Gravity Dam-reservoir System Research Articles

Response spectrum and modal dynamic analyses of gravity dams using ground motion accelerations modified to account for hydrodynamic effects

This research proposes simplified methods for response spectrum and modal dynamic analyses of gravity dams using time-history and spectral seismic accelerations modified to directly account for hydrodynamic effects. The developed methods waive the need for specialized fluid-structure interaction software. They also lead to more accurate assessment of coupled structural flexibility and hydrodynamic effects due to each vibration mode than the static correction method commonly used in traditional simplified methods. The methodology utilizes analytical formulations of hydrodynamic pressure or simplified added masses to obtain the contributions of the selected vibration modes to the total seismic response. A hydrodynamic modification factor characterizing the amplification/de-amplification of acceleration seismic demands due to earthquake-induced hydrodynamic effects is also introduced. The application of the proposed methods is illustrated numerically through examples of two typical gravity dam-reservoir systems subjected to four earthquakes. The obtained results are in excellent agreement with the classical reference solutions. Time-history and spectral seismic acceleration demands modified by hydrodynamic effects as well as selected key response indicators, such as relative displacements and stresses within the studied gravity dams, are discussed.

Time harmonic analysis of concrete gravity dam-reservoir systems by mixed High order-Wavenumber approach for general reservoir bottom condition

Recently, mixed HO-WN (i.e., High order-Wavenumber) method was introduced for dynamic analysis of concrete gravity dam-reservoir systems. This is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the mixed HO-WN (i.e., High order-Wavenumber) condition is imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. The method is derived by combining the High-order and Wavenumber approaches. The present study is an extension of mixed HO-WN approach which allows it to be effectively utilized in the case of absorptive as well as fully reflective reservoir bottom condition. The formulation is initially explained in details and three alternatives are presented for this method. Subsequently, the response of an idealized triangular dam-reservoir system is studied for an absorptive reservoir condition due to horizontal and vertical ground motions. For each alternative, responses are evaluated from accuracy point of view by comparing them against exact solutions for three different values of normalized reservoir length (i.e., L/H ratio). It should be emphasized that a very low value of L/H = 0.2 is also considered for this investigation which makes it a very challenging test for any kind of truncation boundary condition. Moreover, it is worthwhile to stress that although time harmonic analysis is adopted in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Application of G-N high-order boundary condition on time harmonic analysis of concrete gravity dam-reservoir systems

PurposeThe response of an idealized triangular concrete gravity dam is studied due to horizontal and vertical ground motions for both fully reflective and absorptive reservoir bottom conditions. For each combination, in this paper different orders of Givoli-Neta (G-N) high-order truncation condition are aimed to be evaluated from accuracy point of view by comparing the results against corresponding exact solutions which relies on utilizing a two-dimensional fluid hyper-element.Design/methodology/approachIn present study, the dynamic analysis of concrete gravity dam-reservoir systems is formulated by Finite Element (FE)-(FE-TE) approach. In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the G-N high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.FindingsIt was observed that trend in gaining accuracy with increase in the order of G-N condition were basically the same for both horizontal and vertical ground motions under full reflective reservoir bottom condition. Moreover, convergence rate increases for absorptive reservoir bottom condition cases in comparison with fully reflective cases. It is also noticed that in certain cases, the responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on G-N condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete gravity dam-reservoir systems.Originality/valueDynamic analysis of concrete gravity dam-reservoir systems are formulated by a new method. The salient aspect of the technique is that it utilizes G-N high-order condition at the truncation boundary. This is achieved by developing a special truncation element which its generalized matrices are derived for Finite Element Method (FEM) programmers. The method is discussed for all types of excitation and reservoir bottom conditions. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Dynamic analysis of concrete gravity dam-reservoir systems by Wavenumber approach for the general reservoir base condition

