared to simulations without consideration of the installation process. Less permanent deformation is accumulated when the pile is subjected to high-cyclic loading using the HCA model following the installation process. However, for water-saturated initially dense sand and larger pile diameters, such as encountered for foundations for OWTs, less influence of the installation process is found. The better the drainage conditions during driving, the lower the accumulation of permanent deformations during subsequent high-cyclic loading. Lower accumulation of permanent deformations occurs if ideally drained conditions during driving are assumed. In case of clay, jacked piles show less accumulation of deformations when subjected to lateral cyclic loading compared to simulations neglecting the installation process, especially for a larger number of load cycles and for initially overconsolidated soils.

... In order to study the influence of the installation process on the response of piles subjected to lateral (high-)cyclic loading, the model tests performed by Richards et al. (2020) are simulated in this work. The model tests did not only consider onedirectional but also two-directional lateral cyclic loading. ...

... The back-analysis of small-scale model tests on the behavior of piles subjected to high-cyclic loading by Richards et al. (2020) Figure 6. Rotation of the pile in y-direction with respect to the rotation in x-direction in the simulations with and without consideration of the installation process compared to the results of the model tests applying two-directional loading. ...

... a) and b) Dimensions and finite-element mesh of the model tests. c) Photo of the device(Richards et al. 2020) ...

The installation procedure of piles has significant influence on their behavior when subjected to vertical or lateral monotonic or cyclic loading following the installation process. Up to now, the installation induced changes in the soil state are not taken into account in design methods used for the estimation of pile deflection when subjected to lateral loading. In this work, model tests on high-cyclically loaded piles are numerically simulated taking into account the installation process using a Coupled Eulerian-Lagrangian method. Once installed, the pile is subjected to 10,000 lateral loading cycles (tests with one-and two-directional loading are considered), which is simulated using the high-cycle accumulation (HCA) model. It is shown that the incorporation of the installation process leads to better accordance between measurements made in the model tests and the numerical results compared to simulations without incorporation of the installation process. It is concluded that the incorporation of the installation process is necessary in order to capture the lateral loading behavior of piles correctly.

... For a rigid pile foundation embedded in cohesionless soil, cyclic lateral loads can cause a densification or loosening of the surrounding soil (Reese and Van Impe, 2000). In a loose sand, repeated load has been shown to increase stiffness and capacity of single piles (Klinkvort et al., 2010;Nicolai et al., 2017;Abadie et al., 2019b;Richards et al., 2020). A contrary phenomenon is found in dense sand due to the disturbed adjacent soil (Paik, 2010;Nicolai et al., 2014;Baek et al., 2018). ...

... The permanent strains and cumulative deformations of pile foundations subject to two-way cyclic lateral loading are less significant than one-way cyclic lateral loading (Long and Vanneste, 1994;He et al., 2017). Furthermore, the unsymmetrical two-way loadings have been found to cause the highest rate of deflection accumulation for rigid piles at a constant maximum load magnitude Arshad and O'Kelly, 2017;Richards et al., 2020). The multi-directional lateral loadings can induce a more significant increase in lateral displacement accumulation than a unidirectional loading, which has been verified via numerical methods (Su and Li, 2013;Lovera et al., 2021;Jenck et al., 2021) and centrifuge experiments (Rudolph et al., 2014;Frick and Achmus, 2019;Richards et al., 2020). ...

... Furthermore, the unsymmetrical two-way loadings have been found to cause the highest rate of deflection accumulation for rigid piles at a constant maximum load magnitude Arshad and O'Kelly, 2017;Richards et al., 2020). The multi-directional lateral loadings can induce a more significant increase in lateral displacement accumulation than a unidirectional loading, which has been verified via numerical methods (Su and Li, 2013;Lovera et al., 2021;Jenck et al., 2021) and centrifuge experiments (Rudolph et al., 2014;Frick and Achmus, 2019;Richards et al., 2020). ...

Pile foundations for many infrastructures, such as bridges, oil rigs, electricity towers, wind, and wave turbines, sustain cyclic lateral loads from wind or wave actions. The long-term response of pile foundations under cyclic lateral loading conditions is one key factor to consider in the design, which is commonly explored by cyclic pile load tests or step-by-step numerical procedures with empirical degradation factors. Shakedown analysis provides an alternative and efficient means of predicting limiting loads of the pile foundations against excessive accumulated permanent deformation under cyclic lateral loads. In this study, a generalised shakedown approach is proposed, with flexible linear modifications, to solve the stability problem of three-dimensional geotechnical structures under cyclic loads. It provides a novel concept of pursuing the final residual stresses at the shakedown limit in one cycle period. The co-operation between ABAUQS and Python in this approach offers a great potential for extended applications. The generalised shakedown approach is first implemented into classical problems with Von-Mises, Tresca, and hyperbolic Mohr-Coulomb criteria considering an associated or a non-associated flow rule. In central-holed plate problems, the approach demonstrates its remarkable performance for the accurate and efficient prediction of shakedown behaviour. The general feasibility of the approach is further proved by solving pavement problems. Both the shakedown limits and the residual stress distributions against depth are in excellent agreement with theoretical results. The main focus of the current research is concerned with the shakedown behaviour of pile foundations under cyclic lateral forces. A series of well-designed models is utilised to examine the effects of pile geometry, soil property, and interaction parameters. Both rigid pile and flexible pile are studied. The results reveal a distinguished capability of the two piles enduring repeated moment, horizontal forces, or a combination. The ratio of shakedown limit to plastic limit decreases with the rise of length to diameter ratio. Moreover, a two-way repeated loading yields a smaller shakedown limit than a one-way cyclic loading. Finally, a study of pile group efficiency is carried out using the current approach to check the influence of group effects on the shakedown limit. A general pile group design procedure is followed according to the previous conclusions, which demonstrates the great importance of shakedown analysis in the design of pile foundations.

... high f b and low f c ). As a whole, there is a high probability that the cyclic loading intensity f b is lower than 0.25 during normal operation conditions in real site (Richards, Byrne, and Houlsby 2019). There also remains a difference between the large number of extreme cyclic loads applied to the model tests and the true storm loads that act on OWT prototypes to investigate the pile failure mechanism, with a particular focus on the accumulated tilt. ...

... It can be seen that tilt is liable to be stable in test CT11 and even decreases in tests CT1 and CT2 after 10000 cycles, which are similar consequences to those reported by Rudolph, Grabe, and Bienen (2014) and means that the cyclic plateau state may be impacted by the loading magnitude. The variation in a with f b is provided in Figure 9a, which is opposite to the constant parameter a ¼ 0.31 for the monopile foundation in sand (LeBlanc, Houlsby, and Byrne 2010), a ¼ 0.28 for the suction caissons in layered soil (Zhu et al. 2018) and the variable a that depends on the relative density D r , cyclic symmetry f c and spread angle U in fanloading (Truong et al. 2019;Richards, Byrne, and Houlsby 2019). However, a is the critical part to induce the accumulated rotation that exceeds the SLS and ULS limitations, thus resulting in failure. ...

... It is believable that the investigations and interpretations of small-scale tests in this study can assist with the in situ design of a dynamic response under cyclic loading. Yet, it is noted that there is still a lack of experience in applying small-scale response to prototypes (Richards, Byrne, and Houlsby 2019); hence, field tests and comprehensive similitude relationships need to be carried out for verification and calibration scale test results. Besides, the wind and wave loading directions were assumed to be collinear in this test, and further investigation should focus on the misalignment of wind and wave loading directions, as well as various relative densities and layered soil. ...

Monopiles are popular solutions as the foundation to support offshore wind turbines (OWTs), which suffer from various amplitudes of continuous lateral cyclic wind and wave loading. The accumulation of tilt and change of the natural frequency of OWTs under cyclic loading have become crucial issues for OWT design. Hence the monopile-tower-soil system was established at the small-scale level based on similarity laws with a suit of constant-amplitude and multi-amplitude tests in dense sand. Two sets of gear-driving assembly were successfully set up to achieve the application of cyclic loading to the model OWT. The amplitude and symmetry of cyclic loading were specified as three indicative regions according to those of real wind farms. On the basis of test results, the two-way loading was found to be the most hazardous situation and the preloading condition led to a high accumulation of tilt. The change of natural frequency was controlled by the load magnitude and tended to increase during cyclic loads, while a sharp decrease was observed when sand subsidence was generated. The post-cyclic lateral capacity seemed to be a slight increase compared with the static capacity. The relevant analyses based on test results can provide practical recommendations for OWT design.

... Although non-stationary and multi-directional in nature (Rudolph et al., 2014;Richards et al., 2019), only unidirectional lateral loading applied in single-amplitude cycles was considered in this first study. The core of this work's FE simulation programme relates to the cases listed in Table 3, Table 3. Numerical simulation programme and corresponding T b -T c values inferred from FE results based on equation (6) with a single accumulation exponent (α = 0·5) ...

... Experimental and numerical results regarding monopile tilt are compared in Fig. 12 in relation to pure one-way cyclic loading (ζ c ¼ 0) of different amplitude ratio ζ b (equation (5)) -3D FE tilt trends were plotted by selecting, for each cycle, monopile rotation values associated with the maximum load amplitude. The 1g small-scale experimental results from Richards et al. (2019) (Fig. 12(a) -D r ¼ 1%; Fig. 12(b) -D r ¼ 60%) and LeBlanc et al. (2010) (Fig. 12(c) -D r ¼ 4%; Fig. 12(d) -D r ¼ 38%) were selected for semi-quantitative comparison. A well-known point of attention with regard to 1g physical modelling relates to the scaling of sand's dilatancy, which is inherently stress dependent (Bolton, Fig. 11. ...

... Similarly, Fig. 15 presents a comparison between numerical T c -ζ c trends and those associated with selected experimental datasetsnamely, from LeBlanc et al. (2010); Nicolai & Ibsen (2014); Albiker et al. (2017) and Richards et al. (2019). In agreement with observations by LeBlanc et al. (2010), the T c values emerging from numerical simulations are markedly insensitive to D r . ...

Serviceability criteria for offshore monopiles include the estimation of long-term, permanent tilt under repeated operational loads. In the lack of well-established analysis methods, experimental and numerical research has been carried out in the last decade to support the fundamental understanding of monopile–soil interaction mechanisms, and the conception of engineering methods for monopile tilt predictions. With a focus on the case of monopiles in sand, this work shows how step-by-step/implicit, three-dimensional (3D) finite-element (FE) modelling can be fruitfully applied to the analysis of cyclic monopile–soil interaction and related soil deformation mechanisms. To achieve adequate simulation of cyclic sand ratcheting and densification around the pile, the recently proposed SANISAND-MS model is adopted. The link between local soil behaviour and global monopile response to cyclic loading is discussed through detailed analysis of model prediction. Overall, the results of numerical parametric studies confirm that the proposed 3D FE modelling framework can reproduce relevant experimental evidence about monopile–soil interaction, and support future improvement of engineering design methods.

... This paper extends the work of Richards et al. (2019) and specifically addresses the important issue of stress level, presenting the response of a monopile in dry sand to monotonic, unidirectional cyclic and multidirectional cyclic loading at three g-levels. ...

... Ratcheting is interpreted in terms of accumulated mean displacement at the load application point (Δu M ), following the approach of Richards et al. (2019), but with displacement instead of rotation as the strain variable. ...

... This implies that for a given mean load H AV and cyclic load amplitude H CYC , the direction of cyclic loading relative to the mean load has an insignificant impact on the cyclic response. Ratcheting is also seen to occur in the direction of the mean load at all stress levels, regardless of the cyclic loading direction, in agreement with Richards et al. (2019). These observations have important modeling implications and suggest that misaligned wind and wave loading may be as damaging as aligned wind and wave loading. ...

Monopile foundations supporting offshore wind turbines are exposed to cyclic lateral loading, which can cause accumulated pile displacement or rotation and evolution of the dynamic response. To inform the development of improved design methods, the monopile's response to cyclic lateral loading has been explored through small-scale physical modeling at 1g and in the centrifuge, as well as at large-scale in the field. There are advantages and disadvantages to each physical modeling technique, and the response may be most efficiently explored through a combination of modeling techniques. However, stress levels vary significantly between these techniques, and only centrifuge testing can simulate full-scale stress levels. This paper explores the effect of stress level on the response of a monopile foundation in dry sand to monotonic, unidirectional cyclic and multidirectional cyclic lateral loading with small-scale tests at 1g and in the centrifuge at 9g and 80g. With an identical setup at each g-level, stress-level effects were isolated. Qualitatively, the responses are similar across the stress levels, but some important quantitative differences are revealed. In particular, the rate of accumulation of pile displacement and the rate of change of secant stiffness under cyclic loading are found to reduce with increasing stress level. The results highlight the need to simulate full-scale stress levels to thoroughly understand foundation behavior, but also demonstrate the qualitative insight that can be gained through 1g physical modeling. The data and trends presented in this paper provide input for the modeling of monopile responses at different stress levels.

