Winkler model for dynamic response of composite caisson–piles foundations: Seismic response

A simplified method with a dynamic Winkler model to study the seismic response of composite caisson–piles foundations (CCPF¹) is developed. Firstly, with the dynamic Winkler model, the kinematic response of the CCPF subjected to vertically propagating seismic S-wave is analyzed by coupling the responses of caisson part and pile part. Secondly, a simplified model for the foundation–structure system is created with the structure simplified as a lumped mass connected to the foundation with an elastic column, and through the Fast Fourier Transformation (FFT) this model is enabled to solve transient seismic problems. Thirdly, the proposed method for the seismic response of CCPF-structure systems is verified by comparison against 3D dynamic finite element simulation, in which the Domain Reduction Method (DRM²) is utilized. Lastly, the mechanism and significance of adding piles in improving the earthquake resistance of the foundation and structure is analyzed through an example with different soil conditions. Discovered in this study is that adding piles under the caisson is an efficient way to increase seismic resistant capability of the soil–foundation–structure system, and the main mechanism of that is the elimination of the pseudo-resonance.     

Slab foundation subjected to thrust faulting in dry sand: Parametric analysis and simplified design method

Motivated by recent case histories of faulting-induced damage to structures (Chi-Chi, 1999; Wenchuan 2008), this paper applies a thoroughly validated finite element analysis methodology to study the response of slab foundations subjected to thrust faulting. A parametric study is conducted, investigating the effect of key response parameters. It is shown that the stressing of the foundation, and consequently of the superstructure, stems mainly from loss of support. Depending on the geometry, loss of support takes place either under the edges or under the middle of the foundation, generating hogging or sagging deformation, respectively. Increasing the weight of the structure and/or decreasing soil stiffness leads to less stressing of the foundation. Surprisingly, even when the fault rupture emerges beyond the structure, completely avoiding the foundation, substantial foundation distress may still be generated. Exploiting the results of the parametric study, a simplified design method is developed, calling for conventional static analysis of a slab on Winkler supports, “simulating” the fault rupture by removing Winkler springs from equivalent area(s) of loss of support. The latter can be estimated with the help of design charts, further facilitating its use in practice. The proposed simplified method should not be viewed as a general design tool, but as a first idea of a practical solution to the investigated problem.     

Prediction of the measured response of a scaled soil-pile-superstructure system

The validity of the Winkler foundation model is investigated by predicting the experimentally measured displacement transfer functions and strain spectra of a single pile embedded in a sandbox and supporting a single-degree-of-freedom superstructure. The foundation-superstructure system is a scale model and was subjected to shake table excitations. The distributed springs and dashpots of the Winkler foundation model are frequency dependent and the calibrated model predicts satisfactorily the displacement transfer function at different depths for both fixed- and free-tip pile conditions. On the other hand, the pile-axial-strains are substantially underestimated when expressed in terms of the second derivative of the computed elastic line of the pile. It is shown that a much more dependable prediction is achieved when pile-axial-strains are expressed in terms of the inertial forces acting along the pile-superstructure system.     

Calibration of dynamic analysis methods from field test data

In view of the heterogeneity of natural soil deposits and approximations made in analysis methods, in situ methods of determining soil parameters are highly desirable. The problem of interest here is the nonlinear dynamic behavior of pile foundations. It is shown in this paper that soil parameters needed for simplified dynamic analysis of a single pile may be back-calculated from the dynamic response of the pile measured in the field. A pile was excited by applying a large horizontal dynamic force at the pile-head level, and the response measured. In this paper, two different (simplified) methods of modeling the dynamic response of the pile are considered. One of the methods is based on the Winkler foundation approach, with the spring constant characterized by the so-called nonlinear p–y springs. The second method is based on the equivalent-linear finite element approach, with the nonlinearity of shear modulus and damping accounted for by employing the so-called degradation relationships. In the latter, the effect of interface nonlinearity is also considered. Starting with best estimates of soil parameters, the experimental data on the response of pile is used to fine-tune the values of the parameters, and thereby, to estimate parameters that are representative of in situ soil conditions.     

