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Fully-Coupled cyclic time-history analyses of monopile foundations in sand
... The model is limited to isotropic clay (not sand nor layered soils) for monopiles under cyclic loadings; the installation method effect on pile response is not considered; and simplification of foundation effect on support structure as an external force. Chaloulos et al. (2024) presented the results of 3D coupled cyclic time history numerical analyses of monopiles supporting a 12 MW OWT to assess conservatism in monopile analysis approaches and evaluate the impact of drainage conditions on monopile response accurately. The monopile is installed in dense cohesionless soils and subjected to a 600-s load history corresponding to the high phase of a 35-h design storm. ...
The offshore wind energy sector is growing rapidly as a means to achieving target net zero GHG (Greenhouse gas) emission by 2050. This technology is been expanded to the offshore wind turbines (OWTs) both bottom-fixed and floating foundations. The foundations of such structures have to be optimized geometrically such that they are robust and resilient against environmental loads from wind, waves and currents which are usually cyclic, multidirectional and complex in nature.
Accurate modelling of the foundation behavior for bottom-fixed and floating OWTs is critical in predicting the global response of the system. This aspect of the integrated design of the entire OWT system is not very much understood in design software programs, typically resulting in empirical modelling to represent the constitutive behavior of the foundation or, and in extreme cases, models that assume the foundation is infinitely rigid (fixed) in many structural and geotechnical engineering applications.
The foundation modeling for OWTs requires considering accumulated rotational deformations due to combined cyclic and sustained loading, which affects the foundation stiffness. Additionally, it needs to account for the coupling of loads from different directions. Such effects have been rarely accounted for comprehensively with simple numerical models.
But, there exists certain specialized models like the Houlsby-Abadie Ratcheting Model (HARM) strongly rooted in the kinematic hardening principles within the hyperplasticity (thermo-mechanical) framework, which enables capturing of the accumulated deformations over many cycles (typically millions) of cyclic loadings. Then, there is the REDWIN model which is an acronym referring to “REDucing cost in offshore WINd by integrated structural and geotechnical design”, and it account for the multidirectional load coupling.
This research focuses on programming, improving, and developing a novel constitutive model called CLAP an acronym for “Cyclic Loading & Analysis of Piles”. The output of this work can be further enhanced and used for various applications and case studies on complex multidirectional cyclic loading in the offshore industry.
... The study by Chaloulos et al. (2024) explores the response of monopile foundations for offshore wind turbines (OWTs) in dense sand under cyclic loading conditions. Utilising a three-dimensional coupled cyclic time-history numerical analysis, the research focuses on the effects of drainage conditions on the performance of monopiles. ...
This research comprises an in-depth review of monopile foundations for offshore wind turbines un-der monotonic and cyclic loads. The review study was complemented with performance evaluation of the current design methodologies using advanced finite-element analyses. Overview of intricate nature of pile-soil interactions conducted yielded inadequacy of conventional monotonic p-y curves, which were historically tailored for the oil and gas industry. The paper dives into the effects of cyclic loads on soil stiffness around monopile foundations which indicated dissensus in the scientific community. In the realm of soil damping for monopile foundations, the study underscores the com-plexities of damping and the general neglect of directly calculated soil damping ratio. Performance assessment of various design methodologies is central to this research. By comparing the conventional API p-y curves, the PISA design method, and the new ISO/API p-y curves with three-dimensional finite element analyses, a discerning evaluation emerges, pinpointing the strengths and drawbacks of the current engineering methodologies. Overall, the study concludes the pressing need for refined, evidence-based geotechnical strategies in the realm of monopile foundation de-sign and assessment.
To evaluate lateral resistance of the rigid monopile for the wind turbine in dense sand under the lateral cyclic loading, centrifuge model tests are performed, focusing on the base resistance and degradation of the soil resistance under two-way lateral cyclic loading in short-term. The slenderness ratio (= embedded pile length to diameter) is varied from 3.75 to 8 and the loading frequency is ranging from 0.002 Hz to 0.4 Hz in the prototype scale. In cyclic loadings with a maximum horizontal displacement of 5% of the pile diameter, build-up of the excess pore water pressure is observed but the maximum value of the average excess pore water pressure ratio is around 50% in steady-state for the dense sand whose relative density is 80%. A simple analytical model for the rigid pile with considering the base resistance is derived and is used to quantify the significance of the resistance at the pile base and degradation of the soil resistance under the cyclic loading. When the slenderness ratio is less than five, the significant contribution of the moment resistance at the base is confirmed. Estimation of the degradation of the horizontal subgrade reaction coefficient using the simple analytical model suggests that, by cyclic shear tests for determination of deformation properties of soil in a laboratory, it is possible to estimate the degradation of the soil stiffness and parameters for the reduced sway-rocking type foundation model.
