Seismic analysis of non-linearly base-isolated soil-structure interacting reactor building by way of the hybrid frequency-time-domain procedure

The seismic analysis of a reactor building on a sliding-type base isolation is performed by way of the hybrid frequency-time-domain procedure. The frequency dependence of the foundation stiffness coefficients is duly accounted for in the analysis, although the problem is non-linear. The response results are shown to be reliable by way of comparison with the results of a time-stepping algorithm in the specialized case of constant foundation stiffness coefficients. The fact that such an analysis can be performed is an outstanding result, particularly when considering that no difficulties are encountered in the implementation and in the calculation. The flow chart used to implement the procedure is presented in the paper. The reactor building is analysed for three different sites with each site having three sets of material properties. It appears that the structural response is not strongly affected by the frequency dependence of the foundation stiffness coefficients. This also holds true as far as the response of equipment attached to the superstructure is concerned. For all practical purposes this frequency dependence may be disregarded in favour of constant spring and damping coefficients.     

An incremental mode-superposition for non-linear dynamic analysis

This paper uses an incremental mode-superposition procedure to compute the inelastic dynamic response of multi-degree-of-freedom systems. A damping matrix proportional to the instantaneous properties is used throughout the analysis. The non-linear response of several shear type plane and space frames with elastic-plastic and bilinear column properties subjected to ground excitation was computed by both the incremental mode-superposition and the direct integration of the coupled equations of motion. When all modes are considered, the responses computed by the incremental mode-superposition are identical to those from the direct integration. Fewer modes can also be used to compute the response with reasonable accuracy by performing the modal truncation for each time increment. The study shows that incorporating instantaneous damping in non-linear dynamic analysis is relatively simple and requires less computational time than the direct integration.     

An imposed force summation method for non-linear dynamic analysis

A method of obtaining the response of a non-linear system is proposed, which involves imposing the solution upon the equations of motion for a linear system and solving using selected modes of vibration. Contribution from the remaining modes of the system is included in terms of their quasi-static response. The method is developed and illustrated with reference to a system with material non-linearity and special reference is given to the dynamic analysis of embankment dams.     

A modal procedure for seismic analysis of non-linear base-isolated multistorey structures

A modal procedure for non-linear analysis of multistorey structures with high-damping base-isolation systems was proposed. Two different isolation devices were considered in the analysis: an high-damping laminated rubber bearing and a lead-rubber bearing. Starting from deformational properties verified by tests, the isolation systems were characterized using three different analytical models (an Elastic Viscous, a Bilinear Hysteretic and a Wen's Model) with parameters depending from maximum lateral strain. After non-linear modelling of isolation and lateral-force-resisting systems, the effects of material non-linearities were considered as pseudo-forces applied to the equivalent linear system (Pseudo-Force Method) and the formally linearized equations of motion were uncoupled by the transformation defined by the complex mode shapes. The modal responses were finally obtained with an extension of Nigam–Jennings technique to non-linear and non-classically damped systems, in conjunction with an iterative technique searching for non-linear contributions satisfying equations of motion and constitutive laws. Since the properties of the isolated structure usually change with maximun lateral strain of isolation bearings, the integration of a new set of governing equations was required for each design-displacement value. The procedure proposed was described in detail and then applied for the determination of modal and total seismic responses in some real cases. At first, a very good agreement between non-linear responses obtained with the proposed mode superposition and with a direct integration method was observed. Then a comparison of results obtained with the three different analytical models of the isolation bearings was carried out. At last, the exact modal response obtained with analytical models depending from the design displacement of the isolation bearings was compared with two different approximated solutions, evaluated using mode shapes and isolation properties, respectively, calculated under simplified hypothesis.© 1998 John Wiley & Sons, Ltd.     

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing (RTDHT).This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT.The exponential delay term is transferred into a rational fraction by the Padé approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique.First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure.The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness.For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay.For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode.Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable.Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.     

A simple error estimator and adaptive time stepping procedure for dynamic analysis

A simple local error estimator is presented for time integration schemes in dynamic analysis. This error estimator involves only a small computational cost. The time step size is adaptively adjusted so that the local error at each time step is within a prescribed accuracy. It is found that the estimator performs well under various circumstances and provides an economical adaptive process. Attempts to estimate the global time integration error are also reported.     

A computational procedure for the implementation of equivalent linearization in finite element analysis

This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE‐analysis to evaluate non‐linear structural response under random excitation. A computational procedure is presented which requires the non‐linear part of the system to be subdivided into suitable sub‐domains (elements). Each element is independently linearized using only a minimum number of co‐ordinates. A local co‐ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non‐linear constitutive laws are defined by the local co‐ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE‐models. To illustrate the applicability of the procedure, two different non‐linear systems are analysed under bi‐directional earthquake excitation. Copyright © 2000 John Wiley & Sons, Ltd.     