地基弹性参数对于长型大截面地下结构横向自由振动的影响

自由振动分析是地下结构地震动力响应分析的基础。本文利用笔者先前得到的长型地下结构的自由振动方程,研究了地基弹性参数对地下结构自由振动的影响。由分析可以看出,随着地基弹性参数值的增加,结构中波速值总的趋势是增加,但是温克尔地基参数对结构中波速的影响远大于第二地基参数的影响;地下结构振动频率总的趋势是随着温克尔地基参数k和第二地基参数gP值的增加而增加;与地基参数对地下结构中波的传播速度的影响不同,k和gP对地下结构振动频率的影响是同阶的,因此不能忽略gP对地下结构自由振动的影响。     

A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete modelling of vertical track–soil coupling for vehicle–track dynamics

This paper presents a coupled lumped mass model (CLM model) for the vertical dynamic coupling of railway track through the soil. The well-known Winkler model and its extensions are analysed and fitted on the result obtained numerically with a finite–infinite element model in order to validate the approach in a preliminary step. A mass–spring–damper system with frequency independent parameters is then proposed for the interaction between the foundations, representing the contact area of the track with the soil. The frequency range of track–soil coupling is typically under 100 Hz. Analytical expressions are derived for calibrating the system model with homogeneous and layered half-spaces. Numerical examples are derived, with emphasis on soil stiffness and layering. The dynamic analysis of a track on various foundation models is compared with a complete track–soil model, showing that the proposed CLM model captures the dynamic interaction of the track with the soil and is reliable to predict the vertical track deflection and the reaction forces acting on the soil surface.     

Discrete modelling of vertical track–soil coupling for vehicle–track dynamics

This paper presents a coupled lumped mass model (CLM model) for the vertical dynamic coupling of railway track through the soil. The well-known Winkler model and its extensions are analysed and fitted on the result obtained numerically with a finite–infinite element model in order to validate the approach in a preliminary step. A mass–spring–damper system with frequency independent parameters is then proposed for the interaction between the foundations, representing the contact area of the track with the soil. The frequency range of track–soil coupling is typically under 100 Hz. Analytical expressions are derived for calibrating the system model with homogeneous and layered half-spaces. Numerical examples are derived, with emphasis on soil stiffness and layering. The dynamic analysis of a track on various foundation models is compared with a complete track–soil model, showing that the proposed CLM model captures the dynamic interaction of the track with the soil and is reliable to predict the vertical track deflection and the reaction forces acting on the soil surface.     

Winkler model for dynamic response of composite caisson-piles foundations: Lateral response

As the first part of a sequence focusing on the dynamic response of composite caisson-piles foundations (CCPFs¹), this paper develops a simplified method for the lateral response of these foundations. A Winkler model for the lateral vibration of the CCPF is created by joining the two components, the caisson and the pile group, where the four-spring Winkler model is utilized for the caisson and axial–lateral coupled vibration equations are derived for the pile group. For determining the coefficients of the four-spring Winkler model for the caissons, embedded footing impedance is used and a modification on the rotational embedment factor is made for the sake of the geometrical difference between shallow footings and caissons. Comparisons against results from finite element simulations demonstrate the reliability of this modified four-spring Winkler model for caissons in both homogenous and layered soils. The proposed simplified method for the lateral vibration of CCPFs is verified also by 3D finite element modeling. Finally, through an example, the idea of adding piles beneath the caisson is proved to be of great significance to enhance the resistance of the foundation against lateral dynamic loads.     

Dynamics of flexible systems with partial lift-off

The dynamic behaviour of a simplified model of a multi-storey building, supported by an elastic foundation and allowed to uplift, is examined. The building is modelled by an n-degree-of-freedom oscillator, while the foundation is represented by a viscously damped two-spring model which permits uplift. This model has been shown in previous studies to be an accurate approximation to the more realistic but more complex Winkler foundation. Approximate values for the characteristic frequencies of the interacting system are presented and a simple, first-mode solution is developed. The response of the system is non-linear and the apparent fundamental period increases with the amount of lift-off. In contrast to the first mode of the superstructure which participates strongly in the interaction, the second and higher modes of the building are not affected significantly by either the interaction with the soil or the uplift. The study shows that lift-off results in larger rocking motion of the structure, but it is not clear from the analysis and the example whether the interfloor displacements are consistently increased or decreased, since this appears to depend on the properties of the system and the excitation.     