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.
The Ta-Ger constitutive model for sand implemented in the finite difference code FLAC 3D was used to simulate selected field tests of monopiles in Dunkirk sand conducted as part of the PISA program. The test piles simulated were medium diameter piles subjected to both monotonic and cyclic lateral and overturning loading. Comparison between numerical results and test measurements show that the simulations can reproduce the basic mechanisms of the monopile/soil system response, under both monotonic and cyclic loading. Features reproduced in the simulations include the increase of the system stiffness during cyclic loading and the associated decreasing rate of accumulation of lateral displacement and rotation. Lateral soil support in terms of p-y curves as well as distributed moment due to vertical shear stresses along the pile perimeter were obtained from the numerical analysis. It is shown that the numerical methodology can be used to gain insight into soil-OWT foundation interaction mechanisms and derive the soil reactions acting on the foundations as a result of lateral and overturning loads.
Based on advanced 3D finite element modelling, this paper analyses the stress paths experienced by soil elements in the vicinity of a monopile foundation for offshore wind turbines subjected to cyclic loading with the aim of informing soil laboratory testing in support of monopile foundation design. It is shown that the soil elements in front of the laterally loaded monopile are subjected to complex stress variations, which gradually evolve towards steady stress cycles as the cyclic lateral pile loading proceeds. The amplitude, direction and average value of such steady stress cycles are dependent on the depth and radial distance from the pile of the soil element, but it also invariably involves the cyclic rotation of principal stress axes. Complementary laboratory testing using the hollow-cylinder torsional apparatus was carried out on granular soil samples imposing cyclic stress paths (with up to about 3 × 104 cycles) which resemble those determined after 3D finite element analysis. The importance of considering the cyclic rotation of principal stress axes when investigating the response of soil elements under stress conditions mimicking those around a monopile foundation subjected to cyclic lateral loading is emphasised.
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.
Bucket foundations have been increasingly used to support offshore wind turbines as alternatives to monopiles. Despite the substantial research effort on the bearing capacity and stiffness of such foundations in recent year, there is still a lack of knowledge regarding their cyclic response in saturated sand. In this paper, the multiaxial sand constitutive model Ta-Ger implemented in the finite deference code FLAC3D is employed in the analysis of the lateral response of bucket (skirted) foundations subjected to wind/wave loading. The model is reformulated to reproduce the cyclic response of sand for undrained, fully drained and partially drained conditions, using a unique set of calibration parameters. Having been calibrated against laboratory data available in literature, it is then used to predict the long-term cyclic lateral response of a bucket foundation in dry medium dense sand from a centrifuge experiment. After building confidence in the numerical approach the drainage effects are investigated. To gain qualitative insights into the effect of drainage conditions, the 3D numerical model, used to simulate the centrifuge test, was analyzed under saturated conditions and a range of soil permeabilities. It was shown that when flow is allowed the response up to a number-of-cycles threshold resembles that of fully drained conditions. Above this threshold, significant and abrupt increase of excess pore water pressures occurs causing liquefaction. Increasing the permeability delays the occurrence of liquefaction and the associated development of large deformations
When discussing the connection of wind energy and climate change, normally, the potential of wind energy to reduce green house gas emissions is emphasised. Hence, effects of wind energy on climate change are analysed. However, what about the other direction? What is the impact of climate change on wind energy? Recently, the effect of a reversal in global terrestrial stilling,that is, an increase in global wind speeds in the last decade, on the wind energy production has been analysed. Certainly, knowledge about potential changes in energy production is essential to plan future energy supply. Nonetheless, at least similarly important is the effect on loads acting on wind turbines. Increasing loads due to higher wind speeds might reduce wind turbine lifetimes and yield higher costs. Moreover, especially for already existing turbines, it might even affect the structural reliability. Since the impact of climate change on wind turbine loads is largely unknown, it is studied in this work in more detail. For this purpose, different existing models for predicted changes in wind speed and air temperature and their uncertainties are used to forecast the environmental conditions an exemplary offshore wind turbine is exposed to. Subsequently, for this turbine, the lifetime fatigue damages are calculated for different prediction models. It is shown that the expected changes in lifetime fatigue damages are present but relatively small compared to other uncertainties in the fatigue damage calculation.
