Experimental Hybrid Simulation of Severe Aftershocks Chains on Buildings Equipped with Curved Surface Slider Devices

Abstract

In this research work the outcomes of a hybrid experimental campaign are analyzed, in order to evaluate the influence of aftershock events on the frictional response of sliding-based isolation devices for buildings. To achieve this, a hybrid testing framework was accordingly defined, by considering a numerical substructure, in terms of a simplified analytical model of a case study structure, and a physical substructure, as a full-scale Curved Surface Slider device, tested within the Bearing Tester System of the EUCENTRE Foundation Laboratory in Pavia (Italy). The tested isolator was equipped with a special sliding material, made up of a Poly-Tetra-Fluoro-Ethylene-based compound (PTFE), filled with carbon fibers and with a solid lubrication. The hybrid tests were performed, in terms of earthquake simulations, and the response of the base-isolated structural system was computed, by applying single-events, rather than aftershock chains. Results lead to a better understanding of the behavior of sliding-based seismic isolation systems, characterized by medium-to-high tribological properties, in terms of peak and residual displacements for both the single-event and the mean responses. Specifically, this work provides hybrid experimental evidence of the influence of an initial displacement offset on the overall behavior of the considered structural system.

1. Introduction

The knowledge about the effects induced by earthquake excitations on structural systems has grown exponentially in last decades, also as a result of a number of natural disasters occurring in several locations worldwide. Human losses and economic exposure in countries that experienced severe seismic events led to the need to understand all the possible strategies for the most efficient reduction of the vulnerability of building and bridge structures, in order to limit the overall seismic risk level. One of the most innovative solutions for the mitigation of the vulnerability of structural systems is represented by seismic isolation, which consists of the design of special devices that introduce a low-stiffness layer between the ground and the considered structure, which provide a period shift and a consequent reduction of the overall base shear and internal forces [1,2,3]. At the same time, the resulting high displacements are limited by a certain dissipative capacity of the installed isolators, which is fairly represented by the hysteresis of the force displacement response. Among the possible technical solutions, Curved Surface Slider devices are able to provide sufficiently low force responses, together with a high energy dissipation, through the frictional motion [4,5,6,7,8,9,10]. Research activities from both the numerical and experimental perspectives have led to a high level of accuracy in predicting the performance of such isolation systems, and more and more realistic results can be achieved [11,12,13,14,15]. Concerning experimental techniques, shake table tests, which generally provide the most realistic behavior of a structural system, can not be easily defined for base-isolated structures, without a proper scaling procedure, which my lead to unrealistic stress distributions inside the devices. Consequently hybrid simulations are currently widely used for the evaluation of the seismic response of not only base isolated buildings, but generally for any kind of structural and non-structural systems, by considering numerical and physical substructures [16,17,18,19,20,21]: consequently, much more realistic results can be achieved, extremely close to what could be obtained through full-scale shake table tests. Although sliding isolators have significantly good performance under seismic loading, residual displacements at the end of a single event could represent an important issue, due to the eventual high-frictional properties, specifically designed for some applications. Earthquakes are commonly considered as the mainshock, which is generally the event with the highest peak ground acceleration of a global seismic sequence. However, in some cases, aftershock events can have amplitudes more or less comparable to the corresponding mainshock value, and possible cumulative residual displacements can occur and the collapse of some devices can be achieved. As highlighted in recent research applications, the evaluation of residual displacements at the end of subsequent seismic events can lead to significantly high values [22,23,24]. Such residual deformations represent an initial offset for the device, with a non-negligible reduction of the maximum stroke along one direction. Numerical results show that if multiple earthquake excitations are subsequently applied, as a seismic chain of events, the residual displacement at the end of the considered ground motions gains with the number of the considered aftershocks [25,26]. Nonetheless, in the scientific literature, results are available for numerical simulations only, and no experimental data are publicly available for full-scale structural systems. The reason is mainly due to a number of issues related to the actual possibility of performing shake table tests on full-scale base-isolated systems, since the maximum geometrical characteristics of specimens do not allow to obtain realistic loading conditions for the implemented isolators, and, consequently, alternative testing strategies are needed [27,28].

