Laterally-loaded Piles Research Articles

Optimising the embodied carbon of laterally loaded piles using a genetic algorithm and finite element simulation

With the need to cut embodied carbon from the construction industry, there has been a growing interest in optimising the design of different structural elements. This paper, for the first time, minimises the embodied carbon of laterally-loaded piles using a hybrid genetic algorithm. The research is split into four stages. Firstly, the optimisation algorithm is set and run to produce the optimal piles of lateral capacity 0.5 MN at a 25 mm lateral displacement limit, the embodied carbon of solid cylindrical and hollow cylindrical optimised pile designs is compared showing a significant reduction in the embodied carbon when the hollow geometry is used. Then an analysis is presented to test the effect of different displacement limits on the resulting embodied carbon, showing that the lateral displacement limit has a significant effect on the overall embodied carbon of the pile designs, highlighting a scope for reducing the embodied carbon if more pile displacement is permissible. A finite element model is built using ABAQUS simulation package to investigate the soil-pile interaction and compare the two optimal pile designs. Finally, the lateral load capacity of four different pile geometries is calculated to demonstrate the effect of pile geometry on its lateral load capacity, hollow cylindrical piles, showed to have the highest lateral load capacity compared to the other pile types. We conclude that the opportunity for significant carbon savings exists in laterally loaded piles through both optimisation and careful consideration of performance criteria.

A small-strain soil constitutive model for initial stiffness evaluation of laterally loaded piles in drained marine sand

Three-Dimensional Finite-Element Method (3-D FEM) analyses were performed to investigate the initial stiffness of the laterally loaded piles in drained marine sand. A small-strain soil constitutive model developed based on Menq model was implemented in the 3-D FEM model to simulate the response of laterally-loaded piles in the sand over a range of small displacements. The model incorporated how the shear modulus for sand increased with the mean effective stress and decreased non-linearly with the increasing shear strain. The procedure of calibrating the model was proposed based on fitting the measurements from both laboratory tests and in-situ site investigation This soil constitutive model was implemented within a 3-D FEM analysis using an isotropic material with strain-induced anisotropy behavior in order to simulate the response of laterally-loaded piles under monotonic loading. A comparison of model predictions with laboratory and field test results indicated that this model had the promise to simulate the non-linear relationship between lateral load and pile-head deflection for mudline deflections ranging from less than 0.25-percent of the pile diameter.

Simulation of cyclic laterally-loaded piles in undrained clays accounting for soil small-strain characteristics

The performance of pile foundations subjected to cyclic lateral loading is central to offshore geotechnical engineering. Although non-linearity and path-dependence of soil mechanical behavior at small strains are widely recognized, the influences of these local behavior on global response of pile foundations are less explored. This work presents numerical analyses of cyclically-loaded piles in undrained clays that explicitly account for soil small-strain characteristics. By using intergranular strain (IGS) elasticity method, a soil model proposed by the authors for undrained clays during cyclic loading is extended to include non-linear small-strain behavior. Via comparing against element tests, the constitutive relation is shown capable of representing the observed variation of soil stiffness and damping with strain magnitudes, as well as the dependence of such non-linearity on stress paths. Based on the above soil model, finite element simulations are performed to interpret the response of laterally loaded piles from geotechnical centrifuge tests. The impacts of soil small-strain behavior on pile force–displacement relations, hysteric loops, and the ability of a pile–soil system to dissipate energy are investigated. This work highlights that the sensitivity of these foundation responses to small-strain non-linearity of soils can vary considerably, depending on pile geometry features and head constraint conditions.

