Dynamic response of a pair of walls retaining a viscoelastic solid

Making use of a previously reported, simple, approximate method of analysis, a critical evaluation is made of the dynamic pressures and forces induced by horizontal ground shaking on a pair of infinitely long, parallel walls retaining a uniform viscoelastic solid. The walls are presumed to be rigid but elastically constrained against rotation at their base. The effects of both harmonic and earthquake-induced excitations are examined. The accuracy of the method is assessed by comparing its predictions for the special case of fixed-based walls with those obtained by an exact method, and comprehensive numerical data are presented which elucidate the underlying response mechanisms, and the effects and relative importance of the parameters involved. The parameters examined include the characteristics of the ground motion, the ratio of the distance between walls to the height of the contained material, and the flexibility of the rotational wall constraints. In addition to valuable insights into the responses of the systems investigated, the results presented provide a convenient framework for the analysis of more complex systems as well.     

Soil-structure interaction effects for laterally excited liquid storage tanks

A comprehensive study is made of the effects of soil-structure interaction on the response of liquid containing, upright, circular cylindrical tanks subjected to a horizontal component of ground shaking. A simple, physically motivated method of analysis is employed which elucidates the effects and relative importance of the principal actions involved. Both the impulsive and convective actions of the liquid are examined. The interrelationship of the tank responses to horizontal and rocking actions of the foundation is established, and the well known mechanical model for laterally excited, rigid tanks supported on a non-deformable medium is generalized to permit consideration of the effects of tank and ground flexibilities and base rocking. Critical responses are evaluated for harmonic and seismic excitations over wide ranges of tank proportions and soil stiffnesses, and the results are presented in a form convenient for use in practical applications. In addition to a precise method of analysis, an approximate, hand-computation method is presented with which the effects of the primary parameters may be evaluated readily. The soil-structure interaction effects in the latter approach are provided for by modifying the natural frequency and damping of the tank-liquid system and evaluating its response to the prescribed free-field ground motion considering the tank to be rigidly supported at the base. The requisite modifications may be determined from information presented herein. It is shown that soil-structure interaction may reduce significantly the impulsive components of response but that it has a negligible effect on the convective components.     

Dynamic soil pressures on rigid vertical walls

A critical evaluation is made of dynamic pressures and the associated forces induced by ground shaking on a rigid, straight, vertical wall retaining a semi-infinite, uniform viscoelastic layer of constant thickness. The effects of both harmonic and earthquake-induced excitations are examined. Simple approximate expressions for the responses of the system are developed, and comprehensive numerical data are presented which elucidate the effects and relative importance of the various parameters involved. These solutions are then compared with those obtained by the use of a simple model previously proposed by Scott, and the accuracy of this model is assessed. Finally, two versions of an alternative model are proposed which approximate better the action of the system. In the first, the properties of the model are defined by frequency-dependent parameters, whereas in the second, which is particularly helpful in analyses of transient response, they are represented by frequency-independent, constant parameters.     

Hydrodynamic effects in rigid tanks containing layered liquids

As a supplement to a recently reported study, the hydrodynamic wall pressures and the associated tank forces induced by horizontal ground shaking in a rigid, vertical, circular cylindrical tank containing liquid layers of different thicknesses and mass densities are examined, and comprehensive numerical solutions are presented for two-layered and some three-layered systems which elucidate the underlying response mechanisms and the effects of the various parameters involved. Both the impulsive and convective actions are studied. Additionally, solutions are presented for multi-layered systems approximating a liquid with an exponential, continuous variation in density, and the interrelationship of the solutions for the continuous system and its discretized, layered approximation is discussed.     

Dynamic response of rigid tanks with inhomogeneous liquids

A study of the response to horizontal ground shaking of a rigid cylindrical tank containing an inviscid liquid with a continuous vertical variation in density is presented. In addition to the free vibrational sloshing characteristics of the liquid, the responses examined include the vertical displacements at the free surface, and the impulsive and convective components of the hydrodynamic wall pressures and associated tank forces. The equations of motion for the system are formulated for an arbitrary variation in liquid density but the solutions presented are for a density that increases exponentially from top to bottom. Comprehensive numerical data are included which elucidate the underlying response mechanisms and the effects and relative importance of the various parameters involved. The solution for the continuous density variation considered herein is also compared with a previously reported solution in which the liquid was modelled as a multi-layered, discrete system.     

