Boundary element reservoir model for seismic analysis of gravity dams

The boundary element method has been successfully applied in the past to the analysis of hydrodynamic forces in two- and three-dimensional finite water reservoirs subjected to seismic ground motions. In extending the method to an infinite reservoir, the loss of energy due to pressure waves moving away towards infinity must be taken into account. In addition, for both finite and infinite reservoirs, energy is lost owing to partial absorption of the waves incident on a flexible bottom consisting of alluvial deposits. This paper presents the results of more recent research on the application of the boundary element method to the analysis of 2D reservoir vibration. Two different formulations are used: a constant boundary element formulation and a linear boundary element formulation. Special boundary conditions to treat infinite radiation and foundation damping have been incorporated in both formulations. Numerical results have been obtained for each of the two alternative formulations and compared against each other as well as with classical solutions and results obtained by other researchers.     

某高精密设备平台基础隔振措施分析

结合某高精密设备平台基础隔振实际工程,基于UPFs(User Programmable Features)二次开发特点,提出考虑基础-地基-基础动力相互作用计算基础隔振分析的三维有限元方法。该方法首先将动力机器、周围地基以及高精密设备平台基础作为完整的研究对象,通过引入三维紧支黏弹性边界单元模拟半无限地基辐射阻尼效应和远场介质的弹性恢复性能,并在通用有限元软件ANSYS中实现。进而基于最小二乘方法回归分析得到振动衰减关系曲线,通过其与数值分析结果的对比验证计算模型的合理性。最后针对此工程场地条件建立隔振沟减振隔振措施的有限元模型,并对隔振沟影响因素的减振效果进行分析。计算结果表明,隔振沟的位置、深度以及长度是实际工程中需要考虑的重要因素,对其进行合理的选取可获得较好的隔振效果。     

Effective ambient vibration testing for validating numerical models of concrete dams

Ambient vibration tests were conducted on a 56 metre high concrete gravity dam to measure its modal properties for validating a finite element model of the dam–reservoir–foundation system. Excitation was provided by wind, by reservoir water cascading down the spillweir, and by the force of water released through outlet-pipes. Vibrations of the dam were measured using accelerometers, and 3-hour data records were acquired from each location. Data were processed by testing for stationarity and rejecting non-stationary portions before Fourier analysis. Power spectra with low variance were generated from which natural frequencies of the dam were identified clearly and modal damping factors estimated. Modal analysis of the frequency response spectra yielded mode shapes for the six lowest lateral modes of vibration of the dam. The finite element model for the dam was analysed using EACD-3D, and the computed mode shapes and natural frequencies compared well with the measured results. The study demonstrates that ambient vibration testing can offer a viable alternative to forced vibration testing when only the modal properties of a dam are required. Copyright © 1999 John Wiley & Sons, Ltd.     

Hydrodynamic effects in a reservoir with semicircular cross-section and absorptive bottom

A three-dimensional dam-reservoir system under seismic load is analysed. The dam is assumed to be rigid. The reservoir is an infinite channel with semi-circular cross-section. The exact analytical solution, based on the assumption of potential fluid motion is presented, as well as numerical results for selected parameters.The most significant parameters are: the direction and frequency content of the seismic input; the radiation damping at the reservoir bottom; and the compressibility of the fluid. The response of the system depends strongly on the direction of the input ground motion. This is shown by the transfer functions as well as by the pressure time histories due to two earthquakes with different frequency content. The energy absorption at the reservoir bottom is important. A simple plane-wave model shows, that even for a rock foundation, the amount of transmitted energy can reach up to 80%. For comparison the case without bottom absorption is also shown. Compressbility has to be included to capture the resonance effects. The exact analytical solution is also used to verify numerical results obtained by a new method that combines a finite element model with a rigorous radiation boundary for the infinite channel in the time domain.     

Free‐vibration analysis of a three‐dimensional soil–structure system

A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd.     

