Deflection amplification factor for estimating seismic lateral deformations of RC frames

Different values have been assigned to the ratio of the defl ection amplifi cation factor(Cd) to the response modifi cation factor(R) for a specifi ed force-resisting system in the seismic design provisions while the same application is defi ned for it. An analytical study of the seismic responses of several reinforced concrete frames subjected to a suite of earthquake records performed in this research indicate that the stories’ overstrength and stiffness distribution along the structural height can affect local defl ections more than global ones. Therefore, the Cd/R ratio is calculated based on the ratio of both maximum inelastic to maximum elastic displacements and interstory drifts. Due to damage concentration in some specifi c stories, the defl ection amplifi cation factor calculated based on inelastic interstory drifts was larger than that of the inelastic displacements. Consequently, a minimum value of 1.0 is recommended for the Cd/R ratio in order to estimate maximum inelastic drifts. The ratio of inelastic to elastic displacement was generally found to increase slightly along the structural height for the studied RC models. In addition, it was detected that the story damage indices of the studied RC frames decrease when the inverted value of inelastic interstory drift ratios are increased through a(negative) power form.     

The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid

This paper discusses surface displacements, surface strain, rocking, and energy partitioning during reflection-of-plane waves in a fluid-saturated poroelastic half-space. The medium is modeled by Biot's theory, and is assumed to be saturated with inviscid fluid. A linear porosity-modulus relation based on experimental data on sandstones is used to determine the material parameters for Biot's model. Numerical results in terms of angle of incident waves and Poisson's ratio are illustrated for various porosities and degrees of solid frame stiffness. The results show that the amount of solid frame stiffness controls the response of a fluid-saturated porous system. A poroelastic medium with essentially dry-frame stiffness behaves like an elastic medium, and the influence of pore fluid increases as dry-frame stiffness is reduced. The effects of a second P-wave become noticeable in poroelastic media with low dry-frame stiffness.     

Transient response of single piles under horizontal excitations

The general time-domain boundary element in cylindrical co-ordinates developed for the study of wave propagation in a layered half-space is extended to the response analysis of single piles under horizontal transient excitations. The pile is treated as a beam, and therefore, only the bending stiffness has to be considered in the analysis. As required by the non-axisymmetric nature of the problem, the soil is modelled by boundary (cylindrical) elements with the vertical, radial and tangential displacements as well as their corresponding tractions as independent variables. The characteristic matrices for the two different types of element can be formed in the usual manner, and they are combined to form the equation of motion for the whole system by virtue of compatibility and equilibrium conditions along the pile-soil interface. The transient responses of a pile under Heaviside loads are found to converge to the static values. Parametric studies are carried out to reveal the influences of pile-soil stiffness ratio (E_p/E_s) and soil layering.     

复合外套型特高压交流CVT抗震与减震试验研究

为研究复合外套型电气设备的抗震性能与安装减震装置后的减震效果,对其进行特高压交流CVT地震模拟振动台试验研究,分析设备的动力特性与地震响应。白噪声试验结果表明试验设备安装减震器后其结构第一阶频率由1.07Hz略降低至1.04Hz,即减震装置对结构的整体刚度影响较小;人工波试验中原结构在地震动峰值加速度0.2g(PAG=0.2g)抗震试验中设备最大应力与位移响应为46.33 MPa与349.12mm,减震结构在PAG=0.5g抗震试验中,设备最大应力与位移响应为27.64 MPa与330.06mm,设备安装减震装置后抗震性能得到显著提升。试验研究结果可为复合材料电气设备抗震性能研究与减震装置应用提供参数数据。     

Dynamic interaction analysis of a circular cylindrical shell of finite length in a half-space

A study on the transient response of a circular cylindrical shell of finite length embedded in a homogeneous, isotropic and linear elastic half-space is presented. The soil-structure system is subjected to suddenly applied explosion waves. The numerical method employed is a combination of the time domain semi-analytical boundary element method used for the semi-infinite soil medium and the finite strip method used for the circular cylindrical shell. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. The dynamic responses at the interface between the soil medium and the structure for every time step are obtained. Numerical examples are presented in detail to demonstrate the use and versatility of the proposed method. The following parameters are found to affect the response: (1) the slenderness ratio of the length over the diameter of the shell, L/D; (2) the relative wall thickness, h/a; (3) the relative stiffness ratio between the shell and the medium, E_s/E_m; and (4) the incidence angle of the explosion wave, α.     