With the offshore wind industry rapidly expanding worldwide, geotechnical research is being devoted to foundation optimisation – most intensively for large-diameter monopiles. The analysis and design of monopiles still suffers from significant uncertainties in relation to cyclic/dynamic loading conditions. The aim of this work is to shed new light on dynamic soil–monopile interaction, based on the results of unique full-scale experiments performed at the Westermeerwind wind park (Netherlands). The response of a 24 m long, 5 m diameter monopile to harmonic lateral loading of varying amplitude and frequency is inspected. The analysis of original field measurements (soil accelerations and pore pressures) enables the lateral stiffness observed at the monopile head to be linked to dynamic effects occurring in the surrounding soil. The interpretation of measured data is supported by three-dimensional finite-element studies, also looking at the influence of drainage conditions and monopile size. The set of results presented supports the need for dynamics-based monopile design, as higher frequencies gain relevance in the most recent offshore wind developments.
In order to perform optimised and safe design of foundations for offshore wind turbines (OWT), it is important to have calculation tools that describe the key features of water-saturated soil subjected to complex and irregular loading over a wide range of strain levels. Soils subjected to cyclic loading are prone to strain accumulation. The accumulated (plastic) volumetric strain may result in excess pore pressure or stress relaxation, which will reduce the effective stresses, stiffness and strength of the material. Strain accumulation in dense sand is a complex mechanism of deformation and it is challenging to describe it properly. Four different soil models to describe the stress–strain relationships of dense sand are evaluated in this paper: two implicit models that follow the actual stress history and two explicit models that calculate the accumulated strains as a function of number of cycles. These models are first evaluated on the basis of their theoretical framework and back-calculations of laboratory tests specifically carried out for the design of OWT foundations in dense sand. Second, the models are implemented in finite-element analyses and evaluated on the basis of the analyses of an OWT monopile subjected to different loading conditions.
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.
Concerning on the liquefaction behavior of a type of bulk cargoes, iron ore fines (IOF), during maritime time transportation, systematic experimental and numerical programs were conducted. In this study, as an important parameter for seepage analysis, permeability of saturated and unsaturated typical IOF were evaluated in a triaxial system. As a comparison, similar tests were also conducted on a widely used laboratory material, Toyoura sand. The tests were conducted very carefully considering effects of system head loss and filter clogging issues on the hydraulic gradient applied to specimens. It was revealed that coefficient of permeability (k) of the typical IOF with compaction degree of 91-93% was about 1×10-5m/s for saturated condition (Sr=100%) and 2×10-7 m/s for Sr=84%. In addition, k of IOF-B in a full Sr range was estimated based on water retention data and k of unsaturated Toyoura sand in the past studied were summarized, which suggested that the testing system performed reasonably well.
A multiaxial constitutive model for sand (Ta-Ger model) based on a smooth-hys-teresis plasticity framework, implemented in the finite difference code FLAC and FLAC3D, is used for the 2D and 3D simulation of liquefaction-induced settlements of shallow foundations in centrifuge experiments. The same set of calibrated parameters were used in both 2D and 3D sim-ulations. It is shown that 3D analyses are in close agreement with the experimental results both in terms of foundation settlements and excess pore pressures, whereas the 2D analyses tend to overpredict the measured foundation settlements.
This paper reviews foundations for offshore wind energy convertors considering the significant growth of offshore wind energy since the early 2000s. The characteristics of various foundation types (i.e., gravity, pile, suction caisson, and float type) and the current status of field application are discussed. Moreover, the mechanical characteristics of soil are described in the sense that these characteristics including modulus, strength, damping, and modulus degradation of soil play critical roles for the design of offshore foundations. By using these mechanical properties of soil, theoretical studies to consider structure-soil interaction are classified (into equivalent spring models, distributed spring models, and continuous element models) and explained. Field and laboratory experiments on the response of structure embedded in soil to static and dynamic loads are discussed. Based on the review of previous studies, directions for future research and study on offshore wind turbine are suggested.
