Response spectrum techniques for three-component earthquake design

An evaluation is made of response spectrum techniques as applied to seismic analysis and design of steel template offshore platforms. Such structures are designed as braced space frames for several loading conditions, including the simultaneous action of three earthquake components. Base shears as well as gross forces and combined stresses in members of three different platforms are computed for 30 real, three-component earthquakes and response spectrum predictions, obtained by several modal-spatial combination methods, are compared to time history solutions. Results are presented in the form of error statistics. The three approximations examined are: (a) combination of modes for one component input, (b) combination of the three partial responses to obtain estimates of total response and (c) combination of gross forces to derive maximum design stresses at a section. Attention is focused on corner piles because these are among the most heavily penalized members by three-component excitations. It is shown that commonly used spatial combination rules may underestimate gross forces in design controlling corner members by 15–30 per cent on the average. This is attributed to correlations between motion components that create additive effects along certain directions. Typical estimates of combined stresses, however, are found to be slightly conservative.     

Seismogenic potential and earthquake hazard assessment in the Tell Atlas of Algeria

Seismotectonic zonation studies in the Tell Atlas of Algeria, a branch of the Africa-Eurasia plate boundary, provide a valuable input for deterministic seismic hazard calculations. We delineate a number of seismogenic zones from causal relationships established between geological structures and earthquakes and compile a working seismic catalogue mainly from readily available sources. To this catalogue, for a most rational and best-justified hazard analysis, we add estimates of earthquake size translated from active faulting characteristics. We assess the regional seismic hazard using a deterministic procedure based on the computation of complete synthetic seismograms (up to 1 Hz) by the modal summation technique. As a result, we generate seismic hazard maps of maximum velocity, maximum displacement, and design ground acceleration that blend information from geology, historical seismicity and observational seismology, leading to better estimates of the earthquake hazard throughout northern Algeria. Our analysis and the resulting maps illustrate how different the estimate of seismic hazard is based primarily on combined geologic and seismological data with respect to the one for which only information from earthquake catalogues has been used.     

Peak earthquake response of structures under multi-component excitations

Accurate estimation of the peak seismic responses of structures is important in earthquake resistant design. The internal force distributions and the seismic responses of structures are quite complex, since ground motions are multi- directional. One key issue is the uncertainty of the incident angle between the directions of ground motion and the reference axes of the structure. Different assumed seismic incidences can result in different peak values within the scope of design spectrum analysis for a given structure and earthquake ground motion record combination. Using time history analysis to determine the maximum structural responses excited by a given earthquake record requires repetitive calculations to determine the critical incident angle. This paper presents a transformation approach for relatively accurate and rapid determination of the maximum peak responses of a linear structure subjected to three-dimensional excitations within all possible seismic incident angles. The responses can be deformations, internal forces, strains and so on. An irregular building structure model is established using SAP2000 program. Several typical earthquake records and an artifi cial white noise are applied to the structure model to illustrate the variation of the maximum structural responses for different incident angles. Numerical results show that for many structural parameters, the variation can be greater than 100%. This method can be directly applied to time history analysis of structures using existing computer software to determine the peak responses without carrying out the analyses for all possible incident angles. It can also be used to verify and/or modify aseismic designs by using response spectrum analysis.     

大跨度空间网格结构多维多点随机地震反应分析

本文建立了三维正交地震动多点激励下大跨度空间网格结构的随机地震反应分析方法,依据现行抗震设计规范的有关规定,确定了平稳随机地震动功率谱密度的模型参数。数值仿真分析了一柱距80m的正方形平板网架分别在一维地震动或三维地震动的一致激励、行波激励和考虑部分相干效应的随机激励下的地震反应。结果表明:考虑地震动的空间效应会很大程度地改变结构杆件的内力,其中控制杆件的内力增幅达到30%;地震动的行波效应对结构杆件内力的影响比随机地震动的部分相干效应的影响更大;三维地震作用比一维地震作用下结构杆件的内力大。由此得出结论,对于大跨度空间网格结构,必须进行多维多点地震激励下的随机地震反应分析。     

Three-dimensional nonlinear seismic analysis of concrete faced rockfill dams subjected to scattered P,SV, and SH waves considering the dam–foundation interaction effects

In this study, the nonlinear seismic analysis of a typical three-dimensional concrete faced rockfill dam is reported. Three components of the Loma Prieta (Gilroy 1 station) earthquake acceleration time history are used as input excitation. The dam under study is considered as if it were located in a prismatic canyon with a trapezoidal cross-section. A nonlinear model for the rockfill material is used, and contact elements with Coulomb friction law are utilized at the slab–rockfill interface. Vertical joints in the face slab are also considered in the finite element model. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite element method (SBFEM), is used to obtain the scattered motion and interaction forces along the canyon. The dam is subjected to spatially variable P, SV, and SH waves, and the effect of dam–foundation interaction and the reservoir water effects are considered. The results are compared with the non-scattered input motion analysis. Results of the analyses indicate that due to applying the scattered motion to the canyon the response of the dam and concrete face slab significantly increases. The reservoir water pressure affects the tensile stresses induced in the face slab by reducing the uplift movement of the concrete panels.Large horizontal axial forces are induced in the face slab due to out-of-phase and out-of-plane motions of the abutments. Although the normal movements of vertical joints are reduced due to the reservoir water confinement, the opening movements are still significant, and the local failure of construction joints is inevitable.     

