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.     

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.     

Nonuniform earthquake input for arch dam–foundation interaction

Wave scattering and dam–foundation interaction are important aspects of a realistic earthquake analysis of arch dams. In the first part of this paper it is shown how the motion obtained from a two-dimensional scattering analysis can be used as an input for a three-dimensional dam–foundation analysis. In the second part, a method for calculating the scattered motion is explained. The scattered motion is obtained via the two-dimensional dynamic stiffness matrix. The dynamic stiffness matrix for an out-of-plane motion is calculated by the Complementary-Domain Method (CDM). Some examples are presented to verify the method and to show the influence of the scattering of the seismic ground motion.     

Earthquake analysis of concrete gravity dams including reservoir bottom absorption and dam-water-foundation rock interaction

The available substructure method for the earthquake analysis of concrete gravity dams, including the dynamic effects of the impounded water and the flexible foundation rock, is extended to include the effects of alluvium and sediments invariably present at the bottom of actual reservoirs. Modelled approximately by a reservoir bottom that partially absorbs incident hydrodynamic pressure waves, these effects are incorporated into the continuum solution for the hydrodynamic pressure. The dam-water-foundation rock system is idealized as a two-dimensional system and analysed under the assumption of linear behaviour. An example earthquake analysis is presented to demonstrate the results obtained from the analytical procedure. Computation times for several cases illustrate the efficiency of the analytical procedure. In particular, the additional computation time required to include reservoir bottom absorption is shown to be very small.     

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.     

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.     

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.     

Seismic response of intake towers including dam–tower interaction

The seismic response of the intake–outlet towers has been widely analyzed in recent years. The usual models consider the hydrodynamic effects produced by the surrounding water and the interior water, characterizing the dynamic response of the tower–water–foundation–soil system. As a result of these works, simplified added mass models have been developed. However, in all previous models, the surrounding water is assumed to be of uniform depth and to have infinite extension. Consequently, the considered added mass is associated with only the pressures created by the displacements of the tower itself. For a real system, the intake tower is usually located in proximity to the dam and the dam pressures may influence the equivalent added mass. The objective of this paper is to investigate how the response of the tower is affected by the presence of the dam. A coupled three‐dimensional boundary element‐finite element model in the frequency domain is employed to analyze the tower–dam–reservoir interaction problem. In all cases, the system response is assumed to be linear, and the effect of the internal fluid and the soil–structure interaction effects are not considered. The results suggest that unexpected resonance amplifications can occur due to changes in the added mass for the tower as a result of the tower–dam–reservoir interaction. Copyright © 2008 John Wiley & Sons, Ltd.     

Earthquake response analysis of multistorey buildings including foundation interaction

An efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. The analysis procedure is developed and numerical results are presented to demonstrate that excellent results can be obtained by considering only the first few modes of vibration. As the number of unknowns are reduced by transforming to generalized co-ordinates, the method presented is much more efficient than direct methods.     

Three-dimensional boundary element reservoir model for seismic analysis of arch and gravity dams

The boundary element method has been successfully applied in the past to the analysis of hydrodynamic forces in two-dimensional infinite as well as two- and three-dimensional finite reservoirs subjected to seismic ground motions. This paper presents the results of more recent research on the application of the constant boundary element method to the 3D analysis of reservoir vibration. Special boundary conditions, previously used in the 2D case, to treat infinite radiation damping and damping from foundation soil and banks have been incorporated in this formulation. Numerical results for vibration of a 3D infinite rectangular reservoir as well as of a 3D infinite reservoir impounded by an arch dam are presented and compared with some existing results obtained by other researchers.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

Influence of time-domain dam–reservoir interaction on cracking of concrete gravity DAMS

Based on a non-linear dam-reservoir interaction model, a study investigating the earthquake response of concrete gravity dams is presented. For the propagation of cracks in unreinforced mass concrete, a discrete crack approach formulation based on the finite element method is applied. A special crack element is used to follow a fictitious crack in order to account for a zone of microcracks developing at the crack tip. The reservoir is modelled using the boundary element method. At a fictitious boundary dividing the irregular finite part of the reservoir from the regular infinite part, the loss of energy due to pressure waves moving away towards infinity is taken into account rigorously. Analyses are performed on the tallest non-overflow monolith of the Pine Flat Dam located in Kern County, California. The interaction of a dam, which may exhibit cracks in mass concrete, with a reservoir domain of arbitrary geometry extending to infinity is studied. Some main parameters are investigated. The importance of tools capable of handling the non-linear dam-reservoir interaction is emphasized.     

