Tuned liquid dampers for controlling earthquake response of structures

Numerical simulations of a single‐degree‐of‐freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structure's response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure's natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water‐depth to tank‐length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water‐mass to structure‐mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure's natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright © 2000 John Wiley & Sons, Ltd.     

A model of tuned liquid damper for suppressing pitching motions of structures

A tuned liquid damper (TLD), which consists of rigid tanks partially filled by liquid, is a type of passive control device relying upon liquid sloshing forces or moments to change the dynamical properties and to dissipate vibrational energy of a structure. An analytical non-linear model is proposed for a TLD using rectangular tanks filled with shallow liquid under pitching vibration, utilizing a shallow water wave theory. The model includes the linear damping of the sloshing liquid, which is an important parameter in the study of a TLD as it affects the efficiency of the TLD. Shaking table experiments were conducted for verification; good agreement between the analytical simulations and the experimental results was observed in a small excitation amplitude range. The simulations of TLD-structure interaction by using the proposed model show that the TLD can efficiently suppress resonant pitching vibration of a structure. It is also found that the effectiveness of a TLD for suppressing the pitching vibration depends not only on the mass of liquid in the TLD but also on the configuration of the liquid as well as upon the position where the TLD is located. If the configuration of the liquid, i.e. the liquid depth and the TLD tank size, is designed suitably, the TLD can have a large suppressing moment and can be very effective even with a small mass of liquid.     

A nonlinear numerical model for sloped‐bottom tuned liquid dampers

Shaking‐table data for a tuned liquid damper with a sloped bottom of 30° with the horizontal are investigated using a non‐linear numerical model previously developed by Yu, Jin‐kyu, Nonlinear characteristics of tuned liquid dampers. Ph.D. Thesis, Department of Civil Engineering, University of Washington, Seattle, WA, 98195 (1997). Stiffness and damping parameters for this model are obtained and compared with those previously derived for box‐shaped tanks. The values for these parameters reflect the softening spring behaviour of the sloped‐bottom system in contrast to the hardening system evident for the box‐shaped TLD. Consequently, the sloped‐bottom tank should be tuned slightly higher than the fundamental structural frequency in order to obtain the most effective damping. Copyright © 2001 John Wiley & Sons, Ltd.     

The properties of tuned liquid dampers using a TMD analogy

Liquid motions in shallow Tuned Liquid Dampers (TLDs) with rectangular, circular, and annular tanks, subject to harmonic base excitation, are measured experimentally. Using a Single-Degree-of-Freedom (SDOF) Tuned Mass Damper (TMD) analogy, equivalent mass, stiffness and damping of the TLD are calibrated from the experimental results. These parameters are functions of the TLD base amplitude. Some important properties of the TLD are discussed on the basis of these results.     

Investigation of nonlinear sloshing effects in seismically excited tanks

Nonlinear behavior of liquid sloshing inside a partially filled rectangular tank is investigated. The nonlinearity in the numerical modeling of the liquid sloshing originates from the nonlinear terms of the governing equations of the fluid flow and the liquid free surface motion as a not known boundary condition. The numerical simulations are performed for both linear and nonlinear conditions. The computed results using linear conditions are compared with readily available exact solution. In order to verify the results of the nonlinear numerical solution, a series of the shaking table tests on rectangular tank were conducted. Having verified linear and nonlinear numerical models, they are used for computation of near wall sloshing height at a series of real scale tanks (with various dimensions) under the both harmonic and earthquake base excitation. Finally, the nonlinear effects on liquid sloshing modeling are discussed and the practical limitations of the linear solution in evaluating the response of seismically excited liquids are also addressed.     

Tuned liquid dampers simulation for earthquake response control of buildings

This paper is focused on the study of an earthquake protection system, the tuned liquid damper (TLD), which can, if adequately designed, reduce earthquake demands on buildings. This positive effect is accomplished taking into account the oscillation of the free surface of a fluid inside a tank (sloshing). The behaviour of an isolated TLD, subjected to a sinusoidal excitation at its base, with different displacement amplitudes, was studied by finite element analysis. The efficiency of the TLD in improving the seismic response of an existing building, representative of modern architecture buildings in southern European countries was also evaluated based on linear dynamic analyses.     

Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations

A numerical and experimental study on the sloshing behaviours of cylindrical and rectangular liquid tanks is addressed. A three‐dimensional boundary element method for space with the second‐order Taylor series expansion in time is established to simulate the sloshing phenomenon and its related physical quantities inside a liquid tank subjected to horizontal harmonic oscillations or recorded earthquake excitations. The small‐scale model experiments are carried out to verify some results of numerical methods in this study. The comparisons between numerical and experimental results show that the numerical method is reliable for both kinds of ground excitations. Finally, the water wave and the base shear force of a rectangular tank due to harmonic excitation are also presented at different frequencies. A huge cylindrical water tank subjected to a recorded earthquake excitation is used for application and discussion. Copyright © 2007 John Wiley & Sons, Ltd.     

