Numerical simulation method for stiffness of offshore wind turbine monopile considering long-term circulation and scour

Abstract

The present invention provides a numerical simulation method for stiffness of an offshore wind turbine monopile considering long-term circulation and scour. The present invention uses a linear elastic steel pipe pile model and a Mohr-Coulomb soil model during model establishment, thereby ensuring both accuracy and calculation convenience. By calculating the horizontal ultimate bearing capacity of a monopile, combining a plurality of methods such as a limit analysis method and p-y curve calculation, and considering the influence of different scour depths on a wind turbine, the horizontal load bearing capacity and natural frequency evolution of the monopile are comprehensively evaluated, thereby providing a basis for design and safety assessment. By means of secondary development of Abaqus, a sandy soil stiffness degradation model is established and validated, and the sandy soil stiffness variation under long-term cyclic loading is considered, thereby improving simulation accuracy. A numerical model is validated by means of tests to ensure reliability. The cumulative lateral displacement of a steel pipe pile can also be accurately predicted; the influence of factors including the number of loading cycles, a soil elastic modulus, and an embedding depth on the development of displacement is revealed; the optimization of wind power engineering design is facilitated; and economic efficiency and safety are improved.

Description

Numerical Simulation Method for the Stiffness of Offshore Wind Turbine Monopile Considering Long-Term Cyclic and Scour Technical Field

[0001] This invention relates to the field of wind power engineering, and more specifically, to a numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring. Background Technology

[0002] In wind power engineering construction, the bearing capacity and dynamic characteristics of pile foundations are core issues for ensuring the stable operation of wind turbine generators, which are subjected to various complex loads such as wind and wave loads over long periods in complex natural environments. However, during the long-term service of wind power projects, the bearing characteristics and dynamic response laws of wind turbines under the effects of soil stiffness evolution and scour coupling are still unclear. Currently, most methods for establishing numerical models of pile-soil structures do not fully consider the symmetry of the structure.

[0003] Current technologies for calculating the horizontal ultimate load of monopile foundations rely on relatively simplistic methods, lacking a comprehensive approach. Using only a single calculation method often fails to fully and accurately describe the mechanical behavior of a monopile under horizontal loads, leading to inaccurate assessments of its horizontal load-bearing capacity. This can introduce safety hazards into pile foundation design, resulting in either excessively large piles leading to resource waste or insufficient pile bearing capacity, potentially causing foundation failure under horizontal loads in practical engineering, thus affecting the safety and stability of wind power projects. Furthermore, existing research rarely considers the coupled effects of foundation scour and soil stiffness evolution on wind kinetic and static dynamics. Moreover, existing methods for calculating the horizontal ultimate load may not adequately account for the pile's deformation characteristics and actual pile tip failure modes, resulting in significant discrepancies between calculated results and actual conditions. When simulating the mechanical properties of sandy soil, most existing numerical models do not consider the changes in sand stiffness under long-term cyclic loading. In actual engineering, the stiffness of sand will decrease under long-term wind and wave loads, and existing models cannot accurately simulate this characteristic, resulting in a large error between the simulation results and the actual situation.

[0004] Current technologies lack in-depth research and accurate prediction methods for the deformation and stiffness evolution of wind turbine foundations under long-term cyclic loading. Pile foundations generate cumulative lateral displacement under long-term, low-frequency lateral cyclic forces, but it is currently difficult to accurately predict the cumulative lateral displacement of steel pipe piles during their normal service life. This prevents engineers from fully considering the impact of long-term deformation when designing wind turbine foundations, potentially leading to structural failure due to excessive cumulative lateral displacement during long-term use. Furthermore, the influence of the number of cyclic loading cycles, soil elastic modulus, and steel pipe pile embedment depth on the development of horizontal displacement at the pile top and lateral displacement within the pile body is insufficiently understood, making it difficult to rationally select parameters based on actual engineering conditions and optimize pile foundation design, thus affecting the economy and safety of wind power projects. Therefore, we propose an improvement by developing a numerical simulation method for the stiffness of single piles in offshore wind turbines that considers long-term cyclic loading and scouring. Summary of the Invention

[0005] The purpose of this invention is to address the problems identified in the existing background technology. To achieve the above-mentioned objective, this invention provides the following technical solution: a numerical simulation method for the stiffness of a single pile in an offshore wind turbine considering long-term cycling and scouring, comprising the following steps:

[0006] Step 1: Numerical model establishment. A three-dimensional finite element model of a single pile foundation is established using finite element analysis software. Due to the stress conditions and the symmetry of the pile-soil structure, half of the pile-soil structure is used for analysis.

[0007] Step 2: Calculate the horizontal ultimate load of the single pile foundation and the horizontal ultimate bearing capacity H of the single pile. u The horizontal ultimate bearing capacity is used to measure the ability of a single pile to withstand horizontal loads.

[0008] Step 3: Implementation and experimental verification of the numerical model. Through secondary development of Abaqus, a stiffness attenuation model for sand was established in the numerical analysis program and verified.

[0009] Step 4: Analyze the deformation and stiffness evolution of wind power foundations under long-term cycling. The pile foundation will continuously bear long-term, low-frequency lateral cyclic forces brought about by wind loads and wave loads. Through analysis, the cumulative lateral displacement generated by the steel pipe piles during their normal service life can be accurately predicted.

[0010] As a preferred technical solution of the present invention, in step 1, the numerical model is established. The steel pipe pile adopts a linear elastic model with a pile diameter D = 6.3m, a wall thickness s = 0.64mm, and an elastic modulus E. p=210 GPa; The Mohr-Coulomb ideal elastic-plastic model was selected for the soil, which is simple and clear and can well reflect the loading characteristics of sand. Contact surfaces were set between the pile and the soil, with hard contact for normal contact and friction contact for tangential contact. The friction coefficient was two-thirds of the internal friction angle. The soil cohesion was c = 5 kPa; the internal friction angle φ′ = 32°, the dilatation angle ψ = 0°, and the effective unit weight γ′ = 19.4 kg / m³. 3 Poisson's ratio v = 0.4, and the elastic modulus is taken as follows:

[0011] In the formula: σ at The pressure is atmospheric pressure, taken as 101 kPa; σ m η represents the average soil stress; k and η are dimensionless constants, and in this paper, k = 560 and η = 0.6 are taken.

