Influence of Vertical Load on Lateral-Loaded Monopiles by Numerical Simulation

Monopiles are the most common foundation form of offshore wind turbines,which bear the vertical load,lateral load and bending moment.It remains uncertain whether the applied vertical load increases the lateral deflection of the pile.This paper investigated the influence of vertical load on the behaviour of monopiles installed in the sand under combined load using three-dimensional numerical methods.The commercial software PLAXIS was used for simulations in this paper.Monopiles were modelled as a structure incorporating linear elastic material behaviour and soil was modelled using the Hardening-Soil(HS)constitutive model.The monopiles under vertical load,lateral load and combined vertical and lateral loads were respectively studied taking into account the sequence of load application and pile slenderness ratio(L/D;L and D are the length and diameter of the pile).Results suggest that the sequence of load application plays a major role in how vertical load affects the deflection behaviour of the pile.Specifically,when L/D ratios obtained by lengthening the pile while keeping its diameter constant are 3,5 and 8,the relationships between lateral load and the deflection behaviour of the pile under the effect of vertical load demonstrate a similar trend.Furthermore,the cause of increased lateral capacity of the pile under the action of applied vertical load in the common practical application case and in the VPL case was analyzed by studying the variation law of soil stress along the pile embedment.Results confirm that the confining effect of vertical load increases means effective stress of the soil around the pile,thus increasing soil stiffness and pile capacity.

Reliability analysis of piles constructed on slopes under laterally loading

Response surface method is used to study the reliability analysis of laterally loaded piles in sloping ground. A development load-displacement （p-y） curve for laterally loaded pile response in sloping ground is used to model the pile-soil system, both the pile head displacement and the maximum bending moment of the piles are used as the performance criteria in this study. The reliability analysis method of the laterally loaded pile in sloping ground under the pile head displacement and the maximum bending moment failure modes is proposed, which is in good agreement with the Monte Carlo method. The influences on the probability index of failure by a number of parameters are discussed. It is shown that the variability of pile head displacement increases with the increase in the coefficients of variation of ultimate bearing capacity factor （Npu）, secant elastic modulus at 50%（E50） and level load （H）. A negative correlation between Npu and non-dimensional factor （λ） leads to less spread out probability density function （PDF） of the pile head displacement;in contrast, a positive correlation between Npu andλgives a great variation in the PDF of pile head displacement. As for bearing capacity factor on ground surface （Npo） and λ, both negative and positive correlations between them give a great variation in the PDF of pile head displacement, and a negative correlation will obviously increase the variability of the response.

Investigating the Efficiency Coefficient of Pile Group in Clay Under Two-Way Lateral Load

This research investigates the behavior of a 2×2 pile group under two-directional lateral loads in addition to the vertical load.Through three-dimensional numerical modeling based on Flac 3D software,the study examines the total bearing capacity and efficiency coefficient of the pile group,considering factors such as the angle of lateral load,relative pile spacing,and relative stiffness of the pile-soil system.The findings highlight the significance of these factors in understanding and predicting the response of pile groups to changing lateral load directions.The results reveal that increasing the angle of the lateral load from 0°to 45°enhances both the maximum total lateral load and the efficiency coefficient of the pile group.When the relative stiffness of the pile-soil system significantly increases,soil stiffening occurs and reducing the relative spacing of the piles from 7 to 3 times the diameter of the piles diminishes the influence of the pile group.Consequently,the response of the pile group to lateral loads becomes more linear,with only a slight alteration in the maximum total lateral load and the efficiency coefficient when the lateral load is angled from 0°to 45°.Conversely,increasing the relative distance between the piles,specifically from 3 to 7 times the diameter of the piles,amplifies the influence of the pile group.Both the maximum total lateral load and the efficiency coefficient of the pile group exhibit an observed increase.These provide insights for designing pile groups and optimizing their performance under lateral loading conditions.