基于动力BNWF法的冻土-桩相互作用模型研究

基于水平循环荷载作用下不同负温冻土环境中单桩动力特性模型试验结果,在已有分析桩-土-结构相互作用的动力BNWF模型的基础上,提出改进的冻土-桩基动力相互作用非线性反应分析模型。在该模型中,利用改进的双向无拉力多段屈服弹簧考虑桩侧冻土的水平非线性力学特性,同时兼顾桩侧与冻土间的竖向非线性摩擦效应、桩尖土的挤压与分离作用以及远场土体阻尼对桩基动力特性的影响。其中桩侧水平多段屈服弹簧参数根据冻土非线性p-y关系获得,该关系曲线以三次函数曲线段及常值函数段共同模拟,并由室内冻土压缩试验结果确定。最后基于改进的动力BNWF模型,提取动位移荷载作用下该桩顶力-位移滞回曲线及桩身不同埋深处的弯矩动响应数值分析结果,并与相应的模型试验结果对比,二者具有较好的拟合度,表明本文所提出的改进模型在分析冻土-桩动力相互作用时有较好的适用性。     

考虑基础提离与塑性的桥墩地震反应

浅平基桥墩在承受强震作用时,其基础与地基之间会发生提离,地基土会进入塑性状态.精确模拟上述两个问题是非常困难的.本文分析中地基采用了能考虑基础提离及地基塑性的弹塑性Winkler地基模型,采用1940年El Centro(NS)地震记录作为输入,对三个不同高度的双柱式浅平基桥墩进行了非线性时程分析.研究结果表明,基础提离和地基塑性对双柱式桥墩的地震反应有很大影响.考虑地基非线性后,墩顶位移增大,剪力减小,对保护桥墩减小震害是有利的.     

Rocking response of SDOF systems on shallow improved sand: An experimental study

Recent studies have highlighted the potential advantages of allowing inelastic foundation response during strong seismic shaking. Such an alternative seismic design philosophy, in which soil failure is used as a “fuse” for the superstructure has recently been proposed, in the form of “rocking isolation”. Within this context, foundation rocking may be desirable as a means of bounding the inertia forces transmitted onto the superstructure, but incorporates the peril of unacceptable settlements in case of a low static factor of safety FS_v. Hence, to ensure that rocking is materialized through uplifting rather than sinking, an adequately large FS_v is required. Although this is feasible in theory, soil properties are not always well-known in engineering practice. However, since rocking-induced soil yielding is only mobilized within a shallow layer underneath the footing, “shallow soil improvement” is considered as an alternative approach to release the design from the jeopardy of unforeseen inadequate FS_v. For this purpose, this paper studies the rocking response of relatively slender SDOF structures (h/B ratio equals 3 and rocking dominates over sliding), with emphasis on the effectiveness of shallow soil improvement stretching to various depths below the foundation. A series of reduced-scale monotonic and slow-cyclic pushover tests are conducted on SDOF systems lying on a square surface foundation. It is shown that shallow soil improvement may, indeed, be quite effective provided that its depth is equal to the width of the foundation. For lightly-loaded systems, an even shallower soil improvement may also be considered effective, depending on design requirements. The effectiveness of shallow soil improvement is ameliorated with the increase of cyclic rotation amplitude, and with repeating cycles of loading.     

Inelastic displacement ratios for soil–structure systems allowed to uplift

The simultaneous effects of soil–structure interaction, foundation uplift and inelastic behavior of the superstructure on total displacement response of soil–structure systems are investigated. The superstructure is modeled as an equivalent single‐degree‐of‐freedom system with bilinear behavior mounted on a rigid foundation resting on distributed tensionless Winkler springs and dampers. It is well known that the behavior of soil–structure systems can be well described using a limited number of nondimensional parameters. Here, by introducing two new parameters, the concept is extended to inelastic soil–structure systems in which the foundation is allowed to uplift. An extensive parametric study is conducted for a wide range of the key parameters through nonlinear time history analyses. It is shown that while uplifting soil–structure systems experience excessive displacements, in comparison with systems that are not allowed to uplift, ductility demand in the superstructure generally decreases owing to foundation uplift. A new inelastic displacement ratio (IDR) is proposed in conjunction with a nonlinear static analysis of uplifting soil–structure systems. Simplified expressions are also provided to estimate the proposed IDR. Copyright © 2014 John Wiley & Sons, Ltd.     