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion,including its evaluation for tall buildings

The modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

复杂软土盾构隧道纵向抗震分析

以天津Z2线盾构隧道工程为实例,基于ABAQUS有限元软件,建立三维梁-弹簧模型模拟盾构隧道,采用反应位移法对盾构隧道进行纵向抗震分析.根据盾构隧道接头实际情况,计算环间接头弹簧刚度.将地震作用下的自由场最大水平位移幅值,以简谐波的形式施加到盾构隧道轴向和横向.提出一种同时考虑轴向和横向水平地震动耦联效应的方法,通过调...     

Frequency domain modal analysis of earthquake input energy to highly damped passive control structures

A new complex modal analysis‐based method is developed in the frequency domain for efficient computation of the earthquake input energy to a highly damped linear elastic passive control structure. The input energy to the structure during an earthquake is an important measure of seismic demand. Because of generality and applicability to non‐linear structures, the earthquake input energy has usually been computed in the time domain. It is shown here that the formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions and for understanding the robustness of passively controlled structures to disturbances with various frequency contents. From the viewpoint of computational efficiency, a modal analysis‐based method is developed. The importance of overdamped modes in the energy computation of specific non‐proportionally damped models is demonstrated by comparing the energy transfer functions and the displacement transfer functions. Through numerical examinations for four recorded ground motions, it is shown that the modal analysis‐based method in the frequency domain is very efficient in the computation of the earthquake input energy. Copyright © 2004 John Wiley & Sons, Ltd.     

Complex complete quadratic combination method for damped system with repeated eigenvalues

A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.     

Enhanced reduced model for elastic earthquake response analysis of a class of mono-symmetric shear building structures with constant eccentricity

An enhanced reduced model is proposed for elastic earthquake response analysis of a class of mono-symmetric shear building structures with constant eccentricity. The proposed reduction method consists of two parts. The first stage is the construction of a reduced structural model with the degrees of freedom at representative floor levels only. In this stage, an inverse eigenmode-problem formulation is used to guarantee the limited equivalence between the original model and the reduced model. The reduced model is constructed so as to have the same fundamental natural frequency and the same lowest-mode component ratios at the representative floor levels as those of the original model. The second stage is the transformation of earthquake input forces into a set of reduced input forces. This transformation utilizes the static equivalence of lateral-torsional stiffness between these two models and is introduced to enhance the accuracy level of the reduced model. Several examples of a three-dimensional mono-symmetric ten-story shear building model with constant eccentricity are presented to demonstrate the validity and accuracy of the proposed reduction method for earthquake response analysis.     

多维地震输入下首都机场航站楼T3反应谱分析

首都机场航站楼(T3)下部为混凝土和钢混合框架,上部为复杂的双曲面形双层扁网壳,长960 m,宽780 m,为超大体量大跨度复杂空间钢结构体系。本文采用SAP2000有限元软件,对其进行了单维和多维地震输入下的反应谱分析,研究了单维和多维地震输入对构件内力、节点位移和地震总剪力的影响;研究了多维地震输入下地震响应值与按规范地震组合公式计算所得地震响应值的关系;研究了模态提取数目和质量参与系数的关系,CQC法中参与组合的模态数目与结构地震响应的关系。研究表明,采用振型分解反应谱法时,模态频率越高,对结构内力的影响越小,对于对结构影响较小的高频模态,可以忽略其对结构的影响;根据单维和多维地震反应的对比分析,对超大跨度复杂钢结构宜进行三维地震输入的反应谱分析。另外,本文提出了一种新的地震效应组合方法,可替代多维地震反应分析,并弥补现行规范的不足。     

Influence of seismic input mechanisms and radiation damping on arch dam response

In this study, two different earthquake input models are introduced, i.e. massless foundation model and viscous-spring boundary input model considering radiation damping. Linear elastic and nonlinear contraction joint opening analyses of the 210 m high Dagangshan arch dam under construction in China are performed using the two different earthquake input models. First, the responses of the three-dimensional (3-D) canyon without the dam are analyzed, respectively, with massless-truncated foundation and with viscous-spring boundary; second, linear and nonlinear analyses of the dam–foundation system are performed and compared by using the two input models. Hydrodynamic effects are considered using finite element discretization for incompressible reservoir fluid. It is concluded that stresses and displacements and contraction joint opening in the dam are significantly reduced both in linear and nonlinear analyses when using viscous-spring boundary model. Interestingly, in the case of linear analysis of the Dagangshan, the massless foundation input model with a relatively higher damping ratio of 10% leads to a comparable response of the dam to that using viscous-spring boundary model. In addition, the maximum tensile stresses from nonlinear analysis are 10–25% larger than that of the corresponding linear cases due to a partial release of the arch action.     

