Evidence of significant forward rupture directivity aggravated by soil response in an Mw6 earthquake and the effects on monuments

While strong directivity effects have been mostly recognized in M_w > 6.5 earthquakes, the paper investigates the case of a strong such effect in a relatively small‐magnitude event on 3 February 2014 in the island of Cephalonia, Greece. The second of two events (both of M_w ≈ 6) produced a pernicious accelerogram in the region's main town, Lixouri. The paper provides evidence from geology, interferometry, and seismology to convince that the motion was the result of constructive interference in front of the direction of rupture of the obliquely‐strike‐slip fault. The nature of the record is explored to demonstrate that its frequency content, its high velocity pulse, and its strong fault‐normal (FN) favorable polarity are associated with directivity. Moreover, the broad spectral acceleration peak (of 1.7 g) of the FN motion, centered at a period (T ≈ 1.4 s) which almost coincides with the period of the velocity pulse, is shown to have also been affected by soil amplification, in quantitative agreement with Bray et al. (2009). Such a directivity‐and‐soil‐affected motion explains much of the profound damage to monuments, slopes, and harbor quaywalls. In particular, toppling (as well as excessive rotation and sliding) of nearly‐all the tombstones in Lixouri cemetery are shown to correlate well with characteristics of the FN component of motion. By contrast, the excellent performance of the building stock — despite the destructive shaking that prevailed — is persuasively attributed to conservatively‐robust construction practices of the past and the high base shear coefficient of the strict latest (2000) seismic code. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic performance of an existing bridge with scoured caisson foundation

A three-dimensional rigid body on the shape of a parallelepiped is modelled in order to rock on a side or a vertex of the base,in order to evaluate the seismic response of rigid blocks lying on a horizontal support.The center of mass of the body is considered as eccentric with respect to its geometric center.As seismic input,three Italian recorded accelerograms,with different spectral content,are used.The study is mainly conducted to highlight the differences between the seismic response of 2D and 3D models of rigid blocks,with the aim to understand if,in some cases,the use of the 3D model of rigid block is required to obtain safer results.In fact,the outcomes show that in some ranges of the geometrical and mechanical parameters that characterize the excitation and the body,a two-dimensional model,which is not able to consider the 3D rocking on a vertex,can provide unsafe results.In particular,it is found that the overturning process of the three-dimensional block can occur under excitations which are lower than those which overturn a corresponding two-dimensional block.     

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free‐ standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical model and dynamic analysis of multi degree of freedom masonry arches

A new model is presented for planar multi-block arches subjected to earthquakes. The blocks are assumed to be rigid, and every interface between the blocks may split open and may close, ie, the blocks may impact to each other. During impact, both the classical Housner's approach and improved models with lower energy dissipation are considered. The arch model is verified by comparisons with the available results in the literature. Using the new model, it was found that the circular arch moves as a four-hinge mechanism typically only at the beginning of excitation, and several cracks split open during motion; furthermore, that modeling a multi-block arch by a single degree of freedom (SDOF) four-hinge mechanism may significantly overestimate its collapse load. While, in accordance with the literature, the overturning curves of single blocks and arches with symmetrically located four hinges are similar; for multi-block arches where several hinges may occur they can be very different.     

The dynamics of an elastic structure coupled with a rocking wall

This paper investigates the dynamic response of an elastic single‐degree‐of‐freedom oscillator coupled with a rocking wall. Both configurations of a stepping rocking wall and a pinned rocking wall that have been reported in the literature are examined. The full nonlinear equations of motions are derived, and the paper shows through a comprehensive parametric analysis that the coupling with a rocking wall has mixed results on suppressing the dynamic response of the elastic oscillator. The stepping rocking wall is most effective in suppressing displacements of relative flexible structures with a heavier wall being most effective. In contrast, the pinned wall amplifies the displacements along a wide range of the spectrum with a heavier wall being most detrimental. This happens partly because in a pinned wall the moment from its weight works against stability. Copyright © 2016 John Wiley & Sons, Ltd.     

Behavior of rigid blocks with geometrical defects under seismic motion: an experimental and numerical study

The present work investigates the influence of small geometrical defects on the behavior of slender rigid blocks. A comprehensive experimental campaign was carried out on one of the shake tables of CEA/Saclay in France. The tested model was a massive steel block with standard manufacturing quality. Release, free oscillations tests as well as shake table tests revealed a non‐negligible out‐of‐plane motion even in the case of apparently plane initial conditions or excitations. This motion exhibits a highly reproducible part for a short duration that was used to calibrate a numerical geometrically asymmetrical model. The stability of this model when subjected to 2000 artificial seismic horizontal bidirectional signals was compared with the stability of a symmetrical one. This study showed that the geometrical imperfections slightly increase the rocking and overturning probabilities for earthquake signals in a narrow range of peak ground acceleration. Copyright © 2016 John Wiley & Sons, Ltd.     