The recently developed constitutive model for sand, designated as Ta-Ger sand (as described by the present authors in another recent paper), is reformulated to account for intrinsic and stress-induced anisotropy. The model combines features of bounding surface plasticity and Bouc–Wen type hysteresis, and incorporates Rowe's dilatancy theory and the critical state concept. A physically motivated calibration methodology is developed with the aim to reduce the number of internal model parameters by expressing them as functions of four state variables: (a) Bolton's relative density index, Ir, for measuring the ‘distance’ between the current stress state and the critical state; (b) cumulative absolute deviatoric strain increment for controlling the evolution in stress space of the bounding and phase transformation lines; (c) principal stress rotation angle; and (d) intermediate stress ratio accounting for stress-induced anisotropy. The calibration procedure is step-by-step validated against experimental data for various drained and undrained loading paths (including triaxial compression and extension, plane-strain compression and direct simple shear) and initial states (relative density and pressure). Three different types of sand are examined to account for diverse behaviour, even for the same initial states and applied stress paths, due to intrinsic anisotropy attributed to fabric effects (e.g. grain size, shape and packing).
Foundation design of structures subjected to cyclic loading, including stability, cyclic and permanent displacements, soil stiffness for use in dynamic analyses, and soil reactions, requires that effect of cyclic loading is accounted for in the soil parameters. A primary goal of this paper is to provide correlations of these parameters with index parameters for use in practical design. The contour diagram framework for interpretation and presentation of cyclic soil behavior is summarized, as well as pore pressure and cyclic strain accumulation procedures to establish equivalent number of maximum loads, Neq, that gives the same degradation as the irregular cyclic load history. Guidance is given on how the soil parameters can be applied in design, and calculated and measured prototype observations and model test results are used to validate the soil parameter framework. Focus is given to foundation design of structures, but a procedure to analyze the stability of slopes subjected to cyclic loading is also included.
A revised copy of the manuscript, in which some of the figures given in the original article have been amended, can be downloaded from the following link. The link also contains a video of the presentation and a copy of the power point presentation.
http://www.issmge.org/committees/technical-committees/applications/offshore
and clicking on “Additional Information”.
To understand the post-liquefaction behavior of liquefied ground, it is important to get a better understanding and a more suitable characterization of the variation of excess pore pressure after liquefaction. In this paper, the soil permeability is considered as one of the key soil parameters for clarifying the mechanism of post-liquefaction behavior of liquefied ground. For this reason, a series of shaking table tests were conducted for a Toyoura sand deposit with different soil permeability values. Polymer fluid was used in model tests to vary the permeability of sand deposits. Excess pore pressures and settlements were measured in each test. A basic mechanism in post-liquefaction behavior and the solidification phenomenon after liquefaction were discussed based on these test results. Also, a new method for predicting the dissipation of excess pore pressure was developed. This study provides evidence of the important effect of soil permeability on the velocity with which the solidification front moves upward in liquefied ground. It is suggested that the value of coefficient of permeability of liquefied sand can increase to about 4.0 times the initial value. This variation of permeability after liquefaction should be taken into account in post-liquefaction analysis.
The seismic performance of an LNG tank on liquefiable soil improved with stone columns is assessed through 3D effective stress time history analyses. The numerical methodology, which is validated against centrifuge tests, uses the Ta-Ger model to capture the complex sand response under earthquake loading while it simultaneously accounts for Soil-Foundation-Structure interaction by incorporating tank inertial response and both convective and impulsive hydrodynamic actions through a system of properly calibrated oscillators. The methodology introduces a novel technique for incorporating the "improvement" effect of the stone columns by means of "equivalent" soil properties calibrated through separate analyses of a representative remediated 3D soil "cell" explicitly simulating the stone columns within the soil. The analyses show that the presence of the stone columns substantially reduces shear deformations in the improved soil. During shaking, tank settlements accumulate through a rocking, downwards ratcheting, mechanism, which is however constrained by the formation of a stable, nonliquefied soil zone below the tank. Post-seismic, reconsolidation settlements, primarily originating from unimproved zones below the stone columns, are also assessed. Once the complex soil behavior-and dynamic load-mechanisms are comprehensively addressed, differential settlements remain well below allowable limits, demonstrating adequate structure performance even under the high design shaking levels.