核电结构PCS水箱液动压力分析等效模型

中国核电厂抗震设计规范推荐采用的Housner模型不适用于复杂形状核电储液结构的流固耦合分析。对于AP1000和CAP1400核电站屏蔽厂房顶部非能动安全壳冷却系统重力水箱(简称PCS水箱),基于圆柱形水箱的Housner等效质量-弹簧模型,通过引入水箱体积修正参数,提出PCS水箱的三维等效质量-弹簧模型。采用有限元软件ADINA建立水箱结构流固耦合整体有限元模型以进行模态分析,计算分析PCS水箱和对应环形水箱在不同尺寸和液体深度条件下的液体晃动自振特性。对比整体有限元模型与三维等效质量-弹簧模型计算结果发现,提出的PCS水箱三维等效质量-弹簧模型能给出其内液体晃动各阶振型的液动压力合理估计值,适用于具有复杂形状的PCS水箱液动压力分析。本文的等效模型方法可推广应用于其他复杂形状水箱的液动压力分析。     

Modelling the non‐linear hydrological behaviour of a small Mediterranean forested catchment

A progressive perceptual understanding approach was used to identify a model structure able to represent the non‐linear behaviour of the hydrological cycle in a small intermittent Mediterranean stream. The initial lumped model structure consisting of a series of four connected water tanks (LU3) progressed to a model with five tanks (LU4), and finally to a semidistributed model structure (SD4) in which spatial variability of the evapotranspiration according to the vegetation cover and to the local aspect was considered. In the final model structure, which gave the best fit (Nash–Sutcliffe efficiency index = 0·78), an additional tank representing the riparian zone was included (SD4‐R). Results showed that the abrupt changes of the riparian water table during summer and the formation of a perched water table during the transition from dry to wet conditions were the main mechanisms leading to the non‐linear hydrological behaviour. The transpiration process from the saturated zone and the spatial variability of evapotranspiration resulted in key factors successfully representing the annual water balance. The spatial and temporal validations carried out for each of the four model structures considered in this study supported the hypothesis adopted during the calibration process. Copyright © 2008 John Wiley & Sons, Ltd.     

Field investigation and modelling of coupled stream discharge and shallow water‐table dynamics in a small Mediterranean catchment (Sardinia)

In the semi‐arid Mediterranean environment, the rainfall–runoff relationships are complex because of the markedly irregular patterns in rainfall, the seasonal mismatch between evaporation and rainfall, and the spatial heterogeneity in landscape properties. Watersheds often display considerable non‐linear threshold behavior, which still make runoff generation an open research question. Our objectives in this context were: to identify the primary processes of runoff generation in a small natural catchment; to test whether a physically based model, which takes into consideration only the primary processes, is able to predict spatially distributed water‐table and stream discharge dynamics; and to use the hydrological model to increase our understanding of runoff generation mechanisms. The observed seasonal dynamics of soil moisture, water‐table depth, and stream discharge indicated that Hortonian overland‐flow was negligible and the main mechanism of runoff generation was saturated subsurface‐flow. This gives rise to base‐flow, controls the formation of the saturated areas, and contributes to storm‐flow together with saturation overland‐flow. The distributed model, with a 1D scheme for the kinematic surface‐flow, a 2D sub‐horizontal scheme for the saturated subsurface‐flow, and ignoring the unsaturated flow, performed efficiently in years when runoff volume was high and medium, although there was a smoothing effect on the observed water‐table. In dry years, small errors greatly reduced the efficiency of the model. The hydrological model has allowed to relate the runoff generation mechanisms with the land‐use. The forested hillslopes, where the calibrated soil conductivity was high, were never saturated, except at the foot of the slopes, where exfiltration of saturated subsurface‐flow contributed to storm‐flow. Saturation overland‐flow was only found near the streams, except when there were storm‐flow peaks, when it also occurred on hillslopes used for pasture, where soil conductivity was low. The bedrock–soil percolation, simulated by a threshold mechanism, further increased the non‐linearity of the rainfall–runoff processes. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

Equivalent mechanical models of sloshing fluid in arbitrary‐section aqueducts

This paper reports on a semi‐analytical/numerical method to model sloshing water in an arbitrarily shaped aqueduct. The water motion is assumed to be inviscid, compressible, and linear (small displacement). The transverse sloshing fluid in an aqueduct is equivalently simplified as a fixed rigid mass M₀ and a mass–spring system (M₁, K₁). According to a rule that the actual fluid (computed with finite element model) and its equivalent mechanical model have the same first sloshing frequency and acting effects on the aqueduct, the analytical solutions of the fixed (impulsive) mass M₀, sloshing (convective) massM₁, spring stiffness K₁, and their locations in the aqueduct body are acquired by the least squares (curve fitting) algorithm. Applying this equivalent principle, the equivalent mechanical models are respectively obtained for the sloshing water in rectangular, semicircular, U‐shaped, and trapezoid aqueducts. The equivalent principle and fluid models are validated through comparison investigations involving rectangular and U‐shaped aqueducts. The dynamic properties and seismic responses of the original and equivalent systems are simulated, compared, and discussed for a U‐shaped aqueduct bridge. The main purpose of this paper is to provide a simplified model of sloshing fluid for the seismic/wind‐resistant computation of the support structures of the aqueduct bridge. Copyright © 2011 John Wiley & Sons, Ltd.     