The present research aims at investigating the influence of residual displacements on the overall response of a case study structure, evaluated through experimental hybrid tests. The numerical substructure consists of a simplified analytical model of the building, whereas a full-scale isolation device was considered as physical substructure, tested within the Bearing Tester System of the EUCENTRE Foundation Laboratory in Pavia (Italy). Results are provided by comparing the response of the system when single events and aftershock chains are applied, and the effects of possible initial displacement offset are discussed.

2. Case Study Structure

In this work, a case study structure was studied in order to evaluate the influence of severe aftershock events on the overall response of the isolation system. More specifically, a Reinforced Concrete frame structure was considered, laid on a reinforced concrete slab, which represents the actual interface between the superstructure and the isolation system. In agreement with the Italian Building Code, external loads were combined, in order to consider the seismic combination, by considering permanent structural (3.65 kN/m²) and non-structural (1.55 kN/m²) self-weights of the flooring system, 30% of the live load related to residential buildings (30% of 2.0 kN/m²–0.6 kN/m²), and the self weight of beams columns plates, which is automatically computed by the software. The concrete class is C40/50, which is associated with a characteristic value of cylindrical compression strength of 40 MPa, whereas the reinforcement steel grade is B450C, with a characteristic value of yielding strength of 450 MPa. All the building elements were modeled by means of linear-elastic frame elements, since the response of the superstructure is expected to be within the elastic range, and the slab interface was implemented by means of a mesh of shell elements. In Figure 1a 3D rendering of the overall structural system is shown.

Along both x and y directions four spans are designed, with equal span length (6 m each), with a constant interstorey height of 3 m. The reinforced concrete slab at the base of the building has thickness of 500 mm, and plan dimensions were obtained, by considering the plan development of the superstructure, with an additional offset of 1.5 m along both directions x and y directions (consequently, 27 m × 27 m). In order to consider the effective flexural stiffness of all the frame elements, moment of inertia of all the implemented sections was reduced through ad hoc reduction factors, which are higher for columns, in order to take into account the effect of the axial load. As a consequence, the linear-elastic branch of the bi-linear approximation of the capacity curve, returned by distributed-plasticity modeling, results aligned with respect to the capacity curve of the linear-elastic model, as reported in Figure 2.

The non-linear capacity curve is represented as the normalized base-shear with respect to the total mass of the building in fixed-base configuration vs. building total drift, as the ratio between the roof displacement and the total height: results were computed by means of a pushover analysis, which was performed with the software SeismoStruct [29]. In details, all frame elements were implemented with force-based inelastic frames, with distributed plasticity, defined according to specific non-linear constitutive laws for materials (Mander’s model for Concrete and Menegotto-Pinto’s model for steel reinforcement [30,31]); in addition, the inelastic frame elements related to concrete columns were defined with the proper confinement coefficients, which provide the correct influence of lateral reinforcements in the increase of both compressive strength and ductility capacities of the concrete core, aiming at obtaining the most realistic response for the building. More specifically, for both columns and beams Force-Based inelastic frame elements were implemented, represented by five Gauss’ integration points. The overall force-based formulation provide a strong form of the solution, and consequently a single frame element can be adopted for all the elements, and no longitudinal mesh has to be defined (which is fundamental for the proper approximation of Displacement-Based weak formulations). For all sections, a large number of fibers was set up, aiming at obtaining the most realistic representation of both concrete and steel rebar contributions. The capacity curve related to the fixed-base configuration of the building was returned by push-over analysis under displacement control, for the proper evaluation of possible softening behaviors after the achievement of the peak strength [32]. The adopted isolators consist of Curved Surface Slider devices, which can provide high dissipative capacity through the frictional response, together with a certain recentering behavior, induced by the spherical shape of the sliding surfaces [33,34,35,36,37].

3. Seismic Input

In order to perform earthquake simulations by using the Hybrid testing technique, a suite of seven one-directional natural seismic events was considered [38]. More specifically, the ground acceleration time series were selected, as ruled by the Italian Building Code [39], in agreement with the seismic hazard level defined for the construction site. For the adopted case study structure, the construction site is assumed to be located at L’Aquila (Italy), and Soil class B and topography category T₁ were considered. Since this work focuses the attention on the behavior of the isolation devices, the Collapse Limit State was studied, and consequently 5% probability of exceedance in the reference life of the structural system was assumed. Thus, with a reference life period of 50 years, a return period of 975 years is obtained. The spectrum-compatibility of the adopted suite of natural records was studied, in agreement with the Italian Building Code. Hence, the mean response spectrum of the records selection, obtained by computing the average spectral coordinate at all period values, was ensured to be bounded between the lower and upper limits, corresponding to 90% and 130% respectively of the target value, within a period range between 0.15 s and 3.0 s. In

Table 1. Selection of natural seismic events.