... The comparison of the 1D and 0D models provides confidence that similar ratcheting parameters can be used in each of these approaches. The importance of stress level and scale needs to be further explored, e.g., Richards et al. (2020). • Experimental results from model-scale tests (e.g., LeBlanc et al. 2010b;Klinkvort 2012;Abadie 2015;Kirkwood 2015) demonstrated a change in secant stiffness with load history. ...

... However, full-scale monopile loading is likely to be multidirectional. It is anticipated that multidirectionality may have a beneficial effect on the accumulated rotation and any subsequent change of foundation properties (e.g., damping and stiffness) (e.g., Richards et al. 2020). • The PISA tests identified that rate effects are important for both the Cowden clay and the Dunkirk sand site, France (Byrne et al. 2020b;McAdam et al. 2020). ...

This paper explores the application of a numerical method for modeling pseudorandom cyclic loading, at very large cycle numbers , to the design of offshore wind turbine foundations. The work expands the development of a novel constitutive modeling framework, the hyper-plastic accelerated ratcheting model (HARM), for which the key constitutive equations and the calibration method are presented. HARM captures both the nonlinear hysteretic behavior during cycling and the accumulation of permanent deformation (ratcheting) with large cycle numbers in a rigorous, yet computationally efficient manner, enabling the computation of foundation response over a lifetime of loading. This paper demonstrates how the approach can be applied to the cyclic pile field testing from the pile soil analysis (PISA) project. Following calibration, the model is used to assess pile response to three load signals representative of operational and extreme loads throughout the lifetime of a full-scale wind turbine foundation: (1) a short storm, (2) a 35-h storm, and (3) lifetime loading. The paper discusses how computational efficiency can be achieved while maintaining a high level of calculation accuracy.

... Numerous experimental investigations using small-scale model tests (see e.g. (Leblanc et al., 2010;Yu et al., 2015;Arshad and Kelly, 2017;Rudolph et al., 2014;Richards et al., 2019)) and centrifuge tests (Li et al., 2010;Bayton et al., 2018;Truong et al., 2019) are reported in the literature which are suitable for the present purpose. Being well described and often referred to, the small scale experiments performed by Leblanc et al. (Leblanc et al., 2010) are considered in this work. ...

... As mentioned beforehand, the driving force used in the experiments performed by Leblanc et al. (Leblanc et al., 2010) is unknown. However, Richards et al. (Richards et al., 2019) have performed very similar tests at the same institute (Oxford University) using almost identical geometrical specifications for the model tests. For these tests the driving force is known and has been adopted for the simulation of the tests by Leblanc et al. as well. ...

The back-analysis of model tests on piles subjected to high-cyclic lateral loading using the high-cycle accumulation (HCA) model is presented. The installation of the pile prior to the lateral loading is taken into account using a Coupled-Eulerian-Lagrangian method. A comparison between the measured pile rotation and the results of simulations with incorporation of the installation-induced soil changes as well as simulations assuming wished-in-place initial conditions is made. A distinct influence of the installation process on the lateral response of the pile is observed. The installed piles exhibit larger resistance and less accumulation of deformation during the cyclic loading. The simulations taking into account the installation process are in better accordance with the measurements in the model tests compared to the wished-in-place simulations. It is concluded that the consideration of the installation process in a back-analysis of driven piles subjected to monotonic or cyclic loading is of great importance.

... Furthermore, the model testing setup is usually solely Energies 2020, 13, 3915 8 of 22 either one-way or two-way, whereas the loading on an offshore wind foundation is a combination of the two with cyclic load packets of different means and ranges. However, recent scaled tests by Richards et al. [17], Truong et al. [18], and Abiker and Achmus [19] show that the effect of two-way loading is less severe than the ones previously reported in LeBlanc et al. [11]. It is shown that the load factor for partial two-way loading factor T c can be reduced from 4, as originally presented, to a number in the range of 2-3, which has a significant impact on the effect of accumulated rotation considering the total number of cycles in a given storm. ...

... Albiker & Achmus [19] Presented a model for stiffness degradation in a finite element model Applicable to one-way loading in drained conditions Method compared to and validated against Li et al. [10] Richards et al. [17] Laboratory scaled tests for rigid monopiles in sand Partial two-way loading results in a much higher degradation and leads to more rotation accumulation than one-way loads, however with a smaller factor than LeBlanc et al. [11] Tests were performed on a rigid pile in sands for up to 10,000 loading cycles. The response of the monopile to multi-directional storm loading was also studied ...

Monopiles supporting offshore wind turbines can experience permanent non-recoverable rotations (or displacements) during their lifetime due to the cyclic nature of hydrodynamic and aerodynamic loading exerted on them. Recent studies in the literature have demonstrated that conventional cyclic p–y curves recommended in different codes of practice (API-RP-2GEO and DNVGL-RP-C212) may not capture the effects of long-term cyclic loads as they are independent of the loading profile and the number of applied cycles. Several published methodologies based on laboratory scaled model tests (on sands) exist to determine the effect of cyclic lateral loads on the long-term behaviour of piles. The tests vary in terms of the pile behaviour (rigid or flexible pile), number of applied loading cycles, and the load profile (one-way or two-way loading). The best-fit curves provided by these tests offer practical and cost-efficient methods to quantify the accumulated rotations when compared to Finite Element Method. It is therefore desirable that such methods are further developed to take into account different soil types and the complex nature of the loading. The objective of this paper is to compare the performance of the available formulations under the actions of a typical 35-h (hour) storm as per the Bundesamt für Seeschifffahrt und Hydrographie (BSH) recommendations. Using classical rain flow counting, the loading time-history is discretized into load packets where each packet has a loading profile and number of cycles, which then enables the computation of an equivalent number of cycles of the largest load packet. The results show that the loading profile plays a detrimental role in the result of the accumulated rotation. Furthermore, flexibility of the pile also has an important effect on the response of the pile where predictions obtained from formulations based on flexible piles resulted in a much lower accumulated rotation than tests based on rigid piles. Finally, the findings of this paper are expected to contribute in the design and interpretation of future experimental frameworks for Offshore Wind Turbine (OWT) monopiles in sands, which will include a more realistic loading profile, number of cycles, and relative soil to pile stiffness.

... So, they are recommended by DNV (DET NORSKE VERITAS) code to be the well suited foundation type in the offshore wind power industry for water depths below 25 m [1]. Richards and Byrne [2] pointed out that 87% of the built foundations of offshore wind turbines are monopile foundations with large diameters. In recent years, monopiles are also widely used in Jiangsu, Zhejiang and other coastal areas of China where the surface layer of the seabed is mostly soft soil, while the bottom layer of the seabed is mainly fine sand. ...

... Model experiments: Goit et al. [22] conducted dynamic experiments model soil-pile tests on a shaking table; Bhattacharya et al. [23] studied dynamic soil-pile interaction using a 1 g scale model test; Manna and Baidya [24] calculated the dynamic stiffness and damping of a slender pile and observed that the stiffness and damping decrease as the amplitude of load increases; Mohamed and Hesham [25] investigated the lateral vibration performance of two full-scale large-capacity helical piles and one driven pile installed in overconsolidated and structured clay, and observed a similar phenomenon to Manna and Baidya [24]; Lombardi et al. [5] investigated changes in pile natural frequency and damping after 32,000-172,000 cycles of horizontal loading; He et al. [26] studied the decreases of the pile's natural frequencies with the existence of a scour hole; Futai et al. [4] measured the natural frequency of piles in centrifuge tests by FFT (Fast Fourier Transform), and investigated the influences of the density of sand and the ratio of free length to embedded depth; Leblanc et al. [27] carried out a series of laboratory tests where a stiff pile in dry sand was subjected to 8000-60,000 cycles of combined moment and horizontal loading, and presented the accumulated rotation and changes in stiffness after long-term cyclic loading; Richards et al. [2] presented results from laboratory tests in dry sand, which explored pile rotation with multidirectional cyclic loadings. ...

Monopiles are widely used to support offshore wind turbines as a result of the extensive development of offshore wind energy in coastal areas of China. An offshore wind turbine is a typical high-rise structure sensitive to dynamic loads in ocean environment such as winds, water waves, currents and seismic waves. Most of the existing researches focus on elastic vibration analysis, bearing capacity or cyclic degradation problems. There’re very few studies on vibration of monopiles, especially considering the influence of static loads with different amplitudes, directions, and loading-unloading-reloading processes. In this paper, laboratory-scale 1 g model tests for a monopile in dry sands were carried out to investigate the frequency responses of the monopile under different loading conditions. The bearing capacities of the model monopile were obtained as references, and dynamic loads and static loads with different amplitudes were then applied to the monopile. It was found that (1) the first resonant frequency of the monopile decreases with the increase of dynamic load amplitudes; (2) the first resonant frequency of the monopile steadily increases under the lateral static load and loading-unloading-reloading processes; (3) the frequency responses of the monopile with static loads in different directions are also quite different; (4) damping of the monopile is influenced by the load amplitudes, load frequencies, load directions and soil conditions. Besides, all the tests were conducted in both loose sand and dense sand, and the results are almost consistent in general but more obvious in the dense sand case.

... Figure 7A illustrates the lateral displacements of the monopile subjected to different loading conditions, while Figure 7B The loading characteristics vary according to the significant spatial variations of the wind and waves in the application area, but the most frequently used cyclic loading frequencies are in this range. 39 In the initial model, loading was applied with a frequency of 0.16 Hz, and then parametric studies were carried out with different frequencies. ...

Offshore wind turbines play a critical role as a renewable energy source and are experiencing continuous growth in usage. Both the design and implementation phases of constructing these structures present difficulties. It is crucial to ensure these structures are built to resist such conditions, assuring their durability, as they are exposed to lateral external influences such as wind and wave loads. This study investigated how monopile foundations behave in saturated sandy soil under cyclic loading. Pore water pressure accumulations in saturated sandy soil, monopile head lateral displacements, and vertical settlements around the monopile are investigated using the hypoplastic material model and two‐phase element with the ANSYS finite element program. Analyses conducted in this study demonstrated that lateral cyclic loads could cause excessive pore water pressure accumulations around the monopile, leading to displacements in the monopile head and soil settlements around it, highlighting the importance of carefully considering loading characteristics during the design process to provide the security and longevity of offshore wind turbines.

... The hyperplastic ratcheting models can be divided into series and parallel versions by arranging the individual surfaces in different ways. As described by Abadie (2015) and Richards (2019), it is most obvious and possibly computationally beneficial to construct models in series when computing strains from a stress input since strains are addictive. For the parallel version, stresses are additive and the same strain is applied to each parallel spring-slider elements. ...

Fatigue life is an important factor to be considered in foundation design of offshore wind turbines (OWTs), and accurate prediction of fatigue damage is dependent on an appropriate foundation model. Currently, the rigid foundation is widely used to model the monopile foundation in most aero-hydro-servo-elastic simulation tools, and soil stiffness and damping are not considered. This will lead to an inaccurate estimation of fatigue damage of monopile-supported OWTs. Given this limitation, hyperplastic ratcheting model is incorporated into FAST v7, the variations of stiffness, damping and accumulated displacement for monopile-supported OWTs subjected to cyclic loadings are well considered. The validity of the implementation is demonstrated by presentation of non-linear soil resistance-displacement curves, and a series of hysteresis loops can be observed. Based on this integrated tool, extensive simulations and analyses for monopile-supported OWTs under different environmental states are performed. Furthermore, the effect of pile-soil interaction on fatigue life of monopile is quantified. The aim of this paper is to provide an accurate model to estimate fatigue life of monopile-supported OWTs.

... We take as an example the loading of a model monopile in loose sand, see Richards et al. (2018), Richards (2019). The "stress" and "strain" variables in this case in fact represent the applied moment on the model monopile (in Nm) and the rotation (in degrees), but we retain the σ, ε notation for consistency with the rest of this paper. ...

... RUDOLPH & GRABE 2013; RUDOLPH et al. 2014;LE et al. 2017;RICHARDS et al. 2020).The results are not comparable because the variation of loading direction was executed differently.DÜHRKOP & GRABE (2008) andRUDOLPH & GRABE (2013) carried out 1g scale model tests with one-way cyclic lateral loading. The angle of loading direction in the horizontal (x-y) plane was varied continuously and swept an angle from 0° (unidirectional) to 120° (multidirectional).RUDOLPH et al. (2014) carried out very similar investigations in the centrifuge. ...

