Vibration of surface foundations of arbitrary shapes

Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed.     

Vibration of beams on non-homogeneous elastic foundations

The natural response of a beam or pile supported by an elastic foundation is investigated for the case when the coefficient of subgrade reaction varies linearly along the span of the member.     

Vibration of beams on partial elastic foundations

The natural response of a beam or pile having only a portion of its span supported by an elastic foundation is investigated for the two cases when both ends are either simply supported or free. The derivation of the shape functions and the computed natural frequencies are compared with the extreme cases where the element is either completely supported by, or fully detached from, the elastic foundation.     

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.     

动力基础系统非线性本构关系的研究

采用理想集总参数计算体系,以三次幂多项式模型反映动力地基的非线性特性,将非线性幂函数作为循环荷载作用下系统位移-力关系的主干骨线,在此基础上按照Masing二倍法则,将骨线拓展为位移一力的滞回曲线,建立了动力基础双曲线滞回动力学模型。提出了非线性广义刚度函数的概念,建立了动力基础系统在不同振动形式下的非线性本构关系。     

动力基础系统非线性力学模型

采用定参理想集总参数计算体系，以动力基础非线性动力学模型和非线性广义刚度函数的概念为基础，将动力基础模型从竖向非线性振动推广至水平非线性振动、扭转非线性振动以及水平-回转二自由度耦合非线性振动和竖向-水平-回转三自由度非线性耦合振动，建立了动力基础非线性动力学模型的一般表达式，为动力基础非线性设计提供了理论。     

Stochastic response of rigid foundations

While the study of kinematic interaction (i.e. the dynamic response of massless foundations to seismic loads) calls, in general, for advanced analytical and numerical techniques, an excellent approximation was proposed recently by Iguchi.^1,2 This approximation was used by the authors to analyse embedded foundations subjected to spatially random SH-wave fields, i.e. motions that exhibit some degree of incoherence. The wave fields considered ranged from perfectly coherent motions (resulting from seismic waves arriving from a single direction) to chaotic motions, resulting from waves arriving simultaneously from all directions. Additional parameters considered were the shape of the foundation (cylindrical or rectangular) and the degree of embedment. It was found that kinematic interaction usually reduces the severity of the motions transmitted to the structure, and that incoherent motions do not exhibit the frequency selectivity (i.e. narrow valleys in the foundation response spectra) that coherent motions do.     

Macroseismic foundations of seismic microzoning

The Russian seismic safety regulations are based on macroseismic evaluations in terms of seismic intensity values. According to the seismic scale, intensity value determines both the degree of destruction of buildings and engineering structures and such parameters of seismic impacts as peak ground accelerations and response spectra. Application of macroseismic approach in various aspects of seismic microzoning has led to achievements in earthquake engineering; these aspects are discussed. The advantages and disadvantages of the macroseismic approach are considered.     

Uplift in hammer foundations

Response of hammer foundations to the blows of the head is analyzed allowing for the uplift of both the anvil and the foundation block. Damping as well as stiffness of the system are accounted for in a rational way. The validity of the response prediction on the basis of the standard theory in which uplift is omitted, is examined. One and two mass systems are considered. The theory is compared with the results of tests conducted with a hammer foundation in operation.     

Vertical vibration of ring foundations

A comprehensive analysis is made of the harmonic response of vertically excited, massless, rigid ring foundations supported at the surface of an homogeneous elastic halfspace. The parameters considered include the thickness to radius ratio for the ring, the frequency of the exciting force and of the resulting steady-state response, and Poisson's ratio for the supporting medium. The response quantities examined include the stiffness and damping coefficients of the system in an equivalent spring–dashpot representation of the supporting medium, the displacements of the foundation and of points on the ground surface away from the foundation, and the normal pressure at the foundation–medium interface. The results in each case are compared with those obtained for a solid disk having the same radius as the outer radius of the ring, and a simple approximate model is used to interpret the results and to provide insight into the action of the system. The reported data are computed by a method of analysis that takes due account of the mixed boundary conditions at the surface of the halfspace, and are believed to be of high accuracy.     

Nonlinear rocking stiffness of foundations

The response of surface foundations to large overturning moments is studied under undrained conditions. Rigid circular, strip, and rectangular footings of various aspect ratios are considered, with the soil modeled as an inelastic homogeneous deposit, characterized by an elastic (small-strain) shear modulus G_o, an undrained shear strength S_u, and a G/G_o versus γ curve appropriate for medium-plasticity clays. Three stages of foundation performance, ranging from the initial elastic fully-bonded response, to the nearly-elastic but nonlinear response with the foundation partially detaching and uplifting from the soil, and finally to the ultimate stage where full mobilization of soil bearing failure mechanisms develop. Simple to use formulas or charts are developed for all stages of response in terms of dimensionless parameters, prominent among which is the static factor of safety against bearing-capacity failure under purely-vertical loading.     

