Dam-reservoir Interaction Research Articles

Analysis of dam-reservoir interaction by using homotopy analysis method

In this paper, dam-reservoir interaction for a vibrating structure in an unbounded and incompressible and inviscid fluid is analyzed by using homotopy analysis method. In the derivation of the hydrodynamic pressure variable, it is assumed that vibration of dam is in the normal direction of dam-reservoir interface and this interface is vertical. Moreover, bottom of fluid is rigid and horizontal. The results are compared with finite element method and analytical ones. It is seen that the results are efficient and gives better values than the previous published results and this method can be extendable for compressible fluid domains.

High-order adjustable boundary condition for absorbing evanescent modes of waveguides and its application in coupled fluid–structure analysis

The high-order local transmitting boundary conditions are one of the most efficient techniques for including the effect of unbounded media in a mathematical model. In spite of the previous developments in this field, the behavior of this sort of boundary condition needs to be improved in particular type of practical problems. In this paper, certain capabilities have been added to the multidirectional boundary condition to enhance its application in the dam–reservoir interaction problem. In this problem, the infinite reservoir’s bottom should be able to radiate and absorb pressure waves during the analysis procedure. Besides, the boundary condition should be able to absorb evanescent waves below the cutoff frequency. By including these competencies into the high-order boundary condition, this approach is implemented in the finite element method. The numerical experiments carried out on this technique show significant improvements compared to the previous studies.

Transient Analysis of Dam-Reservoir Interaction Based on Dynamic Stiffness of SBFEM

The scaled boundary finite element method (SBFEM) was extended to solve dam-reservoir interaction problems in the time domain and a dynamic stiffness used in the SBFEM of semi-infinite reservoir in the time domain was proposed, which was evaluated by the Bessel function. Based on the dynamic stiffness, transient responses subjected to horizontal ground motions were analyzed through coupling the SBFEM and finite element method (FEM). A dam was modeled by FEM, while the whole fluid in reservoir was modeled by the SBFEM alone or a combination of FEM and SBFEM. Two benchmark examples were considered to check the accuracy of the dynamic stiffness. Results were compared with those from analytical or substructure methods and good agreements were found.

Application of H–W boundary condition in dam–reservoir interaction problem

One of the most efficient techniques for considering the unbounded media in a mathematical model is the local non-reflecting boundary conditions (NRBCs). A relatively recent approach in this context is the one proposed by Hagstrom and Warburton (H–W boundary condition). This approach is available for scalar wave equation. This equation governs the hydrodynamic pressure distribution inside a reservoir and hence, the H–W boundary condition may be used to solve the corresponding problems. A well-known case in which one has to deal with the dynamic analysis of unbounded reservoir is the dam–reservoir interaction problem. In this study the H–W NRBC has been applied to this problem and its harmonic response is calculated. By comparing the results with the exact solution, the performance and accuracy of this NRBC is examined. The numerical results confirm the very good behavior of the NRBC in the frequencies above the fundamental frequency of the reservoir. However, below this frequency range, this boundary condition does not perform very well, especially when it is applied in close distances from the dam.

A hybrid distinct element–boundary element approach for seismic analysis of cracked concrete gravity dam–reservoir systems

This paper proposes a new algorithm for modeling the nonlinear seismic behavior of fractured concrete gravity dams considering dam–reservoir interaction effects. In this algorithm, the cracked concrete gravity dam is modeled by distinct element (DE) method, which has been widely used for the analysis of blocky media. Dynamic response of the reservoir is obtained using boundary element (BE) method. Formulation and various computational aspects of the proposed staggered hybrid approach are thoroughly discussed. To the authors' knowledge, this is the first study of a hybrid DE–BE approach for seismic analysis of cracked gravity dam–reservoir systems. The validity of the algorithm is discussed by developing a two-dimensional computer code and comparing results obtained from the proposed hybrid DE–BE approach with those reported in the literature. For this purpose, a few problems of seismic excitations in frequency- and time-domains, are presented using the proposed approach. Present results agree well with the results from other numerical methods. Furthermore, the cracked Koyna Dam is analyzed, including dam–reservoir interaction effects with focus on the nonlinear behavior due to its top profile crack. Results of the present study are compared to available results in the literature in which the dam–reservoir interaction were simplified by added masses. It is shown that the nonlinear analysis that includes dam–reservoir interaction gives downstream sliding and rocking response patterns that are somehow different from that of the case when the dam–reservoir interaction is approximated employing added masses.