Event [#] 1	Station ID	Earthquake Name	Component	Mw	Fault Mechanism	Epicentral Distance [km]	Original PGA [g]	Scaled PGA [g]	Scale Factor [#]
1	ST_58065	Loma Prieta	y	6.9	oblique	27.59	0.512	0.379	0.74
2	HEC	Hector Mine	x	7.1	strike-slip	28.61	0.336	0.420	1.25
3	ST_58065	Loma Prieta	x	6.9	oblique	27.59	0.324	0.356	1.10
4	AQG	L’Aquila mainshock	x	6.3	normal	4.39	0.445	0.758	1.70
5	LGPC	Loma Prieta	x	6.9	oblique	18.75	0.586	0.586	1.00
6	LGPC	Loma Prieta	y	6.9	oblique	18.75	0.965	0.482	0.50
7	KAR	Gazli	x	6.7	reverse	12.78	0.717	0.789	1.10

¹ [#] units correspond to dimensionless parameters.

the selected seismic events are listed, together with some of the main characteristics.

It has to be noted that the selection of seismic events contains seven individual signals, even though some of them are related to the same earthquake; nonetheless, they were recorded at different stations, thus are associated with different stations, rather than along opposite directions. In order to be consistent with the characteristics of the construction site, the suite of natural seismic events was selected in the available databases of the software REXEL by limiting soil classification to the same properties of the target spectrum (i.e., Soil Class B). This is commonly performed in real applications, in order to consider earthquake excitations which are more comparable to what is expected at the construction site of the case study structure under investigation. Furthermore, the disaggregation analysis was considered for the proper selection of the seismic events by setting specific ranges for magnitude and epicentral distance which led to the highest contributions in the definition of the overall seismic hazard. It has to be noted that all these limitations and boundaries increase the probability to not achieve convergence, and maybe no selection can be obtained in some cases. In addition, records were scaled in order to better achieve the spectrum compatibility, also from a single-event perspective; moreover, all scale factors were limited between 0.5 and 2.0, in order not to obtain unrealistic signals, characterized by inconsistent balance between the frequency content and the considered Peak Ground Acceleration (PGA) values.

In Figure 3 graphical results for the spectrum compatibility study are provided in terms of single-event and mean response spectra, in comparison to the target, together with the code-based lower and upper bound.

Thanks to the aforementioned spectrum-compatibility study, the single-event discrepancy between the related response spectrum and the target spectral coordinates is very limited in the period range of interests for the designed structural system (values higher than 2.0 s). The selected records were applied both as single events and as three different chains of aftershocks earthquakes. It is highlighted that the adopted approach is the most demanding, since individual mainshocks events were applied consecutively: results are expected to provide a big picture of what happens in the very worst case.

4. Hybrid Simulation Framework

This section provides the description of the framework designed for experimental hybrid simulations of the previously described case study structure, performed at the Laboratory of EUCENTRE Foundation in Pavia (Italy). More specifically, the reinforced concrete building was numerically modeled through a statically condensed multi degree of freedom oscillator, by computing the actual stiffness and mass matrices from the full three-dimensional Finite Element Model (F.E.M.). On the other hand, the base-isolation system was represented by the response of a single physical full-scale isolator, which is assumed to be representative of the whole isolation system: in order to obtain the actual force response of the isolation system, the force feedback returned by the testing equipment is scaled by the ratio between the total structural weight and the applied vertical load to the physical device. Consequently, purely translational motions are considered, with no torsional movements of the superstructure [40,41].

