Determination of ductility factor considering different hysteretic models

In current seismic design procedures, base shear is calculated by the elastic strength demand divided by the strength reduction factor. This factor is well known as the response modification factor, R, which accounts for ductility, overstrength, redundancy, and damping of a structural system. In this study, the R factor accounting for ductility is called the ‘ductility factor’, R_μ. The R_μ factor is defined as the ratio of elastic strength demand imposed on the SDOF system to inelastic strength demand for a given ductility ratio. The R_μ factor allows a system to behave inelastically within the target ductility ratio during the design level earthquake ground motion. The objective of this study is to determine the ductility factor considering different hysteretic models. It usually requires large computational efforts to determine the R_μ factor. In order to reduce the computational efforts, the R_μ factor is prepared as a functional form in this study. For this purpose, statistical studies are carried out using forty different earthquake ground motions recorded at a stiff soil site. The R_μ factor is assumed to be a function of the characteristic parameters of each hysteretic model, target ductility ratio and structural period. The effects of each hysteretic model to the R_μ factor are also discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Mechanical behavior of lead rubber bearings under and after nonproportional plane loading

Lead rubber bearings, which have been extensively applied in many seismic isolation designs for buildings, infrastructures, and facilities worldwide, were tested under unilateral reversal loading as well as nonproportional plane loading including circular, figure-eight, and square orbits in this study. The test results indicate that unlike the unilateral hysteretic behavior, the bilateral one of lead rubber bearings is too complicated to be characterized adequately by a simplified bilinear hysteretic model. It is mainly attributed to the bilateral coupling effect, which can be clearly observed from the abnormal deformation of the mesh pattern drawn on the rubber cover during the tests. In addition, after being subjected to nonproportional plane loading, the tested bearings reveal visible permanent twisting deformation. The profiles of the cut bearings present the fracture of the inside lead plugs. Even so, the further unilateral reversal loading test results prove that the fracture might not affect the whole hysteretic behavior and mechanical properties very much. The applicability, robustness, and generalization of adopting three previously developed analytical models for describing the coupled bilateral hysteretic behavior of lead rubber bearings are further demonstrated by comparing their predictions with the nonproportional plane loading test results. Although the coefficients are identified from unilateral reversal loading tests, the three analytical models can still have an acceptable prediction capability.     

A novel type of angle steel buckling‐restrained brace: Cyclic behavior and failure mechanism

A novel type of angle steel buckling‐restrained brace (ABRB) has been developed for easier control on initial geometric imperfection in the core, more design flexibility in the buckling restraining mechanism and easier assembly work. The steel core is composed of four angle steels to form a non‐welded cruciform shape restrained by two external angle steels, which are welded longitudinally to form an external tube. Component test was conducted on seven ABRB specimens under uniaxial quasi‐static cyclic loading. The test results reveal that the consistency between the actual and design behavior of ABRB can be well achieved without the effect of weld in the core. The ABRBs with proper details exhibited stable cyclic behavior and satisfactory cumulative plastic ductility capacity, so that they can serve as effective hysteretic dampers. However, compression–flexure failure at the steel core projection was found to be the primary failure mode for the ABRBs with hinge connections even though the cross‐section of the core projection was reinforced two times that of the yielding segment. The failure mechanism is further discussed by investigating the N_u– M_u correlation curve. It is found that the bending moment response developed in the core projection induced by end rotation was the main cause for such a failure mode, and it is suggested that core projection should be kept within elastic stage under the possible maximum axial load and bending moment response. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental simulations of gas-driven eruptions: kinetics of bubble growth and effect of geometry

 Simulated gas-driven eruptions using CO₂–water-polymer systems are reported. Eruptions are initiated by rapidly decompressing CO₂–saturated water containing up to 1.0 wt.% CO₂. Both cylindrical test cells and a flask test cell were used to examine the effect of magma chamber/conduit geometry on eruption dynamics. Bubble-growth kinetics are examined quantitatively in experiments using cylindrical test cells. Uninhibited bubble growth can be roughly expressed as dr/dt≈λD(β-1)/(γt ^1/3) for a CO₂–water-polymer system at 0–22  °C and with viscosities up to 5 Pa·s, where r is the radius of bubbles, λ and D are the Ostwald solubility coefficient and diffusivity of the gas in the liquid, β is the degree of saturation (decompression ratio), and γ characterizes how the boundary layer thickness increases with time and is roughly 1.0×10^–5 m/s^1/3 in this system. Unlike the radius of cylindrical test cells, which does not affect the eruption threshold and dynamics, the shape of the test cells (flask vs cylindrical) affects the dynamics but not the threshold of eruptions. For cylindrical test cells, the front motion is characterized by constant acceleration with both Δh (the height increase) and ΔV (the volume increase) being proportional to t ²; for the flask test cell, however, neither Δh nor ΔV is proportional to t ² as the conduit radius varies. Test-cell geometry also affects foam stability. In the flask test cell, as it moves from the wider base chamber into the narrower conduit, the bubbly flow becomes fragmented, affecting the eruption dynamics. The fragmentation may be caused by a sudden increase in acceleration induced by conduit-shape change, or by the presence of obstacles to the bubbly flow. This result may help explain the range in vesicularities of pumice and reticulite. Received: 16 May 1997 / Accepted: 11 October 1997     

