极限安全地震动下考虑土-结构相互作用的核电站安全壳响应分析

根据黏弹性人工边界的基本原理,结合有限元分析软件ABAQUS和MATLAB辅助程序,在地基有限区域上添加黏弹性人工边界并实现极限安全地震动的输入。基于ABAQUS软件平台,对CPR1000安全壳构建了土-结构相互作用体系的数值模拟模型,分析其在极限地震动下的动力响应,并将计算结果与考虑刚性基础的安全壳结构响应数据进行对比。结果表明:核电站CPR1000安全壳结构在极限安全地震动下仍能保持良好的密闭性。考虑土-结构相互作用后分析所得安全壳结构受到的应力、加速度峰值和相对位移均有所增大,使用刚性地基模型要偏于危险。     

Nonlinear hysteresis curve derived by direct numerical investigation of acceleration data

Acceleration measurements often provide engineers with a means by which to determine the forces within dynamic structural systems; however, for certain problems, information about the structural motion and the displacement-time history may also be of interest. One such application deals with the evaluation of stiffness in reinforced concrete structures during seismic events. Scaled model test of these events suggest that the stiffness of these structures often degrades drastically. The displacement response of these seismic events is required both for the hysteresis curve (load vs displacement) and evaluation of postulated structural stiffness models. By applying data processing techniques to acceleration data obtained from scaled model tests, displacement-time histories were obtained for low aspect shear walls subjected to simulated seismic loadings. Procedures, difficulties, and results of this work are discussed herein.     

Time harmonic point load and dynamic contact problem of contacting fluid and poroelastic half-spaces

The dynamic response of contacting fluid and fluid-saturated poroelastic half- spaces to a time-harmonic vertical point force or a point pore pressure is investigated. The solutions are formulated using the boundary conditions at the fluid-porous medium interface. The point load solutions are then used to solve the dynamic problem of the vertical vibration of a rigid disc (both permeable and impermeable discs are included) on the surface of the poroelastic half-space. The contact problems are solved by integrating the point force and point pore pressure solutions over the contact area with unknown discontinuous force and pore pressure distributions, which are determined from the boundary conditions. The solutions are expressed in terms of dual integral equations, which are converted to Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic compliance coefficient for the cases with or without fluid overlying the poroelastic half-space are presented to show the effects of the fluid. The influence of the permeability condition of the disc on the compliance of the poroelastic half-space is investigated. The displacement, vertical stress, pore pressure in the poroelastic half-space and water pressure in the fluid half-space are also examined for different poroelastic materials and frequencies of excitation. The present results are helpful in the study of the dynamic response of foundations on the seabed under seawater.     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

NUMERICAL MODELLING OF STANDARD AND CONTINUOUS VERTICAL ELECTRICAL SOUNDINGS1

Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration. This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.     

Three-dimensional dynamic soil–structure interaction analysis in the time domain

A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd     

An effective approach to determine the dynamic source parameters

In this study, we present a new and effective method to determine the dynamic source parameters (i.e., stress drop and strength distribution). We first assume that the kinematic source parameters, i.e., the slip and rupture time distributions on the fault plane, are known from the previous source inversion studies. Then, using the seismic source representation theorem we determine the dynamic stress field on a fault plane from known kinematic parameters. Finally, we determine the strength of the fault defined as the peak stress just before the rupture. We have tested the validity of this method by using an illustrative two-dimensional analytical example. To assess the applicability of this method, we have applied it to study the 1979 Imperial Valley earthquake, and obtained consistent results with those ofMiyatake's (1992) andQuin's (1990). Compared with previous methods, this new method is simple, straightforward and accurate, and needs much less calculation. Therefore, it is expected to be useful in exploring the seismic source process.     

