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1.
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. 相似文献
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In this study, the efficiency of conventional shotcrete technique for strengthening of Un-Reinforced Masonry (URM) walls was shown using an experimental program. In addition, in this program the possible benefit of using anchors for connecting the shotcrete reinforcement layer to the R/C foundation was studied. The experimental program consisted of testing five full scale specimens with two different height-to-length aspect ratios and so different failure modes, under in-plane cyclic loading conditions. Two specimens were tested as reference and others were strengthened on a single-face using shotcrete layer. According to the results, strengthening of URM walls using traditional shotcrete approach created a completely stiff panel and prevented the formation of cracks. The failure mode in both reference and strengthened short length walls was rocking and the shotcrete layer could increase the strength capacity, energy dissipation, and stiffness of wall due to yielding and rupture of steel bars anchored to the foundation. On the other hand, in strengthened long length walls, shotcrete layer increased the shear sliding capacity with no or small increasing in their rocking capacity. Therefore, the failure mode of strengthened walls converted from shear sliding to rocking, even in the specimen with anchorage system. The distributed type of anchorage system could not improve the strength capacity of long length wall. Anchorage system was able to improve the out-of-plane performance of strengthened walls. 相似文献
3.
A freestanding rigid block subjected to base excitation can exhibit complicated motion described by five response modes: rest, pure rocking, pure sliding, combined sliding-rocking, and free flight. Previous studies on the dynamics of a rocking block have assumed that the block does not interact with neighboring objects. However, there are many applications in which the block may start or come in contact with an adjacent boundary during its motion, for example, a bookcase or cabinet colliding with a partition wall in an earthquake. This paper investigates the dynamics of a sliding-rocking block considering impact with an adjacent wall. A model is developed in which the base and wall are assumed rigid, and impact is treated using the classical impulse and momentum principle. The model is verified by comparing its predictions in numerical simulations against those of an existing general-purpose rigid-body model in which impact is treated using a viscoelastic impact model. The developed model is used to investigate the effects of different parameters on the stability of a block subjected to analytical pulse excitations. It is found that wall placement (left or right) has a dominant effect on the shape of the overturning acceleration spectra for pulse excitations. In general, decreasing the gap distance, base friction coefficient, and wall coefficient of restitution enhance the stability of the block. Similar observations are made when evaluating the overturning probability of a block using earthquake floor motions. 相似文献
4.
Umberto Tomassetti Francesco Graziotti Luigi Sorrentino Andrea Penna 《地震工程与结构动力学》2019,48(11):1277-1296
The assessment of the out-of-plane response of masonry structures has been largely investigated in literature assuming that walls respond as rigid or semi-rigid bodies, and relevant equations of motion of single-degree-of-freedom and multi-degree of freedom systems have been proposed. Therein, energy dissipation has been usually modelled resorting to the classical hypotheses of impulsive dynamics, delivering a velocity-reduction coefficient of restitution applied at impact. In fewer works, a velocity-proportional damping force has been introduced, by means of a viscous coefficient being constant or variable. A review of such models is presented, a criterion for equivalence of dissipated energy is proposed, equations predicting equivalent viscous damping ratios are derived and compared with experimental responses. Finally, predictive equations are examined in terms of incremental dynamic analyses for large sets of natural ground motions. 相似文献
5.
