Evaluation of seismic displacement demands from the September 19, 2017 Puebla‐Morelos (Mw = 7.1) earthquake in Mexico City

This short communication presents the assessment of seismic inelastic and elastic displacement demands computed from earthquake ground motions (EQGMs) recorded in Mexico City during the intermediate‐depth intraslab Puebla‐Morelos earthquake on 19 September 2017 (Mw = 7.1). Evaluation is conducted by means of peak elastic and inelastic displacement demand spectra, inelastic displacement ratio, C_R, spectra, and generalized interstory drift spectra computed for selected recording stations located in different soil sites of Mexico City, including those located in areas of reported collapsed buildings. Results of this study confirm previous observations made from interplate (subduction) EQGMs that peak inelastic displacement demands are greater than corresponding elastic counterparts for short‐to‐medium period structures, while the opposite is true for medium‐to‐long period structures. Possible basin site effects were identified from generalized interstory drift spectra. It is also shown that an equation introduced in the literature to obtain estimates of C_R developed from interplate EQGMs provides also a good estimate for mean C_R computed from the intermediate‐depth intraslab EQGMs.     

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.     

Evaluation of the response modification coefficient and collapse potential of special concentrically braced frames

Special concentrically braced frames (SCBFs) are commonly used for seismic design of buildings. Their large elastic stiffness and strength efficiently sustains the seismic demands during smaller, more frequent earthquakes. During large, infrequent earthquakes, SCBFs exhibit highly nonlinear behavior due to brace buckling and yielding and the inelastic behavior induced by secondary deformation of the framing system. These response modes reduce the system demands relative to an elastic system without supplemental damping using a response modification coefficient, commonly termed the R factor. More recently, procedures put forth in FEMAP695 have been made to quantify the R factor through a formalized procedure that accounts for collapse potential. The primary objective of the research in this paper was to evaluate the approach for SCBFs. An improved model for SCBFs that permits simulation of brace fracture was used to conduct response history analyses. A series of three‐story, nine‐story and 20‐story SCBFs were designed and evaluated. Initially, the FEMAP695 method was conducted to estimate collapse and the corresponding R factor. An alternate procedure for scaling the multiple acceleration records to the seismic design hazard was also evaluated. The results show significant variation between the two methods. Of the three variations of buildings studied, the largest vulnerability was identified for the three‐story building. To achieve a consistent margin of safety against collapse, a significantly lower R factor is required for the low‐rise SCBFs (three‐story), whereas the mid‐rise and high‐rise SCBFs (nine‐story and 20‐story) may continue to use the current value of 6, as provided in ASCE‐07. Copyright © 2013 John Wiley & Sons, Ltd.     

Consistent inelastic design spectra: Strength and displacement

A procedure for the determination of inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor has been developed. All the spectra are consistent (interrelated and based on the same assumptions). This is the first of two companion papers which deals with the ‘classical’ structural parameters: strength and displacement. The input data are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum. Simple, approximate expressions for the strength reduction factor R are proposed. The value of R depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour, damping and ground motion. Fairly accurate approximations to the inelastic spectra for strength and displacement can be derived from the elastic spectrum using the proposed values for R.     

Additional seismic inelastic deformation caused by structural asymmetry

Using a single mass monosymmetric model, this paper examines the additional seismic inelastic deformations and displacement caused by structural asymmetry of the model. Stiffness eccentricity and resistance eccentricity are used as measures of asymmetry in the elastic and inelastic range respectively. Seven ways of specifying strength distribution among resisting elements are considered, including code provisions from Canada, Mexico, New Zealand and the United States. These specifications are related t o the model resistance eccentricity. It is shown that when torsional shears are included in the strength design of the elements, the structure in general will have small resistance eccentricity, even if it has large stiffness eccentricity in the elastic range. For structures which are designed with allowance for torsional shears, the ductility demands on the elements are similar to those when the structure is symmetrical. However, the edge displacements can be up to three times that if the system is symmetrical. This finding has significant implications in evaluating adequate separation between buildings to avoid the pounding problem during earthquakes.     

