1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

Wave dispersion in dry granular materials by the distinct element method

Numerical studies are conducted to investigate the existence of wave dispersion in resonant column tests on dry granular soil. To this end, the two-dimensional distinct element method (DEM) in the time domain is employed. The investigations focus on the effect of sample width, voids ratio, viscous damping and wavelength, on propagation velocities of longitudinal harmonic waves in rectangular samples of uniform grains. It is shown that granular materials may exhibit anomalous dispersion that is, wave velocities that increase with increasing excitation frequency. This increase may exceed 20% for squatty samples, but becomes less pronounced for slender samples. Similar findings have been reported in some experiments on granular materials, but have not been systematically explored by numerical means. Results are presented in the form of dimensionless graphs and charts that elucidate the salient features of the problem. Comparisons with findings from gradient elastodynamic and viscoelastic theories are discussed.     

A comparison of material damping measurements in resonant column using the steady-state and free-vibration decay methods

The study reports results associated with the small to medium strain range material damping of quartz sand. The experiments were conducted in a fixed-free type resonant column and the samples were subjected to torsional mode of vibration at their first natural frequency. A comparison between the derived damping values using two different methods is presented: the steady-state vibration method (SSV) and the free-vibration decay method (FVD). Within the scatter of the data the two different methods in measuring material damping provided comparable results with a scatter, in most cases, of less than ±15% for the working strain range of the resonant column method. The damping values derived from the FVD and SSV methods were also compared with proposed models in the literature by means of stiffness degradation–damping increase correlation.     

Vibration of three-dimensional rigid raft foundation on viscoelastic medium

Using the coupled model of finite and infinite elements, the compliance of a rigid raft (plate) on a viscoelastic medium is calculated in this paper. Further, the effects of different proportions of radiation damping and material damping in the total damping and the distribution of wave motion in the near field are also investigated. From the numerical results, it can be concluded that: (1) the radiation damping plays an important role in the total damping, compared to the material damping; (2) the material damping has some effect on the compliance of the raft; (3) under the action of harmonic concentrated loads, the displacement amplitudes in the near field gradually decrease with the increase in the distance from the raft and the material damping; (4) the strata characteristics of the soil medium have considerable influence on the compliance of the raft and the distribution of wave motion in the near field.     

近地表强衰减介质中的地震波传播模型

建立符合油气储层近地表复杂介质强衰减性质的数学-物理模型是油气勘探和开发的重要课题.本文针对D'Alembert黏弹性介质模型存在的量纲不统一和不能充分刻画孔隙介质结构的不足,通过引入孔隙度和渗透率等参数修改耗散项,改进了原D'Alembert模型,获得了能精细刻画具有强吸收衰减特征的近地表复杂介质模型,即改进的近地表黏弹性模型.基于这种改进的模型,推导了波频散和衰减的表达式,并研究了孔隙度、流体黏度等物理参数对波频散和衰减的影响,获得了相应的规律性认识.为了验证新模型预测近地表介质中波衰减的有效性,本文将新模型应用于胜利油田YX工区的近地表实测数据,同时与弹性Biot模型和BISQ模型以及黏弹性BISQ模型进行了比较.结果表明,与其它三个模型比较,改进的近地表黏弹性模型能够很好地刻画近地表介质的强衰减性,而且新模型所涉及到的物理参数明显少于其它几种模型,有利于新模型在油气储层近地表复杂介质地震勘探的实际应用.     

Shear modulus and damping ratio of grouted sand

An experimental comparative study of three different grouted sands in terms of their effects on the values of two dynamic properties is presented. The dynamic properties studied are the shear modulus and the damping ratio which are determined with resonant column tests and cyclic triaxial tests. The behaviour of a pure Fontainebleau sand is compared with the behaviour of a Fontainebleau sand grouted with a silicate grout, a micro-fine cement grout and a mineral grout. The effects of the grouting treatment, the type of grout, the confining pressure, and the strains, on the shear modulus and the damping ratio are studied. The test results have shown that grouting improves the stiffness of the sand especially for small strains. Whatever the type of material, confining stress improves the shear modulus whereas it has a negligible effect on the damping ratio. When strain increases, the shear modulus decreases and the damping ratio increases.     