Juan C. Reyes Francisco A. Galvis Luis E. Yamin Cristian Gonzalez Juan D. Sandoval Pablo Heresi 《地震工程与结构动力学》2019,48(8):888-909
Historic adobe structures pose a high seismic risk mainly because of the poor out-of-plane bending response of their walls that may produce fatalities and significant economic, cultural, and heritage losses. In this paper, we propose a retrofitting technique that increases the wall strength for both in-plane and out-of-plane directions. This technique consists of vertical and horizontal timber elements symmetrically installed on each face of the wall to form a confining wood frame, supplemented with vertical tensors that pre-compress the wall. This study evaluates the performance of this retrofitting technique with a two-set experimental program on full-scale historic adobe walls. On the first set, four specimens were subjected to a static overturning test with boundary conditions representing the confinement effect at both ends by orthogonal walls. On the second set, three full-scale specimens, one unretrofitted and two retrofitted, were subjected to four ground motion records on a shaking table to assess the out-of-plane dynamic behavior of typical corner walls. The unretrofitted specimen collapsed during the second motion (peak ground acceleration [PGA] = 0.39 g), while both retrofitted walls survived all four motions (maximum PGA of 0.75 g) proving the high effectiveness of the proposed retrofitting. The addition of base anchors as a variation of the retrofitting technique significantly reduced the rocking effects and the residual drifts of the system, thus improving its overall seismic performance. Further research is needed to develop guidelines for seismic retrofit of heritage buildings including multistory full-scale tests of specimens with various types of openings and retrofitting strategies that minimize their architectural impact. 相似文献
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Precast concrete walls with unbonded post‐tensioning provide a simple self‐centering system. Yet, its application in seismic regions is not permitted as it is assumed to have no energy dissipation through a hysteretic mechanism. These walls, however, dissipate energy imparted to them because of the wall impacting the foundation during rocking and limited hysteretic action resulting from concrete nonlinearity. The energy dissipated due to rocking was ignored in previous experimental studies because they were conducted primarily using quasi‐static loading. Relying only on limited energy dissipation, a shake table study was conducted on four single rocking walls (SRWs) using multiple‐level earthquake input motions. All walls generally performed satisfactorily up to the design‐level earthquakes when their performance was assessed in terms of the maximum transient drift, maximum absolute acceleration, and residual drift. However, for the maximum considered earthquakes, the walls experienced peak lateral drifts greater than the permissible limits. Combining the experimental results with an analytical investigation, it is shown that SRWs can be designed as earthquake force‐resisting elements to produce satisfactory performance under design‐level and higher‐intensity earthquake motions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
7.
This paper presents the results of an experimental investigation on the rocking behavior of rigid blocks. Two types of test specimens have been tested, namely M and C types. Nine blocks of the M type and two blocks of the C type with different aspect ratios were tested with varying initial rotational amplitudes and with different materials at the contact interface, namely concrete, timber, steel, and rubber. The results showed that the interface material has significant influence on the free rocking performance of the blocks. Blocks tested on rubber had the fastest energy dissipation followed by concrete and timber bases, respectively. Analysis of the test results has shown that the energy dissipation in the case of tests on a rubber base is a continuous mechanism whereas in the case of tests on rigid bases, i.e. timber and concrete, energy dissipation is a discrete function. Finally, the rocking characteristics of the blocks were calculated using piecewise equations of motion and numerical analysis. It was possible to predict the correct free rocking amplitude response when a reliable value for the coefficient of restitution was used. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
8.
In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
The present study explores analytically the concept of rocking isolation in bridges considering for the first time the influence of the abutment-backfill system. The dynamic response of rocking bridges with free-standing piers of same height and same section is examined assuming negligible deformation for the substructure and the superstructure. New relationships for the prediction of the bridge rocking motion are derived, including the equation of motion and the restitution coefficient at each impact at the rocking interfaces. The bridge structure is found to be susceptible to a failure mode related to the failure of the abutment-backfill system, which can occur prior to the well-known overturning of the rocking piers. Thus, a new failure spectrum is proposed called Failure Minimum Acceleration Spectrum (FMAS) which extends the overturning spectrum put forward in previous studies, and it differs in principle from the latter. The comparison with the dynamic response of bridges modelled as rocking frames without abutments reveals not only that seat-type abutments and their backfill have a generally beneficial effect on the seismic performance of rocking pier bridges by suppressing the free rocking motion of the frame system, but also that the simple frame model cannot capture all salient features of the rocking bridge response as it misses potential failure modes, overestimating the rocking bridge's safety when these modes are critical. 相似文献
10.
The evaluation of the out‐of‐plane behaviour of unreinforced walls is one of the most debated topics in the seismic assessment of existing masonry buildings. The discontinuous nature of masonry and its interaction with the remainder of the building make the dynamic modelling of out‐of‐plane response troublesome. In this paper, the results of a shaking table laboratory campaign on a tuff masonry, natural scale, U‐shaped assemblage (façade adjacent to transverse walls) are presented. The tests, excited by scaled natural accelerograms, replicate the behaviour of external walls in existing masonry buildings, from the beginning of rocking motion to overturning. Two approaches have been developed for modelling the out‐of‐plane seismic behaviour: the discrete element method and an SDOF analytic model. Both approaches are shown to be capable of reproducing the experimental behaviour in terms of maximum rotation and time history dynamic response. Finally, test results and numerical time history simulations have been compared with the Italian seismic code assessment procedures. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
A new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification 
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下载免费PDF全文 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. 相似文献
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Though rocking shallow foundations could be designed to possess many desirable characteristics such as energy dissipation, isolation, and self-centering, current seismic design codes often avoid nonlinear behavior of soil and energy dissipation beneath foundations. This paper compares the effectiveness of energy dissipation in foundation soil (during rocking) with the effectiveness of structural energy dissipation devices during seismic loading. Numerical simulations were carried out to systematically study the seismic energy dissipation in structural elements and passive controlled energy dissipation devices inserted into the structure. The numerical model was validated using shaking table experimental results on model frame structures with and without energy dissipation devices. The energy dissipation in the structure, drift ratio, and the force and displacement demands on the structure are compared with energy dissipation characteristics of rocking shallow foundations as observed in centrifuge experiments, where shallow foundations were allowed to rock on dry sandy soil stratum during dynamic loading. For the structures with energy dissipating devices, about 70–90% of the seismic input energy is dissipated by energy dissipating devices, while foundation rocking dissipates about 30–90% of the total seismic input energy in foundation soil (depending on the static factor of safety). Results indicate that, if properly designed (with reliable capacity and tolerable settlements), adverse effects of foundation rocking can be minimized, while taking advantage of the favorable features of foundation rocking and hence they can be used as efficient and economical seismic energy dissipation mechanisms in buildings and bridges. 相似文献
15.