Different approaches are utilized for dynamic analysis of concrete gravity dam-reservoir systems. The rigorous approach for solving this problem employs a two-dimensional semi-infinite fluid element (i.e., hyper-element). Recently, a technique was proposed for dynamic analysis of dam-reservoir systems in the context of pure finite element programming which was referred to as the Wavenumber approach. Of course, certain limitations were imposed on the reservoir base condition in the initial form of this technique to simplify the problem. However, this is presently discussed for the general reservoir base condition, contrary to the previous study which was merely limited to the full reflective reservoir base case. In this technique, the wavenumber condition is imposed on the truncation boundary or the upstream face of the near-field water domain. The method is initially described. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by this approach, and the results are compared against the exact response. Based on this investigation, it is concluded that this approach can be envisaged as a great substitute for the rigorous type of analysis under the general reservoir base condition.

Dynamic analysis of concrete gravity dam-reservoir systems by approximate wavenumber approach

Purpose Recently, the original Wavenumber approach was introduced for dynamic analysis of dam-reservoir systems in frequency domain in the context of pure finite element programming. But its main disadvantages are that it cannot be implemented in time domain. The purpose of this paper is to propose an approximation to the original approach which enables one to carry out this effective method in time domain as well as in frequency domain. Based on the present investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain. Design/methodology/approach The method is described initially. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by the proposed approach as well as by applying two other well-known absorbing conditions which are widely utilized in practice. The results are also controlled against the corresponding exact responses. It should be emphasized that all results presented herein are obtained by the FE-FE method under different absorbing conditions applied on the truncation boundary. These include two well-known absorbing conditions referred to as Sommerfeld and Sharan as well as the proposed approach of the present study (i.e. Approximate Wavenumber condition). Findings It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect. The fundamental frequency of the system is captured correctly for the Approximate Wavenumber approach, even in cases of low reservoir length. Originality/value Based on this investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain. It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect.

Transient analysis of concrete gravity dam-reservoir systems by Wavenumber-TD approach

The Wavenumber approach was initially introduced as an ideal substitute for the rigorous type of analysis which had been the basis of extensive studies in seismic analysis of concrete gravity dams. The former technique is formulated in the context of pure finite element programming, while the latter relies heavily on a two-dimensional semi-infinite fluid element (i.e., hyper-element). Recently, a variation of Wavenumber method was proposed which was referred to as Wavenumber-TD approach. The approximation to the original technique improves its realm of application and allows it to be carried out in time domain as well as frequency domain. In that study, the formulation was examined for harmonic type of excitation which proved to be promising. Herein, this will be evaluated for its real intended application, which is transient analysis of dam-reservoir systems. For this aim, the prepared special purpose finite element program is modified and the analysis of Pine Flat dam is considered as a typical example. Several models are considered with different values of normalized reservoir length. In each case, the reservoir truncation surface is treated by Wavenumber-TD and the extensively utilized Sommerfeld conditions. The dynamic loading considered is the S69E component of Taft earthquake record. Furthermore, two types of reservoir bottom condition of full reflective as well as absorptive, are adopted. Overall, this will allow for a thorough examination and evaluation of Wavenumber-TD approach in regard to its effectiveness.

The Effects of Saturated Sediment Layer on Seismic Wave Motion of Gravity Dams

Sediment layer can change the dynamic property of reservoir water. As a result, the dynamic response of dam body would be affected. In this paper, the sediment layer is simulated as saturated liquid-solid two-phase media, and the finite element model of gravity dam-reservoir water-sediment system is established with the gradual enlargement mesh method. Then the influence of sediment layer on seismic wave motion is studied with this model. The calculation result shows that the energy radiation of far field of foundation, reservoir water and sediment can be considered efficiently in this model, and with the thickening of sediment layer the dynamic water pressure on dam face decreases.

