Winkler Springs Research Articles

Effect of in-situ variability of soil on seismic design of piled raft supported structure incorporating dynamic soil-structure-interaction

Inherent variability of soil considerably affects the seismic design of piled raft supported structures. Conventional design of such structure adopts fixity at base level of superstructure and pile head. However, soil–pile–superstructure interaction largely affects the fundamental frequency and design forces in columns and piles. In contrast, fixed base assumption cannot capture soil structure interaction (SSI) effect. In addition, uncertainty in soil may further leads to a change in the dynamic behavior of the system. This study examines the effect of inherent variability of undrained shear strength of soil in seismic design of structures supported by piled raft foundation embedded in soft clay. Superstructure is modeled as lumped mass stick model and piled raft slab is modeled as rigid plate. Pile is modeled as Euler–Bernoulli beam element and soil resistance is modeled using linear Winkler springs attached to the pile. Dynamic analysis is carried out in time domain to estimate the responses. Monte Carlo simulation technique is used for probabilistic assessment of the fundamental frequency and forces at column and pile attributing a wide range of parametric variation of a representative soil–piled raft–superstructure system. The study shows that the fundamental frequency and forces in column and pile changes significantly due to soil variability.

지반조건 상호작용을 고려한 풍력발전타워의 공진회피 진동수 산정을 위한 고유진동수 해석 연구

Abstract Global warming and the depletion of fossil fuels have been caused by decades of reckless development.Wind energy is one form of renewable energy and is considered a future energy source. The wind tower is designedwith a fundamental frequency in the soft-stiff design between the 1P and 3P range to avoid resonance. Usually, toperform natural frequency analysis of a wind tower, the boundary condition is set to the Fixed-End, and soil-pile interaction is not considered. In this study, consideration of the effect of soil-pile interaction on the wind tower wasincluded and the difference in the natural frequency was studied. The fixed boundary condition was not affected bythe soil condition and depth of the pile and the coupled spring boundary condition was unaffected by the depth of pile but affected by the depth of the pile, and the Winkler spring boundary condition is affected by both the soilcondition and the depth of the pile. Therefore, the coupled spring boundary condition should be used in shallow depth soil conditions because the soil condition does not take the shallow depth soil into consideration.

Fatigue analysis of offshore well conductors: Part II – Development of new approaches for conductor fatigue analysis in clays and sands

This paper, Part II, presents two soil modelling approaches developed specifically for fatigue analysis of well conductors. The first approach uses Winkler springs and can account for soil damping. The second approach is based on continuum soil mechanics and uses the kinematic hardening principles. They focus on cyclic soil behaviour at the steady-state condition. The paper demonstrates appropriateness of the approaches in predicting fatigue damage through comparisons with the centrifuge fatigue lives measured from the Series 1 tests in NC to lightly OC kaolin clay. It also presents and discusses the analyzed data and the fatigue lives measured from the Series 2 (medium-dense sand), Series 3 (NC to lightly OC GoM clay), and Series 4 (OC natural clay) tests. Finally, soil models (based on the first approach) are presented for fatigue analysis of well conductors installed in NC to lightly OC clays, over-consolidated (OC) clays and medium-dense sands, and their ability to predict conductor fatigue damage under wide range of loading conditions is demonstrated. Overall, the accuracy of fatigue life predictions using these novel soil models is very high – generally within about a few percentages of the measured values.