Cyclic loading of saturated sand under partially drained conditions may lead to accumulated strains, pore pressure buildup, and 7 consequently reduced effective stress, stiffness, and shear strength. This will affect the ultimate limit state capacity of monopile foundations in 8 sand for offshore wind turbines. This paper calculates the performance of large-diameter monopile foundations, which are installed in uniform 9 dense sand, subjected to storm loading using the partially drained cyclic accumulation model (PDCAM). The simultaneous pore pressure 10 accumulation and dissipation is accounted for by fully coupled pore water flow and stress equilibrium (consolidation) finite element analyses. 11 Drainage and cyclic load effects on monopile behavior are studied by comparing the PDCAM simulation results with simulation results using 12 a hardening soil model with small strain stiffness. At the end, a simplified procedure of PDCAM, named PDCAM-S, is proposed, and the 13 results using this approach together with PLAXIS 3D and the NGI-ADP soil model are compared with the PDCAM results.
The analysis of cyclically loaded piles is acquiring ever greater relevance in the field of geotechnical engineering, most recently in relation to the design of offshore monopiles. In this area, predicting the gradual accumulation of pile deflection under prolonged cycling is key to performing relevant serviceability assessments, for which simplified pile–soil interaction models that can be calibrated against common geotechnical data are strongly needed. This study proposes a new cyclic p−y model for piles in sand that takes a step further towards meeting the mentioned requirements. The model is formulated in the framework of memory-enhanced bounding surface plasticity, and extends to cyclic loading conditions the previous monotonic, CPT-based p−y formulation by Suryasentana and Lehane (2016); additionally, detailed modelling of pile–soil gapping is introduced to cope with the presence of unsaturated sand layers or, more generally, of cohesive soil behaviour. After detailed description of all model capabilities, field data from an onshore cyclic pile loading test are simulated using the proposed p−y model, with the most relevant parameters calibrated against available CPT data. Satisfactory agreement is shown between experimental and numerical results, which supports the practical applicability of the model and the need for further studies on a fully CPT-based calibration.
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.
In order to study the effect of typhoons on the accumulated deformation of monopile foundations for offshore wind turbines, a series of 1-g laboratory model tests with a geometrical scale of 1:100 were carried out. Through the horizontal static and cyclic loading tests of a stiff pile embedded in a medium dense sand deposit, the relationship between the accumulated rotation of the pile and the number of loading cycles under different loading conditions was obtained. The results show that the final accumulated rotation is mainly caused by the typhoon load series and is not affected by the loading sequence. Based on these results, a method is presented to predict the accumulated rotation of the monopile foundation during its service life, and a case study of a 6 MW wind turbine supported by a monopile at a water depth of 30 m in sand is conducted by using the method. The results show that the permanent accumulated rotation of the monopile throughout the design life is mainly contributed by cyclic loading induced by typhoons and the contribution of cyclic loading with small amplitudes can be ignored.
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.
Perspectives on design of offshore wind turbine (OWT) monopile foundations are provided in this paper by logically adopting optimal analysis choices with a balance between accuracy and computational efficiency. A newly developed analysis framework is used for this purpose. The analysis framework consists of dynamic analysis with linear viscoelastic soil and static analysis with nonlinear elastic soil. The framework is used to show that the Timoshenko beam theory produces most accurate monopile response although the Euler-Bernoulli beam theory produces optimal results maintaining a balance between accuracy and computational efficiency. The rigid beam theory can be used only under very restricted soil and monopile conditions. The analysis further demonstrates that static analysis is sufficient and optimal in producing monopile-soil stiffness values that can be used for determining the natural frequency of vibration of the OWTs. Moreover, nonlinear elastic analysis is sufficiently accurate and quick to produce monopile responses that can be used in design and there is no need for elasto-plastic analysis. The aspect of cyclic degradation of soil stiffness over the design life of monopiles is not considered. Thus, an optimal pathway for monopile design is described using the newly developed analysis framework and demonstrated through a design example.
