Linear analysis of concrete arch dams including dam–water–foundation rock interaction considering spatially varying ground motions

The available substructure method and computer program for earthquake response analysis of arch dams, including the effects of dam–water–foundation rock interaction and recognizing the semi‐unbounded size of the foundation rock and fluid domains, are extended to consider spatial variations in ground motions around the canyon. The response of Mauvoisin Dam in Switzerland to spatially varying ground motion recorded during a small earthquake is analyzed to illustrate the results from this analysis procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear earthquake analysis of high arch dam–water–foundation rock systems

A nonlinear finite element model for earthquake response analysis of arch dam–water–foundation rock systems is proposed in this paper. The model includes dynamic dam–water and dam–foundation rock interactions, the opening of contraction joints, the radiation damping of semi‐unbounded foundation rock, the compressibility of impounded water, and the upstream energy propagating along the semi‐unbounded reservoir. Meanwhile, a new equivalent force scheme is suggested to achieve free‐field input in the model. The effects of the earthquake input mechanism, joint opening, water compressibility, and radiation damping on the earthquake response of the Ertan arch dam (240 m high) in China are investigated using the proposed model. The results show that these factors significantly affect the earthquake response of the Ertan arch dam. Such factors should therefore be considered in the earthquake response analysis and earthquake safety evaluation of high arch dams. Copyright © 2011 John Wiley & Sons, Ltd.     

Direct finite element method for nonlinear earthquake analysis of 3‐dimensional semi‐unbounded dam–water–foundation rock systems

A direct finite element method for nonlinear earthquake analysis of 2‐dimensional dam–water–foundation rock systems has recently been presented. The analysis procedure uses standard viscous‐damper absorbing boundaries to model the semi‐unbounded foundation‐rock and fluid domains and specifies the seismic input as effective earthquake forces at these boundaries. Presented in this paper is a generalization of the direct finite element method with viscous‐damper boundaries to 3‐dimensional dam–water–foundation rock systems. Step‐by‐step procedures for determining the effective earthquake forces starting from a ground motion specified at a control point on the foundation‐rock surface is developed, and several numerical examples are computed and compared with independent benchmark solutions to demonstrate the effectiveness of the analysis procedure for modeling 3‐dimensional systems.     

Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of concrete gravity dams

As the forward directivity and fling effect characteristics of the near-fault ground motions, seismic response of structures in the near field of a rupturing fault can be significantly different from those observed in the far field. The unique characteristics of the near-fault ground motions can cause considerable damage during an earthquake. This paper presents results of a study aimed at evaluating the near-fault and far-fault ground motion effects on nonlinear dynamic response and seismic damage of concrete gravity dams including dam-reservoir-foundation interaction. For this purpose, 10 as-recorded earthquake records which display ground motions with an apparent velocity pulse are selected to represent the near-fault ground motion characteristics. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions. The Koyna gravity dam, which is selected as a numerical application, is subjected to a set of as-recorded near-fault and far-fault strong ground motion records. The Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is employed in nonlinear analysis. Nonlinear dynamic response and seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. Both local and global damage indices are established as the response parameters. The results obtained from the analyses of the dam subjected to each fault effect are compared with each other. It is seen from the analysis results that the near-fault ground motions, which have significant influence on the dynamic response of dam–reservoir–foundation systems, have the potential to cause more severe damage to the dam body than far-fault ground motions.     

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.     

Dam-foundation rock interaction effects in frequency-response functions of arch dams

The linear response of a selected arch dam to harmonic upstream, vertical or cross-stream ground motion is presented for a wide range of the important system parameters characterizing the properties of the dam, foundation rock, impounded water and reservoir boundary materials. Based on these frequency-response functions, the dam-foundation rock interaction effects in the dynamic response of arch dams are investigated.     

古田地震水口水电站重力坝强震观测记录的谱结构特征

通过对水口水电站重力坝强震反应台站在古田地震中获取的强震反应观测资料进行信噪比、反应谱和功率谱分析,得到如下结论:①大坝在0.7～15 Hz频率段的振动特性较为可信;②坝基和自由场输入地震动富于高频,峰值加速度反应谱存在较大差异;③坝基输入地震动存在差异性,建议今后此类大坝抗震设计时考虑多点地震动输入;④单个卓越频率携带的能量对反应谱影响不大,反应谱是和输入地震动总能量相关的;⑤坝体刚度较大,此次地震中还处于线弹性状态。初步了解了强震记录的地震动特性和大坝结构的抗震性能,对认识水库地震近场地震动特性和重力坝地震反应有一定的参考意义。     

Direct finite element method for nonlinear analysis of semi‐unbounded dam–water–foundation rock systems

A direct finite element method is presented for nonlinear earthquake analysis of interacting dam–water–foundation rock systems. The analysis procedure applies viscous damper absorbing boundaries to truncate the semi‐unbounded fluid and foundation‐rock domains and specifies at these boundaries effective earthquake forces determined from the design ground motion defined at a control point on the free surface. The analysis procedure is validated numerically by computing the frequency response functions and transient response of an idealized dam–water–foundation rock system and comparing with results from the substructure method. Because the analysis procedure is applicable to nonlinear systems, it allows for modeling of concrete cracking, as well as sliding and separation at construction joints, lift joints, and at concrete–rock interfaces. Implementation of the procedure is facilitated by commercial finite element software with nonlinear material models that permit modeling of viscous damper boundaries and specification of effective earthquake forces at these boundaries. Copyright © 2017 John Wiley & Sons, Ltd.     