Monopiles are the preferred foundation for offshore wind turbines in Europe. These large-diameter pipe piles transfer predominantly horizontal loads to the soil by means of lateral bedding. The piles are commonly installed by impact driving. Vibratory driving as alternative installation method has advantages regarding installation time, fatigue and environmental aspects. However, the experiences with this installation technique for offshore foundations are limited. There are concerns regarding the influences on the load-bearing behaviour. To close this gap, comparing scale model tests were carried out with impact and vibratory driven pipe piles.
During the installation of the model piles, forces and motions were measured at the pile head and radial stresses were measured in the soil. Soil stress developments known from impact driven piles were also witnessed in certain cases of vibratory installation. In such cases, a specific 'vibratory driving mode' could be identified from the pile head motion. After end of driving, increased soil stresses remained especially near the pile toe ('installation effect').
During subsequent cyclic loading, the load-displacement behaviour of the first cycle, the displacement accumulation as well as lateral stiffness over cycle count and the further development of soil stresses were analysed. Different lateral behaviour depending on the installation parameters could be identified. The 'certain' vibrated piles mentioned above showed similar lateral behaviour as impact driven piles while other vibrated piles behaved softer. Due to changes of loading direction, a back-accumulation of pile head displacement together with re-arrangements of soil stresses could be witnessed. The increased soil stresses near the pile toe observed at certain piles largely remained after cyclic loading.
For the static lateral calculation of monopile foundations, a one-dimensional bedded beam (Winkler foundation) on nonlinear springs (p-y curves) is commonly used. A modified p-y approach considering the soil stresses due to pile installation effects was developed and shows good agreement with the first loading cycle of each model test. For offshore cases, the influence of increased soil stresses near the pile toe on the static lateral behaviour was predicted as well. The activation of lateral bedding below the point of zero displacement ('toe kick') is decisive for this behaviour. For the lower displacement accumulation during cyclic loading in case of increased soil stresses, a possible explanation could be found as well.

... In order to study the effects of multi-directional cyclic loading on the lateral response of monopiles, small-scale experimental studies have been recently performed, e.g., regarding the application of T-and L-shaped loading paths (Figs. 3(c)-3(d)) to investigate unexplored load misalignment effects (Richards, 2019;Richards et al., 2020Richards et al., , 2021. In this respect, the combination of static and cyclic load components is typically regarded as an idealised representation of, respectively, slow/nearly-steady wind loading and substantially variable (cyclic) wave loading. ...

Offshore monopile foundations are exposed to misaligned wind and wave loadings, which are respectively dominated by (nearly) static and cyclic load components. While the response of these systems to unidirectional cyclic loading has been extensively investigated, only a few studies have been devoted to the realistic case of misaligned static and cyclic loads, and particularly to the effects of such misalignment on the accumulation of pile rotation under prolonged cycling. This paper presents a 3D finite-element (FE) modelling study on the relationship between load misalignment and cyclic monopile tilt under drained conditions, based on the use of the SANISAND-MS model to enable accurate simulation of cyclic sand ratcheting. After qualitatively identifying the relationship between relevant loading parameters and cyclic stress/densification mechanisms in the soil, specific parametric studies are performed to explore the impact on pile tilt accumulation. The results show that, in comparison to unidirectional loading, misaligned static-cyclic loading gives rise to lesser-known pile-soil interaction mechanisms: when the direction of cycling deviates from that of the static load, ''cyclic compression'' and ''direct cyclic shearing'' mechanisms begin to co-exist. This is quantitatively captured by a newly proposed empirical equation for monopile tilt calibrated against the 3D FE simulation results obtained in this work.

... When parcel (equal to ) was applied, the piles experienced an overall unloading and responded to cyclic loading with a permanently open gap, which explains the drop in as a consequence of lateral resistance being provided only by the soil below the gap. With no further gap opening, gradually increased during cycling, in a way already reported in the literature based on small-scale pile tests in dry sand (i.e., without appreciable gapping effects) (Klinkvort et al., 2010;LeBlanc et al., 2010;Abadie, 2015;Abadie et al., 2019;Richards, 2019). ...

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). While the results of the installation tests are presented by Tsetas et al. (2023), this work focuses on the post-installation performance of GDP-driven piles under a sequence of slow/large-amplitude (cyclic) and faster/low-amplitude (dynamic) load parcels. The field data point out the influence of onshore unsaturated soil conditions, which result in complex cyclic pile stiffness trends due to the interplay of pile–soil gapping and soil’s fabric changes. The pile stiffness under small-amplitude vibrations is strongly correlated with the previous response to large load cycles, and noticeably frequency-dependent for load cycles with a period lower than 1 s. Overall, the post-installation performance of GDP-driven piles appears to be satisfactory, which encourages further development and demonstration at full scale.

... Wave-induced forces may be capable of inducing a dynamic response which may be detrimental to structural and foundation integrity if not properly accounted for in the design process, as a dynamic response can increase the effects of fatigue and accumulated foundation displacement (Richards et al. 2020). Monopiles for offshore wind turbines are typically designed, so that the structural natural frequency is around two or three times the frequency of severe storm waves (Kallehave et al. 2015) and in between the rotor-and blade-passing frequencies of the turbine. ...

We investigate the harmonic structure of wave-induced loads on vertical cylinders with dimensions comparable to those used to support offshore wind turbines. Many offshore wind turbines are designed, so the structural resonance is two or three times the fundamental wave loading period, which may be excited by higher harmonics of wave loading. The suitability of a ‘Stokes-type’ model for force is examined. We analyse experimental data for unidirectional and directionally spread sea-states. We demonstrate that approximate harmonic components may be extracted from a random time series, using a novel signal processing method. The extracted harmonics are shown to follow a ‘Stokes-like’ model, where the higher harmonics in frequency are proportional to the n-th power of the linear inline force component and its Hilbert transform. Results show that the third harmonic component of force is fitted less well by this model, which is consistent with the literature. A key new result is that the harmonic coefficients for spread and unidirectional seas are nearly identical when fitted as powers of the linear inline force and its Hilbert transform. This finding has the potential to greatly simplify the process of generating harmonic data for new wavelength to cylinder and wavelength to depth ratios. This also implies that the size of the inline component of the $$n\textrm{th}$$ n th harmonic for force in a directional sea relative to the same component in a unidirectional sea scales as $$\cos ^n \sigma _\theta $$ cos n σ θ , where $$\sigma _\theta $$ σ θ is the rms directional spreading angle of the incident wave field. Hence, higher harmonics will be of less importance in directionally spread seas than unidirectional ones. We show that the computationally fast harmonic decomposition approach taken here can reproduce the shape and magnitude of the loading from non-breaking waves waves in a wide range of realistic unidirectional and directionally spread sea-states. The proposed force model has potential as an engineering tool for computationally fast prediction of nonlinear wave loads.

... • the influence of long-term quasi-static cyclic loading on pile response and permanent deformation (e.g. Leblanc et al., 2010;Houlsby et al. 2017;Richards et al. 2019;Staubach and Wichtmann 2020;Klinkvort et al. 2020; and currently under development, the PICASO project, Byrne et al. 2020;) • better integrated structural and geotechnical design tools (e.g. the REDWIN project, Skau et al. 2018;the WAS-XL project, Paget et al., 2020). ...

The seismic response of monopile foundations is a growing area of research as the offshore wind industry expands worldwide, including in earthquake prone regions of the world. This paper presents dynamic centrifuge tests aimed at investigating the dynamic response of monopiles in both dry and saturated sandy soils. The latter case includes soil liquefaction under strong input motions, with measured excess pore pressures indicating liquefaction. The natural frequency of the monopile-soil system is experimentally determined by measuring the response to a sine sweep motion. Strong earthquakes are then applied at this frequency and its harmonics. This paper discusses the response of the monopile in terms of the peak accelerations observed in the dry and saturated tests, as well as using response spectra and amplification ratios. The dynamic bending moments along the pile are also measured to infer the bending moment profile with depth. Finally, two identical monopiles are pushed-over in each of the centrifuge tests to establish the pre and post-earthquake monotonic response, including the lateral stiffness and capacity, which are compared for the dry model tests and the saturated case.

... As more offshore wind farms are planned/constructed in liquefiable soil sites, monopile behavior under different soil drainage conditions needs critical assessment. Many efforts from experimental perspective have been devoted for such a purpose, spanning from small-scale single gravity tests (LeBlanc et al., 2010;Richards et al., 2020) to centrifuge tests (Klinkvort, 2013;Truong et al., 2019). However, due to the practical difficulties in test design and restrictions from test equipment, most experimental works have been limited to dry or fully drained load conditions. ...

Monopile response under undrained conditions in sand is gaining increasing interests owing to the recent development of offshore wind farms in seismic regions. Pore pressure evolution in liquefiable soil can significantly reduce the strength and stiffness of the soil which in turn affects the structural dynamic response. Several numerical models have been developed in the last two decades to enhance understanding of the mechanism of monopile–soil interaction with the existence of pore water pressure. In this study, the effects ofgeometry and static vertical load on monopile lateral response were studied using three-dimensional finite element methods that consider the existence of lateral cyclic load-induced pore water pressure. To achieve reliable simulation results of pore pressure development and pile displacement accumulation during cyclic loading, the simple anisotropic sand model with memory surface for undrained cyclic behavior of sand was adopted. For piles with the same diameter, the accumulated pile head displacement during lateral cyclic loading decreased linearly with increasing pile embedded length but increased with increasing eccentricity. Static vertical load had minor effects on pile cyclic lateral response. The distributions of mean effective stress and pore water pressure in the soil domain were presented. The pile reaction curve (cyclic soil reaction against pile defection) of the monopile was extracted. The numerical results aim to provide reference for optimized engineering design procedures.

... ey believed that the cumulative stress and deformation of pile foundation under horizontal cyclic loading was related to the unloading stiffness, and the expression formula was given. Arshad [17] and Richards et al. [18] compared the model test of one-way and two-way cyclic loading and found that under the same load amplitude, the cumulative deformation caused by twoway cyclic loading was greater than that caused by one-way cyclic loading. Bolton [19], Alizadeh, Davisson [20], Little [21], Long [22], and Verdure [23] established a logarithmic function or power function model between the development trend of pile foundation's cumulative deformation and the number of cycles under horizontal cyclic load through model tests and field tests. ...

