Horizontal impedance of square foundation in layered soil

This paper presents an extensive investigation into the influence of key mechanical and geometrical parameters on horizontal impedance of square foundations resting on or embedded in a two-layer soil deposit. The parameters investigated are the ratio of shear-wave velocities, the thickness of the top layer, the depth of embedment and the degree of contact between the footing-sidewall with backfill-soil. The results are presented in the form of simple and versatile dimensionless graphs, which should prove to be useful in understanding the steady-state harmonic response of square foundations in layered soils due to horizontal excitation. The investigation was conducted using a rigorous boundary element algorithm incorporating isoparametric boundary elements. Higher order quadratic elements were used since they can model the wavy nature of the dynamic problem investigated more accurately.     

A practical method for estimating dynamic soil stiffness on surface of multi‐layered soil

It is important to estimate the influence of layered soil in soil–structure interaction analyses. Although a great number of investigations have been carried out on this subject, there are very few practical methods that do not require complex calculations. In this paper, a simple and practical method for estimating the horizontal dynamic stiffness of a rigid foundation on the surface of multi‐layered soil is proposed. In this method, waves propagating in the soil are traced using the conception of the cone model, and the impulse response function can be calculated directly and easily in the time domain with a good degree of accuracy. The characteristics of the impedance, that is the transformed value to the frequency domain of the obtained impulse response, are studied using two‐ to four‐layered soil models. The cause of the fluctuation of impedance is expressed clearly from its relation to reflected waves from the lower layer boundary in the model. Copyright © 2005 John Wiley & Sons, Ltd.     

Wolf JP,Preisig M. Dynamic stiffness of foundation embedded in layered halfspace based on wave propagation in cones. Earthquake Engineering and Structural Dynamics 2003; 32:1075–1098

The original article to which this Erratum refers was published in Earthquake Engineering and Structural Dynamics 2003; 32 : 1075–1098.     

Spring-dashpot-mass models for foundation vibrations

The foundation on deformable soil, which, in general, radiates energy, can be represented in structural dynamics as a simple spring-dashpot-mass model with frequency-independent coefficients. For the two limiting cases of a site, the homogeneous half-space and the homogeneous layer fixed at its base, the coefficients are specified in tables for varying parameters such as ratios of dimensions and Poisson's ratio. Rigid foundations on the surface and with embedment are considered for all translational and rotational motions. In a practical analysis of soil–structure interaction this dynamic model of the foundation is coupled directly to that of the structure, whereby a standard dynamics program is used. © 1997 by John Wiley & Sons, Ltd.     

Impedance matrices for circular foundation embedded in layered medium

A numerical scheme is developed in the paper for calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme, the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions with unknown coefficients are obtained by solving three-dimensional (3D) wave equations in cylindrical coordinates satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are also obtained by solving the same 3D wave equations satisfying the homogeneous boundary conditions and the prescribed boundary conditions. The prescribed conditions are the interaction tractions at the interfaces between embedded foundation and surrounding soil. The interaction tractions are assumed to be piecewise linear. The piecewise linear tractions at the bottom surface of foundation will be decomposed into a series of Bessel functions which can be easily fitted into the general solutions of wave equations in cylindrical coordinates. After all the analytic solutions with unknown coefficients for both interior and exterior domains are found, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions.     

Cone model for two surface foundations on layered soil

In this paper, the cone model is applied to the vibration analysis of two foundations on a layered soil half space. In the analysis, the total stress field in the subsoil is divided into the free-field and the scattering field. Seed＇s simplified method is adopted for the free-field analysis, while the cone model is proposed for analyzing the dynamic scattering stress wave field. The shear stress field and the compressive stress field in the layered stratum with two scattering sources are calculated by shear cone and compressive cone, respectively. Furthermore, the stress fields in the subsoil with two foundations are divided into six zones, and the P wave and S wave are analyzed in each zone. Numerical results are provided to illustrate features of the added stress field for two surface foundations under vertical and horizontal sinusoidal force excitation. The proposed cone model may be useful in handling some of the complex problems associated with multi-scattering sources.     