[0012] As a preferred technical solution of the present invention, step 2, calculating the horizontal ultimate load of a single pile foundation, adopts the limit analysis method.

[0013] The deformation of a single pile exhibits the deformation characteristics of a rigid pile. The pile tip exhibits a kick-out failure pattern, and the entire pile rotates around a point on the pile tip. The horizontal ultimate bearing capacity is represented by H. u for:

[0014] Where: h is the height of the mud surface from the top of the pile; D is the pile diameter; L is the unit weight of the soil; γ s Unit weight of soil; K P Rankine's passive earth pressure coefficient.

[0015] As a preferred technical solution of the present invention, step 2, calculating the horizontal ultimate load of a single pile foundation, adopts the limit analysis method: for a pipe pile, its yield moment can be expressed as:

[0016] In the formula: I P Moment of inertia of the pile section; σ y Yield strength of the pile material.

[0017] As a preferred technical solution of the present invention, step 2, calculating the py curve of the horizontal ultimate load of a single pile foundation:

[0018] When y < 3y 50 hour,

[0019] When y>3y 50 When x>x r At that time, p = 0.72p u

[0020] x <x r hour

[0021] In the formula, y represents the deflection of the pile; 50 x represents the pile displacement when the soil resistance reaches half of its ultimate limit; x is the depth below the mud surface; x r p is the critical depth; p is the soil resistance around the pile; p u The ultimate soil resistance around the pile is equal to the undrained shear strength C. u and ε 50 related.

[0022] As a preferred technical solution of the present invention, step 3, the specific implementation and experimental verification of the numerical model: calculation of the formula below the deep soil layer: p us =(C1X+C2b)γ · X p ud =C3bγ · X

[0023] In the formula, p u γ is the ultimate soil resistance per unit pile length; γ· is the effective unit weight of the soil; X is the depth below the mud surface; C1, C2, and C3 are coefficients related to the internal friction angle φ; and b is the average pile diameter from the mud surface to the depth in question.

[0024] As a preferred technical solution of the present invention, a three-dimensional finite element model of a large-diameter single pile under horizontal load in sand is established, in-situ stress equilibrium is achieved, and a vertical load V is applied. The initial principal stress of each soil element is calculated and extracted. and minor principal stress

[0025] A horizontal load H is applied at the loading point, corresponding to the peak phase of the cyclic load. The major principal stresses under horizontal loading are calculated and extracted for each soil element. and minor principal stress

[0026] Extracted The confining pressure σ experienced by each soil element c Extracted from (2) Extracted from (1) By subtracting the values, we obtain the level of deviatoric stress σ experienced by each soil element. d Substituting into equation (10), we obtain the cyclic stress ratio X of each soil element, i.e.

[0027] The cyclic stress ratio of each soil element is written into the usdfld subroutine. The software will call this subroutine during the analysis and calculate the stress characteristics of the pile foundation under N cycles of loading based on the attenuation stiffness of each soil element after N cycles, where x is the horizontal displacement of the loading point; H u This is the ultimate horizontal static load of the pile foundation.

[0028] As a preferred technical solution of the present invention, step 4, analyzing the deformation and stiffness evolution of the wind power foundation under long-term cyclic loading, shows that the horizontal displacement value at the top of the pile decreases after cyclic loading. As h / L increases, the decreasing trend continues to increase. When h / L is 0.294, the cumulative horizontal displacement value at the top of the pile decreases to 30% of the original value.

[0029] As a preferred technical solution of the present invention, step 4, analyzing the deformation and stiffness evolution of the wind power foundation under long-term cyclic loading, examines the lateral displacement development of a steel pipe pile with an embedment depth of 34m under a horizontal cyclic load of 0.25Hu. Under the horizontal load, the horizontal displacement at the top of the pile continuously develops as the cycle progresses. In the initial stage of the cyclic load, the lateral displacement of the steel pipe pile develops rapidly, and after more than 100 cycles, the lateral displacement development slows down and gradually stabilizes.

[0030] As a preferred technical solution of the present invention, step 4, analyzing the deformation and stiffness evolution of the wind power foundation under long-term cycling, shows that the horizontal displacement at the pile top decreases as the elastic modulus of the soil increases; the embedment depth of the steel pipe pile is relatively small, and the reduction is significant; as the embedment depth of the steel pipe pile increases, the reduction in its lateral displacement gradually decreases.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] In establishing the numerical model, this invention utilizes the stress conditions and the symmetry of the pile-soil structure, analyzing only half of the pile-soil structure. This simplification significantly reduces the computational load and time, lowers the demand for computational resources, and enables faster simulation analysis under limited computational resources, improving the efficiency of the entire simulation process. This helps engineers obtain simulation results and make decisions in a shorter time. The steel pipe piles in this invention use a linear elastic model, while the soil uses the Mohr-Coulomb ideal elastoplastic model. The linear elastic model can accurately reflect the mechanical properties of the steel pipe pile to a certain extent, and its calculation is relatively simple; while the Mohr-Coulomb ideal elastoplastic model is simple and clear, and can better reflect the loading characteristics of sandy soil. The reasonable combination of the two ensures both the accuracy of the model and the convenience of calculation, providing a reliable foundation for subsequent simulation analysis. This invention calculates the horizontal ultimate bearing capacity of a single pile and uses this to measure the horizontal load-bearing capacity of a single pile, providing an important basis for the design and safety assessment of pile-soil structures in wind power projects. Accurate calculation of the horizontal ultimate load helps determine the appropriate size and arrangement of piles, ensuring that the piles can withstand the corresponding horizontal loads in actual engineering projects, avoiding pile foundation failure due to horizontal loads, and improving the safety and stability of wind power projects. This invention uses the limit analysis method to calculate the horizontal ultimate load of a single pile foundation, and combines it with multiple methods such as Py-curve calculation to analyze the horizontal stress characteristics of a single pile from different perspectives. This multi-method approach can more comprehensively and accurately describe the mechanical behavior of a single pile under horizontal loads, providing richer and more reliable data for design and analysis, enabling engineers to better understand the performance of pile foundations and optimize design schemes.

