Consistent inelastic design spectra: Hysteretic and input energy

This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a² dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E_HE_I) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E_H/E_I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and E_H/E_I     

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy (R_E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude.Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio.The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.     

Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

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Cumulative damage‐based inelastic cyclic demand spectrum

The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor R_μ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 John Wiley & Sons, Ltd.     

Fractal and chaotic phenomena of seismic dissipated energy in an energy system of engineering structures

Fractal and chaotic phenomena in engineering structure are discussed in this paper, it means that the characters of fractal and chaos on dynamic system of seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e are analyzed carefully. Based on the conceptions of the energy system of engineering structures Θ, seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e, the chaotic phenomena of dynamic systems E _d and I _e are discovered by theoretic derivation, then the fractal characters of them are also discovered from theoretical inferring and numerical computation. Attractor of relative dimension d ₂, Renyi entropy of the second order k ₂, mean predictable time scale 1/k ₂ and other parameters of the dynamic system which were constructed in light of a large number of actual measuring seismic data have been achieved in the end. These parameters are exactly what the fractal and chaotic phenomena have represented in practical dynamic system, which may be valuable for earthquake-resistant theory and analytical method in practical engineering structures.     

Optimal yield level of bilinear seismic isolation devices

The yield level of an insulator is one of the important parameters which are related to responses and absorbing energy under seismic input energy in isolated structures. The purpose of this paper is to determine the optimal ratios of yield force of the isolator (Q_y) to the total weight of the structures (W). To obtain the optimal ratio, 1044 two-degree-of-freedom isolated bridge models, which have bilinear isolators, were selected. These 2-DOF isolated bridge models with superstructure isolation can consider pier flexibility and various parameters of the isolator. Two formulas for determining the optimal yield ratio are proposed and compared with the previous researches. RAE (the ratio of absorbed energy by the isolator to the total input energy) is related directly to structural responses, and Optimal Yield Ratio (OYR), defined as a yield ratio at maximum RAE, can be obtained from the relationship between RAE and Q_y/W. Here, we found that RAE is a reliable factor to evaluate OYR, and it is proportional to earthquake amplitudes under the same kinds of earthquake loadings. Using the proposed formulas, OYR is determined and the optimal yield force of the isolator can be obtained easily and reliably at a seismic isolation design stage. Copyright © 1999 John Wiley & Sons, Ltd.     

公路简支梁桥的地震能量响应分析

利用有限元软件SAP2000建立了某公路简支梁桥的有限元模型,以7条典型强震记录为输入,研究了公路简支梁桥的地震能量响应及其分配规律。结果表明:①地基柔性效应对公路简支梁桥的地震能量响应及其分配规律的影响较小;②当场地土质变软时,地震总输入能、结构阻尼耗能和结构阻尼耗能比均呈递增趋势,而结构滞回耗能和结构滞回耗能比则不断减小,即地基土体作为桥梁动力系统的一部分,增大了系统阻尼,并分担了部分非弹性变形;③随着PGA增大,输入结构的地震能量也增加,导致塑性铰的非弹性变形增加,即结构滞回耗能和结构阻尼耗能增大。     

A seismic index method for vulnerability assessment of existing frames: application to RC structures with wide beams in spain

A method for assessing the vulnerability of existing frames in terms of an energy-based seismic index is proposed. The ground motion is characterized by the so-called Seismic Hazard Energy Factor AE _I , and the susceptibility of the frame to damage is a function of two counterpart energy factors, AE _IS and AE _IU . AE _IS represents the level of the “maximum earthquake” that the frame can sustain within the elastic range. AE _IU characterizes the level of the “ultimate earthquake” associated with the collapse of the structure. The procedure takes into account the relation between the dynamic properties of the existing frame and the spectral shape of the ground motion expected at the site. The seismic index used by the method has a transparent and direct physical meaning; thus, it is useful not only for screening existing buildings but also to design a seismic retrofit solution, if needed. The method is applied to reinforced concrete frames with wide beam-column connections built in the southern part of Spain during the 1970’s, 1980’s and 1990’s.     

Seismic motion and response prediction alternatives

Statistical methods are available which predict the maximum response of simple oscillators given the peak acceleration (A_p), peak velocity (V_p) or peak displacement (D_p) of seismic ground motions. An alternative parameter, namely an ordinate (or ordinates) of the Fourier amplitude spectrum of ground motion acceleration, FS(f), may in fact be a preferred predictor of peak response, especially in a frequency range close to f. Other statistical methods (attenuation laws) use distance R and other parameters such as magnitude (M), Modified Mercalli epicentral Intensity (I_o) and Modified Mercalli site Intensity (MMI or I_s) to predict spectral velocity (S_v(f)), etc. In using such approaches, it is most desirable to know the total uncertainty in the predicted peak response of the system given the starting parameter values. An extensive strong motion data set is used to study these questions, The most direct prediction models are found to be preferable (have lower prediction dispersion) but data may not be available in all regions to permit their use.     