Soil-pile interaction in horizontal vibration

Interaction between soil and an elastic pile vibrating horizontally is theoretically examined. The soil is modelled as a linear, viscoelastic layer overlying rigid bedrock. The pile is assumed to be vertical and point bearing. This study utilizes the definition of soil resistance presented in a preceding paper.¹ A direct solution is developed which yields closed form formulas for pile displacement, stiffness and damping. A parametric study clarifies the role of the parameters involved, illustrates the interaction between the soil and the pile and shows the stiffness and damping properties of the soil-pile system for typical values of the governing parameters.     

Seismic isolation effect of lined circular tunnels with damping treatments

The Havriliak-Negami model for dynamic viscoelastic material behavior and Biot＇s theory of poroelasticity are employed to develop an exact solution for three-dimensional scattering effect of harmonic plane P-SV waves from a circular cavity lined with a multilayered fluid-filled shell of infinite length containing viscoelastic damping materials and embedded within a fluid-saturated permeable surrounding soil medium. The analytical results are illustrated with numerical examples where the effects of liner/coating structural arrangement, viscoelastic material properties, liner-soil interface bonding condition, seismic excitation frequency, and angle of incidence on the induced dynamic stress concentrations are evaluated and discussed to obtain representative values of the parameters that characterize the system. It is demonstrated that incorporating viscoelastic damping materials with a low shear modulus in the constrained layer configuration is an efficient means of enhancing the overall seismic isolation performance, especially for near-normally incident seismic shear waves where the amplitudes of induced dynamic stresses may be reduced by up to one-third of those without isolation in a relatively wide frequency range. Some additional cases are considered and good agreements with solutions available in the literature are obtained.     

Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.     

Nonlinear surface ground analysis via statistical approach

A statistical approach is proposed for nonlinear surface ground analysis. In contrast to the conventional method which deals with only a single ground motion for equivalent linearization of soil properties, a design response spectrum defined at the upper level (bottom of the surface ground) of an engineering bedrock can be handled as the target design earthquake in the present paper. The effective shear strain in each soil layer is evaluated by means of a statistical procedure in which the mean peak shear strain is computed in terms of its standard deviation and the corresponding peak factor. The stiffness and damping ratio of each soil layer are obtained iteratively from the nonlinear relation of stiffness reduction factors and damping ratios with respect to the strain level. After the evaluation of the equivalent stiffness and damping ratio of every soil layer, the ground surface response spectrum is transformed from the design response spectrum defined at the upper level of the engineering bedrock via the one-dimensional wave propagation theory. The reliability and accuracy of the proposed analysis method is examined through the comparison with the results by the conventional method (represented by the program) for many simulated spectrum-compatible ground motions.     

Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity — II. Applications

The results obtained in Part I (Soil Dynam. Earth. Engng, 1996, 15, 119-27) of this work for modelling harmonic wave propagation through viscoelastic heterogeneous media that exhibit a small random fluctuation of their material properties about mean values are now used here to investigate SH wave propagation in two naturally occurring media, namely sandstone and topsoil. These results are in the form of depth dependent, deterministic mean values and non-isotropic covariances for both the wave speed profile in the medium and for the fundamental solution in terms of displacement due to a unit point source. The results are also compared against conventional Monte Carlo simulations.     