Field testing of stiffened deep cement mixing piles under lateral cyclic loading

Construction of seaside and underground wall bracing often uses stiffened deep cement mixed columns （SDCM）. This research investigates methods used to improve the level of bearing capacity of these SDCM when subjected to cyclic lateral loading via various types of stiffer cores. Eight piles, two deep cement mixed piles and six stiffened deep cement mixing piles with three different types of cores, H shape cross section prestressed concrete, steel pipe, and H-beam steel, were embedded though soft clay into medium-hard clay on site in Thailand. Cyclic horizontal loading was gradually applied until pile failure and the hysteresis loops of lateral load vs. lateral deformation were recorded. The lateral carrying capacities of the SDCM piles with an H-beam steel core increased by 3-4 times that of the DCM piles. This field research clearly shows that using H-beam steel as a stiffer core for SDCM piles is the best method to improve its lateral carrying capacity, ductility and energy dissipation capacity.

Numerical Analysis of Laterally Loaded Long Piles in Cohesionless Soil

The capability of piles to withstand horizontal loads is a major design issue.The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model.The governing differential equation for a laterally loaded pile on elastic subgrade is derived.Based on LegendreGalerkin method and Runge-Kutta formulas of order four and five,the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free-and fixed-headed piles.Mathematica,as one of the world’s leading computational software,was employed for the implementation of solutions.The proposed numerical techniques provide the responses for the entire pile length under the applied lateral load.The utilized numerical approaches are validated against experimental and analytical results of previously published works showing a more accurate estimation of the response of laterally loaded piles.Therefore,the proposed approaches can maintain both mathematical simplicity and comparable accuracy with the experimental results.

Flexural Behavior of Laterally Loaded Tapered Piles in Cohesive Soils

In this paper, the flexural behavior of laterally loaded tapered piles in cohesive soils is investigated. The exact solution for the governing differential equation of the problem is obtained based on the beam-on-elastic foundation approach in which the soil reaction on the pile is related directly to the pile lateral deflection. In this investigation, the modulus of subgrade reactions is assumed to be constant along the pile depth. Parametric study through numerical examples is carried out to prove the validity and accuracy of the obtained results. In general, the derived displacement field can be used to study pile response in multilayered soil profiles by subdividing the pile into a number of elements. It is found that tapered piles show stiffer behavior than that for prismatic ones having the same material volume with an optimum stress distribution along the pile depth. Accordingly, tapered piles are more efficient and economic than those having the same material volume. Verification is also carried out for the obtained results through finite element analysis and the selected number of elements gives a very good agreement for lateral deflection and a larger number of elements is required to obtain better results for bending moment because of moment loss resulting from the lack of shear diagram.

Influence of vertical loads on lateral response of pile foundations in sands and clays

Although the load applied to pile foundations is usually a combination of vertical and lateral components,there have been few investigations on the behavior of piles subjected to combined loadings.Those few studies led to inconsistent results with regard to the effects of vertical loads on the lateral response of piles.A series of three-dimensional(3D) finite differences analyses is conducted to evaluate the influence of vertical loads on the lateral performance of pile foundations.Three idealized sandy and clayey soil profiles are considered:a homogeneous soil layer,a layer with modulus proportional to depth,and two-layered strata.The pile material is modeled as linearly elastic,while the soil is idealized using the Mohr-Coulomb constitutive model with a non-associated flow rule.In order to confirm the findings of this study,soils in some cases are further modeled using more sophisticated models(i.e.CYsoil model for sandy soils and modified Cam-Clay(MCC) model for clayey soils).Numerical results showed that the lateral resistance of the piles does not appear to vary considerably with the vertical load in sandy soil especially at the loosest state.However,the presence of a vertical load on a pile embedded in homogeneous or inhomogeneous clay is detrimental to its lateral capacity,and it is unconservative to design piles in clays assuming that there is no interaction between vertical and lateral loads.Moreover,the current results indicate that the effect of vertical loads on the lateral response of piles embedded in twolayered strata depends on the characteristics of soil not only surrounding the piles but also located beneath their tips.

Stereo particle image velocimetry measurement of 3D soil deformation around laterally loaded pile in sand

A developed stereo particle image velocimetry(stereo-PIV) system was proposed to measure three-dimensional(3D) soil deformation around a laterally loaded pile in sand.The stereo-PIV technique extended 2D measurement to 3D based on a binocular vision model,where two cameras with a well geometrical setting were utilized to image the same object simultaneously.This system utilized two open software packages and some simple programs in MATLAB,which can easily be adjusted to meet user needs at a low cost.The failure planes form an angle with the horizontal line,which are measured at 27°-29°,approximately three-fourths of the frictional angle of soil.The edge of the strain wedge formed in front of the pile is an arc,which is slightly different from the straight line reported in the literature.The active and passive influence zones are about twice and six times of the diameter of the pile,respectively.The test demonstrates the good performance and feasibility of this stereo-PIV system for more advanced geotechnical testing.