[0033] This invention analyzes the deformation and stiffness evolution of wind turbine foundations under long-term cyclic loading, enabling accurate prediction of the cumulative lateral displacement of steel pipe piles during their normal service life. This is crucial for the long-term stability assessment of wind power projects. Engineers can take corresponding measures based on the prediction results, such as adjusting pile design parameters and strengthening the foundation, to ensure that the wind turbine foundation does not suffer structural damage due to excessive cumulative lateral displacement during long-term use. The analysis results of this invention reveal the influence of the number of cyclic loads, soil elastic modulus, and steel pipe pile embedment depth on the development of horizontal displacement at the pile top and lateral displacement within the pile body. Attached Figure Description

[0034] Figure 1 is a schematic diagram of the force analysis provided by the present invention;

[0035] Figure 2 is a schematic diagram of several different methods provided by the present invention for determining the horizontal ultimate bearing capacity of a single pile;

[0036] Figure 3 is a schematic diagram comparing the method provided in this paper with the experimental results;

[0037] Figure 4 is a diagram of the passive protection measures provided by the present invention;

[0038] Figure 5 is a geological cross-section diagram provided by the present invention;

[0039] Figure 6 is a diagram of a single pile foundation provided by the present invention;

[0040] Figure 7 is a diagram of the multi-pile foundation provided by the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention.

[0042] Example 1: Numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term circulation and scouring. Around the foundation, the water flow velocity increases due to the obstruction of the foundation, creating vortex structures that can carry sediment, leading to localized scouring. Since foundation scouring is difficult to completely avoid in engineering practice, appropriate scouring protection measures are highly effective in reducing localized scouring and improving the stability of the foundation structure. Foundation scouring is a crucial issue to consider in ensuring the safety and stability of the foundation.

[0043] The geological data mainly referenced is the "Survey Report of the 300MW Demonstration Project of Tangshan Leting Putuo Island Offshore Wind Farm". The site is located in the nearshore waters of the Bohai Sea, with a water depth of approximately 7-28m and the center of the site approximately 18km from the coastline. In some areas north, south, and north of the site, the water depth varies considerably due to sand mining. The seabed topography of the proposed project area has significant elevation differences, generally trending downwards in the south and north, and downwards in the west and east. The seabed elevation ranges from -7.10 to -29.80m. The northwest side is adjacent to the Xikengtuo sandbar, where the water depth is relatively shallow, while the east and south sides have greater water depth and are open waters. The geomorphological type is a nearshore underwater sedimentary plain in the Bohai Bay located at the edge of the sandbar area.

[0044] The centrifuge data acquisition and processing system is a specialized measurement device developed and manufactured by ANCO Corporation in the United States. It consists of a data acquisition unit, lower-level hardware, and data processing software. The data acquisition system employs a combination of static and dynamic data acquisition methods, forming a 128-channel data acquisition system. Each channel has a sampling rate of no less than 30K. When used for geotechnical centrifuge simulation tests, it can measure and acquire various changing data of the test model, such as earth pressure, water pressure, displacement, distance, and dynamic strain. It is also equipped with a high-speed photographic and video system, enabling PIV analysis of the test model.

[0045] Test Plan

[0046] Centrifuge Model Scale and Similarity Relationship

[0047] When a physical phenomenon can be described by the functional relationship of n physical quantities, and these physical quantities include m fundamental dimensions, then dimensionless groups (nm) can be obtained using dimensional analysis. The characteristics of this phenomenon can be expressed using the relational form of these (nm) dimensionless groups. This special experiment requires determining three aspects of similarity scale: soil material similarity, structural material similarity, and model similarity scale. Based on the aforementioned geometric dimensions of the structures and the dimensions of the model box, the acceleration of the centrifuge model test is planned to be 100g, i.e., the geometric scale of the model is N = 100. Dimensional conversion is performed according to bending stiffness.

[0048] Centrifuge model test scale relationship

[0049] Model Design

[0050] Taking into account both manufacturing difficulty and precision control factors, aluminum tubes were used for the design and fabrication of both single-pile and multi-pile cap wind turbine models. Since the horizontal resistance and natural vibration of the pile foundation and structure are closely related to the bending stiffness of the structure, a scaled-down model was designed based on the bending stiffness, and the wind turbine structure model was obtained through calculation formulas.

[0051] In the formula, E m E represents the elastic modulus of the model material aluminum. p D is the elastic modulus of the prototype material, steel. m d m D represents the outer and inner diameters of the model. p d p The outer and inner diameters of the prototype.

[0052] For monopile foundations, the tower and piles are connected via flanges. A concentrated mass block, measuring 74.4mm × 20mm × 20mm, is located at the top of the tower. For multipile foundations, the piles are connected to the tower via a pile cap, which is made of aluminum and is bonded to the piles as a single unit.

[0053] Test conditions and scour pit construction

[0054] This experiment aims to study the natural frequency variation and horizontal bearing capacity characteristics of offshore wind turbines with monopile and multipile foundations under different scour depths. Test conditions for wind turbine frequency and bearing capacity at different scour depths will be implemented. For monopile foundations, the natural frequency will be tested at scour depths of 0m, 5m, 10m, and 15m, and the ultimate bearing capacity will be tested at scour depths of 5m, 10m, and 15m. For multipile cap foundations, the natural frequency will be tested at scour depths of 0m, 3m, 6m, 10m, 12m, and 15m, and the ultimate bearing capacity will be tested at scour depths of 6m and 12m. Two sets of wind turbine foundation models will be placed in each model box to improve test efficiency. Scour pits, approximately frustum-shaped, will be excavated around the perimeter of both monopile and multipile foundations using a grinding tool. The excavation depth will be determined according to the different test conditions.