梁铰型屈服RC框架结构地震弹塑性位移增大系数研究

本文通过弹性和弹塑性时程分析,研究了水平地震作用下梁铰型屈服RC框架模型结构的楼层屈服剪力系数、基本自振周期、楼层数3个因素对弹塑性位移增大系数的影响,通过非线性回归分析给出了弹塑性层间位移增大系数经验公式;通过分析滞回耗能沿楼层高度的分布,初步确定了梁铰型屈服RC框架结构的薄弱楼层位置;基于结构损伤分析,讨论了抗震规范中RC框架结构弹塑性层间位移角限值的水准。     

Seismic design factors for RC special moment resisting frames in Dubai, UAE

This study investigates the seismic design factors for three reinforced concrete (RC) framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code (IBC’09). Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years (10/50 and 2/50, respectively) are used. The nonlinear dynamic responses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor (R), deflection amplification factor (Cd), system overstrength factor (Ωo), and response modification factor for ductility (Rd) in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion (10/50 versus 2/50). Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the Ωo factor, which shows a mere 30% increase. Based on the observed trends, period-dependent R and Cd factors are recommended if consistent collapse probability (or collapse prevention performance) in moment frames with varying heights is to be expected.     

GPS观测得到的大地震前兆地壳形变震例

综合介绍2008年汶川大地震以来,GPS观测得到的国内外10多次6—9级,不同构造、不同类型的大地震前兆地壳形变震例:2008年汶川8级大地震、2011年东日本9级巨震、2013年芦山7级,直至2020年6月墨西哥7.4级地震和7月美国阿拉斯加州以南海域7.8级地震等。利用GPS连续观测站区域参考框架水平位移时间序列和水平位移场,特别是水平位移向量时间序列的研究证明,同震水平位移是研究地震前兆形变存在的关键;利用垂直位移和水平位移向量时间序列、同震垂直位移及同震水平位移向量的分解,揭示地震弹性回跳真实方式;提出了符合GPS观测和岩石破裂试验结果的地震压-剪弹性回跳模型;根据已有震例,提出预报不同震级地震的可能性和监测临震前兆形变的GNSS站布设设想。      

Shake table testing of a multi-tower connected hybrid structure

Many single-tower reinforced concrete core wall-steel frame (RCC-SF) buildings have been built in China, but there are no buildings of different-height multi-tower hybrid system. A multi-tower RCC-SF tall building was thus studied because of its structural complexity and irregularity. First, a 1/15 scaled model structure was designed and tested on the shake table under minor, moderate, and major earthquake levels. Then, the dynamic responses of the model structure were interpreted to those of the prototype structure according to the similitude theory. Experimental results demonstrate that, despite the complexity of the structure, the lateral deformation bends as the "bending type" and the RC core walls contribute more than the steel frames to resist seismic loads. The maximum inter-story drift of the complex building under minor earthquakes is slightly beyond the elastic limitation specified in the Chinese code, and meets code requirements under major earthquakes. From the test results some suggestions are provided that could contribute favorable effect on the seismic behavior and the displacement of the building.     

Seismic retrofitting with buckling restrained braces: Application to an existing non-ductile RC framed building