An energy-based procedure for the assessment of seismic capacity of existing frames: Application to RC wide beam systems in Spain

A methodology for assessing the seismic capacity of existing frames in terms of energy is proposed. It estimates the global amount of input energy—in form of a factor AE_IU—and hysteretic energy that the overall structure can dissipate until collapse under earthquake-type loadings. The method requires static pushover analyses to determine the ductility factor and energy shape of an equivalent single-degree-of-freedom system for the first—two or more—modes. The procedure accounts for the relation between the frequency content of the earthquake expected at the site and the dynamic properties of the existing structure. It can be useful for evaluating the possible deficit on energy dissipation capacity of existing structures, and for designing seismic retrofit solutions. Finally, the methodology is applied to reinforced concrete frames with wide beam-column connections representative of existing post-1970 buildings located in the earthquake-prone southern part of Spain.     

A method to estimate the total magnetization direction from a distortion analysis of magnetic anomalies1

Knowledge of the declination and inclination of the total and induced magnetization vectors is normally required for the interpretation and analysis of magnetic anomalies. A new method of estimating the direction of the total magnetization vector of magnetized rocks from magnetic anomalies is proposed. The unknown declination and inclination (D*_T and I*_T) can be found by applying a reduction-to-the-pole operator to the measured anomalies for different couples of total magnetization direction parameters (D_T and I_T) and by observing the variation of the anomaly minimum as a function of both D_T and I*_T.and D*_T are estimated using the maximum of this function. Comparing our method to previous methods, one advantage is that our estimates are not zero-level dependent; furthermore, the method allows inclinations to be well estimated, with the same accuracy as declinations; finally declinations are not underestimated. Our method is applied to a real case and meaningful results are obtained; it is shown that the feasibility of the method is improved by removing the low-frequency components.     

钢筋混凝土框架抗震结构地震能量分布及耗散研究

基于能量平衡原理,对多层钢筋混凝土框架结构的地震输入能量的分布及耗散规律进行了研究。选用8条天然地震波和2条人工波,运用Perform-3D软件,对多层钢筋混凝土框架结构模型在7度罕遇地震作用下的弹塑性能量进行数值仿真计算。计算了钢混框架结构在不同地震波下的地震总输入能量、滞回耗能、阻尼耗能以及滞回耗能占总耗能的比例时程,分析了地震能量在各分量中的分布及分配规律;分析了阻尼比和延性比对地震输入能量的影响,确定了滞回耗能随阻尼比和延性比的变化规律;研究了钢筋混凝土框架结构梁柱构造和竖向侧移刚度变化对地震输入能及其分量的影响,确定了多层钢筋混凝土框架结构滞回耗能沿竖向的分布规律及沿横向在框架构件中的分配,研究了框架结构存在薄弱层情况下的滞回耗能的分布规律。揭示了多自由度钢筋混凝土框架结构地震输入能量及其分布规律,可为基于能量平衡原理的抗震设计理论在工程实际中的运用提供有益的参考。     

Characterization of rainfall generated by dripper‐type rainfall simulator using piezoelectric transducers and its impact on splash soil erosion

Rainfall erosivity represents the primary driver for particle detachment in splash soil erosion. Several raindrop erosivity indices have been developed in order to quantify the potential of rainfall to cause soil erosion. Different types of rainfall simulators have been used to relate rainfall characteristics to soil detachment. However, rainfall produced by different rainfall simulators has different characteristics, specifically different relationships between rainfall intensity and rainfall erosivity. For this reason, the effect of rainfall characteristics produced by a dripper‐type rainfall simulator on splash soil erosion (D_s) has been investigated. The simulated rainfall kinetic energy (KE) and drop size distribution (DSD) were measured using piezoelectric transducers, modified from the Vaisala RAINCAP^® rain sensor. The soil splash was evaluated under various simulated rainfall intensities ranging from 10 to 100 mm h^?1 using the splash‐cup method. The simulated rainfall intensity (I) and kinetic energy relationship (I–KE) was found to be different from natural rainfall. The simulated rainfall intensity and splash soil erosion relationship (I–D_s) also followed this same trend. The I–KE relationship was found to follow the natural rainfall trend until the rainfall intensity reached 30 mm h^?1 and above this limit the KE started to decrease. This emphasizes the importance of the I–KE relationship in determining the I‐D_s relationship, which can differ from one rainfall simulator to another. D_s was found to be highly correlated with KE (r = 0·85, P < 0·001), when data produced by the rainfall intensity ranged from 10 to 100 mm h^?1. However, when the threshold rainfall intensity (30 mm h^?1) was considered, the correlation coefficient further improved (r = 0·89, P = 0·001). Accordingly, to improve the soil splash estimation of simulated rainfall under various rainfall intensities the I–KE characterization relationship for rainfall simulators has to be taken into account. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacity- demand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.     