层状地基环形沟隔振效果影响因素分析

为探究层状地基环形沟隔振中几何参数对其隔振效果的影响规律,文章采用振幅衰减比Ar值进行评价分析,并定义沟后Ar≤0.4区域为有效隔振区域,通过改变环形沟的几何参数,得到其对有效隔振区域影响变化规律,从而确定环形沟不同几何参数对其隔振效果的影响.结果表明:层状地基土中环形沟深度位于土层分界面附近时,环形沟隔振效果相对较弱...     

基础动力刚度的精确数值解及集中参数模型

土－结构相互作用分析的关键是建立以土－结构界面定义的无限半空间的动力刚度矩阵。本文介绍了一种求解半无限地基动力刚度的新方法，通过两个算例验证了该方法的精度，并给出了一种利用频域刚性基础动力刚度计算基础时域荷载响应的实用方法，该研究为刚性基础设计提供了一种新的，可靠的理论方法。     

Filtering action of embedded massive foundations: New analytical expressions and evidence from 2 instrumented buildings

This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.     

碎石桩复合地基振动响应试验分析

采用激振法和衰减测试对碎石桩复合地基块体振动响应进行现场试验，分析了该复合地基在不同激振方式下的振动反应规律，提出了碎石桩复合地基抗压、抗弯、抗剪刚度系数线性关系。同时通过试验对比，分析了自由振动与强迫振动两种测试方法对于碎石桩复合地基测试结果的适宜性，这对复合地基的理论研究及动力基础的天然地基的设计、试验和研究都具有实际意义。     

Dynamic stiffness of deep foundations with inclined piles

The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Rocking vibrations of a rigid embedded foundation in a poroelastic soil layer

An approximate analytical method is presented for the dynamic response of a rigid cylindrical foundation embedded in a poroelastic soil layer under the excitation of a time-harmonic rocking moment. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The accuracy of the present solution is verified by comparisons with existing solutions obtained from other researchers. Numerical results for the rocking dynamic impedance and dynamic response factor are presented to demonstrate the influence of nondimensional frequency of excitation, poroelastic soil layer thickness, depth ratio of the foundation and internal friction of the poroelastic soil.     

三维层状场地的精确动力刚度矩阵及格林函数

本文对Wolf二维层状场地精确动力刚度矩阵进行推广,给出了三维层状场地的精确动力刚度矩阵。刚度矩阵具有对称的特点,且因刚度矩阵是精确的,计算结果不受土层单元厚度的影响,可以大大提高计算效率。文中对刚度矩阵进行了数值验证。利用三维层状场地动力刚度矩阵,计算分析了基岩上单一土层场地的动力响应。最后作为动力刚度矩阵的另一重要应用,给出了表面或埋置矩形均布荷载或集中荷载的动力格林函数计算方法。     

水平向不均匀土对箱基动力阻抗的影响

采用薄层元素法和有限单元法,建立了地基-箱形基础动力相互作用的三维分析模型,该模型可考虑箱形基础周围土的不均匀性影响.利用该模型,分析了水平方向不均匀土对箱形基础的水平和摇摆阻抗的影响.分析了水平方向不均匀土的厚度、剪切弹性模量以及材料阻尼比的影响.分析结果表明:水平方向不均匀土使得箱形基础的各种阻抗均降低,特别是阻抗的虚部.水平方向不均匀土对摇摆阻抗的影响较大.水平方向不均匀土的剪切弹性模量的影响较大而其材料阻尼的影响较小.随着水平方向不均匀土的厚度的增加和基础埋深的增加,其影响增大.     