Recent Advances in Laterally-Loaded Piles within Mechanically-Stabilized Earth Walls

Pile foundations have been increasingly installed within mechanically-stabilized earth walls (MSE) on rocks or compressible soils to support structural loads. Integral abutment bridges, sound walls, and traffic signs are common examples of the structures supported by pile foundations installed within or behind MSE walls. These structures are often subjected to lateral loads resulting from earthquakes, traffic loads, wind loads, and/or thermal expansion and contraction of bridge girders. Typical approaches available to design MSE walls are limited to MSE walls without pile foundations present within reinforced fill. To minimize the interaction between piles and the MSE wall, designers often suggest to place the piles at a distance of six to eight times the pile diameter and/or isolate the piles from the MSE wall by using corrugated pipes. These suggested designs lead to increasing the cost of projects by increasing the length of bridge spans or the diameter of piles and requiring pile embedment. Recently, several studies have been conducted to understand the interaction between piles and MSE walls when the piles are constructed within and close to wall facing. This paper provides a literature review on full-scale tests, reduced-scale tests, and numerical studies of piles constructed within or behind MSE walls. The review will focus on the effects of three key influence factors on lateral capacities of laterally-loaded piles and facing deflections of MSE walls including the plie location behind the wall facing, the ratio of the reinforcement length to the wall height, and the stiffness of the reinforcement layer. This paper will also discuss the available approaches to estimate the forces in the reinforcement layers and the lateral earth pressures behind the MSE wall facing due to the laterally-loaded piles.

Innovative Timoshenko soil-pile integrated element for lager diameter laterally-loaded piles considering soil-pile interactions

The large diameter piles (LDP) are designed to provide strong bearing capacity, which should be carefully analysed to ensure the superstructures’ reliability. The conventional discrete spring element (DSE) method with the Euler-Bernoulli beam element is inappropriate for LDPs as the pile’s shear deformations may be considerable. Besides, the nonlinear soil-pile interactions (SPI) cannot be conveniently simulated with the DSE method. To accurately and effectively evaluate the lateral performance of LDP under extreme load, this paper develops an innovative soil-pile integrated element based on the Timoshenko beam theory. The Green-Lagrange strain is used to formulate the potential energy function with the SPI considered. The Gauss integration method is adopted to simplify the element formulation and evaluate the SPI within the element end nodes. The secant and tangent matrixes are derived for calculating the element deformations and internal forces. The transformation matrix describing the nodal parameters’ relation between element local and global coordinate is presented for practical numerical analysis. The soil-pile integrated element avoids using discrete soil spring elements, significantly reducing the modelling and computing efforts. The verification examples demonstrate that the proposed soil-pile integrated element has high accuracy and efficiency in geometrically nonlinear analysis.

Laterally-loaded pile-MSE wall system performance under different design configurations

The need for constructing a shallow or deep foundation (e.g. piles) in a mechanically stabilized earth (MSE) wall for superstructure support has increased. However, the performance of laterally loaded piles within the MSE wall and their interaction with soil and reinforcement are not fully understood. Limited full-scale tests and numerical studies have been conducted to evaluate the behavior of laterally-loaded piles within MSE walls. In this study, thirteen reduced-scale model tests were performed to investigate the effects of changing the wall configuration (wall height, and reinforcement spacing and length) and the pile location on the performance of the pile-MSE wall system under static lateral loads. This experimental study found that the piles in high walls could develop larger maximum compressive and tensile strains. Low walls resulted in larger wall facing deflections and maximum tensile strains in the geogrid reinforcement. Small reinforcement spacing and long reinforcement length resulted in higher pile lateral load capacities, smaller wall facing deflections, and smaller reinforcement tensile strains. The pile offset from the back of the wall facing is a critical factor that affected the pile capacity, the wall facing deflection, the reinforcement tensile strain, and the lateral earth pressure distribution behind the wall facing.

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%.

Response of pile groups in layered soil to dynamic lateral loads

This paper presents an analytical solution that provides the dynamic response of laterally-loaded pile groups with an arbitrary number of piles installed in layered soil. The solution allows modelling robustly pile-to-pile interaction effects via a new stress-based interaction factor, that considers the fact that soil displacements along the periphery of large-diameter piles of a group subjected to lateral loads will not be in-phase. Layered soil conditions are introduced in the solution by modelling wave propagation in the soil surrounding the piles with the popular plane-strain model and considering soil as viscoelastic material. These idealisations greatly simplify the formulation, at no expense of accuracy when considering loading of relatively stiff piles under serviceability conditions. The solution provides the Winkler modulus for each pile in the group as function of problem parameters that have direct phenomenological meaning, and allows direct calculation of the horizontal impedance of the entire pile group. The presentation concludes with results of a parametric analysis, to demonstrate the effect of considering layered soil conditions and the cross-sectional dimensions of the piles on the response of the group.