The hybrid simulation was set up as an equivalent time history analysis, by applying at each time instant the selected ground motion time series to the dynamic system of the Multi Degree of Freedom (MDOF) system [42] (i.e., the numerical substructure); the resulting value of displacement at the isolation level is then applied to the full-scale device (i.e., the physical substructure), tested within the Bearing Tester System (BTS), and the consequent force feedback value is used for the next iteration in the dynamic system. The stepwise interaction between the numerical and the physical substructures leads to the final solution of the time integration of the dynamic systems, which consists of the displacement time series at all levels of the building, together with all the feedback signals recorded by the testing equipment of the bearing.

In order to obtain the most realistic results possible, a time scale factor equal to 8.0 was adopted, which has provided structural responses significantly close to real-time. Consequently, the motion applied to the physical device through the Bearing Tester System is represented by the same displacement amplitudes in comparison to the real-time numerical simulation, even though velocities values are scaled by 8.0. The assumption of the proper scale factor for experimental hybrid simulations could be crucial, especially for rate-dependent devices, such as the ones adopted in this study, which present the commonly known “velocity effect”. Nonetheless, thanks to the low scale factor, and given the high values of sliding velocity achieved during earthquake simulations, the device is subjected to motions which imply a constant friction coefficient, the peak velocity value being greater than the value correspondent to the end of the increasing transition branch of the frictional properties.

4.1. Physical Substructure

A Double Curved Surface Slider isolator [5] was considered as the physical substructure, being one of the most typical configuration of sliding-based devices adopted for real practice applications. In Figure 4, a section of the 3D rendering of the device is provided, which shows all the internal components. Such an isolator is made up of two individual spherical backing plates, which were realized with the same radius of curvature and with structural steel material S355JR. Within counterbore gaps of 5 mm stainless steel sliding surfaces are provided, with a thickness of 2 mm, and both are polished to mirror finish in order to achieve a roughness index Ra of 0.2 [40]. In the middle of the sliding surfaces, a non-articulated slider is installed, which is a unique steel block (material S355JR). The internal slider houses two circular sliding pads, made up of a special sliding material with the same diameter (160 mm), in order to consider the same frictional response at both the sliding interfaces. The overall equivalent radius of curvature of the device can be obtained by the summation of the radii of curvature of the spherical surfaces (1600 mm each), and by subtracting the height of the internal slider (120 mm): thus, the equivalent radius of curvature of the isolator is equal to 3080 mm.

Both the backing plates of the isolator have an external diameter equal to 548 mm, whereas the inner slider diameter is equal to 170 mm: consequently, the maximum displacement allowed by the geometrical configuration of the device is equal to 360 mm. A special sliding material was adopted within the sliding interfaces of the device, which consists of pigmented graded Polytetrafluoroethylene (PTFE) filled with carbon fibers, with a solid lubrication: such a sliding material showed significantly good frictional properties, together with a negligible break-away and stick slip friction coefficients and with low damage after several dynamic tests. During the hybrid simulations the physical device was subjected to vertical load equal to 400kN. In order to evaluate the tribological properties of the device, a number of characterization tests were performed, as ruled by the European Standard Code for Anti-Seismic devices UNI:EN15129:2009 [43], and consequently the reference friction coefficient was computed:

$$\mu =\frac{EDC}{4D_{max}W}$$

(1)

EDC is the Energy Dissipated per Cycle, obtained as the integral of the force-displacement hysteretic loop, D_max is the maximum displacement of the test and W is the applied vertical load. According to the assumed vertical load, a friction coefficient value equal to 0.10 (10%) was computed.

Such frictional characteristics are generally provided by medium to high tribological properties of the sliding material commonly adopted in real applications and is expected to lead to interesting results, since in this work special attention is focused on the influence of initial offset and residual displacements on the response of aftershocks events.

4.2. Numerical Substructure

The case study structure was numerically modeled as an equivalent Multi Degree of Freedom oscillator (MDOF), thanks to a special static condensation procedure, which was applied to the full 3D Finite Element Model (F.E.M.) of the structure ([41]; Figure 5).