成层粘弹性土中桩土耦合纵向振动时域响应研究

从三维轴对称角度出发,采用粘性阻尼粘弹性连续土介质模型,考虑桩土相互作用效应,对成层土中桩土纵向耦合振动时的桩顶时域响应进行了解析研究。求解时,首先建立定解问题,然后利用拉氏变换先对底部土层进行求解得到其振动位移形式解,然后利用桩土接触界面连续条件来考虑桩土耦合作用,分析底层土中桩段的动力反应,然后利用桩段阻抗函数的传递性,进行逐层递推求解,最终得到桩顶时域和频域响应的半解析解。通过参数影响分析和与工程实测曲线的对比,讨论分析了成层土中桩土耦合振动的响应特性,验证了本文解。基于本文研究可为桩基抗震、防震设计、桩基动力检测提供新的理论支持。     

成层土中桩土耦合扭转振动特性理论研究

假设桩周土层为成层黏弹性体,土体材料阻尼为黏性阻尼,从三维轴对称角度出发,对任意激振扭矩作用下,成层土中完整桩与土扭转耦合振动时的桩顶振动特性进行了理论研究.首先建立定解问题,然后利用拉氏变换求解得到其振动角位移的形式解,并利用桩土接触界面处的连续条件来考虑桩土耦合作用,使用桩段阻抗函数的传递性进行逐层递推求解,最终得到桩顶频域和时域响应的理论解.通过参数影响分析研究发现,成层土中桩顶复刚度主要受上部土层动力特性及性质影响;随着上层土模量增大桩顶复刚度的刚度部分也相应增大,阻尼部分相应减小.成层土由于土层模量变化,桩的导纳曲线有大峰夹小峰循环的特征.当上层土模量大于下层土模量时,在土层分界面时域波形与初始脉冲反向,反之则同向,土模量突变导致的时域波形的特征反射较平缓,幅度不大.     

层状饱和场地中圆柱形基础的阻抗函数

本文利用间接边界元法,建立层状饱和场地中三维土-基础动力相互作用模型,研究了孔隙中流体的存在、场地动力特性和圆柱形基础的高度对基础阻抗函数的影响。数值结果表明,孔隙中流体的存在对基础阻抗函数有明显的影响,尤其是水平和竖向分量;场地动力特性也对基础阻抗函数有明显的影响,层状饱和场地中阻抗函数围绕相应均匀半空间结果振荡,且基岩与土层刚度比越大或土层厚度越小,振荡的幅度越大,土层厚度越小,振荡的周期越小;另外,基础高度也对阻抗函数有明显的影响,随基础高度增大,阻抗函数逐渐增大。     

Experimental investigation on seismic behavior of scoured bridge pier with pile foundation

This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 John Wiley & Sons, Ltd.     

层状结构岩质边坡动力稳定性试验研究

介绍了所进行的层状结构岩质边坡动力稳定性试验。结果表明，在水平地震动加速度达到0．4g时，层状结构岩质边坡就会出现局部的层间错动现象，当水平地震加速度达到0．8g时，层间结合力较弱的边坡将发生大面积的表面滑动和崩塌。而在铅直地震力作用下，当地震加速度达到1.0g时，才会出现破坏现象。因而对层状结构岩质边坡来说，其水平地震力造成的危害是主要的。     

The effect of foundation embedment on inelastic response of structures

In this research, a parametric study is carried out on the effect of soil–structure interaction on the ductility and strength demand of buildings with embedded foundation. Both kinematic interaction (KI) and inertial interaction effects are considered. The sub‐structure method is used in which the structure is modeled by a simplified single degree of freedom system with idealized bilinear behavior. Besides, the soil sub‐structure is considered as a homogeneous half‐space and is modeled by a discrete model based on the concept of cone models. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. The soil–structure system is then analyzed subjected to a suit of 24 selected accelerograms recorded on alluvium deposits. An extensive parametric study is performed for a wide range of the introduced non‐dimensional key parameters, which control the problem. It is concluded that foundation embedment may increase the structural demands for slender buildings especially for the case of relatively soft soils. However, the increase in ductility demands may not be significant for shallow foundations with embedment depth to radius of foundation ratios up to one. Comparing the results with and without inclusion of KI reveals that the rocking input motion due to KI plays the main role in this phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.