[0055] Test of basic frequency of blower at different scour depths

[0056] Wind turbine foundation bearing capacity test at different scour depths

[0057] Establishment of numerical models

[0058] The linear elastic model is based on the generalized Hooke's law and includes isotropic, orthotropic, and anisotropic models. The linear elastic model is applicable to any element. In the pile-soil system of this study, the pile can be considered as a linear elastic model.

[0059] (1) Isotropic elastic model

[0060] The stress-strain expression for an isotropic linear elastic model is:

[0061] There are two parameters involved here, namely the elasticity model E and the Poisson's ratio v, which can vary with temperature and other field variables.

[0062] (2) Orthogonal anisotropic elastic model

[0063] The independent model parameters for orthogonal anisotropy are Young's moduli E1, E2, and E3 in three orthogonal directions, three Poisson's ratios v12, v13, and v23, and three shear moduli G12, G13, and G23. Its stress-strain expression is as follows:

[0064] In the orthogonal anisotropic model, if the properties of a material are the same on a certain plane, it is a transversely isotropic elastic body. Assuming plane 1-2 is an isotropic plane, then we have E1 = E2 = Ep, ν31 = ν32 = νtp, ν13 = ν23 = νpt, and G13 = G23 = Gt, where p and t represent the transverse and longitudinal directions of the transversely isotropic body, respectively. Therefore, the stress-strain expression for a transversely isotropic body is:

[0065] Among them, G p =E p / 2(1+v p Therefore, the model has 5 independent parameters. The usage of the transversely isotropic elastic model is the same as that of the orthogonal anisotropic model.

[0066] (3) Anisotropic elastic model

[0067] The fully anisotropic elastic model has 21 independent model parameters, and its stress-strain expression is as follows:

[0068] The data analysis results were converted to the prototype structure based on the similarity scale of the centrifuge model test. The horizontal thrust and horizontal displacement at the mud surface were extracted at each moment to obtain force-displacement curves at different scour depths. At each scour depth, the larger the mud surface displacement, the greater the required horizontal thrust, and the force-displacement curve gradually flattens as the mud surface displacement increases. The smaller the scour depth, the greater the horizontal thrust required to reach a certain mud surface displacement. When there is no scour around the pile, the horizontal load required to reach a mud surface displacement of 0.1D, i.e., the ultimate horizontal bearing capacity, is the largest, at 45.1MN; when the scour depth is 15m, the ultimate horizontal bearing capacity is the smallest, at 14.8MN, which is more than 80% lower than when there is no scour. The numerical calculation results are consistent with the centrifuge experiment results, that is, with the increase of scour depth, the ultimate horizontal bearing capacity of the pile does not decrease significantly.

[0069] Based on indoor dynamic triaxial tests of sand, Achmus proposed a research method using a stiffness decay model. Because this model considers the decrease in soil stiffness with the number of cycles in its calculation, and its formula is simple, it shows promising application prospects. This method not only conforms to the essence of cumulative plastic deformation of soil under long-term cyclic loading, but also avoids the drawbacks of excessive time consumption and accumulated calculation errors associated with using general numerical analysis methods to study long-term cyclic problems. Therefore, it is an effective analytical method for the cumulative plastic deformation of cohesionless soils. Thus, this project uses this theoretical model to study the cyclic stiffness evolution of soil.

[0070] Experimental design

[0071] The confining pressure and cyclic stress considered in this unit test of soil cyclic loading are designed based on the actual stress conditions of offshore wind power projects. According to the foundation design of the Tangshan Leting Putuo Island offshore wind farm project, the maximum depth of the pile foundation is approximately 66m. Considering a soil buoyancy of 10kN / m³ and a lateral pressure coefficient of 0.5, the maximum confining pressure around the pile is approximately 330kPa. Therefore, the maximum confining pressure in this test is considered to be 500kPa. Furthermore, since the main horizontal cyclic loads of offshore wind power come from the wind, waves, and currents above, the horizontal cyclic loads on the soil are mainly caused by the bending deformation of the pile foundation due to these external loads. According to the deformation law of pile foundations, the horizontal deformation decreases with increasing pile depth. Therefore, the cyclic stress ratio in this test is also related to the magnitude of the confining pressure; the larger the confining pressure, the smaller the considered cyclic stress ratio. The cyclic load loading test scheme for this test is shown in the table below.

[0072] Soil sample preparation: Due to the lack of on-site soil sampling conditions for this study, the model soil for this experiment was prepared by mixing quartz sand of different particle size ranges according to the on-site particle size distribution. The standard soil specimen for the dynamic triaxial test was cylindrical, made using a standard mold, with a specimen diameter of 39.1 mm and a height of 80 mm. Based on the basic physical parameters of the soil in the geological survey report, samples were prepared with a dry density of 1.64 g / cm³.

[0073] The sample preparation process is as follows:

[0074] (1) Dry-packing film forming cylinder sample preparation, layered and compacted according to the sample height, and compacted by vibrating hammer. This test is divided into four layers, each layer thickness d=100 / 4=25mm. Before the test, a scale mark can be made on the film forming cylinder. The thickness of the rubber membrane is 0.2mm.

[0075] (2) According to the calculated mass of each soil sample, fill the soil in layers and use a vibrating fork to lightly tap to achieve the corresponding soil sample height and density.

[0076] The sample saturation process is as follows: (1) Calibration of confining pressure, pore pressure and axial pressure during the test (according to the triaxial test principle, while avoiding the initial state of the instrument being non-zero, water is injected into the pressure chamber before loading the sample, the water height reaches the general height of the sample, then the pore pressure, confining pressure and axial pressure parameters are zeroed, and finally the water in the pressure chamber is drained before loading the sample.