Approximate incremental dynamic analysis using the modal pushover analysis procedure

Incremental dynamic analysis (IDA)—a procedure developed for accurate estimation of seismic demand and capacity of structures—requires non‐linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response—all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC‐Los Angeles 3‐, 9‐, and 20‐storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA‐based approximate procedure reduces the computational effort by a factor of 30 (for the 9‐storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses—all the way from elastic behaviour to global dynamic instability—provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9‐ and 20‐storey buildings, although their dynamics is more complex, involving several ‘modes’ of vibration. For all three buildings, the accuracy of the MPA‐based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability. Copyright © 2006 John Wiley & Sons, Ltd.     

On non-linear dynamic analysis in the frequency domain: Algorithms and applications

It is well known that the solution of the forced vibration of a N-DOF dynamical problem is very cumbersome when conditions which allow the equations to uncouple do not exist. In the literature several techniques were proposed to overcome the problem, but they were mainly focused on a particular problem in turn. So, we deemed it useful to search for a unifying procedure able to deal with different sources of non-linear behaviour introducing only minor changes in the operation flow. In this respect, attention is paid to the Alternating Frequency/Time domain method (AFT) which draws its robustness from the speed and switching capabilities of the Fast Fourier Transform; moreover, taking advantage of the pseudo-force concept, we can arrive at a solution method featuring greater generality and able to solve different non-linear dynamical problems by means of specialization of the same conceptual framework (G-AFT or Generalized AFT). In the first section of the paper the theoretical background is discussed in detail and the proposed algorithms are presented. In the second one, several examples of technical relevance are documented and solved, highlighting the efficiency, convergence and accuracy of the presented algorithm. For cases such as an 11-storey building or a block simulated power plant we introduce the soil-structure interaction effect by means of non-proportional damping; the responses computed either by direct frequency analysis or by iteration are compared with existing solutions or with time domain solutions determined through the Newmark β method. An original example prepared by the authors and fully referenced is finally worked out in order to show the capability of the method when Coulomb damping is taken into account; this effect covers a significant practical relevance in the base isolation field.     

土边坡地震反应及其动力稳定性分析

本文建立了计算土边坡地震反应及评价其动力稳定性的一个数值分析模型，将上边坡在动力作用下的应力状态简化为自重应力状态和附加动力状态的叠加，并对这两个应力状态分别进行研究。本文用时域集中质量显式有限元方法结合多次透射公式，研究了无限域中边坡在动力作用下的位移场和应力场，提出了土边坡动力稳定性的定量评价方法。     

Archaeoseismology: Methodological issues and procedure

Archaeoseismic research contributes important data on past earthquakes. A limitation of the usefulness of archaeoseismology is due to the lack of continuous discussion about the methodology. The methodological issues are particularly important because archaeoseismological investigations of past earthquakes make use of a large variety of methods. Typical in situ investigations include: (1) reconstruction of the local archaeological stratigraphy aimed at defining the correct position and chronology of a destruction layer, presumably related to an earthquake; (2) analysis of the deformations potentially due to seismic shaking or secondary earthquake effects, detectable on walls; (3) analysis of the depositional characteristics of the collapsed material; (4) investigations of the local geology and geomorphology to define possible natural cause(s) of the destruction; (5) investigations of the local factors affecting the ground motion amplifications; and (6) estimation of the dynamic excitation, which affected the site under investigation. Subsequently, a ‘territorial’ approach testing evidence of synchronous destruction in a certain region may delineate the extent of the area struck by the earthquake. The most reliable results of an archaeoseismological investigation are obtained by application of modern geoarchaeological practice (archaeological stratigraphy plus geological–geomorphological data), with the addition of a geophysical-engineering quantitative approach and (if available) historical information. This gives a basic dataset necessary to perform quantitative analyses which, in turn, corroborate the archaeoseismic hypothesis. Since archaeoseismological investigations can reveal the possible natural causes of destruction at a site, they contribute to the wider field of environmental archaeology, that seeks to define the history of the relationship between humans and the environment. Finally, through the improvement of the knowledge on the past seismicity, these studies can contribute to the regional estimation of seismic hazard.     

A hybrid analysis method for linear dynamic soil-structure interaction in time and frequency domain

IntroductionThe analysis of dynamic soil-structure interaction for important engineering project is still based on linear model (including equivalent linear model) with complex damping, and traditional frequency domain method (Lysmer, et al, 1975, 1981; DING, et al, 1999). Namely, first calculating frequency domain solution by Fourier transform, and then calculating time domain solution by Fourier inverse transform. The motion equation of a system in frequency domain is usually written as (…     

动力反应分析的显式积分方法及其稳定性

Newm ark-更新精细积分法是动力方程求解的隐式的时域逐步积分法,其稳定性条件非常容易满足。与隐式方法相比较,显式积分方法不需要求解耦联的方程组,可以有效地减少内存占用和机时耗费。因此,根据显式积分方法的特点和优点,基于Newm ark-更新精细积分法的基本思想,提出其显式积分格式。对显式积分方法的精度与稳定性进行了初步的分析,指出该显式积分方法具有极好的稳定性,其精度比隐式积分方法的精度稍低。随着时间步长的增加,其精度优于传统的方法。     

Reliability analysis of three-dimensional dynamic slope stability and earthquake-induced permanent displacement