Dam-Reservoir Interaction Including the Effect of Vertical Component of Earthquake Acceleration on Hydrodynamic Pressure

In this paper, time domain transient analysis of dam-reservoir interaction is studied. Resulting hydrodynamic pressure is exactly calculated including the effect of vertical component of earthquake acceleration as well as the horizontal component. Method of separation of variables is applied to solve resulting partial differential equation after applying Laplace transform. Sommerfeld’s boundary condition is used in far end of the infinite reservoir. Finally, a comparison is made between the results of the case involving both horizontal and vertical accelerations and the case of applying vertical component only using El Centro earthquake (1940) data.

Time-domain analysis of gravity dam–reservoir interaction using high-order doubly asymptotic open boundary

A procedure for the time-domain analysis of gravity dam–reservoir interaction is proposed. The dam and a part of the reservoir with irregular geometry are modeled with finite elements. A high-order doubly asymptotic open boundary condition is developed to model the remaining part of the reservoir simplified as a semi-infinite layer of constant depth. This open boundary is temporally local, stable and converges rapidly as the order increases. It is directly coupled with the commercial software ABAQUS by using a sequential staggered implicit-implicit partition algorithm. Numerical examples demonstrate the high accuracy and long-time stability of the proposed technique.

System identification of concrete gravity dams using artificial neural networks based on a hybrid finite element–boundary element approach

System identification is an emerging field of structural engineering which plays a key role in structures of great importance such as concrete gravity dams. In this study, an artificial neural network (ANN) procedure is proposed for the identification of concrete gravity dams, in conjunction with a hybrid finite element–boundary element (FE–BE) analysis for the prediction of dynamic characteristics of an existing concrete gravity dam with an empty reservoir. First, a dam–reservoir interaction analysis is carried out by the hybrid FE–BE approach in the frequency domain. A two-dimensional (2D) FE model (FEM) is used for linear-elastic analysis of the gravity dam on a rigid foundation, while the unbounded reservoir with inviscid, compressible, and frictionless fluid is discretized by BEs. Various analyses are performed for different height to base width ratios of dams in terms of different wave reflection coefficient of the reservoir bottom. The use of ANNs is motivated by the approximate concepts inherent in system identification approaches, and the time-consuming repeated analyses required for dam–reservoir interacting systems. The conjugate gradient algorithm (CGA) and the Levenberg–Marquardt algorithm (LMA) are implemented for training the ANNs, using available data generated from the results of coupled dam–reservoir system analyses. The trained ANNs are then employed to compute the dynamic amplification of dam crest displacement and natural frequencies of existing concrete gravity dams through forced vibration tests. The results obtained by solving the present inverse problem are compared with existing FEM solutions to demonstrate the accuracy and efficiency of the proposed method.

The effect of concrete slab–rockfill interface behavior on the earthquake performance of a CFR dam

Earthquake response of the concrete slab is mostly depended upon its conjunction with rockfill. This study aims to reveal the effect of concrete slab–rockfill interface behavior on the earthquake performance of a concrete-faced rockfill dam considering friction contact and welded contact. Friction contact is provided by using interface elements with five numbers of shear stiffness values. 2D finite element model of Torul concrete-faced rockfill dam is used for this purpose. Linear and materially non-linear time-history analyses considering dam–reservoir interaction are performed using ANSYS. Reservoir water is modeled using fluid finite elements by the Lagrangian approach. The Drucker–Prager model is preferred for concrete slab and rockfill in non-linear analyses. Horizontal component of 1992 Erzincan earthquake with peak ground acceleration of 0.515g is used in analyses. The maximum and minimum displacements and principal stresses are shown by the height of the concrete slab and earthquake performance of the dam is investigated considering different joint conditions for empty and full reservoir cases. In addition, potential damage situations of concrete slab are evaluated.

