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.     

Fluid–foundation interaction in the seismic response of gravity dams

The seismic response of a dam is strongly influenced by its interaction with the water reservoir and the foundation. The hydrodynamic forces in the reservoir are in turn affected by radiation of waves towards infinity, wave absorption at the reservoir bottom, and cross-coupling between the foundation below the dam and the reservoir bottom. The fluid–foundation interaction effect, i.e. the wave absorption along the reservoir bottom, can be accounted for by using either an approximate one-dimensional (1D) wave propagation model or a rigorous analysis of interaction between the flexible soil along the base and the water. The rigorous approach requires enormous computational effort because of (a) cross-coupling between the foundation of the dam and the soil below the reservoir and (b) frequency dependence of the boundary condition along the fluid-foundation interface. The analysis can be simplified by ignoring the cross-coupling and by using the approximate 1D wave propagation model. The effects of each of these two simplifications on the accuracy and computational efficiency of the procedure used for the seismic response analysis of a dam are examined. Analytical results are presented for the complex frequency-response functions as well as the time histories of the response of Pine Flat dam to Taft and E1 Centro ground motions.     

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.     

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.     

Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

The important effects of bottom sediments on the seismic response of arch dams are studied in this paper. To do so, a three‐dimensional boundary element model is used. It includes the water reservoir as a compressible fluid, the dam and unbounded foundation rock as viscoelastic solids, and the bottom sediment as a two‐phase poroelastic domain with dynamic behaviour described by Biot's equations. Dynamic interaction among all those regions, local topography and travelling wave effects are taken into account. The results obtained show the important influence of sediment compressibility and permeability on the seismic response. The former is associated with a general change of the system response whereas the permeability has a significant influence on damping at resonance peaks. The analysis is carried out in the frequency domain considering time harmonic excitation due to P and S plane waves. The time‐domain results obtained by using the Fourier transform for a given earthquake accelerogram are also shown. The possibility of using simplified models to represent the bottom sediment effects is discussed in the paper. Two alternative models for porous sediment are tested. Simplified models are shown to be able to reproduce the effects of porous sediments except for very high permeability values. Copyright © 2004 John Wiley & Sons, Ltd.     

基于相控的振幅补偿法在渤海B油田储层预测中的应用

渤海B油田主要目的层为东营组,与上覆馆陶组底部相距50~80 m。馆陶组底部发育1套或多套高速高密砾岩,局限分布,致能量损失,使下伏储层的地震响应变弱,严重影响着储层真实范围的识别。为此,本文首先从地震波传播理论出发,分析砾岩致能量的反射与透射损失效应。其次基于正演模拟,分析砾岩致能量损失程度,相同的累积厚度,砾岩的层数越多,损失越大;据正演模拟结果及井震结合,描述3种地震相即单套砾岩、多套砾岩、无砾岩的平面展布形态,再结合地震属性定量分析储层能量损失程度的平面分布范围。然后提取不同地震相的能量补偿因子,提出基于相控的能量补偿法进行相应的振幅补偿,即单套砾岩造成的能量损失主要进行反射系数补偿,对多套砾岩造成的能量损失主要进行多次透射系数的补偿。最后定量消除上覆馆陶组砾岩对下伏东营组储层的能量屏蔽影响,刻画出储层的真实平面范围,并获得钻井成功,充分证明了本次研究的有效性,并实现精确预测潜力区域。      

Effect of impervious members and reservoir bottom sediment on dynamic response of embankment dams

In this paper, a systematic investigation into the effect of both the type of impervious members and the reservoir bottom sediment on the dynamic response of embankment dams has been carried out using the finite and infinite element coupled method. It has been demonstrated from the numerical results that: (1) the resonant frequencies of an embankment dam—foundation system with an upstream inclined concrete apron are different from those with a central clay core; (2) the type of impervious members has a significant influence on the amplification factors of the system in the low frequency range of excitation, but has little effect in the high frequency range of excitation; (3) the foundation material of an embankment dam affects the dynamic response of the dam drastically; (4) the inclusion of the reservoir bottom sediment has a considerable effect on amplification factors of embankment dams in the case of P-wave incidences, but has little influence in the case of SV-wave vertical incidences; and (5) the reservoir bottom sediment also has a profound effect on the deformed shape of the embankment dam for both P-wave and SV-wave incidences.     