Linear‐elastic lateral load analysis and seismic design of pin‐supported wall‐frame structures with yielding dampers

This paper describes an analytical investigation on a reinforced concrete lateral load resisting structural system comprising a pin‐supported (base‐rocking) shear wall coupled with a moment frame on 1 or both sides of the wall. Yielding dampers are used to provide supplemental energy dissipation through the relative displacements at the vertical connections between the wall and the frames. The study extends a previous linear‐elastic model for pin‐supported wall‐frame structures by including the effects of the dampers. A closed‐form solution of the lateral load behavior of the structure is derived by approximating the discrete wall‐frame‐damper interactions with distributed (ie, continuous) properties. The validity of the model is verified by comparing the closed‐form results with computational models using OpenSees program. Then, a parametric analysis is conducted to investigate the effects of the wall, frame, and damper stiffness on the behavior of the structure. It is found that the damper stiffness significantly affects the distribution of shear forces and bending moments over the wall height. Finally, the performance‐based plastic design approach extended to the wall‐frame‐damper system is proposed. Case studies are carried out to design 2 damped pin‐supported wall‐frame structures using the proposed approach. Nonlinear dynamic time‐history analyses are conducted to verify the effectiveness of this method. Results indicate that the designed structures can achieve the performance level with the story drift ratios less than target values, and weak‐story failure mechanism is not observed. The approach can be used in engineering applications.     

多层砖房底部两层框架抗震变形性能分析

为实现多层砖房底部两层框架结构的加固,需要研究其抗震变形性能。以某底部两层框架、上部四层砖房建筑为对象,通过STRAND7有限元软件构建有限元计算模型,考虑水平荷载与垂直荷载,深入分析多层砖房底部两层框架抗震变形性能。仿真结果表明,建筑结构振型受结构横向楼板刚度的影响较显著,不同振型的频率变化中,X向1阶频率与Y向2阶频率变化最快,楼板平面内弯曲频率变化最慢;整体结构在X向与Y向分别呈现线性剪切变形和弯剪变形,Y向上由于填充墙发挥抗震墙功能,底部两层框架变形较小;在7度多遇地震影响下,底部两层结构中第二层楼板变形较第一层严重,多层砖房底部两层框架建筑结构处于弹性工作状态。     

Behavior of braced excavation in sand under a seismic condition: experimental and numerical studies

The behavior of braced excavation in dry sand under a seismic condition is investigated in this paper. A series of shake table tests on a reduced scale model of a retaining wall with one level of bracing were conducted to study the effect of different design parameters such as excavation depth, acceleration amplitude and wall stiffness. Numerical analyses using FLAC 2D were also performed considering one level of bracing. The strut forces, lateral displacements and bending moments in the wall at the end of earthquake motion were compared with experimental results. The study showed that in a post-seismic condition, when other factors were constant, lateral displacement, bending moment, strut forces and maximum ground surface displacement increased with excavation depth and the amplitude of base acceleration. The study also showed that as wall stiffness decreased, the lateral displacement of the wall and ground surface displacement increased, but the bending moment of the wall and strut forces decreased. The net earth pressure behind the walls was influenced by excavation depth and the peak acceleration amplitude, but did not change significantly with wall stiffness. Strut force was the least affected parameter when compared with others under a seismic condition.     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