Experimental investigation on nonlinear dynamic response of concrete gravity dam-reservoir system

The nonlinear response of concrete gravity dam-reservoir system has been investigated by conducting experiments on small scale model of Koyna dam on a horizontal shake table using sinusoidal chirp motions. Two dimensional models of non-overflow section of Koyna dam have been prepared in the laboratory with a scale ratio of 1:150. To satisfy the laws of similitude, an appropriate ratio of cement, sand, bentonite and water has been mixed to find the target properties of model dam. Dam models have been casted over a wooden base plate using a wooden mould. After setting and drying process the wooden mould has been removed and each dam model has been assembled with a reservoir model after placing them over a horizontal shake table. The interaction between dam and reservoir model has been made in such a manner, so that it can transmit the hydro dynamic force of reservoir water to the dam model without allowing any seepage of water across it. Experiments have been performed on the dam-reservoir system with empty and full reservoir water by applying horizontal sinusoidal chirp excitations to the shake table to observe the basic behaviour, crack formation, crack opening, sliding along crack planes and stability after crack formation of the dam model. The numerical analysis of the system has been carried out using ABAQUS 6.10 considering damage plasticity model. The effect of foundation has been neglected assuming a rigid dam foundation as the dam is placed on a rigid plate. The eigen frequencies of the dam model have been calculated and compared with experimental values to calibrate the analysis model. The crack propagation due to tensile damages is computed and the results are compared with the experimental results. The outcome of the response results shows the correctness of the developed experimental model of dam-reservoir system.

Novel Nonreflecting Boundary Condition for an Infinite Reservoir Based on the Scaled Boundary Finite-Element Method

AbstractThe present paper deals with the hydrodynamic problems of dam-reservoir systems based on the scaled boundary FEM (SBFEM). It provides a novel boundary condition for hydrodynamic pressure simulation on the truncation boundary suited for dam-reservoir interaction analysis. A two-dimensional gravity dam-reservoir system is addressed, where the impounded water is extended to infinity. In the analysis, a truncation boundary is placed at a short distance away from the dam face in the upstream direction to reduce the computational effort. The proposed approach can conveniently consider the water compressibility, the absorption of the reservoir boundary, and the effect of the reservoir geometry. It is applicable to the earthquake excitation either in the stream direction or in the vertical/cross-stream directions. Additionally, it has the potential to extend to the three-dimensional case. Numerical examples are provided to validate the effectiveness of the proposed approach.

Dynamic analysis of concrete gravity dam-reservoir systems by wavenumber approach in the frequency domain

Dynamic analysis of concrete gravity dam-reservoir systems is an important topic in the study of fluid-structure interaction problems. It is well-known that the rigorous approach for solving this problem relies heavily on employing a two-dimensional semi-infinite fluid element. The hyper-element is formulated in frequency domain and its application in this field has led to many especial purpose programs which were demanding from programming point of view. In this study, a technique is proposed for dynamic analysis of dam-reservoir systems in the context of pure finite element programming which is referred to as the wavenumber approach. In this technique, the wavenumber condition is imposed on the truncation boundary or the upstream face of the near-field water domain. The method is initially described. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by this approach, and the results are compared against the exact response. Based on this investigation, it is concluded that this approach can be envisaged as a great substitute for the rigorous type of analysis.

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.

Comparison of coupled and decoupled modal approaches in seismic analysis of concrete gravity dams in time domain

Different methods are available for dynamic analysis of concrete dams. Among these, modal approach is highly popular due to the efficiency of the method. This becomes more significant if the response is to be calculated for several earthquake ground motion records as required in most practical cases. In this study, two different modal approaches have been considered for dynamic analysis of concrete gravity dam–reservoir systems. These are coupled modal method and decoupled modal technique. The former approach utilizes the coupled modes of the system. It is well known that calculation of these modes involves some complications due to its corresponding unsymmetrical eigenproblem. However, the response at each step can be obtained very efficiently in this method. The latter technique, relies on the decoupled modes of the system, which are easily obtained by standard eigenvalue solvers. The equation of motion is also solved with reasonable efficiency in this approach. In the latter part of this paper, analysis of a typical dam–reservoir system is performed by both methods mentioned above. These analyses are compared from accuracy and efficiency point of view.