The resulting mass and stiffness matrices allow to obtain dynamic properties significantly close to the ones returned by the three-dimensional F.E.M. model, in terms of periods, modal shapes and modal participating mass ratios, which were implemented within the commercial software SAP2000 [44]. The full model of the building was developed by considering linear-elastic frame elements for both beams and columns, by considering 30 GPa and 0.25 as Young’s modulus and Poisson’s ratio respectively. It has to be noted that a linear elastic model can fairly represent the response of the building when the isolation system is installed, since all standard codes allow to linearly model the superstructure, thanks to the vulnerability reduction induced by the isolators. The high level of accuracy of the adopted numerical model, despite the simplification of the overall system, is a direct consequence of the static condensation procedure, which actually returns the stiffness and mass characteristics of the structure as a function of the effective flexural behavior of both beams and columns. More specifically, in order to compute the i-th column of the condensed stiffness matrix, the horizontal translational degree of freedom at the i-th level of the system is unrestrained and a unit horizontal force is lumped at the same location. Such a reference point for the i-th floor corresponds to the location of the center of mass, which is connected to the related story by means of a rigid diaphragm constraint, so that the out-of-plane stiffness of beams is considered. On the other hand, the remaining degrees of freedom (centers of mass of the remaining floors) are restrained. Thus, the i-th column of the matrix can be computed by dividing the vector containing the reactions and the lumped force by the horizontal displacement at the i-th unrestrained floor, originated by the applied lumped load.

Such a stiffness matrix is computed without considering any force response coming from the isolation level, since the hysteretic behavior is considered as the horizontal force feedback returned by the testing equipment, within the time integration algorithm which rules the experimental hybrid simulation. Thus, the resulting stiffness matrix is representative of the linear elastic response of the superstructure, by accounting also for the horizontal rigid body translational motion. With the adopted procedure, similar dynamic properties of the full 3D model of the considered structural system can be obtained, since all the implemented structural elements of the model are able to deform, and no restrained behavior is assigned. In agreement with all the aforementioned assumptions, the overall structural system was experimentally evaluated, by performing hybrid earthquake simulation, according to the following dynamic system of motion equations:

$$\overline{\overline{M}}\cdot \left(\begin{array}{c}\underset{\_}{{\ddot{u}}_0}\\ {\ddot{u}}_1\\ {\ddot{u}}_2\\ {\ddot{u}}_3\end{array}\right)+\overline{\overline{C}}\cdot \left(\begin{array}{c}\underset{\_}{{\dot{u}}_0}\\ {\dot{u}}_1\\ {\dot{u}}_2\\ {\dot{u}}_3\end{array}\right)+\overline{\overline{K}}\cdot \left(\begin{array}{c}\underset{\_}{u_0}\\ u_1\\ u_2\\ u_3\end{array}\right)+\langle F_{is}\rangle \cdot \left(\begin{array}{c}\underset{\_}{1}\\ 0\\ 0\\ 0\end{array}\right)=-\overline{\overline{M}}\cdot \left(\begin{array}{c}\underset{\_}{1}\\ 1\\ 1\\ 1\end{array}\right)\cdot {\ddot{x}}_g$$

(2)

where:

• $\overline{\overline{M}}$ is the mass matrix, represented by a diagonal matrix can be obtained, which has the components of the main diagonal equal to the summation of the assembled mass values of all the points of a given storey;
• $\overline{\overline{C}}$ is the viscous damping matrix, defined according to a Rayleigh formulation, with a low damping ratio, namely 2%, in order not to underestimate the overall response;
• $\overline{\overline{K}}$ is the stiffness matrix returned by the applied static condensation procedure;
• $u_i$, ${\dot{u}}_i$ and ${\ddot{u}}_i$ are the translational degrees of freedom and the time derivatives at the i-th level, relative to the ground;
• $\langle F_{is}\rangle$ is the force response feedback, which is stepwise returned by the Bearing Tester System;
• ${\ddot{x}}_g$ is the applied ground motion.

Since earthquake simulations were performed, the structure was assumed to be in equilibrium at the beginning of the motion; thus, zero initial conditions were considered for both displacement and velocity values at all degrees of freedom. Thus, the solution of the dynamic system was returned by the time-integration algorithm, which considers a stepwise interaction between the numerical substructure (i.e., the MDOF oscillator representing the building) and the physical substructure (i.e., the full-scale device tested within the Bearing Tester System), by considering a scaled time axis (time scale factor: 8.0 -Figure 6).

