Non-linear earthquake response of concrete gravity dams part 2: Behaviour

The earthquake response of the idealized Pine Flat Dam—water—foundation system of Part 1 is investigated with emphasis on the non-linear behaviour associated with concrete cracking and water cavitation. It is shown that water cavitation has little effect on the dam response. On the other hand, concrete cracking plays a significant role, as demonstrated by several analyses on dams with initial cracks or weak lift joints and by a final analysis on a homogeneous dam. The analyses encountered a number of numerical difficulties requiring further mesh refinement, and these are described. A possible failure mode associated with inclined cracks is revealed.     

Effects of concrete cracking on the earthquake response of gravity dams

Tensile stresses exceeding the tensile strength of concrete can develop in concrete dams subjected to earthquake ground motion. This study examines the earthquake response of gravity dams including tensile cracking of the concrete. The interaction between the dam and compressible water is included in the analysis using a numerical procedure for computing the non-linear dynamic response of fluid-structure systems. The crack band theory is used to model tensile cracking with modifications to allow for the large finite elements necessary for dam analysis. The earthquake response of a typical gravity dam monolith shows that concrete cracking is an important non-linear phenomenon. Cracking is concentrated near the base of the dam and near the discontinuities in the face slope. The extensive cracking, which develops due to ground motion typical of maximum credible earthquakes, may affect the stability of dams during and after strong earthquakes.     

Effects of reservoir bottom absorption on earthquake response of concrete gravity dams

A procedure is presented to analyse the response of concrete gravity dams due to horizontal and vertical earthquake ground motion components considering dam-water interaction and partial absorption of hydrodynamic pressure waves at the reservoir bottom into the foundation medium. The effects of reservoir bottom absorption on the hydrodynamic force on a rigid dam are examined first. The harmonic response of an idealized dam cross-section is presented for a wide range of parameters characterizing the properties of the dam, the impounded water and the foundation medium. Based on these frequency response functions the effects of dam-water interaction and of reservoir bottom absorption in the response of dams due to horizontal and vertical components of ground motion are investigated.     

Nonlinear dynamic response of concrete gravity dams: cavitation effect

A finite element method for the dynamic analysis of concrete gravity dams is presented. Displacement based formulation is used for both fluid and structural domains. During severe ground motion, the impounding fluid in the reservoir may separate from the dam and cause forming of micro bubbles. As a result, the compressibility of water is reduced. This nonlinear phenomenon of the reservoir is termed cavitation. When the direction of the ground motion is changed, the micro bubble's region of fluid collapses, and an impact will occur. By using different damping ratios in the fluid and solid domains the spurious oscillations which were caused by the impact are removed. The cavitation is confined to the upper part of the reservoir, where it has an effect of paramount importance on the tensile stresses. To illustrate the cavitation effect, the response of the non-overflow monolith of the Pine Flat dam subjected to the first 6.5 s of the May 1940 El-Centro, California earthquake, is considered. In order that the cavitation phenomenon take place more widely, maximum acceleration was scaled to give an amplitude of 1 g.     

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.     

Hydrodynamic effects in the dynamic response of concrete gravity dams

Hydrodynamic effects in the acceleration response of concrete gravity dams to harmonic ground motion are investigated. The effects include the presence of water, compressibility of water, interaction between the fluid and underlying foundation medium, shape of the fluid domain, and the extent of excitation applied to an infinite fluid domain under vertical ground motion.     

The earthquake experience at koyna dam and stresses in concrete gravity dams

A number of questions concerning the response of concrete gravity dams to earthquakes, motivated by the structural damage caused to Koyna Dam, which has an unconventional cross section, by the December 1967 Koyna earthquake, are considered in this work. The study is not restricted to the earthquake experience at Koyna Dam, but includes consideration of a dam with a typical section and another earthquake motion having similar intensity but different peak acceleration and frequency characteristics compared to the Koyna ground motion. The earthquake response in a number of cases is analysed by the finite element method and results are presented. These results lead to a number of conclusions. Significant tensile stresses must have developed in Koyna Dam during the Koyna earthquake and similar stresses would have developed even in typical gravity dam sections. The Koyna ground motion is relatively more severe, compared to California earthquakes of similar intensity, on concrete gravity dams. The extra concrete mass near the crest of a gravity dam to support the roadway, etc. is responsible for causing a significant part of the critical tensile stresses; attention should therefore be given to developing lightweight supporting systems.     

Effect of reservoir bottom on earthquake response of concrete dams

The absorption of hydrodynamic pressure waves at the reservoir bottom has dominant effects on the structural response of the dam when subjected to ground motion. In the present study, a model is proposed for the absorption effects of the reservoir bottom in the earthquake analysis of dams. The model utilizes the wave reflection coefficient approach and is based on the solution of the wave equation in a sediment layer of viscoelastic material with a constant thickness overlying an elastic, semi-infinite foundation. Numerical studies were conducted to evaluate the effect of the sediment layer thickness and material properties as well as the effect of reflection of waves from the underlying rock. It is shown that the current approach of assuming the wave reflection coefficient at the reservoir bottom based on the characteristics of the sediment material and excluding the effect of the reflected waves from the underlying rock, may significantly underestimate the seismic response of the dam.     