Unbonded posttensioning anchors a rocking structural member to its foundation and produces its controlled rocking response when the member undergoes seismic action. Unlike rocking of free-standing bodies, little attention has been given to the dynamic behavior of these controlled rocking members. This paper utilizes experiments of concrete structural members with unbonded posttensioning, varying member geometries, and levels of initial posttensioning force to (a) characterize the associated impact energy loss and (b) improve modeling of controlled rocking motions. Experimental results show that impact energy loss in controlled rocking members can be captured accurately using the coefficient of restitution (r) approach of the modified simple rocking model (MSRM). Based on the MSRM, a controlled rocking model (CRM) is developed that additionally accounts for the variations in contact length at the member-to-foundation (rocking) interface. The CRM reproduces the experimental responses of controlled rocking members with good accuracy and is used to investigate controlled rocking motions under horizontal base excitations. 相似文献
16.
This paper presents a single-degree-of-freedom (SDOF) constitutive model for assessing the performance of freestanding block contents of buildings. The model incorporates a bespoke damper to account for energy dissipation associated with rocking. It is advantageous in its direct correlation, via energy conservation, to the restitution coefficient for impact during rocking. A comparative study with the existing SDOF rocking models shows that the proposed model significantly improves the accuracy of free-rocking simulations, in which inherent damping predominantly affects response. It provides a promising and efficient tool for computationally intensive performance evaluation of nonstructural components.
相似文献17.
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. 相似文献
18.
Rocking (overturning) instability analyses of rigid blocks based on the assumption that the friction between the block and the ground is sufficiently large to exclude the effect of sliding, are reconsidered by including the effect in question. Both modes of overturning instability – without impact and after one impact – are thoroughly discussed in connection with small sliding, whose value depends on the values of kinetic (dry) friction coefficient and the external frequency excitation. Using an energy approach the analytical derivation of the nonlinear differential equations of motion of free-standing rigid blocks under one-sine ground pulse including the effect of sliding, are comprehensively established. The serious difficulties in solving this problem on one hand the change of the kinetic friction coefficient during the motion and on the other hand the reliable evaluation of the actual friction effect when rocking is included, are effectively confronted. This is achieved through a reliable approximation of an equivalent (reduced) coefficient assuming that the major part of friction takes place from the initiation of motion and terminates shortly after the onset of rocking. In cases of slender blocks closed form solutions for overturning due to simultaneous rocking–sliding without or after one impact, are conveniently derived. Among other findings, it was explored that the single block in question for small values of the external frequency (long periods of excitation) the sliding effect is beneficial (stabilizing the block), while for large values of external frequency this effect is detrimental (destabilizing the block). 相似文献
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The highly complex rocking response of free-standing statues atop multi-drum columns underground excitation resulting in insuperable difficulties for obtaining reliable solution is reexamined analytically. This is achieved after simulating the columns by monolithic viscoelastic cantilevers having structural damping, based on experiments, equivalent to the energy dissipation due to impact and sliding of multi-drum columns. Subsequently, the conditions of rocking (overturning) instability of free-standing rigid blocks (representing the statues) after their uplift from the top surface of the laterally vibrating cantilevers, are established, including overturning with or without impact. Attention focuses on the minimum amplitude ground acceleration which leads to an escaped motion through the vanishing of the angular velocity and acceleration. Maximization of such a minimum amplitude (implying stabilization) of the rigid block is obtained by seeking the optimum combination of values of the slenderness ratio of the column and its height. Analytically derived results based on linearised analyses are in excellent agreement with those obtained via nonlinear numerical analyses. 相似文献