Estimation of seismic stress drop from the peak velocity of ground motion

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Study of calibration function for surface wave magnitude of DK1 seismographs

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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     

Resonance capacity method for earthquake response analysis of hysteretic structures

The Resonance Capacity Method is proposed for the earthquake response analysis of hysteretic structures. Resonance Capacity is a physical quantity of structures which is related to the hysteretic energy absorbed by structures in one cycle and is equated to the acceleration, velocity and displacement amplitudes α₀, d₀ and d₀ of earthquake ground motions at resonance.¹ According to the idealized trapezoidal approximation of earthquake ground motions in the logarithmic period–velocity plane as proposed by Veletsos and Newmark,⁸ the Resonance Capacity property applies in each period range, short, medium and long, where α₀, v₀ and d₀ respectively are approximately constant. In the medium range of periods, the energy dissipated in hysteretic loops and the deformation amplitudes of a single-degree system with elasto–plastic force–deformation relationships are calculated for the case of El Centro 1940, 18 May earthquake, by this Resonance Capacity Method. The result is compared with results from conventional numerical response analyses obtained by Berg and Thomaides,¹⁴ Kato and Akiyama¹² and Veletsos and Newmark,⁸ and the general agreement is seen to be good. Therefore, it may be possible to apply this Resonance Capacity Method over the entire range of periods. By means of this method the earthquake response analysis of hysteretic systems can be performed easily, and the hysteretic energy and fatigue characteristics of structures may be taken into account directly, up to the point of fracture.     

A multimodel comparison for assessing water temperatures under changing climate conditions via the equilibrium temperature concept: case study of the Middle Loire River,France

This paper investigates three categories of models that are derived from the equilibrium temperature concept to estimate water temperatures in the Loire River in France and the sensitivity to changes in hydrology and climate. We test the models' individual performances for simulating water temperatures and assess the variability of the thermal responses under the extreme changing climate scenarios that are projected for 2081–2100. We attempt to identify the most reliable models for studying the impact of climate change on river temperature (T_w). Six models are based on a linear relationship between air temperatures (T_a) and equilibrium temperatures (T_e), six depend on a logistic relationship, and six rely on the closure of heat budgets. For each category, three approaches that account for the river's thermal exchange coefficient are tested. In addition to air temperatures, an index of day length is incorporated to compute equilibrium temperatures. Each model is analysed in terms of its ability to simulate the seasonal patterns of river temperatures and heat peaks. We found that including the day length as a covariate in regression‐based approaches improves the performance in comparison with classical approaches that use only T_a. Moreover, the regression‐based models that rely on the logistic relationship between T_e and T_a exhibit root mean square errors comparable (0.90 °C) with those obtained with a classical five‐term heat budget model (0.82 °C), despite a small number of required forcing variables. In contrast, the regressive models that are based on a linear relationship T_e = f(T_a) fail to simulate the heat peaks and are not advisable for climate change studies. The regression‐based approaches that are based on a logistic relationship and the heat balance approaches generate notably similar responses to the projected climate changes scenarios. This similarity suggests that sophisticated thermal models are not preferable to cruder ones, which are less time‐consuming and require fewer input data. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of seismic energy demand

In this paper, a method is proposed in order to obtain a simplified representation of hysteretic and input energy spectra. The method is based on the evaluation of the equivalent number of cycles correlated to the earthquake characteristics by the proposed seismic index I_D. This procedure allows us to obtain peak values of the hysteretic and input energy that depend on the demanded ductility, on the seismic index I_D and on the peak pseudo‐velocity. The assessment of the input energy represents a first step towards the definition of a damage potential index capable of taking into account the effect of the duration of the ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

FRP约束混凝土柱抗震性能若干问题的探讨

基于实验研究和理论分析结果,对纤维增强复合材料(FRP)约束混凝土柱抗震性能研究中存在的若干关键问题进行了探讨,包括FRP约束混凝土构件在往复荷载作用下的受力特点、破坏特征、荷载-位移关系、弯矩-曲率关系、耗能及延性变化规律等,最后重点探讨了FRP约束混凝土柱在往复荷载作用下的刚度特性。     

Optimum strength ratio of hysteretic damper

This paper deals with steel moment frames combined with hysteretic dampers. Specifically, it examines the strength of dampers required to minimize damage to moment frames under earthquake loading. The important structural variables are the ratio of the dampers' shear strength to the maximum resistance, termed β in this study, and the relative stiffness between the damper and the main frame, termed k. The equivalent viscous damping ratio of the entire structural system is affected by the quantities β and k and the ductility ratio of the main frame. The optimum dampers' strength ratio (β_opt), which maximizes the equivalent viscous damping ratio, was formulated as a function of k, and it was found that β_opt is independent of the ductility ratio of the main frame. Earthquake response analysis confirmed that damage to the main frame can be significantly reduced by hysteretic dampers and minimized at the value of β_opt. © 1998 John Wiley & Sons, Ltd.     