Seismic performance and damage incurred by monolithic concrete self-centering rocking walls under the effect of axial stress ratio

Self-centering rocking walls offer the possibility of minimizing repair costs and downtimes, and also nullify the residual drift after seismic events, thanks to their self-centering properties. In this paper, the effect of axial stress ratio on the behavior of monolithic self-centering rocking walls is investigated by utilizing a developed finite element model. To verify the validity of the finite element model, results and observed damage in the model are compared with those of a full-scale wall test. The axial stress ratio is varied from 0.024 to 0.30 while keeping the other structural parameters constant. For qualitative damage evaluation, the observed damage in the model compared with expected damage states of desired performance levels. In order to evaluate the incurred damage quantitatively, the amount of crushing and damage in the wall is calculated by utilizing several ratios (crushing ratio and damage ratio). Furthermore, seismic response factors (i.e., μ, R and C_d) are calculated for different axial stress ratio values. The obtained results showed that, in order to satisfy the requirements of desired performance levels, the maximum axial stress ratio should be approximately within the range of 0.10–0.15. In addition, the maximum overall damage ratio and crushing ratio are suggested to be less than 5%. For axial stress ratio higher than 0.15, the flag-shaped pattern of hysteresis curves completely disappeared and the variation of displacement ductility is less sensitive to axial stress ratio. Considering the maximum axial stress ratio limited to 0.150, values of 4 and 3.5 are conservatively proposed as a period-independent response modification factor and displacement modification factor of the investigated structural wall, respectively.     

A seismic free field input model for FE-SBFE coupling in time domain

A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element (SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space. To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built on unbounded soil. Supproted by: the National Key Basic Research and Development Program under Grant No. 2002CB412709     

Inelastic torsional response of buildings to the 1985 Mexican earthquake: a parametric study

This study aims to determine the influence of torsional coupling on the inelastic response of a series of models representing typical structural configurations in real buildings. The lake bed (SCT) east-west component of the 1985 Mexico City earthquake was employed in the analysis, and is representative of a severe ground motion known to have induced large inelastic structural deformations in a high proportion of those buildings having asymmetrical distributions of stiffness and/or strength. Material non-linearity in lateral load-resisting elements has been defined using a hysteretic Ramberg-Osgood model. Structural eccentricities have been introduced into the building models by (i) asymmetrical distributions of stiffness and/or strength, (ii) asymmetrical configuration of lateral load-resisting elements, or (iii) varying post-elastic material behaviour in the resisting elements. The dynamic inelastic response of these models has been obtained by a numerical integration of the relevant equations of motion, expressed in a non-dimensional incremental form.

In the elastic range, the results correlate well with those of previous studies. In the inelastic range, it is concluded that the peak ductility demand of the worst-affected element increases with the ground excitation level across the range of building periods considered, and that the influence of torsional coupling on the key response parameters is model dependent. Most significantly, the strength eccentricity relative to the centre of mass has been shown to influence the peak edge displacement response more than conventionally employed stiffness eccentricity.     

Dynamic response characterization and simplified analysis methods for viscoelastic dampers considering heat transfer

Viscoelastic (VE) dampers are sensitive to temperature, excitation frequency, and strain level. As they dissipate the kinetic energy from earthquake or wind-induced structural vibrations, their temperature increases from the heat generated, consequently softening their VE materials and lowering their dynamic mechanical properties. Temperature increase can be significant for long-duration loading, but can be limited by heat conduction and convection which depend on damper configuration. The writers analytically explored such effect on the six different dampers by using their previously proposed three-dimensional finite-element analysis method. Results provided better understanding of how heat is generated within the VE material, conducted and stored in different damper parts, and dispersed to the surrounding air. These results also led to characterization of both local (e.g., temperatures, properties, and strain energy density) and global (e.g., hysteresis loops, and stiffness) behavior of VE dampers, and provided a framework for a new simplified one-dimensional (1D) modeling approach for time-history analysis. This new proposed 1D method greatly improves the computation time of the previously proposed long-duration method coupling fractional time-derivatives VE constitutive rule with 1D heat transfer analysis. Unlike the previous method, it idealizes uniform shear strain and VE material property distributions for computational efficiency, but still simulating non-uniform temperature distribution along the thickness direction of the VE material. Despite the approximations, it accurately predicts VE damper global responses.     