The paper evaluates the dynamic performance of existing residential houses affected by gas-extraction-induced earthquakes in an area of low tectonic seismicity where structures have not been designed against earthquake loading. The foundation consists of narrow spread footings (width, B < 0.7 m), while the seismic demand is characterized by low intensity. Nonlinear, effective stress, fully coupled, dynamic soil-structure interaction analyses were performed to develop estimates of liquefaction-induced settlements for buildings on narrow spread
footings, founded in a range of soil conditions, with ground motions and structural characteristics that are typically encountered in the study area. The results verify patterns observed in recent studies for slab foundations and shed light on new mechanisms. For the low magnitude earthquakes considered in this study, the total
foundation settlements were found to be relatively limited, although simplified liquefaction triggering calculations would sometimes predict low factors of safety against liquefaction. A simplified equation was developed from regression of the numerical analyses results to derive estimates of liquefaction-induced settlements for residential buildings that was adopted in the latest update of the relevant seismic building code.
A framework for the estimation of coseismic deformations in the postliquefaction regime is developed based on an extensive database of available cyclic undrained stress-controlled tests on clean sand samples without static shear bias, covering a wide range of relative densities. Based on fundamental experimental observations, a compliance rate is defined as the postliquefaction shear strain rate per cycle over the shear stress amplitude. Semiempirical relationships of the compliance rate as a function of relative density are developed to provide guidance for estimating postliquefaction shear strains. The proposed framework provides a basis for the calibration of advanced constitutive models capable of capturing postliquefaction strain accumulation. A calibration methodology is proposed using both existing liquefaction resistance curves and the newly developed semiempirical relationships for estimating postliquefaction shear strain accumulation. The validity of the proposed methodology is demonstrated by numerical simulations, using the PM4Sand model, of two well-documented centrifuge tests focusing on liquefaction-induced demands on engineering structures.
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.
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.
The Ichthys Riser Support Structure (RSS) is a large subsea structure in 250 m water depth, which comprises a 110 m tall tower with a 130 m wide arch for supporting up to 25 flexible risers and umbilical's as they transition from the seabed to the semi-submersible Central Processing Facility (CPF). The foundation for the RSS comprises a skirted raft approximately 69 m x 38 m in plan with a central cut-out and 6.8 m deep skirts installed in uncemented carbonate sediments through a combination of self penetration and suction assistance. A 40 year design life combined with the requirement for no loss of containment during a 1 in 10,000 year metocean or seismic event made the geotechnical and foundation engineering design a challenge.
This paper will describe the innovations adopted in assessing the RSS foundation capacity against the design in-place loads and the key results and observations with respect to the installation of the foundation.
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.
Commonly used simplified one-dimensional nonlinear seismic site response analyses employ constitutive models based on a variation of the hyperbolic model to represent the initial stress-strain backbone curve. Desirable features of the backbone curve include provision of (1) an initial shear modulus at zero shear strain, (2) a limiting shear stress at large shear strains, and (3) flexible control of the nonlinear behavior between those boundary conditions. Available hyperbolic models have combinations of two of these features. A new general quadratic/hyperbolic (GQ/H) model is developed from the bivariate quadratic equation to provide all desired features. Nonlinear behavior is controlled by a shear-strain-dependent curve-fitting function. The model’s unload-reload rules and coupling with pore-water pressure generation are also presented. Several total-stress site response analyses are presented to demonstrate the performance of the GQ/H model relative to a commonly used hyperbolic model in which the maximum shear stress cannot be defined. The analyses show the importance of properly representing the maximum shear stress in the constitutive model because it may lead to underestimation or overestimation of the computed site response.
Four semi-empirical procedures for construction of p-y curves in cohesionless soils were developed to fit data from a particular load test or a specific set of tests on similar soils. The relative accuracy of these procedures is studied by applying each to a variety of conditions defined in a data base consisting of full-scale lateral load tests in very loose to very dense cohesionless soils and of piles with several cross-sectional shapes and a range of diameters.
A finite element based procedure for calculation of the behaviour of offshore foundations subjected to combined cyclic and average loads is presented. A material model called PDCAM is developed for this purpose. The input to the model is strain and pore pressure contour diagrams from undrained cyclic laboratory tests, stress-strain relationships from drained monotonic triaxial compression and extension tests, non-linear compressibility curves from oedometer tests and permeability coefficients. The applied load history is idealized by a load composition containing load parcels with average and constant cyclic loads in each parcel. The soil is assumed to be perfectly undrained during one single load cycle, while pore pressure dissipation is accounted for under the average loads by a coupled non-linear consolidation phase. The performance of the procedure is demonstrated by some idealized examples and by back calculation of a centrifuge test of a gravity base structure on very dense sand.