The effects of reservoir geometry on the seismic response of gravity dams

Conventional seismic analysis of gravity dams assumes that the behaviour of the dam–water–soil system can be represented using a 2‐D model since dam vertical contraction joints between blocks allow them to vibrate independently from each other. The 2‐D model assumes the reservoir to be infinite and of constant width, which is not true for certain types of reservoirs. In this paper, a boundary element method (BEM) model in the frequency domain is used to investigate the influence of the reservoir geometry on the hydrodynamic dam response. Important conceptual conclusions about the dam–reservoir system behaviour are obtained using this model. The results show that the reservoir shape influences the seismic response of the dam, making it necessary to account for 3‐D effects in order to obtain accurate results. In particular, the 3‐D pressure and displacement responses can be substantially larger than those computed with the 2‐D model. Copyright © 2007 John Wiley & Sons, Ltd.     

Time-domain boundary element method in viscoelasticity with application to a spherical cavity

The weighted-residual technique, the indirect boundary element method, the truncated indirect boundary element method and the direct boundary element method can be used to analyse nonlinear soil-structure interaction in the time domain. They are illustrated and compared by using the one-dimensional dynamic problem of the spherical cavity in an infinite space. For realistic time steps, all formulations lead to accurate results, but the weighted-residual technique and the truncated indirect boundary element method are much more efficient than the direct boundary element method in the time domain. Hysteretic damping leads to noncausal behaviour, which can, however, be neglected from a practical point of view.     

三维层状地基空沟主动隔振分析

基于薄层法在研究层状介质中波的传播问题的高效性、边界单元法处理无限域问题的精确性,结合二者的优点提出三维层状地基薄层法基本解答,建立了基于三维层状半空间薄层法位移基本解答的半解析动力边界元法。该方法可有效的分析多层场地的动力问题,解决土-结构动力相互作用问题。同时分别对粘弹性上软下硬地基及上硬下软地基的三维空沟主动隔振进行了详细的分析。结果表明,两种情况下采用空沟屏障隔振均可以取得一定的隔振效果;同时,地基分层参数对空沟隔振体系的隔振效果影响显著。     

Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered

Starting from an analytical reservoir model that incorporates full interaction with an elastic overburden, a new hybrid mathematical approach is developed by combining two numerical discretization methods. A tabular reservoir (petroleum reservoir or an aquifer) in an infinite or semi-infinite domain is viewed as a macroscopic displacement discontinuity, allowing use of the efficient displacement discontinuity mathematical method to calculate stresses and displacements that arise because of pressure changes. A 3-D finite element method using a poroelastic formulation is used to discretize the reservoir itself. By coupling the displacement discontinuity and finite element methods, a 3-D large-scale poroelastic reservoir can be simulated within an infinite or semi-infinite domain. The numerical model has been verified through comparison to known solutions, and some time-dependent pressure drawdown problems are analyzed. Results indicate that including the complete overburden (reservoir surroundings) response has a significant effect on pressure drawdown in a poroelastic reservoir during pumping, and should be incorporated in appropriate applications such as well test equations and subsidence analyses.     

Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects

An analysis procedure in the frequency domain is developed for determining the earthquake response of two-dimensional concrete gravity and embankment dams including hydrodynamic effects; responses of the elastic dams and compressible water are assumed linear. The dam and fluid domain are treated as substructures and modelled with finite elements. The only geometric restriction is that an infinite fluid domain must maintain a constant depth beyond some point in the upstream direction. For such an infinite uniform region, a finite element discretization over the depth is combined with a continuum representation in the upstream direction. The fluid domain model approximately accounts for interaction between the fluid and underlying foundation medium through a damping boundary condition applied along the reservoir bottom, while the dam foundation is assumed rigid. Several examples are presented to demonstrate the accuracy of the fluid domain model and to illustrate dam responses obtained from the analysis procedure.     