Frequency response functions for arch dams: Hydrodynamic and foundation flexibility effects

The linear response of a selected arch dam to harmonic upstream, cross-stream or vertical ground motion is presented for a wide range of the important system parameters characterizing the properties of the dam, impounded water, reservoir boundary materials and foundation rock. Based on these frequency response functions, the hydrodynamic and foundation flexibility effects in the dynamic response of arch dams are investigated.     

Dynamics of submerged intake towers including interaction with dam and foundation

The dynamics of a coupled concrete gravity dam-intake tower–reservoir water–foundation rock system is numerically studied considering two hollow slender towers submerged in reservoir of gravity dam. The system is investigated in the frequency-domain using frequency response functions of the dam and the towers, and in the time-domain using time-history seismic analysis under a real earthquake ground motion. The analyzes are separately conducted under horizontal and vertical ground motions. The coupled system is three-dimensionally modeled using finite elements by Eulerian–Lagrangian approach. It is shown that presence of the dam significantly influences the dynamic response of the towers under both horizontal and vertical excitations; however the dam is not affected by the towers. When the dam is present in the model, the water contained inside the towers has different effects if the foundation is rigid, but it alleviates the towers motion if the foundation is flexible. It is concluded that the effects of foundation interaction are of much importance in the response of tall slender towers when they are located near concrete gravity dams.     

System identification of a concrete arch dam and calibration of its finite element model

A magnitude 4.3 earthquake occurred near Pacoima Dam on 13 January 2001. An accelerometer array that had been upgraded after the Northridge earthquake recorded the motion with 17 channels on the dam and the dam–foundation interface. Using this data, properties of the first two modes are found from a system identification study. Modal properties are also determined from a forced vibration experiment performed in 2002 and indicate a significantly stiffer system than is estimated from the 2001 earthquake records. The 2001 earthquake, although small, must have induced temporary nonlinearity. This has implications for structural health monitoring. The source of the nonlinear behaviour is believed to be loss of stiffness in the foundation rock. A finite element model of Pacoima Dam is constructed and calibrated to match modal properties determined from the system identification study. A dynamic simulation of the 2001 earthquake response produces computed motions that agree fairly well with the recorded ones. Copyright © 2006 John Wiley & Sons, Ltd.     

Effects of concrete cracking on the earthquake response of gravity dams

Tensile stresses exceeding the tensile strength of concrete can develop in concrete dams subjected to earthquake ground motion. This study examines the earthquake response of gravity dams including tensile cracking of the concrete. The interaction between the dam and compressible water is included in the analysis using a numerical procedure for computing the non-linear dynamic response of fluid-structure systems. The crack band theory is used to model tensile cracking with modifications to allow for the large finite elements necessary for dam analysis. The earthquake response of a typical gravity dam monolith shows that concrete cracking is an important non-linear phenomenon. Cracking is concentrated near the base of the dam and near the discontinuities in the face slope. The extensive cracking, which develops due to ground motion typical of maximum credible earthquakes, may affect the stability of dams during and after strong earthquakes.     

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.     

多维地震动各方向相关性对拱坝动应力的影响

本文将随机振动的虚拟激励法与拱坝-地基动力相互作用FE-BE-IBE时域模型结合，发展了一个可以考虑多维随机地震动作用下的拱坝动力响应计算模型，并用Monte Garlo方法对模型进行了验证，计算结果表明，地震动分量的相关性对结构的动力响应存在一定影响，合理考虑地震动各方向分量的相关性可以更好地计算实际地震作用下的拱坝动力响应。     

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.     

