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

doi:10.1016/0045-7949(95)00309-6

Computers & Structures

Volume 59, Issue 5, 3 June 1996, Pages 877-890

https://doi.org/10.1016/0045-7949(95)00309-6 Get rights and content

Abstract

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.

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It has widely been recognised that the hydrodynamic pressure induced by dynamic dam-reservoir interaction is a key factor that cannot be neglected in comprehensive estimation of dam seismic response [13]. To date, the dam-reservoir interaction can be considered from three aspects [44], i.e. added mass, Eulerian, and Lagrangian approaches. Among them, the added mass approach proposed by Westergaard [28] is adopted in the present study because it has been generally accepted as the most simple and convenient technique to consider the hydrodynamic effects [24].
Proper consideration of external and internal loads acting on concrete gravity dams is of vital importance in concrete dam engineering, since it plays a significant role in the stability assessment of cracked dams under static/dynamic conditions. Several factors which may affect the mechanical response of concrete gravity dams, however, have not been comprehensively accounted for in most previous crack propagation analyses. To adequately evaluate the crack propagation response of concrete gravity dams, a finite element-based numerical analysis is carried out to estimate the crack propagation in a concrete gravity dam under static and seismic loads. In this work, the effects of the water pressure inside the stress-free crack and the fracture process zone (FPZ), the cohesive force within the FPZ, the hydrostatic water pressure, and the dam-reservoir interaction are incorporated via a series of reasonable assumptions. On the basis of a stress intensity factor (SIF)-based mixed mode I-II crack propagation criterion, a generic numerical algorithm is proposed to estimate the crack growth process of concrete gravity dams under static and seismic loads. Application of this algorithm to two case studies of concrete gravity dams under different loading conditions demonstrates the validity of the algorithm in estimating the static and seismic crack propagation response. It is found that when a concrete gravity dam is subjected to static loading, crack initiation does not occur before the reservoir water level exceeds the dam height, and that the water pressure inside stress-free cracks has a slight negative effect on the structural resistance against cracking while the water pressure within the FPZ has no effect on the dam capacity. The seismic crack growth analysis indicates that the water pressure inside cracks causes the crack to propagate at a larger downward angle towards the downstream face with a larger crack growth length.
A nonlinear analysis of dynamic interactions of CFRD–compressible reservoir system based on FEM–SBFEM
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Because of its importance to the evaluation of the seismic safety of a dam, the hydrodynamic pressure on the dam face under seismic action is always a factor of concern in theoretical and numerical calculations. In the analysis of dynamic dam–reservoir interactions, reservoir water compressibility is a critical factor and a focus of research; the relevant studies concentrate primarily on arch and gravity dams [1–4]. Previous research has shown that compared with the assumption of incompressible water, it is more complex and time consuming to solve problems when the compressibility of the reservoir water is considered.
Reservoir water compressibility is a major factor affecting dynamic dam–reservoir interactions, and most studies focus on the analysis of concrete dams. However, few studies have been conducted with respect to the effects of reservoir water compressibility on the dynamic response of CFRDs (concrete-faced rockfill dams). Furthermore, new researches show the hydrodynamic pressure is significant for evaluating the seismic performance of high CFRD. In this paper, a method to calculate the nonlinear dynamic interactions of CFRD–compressible reservoir water system in the time-domain is established based on a FEM–SBFEM approach. The CFRD is discretized using the finite element method (FEM), and the hydrodynamic pressure of the semi-infinite water on the upstream face of the dam is calculated using the efficient scaled boundary finite element method (SBFEM), in which the degrees of freedom of the hydrodynamic pressure to be solved for are relatively few. The objective of this work is to investigate the effects of reservoir water compressibility and the sediment absorption layer at the reservoir bottom and bank slopes on the dynamic response of a high CFRD–reservoir-coupled system under seismic action in various directions. When the reservoir water is considered compressible, partial absorption of the hydrodynamic pressure wave by the sediments can be considered. The results show that water compressibility can significantly affect the stress in the face slabs.
A symmetric implementation of pressure-based fluid–structure interaction for nonlinear dynamic analysis of arch dams
