Lateral Response Of Piles Research Articles

A Lateral-Response Analyzed Model for Piles in Sloping Ground Considering Vertical Resistance Based on Transfer Matrix Method

In order to analyze the lateral response of piles subjected to combinational loads located at sloping ground, a simplified physical model is proposed and developed based on the Timoshenko beam theory and tri-parameter elastic foundation beam model. In this model, the effects of vertical resistance, shear deformation and initial inclination of pile shafts are taken into account, and the semi-analytical solution to the lateral behavior of pile is obtained by utilizing the transfer matrix approach. Specifically, the relative transfer matrix coefficients in the free, passive, and active segment of the pile are analytically determined through Laplace transformation. In addition, the validation of this model is conducted by comparing with field observations and predictions obtained from other existing methods. Moreover, the influences of initial inclination angle, vertical resistance in passive segments and the vertical load on the lateral response of the pile are also discussed in depth. The results indicate that, although there is a significant reduction effect emerged in both the lateral displacement and bending moment with the increase in the vertical resistance, a growth trend for those responses can be obtained with an increase in the initial inclination angle and vertical load.

Examination of the reduction in natural frequency of laterally loaded piles due to strain-dependence of soil shear modulus

Society's transition to low-carbon energy sources has resulted in significant expansion in offshore wind technology. Most offshore wind turbines (OWTs) are founded on large-diameter steel tubular piles driven into the seabed, termed monopiles. OWTs are subjected to large numbers of dynamic and cyclic environmental loads during their lifetime. To avoid fatigue or resonance issues, accurate characterisation of soil-structure interaction under operating and extreme conditions is paramount. There is a need to further improve understanding of the dynamic lateral response of piles after large lateral load cycling (storm events). This paper presents the results of lateral load field tests on piles with two different slenderness ratios, where the natural frequency was measured after a series of applied lateral load-unload events. 1D numerical models of the piles were developed and several operating parameters were varied to identify the parameters of importance in the nonlinear soil-pile interaction. Approaches to estimate the operating soil shear modulus both in-situ and post load-unload were trialled, and five subgrade reaction models were used to couple soil and pile properties, to ascertain the performance at predicting the measured frequencies from the experiments. Results suggest that predicted frequencies are highly sensitive to choice of model and degradation method used.

Influence of Vertical Load on the Lateral Response of Piles in Normally Consolidated and Over-Consolidated Clay: Centrifuge and Numerical Modelling

Although pile foundations are usually subjected to both lateral and vertical loads, there have been few studies on the pile response under the combined loadings. Moreover, those few studies led to inconsistent conclusions concerning the influence of vertical load on the lateral pile response. This study aims to investigate the effect of vertical load on the monotonic and cyclic lateral response of piles in normally consolidated (NC) and over-consolidated (OC) clay through a series of centrifuge tests. Three-dimensional finite element analyses using an advanced hypoplastic clay model were also performed to gain deep insight into the mechanism. It is revealed that after applying the vertical load and allowing the dissipation of the induced excess pore pressure, the lateral initial stiffness and ultimate capacity of the pile in the NC clay increased by 10.0 and 49.4%, respectively. However, in the OC clay, the application of the vertical load resulted in a 12.6 and 32.4% reduction in the lateral pile initial stiffness and ultimate capacity, respectively, showing a distinct response from that in the NC clay. The above-mentioned distinct influence of vertical load for piles can be attributed to the different evolutions of stress ratio (q/p’) of the soil around the pile in the NC and OC clay, which determines the soil mobilisable shear strength and consequently the lateral pile responses.