Effects of reservoir bottom absorption on earthquake response of concrete gravity dams

A procedure is presented to analyse the response of concrete gravity dams due to horizontal and vertical earthquake ground motion components considering dam-water interaction and partial absorption of hydrodynamic pressure waves at the reservoir bottom into the foundation medium. The effects of reservoir bottom absorption on the hydrodynamic force on a rigid dam are examined first. The harmonic response of an idealized dam cross-section is presented for a wide range of parameters characterizing the properties of the dam, the impounded water and the foundation medium. Based on these frequency response functions the effects of dam-water interaction and of reservoir bottom absorption in the response of dams due to horizontal and vertical components of ground motion are investigated.     

水平分层土层系统等效阻尼比的简化计算方法

在实际工程场地中,很多土层可视为水平分层,各层土的物理和力学性质存在差异,其中包括土的振动阻尼比。本文讨论水平分层土层系统的等效阻尼比的近似计算方法,基于5个不同的加权函数推导了10种等效阻尼比的计算公式。通过2个算例,分别以等效阻尼比为参数计算水平分层土层的地震反应,并与准确解相比较,分析了不同等效阻尼比近似计算方法的计算精度。数值结果表明,若等效阻尼比计算方法选择不恰当,会导致土层地震反应的计算结果出现较大误差。针对2种不同类型的水平分层土层,建议采用基于三角形分布的加权函数来计算土层系统的等效阻尼比。     

Dynamic stiffness of parabolic cables

A closed-form expression for the in-plane horizontal stiffness of a viscously damped, uniform, inclined cable in harmonic motion is presented. The cable is presumed to be deflected in a parabolic profile at its position of static equilibrium, and all dynamic displacements are assumed to be small. The stiffness expression is valid for an arbitrary angle of inclination of the cable chord in the range between zero and 90 degrees. In addition, a simpler solution, valid over a narrower range of the parameters, is included and its accuracy examined. Comprehensive numerical data are presented and discussed, with particular emphasis on explaining the physical significance of the results and providing insight into the action of the cable and into the parameters that control it. Finally, a simple, single-degree-of-freedom model is proposed which reproduces with good accuracy the salient features of the response of the prototype cable over a wide range of conditions.     

Hydrodynamic and foundation interaction effects in frequency response functions for concrete gravity dams

The linear response of idealized dam cross-sections to harmonic horizontal or vertical ground motion is presented for a range of the important system parameters characterizing the properties of the dam, foundation rock and impounded water. Based on these frequency response functions, the separate effects of interaction between the dam and water and interaction between the dam and foundation, and the combined effects of the two sources of interaction, on dynamic response of dams are investigated.     

Sloshing response of layered liquids in rigid tanks

The sloshing action of layered liquids in rigid cylindrical and long rectangular tanks is investigated, considering both their free vibrational characteristics and their response to a horizontal component of base shaking. Special attention is given to the maximum surface displacement induced by the base motion. The analysis is formulated for systems with N superimposed layers of different thicknesses and densities, and is illustrated by a numerical example. In addition, comprehensive numerical data are presented for two-layered and some three-layered systems which elucidate the underlying response mechanisms and the effects and relative importance of the numerous parameters involved. It is shown that for each horizontal natural mode of vibration, there are N distinct vertical modes, the frequencies of which are lower than the natural frequency of a homogeneous liquid of the same total depth. It is further shown that the maximum surface sloshing displacement of the base-excited layered system is typically larger than that of the corresponding homogeneous system, and that the results for the long rectangular and cylindrical tanks are quite similar.     

Dynamic pressures on a pair of rigid walls retaining poroelastic soil

This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability.     

Effects of foundation embedment during building–soil interaction

A numerical solution for evaluating the effects of foundation embedment on the effective period and damping and the response of soil–structure systems is presented. A simple system similar to that used in practice to account for inertial interaction effects is investigated, with the inclusion of kinematic interaction effects for the important special case of vertically incident shear waves. The effective period and damping are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-field ground motion. In this way, the use of standard free-field response spectra applicable to the effective period and damping of the system is permitted. Also, an approximate solution for total soil–structure interaction is presented, which indicates that the system period is insensitive to kinematic interaction and the system damping may be expressed as that for inertial interaction but modified by a factor due to kinematic interaction. Results involving both kinematic and inertial effects are compared with those obtained for no soil–structure interaction and inertial interaction only. The more important parameters involved are identified and their influences are examined over practical ranges of interest. © 1998 John Wiley & Sons, Ltd.     