Effects of sedimentary material on the response of concrete gravity dams

The transient response of a concrete gravity dam to a selected earthquake record is determined in order to evaluate the significance of the sedimentary material accumulating on the bottom of the reservoir. The sediment is modelled as a two-phase medium (fluid-filled, poroelastic solid), and the analysis is carried out accounting for all interactions between system components (dam, water, sediment, foundation).     

Seismic stability of concrete gravity dams

Linear finite element analyses are commonly used to simulate the behaviour of gravity dam—foundation systems. However, the foundation is generally unable to develop any significant tensile stresses. Therefore any tension occurring in the vicinity of the dam—foundation interface is largely fictitious. Moreover, the traditional overturning and sliding stability criteria have little meaning in the context of the oscillatory response of dams during earthquakes. In this study, time domain analyses using non-linear contact elements located at the dam—foundation interface have been used to determine the dynamic sliding and uplifting response of gravity dam monoliths considering various elastic foundation properties. The magnitudes of the relative interface displacements, of the percentage of base not in contact (PBNC) and of the compressive stresses at the heel or toe of the dam have been used to monitor the seismic stability. The numerical results have shown that the non-linear behaviour of the dam—foundation interface reduces the seismic response of the system, indicating the possibility of more rational and economical designs. The PBNC was identified as the critical seismic stability response parameter for all analyses except for very flexible foundation conditions where the maximum values of relative interface displacements need to be considered.     

Non-linear seismic response of arch dams

An experimental study of non-linear mechanisms that may occur during intense seismic response of arch dams is described in this paper. The presentation deals with three types of non-linearity that were observed during shaking table model studies: monolith joint opening, cantilever cracking, and reservoir cavitation at the dam face. The monolith joint opening phenomenon was represented by a segmental arch ring model that simulated a horizontal slice of a prototype dam. The cantilever cracking and reservoir cavitation mechanisms were studied using a model gravity dam section. The principal conclusion of the investigation was that shaking table experiments provide a practical means of studying the non-linear earthquake response of concrete arch dams, including their actual failure mechanisms.     

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

This paper presents the application of the finite element method for analysing the two-dimensional response of reservoir-dam systems subjected to horizontal ground motion. The interaction between the dam and the reservoir as well as the compressibility of water has been taken into account. The complete system has been considered to be composed of two substructures, namely the reservoir and the dam. To take into account the large extent of the reservoir, it has been idealized using specially developed infinite elements coupled with standard finite elements while the dam is represented using finite elements alone. Structural damping of the dam and radiation damping in the fluid phase have been accounted for in the analysis. It is concluded that the effect of radiation damping is considerable at high frequencies of excitation. The coupled response of the system is significantly large at and near the fundamental natural frequency of the system in comparison to the uncoupled responses. The method is computationally quite economical, capable of taking into account the arbitrary geometry of the system and is recommended for practical application. Further applications and extensions of the approach to three dimensional analyses are possible.     

Seismic fragility assessment of concrete gravity dams

Many concrete gravity dams have been in service for over 50 years, and over this period important advances in the methodologies for evaluation of natural phenomena hazards have caused the design‐basis events for these dams to be revised upwards. Older existing dams may fail to meet revised safety criteria and structural rehabilitation to meet such criteria may be costly and difficult. Fragility assessment provides a tool for rational safety evaluation of existing facilities and decision‐making by using a probabilistic framework to model sources of uncertainty that may impact dam performance. This paper presents a methodology for developing fragilities of concrete gravity dams to assess their performance against seismic hazards. The methodology is illustrated using the Bluestone Dam on the New River in West Virginia, which was designed in the late 1930s. The seismic fragility assessment indicated that sliding along the dam–foundation interface is likely if the dam were to be subjected to an earthquake with a magnitude of the maximum credible earthquake (MCE) specified by the U.S. Army Corps of Engineers. Moreover, there will likely be tensile cracking at the neck of the dam at this level of seismic excitation. However, loss of control of the reservoir is unlikely. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic fracture analysis of concrete gravity dams

A numerical procedure for evaluation of the fracture process of gravity dams during strong earthquakes is presented. The BEM is used to discretize the dam reservoir system including the crack surfaces, and stress intensity factors at the crack tip are employed in a stage by stage procedure which simulates the crack extension. For each stage of constant crack length the mode superposition technique is applied; this is made possible by simulating the impact process of crack closing by a load pulse applied at the contact points which permits the structural stiffness to be assumed unchanged. To verify the proposed procedure, a cantilever beam model structure made of gypsum was tested on a shaking table. Good correlation with the numerical results was obtained, from which it is concluded that the procedure can be employed for evaluation of the crack propagation process in concrete structures subjected to dynamic loadings.     