Field and numerical study of the lateral response of rigid piles in sand

Large diameter, short monopiles are the preferred foundation type for offshore wind turbines. These piles demonstrate a rigid response with significant rotation of the pile base under ultimate lateral load. As traditional empirical p-y curves used in lateral loaded pile analysis have been derived from tests on small diameter onshore piles, there is some doubt about their applicability to rigid monopiles, particularly in view of the significant difference in the response of the pile base compared with a typical onshore pile. To address this issue, this paper reports on a unique series of field tests using instrumented driven pipe piles, complimented by numerical analysis, which was performed to examine explicitly the contribution of the pile base to the response under lateral load. The field tests, which included tests on pipe piles that had the sand plug removed to below pile tip level prior to testing, confirmed that the influence of the base on the lateral response for the tested 273- and 457-mm-diameter piles was negligible. Numerical analyses that were calibrated using the field test data showed that the contribution of the base to the lateral capacity of a monopile with a diameter as large as 10 m is negligible. Results also indicated that p-y curves are not affected by the length to diameter ratio and can be used to predict the response of monopiles in sand.

Analysis method for bearing capacity of laterally loaded rigid piles on slopes using improved failure wedge model

An improved failure wedge model is proposed to predict the ultimate lateral resistance of rigid piles on slopes. The emphasis of the improved failure wedge model is based on the three-dimensional combination forces and the hyperbolic p-y criterion, which considers the side friction force between the pile and the soil. A judgment method to determine the p-y curve based on theoretical analysis is proposed. To validate the improved failure wedge model, the method in this research is compared with the three-dimensional finite element (3D FEM) tests and existing solutions by using the hyperbolic p-y criterion and Finite Difference Method (FDM). The influence on the lateral pile response of rigid pile at different slope angle (p-y curves and the load–displacement curves), and the effect of the adhesion factor on the lateral rigid pile response are discussed by combining with numerical simulation and existing solutions, respectively. Through comparison, it is found that the curves predicted by the method proposed in this research are in good agreement with those obtained by FEM and actual examples. The results show that the improved failure wedge model is suitable for representing the pile-soil interaction for the lateral rigid pile on slope.

Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil

Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton’s principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green’s function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%.

Integrated analysis of LNG tank superstructure and foundation under lateral loading

Liquefied natural gas (LNG) storage tanks are often supported by very large pile groups (≥100 piles), which can experience substantial lateral loads such as hurricanes, earthquakes, and floods. However, the existing design standards are premised on the experimental results of the small pile groups (<25 piles). Furthermore, the current design practice considers the superstructure and foundation independently, which apparently do not reflect the soil-pile-superstructure interaction. This study aims to observe how the presence of the LNG tank superstructure influences the foundational response of a 1600-pile group and assess whether the current design approach used in practice is suitable. Three-dimensional finite element models were employed to compare traditional, de-coupled foundation models to the integrated tank-foundation models under Category 3 hurricane wind loads. Effects of LNG weight and foundation stiffness were investigated for the comparison. The results found that large pile groups had greater influence depths of lateral responses than small pile groups. The foundation response in the integrated model varied significantly from the foundation-only models. The amount of LNG in the tank, soil condition, and pile spacing also affected the lateral pile responses, particularly the leading and trailing piles.

Effects of scour-hole dimensions and bulb positions on the lateral response of under-reamed pile in soft clay

The failures of pile foundations in water-borne structures are often attributed to the scouring phenomenon. Even though many studies are available on the countermeasures against scour around the pile, no attempt is made to increase the load-carrying capacity of pile foundation by changing the pile geometry. Therefore, in the present study, the effect of scouring on the lateral response of a single under-reamed pile in soft clay is investigated using three-dimensional numerical analysis. The variables considered in the present study are embedment ratio and bulb position of the under-reamed pile, depth, slope angle, and bottom width of the scour-hole. For a given scour-hole dimension, the lateral load-carrying capacity of the under-reamed pile increases; whereas, deflection, maximum negative shear force, and bending moment in the shaft portion reduce compared to the pile without bulb. A notable improvement in the pile response is found when the bulb is placed just below the scour-hole. The lateral load-carrying capacity of the under-reamed pile reduces with an increase in depth and bottom width of scour-hole from the pile surface and a decrease in slope angle of scour-hole. Pile responses reduce with the consideration of stress history due to excavation.