Impedances of embedded rigid strip foundations

This paper is concerned with the dynamic response of rigid strip foundations of arbitrary geometry embedded in a homogeneous elastic half-space. The embedded rigid foundation is modelled by an equivalent domain in a uniform half-space which is subjected to an appropriate body force field. The components of the impedance matrix are determined through the solution of a linear simultaneous equation system which is established by invoking rigid body displacements of discrete locations within the equivalent domain and appropriate equilibrium consideration. It is found that high numerical efficiency and flexibility can be achieved using the body force model when compared to boundary integral formulations through the selection of appropriate displacement influence functions and a ‘parent domain’ in the analysis. Numerical results are presented to illustrate the influence of the embedment ratio, frequency of excitation, foundation geometry and Poisson's ratio on the vertical, horizontal, rocking and coupled impedances of a single embedded foundation. The effect on the impedance due to the presence of an adjacent embedment is investigated for various distances between foundations and embedment ratios.     

Dynamic interaction between adjacent foundations

The results of a parametric study on the dynamic interaction between adjacent foundations are presented. Addressed in this study are the effects of distance, direction of alignment, embedment and structural inertia. Several conclusions are drawn regarding the significance of each of these factors.     

Dynamic response of axisymmetric embedded foundations

The boundary element method is used to obtain dynamic stiffness functions of rigid cylindrical foundations embedded in a uniform or layered viscoelastic half-space. Dynamic stiffness functions of hemispherical foundations embedded in a uniform half-space are also computed. The direct integral equation formulation is used in combination with the complete space point load fundamental solution that is integrated numerically along the azimuthal coordinate. The approach is easy to implement because of the simplicity of the fundamental solution. The numerical results obtained by this method for cylindrical and hemispherical foundations are very close to corresponding published results obtained by different procedures. A parametric study shows the important effects of the Poisson's ratio on the dynamic stiffness functions of cylindrical foundations embedded in a uniform viscoelastic half-space. The effect of the bedrock compliance on the stiffness functions is also shown in the case of cylindrical foundations embedded in a soil layer that rests on a bedrock.     

Control of seismic response of turbomachin foundations

The safety of structures built in seismic regions can be improved by energy absorbing devices. Passive isolation systems such as base isolators are suitable for low-rise structures, but they provide only a partial solution to the problem. Three active control techniques for reducing the dynamic response of machine supporting foundations using various control strategies are presented. The active tendon, active mass damper and active base control systems are studied for active control of machine foundations in seismic regions. Numerical simulations show that active control can reduce the dynamic response of turbomachine foundations under seismic loads. This reduction in dynamic response can limit damage to power plants during earthquakes and restore their operation in a short time.     

Attenuation properties of viscoelastic material

The attenuation properties of eight rheological models have been studied theoretically. The expressions forQ have been obtained by using dissipated and stored energies and/or complex modulus for each model. The dependence ofQ on frequency has been demonstrated. The three-element elastic model appears to be the best one to represent the viscoelastic nature of the earth's material for a finite value ofQ.     

Tidal deformations of viscoelastic body

Summary The tidal deformations of a viscoelastic body are studied using the simple Kelvin-Voigt model. Expressions for the phase lag and amplitude change of the displacement vector are derived. The energy dissipation rate is calculated for the main disturbing bodies and for diurnal and semidiurnal tidal waves.

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Dynamic finite strip analysis of surface foundations

The finite strip method is used to study the dynamic response of surface strip foundations. This method is simple to use and versatile. The two-dimensional problem is effectively reduced to an equivalent one-dimensional problem. The choice of trigonometric series for the displacement functions results in the uncoupling of the terms of the series and a significant reduction in the semi-bandwidth of the complex set of equations, making the method well suited to small computers. Non-homogeneous soil profiles are treated as a matter of course. The finite strip solutions are shown to be in general agreement with other theoretical methods of analysis.     

Dynamic behaviour of structures with embedded foundations

A study of the dynamics of building-soil interaction is presented that includes embedding of the foundation and material damping. By considering buildings on rigid footings embedded into linear elastic soil with hysteretic damping, it is shown that the earthquake response of the building-foundation model may be found from the response to modified excitation of equivalent one-degree-of-freedom linear, viscously damped oscillators resting on rigid ground. For a single-storey building approximate formulas are developed for the modified natural frequency and damping ratio. Results show that the natural frequency and damping in the system increase with embedding. Effective damping also increases with internal friction in the soil. Ignoring these two factors may underestimate considerably the effective natural frequency and damping in the system. In spite of additional sources of energy dissipation provided by the soil, damping in the equivalent oscillator may be greater or smaller than that corresponding to the superstructure alone, depending upon the system parameters. For lightly damped superstructures, the peak amplitude of the steady-state overturning moment at the base of a building supported on flexible soil is significantly smaller than that corresponding to rigid ground. This result has practical implications for earthquake design.