In order to study the cumulative damage and failure characteristics of long spiral belled pile under horizontal cyclic loading of offshore wind and waves, a series of indoor experiments on single piles under horizontal cyclic load were carried out. The cycle times as well as load amplitude at the same frequency were considered during the horizontal pseudo-static cyclic tests. On the basis of the distribution of pile deflection, bending moment, and Earth pressure around the pile, the pile-soil interaction was comprehensively discussed. The cumulative energy dissipation characteristics were introduced to describe the damage of test piles. Meanwhile, the effects of load amplitude and cycle times on the cumulative damage of long spiral belled piles were discussed. A power function model for energy dissipation coefficient prediction under multi-stage cyclic load was proposed. The results show that the horizontal peak bearing capacity of long spiral belled pile is increased by 57.2% and 40.4%, respectively, as compared with the straight pile and belled pile under the same conditions. The horizontal displacement mainly occurs at the upper part of the pile. Under the condition of limited cyclic times, the load amplitude has more significant effect on the bearing characteristics of the long spiral belled pile. In contrast to the straight pile and belled pile, the long spiral belled pile has better energy dissipation capacity, and the rank of the energy dissipation capacity of these three piles is long spiral belled pile > belled pile > straight pile. The power function model can well reflect the cumulative damage characteristics of long spiral belled pile under horizontal cyclic loading, and there is a good linear relationship between power function model parameters and load amplitude. The energy dissipation coefficient of long spiral belled pile with diverse cycle times at different mechanical stages of test pile is analysed. Then, the recommended power function model parameters according to different failure stages are proposed. The verification example indicates that the prediction results are close to the measured values with a calculation error of 22%. The prediction model can provide a certain reference for the application of long spiral belled pile in marine structures.
1. Introduction
Pile foundations in the field of marine engineering are often subjected to horizontal cyclic loading caused by factors such as sea wind and waves. Local permanent cumulative damage at one or several places may appear at a pile under the horizontal cyclic loading, and crack or sudden fracture damage can occur after a certain number of cycles. The phenomena mentioned above can seriously affect the normal use of pile foundation and safety of the superstructure.
The bearing characteristics and deformation law of pile foundation under the horizontal cyclic load of sea waves are interesting topics for domestic and foreign scholars. Rao [1], Basack [2], Achmus [3], Liao [4], and Kong [5] studied the effects of cyclic load amplitude, cycle times, single pile size, and buried depth on the stress characteristics and deformation of single pile, and concluded that load amplitude, cycle times, and single pile size effect have great influence on the stress characteristics and deformation of single pile. Niemann [6, 7] has carried out centrifuge model tests and 1g model tests of single pile and group piles under lateral cyclic load in sand, and discussed the influence of pile group geometry, pile spacing, and cyclic load amplitude on the cumulative displacement of group piles. Cyclic load has a significant impact on the initial stiffness of p-y curve, and the initial stiffness decreases with the increase of cyclic times. Basack [8–10] developed a new lateral cyclic load application device for model pile foundation. Through comprehensive experimental research and finite element analysis, the bending moment distribution and bearing characteristic response of pile groups under horizontal cyclic load in soft soil area were studied, and the influence law of horizontal load parameters, namely, cycle times, frequency, and amplitude on degradation factors, was analysed. A series of summary and analysis were made on the lateral cyclic load of pile foundation in marine environment. According to previous research results, some design suggestions were put forward for pile foundation under cyclic load. Chen [11] carried out an experimental study on the pipe pile in soft soil area under static pressure and cyclic combined load, and explored the influence of static load, cyclic load, and load level. Three modes of cyclic characteristics of pile top displacement are given: rapid stability, gradual development, and severe failure. According to the cycle stability diagram, the cycle stability criterion is divided into stable region, metastable region, and unstable region, and the corresponding limit values are obtained according to the test results. Liu [12] studied the deformation characteristics of composite foundation supported by geogrid piles under cyclic loading through a series of model tests, and analysed the effects of load, geogrid layers, pile types, and other factors on the performance of composite foundation. The relationship between foundation settlement and cycle times is analysed by the numerical fitting method.
Lin [13] applied the concept of strain superposition to evaluate the strain accumulation of laterally loaded piles in sandy soil, and found that soil properties, pile embedding mode, cyclic loading mode, and other factors can significantly affect the performance of horizontally loaded piles. Rosquoet et al. [14]conducted centrifuge tests on sandy soil, and found that the maximum displacement was generated in the first cycle, and the cumulative deformation was mainly generated in the short-term cycle. Zhang et al. [15]conducted a single pile model test in sandy soil foundation and also reached a similar conclusion. The cumulative displacement of pile top was mainly concentrated in the short-term cycle, and the short-term effect of the cycle was greater than the long-term effect. LeBlanc et al. [16] carried out unidirectional and bidirectional cyclic loading tests in dry sand with different dry densities. They believed that the cumulative stress and deformation of pile foundation under horizontal cyclic loading was related to the unloading stiffness, and the expression formula was given. Arshad [17] and Richards et al. [18] compared the model test of one-way and two-way cyclic loading and found that under the same load amplitude, the cumulative deformation caused by two-way cyclic loading was greater than that caused by one-way cyclic loading. Bolton [19], Alizadeh, Davisson [20], Little [21], Long [22], and Verdure [23] established a logarithmic function or power function model between the development trend of pile foundation’s cumulative deformation and the number of cycles under horizontal cyclic load through model tests and field tests. Luo et al. [24], based on numerical simulation, used the power function model to predict the cumulative deformation of pile foundation under different loads. Peralta et al. [25] carried out horizontal cyclic loading tests of rigid pile and flexible pile in sandy soil, discussed the influence law of cyclic number and load amplitude on accumulated damage and deformation of pile foundation, and presented the relationship between cumulative damage and deformation of rigid pile under long-term horizontal cyclic load and times of cyclic loading.
Many researchers have found that the cumulative deformation of single pile under horizontal cyclic loading mainly occurs in short-term cycle, and in the early stage of cyclic loading, the number of cycles and loading mode can obviously affect its bearing characteristics. The long spiral belled pile is made by improving the manufacturing technology and construction equipment of the spiral pile, setting an enlarged head at the pile end on the basis of the spiral pile. A new type of pile is formed, which increases the compaction between pile and soil beside pile due to the existence of enlarged head at pile end and thread of pile body, thus greatly improving the bearing capacity of pile. At present, the long spiral belled pile is widely used in engineering, but its application and research in marine structures are few. Therefore, it is of great significance to study the bearing and damage characteristics of long spiral belled piles under the approximate horizontal cyclic loads such as offshore wind and waves.
This study focuses on the pile-soil interaction and energy dissipation characteristics of offshore long spiral belled piles subjected to the horizontal cyclic loading. Three types of piles, namely, long spiral belled pile, straight pile with equal cross section, and belled pile, are selected. A set of single pile model tests under horizontal cyclic load were carried out with an indoor model box. As limited to the test conditions, the loading frequency is 0.01 Hz. Cyclic reciprocating loads with different load amplitudes are applied at the same frequency in the test. Through the distribution of pile deflection, bending moment, and Earth pressure around the pile, the influence of cyclic load amplitude and cycle times on the interaction between the long spiral belled pile and the soil around the pile is discussed. By analysing its hysteretic characteristics and skeleton curve, the cumulative energy dissipation characteristics are used to reflect the damage of test pile, and the influence of load amplitude and cycle times on the cumulative damage of long spiral belled pile is discussed. The power function prediction model of energy dissipation coefficient under multi-stage cyclic loading is put forward. It provides a reference for the application of long spiral belled pile in offshore engineering.
2. Experiment
2.1. Manufacture of Model Pile
The test model pile is a precast concrete pile, and the similarity ratio is calculated by taking the long spiral belled pile with pile length L = 12m, pile diameter D = 0.6 m, and concrete strength C35 as the prototype. It is determined that the proportional constant SL is 10, the elastic modulus similarity ratio CE = 1/5, and the straight pile and belled pile are set as the control group. The geometric dimensions of the three indoor model piles designed based on the similarity ratio are shown in Table 1.
Pile type
Length (m)
Diameter (mm)
Enlarged head diameter (mm)
Reinforcement
Reinforcement cage length (m)
Long spiral belled pile (LK)
1.2
60
90
8Φ2
1.0
Belled pile (KZ)
1.2
60
90
8Φ2
1.0
Equal cross section straight pile (ZZ)
1.2
60
—
8Φ2
1.0

... Later, SANISAND-MS was applied to boundary problems with a focus on the cyclic monopile-soil interaction mechanisms in dry sand (Cheng et al., 2021;Liu et al., 2021). Satisfactory semi-quantitative comparison between the simulation and the experimental data from the literature (LeBlanc et al., 2010;Richards et al., 2020) has been obtained for the tilt accumulation of monopiles. From this, it is believed that adopting the 'memory surface'-enhanced implicit model in a 3D FE platform will give deeper insight into the controlling factors of the cyclic hydro-mechanical behaviour of monopile. ...

Optimised design is essential to reduce the cost of monopiles for offshore wind turbines. For this purpose, an in-depth understanding of the behaviour of monopile–soil interaction is required. As more wind farms are planned in seismically active areas, the undrained behaviour of sandy soils (and the possibility of soil liquefaction) and these soils’ effects on monopile cyclic response need critical evaluation. Considering the lack of well-established test programs, implicit three-dimensional (3D) finite-element (FE) methods stand out as a robust tool to identify and highlight the governing geo-mechanisms in monopile design. In this work, an implicit 3D FE implementation of SANISAND-MS for undrained soil behaviour, termed SANISAND-MSu, is deployed in OpenSees to serve these objectives. The role of pore-water pressure on monopile performance is comprehensively investigated by comparisons between drained and undrained soil behaviour. Local soil responses are studied in detail in relation to parameters in laboratory soil testing and application to monopile geotechnical design. The results of simulations are also used to evaluate numerical p–y curves as a function of the number of load cycles on the pile. The conclusions in this work contribute to ongoing research on monopile–soil interaction and support the development of lifetime analysis for monopile–soil systems.

... Monopiles with a diameter of 4-10 m and a length-to-diameter ratio of 3-6 are widely used as foundations for offshore wind turbines (OWTs), though to date, limited guidance on evaluating the lateral response has been given in design guidelines such as DNVGL (2016). The conventional p-y method (API 2011;Matlock 1970;Reese et al. 1974) developed for long slender piles subjected to a limited number of load cycles is not applicable for large-diameter monopiles used for OWTs (Abadie et al. 2019;Achmus et al. 2009Achmus et al. , 2005Bayton et al. 2018;Byrne et al. 2015;LeBlanc et al. 2010;Richards et al. 2019;Wu et al. 2019;Zdravković et al. 2015;among others). Significant improvements in the design methods have been achieved in the last few years through two well-known joint industry projects, PISA ) and REDWIN (Skau et al. 2018). ...

Monopiles under in-service conditions are subjected to lateral forces and resultant bending moments from the offshore environment. The subsequent lateral response following installation is significantly influenced by the initial soil state postinstallation, which is influenced by the pile installation process, as demonstrated in previous numerical studies. To date, there are no technical guidelines established for considering the installation effects on the design of laterally loaded monopiles. This paper is the second of a pair of companion papers that investigate the effect of different installation methods on the subsequent response of monopiles under lateral loading. The paper focuses on the quantification of the effect of pile installation on the initial stiffness and lateral capacity. The numerical model is first validated against purpose-designed centrifuge tests. The analysis confirms that impact driven piles have significantly higher initial stiffness and lateral capacity than jacked piles and wished-in-place piles. The effect of installation methods on the lateral response is also influenced by the initial soil density, driving distance, pile geometry, stress level, and load eccentricity. The study highlights the importance of considering the effects of the installation process on the subsequent lateral pile response.

... near the ground surface for embedment lengths of 533 and 355 mm, respectively. A few researchers also proposed a similar criterion for the static capacity of monopiles defined at a ground-line displacement of 0.1B or a ground-level rotation of 2° Abadie et al. 2019;Richards et al. 2019). The respective lateral load capacities (H us ) in medium dense sand for embedment lengths of 533 and 355 mm were 420 and 180 N. Repeatability was ensured by performing an additional monotonic test on the model pile with an embedded length of 355 mm to obtain an identical load-deformation response, as shown in Fig. 4. The limiting capacities serve as the reference value for the maximum load amplitude (H max ) applied in cyclic loading tests. ...

The monopile is the most common form of foundation employed in offshore wind turbines. These foundations are subjected to millions of repeated load cycles, owing to wind and wave action. In this study, a series of six cyclic lateral load tests and two monotonic tests were performed on an aluminum model pipe pile with an outer diameter of 63.5 mm and a wall thickness of 2.5 mm. A model mo-nopile was embedded in medium dense sand (D r = 55%) and subjected to asymmetric two-way cyclic loading. From the experimental investigations, the effects of embedded length and the asymmetric two-way cyclic loads on the lateral pile head displacements and the cyclic secant stiffness of the soil-pile system were studied. Linear regression analysis was also performed to fit the conventional degradation parameters using the minimum number of critical constraints, which included the loading conditions and the flexibility parameters of the soil-pile system. From the test results, it was observed that asymmetric two-way loading causes a reversal of accumulated displacement for a pile embedded at a greater depth (L > 1.91T) under relatively lower amplitudes (ζ b < 0.37). The cyclic secant stiffness was observed to increase at a relatively constant rate (A κ) with the logarithm of the number of cycles. The study also revealed that the magnitude of initial cyclic secant stiffness, in comparison with the monotonic stiffness, exhibited a critical drop near the specific load character, ζ c = −0.38.

... In soft clay, these processes generally increase the subsequent undrained strength and stiffness. Whole-life effects of changing soil properties have been observed during flow round penetrometer tests (Hodder et al. 2013, Cocjin et al. 2014O'Loughlin et al, 2017), interface shear tests (Boukpeti & White 2017), and large scale laboratory tank tests and geotechnical centrifuge tests of pipelines, sliding foundations (Smith & White, 2014, Cocjin et al. 2014, 2017, Han et al. 2016Zhou et al 2019;Lai et al., 2020) and pile foundations (Bayton et al, 2018;Richards et al, 2018Richards et al, , 2019Abadie et al., 2019;Truong et Accepted manuscript doi: 10.1680/jgele.20.00124 al., 2019. ...

This technical note describes a set of Direct Simple Shear (DSS) tests that characterise the evolving geotechnical properties of a soft soil, through a loading history that represents episodic loading and consolidation periods as encountered by some offshore infrastructure. The interpretation uses a critical state soil mechanics (CSSM) framework. CSSM prjavascript:void(0);ovides the necessary building blocks to quantify the balance between undrained cyclic loading and the associated increases in pore pressure, and drainage and consolidation, leading to strength regain.
The results show how DSS tests can characterise the through-life response of soft clays. The measured responses showed the changing strength of the clay due to consolidation effects following loading, and match predictions from simple models. The results show how DSS tests can characterise the types of behaviour also seen in centrifuge models and field penetrometer tests related to the long term response of soft clays under offshore infrastructure.<br/

... The reason for this is the high average load that leads to a higher degree of accumulation. This was for example seen in the model presented in Richards et al. (2019). The analysis of the foundation is performed using average loads and average stress-strain curves that account for the effect of cyclic loading, as illustrated in Fig. 1 (5). ...

Offshore wind turbines are located in harsh environments with cyclic loads from wind, waves and current. These cyclic loads are transferred to the soil through the monopile foundation. As a result, pore pressure accumulation and degradation of the strength and stiffness may occur. This paper presents a consistent, rigorous and super-fast monopile design approach, which allows for time-efficient design. It is based on the NGI approach for cyclic loading in combination with a time-efficient 3D Finite Element Analysis (FEA) and spring calibration approach. The FEA program is used to calculate: the permanent rotation of the monopile at the end of the lifetime (Serviceability Limit State-SLS), the capacity under maximum loads (Ultimate Limit State-ULS) and the pile response during operation (Fatigue Limit State-FLS). The optimal monopile geometry that fulfills the design limit states is then determined and used to calibrate soil reaction curves. This paper presents the approach used in the different limit states, the time-efficient 3D FEA program, the cyclic accumulation, and the optimization methodology to calibrate soil-reaction springs. Finally, the main assumptions and simplifications in the design approach are discussed.

... The prediction of the lateral capacity can be enhanced similarly, for instance by using depth-dependent p-y curves to calculate the pile capacity coupled with a limiting displacement criterion. Such a framework can also include cyclic loading effects, which are not included here but could be predicted through empirical relationships developed for piles (Richards et al., 2019). ...