Offshore wind turbines (OWTs) are generally supported by large-diameter monopiles, with the combination of axial forces, lateral forces, bending moments, and torsional moments generated by the OWT structure and various environmental factors resisted by earth pressures mobilized in the soil foundation. The lateral loading on the monopile foundation is essentially cyclic in nature and
typically of low amplitude. This state-of-the-art review paper presents details on the geometric design, nominal size, and structural and environmental loading for existing and planned OWT structures supported by monopile foundations. Pertinent ocean-environment loading conditions, including methods of calculation using site-specific data, are described along with wave particle kinematics, focusing on correlations between the loading frequency and natural vibration frequency of the OWT structure. Existing methods for modeling soil under cyclic loading are reviewed, focusing in particular on strain accumulation models that consider pile–soil interaction under cyclic lateral loading. Inherent limitations=shortcomings of these models for the analysis and design of existing and planned OWT monopile foundations are discussed. A design example of an OWT support structure having a monopile foundation system is presented. Target areas for further research by the wind-energy sector, which would facilitate the development of improved analyses=design methods for offshore monopiles, are identified.
Based on laboratory tests with constant cyclic shear stress, a method for predicting clay behaviour under storm loading which causes varying cyclic shear stresses is developed. The method is based on accumulated cyclic shear strains, and is used to predict cyclic shear stresses and in tests with strain-controlled cyclic loading.
Friction between sand and steel is studied by laboratory tests under repeated loading. The interface behavior under one-way and two-way repeated loading was compared with the behavior under monotonic loading. Once a sand-steel interface slides, the coefficient of friction at the re-start of sliding becomes different from the peak value in the first. The coefficient of friction under repeated loading converges to a value close to the residual shear stress ratio of the sand mass. A shear zone formation along sand-steel interface was observed with macroscopic photographing. This shear zone formation along the sand-steel interface explains the decrease of upper-limiting value of the coefficient of friction. The amount of particle crushing was evaluated by sieving the sand before and after the friction tests.
As part of various research projects [including the SRS (Savannah River
Site) Project AA891070, EPRI (Electric Power Research Institute)
Project 3302, and ROSRINE (Resolution of Site Response Issues from the
Northridge Earthquake) Project], numerous geotechnical sites were
drilled and sampled. Intact soil samples over a depth range of several
hundred meters were recovered from 20 of these sites. These soil samples
were tested in the laboratory at The University of Texas at Austin (UTA)
to characterize the materials dynamically. The presence of a database
accumulated from testing these intact specimens motivated a
re-evaluation of empirical curves employed in the state of practice. The
weaknesses of empirical curves reported in the literature were
identified and the necessity of developing an improved set of empirical
curves was recognized. This study focused on developing the empirical
framework that can be used to generate normalized modulus reduction and
material damping curves. This framework is composed of simple equations,
which incorporate the key parameters that control nonlinear soil
behavior. The data collected over the past decade at The University of
Texas at Austin are statistically analyzed using First-order,
Second-moment Bayesian Method (FSBM). The effects of various parameters
(such as confining pressure and soil plasticity) on dynamic soil
properties are evaluated and quantified within this framework. One of
the most important aspects of this study is estimating not only the mean
values of the empirical curves but also estimating the uncertainty
associated with these values. This study provides the opportunity to
handle uncertainty in the empirical estimates of dynamic soil properties
within the probabilistic seismic hazard analysis framework. A refinement
in site-specific probabilistic seismic hazard assessment is expected to
materialize in the near future by incorporating the results of this
study into state of practice.
In order to examine the effects of fabric anisotropy on the relationships between the cyclic triaxial and torsional shear strengths, a series of cyclic undrained triaxial and torsional shear tests was performed on three kinds of sands made by three different sample preparation methods.