[0077] (2) Saturation is achieved using a combination of carbon dioxide and back pressure. Specific steps: 1) Before loading the sample, remove air from the GDS confining pressure and back pressure application devices; 2) Initially purge the base and pore pressure sensor with carbon dioxide until bubbles emerge from the vent; 3) After loading the sample, apply a negative pressure of 3-5 kPa, close the base vent, and allow the sample to stand upright before demolding. Inject water into the pressure chamber and maintain a confining pressure of 10 kPa; 4) Connect carbon dioxide to the base vent, release the negative pressure, and close all vents after the negative pressure is completely released; 5) Base II 6) Pass carbon dioxide through the sample, close the vent valve at the top of the sample, and pass carbon dioxide through the base and pore pressure sensor again to remove internal air for 30 minutes to 1 hour; 7) Pass carbon dioxide through the sample, close the valves of the base and sensor, and pass carbon dioxide through the sample for 2 hours until bubbles emerge; 8) Pass water through the base, apply a certain pressure of 5 kPa using GDS, and pass water through the base until it is full, then close the valve of the base; 9) Pass water through the sample, apply a certain pressure of 3 kPa using GDS, and saturate the sample with water for 6 hours.

[0078] The effects of different cyclic stress ratios (X = 0.4, 0.6, 0.8, 1), corresponding to different deviatoric stress amplitudes (20 kPa, 30 kPa, 40 kPa, 50 kPa, 80 kPa), on the maximum plastic strain of the specimens under the same initial physical state and different confining pressure levels (50 kPa, 200 kPa) were compared. It can be seen that the maximum plastic strain of the specimen increases with the increase of the cyclic stress ratio, that is, the maximum plastic strain of the specimen increases with the increase of the dynamic stress amplitude.

[0079] The Mohr-Coulomb elastoplastic model is primarily applicable to granular materials and is widely used in geotechnical engineering. This paper's ABAQUS finite element analysis mainly focuses on the Mohr-Coulomb elastoplastic model.

[0080] Model characteristics

[0081] The constitutive model is an extension of the classical Mohr-Coulomb yield criterion. The Mohr-Coulomb yield function used includes isotropic hardening and softening of cohesion. The flow potential function of the model has a hyperbolic shape on the meridional plane and no sharp corners on the π plane. Therefore, the potential function is completely smooth, ensuring the uniqueness of the plastic flow direction.

[0082] Yield characteristics

[0083] When expressed as strain invariants, the yield surface equation of the Mohr-Coulomb model is: F = R m q-ptanφ-c=0

[0084] R mThe deviatoric stress coefficient of Mohr-Coulomb is defined as:

[0085] In the formula, φ is the angle of the Mohr-Coulomb yield surface on the p-Rmcq plane, which generally refers to the inner angle of the material.

[0086] Friction angle, θ is the generalized shear stress azimuth angle, and p is the effective compressive stress.

[0087] In the formula, Mises effect force; It is the third invariant of the stress deviatoric tensor.

[0088] The friction angle φ also controls the shape of the yield surface of the material in the π plane, and the range of the friction angle is 0°≤φ≤90°. When φ=0°, the Mohr-Coulomb model degenerates into the Tresca model, which is independent of the confining pressure, and the yield surface in the π plane is a regular hexagon; when φ=90°, the Mohr-Coulomb model will change into the Rankine model, and the yield surface in the π plane will be an equilateral triangle.

[0089] Flow Law

[0090] The definition of the flow law is:

[0091] In the formula:

[0092] G is the flow potential function. The yield surface of the traditional Mohr-Coulomb model has sharp angles, which makes the plastic flow direction non-unique, resulting in cumbersome numerical calculations and slow convergence. To avoid these problems, the Mohr-Coulomb model provided by ABAQUS selects a continuous and smooth flow potential function, which is a hyperbola in the meridional plane and an ellipse in the π plane.

[0093] The governing equation for the hyperbolic flow potential function is:

[0094] In the formula:

[0095] In the formula, ψ is the shear dilatation angle under high confining pressure on the meridional plane; c|0 is the initial cohesion; ε and e are the shape parameters defining the flow potential function on the meridional plane and the π plane, respectively. ε is generally taken as 0.1, and e can be expressed as:

[0096] According to the above formula, the convexity and smoothness of the elliptical yield surface require 0.5. <e≤1.0;

[0097] Soil stiffness attenuation model

[0098] When sand is subjected to cyclic loading under drained conditions, the axial plastic strain ε a The increase in axial plastic strain increases with the number of cyclic loading cycles. The increase in axial plastic strain is related to the magnitude of the cyclic stress and the initial confining pressure.

[0099] Idriss (1978) pointed out that the secant elastic modulus of sand decreases continuously with the increase of the number of cycles, and gave an empirical expression for the soil stiffness attenuation coefficient δ:

[0100] E in the formula sN E s1 These are the secant stiffnesses under N cycles of cyclic stress and under the initial stress, respectively. These are the axial plastic strains under N loads and the initial load, respectively. S is the experimental parameter, which is related to the soil properties and the level of cyclic stress.

[0101] Achmus proposed that the axial plastic strain of sand under cyclic loading can be expressed by a semi-empirical formula containing stress parameters, and the axial strain increment ratio It can be represented as:

[0102] In the formula: X is the cyclic stress ratio, and a and b are experimental parameters. The cyclic stress ratio X is defined as:

[0103] Where: σ 1,sf σ is the principal stress of soil failure under static load. 1,cyc The maximum principal stress within one cycle;

[0104] The cyclic stress ratio proposed by Achmus considers the influence of the maximum static and dynamic stresses on the dynamic characteristics of soil, reflecting to some extent the stress level of the soil unit under cyclic loading. However, the expression for the cyclic stress ratio does not consider the influence of dynamic load amplitude and confining pressure. Hardin pointed out that the main factors affecting the dynamic characteristics of sand are effective confining pressure, void ratio, and amplitude. Zhou Jingxing's research shows that the magnitude of dynamic deviatoric stress and confining pressure has a significant impact on the dynamic strength characteristics of sand. Based on this, this paper considers the influence of the magnitude of dynamic deviatoric stress and confining pressure on the dynamic characteristics of sand and establishes a soil stiffness attenuation model that better reflects its mechanical properties. The ratio of confining pressure to dynamic deviatoric stress is used to reflect the cyclic stress level, and the cyclic stress ratio X is defined as:

[0105] Where: σ d Let σ be the amplitude of the deviatoric stress under cyclic loading. c The confining pressure level experienced by the soil.