Screw piles or screw anchors are a promising solution to anchor floating offshore renewable energy devices, such as wind turbines or tidal turbines. The installation generates limited noise (driven piles are noisy) and can be undertaken in all soil conditions. Although they are mainly used for their large uplift capacities, screw anchors can also be designed to provide significant lateral resistance. The optimisation of screw anchor design does not rely only on the geotechnical assessment of the uplift capacity based on soil strength, but also on operational (installation requirements) and structural (helix bending, core section stress, limiting steel plate thickness) constraints. This paper develops a methodology for the design optimisation of screw anchors under lateral loading in dense sand, incorporating all of these constraints, based on simplified analytical or semi-analytical approaches. The results show that it is possible to optimise the anchor design, maximising the anchor lateral capacity, whilst minimising the anchor weight. The maximum embedment depth and then the anchor capacity is mainly limited by the maximum torque available during installation and the short-pile to long-pile failure mechanism transition respectively.

... The long-term behaviour of OWT monopile foundations in sand was studied in small-scale (1-g) or centrifuge (n-g) model tests with various kinds of loading (Cuéllar et al., 2012;Arshad and O'Kelly, 2017;Leblanc et al., 2010a,b;Yu et al., 2015;Bayton et al., 2018;Rudolph et al., 2014;Truong et al., 2019;Richards et al., 2019;Abadie et al., 2019). Furthermore, procedures for the proof of the serviceability of OWT foundations in sand have been proposed (Taşan et al., 2011;Achmus et al., 2008Achmus et al., , 2009Dührkop, 2010), partly based on the API beam-on-elastic foundation approach (API American Petroleum Institute, 2000) or as an extension of the strain wedge model (Norris, 1986;Ashour et al., 1998;Ashour and Norris, 2000). ...

Offshore wind turbines (OWT) are generally founded on piles or gravity base foundations. Up to now, there is a lack of validated and standardized analysis procedures for such foundations, especially for the serviceability limit state, i.e. for the prediction of accumulated deformations. In order to gain experience on the behaviour of a OWT gravity base foundation under typical offshore loading conditions, a full-scale test has been performed near the shore of the North Sea. The test foundation was subjected to about 1.5 million load cycles simulating several storm events. The foundation and the sandy subsoil have been extensively instrumented so that a large amount of measured data on the cyclic soil-structure interaction were collected. Meanwhile, a numerical procedure for the proof of the serviceability for OWT foundations was developed. The procedure is based on finite element (FE) calculations in combination with a high-cycle accumulation (HCA) model. The application of the HCA model in simulations of the full-scale test is described in this contribution. The essential simplification of the subsoil and the determination of the input parameters for the FE simulations are shown. The settlements, pore water pressures and soil pressures predicted by the HCA model are compared to the measurements.

... Moreover, a large number of centrifuge tests with cyclic loading of monopiles have been conducted [6,22,26]. Results of tests with multidirectional cyclic loading, which is also studied numerically within this work, have been recently reported in [21,22]. Field tests on monopiles subjected to cyclic loading have been performed in the framework of the PISA project (see e.g. ...

A parametric study on the long-term deformations of monopile foundations for offshore wind turbines is presented.
The finite element calculations of a monopile in fine sand were performed with a high-cycle accumulation
(HCA) model. The results are analyzed with respect to the horizontal displacements, the tilting of the pile
head, settlement of the ground surface and effective stress changes in the surrounding soil. The dimensions of the
pile (diameter, length of embedding, wall thickness), the initial density of the sand and the cyclic loading
(average value, amplitude, lever arm) have been varied. The influence of the drainage conditions (either fully
drained or partially drained) is also discussed. The validity of Miner’s rule is checked for both types of drainage
conditions. Furthermore, the effect of changes of the direction of the cycles and of a multidimensional cyclic
loading is addressed. The interesting phenomenon of a “self-healing”, i.e. a re-erection of the deformed monopile
after a storm event, is demonstrated based on simulations with small cycles following a large preloading.
Simulations with homogeneous and stochastically fluctuating fields of void ratio are compared.

The large particle sizes of railway ballast and rock fill have meant that conventional techniques used to measure the small strain stiffness of finer geomaterials have not been adopted, with the consequence that their stiffnesses are poorly defined. In a series of tests on a UK railway ballast, simple adaptations were made to existing local strain measuring systems to account for the larger particle sizes. The study showed that the small strain stiffnesses are different in second loading compared to virgin loading, but multiple cycles had little further effect on the stiffness. The large particle size was found rarely to have any detrimental effect on the quality of the strain measurements and the two independent measurements of axial strain taken at diametrically opposite locations were generally as consistent as for finer grained soils. As for other soils, the “external” measurements of strain across the apparatus platens were of little use in determining stiffness. The presence of water did not have a significant effect on the behaviour, and this was confirmed by inter-particle loading tests on single particle contacts. Despite the use of lubricated end platens there was a significant barrelling of the sample at large shear strains so that the internal measurement of the volumetric change diverged from the external measurement at large strains. The very small volumetric strains that occurred during isotropic loading meant that each sample could only be used to obtain one measurement of the virgin loading stiffness.

Rigid foundations supporting offshore wind turbines (OWT) like short piles and caissons can sustain multi-directional lateral loading. Moreover, the monotonic and cyclic response of these foundations can be affected by recent loading history aligned along directions different from the present one. To represent such recent loading history effects, a multi-directional p-y model is proposed for rigid foundations in undrained clays. The model is constructed by extending the uni-directional p-y model previously proposed by the authors based on Total-displacement-loading Extended Mobilisable Strength Design (T-EMSD) approach, and thus considering site-specific soil stress-strain relations and foundation geometries. The crux of the extension is to combine bounding surface plasticity and radial mapping with a moving projection center. The former effectively couples p-y response along orthogonal directions, while the latter is crucial for representing the influences of loading direction reversal and recent loading history effects. The proposed p-y model is evaluated against existing centrifuge tests and finite element analysis (FEA) of this work. Lastly, the proposed p-y model and FEA are used in parallel to highlight the effects of loading path rotation on monotonic and cyclic accumulative foundation response. These comparative analyses indicate that the proposed p-y model can reasonably represent recent loading history effects.

Monopile-supported offshore wind turbines are continuously subjected to stochastic cyclic loadings during its lifetime of 25–30 years and it is challenging to accurately predict the accumulated displacement of monopile. In this paper, a simplified model with two cyclic loading factors is proposed to predict the accumulated displacement of monopile in soft clay. These two cyclic loading factors could consider the effects of the pile diameter, number of cycles, loading profile and undrained shear strength profile on the accumulated displacement. The model is validated by comparing with the centrifuge data and results obtained from the hyperplastic accelerated ratcheting model. Furthermore, the evolution of the accumulated displacements of monopile for the ultimate limit state (ULS) storm loading history and the long-term fatigue limit state (FLS) loading history are also investigated. This paper could provide a method for design codes requiring an accurate estimation of monopile displacements.

The permanent accumulated rotation is of great importance to the design of monopile foundations for offshore wind turbines because it is critical to the final dimensions of the monopile as well as its cost. Although design specifications require that the permanent accumulated rotation meet tolerances, they do not provide engineers with an appropriate method to calculate this value. This paper proposes a simplified method for estimating the permanent accumulated rotation of a monopile throughout its design life. To establish this method, a series of 1-g model tests were conducted in medium-dense sand to investigate the accumulative tendency of monopile rotation under typhoon and non-typhoon conditions. The results showed that the total accumulated rotation was mainly caused by typhoon events, further indicating that the static rotation generated by the maximum load magnitude among typhoon load sequences may maintain a certain proportional relationship with it. Then, the procedure for determining the two parameters in the method was illustrated by an NREL 5 MW wind turbine mounted on a monopile at a water depth of 28 m in the northern South China Sea. This method can provide a convenient tool for calculating the permanent rotation of a monopile foundation throughout its design life.

Large diameter monopiles are usually used as the foundation of offshore wind turbines. Monopile foundations are subjected to laterally cyclic marine environmental loadings which tends to accumulate displacements and rotation of the monopile. To preliminarily evaluate the cyclic responses of monopile in marine clay, 1g model tests have been conducted to combine with reported centrifuge tests to efficiently illustrate the behavior. This study investigates the laterally monotonic and cyclic responses of the model pile embedded in kaolin clay. As expected, obvious differences are observed between results of the 1g model tests and the centrifuge tests owing to the effect of stress levels, but important quantitative relations between results of these two types are revealed: two equations closely related to cyclic loading magnitude ratio ζb with same cyclic loading symmetry ratio ζc, could be qualitatively obtained to predict the pile responses in centrifuge tests by using the result of 1g model tests. The normalized unloading stiffness of model pile in 1g test is less than that of obtained from centrifuge tests with the same ζb values. This result not only highlights that it is necessary to account for the stress level of soil to understand cyclic lateral responses of monopile foundations, but also reveals that it is possible to qualitatively insight responses of monopile through 1g model tests.

Pile foundations in loose sand are occasionally subjected to cyclic loading initiated by the influence of wind, wave, traffic loads, etc. Such load reversals alter the strength and stiffness of surrounding loose sand affecting the ultimate capacity and serviceability of the pile foundation. Although such cyclic loading may be under vertical, lateral or torsional modes or a combination, the lateral cyclic load dominates the other modes. To carry out an in-depth study on pile-soil interaction under lateral cyclic load in loose sand, a series of laboratory model tests were performed with 2 × 2 pile group, followed by developing two alternative numerical models, i.e., boundary element and finite element models (i.e., BEM and FEM). The BEM involved a p-multiplier technique to incorporate the group effect, while the FEM was developed by ABAQUS software incorporating 3D stress conditions. As observed, the BEM slightly over-predicts while the FEM marginally under-predicts the experimental observations. The lateral cyclic loading was found to produce stiffening effect on loose sand which increased the pile capacity and reduced the pile head displacement. Sand relative density is also found to affect the test and numerical results significantly. A set of important conclusions are drawn from the entire study.

The hybrid pile-bucket foundation is an innovative alternative to monopile foundation when used to support offshore wind turbines (OWTs). To understand the load transfer mechanism of the hybrid foundation when loaded horizontally, reduced-scale model tests and numerical modelling were performed to investigated loading/deformation characteristics of the pile-bucket foundation structure and stress-reacting features of the soil surrounding the foundation. Both the pore water pressure (PWP) of the soil and strains of the pile and bucket are recorded from the model test. Furthermore, the pile/bucket load sharing ratio, contours of plastic strain, and excess PWP of the soil are obtained and analyzed via numerical modelling of the model test. The results show that the horizontal load is mostly carried by the bucket, and the overturning moment is mostly resisted by the pile. Compared to the monopile foundation, the soil of the hybrid foundation shows smaller PWP increase and less principle-stress rotation, implying a lower rate of stiffness and strength degradation of the hybrid foundation when subjected to cyclic loadings.

Offshore monopiles accumulate permanent tilt under long-lasting cyclic environmental loads. Accurate prediction of monopile tilt is key to assessing their serviceability, and requires a fundamental understanding of loading history effects. While both experimental and numerical studies are shedding light on this matter, this work uses step-by-step implicit 3D FE modelling to investigate loading history effects in the response to cyclic lateral loading of monopiles in sand and to identify links between local soil behaviour and relevant features of global pile behaviour. For this purpose, the recently developed SANISAND-MS model is adopted to achieve a reliable simulation of sand’s cyclic ratcheting. In particular, the validity of an up-scaled Miner’s rule for monopile tilting under multi-amplitude cyclic loading is assessed based on the results of 3D FE parametric analyses, with emphasis on the role played by the engineering idealisation of random environmental loading. The validity of such a rule has been numerically investigated both in terms of local soil element response and global foundation behaviour — for the particular case of a large-diameter monopile. In respect, the effect of the loading history idealisation is presented, and it is concluded that Miner’s rule does not always rigorously apply to all the cases considered herein. The translation of irregular loading histories into a regular version with loading packages sorted in ascending amplitude order is shown to be a reasonable approach, at least when the possibility of cyclic pore pressure build-up is disregarded.

Monopiles are the most common foundation type for offshore wind turbines. These structures are subjected to millions of cyclic horizontal loads during their lifespans, mainly from waves and wind; however, there are gaps in conventional design methods for different aspects of cyclic loading. The present study examined the cyclic behaviour of monopiles in dry calcareous sand. Centrifuge tests were carried out to investigate the effect of cyclic loading on the accumulated displacement and soil-pile stiffness. The results showed that asymmetric two-way loading is the most damaging load type, although its difference from one-way loading is less than what has been reported previously. Asymmetric two-way loading was found to cause up to 20% more displacement than one-way loading. Furthermore, the secant stiffness of the soil-pile system increased about 15% after 600 cycles, and a logarithmic function has been provided to describe this trend. The slope of this function increased with the maximum cyclic load magnitude; however, an increase in the cyclic load magnitude decreased the soil-pile stiffness. Moreover, the soil-pile stiffness was considerably lower in symmetric two-way loading compared to other load reversal conditions. After each cyclic test, monotonic loading was applied. In most cases, the post-cyclic lateral capacity was nearly equal to the static capacity. A model is proposed to predict the accumulated displacement under cyclic loading.