This paper assesses the seismic performance of typical reinforced concrete (RC) existing framed structures designed for gravity loads only. The sample two-storey structural system exhibits high vulnerability, i.e. low lateral resistance and limited translation ductility; hence an effective strategy scheme for seismic retrofitting was deemed necessary. Such a scheme comprises buckling restrained braces (BRBs) placed along the perimeter frames of the multi-storey building. The adopted design approach assumes that the global response of the inelastic framed structure is the sum of the elastic frame (primary system) and the system comprising perimeter diagonal braces (secondary system); the latter braces absorb and dissipate a large amount of hysteretic energy under earthquake ground motions. Comprehensive nonlinear static (pushover) and dynamic (response history) analyses were carried out for both the as-built and retrofitted structures to investigate the efficiency of the adopted intervention strategy. A set of seven code-compliant natural earthquake records was selected and employed to perform inelastic response history analyses at serviceability (operational and damageability limit states, OLS and DLS) and ultimate limit states (life safety and collapse prevention limit states, LSLS and CPLS). Both global and local lateral displacements are notably reduced after the seismic retrofit of the existing system. In the as-built structure, the damage is primarily concentrated at the second floor (storey mechanism); the computed interstorey drifts are 2.43% at CPLS and 1.92% at LSLS for modal distribution of lateral forces. Conversely, for the retrofitted system, the estimated values of interstorey drifts (d/h) are halved; the maximum d/h are 0.84% at CPLS (along the Y-direction) and 0.65% at LSLS (yet along the Y-direction). The values of the global overstrength Ω vary between 2.14 and 2.54 for the retrofitted structure; similarly, the translation ductility μ_Δ-values range between 2.07 and 2.36. The response factor (R- or q-factor) is on average equal to 5.0. It is also found that, for the braced frame, under moderate-to-high magnitude earthquakes, the average period elongation is about 30%, while for the existing building the elongation is negligible (lower than 5%). The inelastic response of the existing structure is extremely limited. Conversely, BRBs are effective to enhance the ductility and energy dissipation of the sample as-built structural system. Extensive nonlinear dynamic analyses showed that more than 60% of input seismic energy is dissipated by the BRBs at ultimate limit states. The estimated maximum axial ductility of the braces is about 10; the latter value of translation ductility is compliant with BRBs available on the market. At DLS, the latter devices exhibit an elastic behaviour. It can thus be concluded that, under moderate and high magnitude earthquakes, the damage is concentrated in the added dampers and the response of the existing RC framed structure (bare frame) is chiefly elastic.     

Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings

The design provisions of current seismic codes are generally not very accurate for assessing effects of near-fault ground motions on reinforced concrete(r.c.)spatial frames,because only far-fault ground motions are considered in the seismic codes.Strong near-fault earthquakes are characterized by long-duration(horizontal)pulses and high values of the ratio α_(PGA)of the peak value of the vertical acceleration,PGA_V,to the analogous value of the horizontal acceleration,PGA_H,which can become critical for girders and columns.In this work,six- and twelve-storey r.c.spatial frames are designed according to the provisions of the Italian seismic code,considering the horizontal seismic loads acting(besides the gravity loads)alone or in combination with the vertical ones.The nonlinear seismic analysis of the test structures is performed using a step-by-step procedure based on a two-parameter implicit integration scheme and an initial stress-like iterative procedure.A lumped plasticity model based on the Haar-Karman principle is adopted to model the inelastic behaviour of the frame members.For the numerical investigation,five near-fault ground motions with high values of the acceleration ratio α_(PGA) are considered.Moreover,following recent seismological studies,which allow the extraction of the largest(horizontal) pulse from a near-fault ground motion,five pulse-type(horizontal)ground motions are selected by comparing the original ground motion with the residual motion after the pulse has been extracted.The results of the nonlinear dynamic analysis carried out on the test structures highlighted that horizontal and vertical components of near-fault ground motions may require additional consideration in the seismic codes.     

A novel non-iterative direct displacement-based seismic design procedure for self-centering buckling-restrained braced frame structures

Self-centering buckling-restrained braces (SCBRBs) were proposed recently to minimize residual deformation of the braces induced by yielding or buckling. Although earthquake resilience of structures equipped with the SCBRBs can be well achieved using displacement based designs (DBDs), previously proposed DBD procedures generally involve iterations. In this study, a novel direct displacement-based design method with a non-iterative procedure, named R–C_R DDBD, is proposed and applied to design of steel braced frame structures with SCBRBs. Unlike previously adopted DBD, the yield displacement does not need to be assumed initially in the proposed procedure. Instead, the yield strength and yield displacement are determined directly by the predetermined objective drift (ratio), using the relation of the strength reduction factor (R) and constant-strength inelastic displacement ratio spectra (C_R spectra), i.e. the R–C_R relation. Since the derived R–C_R relation is independent with the peak ground acceleration of the earthquake records when stiffness and strength degradation are not considered, the proposed procedure can be accurate for any seismic level. The R–C_R DDBD is supposed to begin with the knowledge of the seismic excitation level (according to the structure category, site classification and owner’s requirements) and the corresponding target drift; the end of the design is to obtain the cross sections of main frame members and all the bracing parameters. The result of two 7-story buildings designed according to the R–C_R DDBD procedure demonstrates that this procedure can be effective and fairly simple for practical seismic design.     