Free vibrations of foundation beams on Green soil in the presence of conservative and nonconservative axial loads

In this paper a general dynamic analysis of a foundation beam on Green-Boussinesq soil is performed, taking into account the instabilizing effect of conservative and nonconservative applied axial loads.The beam is reduced to a finite number of rigid bars, linked together by elastic springs; the equations of motion are written by means of the Lagrange equations. The kinetic energy and the total potential energy are calculated first, and emphasis is placed on the strain energy of the Green soil; then the virtual work of the applied follower loads is detected, which allow us to define the generalized forces. The resulting equations of motion lead to an eigenvalue problem with unsymmetric matrix.Initially, the first free vibration frequencies of simply supported beams, clamped beams and free beams are plotted as functions of the two soil parameters. A more complex beam is also examined, in order to show the method potentialities. A stability analysis in the presence of conservative axial loads is then performed, and the influence of the soil on the critical load is discussed, both for simply supported beams and clamped beams. Finally, the instability mechanism of a clamped - clamped beam subjected to a uniformly distributed follower force is shown to be deeply influenced by the presence of the soil. (A number of graphs and examples conclude the paper.)     

Dynamic analysis of offshore wind turbine in clay considering soil–monopile–tower interaction

A comprehensive study is performed on the dynamic behavior of offshore wind turbine (OWT) structure supported on monopile foundation in clay. The system is modeled using a beam on nonlinear Winkler foundation model. Soil resistance is modeled using American Petroleum Institute based cyclic p–y and t–z curves. Dynamic analysis is carried out in time domain using finite element method considering wind and wave loads. Several parameters, such as soil–monopile–tower interaction, rotor and wave frequencies, wind and wave loading parameters, and length, diameter and thickness of monopile affecting the dynamic characteristics of OWT system and the responses are investigated. The study shows soil–monopile–tower interaction increases response of tower and monopile. Soil nonlinearity increases the system response at higher wind speed. Rotor frequency is found to have dominant role than blade passing frequency and wave frequency. Magnitude of wave load is important for design rather than resonance from wave frequency.     

Earthquake response of structures with partial uplift on winkler foundation

The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.     

循环荷载作用下不均质地层中盾构隧道纵向响应研究

修建在纵向不均质地层中的地铁隧道,由于列车循环荷载的作用,会导致隧道下部的土体产生不均匀沉降,对既有隧道产生不利的影响。针对这一问题,提出考虑隧道剪切效应的地基不均匀沉降对既有隧道竖向变形影响的解析解。既有隧道简化为搁置在Winkler地基上的Timoshenko梁,通过两阶段分析法,分析下卧地层不均匀沉降引起的隧道响应。首先确定列车荷载引起的动偏应力,并运用土层的力学指标计算出静偏应力和破坏偏应力。然后运用累积应变的经验公式计算出隧道下部土体的累计沉降,将土体的沉降转化为力施加在隧道上。基于Timoshenko梁理论,建立考虑隧道剪切效应的隧道竖向变形微分方程,求解得到隧道变形的解析解,进一步可以得到隧道的弯矩、剪力、转角、错台。     

简谐横荷载作用下Winkler地基上有限长梁1/3次亚谐共振分析

基于Winkler地基模型及Euler - Bernoulli梁理论,建立了Winkler地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,得到离散的非线性振动方程,利用多尺度法求得该系统1/3次亚谐共振的一阶近似解.分析了长细比、弹性模量、地基刚度、阻尼、密度等参数对其亚谐共振幅频响...     

Investigation of seismic behavior of fluid–rectangular tank–soil/foundation systems in frequency domain

Main purpose of this study is to evaluate the dynamic behavior of fluid–rectangular tank–soil/foundation system with a simple and fast seismic analysis procedure. In this procedure, interaction effects are presented by Housner's two mass approximations for fluid and the cone model for soil/foundation system. This approach can determine; displacement at the height of the impulsive mass, the sloshing displacement and base forces for the soil/foundation system conditions including embedment and incompressible soil cases. Models and equations for proposed method were briefly explained for different tank–soil/foundation system combinations. By means of changing soil/foundation conditions, some comparisons are made on base forces and sloshing responses for the cases of embedment and no embedment. The results showed that the displacements and base shear forces generally decreased, with decreasing soil stiffness. However, embedment, wall flexibility, and soil–structure interaction (SSI) did not considerably affect the sloshing displacement.