Numerical investigation on bearing capacity of OWT foundation with large diameter monopile under Seismic load
Introduction
In the context of the pressing need for clean and sustainablesources of energy, some countries are adoptingambitious policies for the branch of renewable energies, and the harvest of wind energy through theusage of offshore wind turbines is likely to play a key role, sothe offshore foundations are back into the spotlight of engineeringresearch again.Monopiles are the most commonly used foundation system forsupporting offshore wind turbines (OWT), which are single largediameter open-ended tubular steel piles. With the increase of impeller diameter and tower of offshore wind turbine, the buried depth and the diameter of monopile foundation also increase accordingly.But, there are several special phenomena inherentto the offshore environment compared with the terrestrial environment. On the one hand, the effects on the foundationof a permanent exposure to cyclic loads from wind, wave and seismic load,which are still not well understood and do require considerableefforts in research (e.g. Randolph et al, 2005; Raffaele,2018); On the other hand, it must also be pointed out that apart fromthe excess pore pressure generated by the low frequency wave load and wind load acted on the turbine, the effect of high frequency seismic load may result in a net porepressure accumulation and soil shear strength attenuation within a very short period of time (e.g. Luan et al, 2009; Kaynia,2019; Hu et al,2020), which could causeits foundation to sink, tilt or destruct. So the frontier engineering issues faced by the geotechnicalspecialists for the marine foundation of such offshore wind turbines arefar from closed, and the remarkable feature are aggravated by their large dimensions and especiallyby their high ratios of lateral to vertical load, which makethem unprecedented in the offshore engineering field.
Now, the large monopile foundations of about8m in diameter arecurrently state of the art and plans for future wind farms (Achmus et al, 2009). The behaviour of such foundations underthe effects of a short-term seismic load is currently a subject ofintense research; a typical monopile schematic diagram of offshore wind turbine in two-dimensional planeis shown in the Fig. 1 and is adopted in this paper.However, most design considerations for dynamic seismic effects arebased on pseudo-static approaches where the foundation'sresponse is calculated from a static analysis using degradatedsoil strength properties (e.g. Taiebat 2000, Pablo et al 2014). It can be noted that such‘dynamic degradation'is often just an empirical techniqueby experts to merelyestimate the magnitude of accumulated displacements and doesnot necessarily reflect the actual physical characteristics of the soil due to dynamic cyclic load.
A number of investigations using scaled model test and numerical analysis have been conducted to study the response of pile-soil interaction under environmental cyclic loads (e.g. Brown&Reese,1987; Sadek & Isam,2004; Mayoral et al,2005; Kallehave et al,2012; Lu & He, 2014; Zdravkovic et al, 2015; Byrne et al, 2017; Versteijlen et al, 2017; Kementzetzidis et al, 2019). Moreover, numerical simulation can provide further insights into the failure mechanisms and explain some observations, so using numerical methods to study the soil dynamic deformation and excess pore pressure of foundation have been presented by a number of researchers (e.g. Al-Homoud & Al-Maaitah, 1996; Zhou& Randolph, 2009; Omarov, 2010; Mayoral et al, 2016). In most cases, when seabed soil is withstood cyclic load, some dynamic mechanical characteristics such as the cumulative plastic deformation, the stiffness softening and the strength reduction, usuallyappear clearly (e.g. Tileylioglu et al,2011; Pecker et al, 2012; Li et al,2020). And due to of the complex behaviour of pile-soil interaction, some researchers employed a mathematical models in form of a curve or modified dynamic curve to simulate the soil stress-strain constitutive relationship shown in Fig. 2, where is the cyclic horizontal resistance per unit length of the buried pile and is the corresponding horizontal motion, is the rate of horizontal motion (e.g. Matlock et al, 1978; Randolph, 1981; Naggar et al, 1995; Mohammad et al,2012; Chatterjee et al,2015; Murphy et al,2018). Meanwhile, in order to consider the cyclic weakening of soil shear strength and its corresponding accumulated plastic shear strain, Einav & Randolph (2005) proposed a shear strength degradation curve and an empirical equation. Bayat et al. (2016) suggested a set of theoretical equations to reflect the influence of load rate on soil-pile interaction. And Zhang et al (2019) proposed a simple formula to calculate the dynamicdegradation relation of soil resistance under cyclic numbers as shown in formula (1) below.Where, the parameter expresses the numbers of dynamic cycles, and means the degradation coefficient of soil resistance.
Actually, when subjected to high frequency dynamic seismic load, the horizontal bearing capacity of large-diameter monopile is different from the quasi-static condition; and the soil deformation law and the failure mechanism surrounding the monopile have obvious influence on the horizontal bearing capacity. Moreover, under the dynamic seismic load, the seabed soil tends to exhibit some dynamic characteristics such as the stiffness softening andthe strength weakening, which also affects the interaction between pile and soil.Based on the assumption that the seabed soil presents elastic-plasticity deformation under dynamic load, a dynamic constitutive model of the seabed soil was derived by using the boundary surface theory in this paper; andan interface contact algorithm is also proposed by assuming that there are both tangential and normal constraints on the interface between pile and soil. Then the horizontal ultimate bearing capacity and its corresponding soil deformation law due to cyclic seismic load are analyzed numerically.
Section snippets
Soil dynamic constitutive model
To analyze the surrounding soil deformation law and its corresponding shear strength weakening rule, which is around the three-dimensional large diameter monopile, a dynamic elastic-plasticity memorial nested yield surface model of seabed soil is derived theoretically. In this model, the inverted load surface , the damaged surface and the initial load surface , which are tangential with the inside of inverted load surface, are memorized at the end of any incremental process of loading; and
Boundary value problems
In the process of the monopile and the seabed interaction, a three-dimensional monopile with diameter is first buried into the seabed to an assumed depth and the vertical load and horizontal load are applied on the reference point of monopile; then the dynamic seismic load is applied to the bottom of seabed. According to the actual situation, some appropriate boundary conditions are also applied including of pile-soil sliding interface, fluid permeable boundaries and
Finite element formulations for seabed soil
By adoption the Galerkin numerical method to the Biot's dynamic consolidation governing equations (4), (5) and (6) as mentioned previously. The finite element formulation for an elastic-plasticity seabed due to seismic load could be expressed in the following coupled systems:Where the matrix components are given by
Load mode and implementation framework
In order to simulate the bearing capacity of elasticity monopile and the deformation law of elastic-plasticity seabed under seismic load, a set of detailed numerical model is recommended, which is shown in Fig. 11, including of four typical cylindrical sections and five key points varying with depth. Namely, the , , and cylindrical sections are used to simulate the change law of the soil deformation and excess pore pressure along the radial direction of the monopile, and the
Conclusion
In this paper, a numerical model of three-dimensional monopile bearing capacity subjected to seismic load is proposed and investigated. In order to simulate the surrounding soil resistance, a dynamic boundary surface model of saturated soil is derived; and then the horizontal bearing capacity degradation curves and the surrounding soil deformation law are studied in detail; moreover, some effects of soil characteristic parameters on the excess pore pressure are discussed, which includes soil
Declaration of Competing Interest
The authors declare that they have no known competing financialinterestsor personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This paper is supported by Project of National Natural Science Foundation of China under Grant No. 51679224, this support is gratefully acknowledged.
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