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.     

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.     

Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods

Using reciprocal theorems for dynamic and static boundary value problems, boundary integral equations are presented for wave propagation in elastic, isotropic media and compressible, inviscid fluids in the time domain as well as in the frequency domain. For the analysis of fluid–soil and fluid–structure systems, suitable coupling conditions are prescribed along the interfaces. The numerical treatment of the boundary integral equations consists of a point collocation and of a discretization of the boundary, in which constant and linear approximation functions are assumed. Step-by-step integration is applied to the time-dependent equations, where again the states are taken to be linear and constant over each time interval. These boundary element procedures are used to analyse the response of dams due to horizontal and vertical ground motions considering dam–water interaction and absorption of hydrodynamic pressure waves at the reservoir bottom or at the far end into the soil medium. Both the frequency response and the impulse generated transient response are investigated.     

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 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.     

A discontinuous Galerkin method for seismic soil–structure interaction analysis in the time domain

A technique for modeling transient wave propagation in unbounded media is extended and applied to seismic soil–structure interaction analysis in the time domain. The technique, based on the discontinuous Galerkin method, requires lower computational cost and less storage than the boundary element method, and the time‐stepping scheme resulting from Newmark's method in conjunction with the technique is unconditionally stable, allowing for efficient and robust time‐domain computations. To extend the technique to cases characterized by seismic excitation, the free‐field motion is used to compute effective forces, which are introduced on the boundary of the computational domain containing the structure and the soil in the vicinity of the structure. A numerical example on a dam–foundation system subjected to seismic excitation demonstrates the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

An investigation into the seismic behaviour of dams using dynamic centrifuge modelling

Dynamic response of dams is significantly influenced by foundation stiffness and dam-foundation interaction. This in turn, significantly effects the generation of hydrodynamic pressures on upstream face of a concrete dam due to inertia of reservoir water. This paper aims at investigating the dynamic response of dams on soil foundation using dynamic centrifuge modelling technique. From a series of centrifuge tests performed on model dams with varying stiffness and foundation conditions, significant co-relation was observed between the dynamic response of dams and the hydrodynamic pressures developed on their upstream faces. The vertical bearing pressures exerted by the concrete dam during shaking were measured using miniature earth pressure cells. These reveal the dynamic changes of earth pressures and changes in rocking behaviour of the concrete dam as the earthquake loading progresses. Pore water pressures were measured below the dam and in the free-field below the reservoir. Analysis of this data provides insights into the cyclic shear stresses and strains generated below concrete dams during earthquakes. In addition, the sliding and rocking movement of the dam and its settlement into the soil below are discussed.     

On rigid foundations subjected to seismic waves

In the analysis of structural foundations for seismic loads, it is customary to distinguish two types of soil-structure interaction effect: kinematic interaction (or wave passage), and inertial interaction. The former refers to the phenomenon of wave scattering, which occurs because the foundation is much stiffer than the surrounding soil and cannot accommodate to its distortions. Inertial interaction, on the other hand, is caused by feedback of kinetic energy of the structure into the soil. This paper is concerned only with the first phenomenon. The rigorous analysis of rigid, embedded foundations subjected to seismic disturbances requires, in general, substantial computational effort. Indeed, a typical analysis would normally require models with finite elements and/or boundary elements. Although such methods may be used to find an accurate solution to the problem of kinematic interaction, their use is not always warranted, given the many uncertainties involved and the multitude of assumptions that must be considered. Hence, approximate solutions are attractive for this problem. One such approximate method is the remarkably simple algorithm proposed by Iguchi.³ This paper presents first an appraisal of this method by way of a comparison with accurate numerical solutions for cylindrical foundations; next the algorithm is applied to rectangular (prismatic) foundations. It is found that Iguchi's method gives results that are adequate for engineering purposes, even if not entirely accurate.     

考虑地基不均匀性核反应堆地震响应分析

核电站结构地震响应主要取决于地震动特性、地基土特性以及结构特性.本文以某核电站反应堆厂房结构为对象,研究了考虑土-结构相互作用的不均匀地基土对核反应堆地震响应的影响,包括核反应堆和地基的最大加速度、楼层最大相对位移以及楼层多阻尼反应谱.结构地震响应分析使用SUPERFLUSH/2D软件,地基模型由ANSYS建模;核反应...     

Embedded foundation in layered soil under dynamic excitations

The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.     

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.     

Two‐dimensional modelling of ice cover effects for the dynamic analysis of concrete gravity dams

A two‐dimensional numerical model for determining the effects of the presence of an ice cover on the dynamic behaviour of large gravity dams is presented. Analytical predictions are compared to results obtained during a series of extensive dynamic tests on a large gravity dam. Data were obtained during summer and severe winter conditions to investigate the dynamic interactions between the dam, foundation, reservoir and the ice cover. The analysis includes ice‐reservoir interaction as well as the effects of water compressibility, flexible foundation and reservoir bottom absorption. Good agreement with the experimental findings is obtained. Copyright © 2002 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.     

Three-dimensional nonlinear seismic analysis of concrete faced rockfill dams subjected to scattered P,SV, and SH waves considering the dam–foundation interaction effects

In this study, the nonlinear seismic analysis of a typical three-dimensional concrete faced rockfill dam is reported. Three components of the Loma Prieta (Gilroy 1 station) earthquake acceleration time history are used as input excitation. The dam under study is considered as if it were located in a prismatic canyon with a trapezoidal cross-section. A nonlinear model for the rockfill material is used, and contact elements with Coulomb friction law are utilized at the slab–rockfill interface. Vertical joints in the face slab are also considered in the finite element model. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite element method (SBFEM), is used to obtain the scattered motion and interaction forces along the canyon. The dam is subjected to spatially variable P, SV, and SH waves, and the effect of dam–foundation interaction and the reservoir water effects are considered. The results are compared with the non-scattered input motion analysis. Results of the analyses indicate that due to applying the scattered motion to the canyon the response of the dam and concrete face slab significantly increases. The reservoir water pressure affects the tensile stresses induced in the face slab by reducing the uplift movement of the concrete panels.Large horizontal axial forces are induced in the face slab due to out-of-phase and out-of-plane motions of the abutments. Although the normal movements of vertical joints are reduced due to the reservoir water confinement, the opening movements are still significant, and the local failure of construction joints is inevitable.     

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.     

Earthquake soil‐structure interaction of nuclear power plants,differences in response to 3‐D, 3 × 1‐D,and 1‐D excitations

In soil‐structure interaction modeling of systems subjected to earthquake motions, it is classically assumed that the incoming wave field, produced by an earthquake, is unidimensional and vertically propagating. This work explores the validity of this assumption by performing earthquake soil‐structure interaction modeling, including explicit modeling of sources, seismic wave propagation, site, and structure. The domain reduction method is used to couple seismic (near‐field) simulations with local soil‐structure interaction response. The response of a generic nuclear power plant model computed using full earthquake soil‐structure interaction simulations is compared with the current state‐of‐the‐art method of deconvolving in depth the (simulated) free‐field motions, recorded at the site of interest, and assuming that the earthquake wave field is spatially unidimensional. Results show that the 1‐D wave‐field assumption does not hold in general. It is shown that the way in which full 3‐D analysis results differ from those which assume a 1‐D wave field is dependent on fault‐to‐site geometry and motion frequency content. It is argued that this is especially important for certain classes of soil‐structure systems of which nuclear power plants subjected to near‐field earthquakes are an example.     

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.