A case study on the soil–pile–structure interaction of a long span arched structure

Different concepts for modelling of soil-foundation in complete dynamic interaction analysis for a 110-m height 70-m span arched structure on 180 piles were investigated in this paper. The modelling approaches consisted of a sophisticated procedure to account for soil compliance and foundation flexibility by defining frequency-dependent springs and dashpots; namely, flexible-impedance base model. The results of this model were compared with those of the conventional modelling procedures; namely, fixed base model and flexible base model by defining frequency-independent springs. In the flexible-impedance base model, the substructure approach was employed through finite element modelling. To account for the kinematic interaction, the numerical model of the soil, foundation and piles were developed using a verified finite element model in ABAQUS. The free field time history and design spectrum were modified to obtain the foundation input motion. The impedance of pile groups with different length was obtained by the finite element model to assess the inertial interaction. The comparison of the results of the employed models showed that rocking and torsional responses were greatly affected by soil–structure interaction, indicating redistribution of seismic demands. It was also proven that the internal demands of the conventional model considering frequency-independent Winkler springs might be higher than those of the model including pile–soil–structure interaction effects.

Seismic response of bridges supported on shallow rock foundations considering SSI and pier column inelasticity

Traditionally, shallow spread footing type foundations are used for medium span bridges supported on rock strata. Such bridges are modeled with fixed supports and no Soil-Structure Interaction (SSI) is considered. The investigation presented herein utilized a substructuring technique and Finite Element Method (FEM) model for a medium span 4-span bridge designed for five different rock classes and subjected to an ensemble of actual ground motions. Non-linear behavior of reinforced concrete pier column was modeled for material and geometric non-linearity and incorporated in the overall analysis scheme by equivalent linear model while SSI was included through Winkler springs. The results of the study were evaluated to delineate the effect of SSI and pier column non-linearity on seismic response parameters of bridges founded on shallow foundations in rock strata. It was found that the SSI cannot be neglected in all cases of rock classes and input ground motions. Furthermore, pier column non-linearity influenced bridge displacement and base shear much more significantly than SSI and should not be ignored in the seismic modeling and analysis of these bridges.

Evaluation of seismic performance of pile‐supported models in liquefiable soils

SummaryThe seismic performance of four pile‐supported models is studied for two conditions: (i) transient to full liquefaction condition, i.e. the phase when excess pore pressure gradually increases during the shaking; (ii) full liquefaction condition, i.e. defined as the state where the seismically induced excess pore pressure equalises to the overburden stress. The paper describes two complementary analyses consisting of an experimental investigation, carried out at normal gravity on a shaking table, and a simplified numerical analysis, whereby the soil–structure interaction (SSI) is modelled through non‐linear Winkler springs (commonly known as p–y curves). The effects of liquefaction on the SSI are taken into account by reducing strength and stiffness of the non‐liquefied p–y curves by a factor widely known as p‐multiplier and by using a new set of p–y curves. The seismic performance of each of the four models is evaluated by considering two different criteria: (i) strength criterion expressed in terms of bending moment envelopes along the piles; (ii) damage criterion expressed in terms of maximum global displacement. Comparison between experimental results and numerical predictions shows that the proposed p–y curves have the advantage of better predicting the redistribution of bending moments at deeper elevations as the soil liquefies. Furthermore, the proposed method predicts with reasonable accuracy the displacement demand exhibited by the models at the full liquefaction condition. However, disparities between computed and experimental maximum bending moments (in both transient and full liquefaction conditions) and displacement demands (during transient to liquefaction condition) highlight the need for further studies. Copyright © 2016 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.

Influence of soil–structure interaction on fragility assessment of building structures

In this work, 3D reinforced concrete (RC) and steel building structures have been considered for studying the effect of soil–structure interaction modelling on the structural fragility assessment of such structures. In particular, three foundation models were considered: fixed model where soil–structure interaction is neglected, spring model with single-node Winkler springs and pile foundation model where soil–structure interaction is simulated using beam and quadrilateral finite elements for the pile and soil numerical simulation, respectively. For the assessment of the structural performance and the influence of the various soil–structure interaction numerical simulation models, fragility analysis is applied by considering four limit-states. For the purpose of the current study 3D, low-, mid- and high-rise RC and steel buildings are studied. The test examples employed in this study were designed first according to Eurocodes 2, 3 and 8 using the SCADA Pro analysis and design software and then nonlinear static analyses were performed for developing the fragility curves. Comparing the outcome of fragility analysis it was observed that for the case of the low- and mid-rise buildings, the structural performance was not affected significantly by the foundation system. However, it was observed that the foundation system contributes considerably to the overall structural performance of the high-rise structures examined.

Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation

In this study, free vibration analysis of magneto-electro-thermo-elastic (METE) nanobeams resting on a Pasternak foundation is investigated based on nonlocal theory and Timoshenko beam theory. Coupling effects between electric, magnetic, mechanical and thermal loading are considered to derive the equations of motion and distribution of electrical potential and magnetic potential along the thickness direction of the METE nanobeam. The governing equations and boundary conditions are obtained using the Hamilton principle and discretized via the differential quadrature method (DQM). Numerical results reveal the effects of the nonlocal parameter, magneto-electro-thermo-mechanical loading, Winkler spring coefficients, Pasternak shear coefficients and height-to-length ratio on the vibration characteristics of METE nanobeams. It is observed that the natural frequency is dependent on the magnetic, electric, temperature, elastic medium, small-scale coefficient, and height-to-length ratio. These results are useful in the mechanical analysis and design of smart nanostructures constructed from magneto-electro-thermo-elastic materials.

Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation

In this present study, Chebyshev collocation method is utilized to solve buckling and vibration problems of functionally graded (FG) sandwich beams resting on two-parameter elastic foundation including Winkler and shear layer springs. The faces of FG sandwich beam are assumed to be made by functionally graded materials (FGMs) composing of ceramic and metal phases and the core of the beam is made from homogenous material. Timoshenko beam theory is employed to construct the governing equations of motion in order to cover the significant effects of shear deformation and rotary inertia. The beams with various boundary conditions are considered to find out their critical loadings and natural frequencies. An accuracy of the present solutions is confirmed by comparing with some available results in the literature. Moreover, many important parametric studies of layer and beam thickness ratios, material volume fraction index, spring constants, etc. are taken into investigation. According to numerical exercises, it is revealed that the spring constants of elastic foundation have significant impact on buckling and vibration results of such beams.

Effect of soil-foundation-structure interaction and pier column non-linearity on seismic response of bridges supported on shallow foundations

Traditionally, shallow spread footing-type foundations are used for medium span bridges supported on hard soil and rock strata. Such bridges are modelled with fixed supports and no soil–foundation–structure interaction (SSI) is normally considered. The investigation presented herein utilized a sub-structuring technique and finite element method (FEM) model for the analysis of a four-span bridge designed for five different rock classes and subjected to an ensemble of actual ground motions. SSI was incorporated through Winkler springs while non-linear behaviour of reinforced concrete pier column was modelled by an equivalent linear model. The results of the study were evaluated to delineate the effect of SSI and pier column non-linearity on seismic response parameters of bridges founded on rock. It was found that the soil–foundation–structure interaction couldn’t be neglected in all cases of rock classes and input ground motions. Furthermore, pier column non-linearity influenced bridge displacement and base shear more significantly than SSI. Impact of foundation rocking was also examined and was found to be rather insignificant on bridge response parameters due to high rocking impedance of properly designed bridge foundations.

Non-linear response of geocell reinforced dense granular layer over weak soil under circular loading

A modified Pasternak model has been proposed to predict the behavior of a circular footing resting on a geocell reinforced granular layer overlying soft soil. In this model, the geocell reinforced granular layer was considered as a Pasternak shear layer and the soft soil as a series of Winkler springs to predict the overall behavior. Both linear and non-linear responses of the geocell reinforced bed were considered in the analysis, which correspond to low- (≤1% of footing width) and high-footing settlements (>1% of footing diameter), respectively. An iterative finite difference scheme is employed for obtaining the solution for the governing differential equations and the results presented in non-dimensional form. Results from the present model were validated with independent experimental test data by comparing the load-deformation responses. The model parameters, inverse of normalized shear stiffness of the geocell (α2) and the inverse of normalized ultimate bearing capacity (μ), were varied for the parametric study. It was found that the shear stiffness of the reinforced granular bed, i.e. the product of shear modulus and height of the geocell in a granular bed, plays an important role in improving the performance of the reinforced bed. Design charts were presented in the form of improvement factors for practical range of shear layer width, shear stiffness of the geocell reinforcement, and ultimate bearing capacity of the soft soil.