Free rocking response of a regular stone masonry wall with equivalent block approach: experimental and analytical evaluation

The evaluation of the dynamic behaviour of rocking elements is directly correlated to the energy dissipated because of the impacts at the base interface, which can be represented by means of a coefficient of restitution. This schematization is commonly accepted as representative of the out‐of‐plane response of stone masonry walls. An experimental campaign (in a lab environment) aiming at assessing the value of this coefficient for a sacco granite masonry wall is presented in this work. The rocking motion at a predefined bed joint level was induced in the tested specimens in order to validate a novel test setup designed to assess the coefficient of restitution value by means of a realistic reproduction of the rocking behaviour of a single element, under the hypothesis of an infinitely stiff system above the bed joint level. As the main objective of the work was to assess the rocking behaviour of a masonry wall that looses energy at the impacts at a certain joint level, the flexural behaviour was not desirable and had to be avoided. For this purpose, a test setup based on the equivalent block approach was developed. In the final section of this work, comparisons between experimental and numerical results are presented together with some preliminary conclusions on the appropriate modelling strategy and the values of the coefficient of restitution to be used for the seismic assessment of the out‐of‐plane rocking behaviour of this type of sacco stone masonry walls. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamics of three-block assemblies with unilateral deformable contacts. Part 1: contact modelling

As far as the dynamics of multibody systems is concerned, a brief review has been performed in order to frame the dynamic response of a trilith (the simplest scheme of a colonnade belonging to a temple) into a wide theoretical background. Under the assumption of rigid bodies, two different approaches can be found in the literature: rigid or deformable contacts formulation. In this paper, an effort is made at outlining the principle of rigid contact formulation and of deformable contact formulation. The latter approach can be assumed within the framework of the distinct element method; for this purpose a model of deformable contact has been proposed in order to simulate the real behaviour of stone joints. The sample application referred to the trilith will be presented in Part 2. Copyright © 1999 John Wiley & Sons, Ltd.     

Dimensional analysis of the earthquake‐induced pounding between adjacent structures

In this paper the dynamic response of two and three pounding oscillators subjected to pulse‐type excitations is revisited with dimensional analysis. Using Buckingham's Π‐theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless Π‐terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self‐similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete self‐similarity or self‐similarity of the second kind with respect to the mass ratio. Copyright © 2008 John Wiley & Sons, Ltd.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification

This paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top‐heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non‐dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic fragilities of single-column highway bridges with rocking column-footing

Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures has been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single-column concrete box-girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi-class responses (eg, full contacted or uplifting foundation) and multi-mode damage (eg, overturning, uplift impact, and column nonlinearity). A multi-step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as-built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time.     

A modified Kelvin impact model for pounding simulation of base-isolated building with adjacent structures

Base isolation can effectively reduce the seismic forces on a superstructure,particularly in low-to medium-rise buildings.However,under strong near-fault ground motions,pounding may occur at the isolation level between the baseisolated building(BIB)and its surrounding retaining walls.To effectively investigate the behavior of the BIB pounding with adjacent structures,after assessing some commonly used impact models,a modified Kelvin impact model is proposed in this paper.Relevant parameters in the modifi...     

Seismic performance of buildings with structural and foundation rocking in centrifuge testing

Rocking motion, established in either the superstructure in the form of a 2‐point stepping mechanism (structural rocking) or resulting from rotational motion of the foundation on the soil (foundation rocking), is considered an effective, low‐cost base isolation technique. This paper unifies for the first time the 2 types of rocking motion under a common experimental campaign, so that on the one hand, structural rocking can be examined under the influence of soil and on the other, foundation rocking can be examined under the influence of a linear elastic superstructure. Two building models, designed to rock above or below their foundation level so that they can reproduce structural and foundation rocking respectively, were tested side by side in a centrifuge. The models were placed on a dry sandbed and subjected to a sequence of earthquake motions. The range of rocking amplitude that is required for base isolation was quantified. Overall, it is shown that the relative density of sand does not influence structural rocking, while for foundation rocking, the change from dense to loose sand can affect the time‐frequency response significantly and lead to a more predictable behaviour.     

