Experimental Assessment of the Seismic Response of a Base-Isolated Building Through a Hybrid Simulation Technique

Base-isolated structural systems have been more and more investigated through both numerical and experimental campaigns, in order to evaluate their effective advantages, in terms of vulnerability reduction. Thanks to the lateral response of proper isolation devices, large displacement demands can be accommodated, and the overall energy of the seismic event can be dissipated, by means of hysteretic behaviors. Among the common typologies of isolators, curved surface slider devices represent a special technologic solution, with potentially high dissipative capacities, provided by innovative sliding materials. On the other hand, the overall behavior is highly non-linear, and a number of research works have been developed, aiming at the definition of the most comprehensive analytical model of such devices. The most realistic response of a base-isolated structure could be returned by a shake table test of a full-scale building. However, dimensions of the available shake tables do not allow consideration of the common load conditions, to which the isolation devices are subjected, and consequently, scaled specimens are needed, and unrealistic responses could be found. Hybrid simulations seem to solve such an issue, by accounting for an experimental substructuring, represented by a physical device tested in a testing equipment, and a numerical substructuring, consisting of a numerical model of the superstructure. Thus, a much more realistic response of the full-scale structure can be computed. In this work, the outcomes of a number of hybrid simulations have been deeply analyzed and compared to a similar numerical model. Proper non-linear constitutive laws for isolation devices have been adopted, in order to evaluate the effectiveness of design and assessment procedures, commonly adopted in real-practice applications

INVESTIGATION OF THE LATERAL RESPONSE OF FRICTION-BASED ISOLATORS UNDER MULTI-CYCLIC EXCITATIONS

The frictional response of Concave Surface Slider (CSS) devices has been more and more investigated both experimentally and numerically. These isolators have shown many advantages in comparison to the commonly used typologies of devices, such as lead rubber bearings or low and high damping rubber bearings: when implemented in structural systems, the eccentricity of the resultant base shear with respect to the center of mass is significantly reduced, since the lateral response of the devices is a direct function of the applied vertical force, i.e. the weight of the structure; furthermore new innovative sliding materials have been studied and implemented in real applications, in order to achieve high levels of energy dissipation, together with a high recentering capability, due to the geometry of the steel sliding surfaces. On the other hand, a number of issues about the behavior of friction-based isolators still have to be accurately analyzed. Among the others the distribution of the vertical load applied to the device is usually assumed constantly smeared on the sliding pad: however, recent research works have shown rather than constant distributions of contact pressure and this aspect is expected to cause variations in the commonly known dependency of the friction coefficient on the vertical load. Moreover, when a CSS device is subjected to long lasting dynamic excitations, the so called “cyclic effect” leads to a decay of the friction coefficient during time. Such a decay trend can be analyzed in terms of friction coefficient as a function of the cumulative dissipated energy, and can be fully described by an exponential equation, properly calibrated; the decay behavior is also supposed to be characterized by dependencies on both sliding velocity and contact pressure, i.e. vertical load. Then, a direct comparison between flat and concave sliding motions needs to be carried out, aiming at highlighting the differences in the frictional response of these typologies of movements. In the present work the dynamic behavior of a friction based device has been deeply examined, thanks to the outcomes of a wide experimental campaign carried out at the EUCENTRE TREES Lab in Pavia on full scale flat and curved sliders, equipped with innovative sliding materials. Precisely, the cyclic effect caused on the friction coefficient by long lasting bi-directional dynamic motions has been characterized, by assuming several combination of sliding velocity and vertical load values. Moreover, the comparison among different diameters for the sliding pads in flat motions has been studied, in order to underline any “size effect” on the frictional response. Then, the comparison between flat and curved sliding motions has been carried out. Finally, such results have also been considered analytically, aiming at evaluating the consequences of the aforementioned features on the response of structural system base-isolated with CSS devices

Investigation of the Response Variability of Base-A Isolated Building Equipped With Lead Rubber Bearings