A coupled FE and scaled boundary FE-approach for the earthquake response analysis of arch dam-reservoir-foundation system

For efficient and accurate modelling of arch dam-reservoir-foundation system a coupled Finite Element method (FEM) and Scaled Boundary Finite Element method (SBFEM) is developed. Both the dam-foundation interaction and the dam-reservoir interaction including the effect of reservoir boundary absorption are taken into account. The arch dam is modelled by FEM, while the reservoir domain and the unbounded foundation are modelled by SBFEM. In order to make comparison with the results available in the literature, the Morrow Point arch dam is selected for numerical analysis. The analyses are carried out in the frequency domain, and then the time-domain response of the dam-reservoir-foundation system is obtained by Inverse Fourier Transform.

Simplified evaluation of the vibration period and seismic response of gravity dam–water systems

This paper proposes a practical procedure for a simplified evaluation of the fundamental vibration period of dam–water systems, and corresponding added damping, force and mass, all key parameters to assess the seismic behavior. The proposed technique includes the effects of dam geometry and flexibility, dam–reservoir interaction, water compressibility and varying reservoir level. The mathematical derivations of the method are provided considering both incompressible and compressible water assumptions. In the former case, we propose a closed-form expression for the fundamental vibration period of a dam–reservoir system. When water compressibility is included, we show that the fundamental vibration period can be obtained by simply solving a cubic equation. The proposed procedure is validated against classical Westergaard added mass formulation as well as other more advanced analytical and finite element techniques. Gravity dam monoliths with various geometries and rigidities impounding reservoirs with different heights are investigated. The new approach yields results in excellent agreement with those obtained when the reservoir is modeled analytically, or numerically using potential-based finite elements. The analytical expressions developed and the procedure steps are presented in a manner so that calculations can be easily implemented in a spreadsheet or program for simplified and practical seismic analysis of gravity dams.

INVESTIGATION OF DYNAMIC RESPONSE CHARACTERISTICS OF GRAVITY DAMS BY SUB-STRUCTURE APPROACH

ABSTRACT In the sub-structure approach for dynamic response analysis of gravity dams the dam-foundation rock and the dam-reservoir water interaction forces are first estimated by solving the wave equation for the foundation-rock and the reservoir domains with suitable boundary conditions, and the response of the dam by treating it as a separate sub-structure with the earthquake and the interaction forces applied externally. Using this approach, the effect of various controlling parameters on the dynamic response of the tallest monolith of Koyna dam has been investigated with the accelerogram of the M6.5 earthquake of 10 December 1967 as input excitation. Nine different combinations of the Young's modulus of foundation rock, water level in the reservoir, thickness of the sedimentary deposits in the reservoir, and the Young's modulus of the rock underlying the sedimentary layer have been considered to investigate the significance of each of these parameters on the dam response. It has been established that the sub-structure approach is able to predict the response of gravity dams by accounting for the effect of various interaction forces in a quite realistic way, provided the foundation can be approximated to be a half-space.

Damage mechanics approach and modeling nonuniform cracking within finite elements for safety evaluation of concrete dams in 3D space

An anisotropic damage mechanics approach is introduced which models the static and dynamic behavior of mass concrete in 3D space. The introduced numerical approach is able to model non-uniform cracking within the cracked element due to cracking in Gaussian points of elements. The validity of the proposed model is considered using available experimental and theoretical results under the static and dynamic loads. No instability and stress locking is observed in the conducted analyses. The Morrow Point dam is analyzed including dam-reservoir interaction effects to consider the nonlinear seismic behavior of the dam. It is found that the resulting crack profiles are in good agreement with those obtained from the smeared crack approach. It is concluded that the proposed model can be used in nonlinear static and dynamic analysis of concrete dams in 3D space and enables engineers to define the damage level of these infrastructures. The performance level of the considered system is used to assess the static and seismic safety using the defined performance based criteria.

Coupling FEM and symmetric BEM for dynamic interaction of dam–reservoir systems

A numerical model coupling boundary and finite elements suitable for dynamic dam–reservoir interaction is presented herein. This model involves standard finite element idealization of the dam structure displacements and a new symmetric boundary element formulation of the unbounded reservoir domain leading to an equivalent symmetric stiffness matrix for the discretized pressure field. These two basic parts of the computation are directly coupled by imposing an equilibrium condition at the fluid–structure interface, then the resulting algebraic system is reduced by localizing the coupled terms in the global mass matrix such as usually achieved in the added-mass formulation. Finally, the performance and the accuracy of this model are examined by comparing its results to those obtained from three other numerical models.