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The Lagrangian approach works as an extension of the classical displacement-based theory for fluid domains. The unknown variables in this approach include displacements in both solid and fluid domains (Calayir et al., 1996; Dogangun et al., 1996; Calayir and Karaton, 2005; Amina et al., 2015). Fluid elements are formulated using the same shape functions as solid elements and no special interface treatment is required because the compatibility at the interface is automatically satisfied.
Fluid–structure interaction formulated in the Lagrangian–Eulerian approach with pressure-based fluid elements, which inherently results in non-symmetric matrices, is commonly treated by either direct un-symmetric solvers or staggered solution methods. Developing an in-house finite element code called SNACS, we implement the pressure-based Eulerian formulation so that a usual symmetric solver can be employed for dam–reservoir interaction analyses. The equilibrium equations of motion for such a coupled system are directly integrated herein by the HHT time marching algorithm in an incremental–iterative solution procedure to tackle a highly nonlinear dynamic analysis of jointed arch dams. The HHT time integration scheme is able to damp out high-frequency noises resulting from sudden changes in the stiffness due to opening/closing of pre-existing joints during an earthquake. First, a Pseudo-Symmetric technique is proposed to store the total matrices and solve the coupled non-symmetric equations in a symmetric manner. Then, the interface element formulation and stress update procedures of two discrete crack constitutive models suitable for contraction and peripheral joints of arch dams are detailed. Afterwards, results of the analysis on a typical arch dam are compared with the case in which the interaction is approximately represented by added masses as a widely-used method in dam engineering practice to illustrate the effects of water compressibility and reservoir bottom absorption. Besides, the straightforward implementation of pressure-based fluid–structure interaction utilizing a symmetric solution strategy is validated herein to be efficient for a 3-D large scale practical usage in other finite element codes even the commercial ones to avoid using un-symmetric solvers. Employing this symmetric implementation for the dam–water interaction drastically reduces the computational effort, particularly when an iterative scheme is required to solve such a highly nonlinear system.
Finite element seismic safety assessment of water intake structures
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This paper presents a methodology to assess the seismic safety of concrete gravity water intake structures of typical hydroelectric facilities. Water intake structures are characterized by large voids for the gates and penstock embedded in concrete. In practice, the well-known Westergaard formulation (WF), assuming a vertical rigid wall, is most often used to represent hydrodynamic pressures. However, the validity of the WF for water intake structures has not been addressed in the past. A parametric analysis is performed herein using four 40 m high intake structures with upstream opening void ratio, χ, ranging from 0% to 30% of the concrete surface in contact with water. Three-dimensional finite element models (FEM) with potential-based incompressible fluid elements are used in steady-state and transient seismic fluid–structure interaction (FSI) analyses to consider water in the penstock as well as in the reservoir. Modification factors which depend on χ are derived from the 3D FEM such that a Westergaard modified formulation (WMF) is proposed to represent adequately FSI. Simplified structural models using beam-column elements with section properties accounting for the presence the penstock opening and the proposed WMF are used as an efficient alternative to complex 3D FEM. A seismic safety assessment of an intake considering ground motions of return periods ranging from 200 to 10,000 years are used to assess the safety level of the intake structure. The internal forces and residual sliding displacements are computed. It is shown that the proposed WMF and the simplified stick model formulation provide hydrodynamic thrust within approximately 10% of the reference 3D FEM. The seismic response (i.e. base shear) is also adequately predicted using the proposed simplified modeling strategy.
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Earthquake analysis of gravity dam-reservoir systems using the Eulerian and Lagrangian approaches

Abstract

Nucl. Engng Des.

Comput. Struct.

Comput. Struct.

Dynamic analysis of concrete gravity dams using the Eulerian and the Lagrangian approaches

Earthquake behavior of reservoir-dam systems

J. Engng Mech. Div. ASCE

Earthquake analysis of gravity dams including hydrodynamic interaction

Earthquake Engng Struct. Dyn.

Earthquake analysis of concrete gravity dams including dam-water-foundation rock interaction

Earthquake Engng Struct. Dyn.

Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects

Earthquake Engng Struct. Dyn.

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

Earthquake Engng Struct. Dyn.

A technique for the analysis of the response of dams to earthquakes

Earthquake Engng Struct. Dyn.

The implementation of an efficient computer analysis for fluid-structure systems using the Eulerian approach within SAP-IV

Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements

Earthquake Engng Struct. Dyn.