Site-dependent design spectra and strength modification factors, based on records from Greece

Elastic and inelastic spectra are derived, based on a representative sample of acceleration records from Greece, carefully selected based on magnitude, distance and peak ground acceleration criteria, and grouped into three ground condition categories according to the 2004 Eurocode 8 (EC8) provisions. Using software developed in-house, elastic (pseudoacceleration, pseudovelocity and displacement), as well as inelastic (strength and displacement) spectra are computed for various critical damping ratios and ductility levels. After appropriate scaling, mean spectra are computed both irrespective of, as well as for each different, ground condition, and comparisons with EC8 provisions are made. As a further evaluation of the code spectra, three additional earthquake scenarios are considered representing ground-motion characteristics not reflected in the compiled dataset of records. Subsequently, modification factors for strength (q_μ) are derived from statistical analysis of constant ductility spectra, and corresponding empirical relationships, suitable for design purposes, are proposed.     

Seismic vulnerability evaluation of RC moment frame buildings in moderate seismic zones

A multi‐level seismic vulnerability assessment of reinforced concrete moment frame buildings located in moderate seismic zones (0.25g) is performed on a set of ductile versions of low‐ to mid‐rise two‐dimensional moment frames. The study is illustrated through application to comparative trial designs of two (4‐ and 8‐story) buildings adopting both space‐ and perimeter‐framed approaches. All frames are dimensioned as per the emerging version of the seismic design code in Egypt. These new seismic provisions are in line with current European norms for seismic design of buildings. Code‐compliant designs (CCD), as well as a proposed modified code design relaxing design drift demands for the investigated buildings, are examined to test their effectiveness and reliability. Applying nonlinear inelastic incremental dynamic analyses, fragility curves (FC) for the frames are developed corresponding to various code‐specified performance levels. Code preset lower and upper bounds on design acceleration and drift, respectively, are also addressed along with their implications, if imposed, on the frames seismic performance and vulnerability. Annual spectral acceleration hazard curves for the case study frames are also generated. Estimates for mean annual frequency (MAF) of exceeding various performance levels are then computed through an integration process of the data resulting from the FC with the site hazard curves. The study demonstrates that the proposed design procedure relaxing design drift demands delivers more economic building designs relative to CCDs, yet without risking the global safety of the structure. The relaxed design technique suggested herein, even though scoring higher, as expected by intuition, MAF of exceeding various code‐limiting performance levels expressed in terms of interstory drift ratios, still guarantees a reasonably acceptable actual margin against violating code limits for such levels. Copyright © 2010 John Wiley & Sons, Ltd.     

Inelastic design spectra accounting for soil conditions

This paper is concerned with the effect of soil conditions on the response of single-degree-of-freedom inelastic systems subjected to earthquake motions. The ground motions considered are 72 horizontal components of motion, most of them recorded during the 3 March, 1985 Chile earthquake (M_s = 7·8) and two main aftershocks; among these records are some of the strongest and longer duration earthquake motions ever recorded. The recording station sites were classified in one of three soil types, which can be generically referred to as rock, firm ground, and medium stiffness soil. Response results for each group were analysed statistically to obtain factors for deriving inelastic design spectra of the Newmark-Hall type, as well as alternative simplified spectral shapes suitable for code formulation. Particular attention was given to the response modification factors (R) that are commonly used in seismic codes to reduce the ordinates of the elastic spectrum to account for the energy dissipation capacity of the structure. The response modification factors, known to be function of both the natural period of vibration and the ductility factor, are found to be dependent on soil conditions, particularly in the case of medium stiffness soils. It is also shown that the indirect procedure of applying R to the elastic design spectrum is less accurate than directly using functions that represent the inelastic design spectrum.     