储层古应力场的数值模拟

根据古构造变形采用反演与正演相结合的方法,研究储层古构造应力场。开展以下研究：（１）用板模型趋势法反演与储层古构造变形面对应的驱动力和场内应力;（２）建立一个组合单元模型,用（１）中反演的远场应力作为边界条件,计算储层古构造应力场;（３）用含断层滑动模型的三维实体单元和（１）中给出的边界条件,计算储层古构造应力场;（４）对 ３ 种模型的应用及其检验     

三维直流电阻率有限元-无限元耦合数值模拟

为解决传统有限元截断边界所引起的问题,本文提出了一种新的三维直流电阻率有限元-无限元耦合数值模拟方法.首先推导了无限元三维单元映射函数,然后提出了一种全新的最优的无限元形函数并与多种其他形函数进行了对比,随后将其与非结构化四面体有限元相结合,取代了传统的混合边界条件,使得电位在无限域内连续并在无限远处衰减为零,最终形成的左端矩阵稀疏对称并与场源位置无关.数值计算表明,该方法可以在近似测区大小的计算范围内得到与混合边界条件相当的计算精度,优于相同计算范围下齐次边界条件的解,有利于减少计算节点数;由于左端矩阵不随场源位置改变,有利于加速反演计算.     

Earthquake analysis of gravity dams including hydrodynamic interaction

A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.     

徐淮地区煤矿井筒破裂原因初探

本用震源力学理论和方法研究了徐淮地区从１９７０年以来构造应力场的方向和强度的时空变化过程。结果表明：以唐山地震为分界线，本区的应力场Ｐ轴取向由震前平均６１．８°变为震后平均７７．７°。如果将本区以宿北断裂为界分为南区和北区两个部分，则北区的Ｐ轴取向从６８．１°变７１．２°，而南区的Ｐ轴取向由６２．５°变到８３．６°，南区的变化明显于北区。     

台湾某钢框架大楼采用阻尼器补强结构减震效果评析

阻尼器是一种效果良好的减震装置,将阻尼器安装于结构中能够适时为结构体系提供阻尼力,从而减小地震作用对结构的破坏。黏滞阻尼器对振动的反应比较敏感,在结构受到较小振动时就可以发挥其减震效果,其阻尼力会随着振动周期和使用状态温度的不同而变化。当地震发生时,安装在结构中的阻尼器会消减地震作用,降低传导到主结构体系的地震能量,减小结构相对位移。本文介绍了黏滞阻尼器的工作原理和安装有黏滞阻尼器的结构体系的阻尼比的计算方法,对减震结构的减震效果的评析方法做出探讨,并以一安装有黏滞阻尼器的台湾某既有钢框架结构为例,分析了(1)该结构在遭受地震作用时的地震反应;(2)该结构体系在不同地震作用水平时的阻尼比,包括主体结构阻尼比和黏滞阻尼器阻尼比;(3)结构安装黏滞阻尼器后的减震效果。实例对本文的减震评析方法和减震效果进行了说明和分析,计算及分析结果表明利用黏滞阻尼器加固既有结构能够取得较好的减震效果,本文所提减震效果评析方法是一种实用有效的评析方法,对类似工程的减震评析具有一定的参考价值。     

Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements

This paper presents the application of the finite element method for analysing the two-dimensional response of reservoir-dam systems subjected to horizontal ground motion. The interaction between the dam and the reservoir as well as the compressibility of water has been taken into account. The complete system has been considered to be composed of two substructures, namely the reservoir and the dam. To take into account the large extent of the reservoir, it has been idealized using specially developed infinite elements coupled with standard finite elements while the dam is represented using finite elements alone. Structural damping of the dam and radiation damping in the fluid phase have been accounted for in the analysis. It is concluded that the effect of radiation damping is considerable at high frequencies of excitation. The coupled response of the system is significantly large at and near the fundamental natural frequency of the system in comparison to the uncoupled responses. The method is computationally quite economical, capable of taking into account the arbitrary geometry of the system and is recommended for practical application. Further applications and extensions of the approach to three dimensional analyses are possible.     

