Numerical simulation of earthquake excited dam-reservoirs with irregular geometries using an immersed boundary method

In this work, a ghost-cell immersed boundary method is proposed for the hydrodynamic response of earthquake excited dam-reservoirs. The numerical method employs a second order accurate two-step projection algorithm including compressibility effects in pressure field due to earthquake. The effects of reservoir bottom absorption are treated by introducing damping terms into the momentum equations. Hydrodynamic response of earthquake excited dam with a sloping face is simulated to demonstrate the accuracy of the present numerical method. Numerical results compared with previous numerical and analytical solutions show that the present immersed boundary method can accurately compute the hydrodynamic forces on inclined and curved dam faces including the effects of water compressibility and reservoir bottom absorption for the possibility of resonance. The proposed numerical method was shown to have significant advantages in computational time and memory usage for the hydrodynamic simulation of large dam-reservoirs with arbitrary geometries. Hydrodynamic forces on a double curvature arch dam subjected to real earthquake induced ground motion are also simulated to demonstrate the capability of the method.     

Effect of reservoir bottom on earthquake response of concrete dams

The absorption of hydrodynamic pressure waves at the reservoir bottom has dominant effects on the structural response of the dam when subjected to ground motion. In the present study, a model is proposed for the absorption effects of the reservoir bottom in the earthquake analysis of dams. The model utilizes the wave reflection coefficient approach and is based on the solution of the wave equation in a sediment layer of viscoelastic material with a constant thickness overlying an elastic, semi-infinite foundation. Numerical studies were conducted to evaluate the effect of the sediment layer thickness and material properties as well as the effect of reflection of waves from the underlying rock. It is shown that the current approach of assuming the wave reflection coefficient at the reservoir bottom based on the characteristics of the sediment material and excluding the effect of the reflected waves from the underlying rock, may significantly underestimate the seismic response of the dam.     

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.     

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.     

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.     

Earthquake analysis of arch dams including dam-water-foundation rock interaction

The available substructure method and computer program for the earthquake response analysis of arch dams, including the effects of dam-water interaction, reservoir boundary absorption, and foundation rock flexibility, is extended to include the effects of dam-foundation rock interaction with inertia and damping of the foundation rock considered. Efficient techniques are developed for evaluating the foundation impedance terms, computationally the most demanding part of the procedure.     

江口水库诱发地震的有限元分析

本文利用有限元方法计算了武隆江口水库蓄水后可能引起的水库诱发地震。在水库底部有断裂通过时,对江口水库在不同的假设宽度情况下进行了分析,给出了水库底部各处的最大剪应力。结果表明,水库底部岩石发生破坏的可能性很大,极可能引起水库的诱发地震,其最大震级为5级左右。     

Integrative seismic safety evaluation of a high concrete arch dam

An integrative seismic safety evaluation of an arch dam should include all sources of nonlinearities, dynamic interactions between different components and the external loads. The present paper investigates the calibration procedure and nonlinear seismic response of an existing high arch dam. The first part explains the conducted analyses for the static and thermal calibrations of the dam based on site measurements. The second part investigates the nonlinear seismic analysis of the calibrated model considering the effect of joints, cracking of mass concrete, reservoir–dam–rock interaction, hydrodynamic pressure inside the opened joints and the geometric nonlinearity. Penetration of the water inside the opened joints accelerates the damage process. The integrative seismic assessment of a case study shows that the dam will fail under the maximum credible earthquake scenario. The dam is judged to be severely damaged with extensive cracking and the joints undergo opening/sliding. A systematic procedure is proposed for seismic and post-seismic safety of dams.     

Earthquake analysis of arch dams including dam–water interaction,reservoir boundary absorption and foundation flexibility

The available substructure method and computer program for the steady-state, harmonic response analysis of arch dams, including the hydrodynamic effects, are extended to consider flexibility of the foundation rock and to include Fourier synthesis of harmonic responses to obtain the earthquake response of arch dams. By efficient evaluation of hydrodynamic terms, interpolation of frequency response functions and more efficient computer programming, the computational costs for analysing arch dams have been reduced by an order of magnitude relative to the available procedure.     

Transient pressures in hydrotechnical tunnels during earthquakes

Transient pressures generated by earthquake shaking in hydrotechnical tunnels are evaluated by the discrete Fourier transform technique. The effects of the horizontal ground motion accelerating the closed downstream tunnel gate, as well as the upstream dam face, and the influence of the vertical motion of the reservoir floor are considered in this analysis. An example of a typical bottom outlet is analysed by subjecting it to several computed accelerograms. It is shown that high hydrodynamic pressures can be developed, several times larger than the hydrostatic pressure.     

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.     

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.     

Earthquake analysis of concrete gravity dams including dam-water-foundation rock interaction

A general procedure for analysis of the response of concrete gravity dams, including the dynamic effects of impounded water and flexible foundation rock, 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 the dam. The system is analysed under the assumption of linear behaviour for the concrete, foundation rock and water. The complete system is considered as composed of three substructures—the dam, represented as a finite element system, the fluid domain, as a continuum of infinite length in the upstream direction, and the foundation rock region as a viscoelastic half-plane. The structural displacements of the dam are expressed as a linear combination of Ritz vectors, chosen as normal modes of an associated undamped dam-rock system. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only a few Ritz vectors. The generalized displacements due to earthquake motion are computed by synthesizing their complex frequency responses using Fast Fourier Transform procedures. The stress responses are calculated from the displacements. An example analysis is presented to illustrate results obtained from this analytical procedure. Computation times for several analyses are presented to illustrate the effectiveness of the procedure.     