Probabilistic Seismic Response and Capacity Models of Piles for Statewide Bridges in California

This study develops the probabilistic seismic response and capacity models for the broad collection of standard pile designs that are routinely incorporated into bridges in California. A review of the state bridge inventory indicates considerable variations in design details for different standard pile types used across multiple eras. For each pile type, fiber-section-based pile models attached with p-y soil springs are built to incorporate nonlinear behaviors of soil materials, a wide array of heterogeneous soil profiles, full-range damage states of piles, and realistic connection details between piles and footings (i.e., pile caps). Moreover, force-displacement responses of pile-soil systems under a large number of pushover analyses are regressed as response models consisting of five parameters [termed as response five parameter (R5P) models], which can capture all essential behaviors of laterally-loaded piles. Capacity damage states and limit state models are defined for different pile types by linking pile global responses to fiber-scale material behaviors at plastic hinge locations. Procedures are further provided to expand R5P models to pile foundation models at the regional scale, taking into account the pile group effect and capacities of pile cap backfills. R5P models for all distinct pile types are further summarized in an Excel workbook to facilitate their practical implementations. In general, this study provides a comprehensive and consistent set of response and capacity models to quantify the seismic damage potential of regional pile foundations, as well as to capture their dynamic interplays with other crucial bridge components, such as columns and abutment components. The proposed pile models are expected to significantly enhance the existing modeling capability toward improved seismic risk assessment of California’s bridge infrastructure.

Evaluation of p-y Curves and p-multiplier of Pile Groups Corresponding to Sand Properties Change Based on 3D Numerical Analysis

The <i>p-y</i> curve method and </i>p</i>-multiplier (<i>P<sub>m</sub></i>), which implies a group effect, are widely used to analyze the nonlinear behaviors of laterally loaded pile groups. Factors affecting <i>P<sub>m</sub></i> includes soil properties as well as group pile geometry and configuration. However, research on the change in <i>P<sub>m</sub></i> corresponding to soil properties has not been conducted well. In this study, in order to evaluate the effect of soil properties on the group effect in a laterally-loaded pile group installed in sandy soil, numerical analysis for a single pile and 3×3 pile group installed in loose, medium, and dense sand, was performed using the 3D numerical analysis program, Plaxis 3D. Among the factors considered in this study, the column location of the pile was the most dominant factor for <i>P<sub>m</sub></i>. The effect of the sand property change on <i>P<sub>m</sub></i> was not as significant as that of the column location of the pile. However, as the sand became denser and the friction angle increased, the group effect increased, leading to a decrease in <i>P<sub>m</sub></i> of approximately 0.1. This trend was similar to the result reported in a previous laboratory-scale experimental study.

Analysis of laterally-loaded piles in weathered rock slopes based on p-y curve method

ABSTRACT This study focuses on investigating the lateral behavior of a particular type of two-pile group foundations embedded in steep and weathered rock slopes. Laboratory lateral load tests were conducted on scaled model piles installed in slopes of various angles. The scaled piles were instrumented with strain gages at different depths while pile head deflections were measured by dial gages. Results indicate that the angle of the slope plays an influential role in the pile deflections and bending moments. Using the p-y curve method for rock-pile interaction analysis, an analytical solution was developed for this particular type of pile foundation installed in weathered rock slopes. The passive pressure and the unique rock-pile interaction are incorporated into the analytical solution. The analytical equations were then numerically solved by using the finite difference method. The numerical results are in reasonably good agreement with the measurements from the laboratory model pile tests.

Lateral response of piles subjected to a combination of spudcan penetration and pile head loads

The effects of spudcan penetration on adjacent laterally-loaded piles mainly manifest themselves in the additional lateral shaft loads induced by large soil deformation. This paper presents a procedure to analyze lateral response of piles subjected to a combination of spudcan penetration and pile head loads. First, the Coupled Eulerian-Lagrangian technique (CEL) is post-processed and key model parameters are investigated to generate accurate soil displacement profiles during free-field spudcan penetration. Second, the effects of spudcan penetration on the adjacent piles loaded on the pile head are analyzed in two ways: the passive pile method and the offset p-y curve method. Results of an available centrifuge model test is firstly adopted to certify the effectiveness of the procedure in analyzing piles singly loaded by spudcan penetration. Then a combined-loading 1 g model test is conducted to calibrate the procedure. Agreement between the calculated and measured results is found especially with the combination of the CEL FE method and the passive pile method.