The revised m Lg scale in six eastern provinces of China

The influence of the four different methods of measuring Lg amplitude, and the selection of different geometrical attenuation coefficient ζ-values (=5/6 or 1) on the determination ofγ value of Lg wave are discussed.γ=0.0034±0.0001km⁻¹ (when ζ=5/6) for six eastern provinces is redetermined. The revised magnitude calibration function ofm _Lg (mxh),q _E (Δ)=(5/6)logΔ+0.00147Δ+1.81 is deduced. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 171–178, 1991. Projects sponsored by the Chinese Joint Seismological Science Foundation.     

Direct use of PGV for estimating peak nonlinear oscillator displacements

A predictive model is presented for estimating the peak inelastic oscillator displacements (S_d,ie) from peak ground velocity (PGV). The proposed model accounts for the variation of S_d,ie for bilinear hysteretic behavior under constant ductility (µ) and normalized lateral strength ratio (R) associated with postyield stiffness ratios of α=0 and 5%. The regression coefficients are based on a ground‐motion database that contains dense‐to‐stiff soil site recordings at distances of up to 30 km from the causative fault. The moment magnitude ( M ) range of the database is 5.2? M ?7.6 and the ground motions do not exhibit pulse‐dominant signals. Confined to the limitations imposed by the ground‐motion database, the model can estimate S_d,ie by employing the PGV predictions obtained from the attenuation relationships (ground‐motion prediction equations). In this way, the influence of important seismological parameters can be incorporated to the variation of S_d,ie in a fairly rationale manner. This feature of the predictive model advocates its implementation in the probabilistic seismic hazard analysis that employs scalar ground‐motion intensity indices. Various case studies are presented to show the consistent estimations of S_d,ie by the proposed model. The error propagation in the S_d,ie estimations is also discussed when the proposed model is associated with attenuation relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic vulnerability evaluation of axially loaded steel built-up laced members Ⅱ： evaluations

The test results described in Part 1 of this paper （Lee and Bruneau, 2008） on twelve steel built-up laced members （BLMs） subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller kl/r were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger kl/r could meet the ductility demand in most cases. The normalized energy dissipation ratio, EC/ET and the normalized compressive strength degradation, Cr″/Cr of BLMs typically decrease as normalized displacements δ/δb,exp increase, and the ratios for specimens with larger kl/r dropped more rapidly than for specimens with smaller kl/r; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, kl/r, and width-to-thickness ratio, b/t, experienced a larger number of inelastic cycles than those with larger ratios.     

The 20th September 1999 Chi-Chi Earthquake (Taiwan): a case of study for its aftershock seismic sequence

The purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay of aftershocks temporal series following a mainshock with magnitude M ≥ 7.0. In this paper we present the results for the Taiwan seismic sequence started on 20 September 1999 (M = 7.7) by tuning some seismic parameters that show considerable variations during the aftershock decay process. In here we also present the results obtained using a fractal approach for the seismic sequence. Earthquakes belong to a class of phenomena known as multifractals. In general it is important to define the fractal dimension D, but sometimes is not useful if we are describing a natural phenomenon; so it is necessary to define D ₀ called box-counting dimension and D ₂ called correlation dimension, usually D ₀ ≥ D ₂. In the elaborations of the fractal dimensions, for this sequence, we have obtained values lesser than 1, with a greater tendency of aftershocks to clusterize in time before a large aftershock. This is coherent with the possible existence of seismic anomalies, that could occur before the large aftershock. We also report the results obtained by using the delta/sigma method described firstly in [Caccamo et al., 2005] and later applied to different seismic sequence. The observed temporal series of the aftershocks per day can be considered as a sum of a deterministic and a stochastic contribution. If the decay can be modeled as a non-stationary Poissonian process, the number of aftershocks in a small time interval Δt is the mean value n(t) Δt, with a standard deviation (δ = √n(t)Δt. Investigating both aftershock behavior and a wide spectrum of parameters may find the key to explain better the mechanism of seismicity as a whole.     

Impact of capillary hysteresis and trapping on vertically integrated models for CO2 storage

Vertically integrated models are frequently applied to study subsurface flow related to CO₂ storage scenarios in saline aquifers. In this paper, we study the impact of capillary-pressure hysteresis and CO₂ trapping on the integrated constitutive parameter functions. Our results show that for the initial drainage and a subsequent imbibition, trapping is the dominant contributor to hysteresis in integrated models. We also find that for advective processes like injection and plume migration in a sloped aquifer the correct treatment of the hysteretic nature of the capillary fringe is likely of secondary importance. However, for diffusive/dispersive processes such as a redistribution of the CO₂ plume due to buoyancy and capillary forces, the hysteretic nature of the capillary fringe may significantly impact the final distribution of the fluids and the timescale of the redistribution.     

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.     

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Characteristics of ambient stress values for micro－earthquake sequences in Western Yunnan Earthquake Prediction Experimental Field

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