Experimental investigation on reparability of an infilled rocking wall frame structure

Improving seismic performance is one of the critical objectives in earthquake engineering. With the development of economy and society, reparability and fast resilience of a structure are becoming increasingly important. Reinforced concrete (RC) frame structure is prone to soft story mechanism. As a result, deformation and damage are so concentrated that reparability is severely hampered. Rocking wall provides an available approach for deformation control in RC frame by introducing a continuous component along the height. Previous researches mostly focus on seismic responses of rocking wall frame structures, while damage mode and reparability have not been investigated in detail. In this study, a novel infilled rocking wall frame (IRWF) structure is proposed. A half‐scaled IRWF model was designed according to Chinese seismic design code. The model was subjected to cyclic pushover testing up to structure drift ratio of 1/50 (amplitude 1/50), and its reparability was evaluated thereafter. Retrofit was implemented by wrapping steel plates and installing friction dampers. The retrofitted model was further loaded up to amplitude 1/30. The IRWF model showed excellent reparability and satisfactory seismic performance on deformation control, damage mode, hysteresis behavior, and beam‐to‐column joint rotation. After retrofitting, capacity of the model was improved by 11% with limited crack distribution. The model did not degrade until amplitude 1/30, due to shear failure in frame beams. The retrofit procedure was proved effective, and reparability of the IRWF model was demonstrated. Seismic resilience tends to be achieved in the proposed system.     

A physical model for dynamic analysis of wine barrel stacks

This paper deals with the earthquake response of wine barrel stacks using a physical model of rigid‐body components with discrete flexible and damped contact elements. An analytical 3D formulation of the complex dynamic behavior of different barrel stack configurations is presented. Such behavior includes the real geometry of the bodies, large displacements and rotations, the use of non‐linear contact elements to account for impact and sliding between bodies, and the resulting local energy dissipation at contact. The parameters defining the physical and mathematical model were calibrated experimentally, and the dynamic behavior of a benchmark barrel stack configuration was compared with the experimental results obtained from the literature. It was found that the model is able to predict the exact mode of collapse and the overall behavior of the system. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental testing of a rocking timber shear wall with slip‐friction connectors

Allowing a structure to uplift and rock during an earthquake is one way in which activated forces can be capped and damage to the structure avoided or minimised. Slip‐friction connectors (also known as slotted‐bolt connectors) were originally developed for use in steel construction, but for this research have been adapted for use as hold‐downs in an experimental 2.4 m × 2.4 m rigid timber shear wall. A novel approach is used to achieve the desired sliding threshold in the connectors, and the wall uplifts when this threshold is reached. From a series of quasi‐static cyclic tests, it is shown that slip‐friction connectors can impart ductile and elasto‐plastic characteristics to what would otherwise be essentially brittle structures. Because forces on the wall were capped by the slip‐friction connectors to levels well below the design level, no damage to the wall was observed. Self‐centring potential was also found to be excellent. The slip‐friction connectors themselves are of a unique design and have proven to be robust and durable, adequately performing their duty even after almost 14 m of cumulative travel under high contact pressures. To resist base shear without unduly affecting rocking behaviour, a new type of shear‐key is proposed and implemented, and a procedure developed to quantify its influence on overall wall behaviour. Copyright © 2014 John Wiley & Sons, Ltd.     

On poundings of a seismically isolated building with adjacent structures during strong earthquakes

This paper presents selected indicative results from an extensive parametric investigation that has been performed in order to assess the effects of potential earthquake‐induced poundings on the overall dynamic response of seismically isolated buildings. In particular, a seismically isolated building and its adjacent fixed‐supported buildings are subjected to various earthquake excitations that induce structural impact among the buildings in series. The results indicate that the seismically isolated building may hit against the adjacent buildings at the upper floor levels before the occurrence of any pounding at the isolation level with the surrounding moat wall. The severity of the impact depends on the dynamic properties of the adjacent buildings, in combination with the earthquake characteristics. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑横缝影响的拱坝动力分析

本文在求解三维弹性静力摩擦接触问题的有效方法-非光滑方程组方法的基础上,通过能够近似满足动量、动能守恒条件的速度、加速度的修正方法,将该方法推广到动力接触问题的求解中,以考虑地震时拱坝中横缝的开合、错动对坝体动力响应的影响。同时文中采用由多次透射公式表示的人工边界条件来考虑坝-基动力相互作用的影响。数值算例中分析了横缝的数目和布置位置对拱坝动力响应的影响。     

带窗洞的加气混凝土砌块砌体墙抗震性能分析

为了研究设窗洞的蒸压加气混凝土砌块砌体承重墙的抗震性能,运用ABAQUS有限元分析软件对其进行了非线性分析。首先将有限元模型的计算结果与足尺试件的试验结果进行了对比验证,在此基础上,通过改变墙体的竖向压应力、水平配筋和开洞大小,研究了这些参数对墙体抗震性能的影响。研究表明:随着竖向压应力的增大,墙体水平承载力提高,而极限变形能力则有降低趋势;水平配筋可以提高墙体的承载力和变形性能;增大洞口水平尺寸导致极限承载力明显降低,而对其相应位移的影响则小得多。