SV波斜入射下混凝土重力坝易损性分析

易损性分析是评估不同强度地震作用下混凝土重力坝各级破坏概率的有效方法。目前重力坝易损性分析通常假定地震波为垂直入射,然而在近断层区域,地震波往往是倾斜入射的,地震波斜入射对重力坝地震响应有显著影响。从太平洋地震工程研究中心数据库选取16条地震动记录,采用黏弹性人工边界结合等效节点荷载实现SV波斜入射波动输入。采用增量动力分析方法对地震动峰值加速度进行调幅,以印度Koyna混凝土重力坝为研究对象,以坝顶相对位移为抗震性能指标,建立SV波斜入射下重力坝不同震损等级的易损性曲线。结果表明,与垂直入射相比,相同震损等级和相同地震动强度下,斜入射时重力坝破坏概率减小;当PGA接近重力坝实际遭受的地震动强度时,入射角为15°和30°时破坏概率与垂直入射相比最大减小率分别为27.3%和68.2%;各地震强度下,15°和30°斜入射相对于垂直入射的破坏概率差异值最大分别达36.6%、83.9%。因此,混凝土重力坝抗震性能分析应考虑地震波斜入射的影响。研究结果也可为近断层区域混凝土重力坝安全风险评估提供参考。     

Hydrodynamic effects in dynamic response of simple arch dams

The dynamic responses of simple arch dams, with different radius to height ratios are analysed for three conditions: the dam alone without water, and the dam with full reservoir, considering water to be compressible in one case and neglecting water compressibility in the other case. The complex frequency response functions for accelerations at the dam crest due to the three components of ground motion—upstream-downstream component, cross-stream component and vertical component–are presented. Based on these results, the effects of dam-water interaction, of water compressibility, and of bank motions on dam response are investigated.     

Nonlinear seismic response analysis of arch dam-foundation systems- part I dam-foundation rock interaction

The arch dam–foundation rock dynamic interaction and the nonlinear opening and closing effects of contact joints on arch dam are important to the seismic response analysis of arch dams. Up to date, there is not yet a reasonable and rigorous procedure including the two factors in seismic response analysis. The methods for the analysis of arch dam–foundation rock dynamic interaction in frequency domain are not suitable to the problem with nonlinear behaviors, in this paper, so an analysis method in time domain is proposed by combining the explicit finite element method and the transmitting boundary, and the dynamic relaxation technique is adopted to obtain the initial static response for dynamic analysis. Moreover, the influence of arch dam–foundation dynamic interaction with energy dispersion on seismic response of designed Xiaowan arch dam in China is studied by comparing the results of the proposed method and the conventional method with the massless foundation, and the local material nonlinear and nonhomogeneous behaviors of foundation rock are also considered. The reservoir water effect is assumed as Westergaard added mass model in calculation. The influence of the closing–opening effects of contact joints of arch dam on the seismic response will be studied in another paper.     

Seismic failure modeling of concrete dams considering heterogeneity of concrete

Study on the failure process of high concrete dams subjected to strong earthquakes is crucial to reasonable evaluation of their seismic safety. Numerical simulation in this aspect involves dynamic failure analysis of big bulk concrete dam subjected to cyclic loading. The Rock Failure Process Analysis (RFPA) proposed by C.A. Tang, with successful applications to failure modeling of rock and concrete specimens mainly subjected to static loading, is extended for this purpose. For using the proposed model, no knowledge on the cracking route needs to be known beforehand, and no remeshing is required. Simulation of the whole process of elastic deformation, initiation and propagation of microcracks, severe damage and ultimate failure of concrete dams in earthquakes with a unified model is enabled. The model is verified through a shaking table test of an arch dam. Finally a practical gravity dam is employed as a numerical example. Considering the uncertainty in ground motion input and concrete material, typical failure process and failure modes of gravity dam are presented. Several small cracks may occur due to tension particularly at dam neck, dam faces and dam heel, and a few of them evolve into dominant ones. Relatively smaller earthquake may cause damage to the dam neck while a bigger one may bring on cracks at lower parts of the dams. Cracking at the dam bottom may incline to a direction almost perpendicular to the downstream face after propagating horizontally for a certain distance when the shaking is strong enough.     

Seismic failure modeling of concrete dams considering heterogeneity of concrete

Study on the failure process of high concrete dams subjected to strong earthquakes is crucial to reasonable evaluation of their seismic safety. Numerical simulation in this aspect involves dynamic failure analysis of big bulk concrete dam subjected to cyclic loading. The Rock Failure Process Analysis (RFPA) proposed by C.A. Tang, with successful applications to failure modeling of rock and concrete specimens mainly subjected to static loading, is extended for this purpose. For using the proposed model, no knowledge on the cracking route needs to be known beforehand, and no remeshing is required. Simulation of the whole process of elastic deformation, initiation and propagation of microcracks, severe damage and ultimate failure of concrete dams in earthquakes with a unified model is enabled. The model is verified through a shaking table test of an arch dam. Finally a practical gravity dam is employed as a numerical example. Considering the uncertainty in ground motion input and concrete material, typical failure process and failure modes of gravity dam are presented. Several small cracks may occur due to tension particularly at dam neck, dam faces and dam heel, and a few of them evolve into dominant ones. Relatively smaller earthquake may cause damage to the dam neck while a bigger one may bring on cracks at lower parts of the dams. Cracking at the dam bottom may incline to a direction almost perpendicular to the downstream face after propagating horizontally for a certain distance when the shaking is strong enough.