Dynamics of rigid strip foundations embedded in orthotropic elastic soils

This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations.     

Steady state rocking response of rigid blocks part 1: Analysis

The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning.     

Two-dimensional development of the dynamic coupled consolidation scaled boundary finite-element method for fully saturated soils

The scaled boundary finite-element method is a powerful tool used to analyse far-field boundary soil–structure interaction problems. In this paper, the method is extended to include Biot's coupled consolidation in order to deal with fully saturated soil as a two-phase medium. The advantages of this method are explained in this paper. The detailed formulation considers the general two-dimensional (2D) analysis case, accounting for body forces and surface tractions in both bounded and unbounded media.     

In-plane dynamic Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic(TI)half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf(1985),and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.     

Design of multiple tuned mass dampers by using a numerical optimizer

A new method to design multiple tuned mass dampers (multiple TMDs) for minimizing excessive vibration of structures has been developed using a numerical optimizer. It is a very powerful method by which a large number of design variables can be effectively handled without imposing any restriction before the analysis. Its framework is highly flexible and can be easily extended to general structures with different combinations of loading conditions and target controlled quantities. The method has been used to design multiple TMDs for SDOF structures subjected to wide‐band excitation. Some novel results have been obtained. To reduce displacement response of the structure, the optimally designed multiple TMDs have distributed natural frequencies and distinct damping ratios at low damping level. The obtained optimal configuration of TMDs was different from the earlier analytical solutions and was proved to be the most effective. A robustness design of multiple TMDs has also been presented. Robustness is defined as the ability of TMDs to function properly despite the presence of uncertainties in the parameters of the system. Numerical examples of minimizing acceleration structural response have been given where the system parameters are uncertain and are modeled as independent normal variates. It was found that, in case of uncertainties in the structural properties, increasing the TMD damping ratios along with expanding the TMD frequency range make the system more robust. Meanwhile, if TMD parameters themselves are uncertain, it is necessary to design TMDs for higher damping ratios and a narrower frequency range. Copyright © 2004 John Wiley & Sons, Ltd.     

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue; displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement). Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault. Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly.     

Anti-plane foundationless soil–structure interaction

This paper presents a closed-form wave function analytic solution of two-dimensional scattering and diffraction of anti-plane SH-waves by a two-dimensional foundationless structure that corresponds to a shear wall on an elastic half-space. A wave-function expansion method is used to solve this model by first prescribing a set of wave functions with undetermined coefficients and then assembling them together based on the stress and displacement boundary conditions on the surface between the structure and half space. This results in a set of infinite equations to be solved by truncating to a finite set. The amplitudes and residuals of the displacement and stress distributions around the structure and nearby ground surface will be discussed carefully. While the solution is analytical, the computation of the numerical results involves the evaluation of complicated integrals. This analytic solution will be helpful to the understanding of propagation of seismic or other stress waves within the superstructure(s) undergoing earthquakes or other blast loads.     

Two-dimensional scattering of SH waves in a soil layer underlain with a sloping bedrock

A two-dimensional analysis is applied to examine the effect that a sloping bedrock half-space has on the amplification of an anti-plane shear wave. The direct boundary integral equation method is used for the two-dimensional analysis. The particular soil–rock configuration investigated includes a homogeneous soil layer underlain by a sloping rock half-space. The rock half-space dips for a horizontal distance L and then becomes horizontal so that the overlying soil layer has a thickness H that remains constant from this point to infinity. The materials in the soil–rock configuration are considered viscoelastic except in the rock half-space below soil layer thickness H, which is considered elastic. This limitation in damping is due to the correction used for the truncation of the half-space boundary. Four cases are used to study the relationship between rock slope and surface displacement, vertical, 1:2, 1:4, 1:8. Surface displacements are determined for each of these cases for half-space incidence angles of 90, 75, and 60°. To allow for applicability to a wide range of problems, results are determined as a function of dimensionless parameters. In addition, solutions from a one-dimensional analysis are compared with the results of the two-dimensional analysis to establish limits outside of which a one-dimensional analysis suffices.