Response of fixed offshore structures in random sea

An integrated model is developed for the short-term and long-term dynamic response of an offshore structure subjected to random wave excitation. A discrete linear, elastic model of the upper structure is coupled with an iterative linear quasi-three-dimensional finite element model for the pile-soil medium, and the system is subjected to stochastic storms described by mean rate of arrival, joint probability distribution of storm duration and average intensity, and a random process that describes the variations of a statistical wave height measure during each storm. Sarpkaya's 1977 experimental information is used to specify values for C_M and C_D, in Morison's equation, consistent with the flow and response characteristics. Soil (clay) degradation, due to cyclic excitation, is followed during the passage of a storm. The indicator of soil degradation is taken to be the value of the horizontal foundation stiffness and the stiffness degradation is modelled by a homogeneous Markov process.     

Nonlinear dynamic analysis of reinforced concrete shear wall structures

During strong ground motions, structural members made of reinforced concrete undergo cyclic deformations and experience permanent damage. Members may lose their initial stiffness as well as strength. Recently, Los Alamos National Laboratory has performed experiments on scale models of shear wall structures subjected to recorded earthquake signals. In general, the results indicated that the measured structural stiffnesses decreased with increased levels of excitation in the linear response region. Furthermore, a significant reduction in strength as well as in stiffness is also observed in the inelastic range. Since the in-structure floor response spectra which are used to design and qualify safety equipment have been based on calculated structural stiffness and frequencies, it is possible that certain safety equipment could experience greater seismic loads than were specified for qualification due to stiffness reduction.In this research, a hysteresis model based on the concept of accumulated damage has been developed to account for this stiffness degradation both in the linear and inelastic ranges. Single and three-degrees-of-freedom seismic Category I structures were analysed and compared with equivalent linear stiffness degradation models in terms of maximum displacement responses, permanent displacement, and floor response spectra. The results indicate significant differences in response between the hysteresis model and equivalent linear stiffness degradation model at PGA levels of greater than 0.8 g. The hysteresis model is used in the analysis of reinforced concrete shear-wall structures to obtain the in-structure response spectra. Results of both cumulative and one shot tests are compared.     

储液池的抗震问题探讨

应用流体固体动力耦合统一分析模型的有限元法，进行了储液池的抗震分析。分别探讨了储液池内液体的液面大幅波动、池壁刚度变化、池的深宽比等对地震响应的影响。研究结果表明：储液池壁刚度是比较敏感的物理量，弹性比刚性池壁与液体相互作用的非线性行为强，池壁所受流体的作用力大；液面波的影响也有同样规律，刚性池壁情况下考虑面波与否影响不太大，但弹性池壁却有较大影响；另外宽池比窄池的响应强。     

Elastic period of vibration calculated experimentally in buildings hosting permanent GPS stations

During the earthquake in Emilia (Italy) of 2012, ca. 30 permanent GPS stations were in operation within a radius of about 100 km from the epicenter, each equipped with an antenna rigidly fixed to the host building and sampling the GPS signal at a high rate (> 1 Hz). From the recording of the GPS measurements, the instantaneous displacements s(t) in the North- South and East-West directions of the phase centers of the single GPS antennas at each permanent station during the most important seismic sequences were calculated in kinematic mode. Subsequently, for each of the two displacements considered as two distinct external forces, the elastic response spectra of the building were determined and from them the two periods of vibration T along two orthogonal directions coinciding with the walls of the building were extracted. The experimentally obtained periods of vibration were compared with those inferable from the technical literature. In this way, a sufficiently large sample was obtained per building type, geometry (square, rectangular, regular or irregular planimetry), height (from a minimum of 4 to a maximum of 20 m) and materials (masonry, reinforced concrete, etc.). From the computational point of view, the study confirmed that GPS is an emerging tool for monitoring dynamic displacements and the experimentally estimated value of T is always lower than the one estimated with the formulae reported in the literature. The limitations of the study lie in the impossibility to choose a priori the geometry and/or structural type of the building hosting the GPS station.     