A simple model of hillslope response for overland flow generation

This paper deals with the derivation of the hydrological response of a hillslope on the assumption of quick runoff by surface runoff generation. By using the simple non‐linear storage based model, first proposed by Horton, an analytical solution of the overland flow equations over a plane hillslope was derived. This solution establishes a generalization for different flow regimes of Horton's original solution, which is valid for the transitional flow regime only. The solution proposed was compared successfully with that of Horton and, for the turbulent flow regime, to the one derived from kinematic wave theory. This solution can be applied easily to both stationary and non‐stationary rainfall excess events. An analytical solution for the instantaneous response function (IRF) was also derived. Finally, simple expressions to compute peak and time to peak of IRF are proposed. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparison of two modeling approaches for groundwater–surface water interactions

An assessment of interactions between groundwater and surface water was carried out by applying two different modeling approaches to a small‐scale study area in the municipality of Havelock, Quebec. The first approach involved a commonly used sequential procedure that consists in determining the daily recharge rate using a quasi 2D infiltration model (HELP), applied in the next step as an imposed flux to a 3D finite‐element groundwater flow model. The flow model was calibrated under steady‐state and transient conditions against measured water levels. The second approach was based on a recently developed physically based, 3D fully coupled groundwater–surface water flow model (CATHY) applied to the entire flow domain in an integrated manner. Implementation, calibration, and results of the simulations for both approaches are presented and discussed. For equal annual precipitation (1038 mm/y) and evapotranspiration (556 mm/y), the second approach computed a recharge rate of 233 mm/y (8.9% higher than the first approach) and a net upward flow from the fractured aquifer (the first approach predicted a net downward flow to the rock). The simulated annual discharge was similar for the two approaches (9.6% difference). Both approaches were found to be useful in understanding the interactions between groundwater and surface water, although limitations are apparent in the sequential procedure's inability to account for surface–subsurface feedbacks, for instance near stream reaches where groundwater discharge is prevalent. The decoupled, two‐model approach provides disaggregated surface, vadose, and aquifer flows, and a simple aperçu at the different components of total discharge. The fully coupled model accounts for continuous water exchanges between the land surface, subsurface, and stream channel in a more complex manner, and produces a better match against observed data. Copyright © 2012 John Wiley & Sons, Ltd.     

Fluid–structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM–FEM and comparison with test results

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.     

Predicting Collector Well Yields with MODFLOW

Groundwater flow models are commonly used to design new wells and wellfields. As the spatial scale of the problem is large and much local‐scale detail is not needed, modelers often utilize two‐dimensional (2D) or quasi three‐dimensional models based on the Dupuit‐Forchheimer assumption. Dupuit models offer a robust set of tools for simulating regional groundwater flow including interactions with surface waters, the potential for well interference, and varying aquifer properties and recharge rates. However, given an assumed operating water level or drawdown at a well screen, Dupuit models systematically overpredict well yields. For design purposes, this discrepancy is unacceptable, and a method for predicting accurate well yields is needed. While published methods exist for vertical wells, little guidance is available for predicting yields in horizontal screens or collector wells. In plan view, a horizontal screen has a linear geometry, and will likely extend over several neighboring cells that may not align with rows or columns in a numerical model. Furthermore, the model must account for the effects of converging three‐dimensional (3D) flow to the well screens and hydraulic interference among the well screens; these all depend on the design of a specific well. This paper presents a new method for simulating the yield of angled or horizontal well screens in numerical groundwater flow models, specifically using the USGS code MODFLOW. The new method is compared to a detailed, 3D analytic element model of a collector well in a field of uniform flow.     

水平地震激励下储罐液体晃动与提离分析

在考虑地基与储罐相互作用的情况下,采用有限元法对储罐在水平地震荷载作用下的液面晃动及储罐提离反应进行了分析。结果表明:罐内液体的晃动是长周期运动,其周期受地震动影响。无论是小体积罐还是大体积罐,在一定的地震烈度下均可以发生提离,而且储罐发生提离的时刻大多数是在地震动的峰值过后的一段时间内。大体积的储罐的提离明显小于小体积的罐。底板提离区域为月牙形。     

One‐ and two‐dimensional modelling of overland flow in semiarid shrubland,Jornada basin,New Mexico

Two distributed parameter models, a one‐dimensional (1D) model and a two‐dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event‐based and represent each watershed by an array of 1‐m² cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite‐difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second‐order predictor–corrector finite‐difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large‐scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright © 2006 John Wiley & Sons, Ltd.     

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.