Modelling effects of pile diameter

The most commonly used program for the analysis of piles under static lateral loading is LPILE. The program uses the nonlinear Winkler springs recommended by the American Petroleum Institute (API) to model soil–pile interaction. The p–y (load–displacement) curves were developed from field tests, with pile diameters in the range 0.324–0.67 m. When these p–y curves are used to analyze load tests on piles with larger diameters, the computed load–deflection curves underestimate the stiffnesses of the test piles. This effect is referred to as the pile diameter effect. In this technical note, a very different approach is presented to evaluate the pile diameter effect. Both LPILE and a continuum-based finite element program VERSAT-P3D were calibrated to closely simulate the results of two lateral load tests on small-diameter piles at two different sites. VERSAT-P3D modelled the volume of the pile and LPILE did not. Each program was used to develop p–y curves for increasingly larger pile diameters up to 2.0 m. An important finding for practice is that there was no pile diameter effect for displacements up to 60 mm. LPILE can be used with confidence in practice in this displacement range. Thereafter, the load–deflection curves from LPILE became softer and the pile diameter effect became evident.

Thermoelastic Response of FGM Plates with Temperature-Dependent Properties Resting on Variable Elastic Foundations

This paper deals with thermomechanical bending of functionally graded material (FGM) plates under various boundary conditions and resting on two-layer elastic foundations. One of these layers is Winkler springs with a variable modulus while the other is considered as a shear layer with a constant modulus. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The temperature is obtained by solving the one-dimensional equation of heat conduction. The material properties of the plate are assumed to be graded continuously across the panel thickness. A simple power-law distribution in terms of the volume fractions of the constituents is used for estimating the effective material properties such as temperature-dependent thermoelastic properties. The governing equations are derived based on the sinusoidal shear deformation plate theory including the external load and thermal effects. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the bending of FGM plates are presented.

Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

AbstractAnalyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Numerical modelling of strip footing on geocell-reinforced beds

Geosynthetics in the form of three-dimensional geocells has been in use for some time to improve the performance of foundations. A mathematical formulation was developed to predict the behaviour of a rigid strip footing resting on a geocell-reinforced granular layer overlying soft soil. The combined geocell-reinforced granular layer and the soft soil were considered as Pasternak shear layer and a series of Winkler springs, respectively. Both linear and non-linear responses of the reinforced bed were considered in the analysis, which corresponded to low (< 1% of footing width) and high footing settlements (> 1% of footing width), respectively. An iterative finite-difference scheme was employed to obtain the solution for the governing differential equations and the results are presented in non-dimensional form. The present model was validated with two independent experimental test data by comparing the load–deformation patterns which indicated good agreement. Combined soil–geocell properties were varied to obtain the improved load-carrying capacity of the reinforced ground. It was found that the shear stiffness of the reinforced granular bed, namely the product of shear modulus and height of the geocell in a granular bed, plays an important role in improving the performance of the reinforced bed. The effect of shear layer width, shear stiffness of the geocell-reinforced ground and ultimate bearing capacity of the soft soil that brings in variation in improvement of the ground were analysed and the results are presented in terms of design charts.