A micromechanics-based analytical method for wave propagation through a granular material

This paper describes the creation and use of the stiffness and mass matrices of a granular sample to calculate its modes of vibration and natural frequencies, and obtain its transfer function. This is an important result as it is a necessary prerequisite for the application of linear systems theory to granular materials. The analytical solution for wave propagation through the material is then presented and simulations of bender element tests on an idealised two-dimensional granular sample are used as an example of the applicability of the method. Analysing wave propagation through sand and sandstone in this novel way that is explicitly particle-based can offer significant insights into phenomena such as wave dispersion. It can also offer insight into the interpretation of laboratory bender element tests, which is often challenging. Bender element tests are used to obtain the small-strain stiffness of soil for engineering design and the results generated by applying the analytical method proposed here give insight into the effects of sample aspect ratio and boundary conditions on the observed response. The model presented here allows for comparisons between the static stiffness of the sample and the stiffness value calculated through wave velocities, as obtained by a variety of methods used by experimentalists. This leads to the identification of the best procedure for extracting the small-strain stiffness value for the dry granular sample considered here.     

基于高阻尼纳米复合材料的直角型黏弹性阻尼器的数值模拟

为提高装配式钢结构梁柱节点的抗震性能,首先通过熔融共混法制备高阻尼性能纳米偏高岭土/氟橡胶(NanoGmetakaolin/Fluororubber,NMK/FKM)复合材料,并对该新型材料进行4种频率下的动态力学性能试验和静态力学试验,然后以 NMK/FKM 纳米复合材料为核心耗能材料,对所提出的直角型黏弹性阻尼器进行 ABAQUS有限元模拟分析.研究结果表明:当频率为1．5Hz 时,NMK/FKM 纳米复合材料宽阻尼温域和 TA 值皆达到峰值,该工况下材料的阻尼性能最佳;直角型黏弹性阻尼器表现出刚度随位移幅值的增大而增大的动力特性;当频率为0．5、1．0和1．5Hz 时,阻尼器滞回特性表现出非线性特征,当频率升至2．0Hz时,滞回特性则为线性.随着黏弹性材料层厚度的增大,滞回环面积、阻尼器刚度和最大阻尼力逐渐减小;随着高跨比的增大,阻尼器耗能性能提升.通过调整阻尼器的高跨比和阻尼材料层厚度,可以进一步提高直角型阻尼器的动态响应.     

Numerical estimation of site effects in the city of Arica due to natural soil variability using the spectral elements method

In recent years, because of a seismic gap of 136 years in the north of Chile, several studies have been carried out with the purpose of characterizing the dynamic properties of the soils of the most populated cities in this area. The purpose of this work is to estimate, by numerical modeling, the seismic amplification of a densely populated area of the city of Arica. Spatial distribution of main soil dynamic properties has been obtained from a detailed geophysical survey, including surface-wave based methods and gravimetry. To estimate the site effects, we solve the wave propagation equation in full heterogeneous media by the spectral element method. This method allows including the topography, the irregular contact between soils and bedrock and heterogeneities of main materials’ properties along the computational domain. The inelastic behavior of the soil has been considered, using stiffness degradation and damping curves. The computations were done using the high performance open-source numerical code SPEED. Results from the distribution of the peak ground acceleration are compared against standard 1D horizontally layered modeling using equivalent linear and nonlinear viscoelastic approximations of nonlinear soil behavior. Linear viscoelastic results indicate that the north area of the city of Arica is not especially prone to tridimensional site effects induced by soil’s natural variability and the apparent bedrock geometry. Nevertheless, non-conservative differences of about 20% between 1D v/s 3D analyses were found under inelastic material behavior. In general, the two 3D approaches followed to include soils’ nonlinearity provide similar site amplification estimates.     

山西黄土动剪切模量与阻尼比试验研究

土的动剪切模量与阻尼比作为土动力特性研究的重要参数,一直备受关注。为了研究山西地区黄土的动力特性,对山西某土石坝坝基黄土进行了共振柱与动三轴试验,获得了在较大应变范围内的动剪切模量与阻尼比试验数据。试验结果表明,山西黄土动剪切模量与阻尼比均显著受初始含水率影响,其归一化的动剪切模量能够用修正的Hardin模型进行拟合,并给出了相关参数;阻尼比可以采用本文建议的公式进行拟合,拟合效果良好。最后,采用经验公式确定了不同围压下的最大动剪切模量的参数。     