Seismic behavior of steel buildings with out‐of‐plumb

A structure that has a permanent offset from a true vertical line is commonly referred to as being ‘out‐of‐plumb’. Out‐of‐plumb may result from construction tolerances or post‐earthquake permanent deformations in steel buildings. This paper quantifies the displacements of buildings with out‐of‐plumb in subsequent seismic events by means of inelastic dynamic time history analysis. Structures considered have different structural heights, force design reduction factors (R), and target inter‐story drifts. It is shown that buildings with greater out of plumb and force design reduction factor have larger normalized peak inter‐story drift ratio and ratio of residual‐to‐peak drift. Also, the ratio of residual‐to‐peak drift was not strongly dependent on structural height or design drift. A design procedure and example provided, based on the results obtained, show how peak and residual inter‐story drift ratio can be estimated. Copyright © 2015 John Wiley & Sons, Ltd.     

Field estimate of paleoseismic slip on a normal fault using the Schmidt hammer and terrestrial LiDAR: Methods and application to the Hebgen fault (Montana,USA)

The weathering characteristics of bedrock fault scarps provide relative age constraints that can be used to determine fault displacements. Here, we report Schmidt hammer rebound values (R‐values) for a limestone fault scarp that was last exposed in the 1959 Mw 7.3 Hebgen Lake, Montana earthquake. Results show that some R‐value indices, related to the difference between minimum and maximum R‐values in repeated impacts at a point, increase upward along the scarp, which we propose is due to progressive exposure of the scarp in earthquakes. An objective method is developed for fitting slip histories to the Schmidt hammer data and produces the best model fit (using the Bayesian Information Criterion) of three earthquakes with single event displacements of ≥ 1.20 m, 3.75 m, and c. 4.80 m. The same fitting method is also applied to new terrestrial LiDAR data of the scarp, though the LiDAR results may be more influenced by macro‐scale structure of the outcrop than by differential weathering. We suggest the use of this fitting procedure to define single event displacements on other bedrock fault scarps using other dating techniques. Our preliminary findings demonstrate that the Schmidt hammer, combined with other methods, may provide useful constraints on single event displacements on exposed bedrock fault scarps. Copyright © 2018 John Wiley & Sons, Ltd.     

等位移理论估计高层建筑结构非弹性地震反应的进一步研究

为进一步研究用等位移理论估计高层建筑结构非弹性地震反应,选用五个钢筋混凝土高层结构实例,输入二十条不同场地条件的地震波,采用结构弹性和非弹性地震时程反应分析方法,研究了结构弹性和非弹性最大顶点位移以及最大层间位移角之间的关系。提出可以直接用弹性最大顶点位移估计非弹性最大顶点位移。对于非弹性层间位移角反应,在中、弱非线陛阶段宜可直接用弹性反应结果估计,而在强非线性阶段则需进行一定修正。     

Inclusion of P–Δ effect in displacement‐based seismic design of steel moment resisting frames

A procedure for treating the P– Δ effect in the direct displacement‐based seismic design of regular steel moment resisting frames with ideal elastoplastic material behaviour is proposed. A simple formula for the yield displacement amplification factor as a function of ductility and the stability coefficient is derived on the basis of the seismic response of an inelastic single degree‐of‐freedom system taking into account the P– Δ effect. Extensive parametric seismic inelastic analyses of plane moment resisting steel frames result in a simple formula for the dynamic stability coefficient as a function of the number of stories of a frame and the column to beam stiffness ratio. Thus, the P– Δ effect can be easily taken into account in a direct displacement‐based seismic design through the stability coefficient and the yield displacement amplification factor. A simple design example serves to illustrate the application of the proposed method and demonstrate its merits. Copyright © 2007 John Wiley & Sons, Ltd.     

Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.