The test results showed that the cyclic undrained strengths varied with sample preparation methods. In particular, the effects of sample preparation methods were clearly observed in the triaxial test. The relationships between the cyclic triaxial and torsional shear strengths also varied with sample preparation methods. In addition, it was found that the effects of fabric anisotropy due to the difference in the sample preparation methods appear in the axial deformation and the developed pore water pressure characteristics during the cyclic triaxial test. In order to evaluate quantitatively the effects of fabric anisotropy on the relationships between the cyclic triaxial and torsional strengths, new index parameters were introduced, which express the degree of the anisotropy of specimens. Consequently, it was indicated that there exists a unique rule between these parameters and the ratio of torsional strengths to triaxial strengths.
A cooperative test program of cyclic undrained triaxial tests was performed by five laboratories for both loose (D//r equals 50%) and dense (D//r equals 80%) air-pluviated specimens of Toyoura Sand, which is a clean fine uniform sand having sub-angular to angular shaped particles. This test material has been widely used in Japan for the study of sand liquefaction. The tests were performed following the specified test procedures described in this paper. It was found that the cyclic undrained strength value for a specimen diameter of 5 cm is slightly larger than that for a specimen diameter of 7-10 cm. The major part of the scattering of the data was found due to different specimen diameters. For a similar specimen diameter, a very good degree of agreement for cyclic undrained strength value was obtained.
The effects of sample preparation methods on the cyclic undrained stress-strain behavior of sands were investigated by means of triaxial and torsional shear tests using two kinds of clean sands and one kind of sand including fines, with a wide variation in the sample density. Four different sample preparation methods were adopted; air-pluviation, wet-tamping, wet-vibration, and water-vibration. The differences in the effects of sample preparation methods were found to be significant in both testing methods. However, specific ways in which the sample preparation methods affected the results were not consistent between the triaxial and torsional shear tests. This indicates that the process of estimating cyclic undrained simple shear strengths from triaxial strengths is not as simple as has previously been considered.
It was found that in torsional shear tests the shapes of strength curves in the planes of the cyclic stress ratio and the logarithm of the number of cycles Nc are similar for different sample preparation methods, in the sense that the different curves collapse into a single curve when these curves are moved appropriately along the log Nc-axis. It was also found that for the same sample density the effects of the sample preparation method on the cyclic undrained stress-strain behavior decrease with the increase in strain. A new density index is proposed, from which the cyclic undrained behavior can be estimated for different sample preparation methods and for different kinds of sands until the shear strain becomes around 3% in double amplitude.
A comprehensive numerical model for the analysis of offshore foundations under a general transient loading is presented here. The theoretical basis of the model lies on the Swansea formulation of Biot’s equations of dynamic poroelasticity combined with a constitutive model that reproduces key aspects of cyclic soil behaviour in the frame of the theory of generalised plasticity. On the practical side, the adoption of appropriate finite element formulations may prevent the appearance of spurious numerical instabilities of the pore pressure field. In this respect, the use of a coupled enhanced-strain element is here proposed. On the other hand, the practicality of the presented model depends ultimately on its computational efficiency. Some practical recommendations concerning the solution strategies, the matrix storage/handling procedures and the parallel multi-processor computation are here provided. Finally, the performance of the model with a benchmark study case and its practical application to analyse the soil-structure interaction of an offshore monopile under a realistic transient storm loading are discussed.
A study on the influence of the plasticity index (PI) on the cyclic stress-strain parameters of saturated soils needed for site-response evaluations and seismic microzonation is presented. Ready-to-use charts are included, showing the effect of PI on the location of the modulus reduction curve G/G(max) versus cyclic shear strain-gamma-c, and on the material damping ration gamma-versus-lambda-c curve. The charts are based on experimental data from 16 publications encompassing normally and overconsolidated clays (OCR = 1-15), as well as sands. It is shown that PI is the main factor controlling G/G(max) and lambda for a wide variety of soils; if for a given gamma-c PI increases, G/G(max) rises and lambda is reduced. Similar evidence is presented showing the influence of PI on the rate of modulus degradation with the number of cycles in normally consolidated clays. It is concluded that soils with higher plasticity tend to have a more linear cyclic stress-strain response at small strains and to degrade less at larger gamma-c than soils with a lower PI. Possible reasons for this behavior are discussed. A parametric study is presented showing the influence of the plasticity index on the seismic response of clay sites excited by the accelerations recorded on rock in Mexico City during the 1985 earthquake.