Effect of Local and Global Scour on Lateral Response of Single Piles in Different Soil Conditions

Marine structures, offshore platforms and bridge piers are usually supported on foundation piles. These piles are subjected to lateral loading due to wind, waves and currents. Piles installed in marine or river environments are susceptible to scour depending on wave and current characteristics and soil types. In this paper, the effect of local and global scour on behavior of laterally loaded piles installed in different soil conditions has been investigated. Finite element model (FEM) using the software program PLAXIS and Winkler model using the software program LPILE were used in the analyses. Different parameters were investigated such as soil types, scour depth, scour hole dimension, pile material, submerged condition, magnitude of lateral load and load eccentricity. The results showed that scour has a significant impact on piles installed in sand and a less significant impact on piles installed in clay. Global scour has a significant impact on pile lateral displacement and bending stresses. The effect of scour is more significant if piles are subjected to large lateral loads due to the nonlinear response of pile-soil system. Effect of scour of stiff clayey soils on piles is more pronounced than that of soft clayey soils.

Cyclic Lateral Responses of Monopiles Considering the Influence of Pile−Soil Relative Stiffness in Sand

The existing studies have primarily focused on the effect of cyclic load characteristics(namely,cyclic load ratio and amplitude ratio)on cyclic lateral response of monopiles in sand,with little attention paid to the effect of pile−soil relative stiffness(K_(R)).This paper presents a series of 1-g cyclic tests aimed at improving understanding of the cyclic lateral responses of monopiles under different pile−soil systems.These systems are arranged by two model piles with different stiffness,including four different slenderness ratios(pile embedded length,L,normalized by diameter,D)under medium dense sand.The K_(R)-values are calculated by a previously proposed method considering the real soil stress level.The test results show that the lateral accumulation displacement increases significantly with the increment of the K_(R)-value,while the cyclic secant stiffness performs inversely.The maximum pile bending moment increases with the cycle number for the rigid pile−soil system,but shows a decreasing trend in the flexible system.For an uppermost concern,an empirical model is proposed to predict the accumulated displacement of arbitrary pile−soil systems by combining the results from this study with those from previous experimental investigations.The validity of the proposed model is demonstrated by 1-g and centrifuge tests.

Behavior of Pile Group with Elevated Cap Subjected to Cyclic Lateral Loads

The pile group with elevated cap is widely used as foundation of offshore structures such as turbines, power transmission towers and bridge piers, and understanding its behavior under cyclic lateral loads induced by waves, tide water and winds, is of great importance to designing. A large-scale model test on 3×3 pile group with elevated cap subjected to cyclic lateral loads was performed in saturated silts. The preparation and implementation of the test is presented. Steel pipes with the outer diameter of 114 mm, thickness of 4.5 mm, and length of 6 m were employed as model piles. The pile group was cyclic loaded in a multi-stage sequence with the lateral displacement controlled. In addition, a single pile test was also conducted at the same site for comparison. The displacement of the pile cap, the internal forces of individual piles, and the horizontal stiffness of the pile group are presented and discussed in detail. The results indicate that the lateral cyclic loads have a greater impact on pile group than that on a single pile, and give rise to the significant plastic strain in the soil around piles. The lateral loads carried by each row of piles within the group would be redistributed with loading cycles. The lateral stiffness of the pile group decreases gradually with cycles and broadly presents three different degradation patterns in the test. Significant axial forces were measured out in some piles within the group, owing to the strong restraint provided by the cap, and finally lead to a large settlement of the pile group. These findings can be referred for foundation designing of offshore structures.

