Vibration characteristics of rigid body placed on sand ground

This study aims to investigate experimentally the vibration properties of rigid body placed on sand ground surface. The rigid body models with circular or rectangular base with variable mass, inertial moment and base sizes, were prepared, and the vibration behavior was observed in some series of free vibration tests and forced vibration tests. The observed behavior was analyzed and the vibration mode, vibration period and damping ratio were examined. It was found that the natural vibration period depends not only on the mechanical properties of rigid body and ground, but also on the magnitude of vibration amplitude. This suggested the notable effect of nonlinear strain dependent stiffness of ground material. A physical model with distributed spring–dashpot element was used to model the interactive mechanical behavior between rigid body and ground. The stiffness of the spring–dashpot element was evaluated through the modal analysis of the observed vibration behaviors. The effects of base shape, base size and base pressure on the stiffness of spring–dashpot element are discussed. The spring–dashpot model was verified with the behavior observed in forced vibration tests.     

Material damping for lumped-parameter models of foundations

In foundation dynamics two mechanisms of energy dissipation exist, wave radiation and material damping. Elastic continuum models of the soil capture only the radiation effect. To incorporate material damping, use is made of the fact that the dynamic-stiffness relationships of all elastic foundations may be simulated by discrete assemblages of springs, dashpots and masses. (Such lumped-parameter models are exact for simple cone models of the soil and approximate for more involved cases.) By application of the correspondence principle directly to the discrete elements of the lumped-parameter model, it is possible to introduce Voigt viscoelasticity. Each original spring is augmented by a dashpot, and each original dashpot is augmented by a mass, attached in a special way. Going a step further, more realistic non-linear-hysteretic damping is represented by replacing the augmenting dashpots and masses by frictional elements. The analysis, which is effected solely in the time domain, is illustrated by an example from earthquake engineering.     

马兰黄土剪应力松弛特性研究

运用Riemann-Liouville的分数阶导数理论及经典模型理论相结合的方法,采用Abel黏壶取代在经典模型理论中的Newton黏壶,得出了分数阶标准线性体模型剪应力松弛的解析表达式。采用不同含水量马兰黄土在不同正压力条件下进行直接剪切松弛试验,并对得到的9组剪应力松弛曲线特征进行了研究。考虑到最小二乘法对分数阶标准线性体模型参数进行拟合无法获得确切的结果,采用Monte Carlo方法对试验结果拟合。拟合结果表明,马兰黄土的松弛特性可由分数阶标准线性体模型有效的表征。确定了马兰黄土的松弛时间和粘滞系数,揭示了马兰黄土在直接剪切试验条件下的松弛特性。     

Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are reached: (i) The viscoelastic behavior of the ground may be simply characterized by performing the creep (or the relaxation) test on a specimen of the ground at the given site; (ii) The number of zero crossing of the absolute acceleration at the free field that for the classical TK model is \(\infty \) for a true white noise acceleration, remains finite for the proposed model.     

Simplified approximate method for analysis of rocking systems accounting for soil inelasticity and foundation uplifting

A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil inelasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element (FE) analyses, employing a thoroughly-validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation (C_R–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation (Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing its predictions with the results of 3D FE analyses. The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means, be considered a substitute for more sophisticated analysis methods. However, despite its limitations, it may be utilized for (at least preliminary) design purposes.     

Seismic interaction in linearly connected electrical substation equipment

An electrical substation consists of a complex set of equipment items that are interconnected through conductor buses or cables. If the connections are not sufficiently flexible, significant dynamic interaction may occur between the connected equipment items during a seismic excitation. This interaction is believed to be responsible for some of the observed substation equipment damage in recent earthquakes. This paper investigates the interaction between two equipment items connected by a linear spring‐dashpot or spring‐dashpot‐mass element representing a conductor bus. It is found that the interaction between the two equipment items may significantly amplify the response of the higher‐frequency equipment item. The influences of various key parameters on the interaction effect are quantified. Means for reducing the adverse interaction effect are described. Copyright © 2001 John Wiley & Sons, Ltd.     