[0106] Realization of stiffness decay

[0107] The USDFLD subroutine allows variables obtained at time or material points during calculations to be defined as field variables. These field variables can be imported into the program and established as functions with the material properties related to the solution. Therefore, certain material properties, such as the fundamental mechanical parameters elastic modulus, cohesion, and internal friction angle, can be used as functions of the user-defined field variables. Thus, the USDFLD subroutine can address the problem of weakened soil mechanical parameters.

[0108] The soil sample used for the indoor dynamic triaxial test was fine sand taken from the field. The dynamic triaxial test was a cyclic triaxial compression test under drained conditions, with a half-sine wave loading waveform. The above method was used to compare with a working condition of the indoor dynamic triaxial test. This working condition was as follows: relative density D = 0.68, confining pressure and bias pressure were both 200 kPa, cyclic stress ratio was 0.1, loading frequency was 1 Hz, and loading cycles were 1000.

[0109] The Mohr-Coulomb ideal elastoplastic model was used for the soil. This model is simple and well-defined, and can reflect the loading characteristics of sand well. The loading process of the finite element simulation is consistent with the laboratory test process. The soil cohesion c = 5 kPa. The internal friction angle φ′ = 32°, the dilatation angle ψ = 0°, and the effective unit weight γ′ = 19.4 kg / m³. 3 Poisson's ratio v = 0.4, elastic modulus E = 75 MPa.

[0110] According to the site survey report, in addition to the silty soil on the surface, the most widely distributed soil layer within the pile depth range of the seabed in the wind field area is fine sand, and its particle size distribution and physical and mechanical parameters are shown in the table below.

[0111] Fine sand particle size distribution table

[0112] Table of physical and mechanical parameters of fine sand

[0113] This study investigated the cumulative deformation and stiffness evolution of this soil layer under long-term cyclic loading. Due to the lack of on-site soil sampling conditions, the model soil for this experiment was prepared by mixing quartz sand of different particle size ranges according to the on-site particle size distribution.

[0114] Experimental process

[0115] Static loading test process

[0116] (1) Fabricate wind turbine pile foundation and tower model according to similarity ratio design scheme, and prepare test sand according to actual mix ratio of borehole data.

[0117] (2) Strain gauges are attached to both sides of the pile foundation, with strain gauge leads evenly arranged along the outer wall of the pile. Epoxy resin is applied in layers around the strain gauges and leads. After each layer of epoxy resin is applied, the surface is sanded to ensure adhesion between layers. The thickness of the epoxy resin after multiple layers is approximately 1-1.5 mm.

[0118] (3) The strain gauges are calibrated to obtain the relationship between the voltage and bending moment of each strain gauge.

[0119] (4) Conduct drop height calibration tests for sand rain method mold making to calibrate the relationship between drop height and corresponding sand density. Calibrate dry sand according to density 1.64t / m3.

[0120] (5) Assemble the overall model of the wind turbine and fix it in the model box according to the design position.

[0121] (6) Sand rain method was used to create a model to a uniform elevation. The target soil layer thickness was 720 mm, prepared in 10 layers. After each layer of seabed preparation was completed, the mass of sand used was recorded, and the density and relative compaction of the soil were calculated. The average relative compaction of the entire prepared seabed was 65%.

[0122] (7) Place the model box into the centrifuge, install the laser displacement sensor and axial force gauge sensor, adjust the position of the loading motor, and install the camera, LED lights, and other accessories. Finally, hoist the model box onto the centrifuge platform;

[0123] (8) Allow the soil to stand for 2 hours under an acceleration of 100g until the settlement of the soil stabilizes, and then begin the test.

[0124] (9) Conduct a monotonic static loading test to obtain the ultimate bearing capacity of a single pile; push until the thrust decreases, analyze and obtain the bearing capacity Fu when the mud surface has a displacement of 0.1D, at which time the distance pushed by the hydraulic rod is L;

[0125] (10) Unload the load to 0, stop the machine and lift the model box out to complete the test.

[0126] Cyclic loading test process

[0127] (1) Fabricate wind turbine pile foundation and tower model according to similarity ratio design scheme, and prepare test sand according to actual mix ratio of borehole data.

[0128] (2) Strain gauges are attached to both sides of the pile foundation, with strain gauge leads evenly arranged along the outer wall of the pile. Epoxy resin is applied in layers around the strain gauges and leads, and the surface is sanded to ensure adhesion between layers. The thickness of the epoxy resin after multiple layers is approximately 1-1.5 mm.

[0129] (3) The strain gauges are calibrated to obtain the relationship between the voltage and bending moment of each strain gauge.

[0130] (4) Conduct drop height calibration tests for sand rain method mold making to calibrate the relationship between drop height and corresponding sand density. Calibrate dry sand according to density 1.64t / m3.

[0131] (5) Assemble the overall model of the wind turbine and fix it in the model box according to the design position.

[0132] (6) Sand rain method was used to create a model to a uniform elevation. The target soil layer thickness was 720 mm, prepared in 10 layers. After each layer of seabed preparation was completed, the mass of sand used was recorded, and the density and relative compaction of the soil were calculated. The average relative compaction of the entire prepared seabed was 65%.

[0133] (7) Place the model box into the centrifuge, install the laser displacement sensor and axial force gauge sensor, adjust the position of the loading motor, and install the camera, LED lights, and other accessories. Finally, hoist the model box onto the centrifuge platform;

[0134] (8) Allow the soil to stand for 2 hours under an acceleration of 100g until the settlement of the soil stabilizes, and then begin the test.

[0135] (9) Conduct cyclic loading tests, with 20%, 30%, and 40% Fu being cyclically loaded, and the loading frequency being the highest frequency of 2Hz. Each cycle is 2000 times.

[0136] (10) Unload the load to 0, stop the machine and lift the model box out to complete the test.

[0137] Experimental data analysis

[0138] For cyclic loading tests on sandy soil foundations, the unloading stiffness in the first cycle is smaller than that in subsequent cycles, further illustrating the strong nonlinearity of undisturbed sand. LeBlanc (2009) proposed an expression for the change of unloading stiffness with the number of cycles for rigid piles: k N =k0+bln(N)

[0139] Due to the large dispersion of the unloading stiffness variation, and in order to reduce the influence of the initial state soil nonlinearity, this paper uses the unloading stiffness in the third cycle to normalize the cyclic unloading stiffness, and fits it with the above formula.