Seismic behaviour of cracked concrete gravity dams

A finite element model of incremental displacement constraint equations (IDCE), based on an existing node‐to‐surface concept, is implemented to deal with dynamic contact surfaces in the seismic behaviour analysis of cracked concrete gravity dams. After verification for sliding, rocking and impact, the IDCE model is applied to study the seismic responses of concrete gravity dams with different profiles and crack locations for a variety of parameters, such as coefficient of friction, water level and type of earthquake, as well as impact damping based on the concept of coefficient of restitution. It is revealed that cracked concrete gravity dams can experience not only sliding and rocking modes, but also the drifting mode in some cases of crack either at the base or at a height. Downstream sliding is normally accompanied by rocking, especially for the cases of crack at a height. Due to rocking and drifting, a cracked dam may still acquire a certain amount of residual sliding even if the effective coefficient of friction is relatively high. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of rotational components of earthquake on seismic response of arch concrete dams

The present study deals with dynamic analysis of arch concrete dams, taking rotational components of earthquakes into account. A modified methodology was used to evaluate the rotational components of the earthquake. The translational components of the earthquake have been used in to obtain the rotational components of the earthquake, based on the intersecting isotropic elastic wave propagation. Two rotational components of Taft, Tabas and San-Fernando earthquakes are evaluated based on the translational components of the earthquakes and considering frequency dependencies of incident angle and wave velocity. Finally, dynamic analyses of Morrow Point Dam are presented to evaluate the effects of combined translational and rotational components on the seismic response of the dam. Various conditions of reservoirs, including full and empty state, are considered in the analyses. Fluid–structure interaction was completely taken into account. It was realized that incorporating rotational components increased the maximum compressive and tensile stresses in both empty and full reservoir analyses. Distribution of maximum tensile stresses is very sensitive to the rotational components of the earthquake. Also, it can be concluded that the segregated effect of the rocking component on the response of concrete dams is more effective than the sole effect of the torsional component.     

Hydrodynamic and foundation interaction effects in frequency response functions for concrete gravity dams

The linear response of idealized dam cross-sections to harmonic horizontal or vertical ground motion is presented for a range of the important system parameters characterizing the properties of the dam, foundation rock and impounded water. Based on these frequency response functions, the separate effects of interaction between the dam and water and interaction between the dam and foundation, and the combined effects of the two sources of interaction, on dynamic response of dams are investigated.     

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.     

Earthquake safety assessment of concrete arch and gravity dams

Based on research studies currently being carried out at Dalian University of Technology, some important aspects for the earthquake safety assessment of concrete dams are reviewed and discussed. First, the rate-dependent behavior of concrete subjected to earthquake loading is examined, emphasizing the properties of concrete under cyclic and biaxial loading conditions. Second, a modified four-parameter Hsieh-Ting-Chen viscoplastic consistency model is developed to simulate the rate-dependent behavior of concrete. The earthquake response of a 278m high arch dam is analyzed, and the results show that the strain-rate effects become noticeable in the inelastic range. Third, a more accurate non-smooth Newton algorithm for the solution of three-dimensional frictional contact problems is developed to study the joint opening effects of arch dams during strong earthquakes. Such effects on two nearly 300m high arch dams have been studied. It was found that the canyon shape has great influence on the magnitude and distribution of the joint opening along the dam axis. Fourth, the scaled boundary finite element method presented by Song and Wolf is employed to study the dam-reservoir-foundation interaction effects of concrete dams. Particular emphases were placed on the variation of foundation stiffness and the anisotropic behavior of the foundation material on the dynamic response of concrete dams. Finally, nonlinear modeling of concrete to study the damage evolution of concrete dams during strong earthquakes is discussed. An elastic-damage mechanics approach for damage prediction of concrete gravity dams is described as an example. These findings are helpful in understanding the dynamic behavior of concrete dams and promoting the improvement of seismic safety assessment methods.     

Seismic cracking and energy dissipation in concrete gravity dams

A finite element method for seismic fracture analysis of concrete gravity dams is presented. The proposed smeared crack analysis model is based on the non-linear fracture behaviour of concrete. The following features have been considered in the development of the model: (i) the strain softening of concrete due to microcracking; (ii) the rotation of the fracture band with the progressive evolution of microcrack damage in finite elements; (iii) the conservation of fracture energy; (iv) the strain-rate sensitivity of concrete fracture parameters; (v) the softening initiation criterion under biaxial loading conditions; (vi) the closing-reopening of cracks under cyclic loading conditions. The seismic fracture and energy response of dams and the significance of viscous damping models to take account of non-cracking structural energy dissipation mechanisms are discussed. The influences of global or local degradation of the material fracture resistance on the seismic cracking response of concrete dams were also studied. Two-dimensional seismic response analyses of Koyna Dam were performed to demonstrate the application of the proposed non-linear fracture mechanics model.