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.     

A method for coupled arch dam‐foundation‐reservoir seismic behaviour analysis

This paper presents a method for coupled arch dam–foundation–reservoir seismic behaviour analysis. The dam is discretized by finite elements (FE) and the foundation and reservoir are discretized by boundary elements (BE). The opening of contraction joints and the spatial variability of the seismic action is taken into account. The study of Pacoima dam by this method is also presented. The computed results show that no cracks were to be expected due to the vibrations induced during the Feb. 9, 1971 San Fernando earthquake. Copyright © 2000 John Wiley & Sons, Ltd.     

Earthquake response of concrete arch dams: a plastic–damage approach

There are several alternatives to evaluate seismic damage‐cracking behavior of concrete arch dams, among which damage theory is the most popular. A more recent option introduced for this purpose is plastic–damage (PD) approach. In this study, a special finite element program coded in 3‐D space is developed on the basis of a well‐established PD model successfully applied to gravity dams in 2‐D plane stress state. The model originally proposed by Lee and Fenves in 1998 relies on isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to capture inelastic behaviors of concrete in cyclic or dynamic loadings. The present implementation is based on the rate‐dependent version of the model, including large crack opening/closing possibilities. Moreover, with utilizing the Hilber–Hughes–Taylor time integration scheme, an incremental–iterative solution strategy is detailed for the coupled dam–reservoir equations while the damage–dependent damping stress is included. The program is initially validated, and then, it is employed for the main analyses of the Koyna gravity dam in a 3‐D modeling as well as a typical concrete arch dam. The former is a major verification for the further examination on the arch dam. The application of the PD model to an arch dam is more challenging because the governing stress condition is multiaxial, causing shear damage to become more important than uniaxial states dominated in gravity dams. In fact, the softening and strength loss in compression for the damaged regions under multiaxial cyclic loadings affect its seismic safety. Copyright © 2013 John Wiley & Sons, Ltd.     

Earthquake analysis of concrete gravity dams including base sliding

A numerical method, the hybrid frequency-time domain (HFTD) procedure, is used to compute the earthquake response of concrete gravity dams, including sliding along the interface between the dam base and the foundation rock. The solution procedure accounts for the non-linear base sliding behaviour and the frequency-dependent response of the impounded water and flexible foundation rock. A Coulomb friction model represents the force-displacement relationship for sliding at the base interface. Using the solution procedure, an analysis of a typical dam (122 m high) shows that base sliding will occur during a moderate earthquake but the sliding displacement will be a tolerable amount when dam-foundation rock interaction is considered.     

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.     

A FE–BE method for dynamic analysis of dam–foundation–reservoir systems in the time domain

By coupling FEM and BEM, a numerical method was developed for dynamic response analyses of dam–foundation–reservoir systems in the time domain. During formulation, the weighted residual procedure was applied to the coupling of several equations of motion for solid and fluid in the FE and BE regions, and an algorithm similar to the Newmark beta procedure was finally obtained. The algorithm is advantageous in that it takes into account all the effects of dam–foundation, dam–reservoir and reservoir–foundation interactions, as well as of the absorption of both elastodynamic and hydrodynamic waves at the boundaries of the foundation and the reservoir. To demonstrate the validity of the present method, the impulsive response of a dam–foundation–reservoir system was calculated using the algorithm, and showed a good agreement with the existing results obtained by other researchers.     

Earthquake analysis of intake-outlet towers including tower-water-foundation-soil interaction

The available procedure for earthquake analysis of axisymmetric intake-outlet towers is extended to towers of arbitrary geometry, but with two axes of plan symmetry, and to include the effects of tower-foundation-soil interaction. The total system is represented as four substructures: tower, surrounding water, contained water and the foundation supported on flexible soil. The substructure representation of the system permits use of the most effective idealization for each substructure. An example earthquake response analysis is presented to demonstrate the results obtained from the analysis procedure. Computation times for several cases are included to demonstrate the efficiency of the analysis procedure.