Experimental study on DX pile performance in frozen soils under lateral loading

Experiments about working mechanism and mechanical characteristics of the DX model pile foundation under lateral dynamic and static loading were conducted by using a model system of the dynamic frozen soil-pile interaction. The horizontal displacement-force relationship of the pile head and bending moment distribution along the body in frozen soils of different temperatures were discussed. According to test results, both the horizontal disp!acement-force relationship of the DX pile head and bending moment distribution of the DX pile body are smaller than that of equal-diameter piles under same lateral loads. The piles with different plate positions show different displacements and bending moments. This phenomenon is mainly related to the soil temperature and bearing plates locations. Thus, dynamic response analysis of the pile foundation should be taken into account.

Nonlinear FEA of Pile Group Subjected to Lateral Load

A finite element method based program has been developed to perform the static nonlinear analysis of pile group with six different configurations subjected to lateral loads. The pile has been assumed to remain elastic all the time whereas the soil has been assumed to undergo plastic yielding following von Mises yield criterion. The formulation of elasto-plastic analysis following von Mises yield criterion has been explained. The effect of Drucker-Prager and Mohr Coulomb yield criteria on the response of pile group is also investigated. The whole analysis is based on incremental load application. The external load is applied in small increments and the stresses are initially computed assuming elastic constitutive relation. Significant effect of soil nonlinearity is observed at smaller pile spacing which reduces with increase in spacing.

Fully Stressed Piles and Beams in a Winkler's Medium,End-loaded by an Orthogonal Force,and with Optimum Length

A simplified method of designing fully stressed piles and beams with optimum length in a Winkler's medium,end-loaded by an orthogonal force and without any point constraint,is proposed. A numerical algorithm distributing the mass by means of the Fully Stressed Design ( FSD) method and updating the moment by finite elements has been first implemented. The use of the FSD method is in general quite simple,and allows to obtain optimum,or close to the optimum,solutions. After having distributed the mass through the FSD method,the length has been finally optimised by means of a heuristic procedure.

Prediction of seismic-induced bending moment and lateral displacement in closed and open-ended pipe piles:A genetic programming approach

Ensuring the reliability of pipe pile designs under earthquake loading necessitates an accurate determination of lateral displacement and bending moment,typically achieved through complex numerical modeling to address the intricacies of soil-pile interaction.Despite recent advancements in machine learning techniques,there is a persistent need to establish data-driven models that can predict these parameters without using numerical simulations due to the difficulties in conducting correct numerical simulations and the need for constitutive modelling parameters that are not readily available.This research presents novel lateral displacement and bending moment predictive models for closed and open-ended pipe piles,employing a Genetic Programming(GP)approach.Utilizing a soil dataset extracted from existing literature,comprising 392 data points for both pile types embedded in cohesionless soil and subjected to earthquake loading,the study intentionally limited input parameters to three features to enhance model simplicity:Standard Penetration Test(SPT)corrected blow count(N60),Peak Ground Acceleration(PGA),and pile slenderness ratio(L/D).Model performance was assessed via coefficient of determination(R^(2)),Root Mean Squared Error(RMSE),and Mean Absolute Error(MAE),with R^(2) values ranging from 0.95 to 0.99 for the training set,and from 0.92 to 0.98 for the testing set,which indicate of high accuracy of prediction.Finally,the study concludes with a sensitivity analysis,evaluating the influence of each input parameter across different pile types.

Experimental investigation on seismic behavior of single piles in sandy soil

This paper describes a quasi-static test program featuring lateral cyclic loading on single piles in sandy soil. The tests were conducted on 18 aluminum model piles with different cross sections and lateral load eccentricity ratios, e/d, （e is the lateral load eccentricity and d is the diameter of pile） of 0, 4 and 8, embedded in sand with a relative density of 30% and 70%. The experimental results include lateral load-displacement hysteresis loops, skeleton curves and energy dissipation curves. Lateral capacity, ductility and energy dissipation capacity of single piles under seismic load were evaluated in detail. The lateral capacities and the energy dissipation capacity of piles in dense sand were much higher than in loose sand. When embedded in loose sand, the maximum lateral load and the maximum lateral displacement of piles increased as e/d increased. On the contrary, when embedded in dense sand, the maximum lateral load of piles decreased as e/d increased. Piles with a higher load eccentricity ratio experienced higher energy dissipation capacity than piles with e/d of 0 in both dense and loose sand. At a given level of displacement, piles with circular cross sections provided the best energy dissipation capacity in both loose and dense sand.

