Dynamic Winkler Foundation Research Articles

Kinematic response of a pile within a soil slope to SH wave excitation

It is widely recognized that the topography of a slope can significantly enhance the magnitude of seismic waves. Nevertheless, the mechanism behind the topographic amplification on the kinematic response of a pile within a soil slope remains unclear. Consequently, a newly rigorous method is employed to investigate the kinematic response of a pile within a soil slope. The proposed method which combines the Wave Function Expansion (WFE) method and the Beam on Dynamic Winkler Foundation (BDWF) model advances the rigorous theoretical study for the kinematic response of a pile on slope from the pseudo-static analysis to the frequency-domain analysis. The proposed solution well captures the kinematic response of a piles within a slope. The parametric analysis focuses on investigating the influence of slope topographic amplification effects on pile vibration under different incident frequencies, slope gradients, and pile-to-soil modulus ratios. The results indicate that steep slopes and high pile-to-soil modulus ratios lead to higher topographic amplification effects, with specific frequencies significantly amplifying the kinematic response of pile within a slope. Nonetheless, as the pile located beyond twice the length of the slope, the amplification effect notably diminishes.

Non-linear behaviour of soil–pile interaction phenomena and its effect on the seismic response of OWT pile foundations. Validity range of a linear approach through non-degraded soil properties

The effect of non-linear and inelastic behaviour of the soil–pile interaction on the seismic response of offshore wind turbine pile foundations embedded in sandy soils is analysed. For this purpose, the responses obtained assuming three different Beam on Dynamic Winkler Foundation (BDWF) models are compared: a Plastic Non-Linear Model (PNLM), an Elastic Non-Linear Model (ENLM) and a simple elastic linear model with non-degraded properties of soil (NDLM). The influence of non-linearity and plasticity assumption is studied by evaluating the effects of the kinematic and inertial interaction within soil–pile interaction. Two soil stiffness levels are analysed: very loose and medium dense sand. The seismic response under ten earthquakes is computed in terms of mean envelopes of internal forces along the pile length. The non-linearity and inelastic influence of soil–pile interaction is quantified by means of relative differences with respect to the linear elastic model. Results show that the non-linear and inelastic models acquire relevance when the contribution of the inertial interaction dominates, leading to lower maximum responses than the linear elastic model. If the inertial interaction is not significantly activated, similar results between the three models are obtained, being the linear elastic model enough to reproduce the soil–pile dynamic interaction.

The Horizontal Mode Natural Frequency of a Floating Pile in Layered Soil: Full-Scale Field Test Vs Mathematical Models

Pile supported structures can be subjected to a variety of man-made and naturally occurring dynamic loads. Dynamic loads such as those from rotating machinery include a considerable lateral component. The natural frequency of a pile in the horizontal mode becomes a key parameter in the design of dynamically sensitive equipment foundations. It is not uncommon for structural engineers to estimate the natural frequency of piles using quick linear methods using available soil investigation data before advanced laboratory tests on soil samples can be performed to calibrate nonlinear numerical models. This paper presents results from free and forced vibration tests on a full-scale single pile, designed for a high-speed compressor unit, in Hazira, India. Two different fast mathematical models, one following the Beam on Dynamic Winkler Foundation (BDWF) method, and another involving an FEM–BEM based numerical method were used in predictions against experimental results. The BDWF method was found to produce a preliminary estimate of pile stiffness at low strain levels. However, the selection of soil stiffness and damping models are crucial for the accuracy of BDWF models. It was found that the FEM–BEM model was able to simulate the nonlinear pile response with a moderate overestimation of vibration amplitudes.

Analytical solution for sheet-pile groin vibrations under tidal bore excitation

A sheet-pile groin composed of two rows of piles connected by sheets has been applied to resist tidal bores in recent years, but its dynamic responses have not been thoroughly researched. This paper proposes an analytical solution for the dynamic responses of sheet-pile groins subjected to tidal bore impulses. The piles are modeled as Timoshenko beams to include flexural vibration. Considering the longitudinal vibration and vertical flexural inertia effect, each sheet is modeled with a Rayleigh-Love rod and Timoshenko beam. The dynamic Winkler foundation model simulates the soil around the piles. The tidal bore load acting on the front row of piles is simplified as a lateral semiharmonic concentrated point load. The governing equations are constructed in the time domain and solved in the frequency domain, and the final responses in the time domain are obtained using the discrete inverse Fourier transform. The presented analytical solution is validated by comparison with numerical simulation results. An extensive parametric analysis is then conducted to investigate the influence of the vertical flexural inertia effect on the dynamic responses of a sheet-pile groin. Suggestions based on this study are given to provide guidance for sheet-pile groin design in engineering practice.