Different models were developed for evaluating the probabilistic three-dimensional (3D) stability analysis of earth slopes and embankments under earthquake loading using both the safety factor and the displacement criteria of slope failure. In the 3D analysis, the critical and total slope widths become two new and important parameters.The probabilistic models evaluate the probability of failure under seismic loading considering the different sources of uncertainties involved in the problem, i.e. uncertainties stemming from the discrepancies between laboratory-measured and in-situ values of shear strength parameters, randomness of earthquake occurrence, and earthquake-induced acceleration. The models also takes into consideration the spatial variabilities and correlations of soil properties.Five probabilistic models of earthquake-induced displacement were developed based on the non-exceedance of a limited value criterion. Moreover, a probabilistic model for dynamic slope stability analysis was developed based on 3D dynamic safety factor.These models are formulated and incorporated within a computer program (PTDDSSA).A sensitivity analysis was conducted on the different parameters involved in the developed models by applying those models to a well-known landslides (Selset landslide) under different levels of seismic hazard.The parametric study was conducted to evaluate the effect of different input parameters on the resulting critical failure width, 3D dynamic safety factor, earthquake-induced displacement and the probability of failure. Input parameters include: average values and coefficients of variations of water table, cohesion and angle of friction for effective stress analysis, scales of fluctuations in both distance and time, hypocentral distance, earthquake magnitude, earthquake strong shaking period, etc.The hypocentral distance and earthquake magnitude were found to have major influence on the earthquake-induced displacement, probability of failure (i.e. probability of allowable displacement exceedance), and dynamic 2D and 3D safety factors.     

Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions

Several procedures for non-linear static and dynamic analysis of structures have been developed in recent years. This paper discusses those procedures that have been implemented into the latest European and US seismic provisions: non-linear dynamic time-history analysis; N2 non-linear static method (Eurocode 8); non-linear static procedure NSP (FEMA 356) and improved capacity spectrum method CSM (FEMA 440). The presented methods differ in respect to accuracy, simplicity, transparency and clarity of theoretical background. Non-linear static procedures were developed with the aim of overcoming the insufficiency and limitations of linear methods, whilst at the same time maintaining a relatively simple application. All procedures incorporate performance-based concepts paying more attention to damage control. Application of the presented procedures is illustrated by means of an example of an eight-storey reinforced concrete frame building. The results obtained by non-linear dynamic time-history analysis and non-linear static procedures are compared. It is concluded that these non-linear static procedures are sustainable for application. Additionally, this paper discusses a recommendation in the Eurocode 8/1 that the capacity curve should be determined by pushover analysis for values of the control displacement ranging between zero and 150% of the target displacement. Maximum top displacement of the analyzed structure obtained by using dynamic method with real time-history records corresponds to 145% of the target displacement obtained using the non-linear static N2 procedure.     

Dynamic non-linear analysis of reinforced concrete shear wall by finite element method with explicit analytical procedure

A numerical procedure for a dynamic non-linear finite element analysis is proposed here to analyse three-dimensional reinforced concrete shear wall structures subjected to earthquake motions. A shear wall is modelled as a quasi-three dimensional structure which is composed of plane elements considering the in-plane stiffness of orthogonal flange panels. The proposed constitutive model is based on the non-linearity of reinforcement and concrete in which the tension stiffening in tension and the degradation of stiffness and strength in compression of concrete after cracking are considered. The acceleration-pulse method, which is a kind of explicit analytical procedure, is employed to solve the non-linear dynamic equations, where the dynamic equation can be solved without stiffness matrix and so the iterative procedure is not necessary for descending portion of stress–strain relationship caused by cracking and softening after compressive strength in concrete. The damping effect is considered by assuming equivalent viscous damping which can give good cyclic behaviours of inertia force vs. displacement relationships. This analytical method was applied to a test specimen of a reinforced concrete shear wall with a H-shaped section which was vibrated up to failure by using a large-scale shaking table with high -performance in Japan. The test was performed as one of the dynamic model tests for evaluation of seismic behaviour of nuclear reactor buildings. The calculations were performed sequentially from the elastic range to failure. The comparison with the test results shows that this approach has good accuracy. © 1997 by John Wiley & Sons Ltd     

垃圾填埋场动力稳定机理及稳定分析研究现状与进展

简述国内外在垃圾填埋场动力稳定机理及稳定分析方面的研究现状与最新进展,包括：1．垃圾土（MSW）与接触面的属性参数;2．垃圾土的本构模型;3．填埋场动力分析方法。     

Observations on non-linear dynamic characteristics of suspension bridges

For most forms of loading static and dynamic response of a suspension bridge is modelled adequately by linear analysis. By examining the two principal non-linearities of inclined and vertical hanger suspension bridges the limitations of linear analyses are shown. The inclined hanger configuration is shown to be the more strongly non-linear. Some examples are given for simplified planar analyses of this type of bridge to large amplitude vehicular, random, sinusoidal and propagating earthquake excitation, showing that the effect only becomes significant when deflections approach the extent of cable sag due to cable elasticity.