On the attenuation of transient spherical waves in a four-element viscoelastic model and its implications

Summary In a four-element model, which consists of two Voigt elements in series, the impulse responses of spherical waves for particle displacement, velocity, acceleration and strain are computed numerically. These impulse responses are shown to be useful in synthesis for the desired wave response through convolution, between the input of the source function and the impulse responses. The rate of decay of peak amplitude versus distance, as waves radiate out, is examined in the region close to the source which may be nuclear or dynamite explosives and found to be linear in log-log scale. The amplitude spectra of the unit impulse response are obtained through Fourier analysis, and the model is found to behave as a low pass filter. With the properly chosen elastic constants for springs in the model and damping coefficients for dashpot, it is seen that, like the earth materials, the attenuation exponent (in neper/1000 ft) versus frequency in the model is approximately linear. One of the results observed byCollins andLee [1] is fitted by the model. The model thus simulates more nearly the wave in earth materials close to the source than the Voigt solid.     

A viscous-spring transmitting boundary for cylindrical wave propagation in saturated poroelastic media

Based on the u–U formulation of Biot equation and the assumption of zero permeability coefficient, a viscous-spring transmitting boundary which is frequency independent is derived to simulate the cylindrical elastic wave propagation in unbounded saturated porous media. By this viscous-spring boundary the effective stress and pore fluid pressure on the truncated boundary of the numerical model are replaced by a set of spring, dashpot and mass elements, and its simplified form is also given. A u–U formulation FEA program is compiled and the proposed transmitting boundaries are incorporated therein. Numerical examples show that the proposed viscous-spring boundary and its simplified form can provide accurate results for cylindrical elastic wave propagation problems with low or intermediate values of permeability or frequency content. For general two dimensional wave propagation problems, spuriously reflected waves can be greatly suppressed and acceptable accuracy can still be achieved by placing the simplified boundary at relatively large distance from the wave source.     

Simplified seismic analysis of soil–well–pier system for bridges

Seismic analysis of soil–well–pier system was carried out using three different approaches to evaluate their comparative performance and associated complexities. These approaches were (a) two-dimensional nonlinear (2D-NL), (b) two-dimensional equivalent-linear (2D-EqL), and (c) one-dimensional spring–dashpot (1D). Soil was modeled as 2D plane-strain elements in the 2D-NL and 2D-EqL approaches, and as springs and dashpots in the 1D approach. Nonlinear behavior of soil was captured rigorously in the 2D-NL approach and approximately in the remaining two approaches. Results of the two approximate analyses (i.e., 2D-EqL and 1D) were compared with those of the 2D-NL analysis with the objective to assess suitability of approximate analysis for practical purposes. In the 1D approach, several combinations of Novak's and Veletsos' springs were used to come up with a simplified 1D model using three types of spring–dashpots. The proposed model estimates the displacement and force resultants relatively better than the other 1D models available in literature.     

General dynamic-stiffness matrix of a timoshenko beam for transverse vibrations

The general dynamic-stiffness matrix of a Timoshenko beam for transverse vibrations is presented in this paper. All the effects of rotary inertia of the mass, shear distortion, structural damping, axial force, elastic-spring and dashpot foundation are taken into account in the formulation. As a consequence, the deflection function of the beam vibration is in complex form, and the nature of the beam vibration and the corresponding dynamic stiffnesses of the beam are characterized by general complex wave numbers. The dynamic-stiffness matrix for any special case can be derived easily from the general formula, which may be used directly in standard structural analysis.     

Periodic response of a rigid block resting on a footing subjected to harmonic excitation

This study presents the dynamic behaviour of a rigid block which rests on a footing supported by a spring and a dashpot on a rigid base. The response of the rigid body is examined carefully when the base is excited by a harmonic force. It is found that a periodic motion appears in three different modes: stick-stick, stick-slip and slip-slip. The conditions that initiate the stick-stick and slip-slip modes are derived in explicit forms and the maximum sliding displacement is also obtained analytically. Useful dimensionless parameters are proposed for the presentation of the dynamic behaviour. The accuracy of results is confirmed by the response history computed by the Nigam-Jennings method.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 1: Methodology and analytical tools

During strong ground motion it is expected that extended structures (such as bridges) are subjected to excitation that varies along their longitudinal axis in terms of arrival time, amplitude and frequency content, a fact primarily attributed to the wave passage effect, the loss of coherency and the role of local site conditions. Furthermore, the foundation interacts with the soil and the superstructure, thus significantly affecting the dynamic response of the bridge. A general methodology is therefore set up and implemented into a computer code for deriving sets of appropriately modified time histories and spring–dashpot coefficients at each support of a bridge with account for spatial variability, local site conditions and soil–foundation–superstructure interaction, for the purposes of inelastic dynamic analysis of RC bridges. In order to validate the methodology and code developed, each stage of the proposed procedure is verified using recorded data, finite‐element analyses, alternative computer programs, previous research studies, and closed‐form solutions wherever available. The results establish an adequate degree of confidence in the use of the proposed methodology and code in further parametric analyses and seismic design. Copyright © 2003 John Wiley & Sons, Ltd.     