Das Verhalten granularer Böden unter mehrdimensionaler zyklischer Beanspruchung ist für viele baupraktische Fragestellungen von großer Bedeutung. Beispielsweise können bei Offshore‐Windenergieanlagen (OWEA) Wind‐ und Wellenbelastungen aus unterschiedlichen Richtungen sowie mit einem zeitlichen Versatz auf die geotechnische Struktur einwirken, woraus eine mehrdimensionale zyklische Beanspruchung resultiert. Es ist bekannt, dass eine mehrdimensionale zyklische Beanspruchung zu einer größeren Akkumulation der Verformung im Boden führt als eine eindimensionale Beanspruchung gleicher Amplitude. Werden die akkumulierten Verformungen zu groß, kann dies zu einem unvorhergesehenen Verlust der Gebrauchstauglichkeit führen. Die numerische Erfassung des mehrdimensionalen Problems und die Prognose der zu erwartenden Verformungen sind daher in solchen Fällen unerlässlich. Gegenstand dieses Aufsatzes ist eine Untersuchung des Bodenverhaltens unter mehrdimensionaler zyklischer Beanspruchung. In über 120 zyklischen Triaxial‐ und Hohlzylindertriaxialversuchen wird das Bodenverhalten unter ein‐ bis vierdimensionaler Beanspruchung intensiv untersucht. Erstmals kann dabei die mathematische Formulierung der mehrdimensionalen Dehnungsamplitude im hochzyklischen Akkumulationsmodell (HCA‐Modell) nach Niemunis et al. für ein‐ bis vierdimensionale Beanspruchungen versuchstechnisch überprüft werden. Das HCA‐Modell mit der validierten Definition der Dehnungsamplitude wird anschließend in exemplarischen numerischen Berechnungen einer OWEA‐Monopilegründung unter einer durch Wind‐ und Wellenbelastung hervorgerufenen mehrdimensionalen Beanspruchung studiert. Auf diese Weise werden die Anwendbarkeit und der Mehrwert der Definition der mehrdimensionalen Dehnungsamplitude im HCA‐Modell für baupraktische Zwecke verdeutlicht.

The driven monopile is the most common foundation type for all installed offshore wind turbines. These monopiles are often subject to scour phenomena, which cause a reduction in foundation strength and stiffness. In order to prevent the consequences of this phenomenon, scour protection systems are used to protect the seabed around a monopile structure against scour in practice. This paper presents a numerical model to investigate the effect of scour protection on the natural frequency and lateral responses of monopile-supported offshore wind turbines under the ultimate limit state (ULS), serviceability limit state (SLS) and fatigue limit state (FLS).
This numerical model was validated through a series of model tests, and then applied to the National Renewable Energy Laboratory (NREL) 5-MW offshore wind turbine supported on an Offshore Code Comparison Collaboration (OC3) monopile with riprap rock scour protection system. The study concludes that the scour protection has a slight impact on the first natural frequency and monopile behavior under ULS and FLS. However, the scour protection significantly decreases the pile head rotation at mudline under SLS, which provides the opportunity for further optimization of monopile design by incorporating the contribution of scour protection, thereby leading to a more economical design.

The study of cyclic loading on saturated natural clay deposits is of great interest for the analysis of offshore and onshore structures. Recent experimental research in the field of offshore engineering has indicated that the mechanical behavior of monopiles is strongly influenced by the reconsolidation processes that take place during calm conditions. After the reconsolidation episodes, the soil-pile stiffness considerably increases. Unfortunately, the previous behavior is usually disregarded in the numerical analysis and design of monopiles. In this work, the behavior of monopiles subjected to multiple episodes of cyclic loading and reconsolidation is analyzed from a numerical point of view. For that purpose, the sophisticated hypoplastic model for clays by Mašín (2014) with intergranular strain by Niemunis and Herle (1997) is carefully evaluated under element test conditions and by back-calculating some centrifuge tests. For the calibration of the constitutive model, three undrained monotonic and three undrained cyclic triaxial tests were performed. At the end, the influence of reconsolidation stages on the design of monopiles and the model capabilities to reproduce this behavior are discussed.

The design of OWTs relies on integrated load analyses tools that simulate the response of the entire OWT (including the rotor-nacelle assembly, support structure and foundation) under combined aerodynamic and hydrodynamic loading. Despite all efforts to develop accurate integrated models, these often fail to reproduce the measured natural frequencies, partly due to the current foundation modelling. This paper presents a new foundation model for integrated analyses of monopile-based OWTs. The model follows the macro-element approach, where the response of a pile and the surrounding soil is condensed to a force-displacement relation at seabed. The model formulation uses multi-surface plasticity and it reproduces key characteristics in monopile foundation behaviour that are not accounted for in current industry practice. The basic features of the model are described and its limitations are discussed. The performance of the macro-element model is compared against field test measurements and results from FEA. The comparison indicates that the macro-element model can reproduce accurately the non-linear load-displacement response and hysteretic behaviour measured in field tests and computed in FEA. This confirms that the model can simulate the pile and soil behaviour with the same level of accuracy as FEA, but with a considerable reduction in computational effort.

A series of centrifuge cyclic monopile lateral loading experiments in dry sand are presented. Model foundation tests were performed at 100 gravities (100g) of a prototype pile 5 m in diameter with an embedment depth of L/D = 5. Observations indicate that permanent rotational failure criteria (θ at mudline equal to 0.25 •) may not be reached for load magnitudes 40% or less of the monotonic failure load for 10 7 cycles. A cyclic degradation model for monopile rotation accumulation is also presented. Results from the cyclic tests are used to plot contour lines of predicted rotations based on load magnitude and number of cycles applied. This model is then used to predict cyclic rotational accumulation of a load magnitude ramp test and appears to perform well.

A systematic study into the response of monopiles to lateral cyclic loading in medium dense and dense sand was performed in beam and drum centrifuge tests. The centrifuge tests were carried out at different cyclic load and magnitude ratios, while the cyclic load sequence was also varied. The instrumentation on the piles provides fresh insights into the ongoing development of net stresses, bending moments and deflections as cycling progresses. Parallels between the test results and corresponding cyclic triaxial tests are drawn. The paper combines the results from this study with those from previous experimental investigations to provide empirical design recommendations for monopiles subjected to unidirectional cyclic loading.

This paper outlines experimental and theoretical research exploring the response of rigid piles to cyclic lateral loading, relevant to large diameter monopiles for offshore wind applications. The experimental work comprised of 1-g laboratory scale model tests in sand, where up to 100,000 cycles were applied. The tests were designed specifically for identification of key mechanisms behind the pile response with the results demonstrating that the resulting moment-rotation curves are dominated by ratcheting, whilst also conforming approximately to the extended Masing rules. These results provide impetus for the development of a new constitutive model, HARM, which can accurately capture the pile response to cyclic lateral loading. A brief overview of the model is presented, along with a calibration method and illustrative results. This modelling approach could, in future, be developed further to supplement current design methods for SLS and FLS.

Improved design of laterally loaded monopiles is central to the development of current and future generation offshore wind farms. Previously established design methods have demonstrable shortcomings requiring new ideas and approaches to be developed, specific for the offshore wind turbine sector. The Pile Soil Analysis (PISA) Project, established in 2013, addresses this problem through a range of theoretical studies, numerical analysis and medium scale field testing. The project completed in 2016; this paper summarises the principal findings, illustrated through examples incorporating the Cowden stiff clay profile, which represents one of the two soil profiles targeted in the study. The implications for design are discussed.

The contribution of this paper is a simple method to predict the higher moment capacity of a monopile in dense silica sand after drained cyclic loading. The method accounts for the effect of cyclic load magnitude, symmetry and number of cycles, and is calibrated against a series of single gravity and centrifuge tests. The agreement between the model test data and the predictions is typically within 2%. Application of the method shows that the moment capacity of a monopile in dense sand, for the conditions tested here, is up to 36% higher after cycling. This contrasts with a 10% reduction that would be predicted using the existing industry standard p–y approach for cyclic loading in sand. ICE Publishing: all rights reserved NOTATION C u coefficient of uniformity C–S cyclic test followed by a static test c non-dimensional function D diameter of the monopile D 1 , D 2 , D 3 displacement transducers D R relative density d 10 sand particle size at 10% passing d 50 sand particle size at 50% passing d 60 sand particle size at 60% passing F 1 , F 2 load cells G s specific gravity g gravitational acceleration J screw jack L embedded length of the monopile M moment at seabed M B , M C , M N non-dimensional functions M max maximum moment at seabed M min minimum moment at seabed M R static capacity of the monopile M Rpc static capacity of the monopile after precycling m 1 , m 2 , m 3 loading rig masses m b , m c , ˉ

Large-diameter monopiles are an established foundation type for offshore wind energy converters. A crucial aspect in the design of such piles is the bearing behavior under cyclically acting wind and wave loads, namely the accumulation of deflections and rotations under these loads. Regarding the prediction of the behavior under cyclic one-way load, some empirical approaches and also numerical simulation methods exist. In contrast, the behavior under cyclic two-way loading is widely unclear and must be investigated by pile tests. This paper presents the results of 1 g model tests with large-diameter piles in sand under arbitrary cyclic loading types. It was found that for almost rigid large-diameter piles, the effect of the loading type on the rate of displacement accumulation could be accounted for by a function which is almost independent on the system parameters, e.g., pile stiffness or relative density of the sand, but dependent on load eccentricity. The maximum accumulation rate occurs for asymmetric two-way loading. Using the functions found in the tests, a prediction of displacement accumulation for load spectra consisting of packages of arbitrary loads becomes possible. For flexible piles, a different effect of the loading type on the rate of displacement accumulation was observed. Here, asymmetric two-way loading was obviously not more unfavorable than one-way load.

The monopile is the dominant foundation type for offshore wind turbines, with
current design guidance based on knowledge transferred from the oil and gas industry.
Whilst there are some similarities between wind turbine and oil and gas pile design,
there are also a number of key differences. Notably, offshore wind turbine monopiles
are subjected to many cycles of large horizontal loads during their lifetime, whereas
such loading conditions are not as prevalent in oil and gas design. As a result, the
pile response due to this cyclic loading is poorly accounted for in current practice.
This thesis presents experimental and theoretical research, aimed at improving
the understanding of the behaviour of rigid monopiles in cohesionless soils, when
subjected to lateral cyclic loading. The experimental work involves laboratory
floor model tests, scaled to represent a full-scale wind-turbine monopile. The test
programme is designed to identify the key mechanisms driving pile response. It is
divided into four main parts, investigating loading rate effect, hysteretic behaviour
during unloading and reloading, as well as pile response to long-term single and multiamplitude
cyclic loads. In particular, the results show that the pile response conforms
to the extended Masing rules, with permanent deformation accumulated during nonsymmetric
continuous cyclic loads. This ratcheting behaviour is characterised by
two features: first, the ratcheting rate decreases with cycle number and depends on
the cyclic load magnitude and secondly, the shape of the hysteresis loop tightens
progressively, involving increased secant stiffness and decreased loop area. Tests
investigating multi-amplitude loading scenarios prove that the interaction between
these mechanisms describes the pile response. Finally, the continuous cyclic test
results are interpreted using the p-y method combined with the Degradation Stiffness
Model, and this shows a good fit to the observed pile deformation.
The key experimental findings are used for the development of a constitutive model
that captures ratcheting while conforming to the observed Masing behaviour. The
model, called HARM, is rigorous yet simple, and is framed within the hyperplasticity
approach presented by Houlsby and Puzrin (2006). The model is tuned to capture
the macro response of the pile under monotonic and cyclic loading, and is calibrated
using the experimental data. The results demonstrate that HARM can successfully
reproduce the main elements of the pile response with high accuracy. The method
could easily be within common design approaches, such as the p-y method.

Loads from extreme waves can be dimensioning for the substructures of offshore wind turbines. The DeRisk project (2015-2019) aims at an improved load evaluation procedure for extreme waves through application of advanced wave models, laboratory tests of load effects, development of hydrodynamic load models, aero-elastic response calculations and statistical analysis. This first paper from the project outlines the content and philosophy behind DeRisk. Next, the first results from laboratory tests with irregular waves are presented, including results for 2D and 3D focused wave groups. The results of focused wave group tests and a 6-hour (full scale duration) test are reproduced numerically by re-application of the wave paddle signal in a fully nonlinear potential flow wave model. A good match for the free surface elevation and associated exceedance probability curve is obtained. Finally, the utilization of DeRisk's results in practical design is discussed.