Practical Formulas for Frequency Domain Analysis of Earthquake-Induced Dam-Reservoir Interaction

Dam-reservoir dynamic interactions are complex phenomena requiring advanced mathematical and numerical modeling. Although available sophisticated techniques can handle many aspects of these phenomena, simplified procedures are useful and still needed to globally evaluate the dynamic response of dam-reservoir systems. This paper presents and validates an original practical procedure to investigate earthquake induced dam-reservoir interaction in the frequency domain, including the effects of dam flexibility, water compressibility, and reservoir bottom wave absorption. The procedure relates hydrodynamic pressure due to any deflected modal response of a two-dimensional gravity dam on a rigid foundation to hydrodynamic pressure caused by a horizontal rigid body motion. New analytical expressions that can be easily programmed in a spreadsheet package or implemented in a dam structural analysis program are also proposed to conduct simplified fundamental mode earthquake analysis of gravity dams. The techniques presented can be efficiently used to provide valuable insight into the effects and relative importance of the various parameters involved in the dynamic response of dam-reservoir systems. Although the mathematical derivations and closed-form expressions developed were applied to dam-reservoir systems herein, they can be easily adapted to other fluid-structure interaction problems.

Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section

AbstractTo improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam–reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross‐section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi‐infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd.

Seismic response of intake towers including dam–tower interaction

AbstractThe 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.

Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption

Based on the scaled boundary finite-element method, the governing equations for the analysis of dam-reservoir interaction including the reservoir boundary absorption are developed. Coupling with the equation of dam-unbounded foundation interaction, it can effectively carry out the earthquake response analysis of dam-reservoir-foundation system. The proposed approach has the advantages that the effect of compressibility of reservoir water as well as the energy absorption of reservoir boundary on the earthquake response of arch dams and gravity dams can be efficiently evaluated and higher accuracy can be achieved. In comparison with the methods available in the literature, the computational cost can be reduced to a great extent. It facilitates the application of earthquake response analysis of dam-reservoir-foundation system including reservoir boundary absorption to the engineering practice.

Representation of radiation damping in a dam–reservoir interaction analysis based on a rational stiffness approximation

In this paper, the dam–reservoir interaction problem is solved directly in the time-domain by modelling a part of the reservoir as a semi-infinite fluid-channel. Radiation damping is taken into account rigorously using an analytical solution with respect to the direction of wave propagation. The key step of the method consists of approximating the resulting modal flux–pressure relationship by a rational function in i Ω, which can be replaced by a system of linear equations in the frequency-domain. Two algorithms for the calculation of the coefficients of the rational function are described and compared. Finally, a system of first-order differential equations in the time-domain is obtained which completely represents the semi-infinite fluid-channel and can be coupled to the equations of motion of a dam and a bounded reservoir. The proposed strategy is verified considering a rigid dam. Moreover, the results of an earthquake analysis of a coupled flexible dam–reservoir system are presented.

A symmetric time‐domain model for 3D dam–reservoir interaction including radiation damping

AbstractIn this paper a new strategy for the description of a 3D dam–reservoir system in the time‐domain is proposed. Here, the structure and a finite part of the reservoir of arbitrary geometry and foundation are treated using standard finite elements. In doing so, nonlinearities can be included. Radiation damping is taken into account accurately by means of an adjacent semi‐infinite fluid channel. The key step of the method is the novel treatment of this unbounded part of the system. Based on a semi‐discretization of the latter a frequency‐dependent modal stiffness coefficient relating the pressure at the fluid–fluid interface to the corresponding flux can be derived analytically. A rational approximation and algebraic splitting procedure enable the transformation of this spectral stiffness relationship into the time‐domain. A set of first‐order differential equations to represent the semi‐infinite fluid channel is obtained which can be coupled to the equations of motion of the bounded part of the system. The complete dam–reservoir system is finally described by a symmetric set of second‐order differential equations replacing the pressure by new state variables. Copyright © 2006 John Wiley & Sons, Ltd.