Kinematic Winkler modulus for laterally-loaded piles

Beam-on-dynamic-Winkler-foundation models are widely used to study kinematic soil-pile interaction. Winkler models consider the pile as a flexural beam and simulate the restraining and dissipative action of soil through independent springs and dashpots along its axis. Their performance is related to the proper selection of the spring stiffness and dashpot coefficient which depends on parameters such as pile geometry, pile-soil stiffness ratio and boundary conditions. Expressions for static and dynamic Winkler moduli from literature were implemented in a Winkler model to assess its ability to predict the curvature ratio and kinematic response factors for various pile boundary conditions. Based on an existing static expression, a frequency-dependent, logarithmic-based Winkler modulus is proposed. This modulus offers an attractive and versatile alternative to existing mathematically complex formulations as it is capable of capturing resonant effects and can be used for both inertial and kinematic analyses, while all other frequency-independent expressions from literature are limited by their unique application to kinematic problems. A comprehensive graphical comparison is given between the results from the Winkler model, using existing and proposed moduli, and the more accurate FE solution to guide the user in selecting the most appropriate modulus for the problem to be analyzed.

Soil reaction to lateral harmonic pile motion

The analytical representation of dynamic soil reaction to a laterally-loaded pile using 3D continuum modeling is revisited. The governing elastodynamic Navier equations are simplified by setting the dynamic vertical normal stresses in the soil equal to zero, which uncouples the equilibrium in vertical and horizontal directions and allows a closed-form solution to be obtained. This physically motivated approximation, correctly conforming to the existence of a free surface, was not exploited in earlier studies by Tajimi, Nogami and Novak and leads to a weaker dependence of soil response to Poisson's ratio which is in agreement with numerical solutions found in literature. The stress and displacement fields in the soil and the associated reaction to an arbitrary harmonic pile displacement are derived analytically using pertinent displacement potentials and eigenvalue expansions over the vertical coordinate. Both infinitely long piles and piles of finite length are considered. Results are presented in terms of dimensionless parameters and graphs that highlight salient aspects of the problem. A detailed discussion on wave propagation and cutoff frequencies based on the analytical findings is provided. A new dimensionless frequency parameter is introduced to demonstrate that the popular plane-strain model yields realistic values for soil reaction only at high frequencies and low Poisson's ratios.

Analysis of laterally loaded piles in soft clay considering scour-hole dimensions

Scour is a process of soil erosion around foundations, resulting in a reduced capacity of the foundations or even failure of the structures. When there are isolated foundations in the midst of water currents, scour holes are formed around the foundations. In practice, scour effects on the foundations are evaluated or designed by ignoring the scour-hole geometry. Instead, scour effects are considered by simply removing the whole soil layer to the scour depth. However, scour-hole dimensions include not only scour depth but also scour-hole width and slope angle. To date, the widely used p–y method for analyzing laterally loaded piles cannot consider three-dimensional scour-hole dimensions. For this reason, a simplified method was developed in this study for the analysis of laterally-loaded piles in soft clay under scour conditions by modifying the p–y curves. The simplified method was used to evaluate the effects of scour-hole dimensions on responses of laterally loaded piles in soft clay. The computed results were compared with those from the 3D finite difference method. The analysis indicated that ignoring the scour-hole dimensions could result in 10–19% larger lateral pile-head displacements and 6–8% larger bending moments than what would be computed while considering them.