Skirted gravity base foundations and suction caisson foundations are considered as viable alternatives to monopile foundations for offshore wind turbines. While recent work has focused on the monotonic moment-rotation response for shallow foundations, the cyclic response and the accumulation of rotation over the life of the turbine must also be addressed. This paper presents cyclic loading tests where approximately 10,000 cycles, with different loading characteristics, were applied to a model shallow foundation (a caisson) in loose sand. On the basis of these tests, a framework for assessing the accumulated angular rotation because of cycling was developed. The settlement and cyclic stiffness response of the caisson were also assessed. It was found, not unexpectedly, that the accumulated settlement of the caisson increased with the number of cycles and cyclic amplitude. It was also found that a cyclic loading regime intermediate between one-way and full two-way cycling produced the largest rotations. The cyclic stiffness was relatively unaffected by the number of cycles. Using an appropriate scaling technique, the proposed framework was used to predict the long-term accumulated angular rotation, for an example, the field-scale monocaisson structure. DOI: 10.1061/(ASCE)GT.1943-5606.0000738. (C) 2013 American Society of Civil Engineers.

One of the geotechnical challenges for a monopile-supported offshore wind turbine is to create a foundation design procedure that incorporates the effects of cyclic loading from wind and waves in a safe and easy way. Improved procedures may enable the use of monopiles on deeper waters, but still secure a robust and cost-beneficial foundation design. In order to develop new design procedures it is essential to understand the pile-soil interaction. With centrifuge tests as the basis, this paper discusses the effects of the soil-pile interaction, with the focus on accumulation of displacements and change in secant stiffness in dense sand. Hence a centrifuge test series simulating idealised cyclic loads on a monopile supporting an offshore wind turbine was carried out. The validity of these centrifuge tests is discussed, and a simple design procedure is presented for prediction of the accumulation of displacements and change in secant stiffness based on the results from the centrifuge tests.

Causes of wind-wave misalignment, the difference between wind and mean wave direction, are investigated for stationary and non-stationary situations using numerical modeling. This includes the effects of upwind fetch restrictions, refraction, choice of source terms and integration time step on wind-wave misalignment are illustrated. A statistical analysis is performed to quantify wind-wave misalignment as a function of wind speed and significant wave height. In addition, the effect of spectral partitioning in separate wind sea and swell systems on the statistics of wind-wave misalignment is illustrated. Apart from the differences in mean direction, attention is given to the associated directional spreading. Implications for the design of offshore structures and the movements of moored ships are discussed.

A model for predicting the accumulated rotation of stiff piles under random two-way loading is presented. The model is based on a strain superposition rule similar to Miner's rule and uses rainflow-counting to decompose a random time-series of varying loads into a set of simple load reversals. The method is consistent with the work of LeBlanc et al. (2010) and is supported by 1g laboratory tests. An example is given for an offshore wind turbine indicating that accumulated pile rotation during the life of the turbine is dominated by the worst expected load.

The driven monopile is currently the preferred foundation type for most offshore wind farms. While the static capacity of the monopile is important, a safe design must also address issues of accumulated rotation and changes in stiffness after long-term cyclic loading. Design guidance on this issue is limited. To address this, a series of laboratory tests were conducted where a stiff pile in drained sand was subjected to between 8000 and 60 000 cycles of combined moment and horizontal loading. A typical design for an offshore wind turbine monopile was used as a basis for the study, to ensure that pile dimensions and loading ranges were realistic. A complete non-dimensional framework for stiff piles in sand is presented, and applied to interpret the test results. The accumulated rotation was found to be dependent on relative density, and was strongly affected by the characteristics of the applied cyclic load. Particular loading characteristics were found to cause a significant increase in the accumulated rotation. The pile stiffness increased with number of cycles, which contrasts with the current methodology where static load-displacement curves are degraded to account for cyclic loading. Methods are presented to predict the change in stiffness and the accumulated rotation of a stiff pile due to long-term cyclic loading. The use of the methods developed is demonstrated for a typical full-scale monopile.

Extensive data of the strength and dilatancy of 17 sands in axisymmetric or plane strain at different densities and confining pressures are collated. The critical state angle of shearing resistance of soil which is shearing at constant volume is principally a function of mineralogy and can readily be determined experimentally within a margin of about 1 degree , being roughly 33 degree for quartz and 40 degree for feldspar. The extra angle of shearing of 'dense' soil is correlated to its rate of dilation and thence to its relative density and mean effective stress, combined in a new relative dilatancy index.

The behaviour of pile foundations for offshore wind turbines deviates from classical assumptions and accumulated experience mainly due to their large diameter, reduced slenderness and elevated ratio of lateral to vertical loads. The offshore environment poses the additional challenge of large numbers of load cycles from wind and waves and the possible influence of transient changes of pore water pressure around the pile, both of them issues that are still not well understood and also not being contemplated in current design guidelines. In saturated soils, short-term cyclic loading within the extreme regime often involves a pore-pressure build up that eventually can lead to liquefaction phenomena and foundation failure. On the other hand, the effects of the long-term cyclic loading on the foundation's stability and especially on its serviceability must also be studied. The purpose of this work was to gain an insight into both aspects, while developing a practicable numerical tool for a short-term prognosis and deriving useful criteria for design. To achieve such goals, the investigations have been broadly divided into a first part with a theoretical orientation for the analysis of short-term transient effects in the frame of the Finite Element Method, and a second empirical block for the study of long-term phenomena by means of model tests in a reduced scale. The general picture that arises from these investigations is that of a foundation subject to hardening and soil densification in the long term, but also affected by transient episodes of significant softening during the storms as a consequence of pore pressure accumulation. Hence the importance of considering the coupling effects between soil stress and pore water pressure in design, even for those cases where a soil liquefaction could in principle be disregarded on the grounds of a high relative density of the soil. For practical design purposes, it seems sensible to distinguish between piles in fully drained conditions, in partially drained conditions and in undrained conditions, and analyse them correspondingly employing different strategies. Some considerations in this respect have been given in the final sections of this thesis. Das Verhalten von Pfahlgründungen für Offshore-Windenergieanlagen weicht von den klassischen Annahmen und gesammelten Erfahrungen vor allem wegen der großen Pfahldurchmesser, geringeren Schlankheit und hohen Verhältnisse von lateralen zu vertikalen Lasten ab. Zudem entsteht im Offshore-Bereich die zusätzliche Herausforderung einer großen Anzahl von Lastwechseln aus Wind und Wellen und des möglichen Einflusses von vorübergehenden Veränderungen des Porenwasserdrucks um den Pfahl. Da in diesem Hinsicht noch viel Unkenntniss herrscht, wurden beide Aspekte in den Bemessungsrichtlinien bisher nicht ausreichend in Betracht gezogen. Es ist aber bekannt, dass wassergesättigte Böden unter zyklischer Belastung oft einen Porenwasserdruckaufbau zeigen, der schließlich bis zur Bodenverflüssigung und einem Gründungsversagen führen kann. Andererseits können grosse Lastspielzahlen erhebliche bleibende Verformungen zur Folge haben, die die Gebrauchstauglichkeit der Gründung progressiv gefährden. Wesentliche Ziele dieser Arbeit waren, einen Einblick in beide Aspekte zu gewinnen, ihre Folgen aufzuzeigen und sinnvolle Kriterien für die Pfahlbemessung herzuleiten. Dabei wurde aber auch ein praktikables numerisches Werkzeug entwickelt, um den Einfluss von Kurzzeit-Sturmereignissen auf die Offshore-Pfähle prognostizieren zu können. Die Untersuchungen wur-den deswegen in zwei Hauptrichtungen gegliedert: ein erster Teil, mit einer theoretischen Orientierung, der der Analyse von kurzzeitigen Ereignisse anhand der Finite-Elemente-Methode gewidmet wurde, und ein zweiter empirischer Teil für die Betrachtung von Langzeitphänomene anhand Modellversuchen in kleinem Maßstab. In diesen Untersuchungen konnte gezeigt werden, wie sich der Boden an der Pfahlgründung langfristig progressiv verfestigt (long-time hardening). Vorübergehend kann es aber auch zu einer Entfestigung während der Sturmereignisse kommen (short-time transient softening). Sowohl die abgeminderte Bettungssteifigkeit während der Entfestigung, als auch ihre kummulativen Effekte im Sinne von bleibenden Verformungen, zeigen die Relevanz und Notwendigkeit der Berücksichtigung der Wechselwirkung zwischen Porenwasserdruck und Bodenverformung in der Pfahlbemessung. In der Summe werden die Phänomene und praktischen Folgen für die Bemessung der Pfähle in dieser Dissertation hergeleitet.

This paper presents an analytical methodology for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM, Houlsby et al., 2017 [3]), based on a closed-form expression for the accumulation of ratcheting strain with cyclic history. The proposed method requires the fit of one test response and of a few continuous cyclic tests. The initial motivation for this work is the calibration of models for the design of piles subjected to long-term cyclic lateral loading, and the test results from Abadie et al. (2018, 2015) [1,2] are used for calibration and proofing of the model. Nevertheless, the method is applicable to other problems of similar behaviour.

The development of the offshore wind industry is motivating substantial research efforts worldwide, where offshore wind turbines (OWTs) of increasing size are being installed in deeper water depths. Foundation design is a major factor affecting the structural performance of OWTs, with most installations founded to date on large-diameter monopiles.
This work promotes advanced 3D finite element (FE) modelling for the dynamic analysis of OWT-monopile-soil systems. A detailed FE model of a state-of-the-art 8 MW OWT is analysed by accounting for dynamic soil-monopile interaction in presence of pore pressure effects. For this purpose, the critical-state, bounding surface SANISAND model is adopted to reproduce the hydro-mechanical cyclic response of the sand deposit. The response to realistic environmental loading histories (10 min duration) are simulated, then followed by numerical rotor-stop tests for global damping estimation.
While linking to existing literature, all FE results are critically inspected to gain insight relevant to geotechnical design. The modelling tools adopted (i) support the robustness of ‘soft-stiff’ foundation design with respect to natural frequency shifts, even during severe storm events; (ii) provide values of foundation damping in line with field measurements; (iii) suggest that pore pressure effects might more likely affect soil-monopile interaction under weak-to-moderate environmental loading.

This paper presents experimental work aimed at improving understanding of the behaviour of rigid monopiles, in cohesionless soils, subjected to lateral cyclic loading. It involves 1g laboratory model tests, scaled to represent monopile foundations for offshore wind turbines. The test programme is designed to identify the key mechanisms governing pile response, and is divided into four main parts: (a) investigation of loading rate effects; (b) hysteretic behaviour during unloading and reloading; (c) pile response due to long-term single-amplitude cyclic loading; and (d) multi-amplitude cyclic loads. The results show that the pile response conforms closely to the extended Masing rules, with additional permanent deformation accumulated during non-symmetric cyclic loads. This ratcheting behaviour is characterised by two features: first, the ratcheting rate decreases with cycle number and depends on the cyclic load magnitude, and second, the shape of the hysteresis loop tightens progressively, involving increased secant stiffness and decreased loop area. Test results involving multi-amplitude load scenarios demonstrate that the response of the pile to complex load scenarios can be analysed and understood using the conclusions from single-amplitude cyclic loading. Such test results should be sufficient for deriving the principles of new modelling approaches.

Monopiles are currently the preferred option for supporting offshore wind turbines (OWTs) in water depths up to about 40 m. Whilst there have been significant advancements in the understanding of the behaviour of monopiles, the guidelines on the prediction of long term tilt (Serviceability Limit State, SLS) under millions of cycles of loads are still limited. Observations and analysis of scaled model tests identify two main parameters that governs the progressive tilt of monopiles: (a) Loading type (one-way or two-way) which can be quantified by the ratio of the minimum to maximum mudline bending moments (M min /M max); (b) factor of safety against overturning i.e. the ratio of the maximum applied moment (M max) to the moment carrying capacity of the pile or Moment of Resistance (M R) and therefore the ratio M max /M R. Due to the nature of the environmental loads (wind and wave) and the operating conditions of the turbine, the ratio M min /M max changes. The aim of this paper is to develop a practical method that can predict the nature of loading for the following governing load cases: Normal Operating Conditions, Extreme Wave Load scenario, and Extreme Wind Load scenario. The proposed method is applied to 15 existing wind farms in Europe where (M min /M max) and (M max /M R) are evaluated. The results show that the loading ratio is sensitive to the water depth and turbine size. Furthermore, under normal operating conditions, most of the wind turbine foundations in shallow waters are subjected to one-way loading and in deeper waters and under extreme conditions the loading is marginally two-way. Predictions for the nature of loading for large wind turbines (8 MW and 10 MW) in deeper waters are also presented. The results from this paper can be used for planning scaled model tests and element tests of the soil.

In recent years, several adjustments to the p-y curves in the offshore standards have been suggested in order to improve the design and reduce the uncertainties related to design, installation and project execution for monopile foundations for offshore wind turbines. This paper presents the consequences of the p-y curve selection on monopile design. Five and six published approaches for coarse- and fine-grained materials, respectively, are elucidated with respect to key design drivers. The assessment is undertaken for two generic homogeneous coarse-grained and fine-grained profiles. Furthermore, two layered soil profiles are also considered. The paper elucidates the robustness as well as the advantages and disadvantages of the different p-y approaches.