Seismic pressures on rigid cantilever walls retaining elastic continuously non-homogeneous soil: An exact solution

The dynamic response of an elastic continuously nonhomogeneous soil layer over bedrock retained by a pair of rigid cantilever walls to a horizontal seismic motion and the associated seismic pressure acting on these walls are determined analytically–numerically. The soil non-homogeneity is described by a shear modulus increasing nonlinearly with depth. The problem is solved in the frequency domain under conditions of plane strain and its exact solution is obtained analytically. This is accomplished with the aid of Fourier series along the horizontal direction and solution of the resulting system of two ordinary differential equations with variable coefficients by the method of Frobenius in power series. Due to the complexity of the various analytical expressions, the final results are determined numerically. These results include seismic pressures, resultant horizontal forces and bending moments acting on the walls. The solution of the problem involving a single retaining wall can be obtained as a special case by assuming the distance between the two walls to be very large. Results are presented in terms of numerical values and graphs using suitable dimensionless quantities. The effect of soil non-homogeneity on the system response is assessed through comparisons for typical sets of the parameters involved.     

Effects of reservoir bottom absorption and dam-water-foundation rock interaction on frequency response functions for concrete gravity dams

The linear response of an idealized concrete gravity dam monolith to harmonic horizontal or vertical ground motion is presented for a range of the important system parameters that characterize the properties of the dam, foundation rock, impounded water and reservoir bottom materials. Based on these frequency response functions, the effects of alluvium and sediments at the reservoir bottom on the response of the dam, including its interaction with the impounded water and foundation rock, are investigated. It is shown that the partial absorption of hydrodynamic pressure waves by the reservoir bottom materials has an important effect on the dynamic response of concrete gravity dams.     

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.     

Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

An evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.     

双洞八车道大断面隧道地震动力响应数值分析

为研究双洞八车道超大断面隧道在地震力作用下的动力响应特征,以平潭综合实验区牛寨山隧道为工程背景,建立双洞八车道隧道的三维有限元数值计算模型。采用时程分析方法,在模型底部输入水平向地震动荷载,计算隧道结构在地震动荷载作用下的响应,包括位移、加速度及应力的变化。结果表明:最大水平和竖向位移出现在拱顶处,南线浅埋隧道整体呈剪切响应;隧道最大水平加速度出现在南线隧道拱顶偏左处,最大垂直加速度出现在南线隧道拱顶偏右处,南线隧道洞口由于浅埋,关键部位响应差较北线要大;南线的右拱肩埋深最浅,该部位拉应力最大,而北线拱顶的拉应力区最大,拱脚也出现明显的拉或压应力。建议在隧道洞口段的拱顶、拱脚及埋深最浅的部位应加强抗震设防。     

Seismic passive earth resistance using modified pseudo-dynamic method

In earthquake prone areas, understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures. In this study, the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill. A composite failure surface is considered in the present analysis. Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking. The present method satisfies the boundary conditions. The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion. The acceleration distribution along the depth of the backfill is found to be nonlinear in nature. The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient. The effect of different parameters on the seismic passive earth pressure is studied in detail. A comparison of the present method with other theories is also presented, which shows the merits of the present study.     

Finite element analysis of buried steel pipelines under strike-slip fault displacements

The present paper investigates the mechanical behavior of buried steel pipelines, crossing an active strike-slip tectonic fault. The fault is normal to the pipeline direction and moves in the horizontal direction, causing stress and deformation in the pipeline. The interacting soil–pipeline system is modelled rigorously through finite elements, which account for large strains and displacements, nonlinear material behavior and special conditions of contact and friction on the soil–pipe interface. Considering steel pipelines of various diameter-to-thickness ratios, and typical steel material for pipeline applications (API 5L grades X65 and X80), the paper focuses on the effects of various soil and pipeline parameters on the structural response of the pipe, with particular emphasis on identifying pipeline failure (pipe wall wrinkling/local buckling or rupture). The effects of shear soil strength, soil stiffness, horizontal fault displacement, width of the fault slip zone are investigated. Furthermore, the influence of internal pressure on the structural response is examined. The results from the present investigation are aimed at determining the fault displacement at which the pipeline fails and can be used for pipeline design purposes. The results are presented in diagram form, which depicts the critical fault displacement, and the corresponding critical strain versus the pipe diameter-to-thickness ratio. A simplified analytical model is also developed to illustrate the counteracting effects of bending and axial stretching. The numerical results for the critical strain are also compared with the recent provisions of EN 1998-4 and ASCE MOP 119.