[0140] Numerical simulation of wind power foundation deformation and stiffness evolution under long-term cycling

[0141] Numerical model establishment: A three-dimensional finite element model of a single pile foundation was established using finite element analysis software. Due to the stress conditions and the symmetry of the pile-soil structure, half of the pile-soil structure was analyzed.

[0142] Calculate the horizontal ultimate load of a single pile foundation and the horizontal ultimate bearing capacity H of the single pile.u The horizontal ultimate bearing capacity is used to measure the ability of a single pile to withstand horizontal loads.

[0143] The specific implementation and experimental verification of the numerical model were carried out by establishing a stiffness attenuation model of sand in the numerical analysis program through secondary development of Abaqus, and then verifying it.

[0144] The steel pipe pile adopts a linear elastic model, with a pile diameter D = 6.3m, wall thickness s = 0.64mm, and elastic modulus E. p =210 GPa; The Mohr-Coulomb ideal elastic-plastic model was selected for the soil, which is simple and clear and can well reflect the loading characteristics of sand. Contact surfaces were set between the pile and the soil, with hard contact for normal contact and friction contact for tangential contact. The friction coefficient was two-thirds of the internal friction angle. The soil cohesion was c = 5 kPa; the internal friction angle φ′ = 32°, the dilatation angle ψ = 0°, and the effective unit weight γ′ = 19.4 kg / m³. 3 Poisson's ratio v = 0.4, and the elastic modulus is taken as follows:

[0145] Where: σ at The pressure is atmospheric pressure, taken as 101 kPa; σ m η represents the average soil stress; k and η are dimensionless constants, and in this paper, k = 560 and η = 0.6 are taken.

[0146] The ultimate horizontal load of a single pile foundation is calculated using the limit analysis method.

[0147] The deformation of a single pile exhibits the deformation characteristics of a rigid pile. The pile tip exhibits a kick-out failure pattern, and the entire pile rotates around a point on the pile tip. The horizontal ultimate bearing capacity is represented by H. u for:

[0148] Where: h is the height of the mud surface from the top of the pile; D is the pile diameter; L is the unit weight of the soil; γ s Unit weight of soil; K P Rankine's passive earth pressure coefficient.

[0149] Step 2: Calculate the horizontal ultimate load of a single pile foundation using the limit analysis method:

[0150] For pipe piles, the yield moment can be expressed as:

[0151] In the formula: I P Moment of inertia of the pile section; σ y Yield strength of the pile material.

[0152] Step 2: Calculate the py curve of the horizontal ultimate load of a single pile foundation:

[0153] When y < 3y 50 hour,

[0154] When y>3y 50 When x>x r At that time, p = 0.72p u

[0155] x <x r hour

[0156] In the formula, y is the deflection of the pile; 50 x represents the pile displacement when the soil resistance reaches half of its ultimate limit; x is the depth below the mud surface; x r p is the critical depth; p is the soil resistance around the pile; p u The ultimate soil resistance around the pile is equal to the undrained shear strength C. u and ε 50 related.

[0157] Numerical model implementation and experimental verification: Calculation of formulas below deep soil: p us =(C1X+C2b)γ · X p ud =C3bγ · X

[0158] In the formula, p u γ represents the ultimate soil resistance per unit pile length; · φ is the effective unit weight of the soil; X is the depth below the mud surface; C1, C2, and C3 are coefficients related to the internal friction angle φ; and b is the average pile diameter from the mud surface to the desired depth.

[0159] A three-dimensional finite element model of a large-diameter single pile under horizontal load in sandy soil was established. In-situ stress equilibrium was achieved, and a vertical load V was applied. The initial principal stresses of each soil element were calculated and extracted. and minor principal stress

[0160] A horizontal load H is applied at the loading point, corresponding to the peak phase of the cyclic load. The major principal stresses under horizontal loading are calculated and extracted for each soil element. and minor principal stress

[0161] Extracted The confining pressure σ experienced by each soil element c Extracted from (2) Extracted from (1) By subtracting the values, we obtain the level of deviatoric stress σ experienced by each soil element. d Substituting into equation (10), we obtain the cyclic stress ratio X of each soil element, i.e.

[0162] The cyclic stress ratio of each soil element is written into the usdfld subroutine. The software will call this subroutine during the analysis and calculate the stress characteristics of the pile foundation under N cycles of loading based on the attenuation stiffness of each soil element after N cycles, where x is the horizontal displacement of the loading point; H u This is the ultimate horizontal static load of the pile foundation.

[0163] The deformation and stiffness evolution of wind turbine foundations under long-term cyclic loading were analyzed. The horizontal displacement value at the top of the pile decreased after cyclic loading. As h / L increased, the decreasing trend continued to increase. When h / L was 0.294, the cumulative horizontal displacement value at the top of the pile decreased to 30% of the original value.

[0164] Step 4: Analyze the deformation and stiffness evolution of the wind turbine foundation under long-term cyclic loading. Under a horizontal cyclic load of 0.25 Hu and a depth of 34 m, the lateral displacement of the steel pipe pile is analyzed. Under the horizontal load, the horizontal displacement at the top of the pile continuously develops as the cycle progresses. In the early stage of the cyclic load, the lateral displacement of the steel pipe pile develops rapidly. After more than 100 cycles, the lateral displacement development slows down and gradually stabilizes.

[0165] The deformation and stiffness evolution of wind turbine foundations under long-term cycling were analyzed. The horizontal displacement at the pile top decreased with the increase of the elastic modulus of the soil. The reduction was significant for steel pipe piles with smaller embedment depths. As the embedment depth of steel pipe piles increased, the reduction in lateral displacement gradually decreased.