Large-deformation analysis of pile installation with subsequent lateral loading: Sanisand vs. Hypoplasticity

The simulation of the installation of open-ended piles using a Coupled Eulerian-Lagrangian method in conjunction with two sophisticated constitutive soil models, Sanisand and Hypoplasticity with intergranular strain extension, is presented. Insights into the requirements of numerically stable and efficient implementations of the constitutive models are provided. Following its installation, the response of the pile to lateral loading is investigated and the numerical results are compared to results of model tests. Sanisand is found to be superior in terms of computational performance for the simulation of the pile installation but predicts the pile response to lateral loading following the installation process worse compared to the simulations using Hypoplasticity. The installation-induced changes in the soil state have less influence on the lateral pile response in case of the simulations using Sanisand. It is concluded that both constitutive models are suitable to study large-deformation pile installation processes but the results can differ significantly between the constitutive models despite a careful calibration of the material constants.

Determination of depth-of-fixity point for laterally loaded vertical offshore piles: A new approach

Offshore piles are used as foundations for various marine structures such as quay walls, dolphins, and offshore platforms. Offshore piles are primarily subjected to lateral loads from wind, waves and currents, which is particularly challenging for piles with substantial free length above the seabed. This paper presents a new approach to determine the depth-to-fixity and the depth of the apparent plastic hinge of offshore piles considering the pile head condition, type of soil below, and the soil nonlinearity employing the p-y curve method. A comprehensive numerical investigation was conducted covering a wide range of key parameters governing the lateral response of offshore piles. The results of the parametric analysis were used to establish numerical equations to determine the depth-to-fixity and the depth of the apparent plastic hinge for free and fixed head piles embedded either in sand or in clay. In addition, a closed form solution has been developed utilizing the equivalent cantilever fixed-base model to estimate the lateral capacity of an offshore pile at specified lateral deflection and the corresponding maximum bending moment. The new approach was verified by field load test results conducted on partially embedded piles in sand and clay.

Scour effects on vertical effective stresses and lateral responses of pile groups in sands

For pile-supported structures, scour is a major threat as it removes soils around foundations and causes structural damages. Scour effects on the performance of the pile foundation have been well studied. However, most of these studies are focused on lateral responses of single piles, while very limited research is focused on lateral responses of pile groups. Therefore, prevailing design standards only recommend scour design procedures for single piles. Here, we proposed an improved analytical method (IAM) to analyze laterally loaded pile groups considering various scour-hole dimensions. The IAM was validated against the results of 3D finite element (FE) models calibrated against a full-scale load test. A series of parametric analyses were conducted to investigate the effects of scour-hole depth, scour-hole slope angle, sand relative density, pile spacing, number of piles, and pile group configuration on both post-scour vertical effective stresses and lateral responses of pile groups. Based on the IAM, a simple practical approach called the influence depth method (IDM) was also developed for use in routine design. The feasibility of applying the standard methods for the scoured pile groups was evaluated by comparing them with the 3D FE analyses and the proposed methods (IAM and IDM).

Nonlinear Lateral Response of RC Pile in Sand: Centrifuge and Numerical Modeling

AbstractCentrifuge modeling has been considered as an effective means of studying flexural soil–pile interaction, yet the conventional use of elastic material to model an RC pile prototype is unabl...

Simulation of pile cap contribution to the lateral pile performance due to adjacent excavation

Laboratory and field test data on the lateral pile response with caps due to adjacent excavation are rather limited. The current practice for design of capped piles is to consider the cap resistance and the pile capacity independent of each other. This paper presents some results from three-dimensional finite-difference analyses that couple the constrain effect of pile cap on the lateral pile performance adjacent to an excavation. The analyses were performed in saturated homogeneous clays, and 38 cases of various pile head conditions restrained by caps including embedded depths of the pile into the cap, relative pile cap–pile modulus and pile cap–pile interface stiffness were carried out. The results have shown that the pile–pile cap connections can significantly affect the distribution of lateral pile deflections and bending moments and change the lateral pile performance, especially with a deep-buried and completely fixed cap. To combine the effects of the pile head embedded depths and the cap material properties, a convenient design method based on statistical analysis for estimating the pile–pile cap connections was presented. The proposed constraint coefficient method can be used to assess the lateral performance of the capped pile and simplify the design procedure of the pile cap due to excavations.