水平受荷桩“p-y+M-θ”分析方法

中国近海海上风电机组开发建设中,大直径单桩基础形式使用占比超70%。现行p-y曲线设计方法主要适用于小直径柔性桩,对大直径单桩侧向及桩底受荷描述能力不足,导致其严重低估刚柔性桩和刚性桩(分别常用于中国和欧洲的近海风电工程)的变形和承载能力,过于保守的设计给海上风电降本带来挑战。为此建立了能以统一的方式预测柔性、刚柔性和刚性单桩水平单调受荷响应的“p-y+M-θ”模型,并将该模型推广到循环荷载下单桩的响应分析。通过与相关试验结果比对发现,“p-y+M-θ”模型能较为准确地预测桩基水平加载响应。力图为水平受荷单桩工程设计提供简洁而可行的响应分析方法。

软土区堆载对桥梁桩基偏位影响及纠偏措施

软土区过大堆载将造成邻近桥梁桩基产生明显偏位,对桥梁安全服役极为不利。结合某堆载致软土区桥墩偏移工程案例,考虑软土侧向变形时效性特征,开发软土固结-蠕变材料模型子程序,建立堆载-桩基-桥墩有限元模型,研究堆载作用下软土区桥墩-承台-桩基结构的时效性偏移特性,揭示桥墩-承台-桩基结构横向偏移机理,并针对现场条件提出有效合理纠偏措施。结果表明:随着堆载时间的延长,桩身响应沿深度分布发生显著变化,且堆载引发的软土时效性横向变形致使作用于桩侧的横向附加压力逐渐增大,但其沿深度的分布范围基本不变,并且主要分布在软弱土层深度范围内;基于桩身截面承载极限弯矩的评估,所研究桥墩各桩基仍处于安全状态,但应注意承台与桩基连接处以及软弱层与硬土层界面处的弯矩;提出的卸载+高压旋喷桩加固纠偏措施可以达到预期纠偏效果。

双参数地基横向受荷长桩参数反演方法研究

为了获取mz+C双参数地基模型下横向受荷长桩参数,基于m法原理,在地基系数等于零的位置建立坐标系,将地面以上桩身视为虚拟段。考虑剪力和弯矩共同作用时的情形,根据荷载效应等效原理,将地面处荷载简化到桩顶,建立了横向受荷长桩双参数计算模型。将桩土相对刚度和z0作为未知参数,提出了地基参数反演模型。该反演模型考虑了土抗力对荷载作用形式、地面处桩身位移和转角的影响。根据桩在地面处的位移和转角实测值反演地基参数,并结合算例通过桩身最大弯矩和地面处土抗力验证了反演方法的可行性。结果表明:本研究方法能够保证桩在地面处位移和转角理论值与实测值相符,最大弯矩及其位置误差很小;与m法相比,地面处土抗力变大对桩身弯矩影响程度沿深度先增大后减小,主要影响范围位于最大弯矩位置附近;桩身抗弯刚度与最大弯矩、地面处土体抗力均成线性关系,对二者影响较大且呈反向变化;根据最大弯矩和地面处土抗力实测值可以求得抗弯刚度的合理取值范围,考虑抗弯刚度随着桩顶荷载或位移的变化能够更好地模拟桩土的实际工作状况,可以提高mz+C双参数地基模型计算精度。

海上试桩不同桩型承载力特性研究

天津南港某高桩码头拟建场地有深厚密实砂层,通过试桩测定设计桩型对砂层的穿透及贯入能力,研究不同基桩承载力特性。试验结果表明:混凝土预制桩及钢管桩均有较好的穿透及贯入能力;基桩轴向极限承载力高应变检测结果小于静载试验,误差均在5%以内;混凝土预制桩桩端承载力占总承载力不小于44.6%,钢管桩桩端承载力占总承载力不小于21.9%;相同荷载作用下,混凝土预制方桩静载与动载沉降量之比为1.40,钢管桩为0.90,两者差异明显;基桩承载力达到极值时桩侧摩阻力要明显大于规范极限侧摩阻力,规范取值偏保守。