Dynamics of submerged intake towers including interaction with dam and foundation

The dynamics of a coupled concrete gravity dam-intake tower–reservoir water–foundation rock system is numerically studied considering two hollow slender towers submerged in reservoir of gravity dam. The system is investigated in the frequency-domain using frequency response functions of the dam and the towers, and in the time-domain using time-history seismic analysis under a real earthquake ground motion. The analyzes are separately conducted under horizontal and vertical ground motions. The coupled system is three-dimensionally modeled using finite elements by Eulerian–Lagrangian approach. It is shown that presence of the dam significantly influences the dynamic response of the towers under both horizontal and vertical excitations; however the dam is not affected by the towers. When the dam is present in the model, the water contained inside the towers has different effects if the foundation is rigid, but it alleviates the towers motion if the foundation is flexible. It is concluded that the effects of foundation interaction are of much importance in the response of tall slender towers when they are located near concrete gravity dams.     

Dynamics of towers surrounded by water

The effects of interaction with surrounding water on the dynamic response behaviour of cantilever tower structures are studied. Expressions for response to harmonic ground motion in individual modes of vibration, including hydrodynamic interaction, are presented, the accuracy of responses obtained by ignoring surface waves and compressibility of water in the hydrodynamic solutions is evaluated, the effects of hydrodynamic interaction on the fundamental period of vibration are studied and the commonly used ‘added mass’ approach to account for effects of surrounding water is examined. The conclusions deduced from the results of this investigation include the following. Interaction with surrounding water increases the fundamental period of vibration of the tower and decreases the modal damping ratio. Compressibility of water has essentially no influence in the hydrodynamic effects on slender towers. The traditional definition of added mass is conceptually deficient, but is simple to employ; the errors in this simple added mass representation are negligible for the first mode of vibration of towers.     

A substructure method for earthquake analysis of structures including structure-soil interaction

A general substructure method for analysis of response of structures to earthquake ground motion, including the effects of structure-soil interaction, is presented. The method is applicable to complex structures idealized as finite element systems and the soil region treated as either a continuum, for example as a viscoelastic halfspace, or idealized as a finite element system. The halfspace idealization permits reliable analysis for sites where essentially similar soils extend to large depths and there is no rigid boundary such as soil-rock interface. For sites where layers of soft soil are underlain by rock at shallow depth, finite element idealization of the soil region is appropriate; in this case, the direct and substructure methods would lead to equivalent results but the latter provides the better alternative. Treating the free field motion directly as the earthquake input in the substructure method eliminates the deconvolution calculations and the related assumption—regarding type and direction of earthquake waves—required in the direct method. Spatial variations in the input motion along the structure-soil interface of embedded structures or along the base of long surface supported structures are included in the formulation. The substructure method is computationally efficient because the two substructures—the structure and the soil region—are analysed separately; and, more important, it permits taking advantage of the important feature that response to earthquake ground motion is essentially contained in the lower few natural modes of vibration of the structure on fixed base.     

地震下考虑桩-土-结构相互作用的输电塔-线体系响应分析

本文研究了考虑桩-土-结构相互作用的输电塔-线体系在地震作用下的响应。根据实际工程,采用ABAQUS有限元软件,建立了考虑桩-土-结构相互作用效应的输电塔-线体系有限元模型。选取不同场地类型下的12条天然地震波,研究了不同地震波激励下考虑桩-土-结构相互作用效应输电塔-线体系动力响应。通过与考虑刚性基础的输电塔-线体系动力响应对比,得到了输电塔的薄弱位置,并提出了基于刚性基础的输电塔抗震放大系数,可为输电塔抗震设计提供参考。     

基于增量动力分析和纤维模型的矮塔斜拉桥结构抗震性能研究

基于OpenSees软件及其纤维模型的有限元方法,建立了典型矮塔斜拉桥的非线性数值分析模型,分析各构件的抗震性能指标。采用动力增量分析法（即IDA方法）,对结构进行了非线性动力时程分析,分别探讨了在纵桥向和横桥向地震作用下矮塔斜拉桥结构的构件破坏规律。分析了在不同加速度峰值情况下,矮塔斜拉桥主塔和边墩沿高度变化的应变包络图、主梁内力包络图及支座位移包络图。结果表明：与一般斜拉桥性能要求不同,矮塔斜拉桥的主塔可以发生损伤,塔底和边墩墩底为主要控制截面,支座在纵桥向地震组合作用下较易发生破坏,拉索和主梁是不易损伤的构件,主梁内力包络图的分布情况随着地震峰值的增加发生变化。     

Direct finite element method for nonlinear analysis of semi‐unbounded dam–water–foundation rock systems

A direct finite element method is presented for nonlinear earthquake analysis of interacting dam–water–foundation rock systems. The analysis procedure applies viscous damper absorbing boundaries to truncate the semi‐unbounded fluid and foundation‐rock domains and specifies at these boundaries effective earthquake forces determined from the design ground motion defined at a control point on the free surface. The analysis procedure is validated numerically by computing the frequency response functions and transient response of an idealized dam–water–foundation rock system and comparing with results from the substructure method. Because the analysis procedure is applicable to nonlinear systems, it allows for modeling of concrete cracking, as well as sliding and separation at construction joints, lift joints, and at concrete–rock interfaces. Implementation of the procedure is facilitated by commercial finite element software with nonlinear material models that permit modeling of viscous damper boundaries and specification of effective earthquake forces at these boundaries. Copyright © 2017 John Wiley & Sons, Ltd.     