The presented hybrid simulation framework was implemented within the MATLAB Environment & Simulink [45], and allows to time-integrate the overall dynamic system, by considering the stepwise interaction of both the numerical and physical substructures. Since hybrid tests are performed to simulate earthquake excitation, the presented system is analyzed through a special time-integration algorithm, in order to perform an equivalent Non-Linear Time History Analysis. The non-linearity of all the implemented isolators is fairly and realistically represented by the experimental response of the physical substructure. Consequently, the ground acceleration time series represent the input signals for the dynamic system of the overall base-isolated building, and the displacement response at all levels of the building can be computed through the time-integration of the whole set of dynamic equilibrium equations. More specifically, at each time step, the displacement at the isolation layer becomes the control command for the Bearing Tester System (Figure 7), which is able to apply such a deformation value to the physical isolator, by considering a displacement-control method.

The force feedback response returned by the testing equipment, scaled by the effective ratio between the total weight of the structural system and the vertical load applied to the device, provides an updated force contribution for the dynamic equilibrium equation at the isolation level, which can be further time-integrated. Thanks to the presented algorithm the response of the whole base-isolated building can be obtained.

5. Experimental Results and Discussion

In this section the experimental results are shown for all the hybrid earthquake excitations. Special attention is focused on the global hysteretic response of the single-event cases, in order to experimentally check the tribological properties of the adopted sliding material. Then, the comparison of the displacement time series at the isolation level returned by the single-event excitations are graphically compared to three different aftershock chains, which were defined by considering three different orderings of the adopted earthquakes. The same comparison was studied by analyzing peak displacements and residual displacements as a direct consequence of initial displacement offset when aftershocks are applied.

In Figure 8, results of the adopted single events are provided in terms of hysteretic responses of the isolation layer.

More specifically, on the horizontal axis, the isolation displacement is reported, whereas on the vertical axis the isolation force response is considered, normalized with respect to the total weight of the overall structural system. This representation of the hysteretic response allows to notice the resulting frictional properties, which corresponds to the numerical value of normalized force at zero-displacement configuration: it should be noted that the desired friction coefficient was achieved, approximately equal to 10% in all cases. The mean displacement demand achieves values of about 83 mm, with a coefficient of variation of 43%. Concerning the sliding velocity, a mean value of 46 mm/s was found, related to the experimental response of the physical substructure, which corresponds to approximately 370 mm/s in the numerical real-time simulation, with a coefficient of variation of 35%. With the adopted sliding material being a PTFE-based compound, results of previous characterization testing campaigns have shown that 50 mm/s can be considered as a threshold value related to the achievement of a constant asymptotic value of friction coefficient, regardless of the applied vertical load at the physical device. Consequently, it could be assessed that negligible differences in the presented results could be obtained also for lower time scale factors, which correspond to simulations closer to real time (i.e., time scale factors 4.0, 2.0 or 1.0). In Figure 9, Figure 10 and Figure 11, graphical results are provided, in terms of experimental displacement time series at the isolation level, for both aftershocks chains and single events, by overlapping the obtained signals. It can be noted that all single-events (colored lines) start from the zero-displacement configuration; on the other hand, all the performed aftershock chains (black lines) presents an initial displacement offset, which causes an increase of the peak displacement response. This aspect is amplified by the numerical value of the experimental friction coefficient (10%), which generally leads to non-negligible residual displacements at the end of all the events, even though the recentering contribution induced by the spherical shape of the sliding surfaces provides a certain limitation.

Furthermore, after the strong motion range of all the seismic events, a smoothly decreasing branch of the residual displacement can be detected: this behavior could be attributed to the response of the building, which is subjected to negligible ground acceleration values, and consequently a free-vibrations phase could be considered; such a vibrating motion provides an additional recentering contribution, which gradually decreases the residual displacements for both the single events and the aftershocks chains. The presented results provide evidence that the residual displacement at the end of all aftershocks does not increase significantly, even though all events start with an initial displacement offset.

In order to better understand the overall behavior of the considered structural system, further analyses were computed, by considering the initial offset, the peak and residual displacements and the drift response of the building.

In Figure 12 the building total drift and peak normalized base shear values were analyzed for all the simulations, in order to ensure if the superstructure was subjected to limited plastic deformations, and consequently to prove that the linear elastic modeling assumption for the building is reasonable.