A numerical technique for modeling the behavior of single piles in unsaturated soils

Pile foundations are widely used in both saturated and unsaturated soils. In certain scenarios, these foundations are subjected to combined vertical and lateral loads. Conventionally, saturated soil mechanics principles are routinely used for the design of pile foundations in unsaturated soils. Such approaches contribute to unreliable estimates of the behavior of piles due to ignoring the influence of matric suction. In this paper, a comprehensive numerical technique is proposed for simulating the behavior of single piles subjected to combined vertical and lateral loads in unsaturated soils by taking account of the nonlinear behavior of shear strength and the elastic modulus of unsaturated soils. This is achieved through a subroutine that was developed for use in the ABAQUS software. The proposed numerical method provided reliable prediction of the vertical load-displacement behavior of a published model pile tested in saturated and unsaturated sands. In addition, 3D finite element analysis was extended to simulate the influence of variations in ground water table (GWT) on the vertical bearing capacity and the influence of vertical loads on lateral response of piles. The proposed numerical technique is a promising tool for implementing the state-of-the-art understanding of the mechanics of unsaturated soils into conventional engineering practice.

Influence of Vertical Loading on Behavior of Laterally Loaded Foundation Piles: A Review

The majority of installed offshore wind turbines are supported on large-diameter, open-ended steel pile foundations, known as monopiles. These piles are subjected to vertical and lateral loads while in service. In current design practice, interaction of vertical and lateral loads are not considered, rather piles are designed to resist vertical and lateral loads independently. Whilst interaction effects are widely studied for shallow foundations, the limited research on this topic for pile foundations often produces conflicting results. This paper reviews the research of the influence of vertical loading on the lateral response of pile foundations under combined loads, from the perspective of analytical research, numerical research, and experimental research from tests performed on 1-g (gravitational acceleration) model, centrifuge, and full-scale piles. The potential reasons for the differences among the results of previous research are discussed. Some guidance for future research on the effect of vertical loads on the lateral response of piles is provided.

Closed Form Solutions for Predicting Lateral Response of Tripod Suction Pile for Offshore Wind Turbine Foundation

This study presents a simplified analysis technique capable of predicting the dynamic behavior of a tripod suction pile subjected to a horizontal load. The first natural frequency of the system, horizontal displacement, and allowable rotation angle at the pile head were set as target physical quantities in accordance with substructure design requirements. In consideration of the physical characteristics of the tripod suction pile, the analysis was extended to the single pile-multi-pile-tripod-tower part to derive the influence factors. A possible displacement response function that could be applied to the intermediate pile range was also proposed. Thereafter, a detailed design was determined using an integrated load analysis, which included a turbine based on the basic design of simplified analysis method. Furthermore, the dynamic behavior of the offshore wind turbine at each installation stage was predicted using a numerical analysis and measured via field tests. The displacement at the pile head and the predicted value of the first natural frequency of the system were compared using the field-measured and numerical analysis values. The first natural frequency value produced by the simple analysis method showed an error range within 1%, and the displacement at the pile head also satisfied the structural design requirements. Therefore, this method provides a quick and accurate solution to the lateral response of tripod suction piles as foundations for offshore wind turbines.

Lateral Bearing Behaviors of Slightly Inclined Single Pile with Different Pile Head Restraint Under Combined Loads

For a laterally loaded pile with its head keyed into the cap, pile head actually rotates in spite of the restraint of the cap. Being aware of this fact, some parameters were put forward to represent the degree of rotational restraint at pile top, and many calculation methods of lateral pile responses were then developed. However, the presented solutions are only for piles under pure lateral loads. In fact, they are usually under the vertical loads simultaneously, caused by the weights of themselves and superstructures. Besides, the slight initial inclination of pile shaft is inevitable in engineering. Some researchers raised solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads, but the partially fixed-head condition and the elastoplasticity of soil were not considered. In this study, elastoplastic semi-analytical solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads were deduced, in which the rotational restraint coefficient was used to represent the degree of rotational restraint at pile top, and the three-parameter model of the coefficient of subgrade reaction was employed. The computer program was developed thereafter. The effectiveness and advantage of the obtained solutions were validated by the comparison among existing solutions, presented solutions and model test results. Sensitivity analysis was carried out for parameters such as the initial inclination angle of pile shaft, the rotational restraint coefficient, and the vertical load. Eventually, effects of each parameter on lateral pile responses were presented and discussed.