Performance of laterally loaded piles considering soil and interface parameters

To investigate the soil-pile interactive performance under lateral loads, a set of laboratory model tests was conducted on remoulded test bed of soft clay and medium dense sand. Then, a simplified boundary element analysis had been carried out assuming floating pile. In case of soft clay, it has been observed that lateral loads on piles can initiate the formation of a gap, soil heave and the tension crack in the vicinity of the soil surface and the interface, whereas in medium dense sand, a semi-elliptical depression zone can develop. Comparison of test and boundary element results indicates the accuracy of the solution developed. However, in the boundary element analysis, the possible shear stresses likely to be developed at the interface are ignored in order to simplify the existing complex equations. Moreover, it is unable to capture the influence of base restraint in case of a socketed pile. To bridge up this gap and to study the influence of the initial stress state and interface parameters, a field based case-study of laterally-loaded pile in layered soil with socketed tip is explored and modelled using the finite element method. The results of the model have been verified against known field measurements from a case-study. Parametric studies have been conducted to investigate the influence of the coefficient of lateral earth pressure and the interface strength reduction factor on the results of the model.

Fuzzy analysis of laterally-loaded pile in layered soil

A fuzzy finite-element method for analysis of laterally loaded pile in multi-layer soil with uncertain properties is presented. The finite-element formulation is established using a beam-on-two-parameter foundation model. Uncertainty propagation of the soil parameters to the pile response is evaluated by a perturbation technique. This approach requires a few number of classical finite-element equations to be solved and provides reasonable results. A comparison with vertex method is made in a numerical example.

Numerical Analysis of Piles Under Cyclic Lateral Load

The paper presents the results to study the response of piles in homogeneous and layered soils subjected to quasi-static and cyclic lateral loading using numerical analysis. The analyses are carried out using three-dimensional finite element software, ABAQUS v6.10. Hypoelastic constitutive model is used to simulate the small strain nonlinear behavior of soil observed during the application of cyclic lateral load on piles. The bending moment and deflection responses computed from ABAQUS analyses are compared with the results obtained from the reported case histories of field pile lateral load tests and centrifuge tests. The favorable comparisons established that the three-dimensional numerical analysis can be effective to model complex soil–pile systems. Numerical analysis was also able to simulate a cement injected layer as a reinforcement body to the soft foundation soil, which can affect the pile response. The study was further extended to understand, the effect of flow of surrounding soil around the laterally-loaded piles on the response of piles.

Probabilistic analysis of laterally loaded piles using response surface and neural network approaches

The response surface and the neural network methodologies are two approaches that are commonly used in reliability analysis of geotechnical problems with implicit performance functions, to deal with the complexity of probabilistic analyses. This paper proposes a two-step hybrid approach for reliability analysis. The first step obtains the design point using the first-degree polynomial response surface model. The second step constructs a neural network model of the performance function at the design point. The proposed method is first illustrated for a hypothetical laterally-loaded pile with analytical solutions. The case of a laterally-loaded steel pipe pile in Arkansas River sand is then presented, which involves non-normal random variables and spatial autocorrelation of soil strength parameters. Comparisons are made with Monte Carlo simulations incorporating importance sampling. Reliability-based parametric studies are performed on the Arkansas River example using the proposed hybrid approach. The influences on the reliability index and the probability of failure by the lateral load, depth of water table and correlation coefficient between unit weight and friction angle are investigated and discussed.

Rate-Controlled Lateral-load Pile Tests Using a Robotic Manipulator in Centrifuge

Abstract Robotic manipulators, as a new facility for centrifuge modeling, can provide a platform to carry out complex in-flight simulation of geotechnical problems. In this study, a four-axis robotic manipulator was employed to conduct a series of laterally-loaded pile tests in sand. Four model piles were installed into a sand bed and laterally loaded at different loading rates consecutively without stopping the centrifuge, which accordingly maximized consistency of the soil sample among the tests. Tests in both loose sand and dense sand were conducted. Detailed information of the test devices and procedures of soil sample preparation and load testing is described in this paper. The test results, including horizontal force-displacement curves, bending moment distributions, relationships between lateral resistance and loading rates, and p-y curves derived from the measured bending moment distributions, are presented. In addition, the effects of loading rate and ground surface are discussed based on the test results. It is found that, under the investigated conditions, loading rate has little effect on the horizontal resistance at specified displacements, but has significant effects on the bending moment and soil reaction distributions. The ground surface also has an effect on the behavior of the laterally-loaded piles. A simple modification method is used to consider the effect of ground surface on p-y curves at shallow depths.