Ground viscosity and stiffness measurements for near surface seismic velocity

In land surveys, the weathering layer can often distort the seismic signal due to it passing through rapid velocity and density changes, dispersion, scattering and inelastic absorption. In a simple spring‐dashpot model for the earth response, an equivalent medium groups these complex phenomena into two parameters only; these are called ground viscosity and ground stiffness. The most recent controllers for vibrators can estimate both parameters. To validate these measurements, Saudi Aramco conducted an experiment measuring ground viscosity and stiffness from two different vibrator control systems over an area of varying terrain conditions, including unconsolidated sand and limestone outcrop. The two systems measured different values, but detected similar trends that correlated well with weathering conditions and surface geology, e.g. lower viscosity values on the outcrop than on the sand. The ratio of ground viscosity to ground stiffness can approximate the shallow S‐wave velocity, which we converted into P‐wave velocity through calibration with sparse uphole data. Static corrections incorporating this velocity information somewhat improved the focusing of seismic time sections. This new approach does not require additional acquisition efforts, and can model shallow complex formations in arid areas where classical static methods often fail.     

Reduced‐dimension nonlinear finite‐element analysis of a vibrating disk in an unbounded domain

We present and evaluate the formulation of a reduced‐dimension (one‐dimensional) finite element for the nonlinear analysis of a vibrating disk in a two‐dimensional unbounded domain. As this problem is relevant in studies of the dynamic response of laterally loaded piles, numerous spring‐and‐dashpot representations of the disk undergoing displacement in an unbounded material domain have been developed to date: static and dynamic, linear and nonlinear. With the focus on material nonlinearity, the present simplified formulation circumvents the complications associated with nonlinear springs and dashpots. Indeed, the continuum‐based treatment described herein accounts for the interaction between the two modes of energy dissipation, due to wave propagation in the unbounded domain and loss associated with inelastic behavior. The formulation is a good compromise between the competing desires for realistic representation and efficient computation. Copyright © 2011 John Wiley & Sons, Ltd.     

磁流变阻尼器的两种力学模型和试验验证

本文根据我们设计制作出的磁流变阻尼器的阻尼特性试验结果，提出了描述阻尼器动态特性的两种新的力学模型。一种称之为修正的Bingham模型，它由Bingham单元（库仑摩擦单元与粘滞单元并联）与弹簧单元串联组成。该弹簧单元与磁流变液屈服前区的初始剪切模量和蓄能器的刚度等有关。另一种称为修正的Dahl模型，它采用Dahl模型来模拟库仑摩擦力，克服了常用的Bouc-Wen模型需要确定的参数过多的缺点。为了使模型在阻尼器的电流强度（磁场强度）改变的情况下仍然有效，引入一个内变量描述模型参数与电流强度（磁场强度）的关系。最后，通过理论分析与试验结果的比较，证明本文提出的两种力学模型能够较为精确地描述大多数的磁流变阻尼器在改变电流强度（磁场强度）情况下的动态特性。     

An improved rheology model for the description of the rate-dependent cyclic behavior of high damping rubber bearings

An improved rheology model, inspired from explicit experiments is conceived to represent rate-dependent cyclic shear behavior of high damping rubber bearings at subzero and room temperatures. Total stress has been decomposed into nonlinear rate independent elasto-plastic stress, nonlinear elastic stress and nonlinear visco-elasto-plastic overstress branches. To represent nonlinear viscosity behavior, ‘overstress branch’ has been generalized by putting linear elastic spring in parallel to nonlinear elasto-plastic model, placed in series with nonlinear dashpot. Constitutive relations for model elements have been designated for respective fundamental phenomenon observed in constant strain rate experiments. An optimum calculation approach is developed to determine a unique set of overstress parameters capable not only of representing constant strain rate cyclic tests but also sinusoidal tests with variable input strain rates. Essential abilities of the proposed model and adequacy of estimated parameters have been confirmed by comparing numerical simulation results with experiments conducted at −30 °C, −10 °C and 23 °C.     