弱形式时域完美匹配层——滞弹性近场波动数值模拟

本文旨在构建适用于滞弹性近场时域波动有限元模拟的高精度人工边界条件：完美匹配层（Perfectly Matched Layer：PML）,其中阻尼介质时域本构基于广义标准线性体建立.与以往研究不同,本文采用复坐标延拓技术变换弱形式波动方程构建了可直接用有限元离散的弱形式时域PML,规避以往独立对无限域内波动方程及界面条件进行延拓可导致的PML场方程和界面条件匹配不合理引发数值失稳、计算精度低下等问题.其次,针对PML中多极点有理分式与频域函数乘积的傅里叶反变换难以计算的问题,利用PML精度对复坐标延拓函数中延拓参数微调不敏感这一特点,明确给出了参数微调准则以规避多重极点,进而利用有理分式分解给出了一种普适、简便的计算方法,极大地简化了PML计算.基于该方法可实现任意高阶PML.最后,将本文构建滞弹性PML与高阶勒让德谱元（高精度集中质量有限元）结合得到滞弹性近场波动谱元离散方案.基于算例验证了滞弹性PML的计算效率、精度及新离散方案的长持时稳定特性.新离散方案可应用于计入实际介质阻尼的地震波动正、反问题数值模拟,提高波形模拟的精度以及地下波速结构反演的精度和可靠性.     

Estimation of damping ratio of soil sites using microtremor

It is widely known that the seismic response characteristics of a soil site depends heavily on several key dynamic properties of the soil stratum, such as predominant frequency and damping ratio. A widely used method for estimating the predominant frequency of a soil site by using microtremor records, proposed by Nakamura, is investigated to determine its effectiveness in estimating the damping ratio. The authors conducted some microtremor measurements of soil sites in Hong Kong and found that Nakamura’s method might also be used to estimate the damping ratio of a soil site. Damping ratio data from several typical soil sites were obtained from both Nakamura’s ratio curves using the half power point method and resonant column tests. Regression analysis indicates that there is a strong correlation between the damping ratios derived from these two different approaches. Supported by: Research project (PolyU 5076/97E), of the Department of Civil and Structural Engineering, The Hong Kong Polytechnic University     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

DGZ-1多功能共振柱常规试验可靠性分析

针对新研制的多功能共振柱讕验机常规土类试验,发展此类仪器的试验可靠性分析理论,建立一套检验自身可靠性的分析方法傌技术,包括试验误差分析、试验定量考核、土工试验等多种技术手段。首先建立了共振柱仪动剪切模量误差、应叐误差和阻尼比误差的分析公式,得到了几种主要影响因素及其对试验误差影响程度的新认识。同时,通过若干已知动剪切模量且频率和土频率相接近的钢杆和铝杆试件的自振和共振试验,定量上验证该仪器常规试验结果的可靠性;通过砂土和原状粘土常规试验,定性上检验土工试验结果的合理性。通过对新研制的多功能共振柱试验机的常规试验功能进行可靠性的自身检验,所有试验结果是令人满意和可靠的,结果符合现有规律的认识。     

Impedance of flexible suction caissons

The dynamic response of offshore wind turbines is affected by the properties of the foundation and the subsoil. The aim of this paper is to evaluate the dynamic soil–structure interaction of suction caissons for offshore wind turbines. The investigations include evaluation of the vertical and coupled sliding–rocking vibrations, influence of the foundation geometry and examination on the properties of the surrounding soil. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency‐dependent coefficients corresponding to different degrees of freedom. The dynamic stiffness coefficients for the skirted foundation are evaluated using a three‐dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviours of the foundation are predicted accurately using the applied model. The analysis has been carried out for different combinations of the skirt length, Poisson's ratio of the subsoil and the ratio of the soil stiffness to the skirt stiffness. Copyright © 2007 John Wiley & Sons, Ltd.