A continuum damage concrete model for earthquake analysis of concrete gravity dam–reservoir systems

In this study, the earthquake damage response of the concrete gravity dams is investigated with considering the effects of dam–reservoir interaction. A continuum damage model which is a second-order tensor and includes the strain softening behavior is selected for the concrete material. The mesh-dependent hardening technique is adopted such that the fracture energy dissipated is not affected by the finite element mesh size. The dynamic equilibrium equations of motion are solved by using the improved form of the HHT-α time integration algorithm. Two dimensional seismic analysis of Koyna gravity dam is performed by using the 1967 Koyna earthquake records. The effects of damage on the earthquake response of concrete gravity dams are discussed. Comparison of the Westergaard and Lagrangian dam–reservoir interaction solutions is made. The effects of viscous damping ratio on the damage response of the dam are also studied.

Comparison of stochastic and deterministic dynamic responses of gravity dam–reservoir systems using fluid finite elements

In this paper, stochastic and deterministic dynamic responses of gravity dam–reservoir systems are compared using the displacement fluid finite elements. For stochastic dynamic analysis of gravity dam–reservoir systems, variable-number-nodes two-dimensional fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a general-purpose computer program, which is used for stochastic dynamic analysis of solid systems, STOCAL. The Sarıyar concrete gravity dam, constructed in Turkey is selected for numerical example. The S16E component recorded at Pacoima dam during the San Fernando Earthquake in 1971 is used as a ground motion. Displacements and hydrodynamic pressures occurring on the upstream face of the dam and stresses occurring on the dam section are calculated by using stochastic and deterministic methods and compared with each other.

Seismic analysis of concrete gravity dams by decoupled modal approach in time domain

A modal approach is proposed for dynamic analysis of general concrete gravity dam-reservoir systems in time domain. The method is explained initially, and the analysis of Pine Flat Dam is considered as a verification example. The proposed approach is proved to be a very effective technique. The main advantage being that it relies on eigen-vectors of decoupled system, which can be easily obtained by standard eigen-solution routines.

Nonlinear Seismic Response Analysis of Realistic Gravity Dam-Reservoir Systems

Article Nonlinear Seismic Response Analysis of Realistic Gravity Dam-Reservoir Systems was published on December 1, 2003 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 4, issue 4).

FE-BE Method for Earthquake-induced Cracking of Concrete Gravity Dam-Reservoir Systems

FE-BE Method for Earthquake-induced Cracking of Concrete Gravity Dam-Reservoir Systems

Earthquake analysis of gravity dam-reservoir systems using the Eulerian and Lagrangian approaches

In this study, the two-dimensional earthquake analysis of a gravity dam-reservoir system using both the Eulerian and Lagrangian approaches is performed. To this aim, the effects of the variation of fluid compressibility on the modal behavior were first investigated. Then, the earthquake response of a dam-reservoir system is investigated using the Lagrangian approach. Parametric studies are conducted on increasing the value of fluid bulk modulus. The results obtained for different values of the bulk modulus are also compared with the Eulerian solutions based on incompressible fluid assumption.

Transient response of dam reservoir systems to random earthquake excitation

A simple gravity dam-reservoir system is selected for studying the response of the system under nonstationary random excitation. For random excitations with a zero start and a wide range of Kanai-Tajimi power spectra, the transient response for the structural displacement is obtained. The random response includes the mean square, the nonstationary power spectra, the upcrossing probabilities and the system reliabilities. This study is important because of its practical applicability in the system design to resist earthquake motion.

Transient random interaction of dam reservoir systems

A simple gravity dam-reservoir system is selected for studying the interaction of structure-fluid systems under nonstationary random excitation. For an idealized random excitation with a zero start and a white power spectrum, the transient response mean square for the structural displacement is obtained by a simple time domain approach. Using this transient solution the random interaction effect is examined in detail. This transient interaction effect is important because it simulates random and time dependent earthquake ground accelerations.