Earthquake analysis of intake-outlet towers including tower-water-foundation-soil interaction

The available procedure for earthquake analysis of axisymmetric intake-outlet towers is extended to towers of arbitrary geometry, but with two axes of plan symmetry, and to include the effects of tower-foundation-soil interaction. The total system is represented as four substructures: tower, surrounding water, contained water and the foundation supported on flexible soil. The substructure representation of the system permits use of the most effective idealization for each substructure. An example earthquake response analysis is presented to demonstrate the results obtained from the analysis procedure. Computation times for several cases are included to demonstrate the efficiency of the analysis procedure.     

Vertical earthquake response of megawatt‐sized wind turbine with soil‐structure interaction effects

The dynamic response of a wind turbine on monopile is studied under horizontal and vertical earthquake excitations. The analyses are carried out using the finite element program SAP2000. The finite element model of the structure is verified against the results of shake table tests, and the earthquake response of the soil model is verified against analytical solutions of the steady‐state response of homogeneous strata. The focus of the analyses in this paper is the vertical earthquake response of wind turbines including the soil‐structure interaction effects. The analyses are carried out for both a non‐homogeneous stratum and a deep soil using the three‐step method. In addition, a procedure is implemented which allows one to perform coupled soil‐structure interaction analyses by properly tuning the damping in the tower structure. The analyses show amplification of the ground surface acceleration to the top of the tower by a factor of two. These accelerations are capable of causing damage in the turbine and the tower structure, or malfunctioning of the turbine after the earthquake; therefore, vertical earthquake excitation is considered a potential critical loading in design of wind turbines even in low‐to‐moderate seismic areas. Copyright © 2015 John Wiley & Sons, Ltd.     

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

Ａｎｅｘｐｌｉｃｉｔｆｉｎｉｔｅｅｌｅｍｅｎｔ－ｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅ　ｍｅｔｈｏｄｆｏｒａｎａｌｙｚｉｎｇｔｈｅｅｆｆｅｃｔｏｆｖｉｓｃｏ－ｅｌａｓｔｉｃ　ｌｏｃａｌ　ｔｏｐｏｇｒａｐｈｙ　ｏｎ　ｔｈｅ　ｅａｒｔｈｑｕａｋｅ　ｍｏｔｉｏｎ...     

Direct finite element method for nonlinear earthquake analysis of 3‐dimensional semi‐unbounded dam–water–foundation rock systems

A direct finite element method for nonlinear earthquake analysis of 2‐dimensional dam–water–foundation rock systems has recently been presented. The analysis procedure uses standard viscous‐damper absorbing boundaries to model the semi‐unbounded foundation‐rock and fluid domains and specifies the seismic input as effective earthquake forces at these boundaries. Presented in this paper is a generalization of the direct finite element method with viscous‐damper boundaries to 3‐dimensional dam–water–foundation rock systems. Step‐by‐step procedures for determining the effective earthquake forces starting from a ground motion specified at a control point on the foundation‐rock surface is developed, and several numerical examples are computed and compared with independent benchmark solutions to demonstrate the effectiveness of the analysis procedure for modeling 3‐dimensional systems.     

Earthquake analysis of gravity dams including hydrodynamic interaction

A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.     

Seismic response of intake towers including dam–tower interaction

The 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.     

Seismic response of offshore structures in random seas

A study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil-structure interaction effects and also on the evaluation of non-linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi-Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency-domain random vibration approach. It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil-structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.     

Seismic failure probability of concrete slab on CFR dams with welded and friction contacts by response surface method

In this study, failure probability of the concrete slab on concrete-faced rockfill (CFR) dams with welded and friction contact is investigated under earthquake effects by reliability analysis. For this purpose, Torul CFR dam is selected as an example and numerical solutions are performed by considering combination of reliability analysis–finite element method. 1992 Erzincan earthquake acceleration record is used in the finite element analysis considering deconvolved-base rock input model. In this model, the ground motion to be applied to the foundation base rock is obtained by deconvolution of the free-field surface record. In the materially nonlinear analysis, Drucker–Prager model is used for concrete slab and multi-linear kinematic hardening model is utilized for rockfill. Geometrically nonlinearity is also taken into account. Viscous boundary conditions are defined in the finite element model for both foundation soil and reservoir water. The hydrodynamic pressure of the reservoir water is considered using 2D fluid finite elements based on the Lagrangian approach. Both welded contact and friction contact based on the Coulomb’s friction law are defined in the structural connections. Improved Rackwitz–Fiessler method is used with response surface method in the reliability analysis. The tensile and compression strengths of the concrete slab are utilized in the implicit limit state functions considering various thicknesses. The probability of failure of the most critical points in the concrete slab is obtained. According to this study, the probabilities of failure obtained from the CFR dam including friction contact are lower. When the welded contact is considered in joints, the probability of failure of the concrete slab is 1 due to tensile stress limit state and compression stress limit state only if concrete slab is linear. The most critical probability of failure of the concrete slab appears in the case that the concrete slab is linear and rockfill is materially nonlinear. The probability of failure of the concrete slab decreases if the nonlinearity of the concrete is considered. Also, hydrodynamic pressure decreases the reliability of the concrete slab.     