A high-order time-domain transmitting boundary for cylindrical wave propagation problems in unbounded saturated poroelastic media

Based on the u–p formulation of Biot equation with an assumption of zero permeability coefficient, a high-order transmitting boundary is derived for cylindrical elastic wave propagation in infinite saturated porous media. By this transmitting boundary the total stresses on the truncated boundaries of a numerical model, such as a finite element model, are replaced by a set of spring, dashpot and mass elements, with some additionally introduced auxiliary degrees of freedom. The transmitting boundaries are incorporated into the DIANA SWANDYNE II program and an unconditionally stable implicit time integration algorithm is adopted. Despite the assumption made in the derivation of the transmitting boundary, numerical examples show that it can provide highly accurate results for cylindrical elastic wave propagation problems in infinite saturated porous medium in case the u–p formulation is applicable. Although the direct applications of the proposed transmitting boundary to general two dimensional wave problems in infinite saturated porous media are not highly accurate, acceptable accuracy can still be achieved by placing the transmitting boundary at relatively large distance from the wave source.     

Damage‐based seismic planar pounding analysis of adjacent symmetric buildings considering inelastic structure–soil–structure interaction

In cities and urban areas, building structures located at close proximities inevitably interact under dynamic loading by direct pounding and indirectly through the underlying soil. Majority of the previous adjacent building pounding studies that have taken the structure–soil–structure interaction (SSSI) problem into account have used simple lumped mass–spring–dashpot models under plane strain conditions. In this research, the problem of SSSI‐included pounding problem of two adjacent symmetric in plan buildings resting on a soft soil profile excited by uniaxial earthquake loadings is investigated. To this end, a series of SSSI models considering one‐directional nonlinear impact elements between adjacent co‐planar stories and using a method for direct finite element modeling of 3D inelastic underlying soil volume has been developed to accurately study the problem. An advanced inelastic structural behavior parameter, the seismic damage index, has been considered in this study as the key nonlinear structural response of adjacent buildings. Based on the results of SSSI and fixed base case analyses presented herein, two main problems are investigated, namely, the minimum building separation distance for pounding prevention and seismic pounding effects on structural damage in adjacent buildings. The final results show that at least three times, the International Building Code 2009 minimum distance for building separation recommended value is required as a clear distance for adjacent symmetric buildings to prevent the occurrence of seismic pounding. At the International Building Code‐recommended distance, adjacent buildings experienced severe seismic pounding and therefore significant variations in storey shear forces and damage indices. Copyright © 2016 John Wiley & Sons, Ltd.     

Some analytical results on lateral dynamic stiffness for footings supported on hysteretic soil medium

The nonlinearity of the soil affects soil–structure interaction to a considerable extent. For a reliable and safe analysis of soil interaction effects on the dynamic response of structures, a more realistic and relatively straightforward method incorporating the nonlinear hysteretic nature of the underlying soil–foundation system needs to be developed. The present paper models the soil–foundation system as a single degree of freedom spring–dashpot system with nonlinear hysteresis in form of elasto-perfectly plastic behavior. Analytical results for the lateral dynamic stiffness on footing have been presented. An example study has been carried out in case of circular footings. It is shown how the analytical results can be used to get a preliminary idea of the lateral dynamic stiffness of footings on a soil medium prior to a detailed computational geo-mechanics analysis provided the static nonlinear load–deformation characteristic of the soil medium is known and can be modeled by a hysteretic elasto-plastic behavior. The corresponding results are presented in a graphical form. The results have been computed showing parametric variations with the change in the amplitude and dimensionless frequency of the non-dimensional excitation force. Analytical results are also presented for the asymptotic cases at low and very high values of dimensionless frequency parameter.     

Climate change and sediment flux from the Roof of the World

Potential rises in global temperature are likely to have major impacts on high altitude environments, including glacier recession and permafrost degradation. In turn, these could have far‐reaching impacts on riverine sediment flux. Such impacts are emerging in the Himalayas and Tibet Plateau region, one of the world's largest and most environmentally‐sensitive cold regions. Closer monitoring is urgently required to track changing trends of sediment load from the interactions of glacial recession treat, rainfall changes and human interventions, and to study the implications of such changes for the large Asian river systems of the region. Copyright © 2010 John Wiley & Sons, Ltd.