[0166] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described in the present invention. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or substitutions to the present invention, and all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. Numerical simulation method of offshore wind turbine monopile stiffness considering long-term cyclic and scour, characterized in that, Includes the following steps: Step 1: Numerical model establishment. A three-dimensional finite element model of a single pile foundation is established using finite element analysis software. Due to the stress conditions and the symmetry of the pile-soil structure, half of the pile-soil structure is analyzed. A scour pit model is established according to a certain scour depth. The slope ratio of the scour pit should be determined according to the actual engineering conditions. Step 2, calculate the horizontal ultimate load of single pile foundation, calculate the horizontal ultimate bearing capacity H of single pile u , the horizontal ultimate bearing capacity is used to measure the horizontal load bearing capacity of single pile Step 3: Specific implementation and experimental verification of the numerical model. Through secondary development of Abaqus, a stiffness attenuation model of sand was established in the numerical analysis program and verified. Step 4: Analyze the deformation and stiffness evolution of wind power foundations under long-term cycling. The pile foundation will continuously bear long-term, low-frequency lateral cyclic forces brought about by wind loads and wave loads. Through analysis, the cumulative lateral displacement generated by the steel pipe piles during their normal service life can be accurately predicted.

2. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 1, characterized in that, Step 1: Establish numerical models of the seabed-wind turbine at different scour depths. A linear elastic model is used for the steel pipe piles, with a pile diameter D = 6.3m, wall thickness s = 0.64mm, and elastic modulus E. p =210 GPa; The Mohr-Coulomb ideal elastic-plastic model was selected for the soil, which is simple and clear and can well reflect the loading characteristics of sand. Contact surfaces were set between the pile and the soil, with hard contact for normal contact and friction contact for tangential contact. The friction coefficient was two-thirds of the internal friction angle. The soil cohesion was c = 5 kPa; the internal friction angle φ′ = 32°, the dilatation angle ψ = 0°, and the effective unit weight γ′ = 19.4 kg / m³. 3 Poisson's ratio v = 0.4, and the elastic modulus is taken as follows: In the formula: σ at is the atmospheric pressure, taking the value of 101 kpa; σ m is the average soil stress of the soil body; k, η are dimensionless constants, in this paper, k = 560 and η = 0.

6.

3. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 2, is characterized in that... Step 2: Calculate the horizontal ultimate load of a single pile foundation using the limit analysis method. The deformation of a single pile exhibits the deformation characteristics of a rigid pile. The pile tip exhibits a kick-out failure pattern, and the entire pile rotates around a point on the pile tip. The horizontal ultimate bearing capacity is represented by H. u for: Where: h height of the soil surface from the top of the pile; D diameter of the pile; L unit weight of the soil; γ s Unit weight of the soil; K P Rankine's passive earth pressure coefficient.

4. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 3, is characterized in that... Step 2: Calculate the horizontal ultimate load of a single pile foundation using the limit analysis method: For pipe piles, the yield moment can be expressed as: wherein: I P Moment of inertia of the pile shaft cross-section; σ y Yield strength of the pile shaft material.

5. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 4, characterized in that, Step 2: Calculate the py curve of the horizontal ultimate load of a single pile foundation: When y < 3y 50 hour, When y>3y 50 When x>x r At that time, p = 0.72p u x <x r hour where y is the deflection of the pile; y 50 is the displacement of the pile when the soil resistance reaches half of its ultimate value; x is the depth below the soil surface; x r is the critical depth; p is the soil resistance around the pile; p u is the ultimate soil resistance around the pile, which is related to the undrained shear strength C u and the void ratio ε 50 .

6. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 5, is characterized in that... Step 3, implementation of numerical model and experimental verification: The following formula is used to calculate the deep soil: us = (C1X + C2b)γ · X p ud = C3bγ · X where p u is the unit length ultimate soil resistance; γ · is the effective unit weight of the soil; X is the depth below the mudline; C1, C2, and C3 are coefficients related to the internal friction angle φ, and b is the average pile diameter over the range from the mudline to the depth of interest.

7. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 6, is characterized in that, A three-dimensional finite element model of a large-diameter single pile under horizontal load in sandy soil was established. In-situ stress equilibrium was achieved, and a vertical load V was applied. The initial principal stresses of each soil element were calculated and extracted. and minor principal stress A horizontal load H is applied at the loading point, corresponding to the peak phase of the cyclic load. The major principal stresses under horizontal loading are calculated and extracted for each soil element. and minor principal stress Extracted The confining pressure σ experienced by each soil element c Extracted from (2) Extracted from (1) By subtracting the values, we obtain the level of deviatoric stress σ experienced by each soil element. d Substituting into equation (10), we obtain the cyclic stress ratio X of each soil element, i.e. The cyclic stress ratio of each soil unit is written into the usdfld subroutine, which is called by the software during the analysis and calculates the stress state of the pile foundation under N cyclic loads according to the attenuation stiffness of each soil unit after N cycles, where x is the horizontal displacement of the loading point; H u is the horizontal static ultimate load of the pile foundation.

8. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 7, is characterized in that... Step 4: Analyze the deformation and stiffness evolution of the wind turbine foundation under long-term cyclic loading. The horizontal displacement value at the top of the pile decreases after cyclic loading. As h / L increases, the decreasing trend intensifies. When h / L is 0.294, the cumulative horizontal displacement value at the top of the pile decreases to 30% of the original value.

9. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 8, characterized in that, Step 4: Analyze the deformation and stiffness evolution of the wind power foundation under long-term cyclic loading. Under a horizontal cyclic load of 0.25 Hu and a depth of 34m, the lateral displacement of the steel pipe pile is analyzed. Under the horizontal load, the horizontal displacement of the pile top continuously develops as the cycle progresses. In the early stage of the cyclic load, the lateral displacement of the steel pipe pile develops rapidly. After more than 100 cycles, the lateral displacement development slows down and gradually stabilizes.

10. The numerical simulation method for the stiffness of a single pile of an offshore wind turbine considering long-term cycling and scouring as described in claim 9, characterized in that, Step 4: Analyze the deformation and stiffness evolution of the wind turbine foundation under long-term cycling. The horizontal displacement at the pile top decreases as the elastic modulus of the soil increases. The embedment depth of the steel pipe pile is relatively small, and the reduction is significant. As the embedment depth of the steel pipe pile increases, the reduction in its lateral displacement gradually decreases.

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