Impact of incident angles of P waves on the dynamic responses of long lined tunnels

The impact of the incident angle of earthquake motion on the seismic response of the long lined tunnels is studied. Based on the time‐domain finite element method with the viscous‐spring artificial boundary condition, the earthquake motion of oblique incidence is transformed into the equivalent nodal forces acting on the truncated boundary of finite element model. In the present work, the formulas of equivalent nodal forces for the plane P wave with arbitrary incident angle are deduced and implemented into the commercial software abaqus   1 . The effectiveness of the formulas and its implementation are demonstrated by two numerical examples with the reference solutions. The proposed method is applied to investigate the seismic responses of the long lined tunnels under the obliquely incident P waves. The numerical results indicate that the seismic responses of the long lined tunnels are highly affected by the incident angles of P waves. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations——Ⅰ: Theory

In this paper, wind-induced vibration control of a single column tower of a cable-stayed bridge with a multistage pendulum mass damper (MSPMD) is investigated. Special attention is given to overcoming space limitations for installing the control device in the tower and the effect of varying natural frequency of the towers during construction. First,the finite element model of the bridge during its construction and the basic equation of motion of the MSPMD are introduced.The equation of motion of the bridge with the MSPMD under along-wind excitation is then established. Finally, a numerical simulation and parametric study are conducted to assess the effectiveness of the control system for reducing the wind-induced vibration of the bridge towers during construction. The numerical simulation results show that the MSPMD is practical and effective for reducing the along-wind response of the single column tower, can be installed in a small area of the tower, and complies with the time-variant characteristics of the bridge during its entire construction stage.     

Simulation of near-fault bedrock strong ground-motion field by explicit finite element method

Based on presumed active fault and corresponding model, this paper predicted the near-fault ground motion filed of a scenario earthquake （Mw=6 3/4 ） in an active fault by the explicit finite element method in combination with the source time function with improved transmitting artificial boundary and with high-frequency vibration contained. The results indicate that the improved artificial boundary is stable in numerical computation and the predicted strong ground motion has a consistent characteristic with the observed motion.     

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

A general procedure for analysis of the response of concrete gravity dams, including the dynamic effects of impounded water and flexible foundation rock, to the transverse (horizontal) and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions, considering the transverse vibration of a monolith of the dam. The system is analysed under the assumption of linear behaviour for the concrete, foundation rock and water. The complete system is considered as composed of three substructures—the dam, represented as a finite element system, the fluid domain, as a continuum of infinite length in the upstream direction, and the foundation rock region as a viscoelastic half-plane. The structural displacements of the dam are expressed as a linear combination of Ritz vectors, chosen as normal modes of an associated undamped dam-rock system. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only a few Ritz vectors. The generalized displacements due to earthquake motion are computed by synthesizing their complex frequency responses using Fast Fourier Transform procedures. The stress responses are calculated from the displacements. An example analysis is presented to illustrate results obtained from this analytical procedure. Computation times for several analyses are presented to illustrate the effectiveness of the procedure.     

A numerical approach for modeling near-fault ground motion and its application in the 1994 Northridge earthquake

An approach for simulating near-fault ground motion was presented by combining the finite fault model with a numerical algorithm, named investigated lump method presented in this paper for wave propagation. The investigated lumps are constructed from the auxiliary quadrilateral grids. The dynamic equilibrium equations of a typical investigated lump have been derived and obtained by integrating the stresses along the contour of the investigated lump. The stresses are calculated using the constitutive relations and the interpolation techniques. The investigated lump method is then implemented using the equilibrium equations of investigated lumps and the calculations of stresses alternately in time domain. The stability criterion of the algorithm has been given. Comparisons with the discrete wave-number method solutions for predicting the ground motions at the Pacoima Dam during the San Fernando earthquake show the validity of the method presented in this paper for simulating near-field ground motions. A finite fault source model has been implemented in the algorithm here. The source parameters given by Wald et al. (1996) [18] are applied to synthesize the ground motions at three stations during the 1994 Northridge earthquake. The simulating results qualitatively match to the corresponding ground motion records. The studies demonstrated that the approach presented in this paper is an effective tool for the numerical simulation of near-fault ground motion.     

Response of offshore towers to strong motion earthquakes

Presented is a stochastic method of analysis of offshore towers subjected to strong motion earthquakes. A zero mean ergodic Gaussian process of finite duration is used to characterize horizontal ground acceleration and full fluid structure interaction effects are included. Numerical results for four representative deep water towers having heights of 475, 675, 875 and 1075 ft are compared with corresponding results obtained by the response spectrum method of analysis. Particular emphasis is placed on the maximum or extreme values of total transverse shear and total overturning moment. Comparisons are made with code values and the role of ductility is briefly discussed.