scholarly journals Evaluation of Hydrodynamic Pressure Distribution in Reservoir of Concrete Gravity Dam under Vertical Vibration Using an Analytical Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Majid Pasbani Khiavi ◽  
Ali Sari
Keyword(s):  
Analytical Solution ◽  
Separation Of Variables ◽  
Vertical Component ◽  
Hydrodynamic Pressure ◽  
Vertical Vibration ◽  
Gravity Dam ◽  
Harmonic Load ◽  
Concrete Gravity Dam ◽  
Vertical Excitation ◽  
Hydrodynamic Wave

Fluid-structure interaction causes a hydrodynamic force, which can be exerted to the dam and affects its response. The effect of vertical excitation of ground motion on dynamic behavior of concrete gravity dam is the most important because of the interaction between foundation and reservoir. So, the foundation-reservoir interaction should be taken into account in designing concrete dams. In most studies, the effects of the vertical component of vibration have been ignored. While in vertical vibration, due to the interaction of the reservoir and the foundation, a significant hydrodynamic pressure is produced in the tank, which increases the dam response. In this study, the hydrodynamic pressure wave propagation in the reservoir of a concrete gravity dam caused by interaction with the foundation under vertical vibration is investigated using an analytical method. To achieve an analytical solution, the reservoir is assumed to be rectangular, and a harmonic load is vertically applied on the system from the foundation. Considering the acoustic nature of the reservoir fluid under harmonic vibration, a new method using the separation of variables method has been used for solution of hydrodynamic wave equation. The results show a significant effect of the vertical component of earthquake on the amount of induced pressure distributed in the reservoir, which has been omitted in most previous studies. Obtained results of the proposed model can be extended to more complicated models in terms of different loading and geometrical conditions.

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

2016 ◽  
Vol 33 (7) ◽  
pp. 2045-2066 ◽  
Author(s):  
Seyed Iman Zare Estakhraji ◽  
Vahid Lotfi
Keyword(s):  
Time Domain ◽  
Maximum Error ◽  
Gravity Dam ◽  
Concrete Gravity Dam ◽  
Dam Reservoir ◽  
Effective Technique ◽  
Content Type ◽  
Vertical Excitation ◽  
Reservoir Systems ◽  
Remarkable Result

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.

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

2011 ◽  
Vol 255-260 ◽  
pp. 3493-3499
Author(s):  
Reza Attarnejad ◽  
Amirhossein Bagheri
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Transient Analysis ◽  
Separation Of Variables ◽  
Vertical Component ◽  
Hydrodynamic Pressure ◽  
Horizontal Component ◽  
Dam Reservoir ◽  
Vertical Accelerations ◽  
Infinite Reservoir

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.

Assessment of the Applicability of Pushover Analysis for a Concrete Gravity Dam

2018 ◽  
Vol 9 (5) ◽  
pp. 181
Author(s):  
Machach Laila ◽  
Mouzzoun Mouloud ◽  
Moustachi Oum El Khaiat ◽  
Taleb Ali
Keyword(s):  
Pushover Analysis ◽  
Gravity Dam ◽  
Concrete Gravity Dam

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

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