Dam–water–sediment–rock systems: Seismic analysis

A computational procedure for two-dimensional finite-element analysis of dam–water–sediment–rock systems subjected to seismic excitations is reviewed. In particular, the semidiscrete approximation of the water–sediment–rock region on the upstream side of the dam by means of a hyperelement is described in detail. The sediment is represented in the hyperelement as a fluid-filled porous solid on the basis of the Biot theory of wave propagation in poroelastic media while the water is taken as a compressible, inviscid fluid and the rock as a viscoelastic solid. An application of the procedure to a study of the effects of sediment porosity and thickness on the response of a model dam to horizontal and vertical ground motions is presented and discussed.     

Dam-reservoir-massed foundation system and travelling wave along reservoir bottom

In the present paper, effects of non-uniform excitation due to spatially variation of seismic waves under the reservoir bottom on linear and nonlinear responses of arch dams are studied. Foundation is assumed to be massed and infinite elements are utilized to model semi-infinite medium via the far-end boundary of the foundation FE model. A continuum crack propagation model based on the smeared crack approach in 3D space is introduced. Reservoir's water is assumed compressible and the coupled system is solved using the staggered method. As a case study, Amir-Kabir double curvature arch dam in Iran is selected to investigate seismic behavior of the system. Two cases are analyzed in which wave travelling velocities are taken as 650 m/s and infinity. According to the results, non-uniform excitation leads to reduction in seismic response of the system and, in addition, frequency content of the response is different completely in comparison with the system under the uniform excitation.     

Cone models for a soil layer on a flexible rock half-space

A modified truncated cone model is used to calculate approximately the dynamic response of a disk on the surface of a soil layer resting on flexible rock. The procedure is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient —α at the layer–rock interface is no longer equal to ?1. The modified value of α can be determined straightforwardly by considering one-dimensional wave propagation along the cone. The low- and high-frequency limits lead to a frequency-independent α, which allows the dynamic analysis to be performed directly in the familiar time domain. This cone represents a wave pattern with amplitude decay and also incorporates the reflection at the free surface and the reflection-refraction at the layer–rock interface. The results for the static stiffness of the disk are highly accurate for a wide range of geometrical and material properties of the layer and the rock. For the dynamic stiffness the agreement with the exact solution is satisfactory.     

有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

Effects of sedimentary material on the response of concrete gravity dams

The transient response of a concrete gravity dam to a selected earthquake record is determined in order to evaluate the significance of the sedimentary material accumulating on the bottom of the reservoir. The sediment is modelled as a two-phase medium (fluid-filled, poroelastic solid), and the analysis is carried out accounting for all interactions between system components (dam, water, sediment, foundation).     

深厚库底回填料上面板堆石坝动力反应分析

深厚库底回填料是影响面板堆石坝动力响应的重要因素之一。为深入研究深厚库底回填料对面板堆石坝动力响应的影响,基于某拟建抽水蓄能电站,采用三维动力有限元分析系统研究其上库面板坝的地震反应,主要包括坝体加速度、面板动力响应、接缝变位情况以及库底防渗土工膜的动应变等。计算结果表明:由于库底回填料的存在,坝体加速度放大效应被明显削弱;面板周边以受拉为主,中部大部分区域受压;垂直缝呈现出周边张开、中间闭合的趋势;土工膜的顺河向和坝轴向的动拉应变皆小于屈服应变,最大应变出现在库底材料分界处,为提高坝体渗透安全性,建议对主堆石区与连接板相接处的回填料进行适当范围换填的处理措施。研究成果可以为类似工程提供参考。     

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.     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex.A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed.The formula consists of a free stream velocity and a defect function which contains a phase-lead,boundary layer thickness and mobile sediment bed.Phase-lag of sediment movement is considered in the formula for the mobile sediment bed.The formula needs six dependent variables about asymmetric wave and sediment characteristics.Asymmetry effects on parameters(orbital amplitude,roughness height,bed shear stress,and boundary layer thickness)are properly considered such that the formula can yield velocity differences among onshore,offshore,acceleration,and deceleration stages.The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness.In addition,a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow.Results of the formula are as good as that of a two-phase numerical model.Sheet flow transport induced by asymmetric waves,and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves,can be adequately estimated by the formula with a power sediment concentration function.     