Soil–pile interaction considering structural yielding: Numerical modeling and experimental validation

In the present study the accuracy of an efficient beam formulation for inelastic analysis of pile-foundation systems is validated against a series of Laboratory Pushover tests on vertical single piles embedded in dry sand under different load paths to failure in M–Q space conducted in the Laboratory of Soil Mechanics/Dynamics (LSMD) in NTUA. The obtained results are also compared to those from a fully 3D Nonlinear Finite Element (FE) simulation. The proposed beam formulation is based on the Boundary Element Method (BEM) accounting for shear deformation effect. A displacement based procedure is employed and inelastic redistribution is modeled through a distributed plasticity (fiber) model exploiting pile material constitutive laws and numerical integration over the cross-sections, while the surrounding soil is modeled through independent inelastic Winkler springs. The efficiency of the beam formulation is verified through the good agreement between the measured and the calculated results.

Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation

This paper investigates static and dynamic behavior of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation including shear layer and Winkler springs. The plates are reinforced by single-walled carbon nanotubes with four types of distributions of uni-axially aligned reinforcement material. Exact solutions obtained from closed-form formulation based on generalized shear deformation plat theory which can be adapted to various plate theories for bending, buckling and vibration analyses of such plates are presented. An accuracy of the present solutions is validated numerically by comparisons with some available results in the literature. Various significant parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are taken into investigation. According to the numerical results, it is revealed that the deflection of the plates is found to decrease as the increase of spring constant factors; while, the buckling load and natural frequency increase as the increment of the factors for every type of plate.

A Simple Algorithm for Analyzing a Piled Raft by Considering Stress Distribution

Numerous techniques have been presented by different researchers to analyze piled raft. In order to analyze pile foundation, soil can be modeled as spring, continuous medium, or porous media. Pile can also be modeled as spring or continuous medium. This study includes three main stages: a short description of different types of analysis methods of pile foundation, writing a computer program based on the finite element method (FEM) for analyzing piled raft foundation (in this program, foundation is modeled as a flexible plate, soil and pile are modeled by Winkler springs), and comparison of different concepts of pile group design.

지반강성 산정방법에 따른 해상 모노파일의 설계하중 해석

This study explores methods for modeling the foundation-seabed interaction needed for the load analysis of an offshore wind energy system. It comprises the comparison study of foundation design load analyses for NREL 5 MW turbine according to various soil-foundation interaction models by conducting the load analysis with GH-Bladed, analysis software for offshore wind energy systems. Furthermore, the results of the aforementioned load analysis were applied to foundation analysis software called L-Pile to conduct a safety review of the foundation cross-section design. Differences in the cross-section of a monopile foundation were observed based on the results of the fixed model, winkler spring and coupled spring models, and the analysis of design load cases, including DLC 1.3, DLC 6.1a, and DLC 6.2a. Consequently, under all design load conditions, the diameter and thickness of the monopile foundation cross-section were found to be 7 m and 80 mm, respectively, using the fixed and coupled spring models; the results of the analysis conducted using the winkler spring model showed that the diameter and thickness of the monopile foundation cross-section were 5 m and 60 mm, respectively. The study found that the soil-foundation interaction modeling method had a significant impact on the load analysis results, which determined the cross-section of a foundation. Based on this study, it is anticipated that designing an offshore wind energy system foundation taking the above impact into account would reduce the possibility of a conservative or unconservative design of the foundation.

A variational solution for nonlinear response of laterally loaded piles with elasto-plastic winkler spring model

Piles are frequently used to support lateral loads. Nonlinear p-y analysis is one of the most widely used methods to design laterally loaded piles. However, nonlinear p-y analysis requires special computer programs to perform the analysis. In this paper, an alternative solution based on a variational approach is presented to capture the behaviors of laterally loaded piles using Winkler beams on elastoplastic foundation. The displacements of piles are represented by finite series, and no discretisation of the pile shaft is required. Therefore, the proposed nonlinear solution can be easily implemented using the general computational software such as MATLAB. To facilitate the use of the numerical solution, methods for determining the parameters of the model are provided. The validity of the proposed method is confirmed through comparisons with existing theoretical solutions. Case studies are also presented to show the application of the present method to laterally loaded piles in field. The simplicity and the relative ease of the solution makes the proposed method a good alternative approach to analyze the nonlinear response of laterally loaded piles.