Laboratory and Three-Dimensional Numerical Modeling of Laterally Loaded Pile Groups in Sandy Soils

The lateral response of piles embedded in soil is typically analyzed using the Winkler nonlinear springs method. The predictions of “load–displacement” response of the pile group are needed for a safe and economical design. In this method, the soil–pile interaction is modeled by nonlinear p-y curves in a way that the single pile p-y curve is modified using a p-multiplier for each row of piles in the group. The average p-multiplier is called the group reduction factor. Most research has focused on the behavior of laterally loaded single piles, though piles are most frequently used in groups. The present study was conducted to investigate the effects of various parameters, such as the pile spacing, different layouts, and the lateral load angle change as a new parameter, on the lateral response of piles, group efficiency, and p-multiplier factor in the group. Soil is modeled as an elastic–perfectly plastic material using the modified Mohr–Coulomb constitutive model. In addition, the Abaqus 3D model is validated using load–displacement results from laboratory tests of laterally loaded piles embedded in sand. The p-multiplier factor calculated from this study is well comparable with those of the full-scale tests on pile groups. However, based on the results, the calculated values of the p-multiplier factor at S/D = 3 (obtained from interpolation the values of group reduction factor at S/D= 2.5 and S/D = 3.5) are close to those recommended by the AASHTO, especially for 3 × 3 pile group.

Effects of cross-section shape on cyclic lateral response of steel piles in residual soil

The lateral cyclic loaded piles' behaviour in bonded residual soil is still poorly understood by classical geotechnics. Currently used models reproduce the behaviour of residual soils based on those from other unstructured soils, resulting in a conservative design. This paper thus proposes to evaluate the behaviour of three different shapes of steel piles embedded in bonded residual soil when submitted to cyclic lateral loading tests. These tests encompassed 10 mm displacements performed on the top of the piles (considering service (working) displacements). The piles, with a length of 2·0 m, were equipped with strain gauges at ten levels. The evaluated cross-sections have circular, square and H shapes, all with similar inertia moment and diameter/edge of 0·15 m. The effect of cyclic loading has shown a degradation of available lateral load, mostly in the first 30 cycles. This degradation is also seen at the bending moments obtained. The piles have also shown a short free-headed behaviour that rotates from a certain depth. Finally, the study showed that the square cross-section-shaped pile had the best performance under service (working) cyclic displacements when embedded in bonded residual soil, followed by H cross-sectioned pile and finally the circular cross-sectioned pile.

Equivalent linear model for the lateral dynamic analysis of pile foundations considering pile-soil interface degradation

An equivalent linear BEM-FEM model for the approximate analysis of the time harmonic lateral response of piles considering soil degradation along the soil-pile interface is proposed. The non-degraded soil around the foundation is modelled with boundary elements as a continuum, semi-infinite, isotropic, homogeneous or zoned homogeneous, linear, viscoelastic medium. Piles are modelled with finite elements as beams according to the Bernoulli hypothesis. Differently from what is considered in other BEM-FEM coupled numerical schemes, welded contact conditions are not assumed herein between piles and soil. On the contrary, displacements along FEM piles and within BEM soil are related through distributed springs and dashpots whose properties vary along the pile and that represent the varying stiffness and energy dissipation properties of a pile-soil interface with different levels of degradation at different depths. The developed numerical model is verified by comparison against a more rigorous but much more costly multi-domain boundary element model in which the same degraded soil regions around the pile are modelled as three-dimensional regions.