Self‐centering structural systems with combination of hysteretic and viscous energy dissipations

This paper presents an innovative set of high‐seismic‐resistant structural systems termed Advanced Flag‐Shaped (AFS) systems, where self‐centering elements are used with combinations of various alternative energy dissipation elements (hysteretic, viscous or visco‐elasto‐plastic) in series and/or in parallel. AFS systems is developed using the rationale of combining velocity‐dependent with displacement‐dependent energy dissipation for self‐centering systems, particularly to counteract near‐fault earthquakes. Non‐linear time‐history analyses (NLTHA) on a set of four single‐degree‐of‐freedom (SDOF) systems under a suite of 20 far‐field and 20 near‐fault ground motions are used to compare the seismic performance of AFS systems with the conventional systems. It is shown that AFS systems with a combination in parallel of hysteretic and viscous energy dissipations achieved greater performance in terms of the three performance indices. Furthermore, the use of friction slip in series of viscous energy dissipation is shown to limit the peak response acceleration and induced base‐shear. An extensive parametric analysis is carried out to investigate the influence of two design parameters, λ₁ and λ₂ on the response of SDOF AFS systems with initial periods ranging from 0.2 to 3.0 s and with various strength levels when subjected to far‐field and near‐fault earthquakes. For the design of self‐centering systems with combined hysteretic and viscous energy dissipation (AFS) systems, λ₁ is recommended to be in the range of 0.8–1.6 while λ₂ to be between 0.25 and 0.75 to ensure sufficient self‐centering and energy dissipation capacities, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Prediction of variations from Polar Cap indices using time-delay neural network

The hourly averaged Polar Cap (PC) index was used as the input parameter for the ring current index D_st variation forecasting. The PC index is known to describe well the principal features of the interplanetary magnetic field as well as the total energy input to the magnetosphere. This allowed us to design a neural network that was able to forecast the D_st variations 1 h ahead. 1995 PC and D_st data sets were used for training and testing and 1997 data sets were used for validation. From 15 moderate and strong geomagnetic storms observed during 1997, 10 were successfully forecasted. In 3 cases the observed minimum D_st value was less than the predicted value, and only in 3 cases the neural network was not able to reproduce the features of the geomagnetic storm.     

Evaluation of shear wave velocity profile using SPT based uphole method

The uphole method is a field seismic test which uses receivers on the ground surface and an underground source. A modified form of the uphole method is introduced in order to obtain efficiently the shear wave velocity (V_S) profile of a site. This method is called the standard penetration test (SPT)-uphole method because it uses the impact energy of the split spoon sampler in the SPT test as a source. Since the SPT-uphole method can be performed simultaneously with the SPT test it is economical and not labor intensive compared to the original uphole methods which use small explosives or a mechanical source. Field testing and interpretation procedures for the proposed method are described. To obtain reliable travel time information of the shear wave, the first peak point of the shear wave using two component geophones is recommended. Through a numerical study using the finite element method (FEM), the procedure of the proposed method was verified. Finally, the SPT-uphole method was performed at several sites, and the field applicability of the proposed method was verified by comparing the V_S profiles determined by the SPT-uphole method with the profiles determined by the downhole, the spectral analysis of surfaces waves (SASW) method and from the SPT-N values.     

单自由度自复位体系设计能量谱研究

本文对具有旗帜型滞回模型的单自由度自复位体系提出了设计能量谱的构造方法,包括设计输入能量谱和设计滞回耗能比谱。首先按中国规范场地类别选取360条实际强震记录进行时程分析,对影响单自由度自复位体系输入能量谱和滞回耗能比谱的参数,包括地震波类型、滞回模型、阻尼比、延性系数等进行研究。在此基础上分别建议了设计输入能量谱和设计滞回耗能比谱及其曲线参数的确定方法,并与实际强震记录计算结果进行比较。结果表明结构滞回模型对能量谱影响明显;阻尼比和延性系数对输入能量谱的影响在整个周期范围内有显著差异,但均有明显的削峰作用。建议的两种设计能量谱综合考虑了结构参数、地震波参数和中国场地类别的影响,可以较好的拟合实际情况,并对弹塑性单自由度自复位体系在地震作用下的耗能需求做出较准确的估计。     

Seismic energy release over a broad frequency band

There remains much uncertainty on the absolute elastic wave energy released by fault rupture. Few direct estimates of the partition of seismic wave energy in ground shaking have been made. In this work, ground particle velocities from integrated accelerograms are used to compute the kinetic energy crossing unit area per unit time. Simplified theory for the near-field strong-motion case would appear to give a valid lower energy bound; the wave attenuation does not present a major problem. The partition of energy in predominantly P, S, and surface wave portions, for given frequency windows, is tabulated using strong-motion accelerograms recorded at different azimuths to the fault-sources of six California earthquakes (5.5<M _L<7.2). Checks against earlier magnitudeM _L and momentM ₀ correlations indicate significantly higher overall wave energy outputs than expected, but further calibration is needed.The study demonstrates that stable estimates of frequency-dependent seismic wave energies in the nearfield can be obtained from strong-motion records. Hence, energy flux may have a wider application to risk mapping than previously thought. In particular, a shift from peak acceleration scaling to (kinetic) energy inputs for engineering design appears to involve only routine processing.