Analytical study on the dynamic responses of a sheet-pile groin subjected to transient lateral impulses

A novel sheet-pile groin structure consisting of row piles and a tied sheet has been introduced to resist the impact of tidal bores in recent years. However, the dynamic responses of the structure under tidal bore loads have not been carefully studied before. This paper proposed an analytical solution for the dynamic responses of a sheet-pile groin subjected to transient lateral excitation. To take the flexural and longitudinal vibrations into consideration, the piles and the sheet are modeled by Timoshenko beam (TB) theory and a one-dimensional rod, respectively. The soil around the piles is simulated by the dynamic Winkler foundation model. The excitation is considered by a lateral concentrated point load acting on the front pile. On this basis, the governing equations are constructed in the time domain and solved in the frequency domain, while the time-domain responses are obtained using the inverse Fourier transform. The accuracy of the presented analytical solution is validated by comparison with the results obtained from finite element method (FEM) simulation. The effects of the properties of the sheet, piles and soil on the dynamic responses are investigated through a comprehensive parametric study.

Influence of excavation beneath existing building on dynamic impedances of underpinning pile considering stress history

The addition of basement beneath existing building changes the underpinning pile from fully embedded to partially embedded, and thus influences the mechanical properties of pile. In the past, scholars paid attention to the change in the bearing capacity of pile but neglected the difference of dynamic characteristics before and after construction, and potential changes in stress history of remaining soil are also ignored. In this work, a calculation model is built to investigate the influence of excavation on dynamic impedance of underpinning pile considering the effect of stress history. The soil is simulated by the dynamic Winkler foundation, which is characterized by springs and dashpots. Properties of remaining soil after excavation are updated to consider the effect of stress history through modifying the initial shear modulus and related parameters. The dynamic impedance of pile after excavation is obtained based on the transfer matrix method. The parameter study is carried out to evaluate the dynamic impedance with various excavation depths, considering or ignoring stress history effect, and various element lengths. The results show that shallow soil plays an important role to dynamic impedance, and overestimated dynamic impedance is obtained if not considering the stress history effect.

Relevance of soil-pile tangential tractions for the estimation of kinematic seismic forces: Formulation and setting of a Winkler approach

• A BDWF model including the distributed moments produced by the pile rotation and the action of the seismic field is presented. • The performance of the proposed model for computing the pile seismic internal forces is tested against a BE formulation. • The influence of the contact condition between pile and soil on the pile seismic forces is also analysed. • Depending on the contact condition, pile shear forces can be duplicated, while bending moments remain practically unaltered. The effects of considering the tangential tractions that act on the soil-pile interface in the estimation of the pile seismic response are studied through a Beam on Dynamic Winkler Foundation model, which includes the distributed moments produced by the rotation of the pile cross-section and the action of the incident field. The performance of the developed Winkler formulation is evaluated by using a rigorous continuum model based on boundary elements that allows the use of both smooth and welded contact conditions at the soil-pile interface. In order to do the analyses, the seismic response of a fixed-head single pile embedded in different soils subjected to planar shear waves is computed in terms of envelopes of maximum bending moments and shear forces. Two soil profiles are assumed: homogeneous and two-strata halfspaces. The tangential tractions are found to significantly increase the pile maximum shear forces, but to have a minor impact on the pile maximum bending moments. The proposed Winkler model accurately reproduces the results of the continuum formulation for both contact conditions. However, some differences are found in the evaluation of the inter-layer envelopes, for which the simplified model underestimates their values.

KIN SP: A boundary element method based code for single pile kinematic bending in layered soil

In high seismicity areas, it is important to consider kinematic effects to properly design pile foundations. Kinematic effects are due to the interaction between pile and soil deformations induced by seismic waves. One of the effect is the arise of significant strains in weak soils that induce bending moments on piles. These moments can be significant in presence of a high stiffness contrast in a soil deposit. The single pile kinematic interaction problem is generally solved with beam on dynamic Winkler foundation approaches (BDWF) or using continuous models. In this work, a new boundary element method (BEM) based computer code (KIN SP) is presented where the kinematic analysis is preceded by a free-field response analysis. The analysis results of this method, in terms of bending moments at the pile-head and at the interface of a two-layered soil, are influenced by many factors including the soil–pile interface discretization. A parametric study is presented with the aim to suggest the minimum number of boundary elements to guarantee the accuracy of a BEM solution, for typical pile–soil relative stiffness values as a function of the pile diameter, the location of the interface of a two-layered soil and of the stiffness contrast. KIN SP results have been compared with simplified solutions in literature and with those obtained using a quasi-three-dimensional (3D) finite element code.