Generalized force vectors for multi‐mode pushover analysis of torsionally coupled systems

A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.     

A class of inhomogeneous shear models for seismic analysis of landfills

An analytical/numerical procedure is developed to calculate the shear elasto-plastic earthquake response of hill-shaped landfills. Landfill response is evaluated on the basis of newly developed one-dimensional inhomogeneous shear beam models. In these models, the nonhomogeneity of landfill materials is taken into account by assuming a specific variation of stiffness properties along the depth. Closed-form analytical expressions are derived for natural frequencies, modal displacements, modal participation factors, absolute accelerations and maximum shear strains. Parametric results are presented in graphical and tabular form and conclusions are drawn. Within a numerical implementation framework of the above formulation, the landfill materials may be modeled by an elasto-plastic hysteretic model following the principles of flow or incremental plasticity. The entire numerical procedure may be executed on a personal computer and consequently qualifies as a versatile tool for conducting preliminary design calculations or parametric-type investigations. Using this newly developed procedure, the seismic response of the Fresh Kills landfill in New York City is investigated.     

Sectional forces for seismic design of R/C frames by linear time history analysis and application to 3D single-story buildings

The aim of the present paper is to present a rational procedure for the appropriate selection of the sectional forces needed for the calculation of the longitudinal reinforcement to R/C elements within the context of linear time history analysis. The proposed procedure is based on the maximum normal stresses, which occurs in each relevant cross section, and takes into consideration the critical angle of the seismic excitation, i.e., the angle that yields the maximum value of each response quantity of interest. Moreover, in an attempt to realistically interpret pertinent code provisions, three other code compatible methods of selecting the cross sectional forces are presented and compared to the here proposed method. For this purpose, three single-story buildings subjected to 47 bi-directional strong earthquake ground motions are analyzed. For each ground motion, the longitudinal reinforcement at all critical cross sections is calculated using the above four methods. Furthermore, the necessary reinforcement due to 3 and 7 representative earthquake records, required by the seismic code provisions, is determined. Comparison of results clearly shows that methods compatible with current seismic code provisions can significantly underestimate the necessary reinforcement with regards to the proposed method.     

Enhanced nonlinear static analysis with the drift pushover procedure for tall buildings

In this study a new method for nonlinear static analysis based on the relative displacements of stories is proposed that is able to be implemented in a single stage analysis and considers the effects of an arbitrary number of higher modes. The method is called the extended drift pushover analysis procedure (EDPA). To define the lateral load pattern, values of the relative displacements of stories are calculated using the elastic modal analysis and the modal combination factors introduced. For determining the combination factors, six different approaches are examined. Buildings evaluated in this study consist of four special steel moment-resisting frames with 10–30 stories. Responses including relative displacements of stories, story shear forces and rotation of plastic hinges in each story are calculated using the proposed approaches in addition to modal pushover analysis and nonlinear dynamic time history analyses. The nonlinear dynamic analysis is implemented using ten consistent earthquake records that have been scaled with regard to ASCE7-10. Distribution of response errors of story shears and plastic hinge rotations show that a major part of error corresponds to the second half of the buildings studied. Thus, the mentioned responses are corrected systematically. The final results of this study show that implementing the EDPA procedure using the third approach of this research is able to effectively overcome the limitations of both the traditional and the modal pushover analyses methods and predict the seismic demands of tall buildings with good accuracy.     

A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

Output-only structural identification is developed by a refined Frequency Domain Decomposition(rFDD) approach, towards assessing current modal properties of heavy-damped buildings(in terms of identification challenge), under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type Ⅱ bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames(with variable structural features) are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 "Far-Field"(22 NS, 22 WE) earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.     

适用于结构时程分析法的输入地震波

本文对建筑结构抗震设计时程法所需的输入地震波提出一种基于规范反应谱的、与设防烈度、场地条件、设计近震或远震、结构自振特性有关的选择原则和方法。按远、近震和四类场地标定了反应谱、延性谱和积累损伤谱。通过对六幢不同高度的剪切和弯曲型结构模型的弹塑性分析,表明离差很小。建议在进行结构时程法分析时,按地震加速度反应谱特定的分布规律选择4条加速度记录作为输入计算。两个实际的例子表明按上述方法计算的结果与按底部剪力法计算的结果基本相符。     

关于结构振型参与系数和振型贡献的分析

采用振型分解反应谱法求解多自由度弹性体系的地震反应时,为了在满足所需计算精度的前提下减少工作量,需要对振型数量进行合理的选择,而振型数的确定主要取决于结构各阶振型对总体反应的贡献。通过数学推导,对振型贡献及振型数量的选择问题进行了研究。首先,讨论了振型参与系数的性质,在此基础上给出了能够反映结构振型贡献参数的数学表达式,对这些参数的力学含义进行了解释,并给出了相关证明;其次,对有效质量法、振型位移控制法等基于不同振型贡献标准的确定振型数的方法进行了分析比较,指出了其合理性和不足。本文研究对进一步理解结构振型贡献和振型数的选择问题具有一定的理论意义。     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.