Nowadays analytical models of seismic isolators can fairly reproduce the force response of such devices, when implemented in a large variety of structural systems, such as buildings and bridges. Consequently, realistic hysteretic rules are available for the definition of the dynamic system for Non-Linear Time History Analyses, and earthquake simulations of the considered isolated structural systems can be computed. Such models are generally defined, according to mean values of mechanical properties of isolation devices, even though a certain variability has been experimentally assessed: precisely, statistical analyses of the outcomes of test database have outlined that the main response parameters of isolators should be considered as random variables, rather than as deterministic values. On the other hand, in the common practice both design and assessment procedures are mainly based on deterministic approaches, and bound analyses are ruled in just few standard codes. The present endeavor presents a wide parametric study on a case study structure, in order to assess the variability of the main response parameters, by accounting for random mechanical properties of isolation devices. Precisely, a combination of Lead Rubber Bearings and Flat Slider devices have been considered, and the spatial layout of isolators has been defined, according to a given performance point. The structural response of the case study building has been computed through Non-Linear Time History Analyses, by extracting 10'000 individual values of mechanical properties of devices. Presented results are related to the mean response of a spectrum-compatible set of natural records, in terms of displacement and force of both superstructure and isolation system

Definition and Validation of Fast Design Procedures for Seismic Isolation Systems

The research on traditional and innovative seismic isolation techniques has grown significantly in recent years, thanks to both experimental and numerical campaigns. As a consequence, practitioners have also started to apply such techniques in real applications, and nowadays, seismic isolation is widespread in regions characterized by a high level of seismic hazard. The present work aims at providing practitioners with very simple procedures for the first design of the isolation devices of a building, according to the most common typologies of isolators: Rubber Bearings, Lead Rubber Bearings and Curved Surface Sliders. Such Fast Design Procedures are based on simplified approaches, and the mechanical properties of the implemented devices can be obtained by assuming a performance point of the overall structural system, namely effective period and equivalent viscous damping. Furthermore, some important parameters are defined, according to the outcomes of a statistical analysis of the test database of the EUCENTRE Foundation in Italy. Finally, results of a validation study have been provided by analyzing a case-study structure through a Multi Degree of Freedom oscillator and a full 3D Finite Element model

Numerical assessment on the seismic response of a base-isolated building under Bi-directional motion

Experimental and analytical studies on Concave Sliding Surface devices have un- derlined that the hysteretic characteristics under bi-directional input motion are highly non- linear, in comparison with the uni-directional case. The force response of the device along both directions of motion strongly depend on the shape of the trajectory, because of the step- wise changing of direction of the frictional force, rather than in a uni-directional motion in which all forces have the same direction. Together with these aspects, also the variation of the frictional properties with respect to sliding velocity (Velocity Effect), vertical load (Verti- cal Load Effect) and heating phenomena originated at the sliding interfaces (Cycling Effect) increase the non-linearity of the behavior of such kind of isolators, leading to dispersions of the peak quantities when time history analyses are performed: such dispersions can not be neglected a priori, but they have to be accurately evaluated. In addition, experimental tests have shown widely sparse frictional properties of the sliding materials commonly used for CSS devices, even when the same conditions of loading are considered. Moreover, in real ap- plications, the spatial distribution of both the devices and the isolated building affect the overall response, especially when irregularities in the installation of the isolators are consid- ered, which results into uneven inclinations of the sliding surfaces with respect to the horizon- tal plane. In this endeavor a wide numerical campaign has been carried out on a case study, considering several layout conditions, the actual dispersion of the frictional characteristics of the device, and different models of the friction coefficient for all the isolators. The results of all the numerical simulations, performed by means of time history analyses, have allowed to underline some important aspects which must be accounted for when designing a structural system, isolated using a grid of CSS devices, under bi-directional seismic excitation

Equivalent uniaxial accelerogram for CSS-based isolation systems assessment under two-components seismic events