Influence of reservoir geometry and conditions on the seismic response of arch dams

An analysis of the influence that reservoir levels and bottom sediment properties (especially on the degree of saturation) have on the dynamic response of arch dams is carried out. For this purpose, a Boundary Element Model developed by the authors that allows the direct dynamic study of problems that incorporate scalar (dammed up water), viscoelastic (dam and soil site) and poroelastic media (bottom sediments in the reservoir) is used. All of the regions are discretized using boundary elements, later formulating equations of compatibility and equilibrium that allow their interaction to be rigorously established. The seismic excitation consists in plane longitudinal waves (P waves) and shear waves (S waves) impinging the dam site with an angle of vertical incidence. The analysis is carried out in the frequency domain, and the time response is obtained, for synthesized artificial accelerograms defined in terms of the elastic response spectrum taken from Eurocode 8, using a FFT algorithm. The variables used to characterize the response are: Amplitude of the complex-valued frequency-response function, acceleration response spectra and the integral of velocity of points located at the structure. These variables clearly indicate the importance that the factors analyzed have on the dynamic response.     

Interactions among waves,current, and mud: Numerical and laboratory studies

Interactions between waves, current, mud and turbulence are very complicated in the coastal and estuarine turbid waters. It is still necessary to improve our understanding of the fundamental physical processes governing the cohesive sediment transport in the coastal and estuarine waters. A numerical model is developed to study the interactions among waves, current, and mud. An eddy viscosity model for wave and current is proposed in order to close the equations of wave motion or of current motion in a combined flow, respectively. The equations of mud transport are derived based on the visco-elastic properties of mud. Coupling the equations of wave motion or of current motion for water layer with those of mud layer can give (1) wave height; (2) distributions of current velocities in the water layer; (3) distributions of transport velocities at the water–mud interface; and (4) distributions of mass transport velocities within the mud layer. These modeled results are in a reasonable agreement with experimental results. Results suggest that (1) the rate of wave attenuation increases in the opposing currents (currents against in the direction in which the waves propagate) and decreases in the following currents (currents in the same direction as that in which the waves propagate); (2) the opposing currents would have more significant effects on the rate of wave height attenuation than the following currents; (3) the effect of current on the rate of wave attenuation on the muddy bottom is larger than that on the rigid bottom; (4) mud transport rate increased in the following currents but decreased in the opposing currents; and (5) the rate of wave height attenuation on the mud bottom is one order of magnitude larger than that on the rigid bottom.     

Numerical simulation of reservoir sediment and effects on hydro‐dynamic response of arch dams

Based on the dynamic theory for saturated porous media by Biot (Journal of the Acoustical Society of America 1956; 28 : 168–178), a numerical model is presented to analyse the reflection behaviours of reservoir sediment and compared with those from the visco‐elastic model. It is concluded that the two models give very similar results of reflection coefficient α within the frequency range of interest. Then, using the two models, the change of the reflection coefficients α with various sedimentation parameters and excitation frequencies are studied in detail. The results are further used in the analysis of response functions of hydro‐dynamic pressures on, and structural displacements of the Xiang Hong Dian arch dam, for which some results from a field vibration test are available. It appears that effects of water compressibility with sediment reflection on hydro‐dynamic pressures and structural response are not significant for this specific case. Copyright © 2001 John Wiley & Sons, Ltd.     

地震槽波的数学-物理模拟初探

针对地震槽波在低速层的传播特性,开展了煤层内地震槽波勘探的数值模拟和物理模拟研究的初探工作.在数值模拟研究方面,采用交错网格有限差分法对煤层中的地震槽波进行三分量全波场模拟.基于波场快照和人工合成地震记录研究了不同模型中的波场特征和各种波型的传播规律.在物理模拟方面,通过选用不同配比的环氧树脂和硅橡胶类材料构建地震槽波物理模型,利用透射法和反射法观测系统获得了清晰的地震槽波记录以研究槽波的地震学特征.研究表明,在煤层内槽波的地震波场中,Love型槽波的能量小于Rayleigh型槽波的SV分量,大于Rayleigh型槽波的SH分量.相对于Love型槽波和Rayleigh型槽波的SH分量,Rayleigh型槽波的SV分量在围岩中的泄露能量较强.在煤层界面附近的围岩中,地震波仍以槽波形式传播,随着距离的增加能量逐渐衰减.随着煤层变薄,煤层槽波主频向高频方向移动,频散现象增强,传播速度增大.