Suction caissons are being increasingly considered as an alternative foundation type to monopiles for offshore wind turbines. Single caisson foundations (or monopods) for offshore wind turbines are subjected to lateral cyclic loading from wind and waves acting on the structure. Recent studies have considered the response of suction caissons to such loading in sand, but have generally been limited to a few thousand cycles, whereas offshore wind turbines will generally experience millions of loading cycles over their lifetime. This paper presents the results from a programme of caisson tests in sand, clay and sand over clay seabed profiles, where each test involved about one million cycles of lateral load. The capacity and rotation response is shown to approach that measured in the sand seabed when the sand- clay interface is located at or beneath the caisson skirt tip. In contrast to previously published studies in sand, one-way cyclic loading is the most onerous loading symmetry for a layered seabed with a sand thickness equal to half the skirt length. However, the rotation for this seabed profile is essentially identical if the load is sustained or cyclic, provided that the cyclic loading remains one way. Lateral cyclic loading was seen to increase caisson capacity by up to 30% - with a bias towards clay-dominated seabed profiles - and stiffness by up to 50%. Such stiffness increases need to be considered when assessing the system dynamics for the offshore wind turbine, as demonstrated in the paper.

We present a theoretical model to describe the response of a one dimensional mechanical system under cyclic loading. Specifically, the model addresses the non-linear response on loading, hysteretic behaviour on unloading and reloading, and the phenomenon of ratcheting under very many cycles. The methods developed are formulated within the hyperplasticity framework. The model can be expressed in the form of general incremental relationships, can therefore be applied without modification directly to any loading history, and can be readily implemented within a time-stepping numerical code. A rigorous procedure is described to accelerate the ratcheting process, so that the effects of very large numbers of cycles can be analysed through a reduced number of cycles. A generalisation from unidirectional to multidirectional loading is described, together with a tensorial form for application to material modelling. The original motivation was for the application to design of piles under lateral loading, and an example of this application is provided. However, the model is equally applicable to many other problems involving unidirectional or bi-directional cyclic loading in which the system exhibits a similar character of hysteretic behaviour, with ratcheting under large numbers of cycles.

A simplified design procedure for foundations of offshore wind turbines is often useful as it can provide the types and sizes of foundation required to carry out financial viability analysis of a project and can also be used for tender design. This paper presents a simplified way of carrying out the design of monopiles based on necessary data (i.e. the least amount of data), namely site characteristics (wind speed at reference height, wind turbulence intensity, water depth, wave height and wave period), turbine characteristics (rated power, rated wind speed, rotor diameter, cut-in and cut-out speed, mass of the rotor-nacelle-assembly) and ground profile (soil stiffness variation with depth and soil stiffness at one diameter depth). Other data that may be required for final detailed design are also discussed. A flowchart of the design process is also presented for visualisation of the rather complex multi-disciplinary analysis. Where possible, validation of the proposed method is carried out based on field data and references/guidance are also drawn from codes of practice and certification bodies. The calculation procedures that are required can be easily carried out either through a series of spreadsheets or simple hand calculations. An example problem emulating the design of foundations for London Array wind farm is taken to demonstrate the proposed calculation procedure. The data used for the calculations are obtained from publicly available sources and the example shows that the simplified method arrives at a similar foundation to the one actually used in the project.

Methods are presented for the calculation of deflections, ultimate resistance, and moment distribution for laterally loaded single piles and pile groups driven into cohesionless soils. The lateral deflections have been calculated assuming that the coefficient of subgrade reaction increases linearly with depth and that the value of this coefficient depends primarily on the relative density of the supporting soil. The ultimate lateral resistance has been assumed to be governed by the yield or ultimate moment resistance of the pile section or by the ultimate lateral resistance of the supporting soil. The ultimate lateral resistance is assumed to be equal to three times the passive Rankine earth pressure. The deflections and lateral resistance, as calculated by the proposed methods, have been compared with available test data. Satisfactory agreement was found.

Citation: Arshad, M. and O'Kelly, B.C. (2017) Model studies on monopile behavior under long-term repeated lateral loading, International Journal of Geomechanics, ASCE. vol. 17, issue number 1, 12 pages.
Monopiles are the most commonly used foundation type for offshore wind turbine (OWT) structures and are characterized by relatively large geometric dimensions, compared with offshore pile foundations typically used in the oil and gas industries. To date, there are no established technical guidelines tailored for the design and analysis of OWT monopiles. This paper first identifies various intrinsic drawbacks involved with the existing design and analysis methodologies as applied to OWT monopiles. Next, a comprehensive experimental program of 1g repeated lateral load tests, performed on a scaled rigid monopile installed in dry sand beds, is presented to investigate its behavior under various loading scenarios. The experimental results provide insights into the various blurry issues in the existing literature related to monopile behavior under long-term repeated lateral loading. Lateral soil resistance profiles were determined from the measured pile bending strain data and found to be markedly dependent on the degree of the polynomial function used for curve-fitting of the bending strain data. Finally, an experimental model is presented for estimation of the pile's accumulated rotation, which takes into account various basic characteristics of the applied lateral load cycles.

Monopiles are currently the most common foundations for offshore wind turbines, which are subjected to millions of cyclic loads that are still not well interpreted in the design guidelines. The accumulated rotation of the turbine and the change of foundation stiffness due to the long-term cyclic loading are issues that should be investigated. In the present work, a smallscale test campaign of a stiff pile was performed in order to validate methodologies proposed by recent studies. Cyclic loading was not found to degrade the ultimate static resistance of the pile, which contrasts with current design guidelines. Copyright © 2014 by the International Society of Offshore and Polar Engineers (ISOPE).

Offshore monopiles are usually designed using the p-y method for cyclic loading. While the method works for static loading, it was not developed for high numbers of cycles. Since the turbines are highly sensitive towards tilting, cyclic loading must be considered. The static results should therefore be combined with results from cyclic model tests with a high number of cycles to account for the accumulation of displacement or rotation during the lifetime of these structures. These model tests can underestimate the accumulation, however, as it has recently been shown that a change of loading direction can increase the accumulation considerably. These results have been verified using small scale modeling and centrifuge testing. The results from modeling the full problem of a laterally loaded pile are compared here with results from cyclic simple shear tests with a change of shearing direction during the cyclic loading. For these tests, a newly developed apparatus is used. This allows further insight into the question how a soil can "retain a memory" of its loading history.

Foundation piles supporting offshore structures experience cyclic lateral loading arising from waves and wind, which are not typically uni-directional over the lifetime of the structure. This paper presents results from centrifuge experiments in sand, representing a large diameter prototype tested at stress levels similar to the field subjected to cyclic lateral loading from varying directions. The results demonstrate increased deformation accumulation due to the changing loading direction, compared to the uni-directional case. Displacement accumulation is not limited to the main loading direction but includes transverse movement as well. Similar trends were observed in small-scale 1g modelling that allowed a larger number of load cycles to be applied. The centrifuge test results provide confidence of the applicability of the findings to the prototype. Current methods that neglect the effect of variation of the loading direction will provide predictions of displacement accumulation of piles that are un-conservative. Therefore, a simple approach is proposed here to estimate the augmentation of displacement accumulation due to variation in loading direction compared to the uni-directional case.

Pfahlgründungen sind eine weitverbreitete Gründungsvariante für Offshore-Windenergieanlagen (OWEA) und sind in diesem Anwendungsgebiet erheblichen horizontalen Lasten ausgesetzt. Diese Belastung variiert in ihrer Amplitude, Frequenz sowie Richtung und ist naturgemäß sehr schwierig zu prognostizieren. Bereits existierende Ergebnisse von Modellversuchen berücksichtigen bislang keine Änderung der Lastrichtung und sind daher nur für eindimensionale Belastungen applikabel. Untersuchungen konnten zeigen, dass eine richtungsveränderliche zyklische Belastung zu größeren Verschiebungen führen kann als eine äquivalente eindimensionale zyklische Belastung. In diesem Beitrag wird das Phänomen anhand von Modellvorstellungen erläutert und anhand der Ergebnisse von Modellversuchen quantitativ betrachtet.
On the deformation behavior of laterally loaded piles with cyclic loading from a varying direction. Pile foundations are a common foundation for offshore wind energy converters. In this application area they are subjected to large lateral loading. This loading varies in amplitude, frequency and direction and is difficult to predict. Currently available analytical design methods derived from model tests do not consider a change in loading direction and are therefore applicable for one-dimensional loading only. Investigations have shown that a change in loading direction results in higher displacements compared to an equivalent one-dimensional cyclic loading. In this article models are presented to explain the increasing displacements and to be compared against results from physical modeling.

This paper describes the development and application of design charts for monopile foundations of offshore wind turbines in sandy soil under long-term cyclic lateral load. It outlines a numerical model, working with a numerical concept, which makes the calculation of accumulated displacements based on cyclic triaxial test results possible, and it describes important factors affecting the deformation response of a monopile to cyclic lateral loads. The effects of pile length, diameter and loading state on the accumulation rate of lateral deformation are presented and design charts are given, in which a normalized ultimate lateral resistance of a pile is used. For monopiles with very large diameter, the suitability of the “zero-toe-kick” and “vertical tangent” design critera for determining the required embedded length is discussed.

Small-scale testing under 1 g conditions as well as in the centrifuge presupposes that a model and prototype have comparative behavior. The chief condition for agreement between model and prototype is that the initial soil states of both must be at equal proximity to the steady state line. Then, when stresses are normalized to the initial mean stress, the model will in all aspects behave similarly to the prototype. Scaling rules are presented that indicate the relations between stress, strain, and displacement for the model and the prototype in terms of geometric scale and stress scale. An obvious limit of scales is imposed by that the soil in the model can be no looser than the maximum void ratio. Similarly, it must not be denser than a value that corresponds to a prototype soil at the minimum void ratio. Three main areas of application of the approach in engineering practice are identified: design of representative 1 g small-scale model tests; reanalysis of data from conventional small-scale tests; and improving the versatility of centrifuge facilities in recognition of the fact that the centrifuge test does not need to be performed at equal levels of stress, when designed according to the new approach. Key words : physical modeling, sand, scaling relations, steady state, centrifuge testing.

Die zyklische Horizontalbelastung von Offshore-Monopiles für Windenergieanlagen stellt seit einigen Jahren eine sehr große Herausforderung an die Fachplaner dar, da derzeit kein abgesicherter Bemessungsansatz verfügbar ist. Die in Forschung und Entwicklung eingesetzten Methoden und Verfahren, wie Finite-Elemente-Analysen oder Modellversuche, fokussieren sich im ersten Ansatz auf eindirektionale Schwellbeanspruchung. Die in diesem Beitrag dargestellten Modellversuche zeigen jedoch, dass eine geringfügige Veränderung der Lastangriffsrichtung zu Pfahlkopfverschiebungen führt, die diejenigen eines eindirektional belasteten Pfahls um ein Vielfaches übersteigen. Der Pfahl arbeitet sich zyklisch auf einem Weg des geringsten Widerstands durch den Versuchsboden. Der Pfahl driftet aus der Hauptbelastungsrichtung heraus.
Monopile foundations for offshore-wind power plants – On the influence of multidirectional cyclic loading.
The design of offshore-monopile foundations for wind power plants with focus on cyclic lateral loads poses a great challenge to designers and consultants as recently there are no verified design rules. As a first approach methods used in research and development, like finite element analysis or small scale tests, concentrate on unidirectional swelling loads. However small scale tests described herein demonstrate that minor changes of loading direction provide pile head displacements that exceed those of an unidirectionally loaded pile by far. The pile follows a path of minimum soil resistance. It drifts off main loading direction.

Wind and wave conditions, DOWEC (Dutch Offshore Wind Energy Converter Project

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The overall damping of an offshore wind turbine during different operating conditions. EWEA (European Wind Energy Association) offshore

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Devriendt, C. & Weijtjens, W. (2015). The overall damping of
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Centrifuge modelling of drained lateral pile-soil response

- R Klinkvort

Klinkvort, R. (2012). Centrifuge modelling of drained lateral pile-soil
response. PhD thesis, Technical University of Denmark, Lyngby,
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Scaling effects in the 1g modelling of offshore pipeline ploughs

- K Lauder
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Lauder, K. & Brown, M. J. (2014). Scaling effects in the 1g
modelling of offshore pipeline ploughs. In Physical modelling
in geotechnics -ICPMG 2014 (eds C. Gaudin and D. White),
pp. 377-383. London, UK: CRC Press.

Evaluation of p-y relations in cohesionless soils

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Murchison, J. M. & O'Neill, M. W. (1984). Evaluation of p-y
relations in cohesionless soils. In Proceedings of the ASCE
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Cyclic behaviour of laterally loaded monopiles in sand supporting offshore wind turbines

- G Nicolai

Nicolai, G. (2017). Cyclic behaviour of laterally loaded monopiles in
sand supporting offshore wind turbines. PhD thesis, Aalborg
University, Aalborg, Denmark.

Consequences of p-y curve selection for monopile design for offshore wind turbines

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