Evaluating the inelastic displacement ratios of moment-resisting steel frames designed according to the Egyptian code

Seismic codes estimate the maximum displacements of building structures under the design-basis earthquakes by amplifying the elastic displacements under the reduced seismic design forces with a deflection amplification factor(DAF). The value of DAF is often estimated as ρ× R, where R is the force reduction factor and ρ is the inelastic displacement ratio that accounts for the inelastic action of the structure according to the definition presented by FEMA P695. The purpose of this study is to estimate the ρ-ratio of moment resisting steel frames(MRSFs) designed according to the Egyptian code. This is achieved by conducting a series of elastic and inelastic time-history analyses by two sets of earthquakes on four MRSFs designed according to the Egyptian code and having 2, 4, 8 and 12 stories. The earthquakes are scaled to produce maximum story drift ratios(MSDRs) of 1.0%, 1.5%, 2.0% and 2.5%. The mean values of the ρ-ratio are calculated based on the displacement responses of the investigated frames. The results obtained in this study indicate that the consideration of ρ for both the roof drift ratios(RDRs) and the MSDRs equal to 1.0 is a reasonable estimation for MRSFs designed according to the Egyptian code.     

Approximate analysis method for displacement responses of structures with active variable stiffness systems

The performance of structures with active variable stiffness (AVS) systems exhibits strong nonlinearity due to the variety with time of the stiffness of each storey unit, in which the AVS system is installed. Hence, the classical dynamic analysis method for linear structures, such as the mode-superposition method, is not applicable to structures with AVS systems. In this paper, an approximate analysis method is proposed for displacement responses of structures with AVS systems. Firstly, an equivalent relationship between single-degree-of-freedom (SDOF) structures equipped with AVS systems and so-called fictitious linear structures is established. Then, an approximate mode-superposition (AMS) method is presented for multi-degree-of-freedom (MDOF) structures equipped with AVS systems. The accuracy of this method is investigated through extensive parametrical study using different types of earthquake excitations, and some modification is made to the method. Numerical calculation results indicate that the modified AMS method is effective for estimating the maximum displacements relative to the ground and the maximum interstorey drifts of MDOF structures equipped with AVS systems. Supported by: National Natural Science foundation of China, Grant number 59895410     

Near‐fault effects on residual displacements of RC structures

Residual displacements of single‐degree‐of‐freedom systems due to ground motions with velocity pulses or fling step displacements are presented as a function of period T and of its ratio to the pulse period T_p. Four hysteretic behaviors are considered: bilinear elastoplastic, stiffness‐degrading with cycling, stiffness‐cum‐strength degrading, with or without pinching. When expressed in terms of T/T_p, peak inelastic and residual displacements due to motions with a pulse or fling appear similar to those due to far‐fault motions, if the response to far‐field records are expressed in terms of the ratio of T to the record's characteristic period. However, as the latter is usually much shorter than the pulse period of motions with fling, the range of periods of interest for common structures becomes a short‐period range under fling motions and exhibits very large amplification of residual and peak inelastic displacements. Similar, but less acute, are the effects of motions with a velocity pulse. Wavelets of different complexity are studied as approximations to near‐fault records. Simple two‐parameter wavelets for fling motions overestimate peak inelastic displacements; those for pulse‐type motions overestimate residual displacements. A more complex four‐parameter wavelet for motions with a velocity pulse predicts overall well residual and peak displacements due to either pulse‐ or fling‐type motions; a hard‐to‐identify parameter of the wavelet impacts little computed residual displacements; another significantly affects them and should be carefully estimated from the record. Even this most successful of wavelets overpredicts residual displacements for the periods of engineering interest. Copyright © 2016 John Wiley & Sons, Ltd.     