Concave surface slider (CSS) devices represent an effective solution for base-isolation design problems. In such isolators the energy dissipation capability is induced by the sliding motions which occur at one or more sliding interfaces. The spherical shape of the sliding surfaces provides a significant recentering behavior, by means of the stepwise projection of the applied vertical load with respect to both horizontal directions. For two-components earthquake excitations, the recentering force is computed as a linear spring with respect to displacements along the main directions of motion; whereas, the frictional response is returned by the stepwise projection of the total frictional force, which is aligned with respect to the trajectory of the device: thus, a bi-axial interaction of the directions of motion has to be accounted for, when a friction-based device is modelled. However, available commercial software which can capture such a behavior are limited. In this work an analytical procedure is defined, for the computation of an “equivalent uniaxial accelerogram” for the seismic assessment of a base-isolated structure, subjected to a bi-directional earthquake. Thanks to the proposed theory, it is possible to compute a single ground acceleration time-history, related to a proper direction angle, which can reproduce the same effects of a two-components seismic event on a base-isolated structural system: the analogy between the equivalent uniaxial and the bi-directional events has been studied in terms of acceleration, velocity and displacement spectra respectively. Results for the base-isolated structure have been analyzed in terms of displacement, absolute acceleration and interstorey shear response

Experimental Evaluation of the Size Effect on Flat and Curved Sliding Motions

The experimental behaviour of Concave Surface Slider devices has been deeply investigated in the recent past. Several static and dynamic tests have shown non-negligible dependencies of the friction coefficient on important response parameters, such as sliding velocity and contact pressure at the sliding interfaces. Moreover, an additional decay trend can be noticed, as the isolator is subjected to multi-cycle excitations: precisely, sliding motions produce heating phenomena, which lead to exponentially decreasing values of friction coefficient. Such a dependency can be expressed as a function of the dissipated energy, developed during motion, in terms of integral of the vectorial force-displacement relationship. It has been proved that the decay curve parameters change, when different couples of sliding velocity and contact pressure values are applied to the tested device; thus, the friction coefficient can be generally considered as a function of sliding velocity and contact pressure, whereas the degradation due to sliding interfaces heating can be modelled through an exponential decay function, with parameters which also depend on sliding velocity and contact pressure. Nonetheless, experimental results may be affected by sizes of the tested sliding pads: precisely, if low-to-medium vertical loads are applied to the isolator, a non-constant contact pressure distribution at the sliding interfaces is expected for large sliding pads, differently to what is assumed in designing the devices. This aspect may result into changes in the friction coefficient value and, consequently, can lead to unexpected responses. In this work results of a wide experimental campaign carried out on both Flat and Double Concave Surface Slider devices are discussed. Particularly, three different pad diameters have been implemented for both the Flat and the Curved sliders, and the same testing protocol has been applied, in order to evaluate the effects of the pad size on the frictional response. Bidirectional motions have been considered, with cloverleaf orbit, as ruled for bidirectional dynamic tests by standard code UNI:EN15129:2009. Results have been analyzed by investigating the common dependencies of the friction coefficient with respect to sliding velocity, contact pressure and cyclic decay, by varying device typology and pad sizes

Assessment of the seismic response of Multi-Stage Concave Surface Slider devices

Base isolation represents one of the most effective solution for passive protection of structural systems against earthquakes. The main principle of such a technique is related to the reduction of internal forces and deformation of a given structure, by means of an isolation level, able to dissipate significant amounts of energy and to accommodate large displacement demands. This behavior can be achieved if isolation devices are properly designed. Several isolation technologies have been deeply investigated, such as Rubber Bearings, Lead Rubber Bearings and both Single and Double Concave Surface Sliders. In addition, Multi-Stage Concave Surface Slider devices have been also studied, especially for high seismicity regions. Such devices provide different responses, depending on the achieved displacement demand: high tangent stiffness is provided for both low and high intensity levels, whereas low tangent stiffness is designed for medium seismic excitations. In this work the seismic response of Multi-Stage Concave Surface Slider devices has been analyzed, by considering the available non-linear models found in the scientific literature, according to the experimental behavior. Special attention has been focused on the frictional properties, the definition of the tangent stiffness of each stage and the main modeling scheme of the device

Patterns of reasoning in classroom

In this paper we report on some patterns of reasoning, which emerged during an activity of proving a mathematical statement performed by nine grade and university mathematics students. The statement in question involves drawing figures, working in arithmetic and in algebra. As for secondary students we detected fluency, flexibility and ability of verbalizing their reasoning. In particular, we will focus on the behavior of a student who through drawings succeeded in giving meaning to algebraic manipulation. The solutions of the university students were conditioned by the burden of the formal style used in university course of mathematics