Dynamic Winkler Foundation for vibration analyses of flexible footings

For the design of mitigation measures against railway traffic induced vibrations the interaction between the unbounded soil and the flexibility of the foundation must be taken into account. Common numerical schemes like Boundary Elements, Transmitting Boundaries, and Perfectly Matched Layer bear computational costs which render their application impractical. The concept of Dynamic Winkler Foundation (DWF) is a tempting alternative due to its simplicity, but it neglects certain important peculiarities of soil-structure interaction. Hence, the coefficients of the DWF must be carefully chosen, taking into account the properties of the foundation soil, as well as the properties of the structure. As part of an ongoing research we derive such coefficients and assess their suitability from analyses of a real-world building for which mitigation methods have been implemented.

Dynamic Models of Piled Foundations

The vibration behavior of piled foundations is an important consideration in fields such as earthquake engineering, construction, machine-foundation design, offshore structures, nuclear energy, and road and rail development. This paper presents a review of the past 40 years' literature on modeling the frequency-dependent behavior of pile foundations. Beginning with the earliest model of a single pile, adapted from those for embedded footings, it charts the development of the four pile-modeling techniques: the “dynamic Winkler-foundation” approach that uses springs to represent the effect of the soil; elastic-continuum-type formulations involving the analytical solutions for displacements due to a subsurface disk, cylinder, or other element; boundary element methods; and dynamic finite-element formulations with special nonreflecting boundaries. The modeling of pile groups involves accounting for pile-soil-pile interactions, and four such methods exist: interaction factors; complete pile models; the equivalent pier method; and periodic structure theory. Approaches for validating pile models are also explored.

Study on Damage Mechanism for Foundation Pile of Girder Bridge under Seismic Influence

Based on the analysis for seismic load and failure modes of pile foundation, this article adopts dynamic Winkler foundation beam model, and employs continuous distributional and independent spring and damper, instead of the dynamic resistance of the soil around the pile, and to explore interaction between pile and soil dynamic at horizontal load. In consideration of six kinds of boundary conditions combination, this paper proposes the solution method for displacement and internal force on pile. From analysis of cases, it finds that the effect of pile’s length on dynamic response can be negligible when pile slenderness ratio l/d>20, and the pile can be simplified into infinite long pile. Dynamic response of pile increases with the increase of stiffness ratio. When establish the control equations, influence of axial force can not be ignore. Otherwise, results will be small than the actual value.

Experimental p-y loops for estimating seismic soil-pile interaction

Seismic soil-pile interaction is evaluated in this study based on back-calculated p-y loops constructed from sampled data of pile bending moments. Fundamental properties of p-y loops are implemented to derive distributed springs and dashpots, thereby quantifying soil-pile interaction in the realm of a Beam on Dynamic Winkler Foundation modeling. The procedure is validated by means of well-documented centrifuge tests of a single pile supported structure founded on a two-layer soil profile that comprises of soft clay overlying dense sand. Two shaking levels of a real earthquake motion applied at the base of the soil profile were examined and the generated seismic p-y loops were compared to cyclic p-y curves commonly used in pile design practice. The results demonstrate the strong influence of intensity of the input motion on seismic p-y loops while cyclic p-y curves established for soft clays tend to overestimate soil stiffness under strong excitation. Typical sets of recorded and computed structural response are presented, denoting the ability of the BDWF model related to p-y loops in reproducing adequately fundamental aspects of seismic soil-pile interaction.

Dynamic interaction factor considering axial load

Using the dynamic differential equation of beam and considering the surrounding soil as dynamic Winkler foundation, the simplified dynamic interaction factors of group piles are analyzed with axial load under horizontal harmonic load and horizontal seismic affection. When the axial load was replaced by zero, the expression of dynamic interaction factor would be the same as that deduced by Markris and Gazetas (1992, Earthquake Eng Struct Dyn 21(2):145–162). And under special situation analysis, there would be obvious effect on dynamic interaction factor when the axial load was large. The differences are obvious when considering axial load, and the relative errors would be 14% or greater, so it’s proper to consider axial load when the dynamic interaction factor are calculated.

KINEMATIC SEISMIC RESPONSE OF PILES IN LAYERED SOIL PROFILE

This paper is aimed at highlighting the importance of Kinematic Seismic Response of Piles, a phenomenon often ignored in dynamic analysis. A case study is presented where the end bearing pile is embedded in two layer soil system of highly contrasting stiffness; a typical case where kinematic loading plays important role. The pile soil system is modeled as continuous system and as discrete parameter system. both are based on BDWF (Beam on Dynamic Winkler Foundation) formulation. For discrete parameter system, a finite element software SA P2000 is used and the modeling technique of kinematic interaction in finite element software is discussed. For pile soil system modeled as continuous system, a general MATLAB code is developed capable of performing elastic sate response analysis in two layer soil system, solving differential equation governing kinematic interaction, and giving as output the maximum ground displacement, maximum pile displacement, rotation, moment and shear distribution along pile length. The paper concludes that kinematic seismic actions must be evaluated particularly at the interface of soil layers of significantly differing soil stiffnesses.