An approximate method for soil-structure interaction for sh-waves—the born approximation

An approximate method is proposed for the scattering of SH-waves by foundations of irregular shape and the resulting soil-structure interaction problems. The scattering of elastic waves by the rigid foundation embedded in half-space is solved approximately by using integral representation of the wave equation. The procedure is the Born approximation which has been widely used in quantum mechanics for collision and scattering theory though not well-known in elastodynamics. This paper extends the previous work of the authors on the scattering of waves to account for soil-structure interaction. The motion of the foundation is evaluated by the balance of momentum under stresses due to the incident waves as well as the waves generated by its own motion and the forces coming from the superstructure. The model investigated consists of an infinitely long elastic shear wall of height H and thickness h erected on a rigid infinitely long foundation. Results are presented for the cases with circular, elliptical and rectangular foundations. For a circular foundation, excellent agreement is found with the exact solutions for the foundation displacement and the relative displacement between the top and bottom of the structure for the entire range of wave numbers. For an elliptical foundation, accuracy decreases with increasing wave numbers. Foundation displacements are compared for foundation shapes that are shallow elliptical, deep elliptical, rectangular and circular. It is observed that foundation displacements are dependent on the angle of incidence except for a semi-circle. The results on the details of the scattered field are, however, not as accurate.     

Dynamic response of a group of flexible foundations to incident seismic waves

The dynamic response of a finite number of flexible surface foundations subjected to harmonic incident Rayleigh or SH waves is presented. The foundations are assumed to be resting on an elastic half-space. The results show that the foundation stiffness has a marked effect on the vertical response, while there is only a minor effect on the horizontal displacements. In general, the dynamic response decreases with increasing foundation stiffness. In cases of Rayleigh wave incidence, the existence of an adjacent foundation generates a certain amount of horizontal response in the direction perpendicular to the incident wave and subsequently causes the system to undergo a torsional motion; while in cases of horizontally incident SH waves, a vertical response has been observed and its magnitude is comparable to the response in the direction of the incident wave.     

2011年日本东北地区太平洋近海地震对亚洲板块及韩国大地控制网的影响分析

本研究分析了2011年3月11日发生的M_w9.0日本东北地区太平洋近海地震对亚洲地区和韩国国内GPS卫星常年跟踪站的位移影响.为此,利用了日本东北地区太平洋近海地震发生前后两周(2011年3月4日到3月18日)的GPS站点数据,包括震中附近地区(韩国,中国,中国台湾地区,日本和俄罗斯)55个GPS卫星常年跟踪站和284个IGS 全球跟踪站,并采用GAMIT/GLOBK软件进行处理和平差,估算出所有GPS站点的同震形变.结果显示,日本东北地区太平洋近海地震引起的同震形变影响在亚洲地区比较明显,包括日本和附近国家,距离震中2702 km的中国武汉(WUHN)站也观测到同震形变.为精确分析日本东北地区太平洋近海地震对韩国国家大地控制网的影响,通过GAMIT/GLOBK软件计算出韩国GPS卫星常年跟踪站之间的基线长度变形,并分析出弹性变形量.结果表明:大部分GPS站点均向震中方向膨胀,且向震中的垂直方向收缩.由日本东北地区太平洋近海地震导致的最大剪应变达到韩国国家大地控制网年均变形率的约7倍,对韩国的地壳产生14.5~57.7 mm的水平位移,并导致韩国国家大地控制网产生弹性变形.因此,在不及时更新维护韩国国家大地控制网的情况下,GPS测量成果将会发生最大20 mm的位置误差.     

A note on the effects of material discontinuities on spatial variations of surface displacements from static dislocations

Post-earthquake observations show that permanent static and transient dynamic displacements in the near field of shallow faults can be complex and quite different from theoretical predictions for homogeneous half-space. These complexities are associated with many departures from the linear, elastic, homogeneous, and isotropic representations, and include the consequences of complex three-dimensional (3D) geology surrounding faults. In this paper we illustrate these complexities for a two-dimensional (2D) model of shallow strike-slip fault when it is inside, on the border, and outside a sedimentary basin.