Seismic analysis of dam-foundation-reservoir system including the effects of foundation mass and radiation damping

One of the main concerns in using commercial software for finite element analyses of dam-foundation-reservoir systems is that the simplifying assumptions of the massless foundation are unreliable. In this study, an appropriate direct finite element method is introduced for simulating the mass, radiation damping and wave propagation effect in foundations of damfoundation-reservoir systems using commercial software ABAQUS. The free-field boundary condition is used for modeling the semi-infinite foundation and radiation damping, which is not a built-in boundary condition in most of the available commercial software for finite element analysis of structures such as ANSYS or ABAQUS and thus needs to be implemented differently. The different mechanism for modeling of the foundation, earthquake input and far-field boundary condition is described. Implementation of the free-field boundary condition in finite element software is verified by comparing it with analytical results. To investigation the feasibility of the proposed method in dam-foundation-reservoir system analysis, a series of analyses is accomplished in a variety of cases and the obtained results are compared with the substructure method by using the EAGD-84 program. Finally, the massed and massless foundation results are compared and it is concluded that the massless foundation approach leads to the overestimation of the displacements and stresses within the dam body.     

轨道交通荷载下桩板结构主动隔振效果研究

为了研究在轨道交通荷载作用下桩板结构主动隔振措施的隔振效果,通过无限元边界与有限元边界相结合的有限元分析方法在路基中建立桩板结构模型,并在沙土地基中设置混凝土桩板结构进行模型试验,通过模型试验对有限元数值模拟结果加以验证,将桩长、埋深及置换率3个因素考虑在内,研究其对隔振效果的影响。结果表明:模型试验验证有限元计算方法的可靠性;随桩长增加振幅降低比减小,隔振效果明显,随着振源距离增加其振幅降低比减小明显;埋深为桩板结构主动隔振措施中的主要影响因素,随着埋深增加振幅降低比明显减小,隔振效果越明显;有限元计算过程中置换率对隔振效果的影响不明显,但是在模型试验中置换率对隔振效果影响较显著。     

A non-reflecting boundary condition for the finite element modeling of infinite reservoir with layered sediment

The design of seismic resistant concrete gravity dam necessitates accurate determination of hydrodynamic pressure developed in the adjacent reservoir. The hydrodynamic pressure developed on structure is dependent on the physical characteristics of the boundaries surrounding the reservoir including reservoir bottom. The sedimentary material in the reservoir bottom absorbs energy at the bottom, which will affect the hydrodynamic pressure at the upstream face of the dam. The fundamental parameter characterizing the effect of absorption of hydrodynamic pressure waves at the reservoir bottom due to sediment is the reflection coefficient. The wave reflection coefficient is determined from parameters based on sediment layer thickness, its material properties and excitation frequencies. An analytical or a closed-form solution cannot account for the arbitrary geometry of the dam or reservoir bed profile. This problem can be efficiently tackled with finite element technique. The need for an accurate truncation boundary is felt to reduce the computational domain of the unbounded reservoir system. An efficient truncation boundary condition (TBC) which accounts for the reservoir bottom effect is proposed for the finite element analysis of infinite reservoir. The results show the efficiency of the proposed truncation boundary condition.     

电导率各向异性的海洋电磁三维有限单元法正演

本文提出了一种基于非结构化网格的海洋电磁有限单元正演算法.为了回避场源奇异性,文中选用二次场算法,将背景电阻率设置为水平层状且各向异性,场源在水平层状各向异性介质中所激发的一次场通过汉克尔积分得到.基于Coulomb规范得到二次矢量位和标量位所满足的Maxwell方程组,通过Galerkin加权余量法形成大型稀疏有限元方程,采用不完全LU分解(ILU)预条件因子的quasi-minimum residual(QMR)迭代解法对有限元方程进行求解得到二次矢量位和标量位;进而,利用滑动平均方法得到二次矢量位和标量位在空间的导数,由此得到二次电磁场;通过一维模型对算法的可靠性进行验证,与此同时,针对实际复杂海洋电磁模型,比较有限元模拟结果与积分方程模拟结果,进一步验证算法精度.若干计算结果均表明,文中算法具有良好的通用性,适用于井中电磁、航空电磁,环境地球物理等非均匀且各向异性介质中的电磁感应基础研究.