关于紫坪铺水库蓄水是否与汶川地震有关的影响因素综合分析

汶川地震后,紫坪铺水库蓄水是否触发了汶川地震在国内外学术界引起了广泛关注.除定性讨论外,许多学者也采用定量分析的方法进行了计算,但因计算结果不同而得出了不同的结论.本文从目前紫坪铺水库蓄水不同研究组定量计算中出现的争议为出发点,通过对水库蓄水定量计算基本原理和可能引起计算结果差异可能因素的分析,找出定量计算中的关键影响因素,了解目前水库蓄水定量计算中存在的不确定性问题所在.初步结果显示:计算方法、模型维数、扩散模型、震源参数和扩散系数等的取值不同是造成计算结果差异的主要因素,特别是裂隙岩体的扩散系数.在紫坪铺水库定量计算中模型维数的差别使得汶川地震震源处的库仑应力变化计算结果相差约3倍;仅考虑断层渗透率(把岩体渗透率视为无穷大)或仅考虑均匀各向同性的岩体渗透率(忽视断层渗透率),均具有片面性;震源机制解断层走向倾角的差异,会显著影响库仑应力大小计算结果,可到达2~7倍;不同扩散系数下,孔隙压力相差可达几百倍."紫坪铺水库蓄水是否能够触发汶川大地震的发生?",鉴于目前的研究成果,库仑应力变化在kPa量级,尚不能排除触发的可能性,但得出的蓄水震源处的库仑应力变化太低,在背景构造应力场不明确的情况下,也不能确定一定有联系.在未来的工作中需有针对性的进行野外考察和室内试验,改进模型,采用高性能模拟分析计算,并在此基础上对中国和世界多个水库地震触发机制进行对比研究,探讨不同机制下水库地震触发机制特点,进一步量化分析水库地震发生的力学机制及水库对构造活动的影响和作用机理.     

Seismic failure probability of concrete slab on CFR dams with welded and friction contacts by response surface method

In this study, failure probability of the concrete slab on concrete-faced rockfill (CFR) dams with welded and friction contact is investigated under earthquake effects by reliability analysis. For this purpose, Torul CFR dam is selected as an example and numerical solutions are performed by considering combination of reliability analysis–finite element method. 1992 Erzincan earthquake acceleration record is used in the finite element analysis considering deconvolved-base rock input model. In this model, the ground motion to be applied to the foundation base rock is obtained by deconvolution of the free-field surface record. In the materially nonlinear analysis, Drucker–Prager model is used for concrete slab and multi-linear kinematic hardening model is utilized for rockfill. Geometrically nonlinearity is also taken into account. Viscous boundary conditions are defined in the finite element model for both foundation soil and reservoir water. The hydrodynamic pressure of the reservoir water is considered using 2D fluid finite elements based on the Lagrangian approach. Both welded contact and friction contact based on the Coulomb’s friction law are defined in the structural connections. Improved Rackwitz–Fiessler method is used with response surface method in the reliability analysis. The tensile and compression strengths of the concrete slab are utilized in the implicit limit state functions considering various thicknesses. The probability of failure of the most critical points in the concrete slab is obtained. According to this study, the probabilities of failure obtained from the CFR dam including friction contact are lower. When the welded contact is considered in joints, the probability of failure of the concrete slab is 1 due to tensile stress limit state and compression stress limit state only if concrete slab is linear. The most critical probability of failure of the concrete slab appears in the case that the concrete slab is linear and rockfill is materially nonlinear. The probability of failure of the concrete slab decreases if the nonlinearity of the concrete is considered. Also, hydrodynamic pressure decreases the reliability of the concrete slab.     

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.     

考虑动水压力影响的单柱式桥墩地震反应分析

在Morison方程的基础上,用附加水质量法考虑动水压力对桥墩的影响,以单柱式桥墩为研究对象,以ABAQUS有限元软件为计算平台,建立了考虑桩-土动力相互作用的单柱式桥墩地震反应分析模型,考虑土体和桥墩混凝土的动力非线性特征,分析了地震动作用下动水压力对单柱式桥墩的墩顶相对墩底位移、加速度、剪力和弯矩反应的影响,并探讨了水位对单柱式桥墩地震反应特性的影响。结果表明:动水压力改变桥墩的地震反应特性,增大了桥墩顶部相对底部的位移、墩顶绝对加速度和墩底的内力,水位变化影响桥墩的地震反应特性。对于深水桥墩抗震设计计算,考虑动水压力效应、水位变化是有必要的。     

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.     

An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam–reservoir systems

An efficient procedure is developed for the hydrodynamic analysis of dam–reservoir systems. The governing equations of hydrodynamic pressure in the frequency as well as time domain are derived in the framework of the scaled boundary finite element method. The water compressibility and absorption of reservoir sediments can be conveniently taken into consideration. By extending the reservoir to infinity with uniform cross-section, only the dam–reservoir interface needs to be discretized to model the fluid domain, and the hydrodynamic pressure in the stream direction is solved analytically. Several numerical examples including a gravity dam with an inclined upstream face and an arch dam with a reservoir of arbitrary cross-section are provided to demonstrate the computational efficiency and accuracy of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

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.