As can be noted all drift values are averagely equal to the yielding reference value (9%) among the selected seismic events of the adopted suite of natural earthquakes; only for events #5 and #7 would some limited plastic deformations be considered, even though the variation percentages between such values and the target elastic drift do not exceed 20% in the worst cases. On the other hand, normalized values for building base shear are lower than the corresponding target value at the yielding point of the capacity curve in all cases. Thus, the overall linear elastic modeling assumption for the building can be considered reasonable for the presented study.

In Figure 13, the ratio between the initial offset and the peak displacement of the chain aftershocks are provided (left), together with the percentage variation between the peak displacement response of the single event and the aftershock chains.

Results show that the initial offset at the beginning of all the aftershock events can be a significantly high percentage of the peak displacement response of the isolation system. Approximately the same behavior can be noticed in most cases, regardless of the actual sequence of seismic events, which seems to suggest that the initial offset is strictly related to the overall characteristics of the selected ground motions, with no influence of their position within the aftershocks chains. This is not expected to hold for cases such as the M_W 7.3 earthquake on 9 March 2011 that was followed by the stronger M_W 9.0 Tohoku earthquake on 11 March 2011 in Japan (additional details can be found in [46,47,48] which provide natural time analysis of seismicity). In the worst case, for Event #4, the initial offset is approximately 60% of the peak displacement response of the subsequent event. Nonetheless, as previously assessed for the displacement time series, the initial offset does not increase as the aftershock events occur. As a direct consequence, the ratio between the single event and the aftershock chains peak displacement responses does not increase as well, and very similar variations can be obtained, regardless of the actual position of each event within the performed chains. The initial offset lead to variations in the peak displacement response bounded between −20% and −10% in all cases, which provide evidence that the initial offset leads to an increasing lateral deformation of the isolation layer, which does not gain as all the aftershocks occur.

In Figure 14 results are presented in terms of ratio between the residual displacement for single event and for aftershock chains for all the selected earthquakes.

Additionally for residual displacement response, no significant influence of the actual position of all events within the considered aftershock chains can be averagely detected. Furthermore, as for the peak displacement response, the residual deformation returned by the application of single events is lower than the corresponding value related obtained in the aftershock chain. On the other hand, it can be noted that for some events no relevant differences can be found from the considered approaches. Such an issue seems to highlight again that the main characteristics of the suite of selected ground motions, and no significant influence of the actual sequence of events can be clearly assessed.

Finally, peak displacement and interstory drift responses were analyzed for all the levels of the considered case study structure, as shown in Figure 15 and Figure 16, respectively, in terms of variation percentages between the single event and the aftershock chains values.

Approximately same conclusions drawn for the isolation layer (Level #0) can be considered also for all the levels of the superstructure, which shows that the single-event response is lower in comparison to the application of the same events within aftershock chains.

In addition, it can be assessed that the variation percentage looks to decrease, if higher levels of the building are considered, and the maximum variation at the isolation level (Level #0: −20%) significantly decreases (Level #3: −10%). Concerning the drift response, much lower variation percentages can be computed, averagely bounded between ±5%, and no clear trend can be defined. Consequently, the influence on the building response of the application of a single event, rather than aftershock chains, seems to be negligible, according to the presented experimental results.

6. Conclusions

The presented research provides an investigation of the behavior of friction-based seismic isolators when subjected to subsequent earthquake excitations. To this aim, a special framework for experimental hybrid tests was defined in order to obtain the most realistic results possible. The hybrid tests were set up as seismic simulation of a case study structure, base-isolated by means of Curved Surface Slider devices. More specifically, a numerical substructure was considered within the experimental hybrid algorithm, consisting of a simplified lumped-masses oscillator with the same dynamic properties of the full 3D F.E.M. model; on the other hand, a full-scale device was tested as physical substructure. The time-integration method implemented within the hybrid testing algorithm considers a time scale factor equal to 8.0, which is considerably close to real-time simulations and realistic results can be obtained. The isolator was equipped with an innovative sliding material, filled with carbon fibers and solid lubrication, which provides 10% friction coefficient at the applied vertical load. The results were obtained, by performing hybrid earthquake simulations on both single-events and with aftershock chains. By analyzing the results, that the following can be concluded:

• The outcomes of the displacement response at all levels showed that the application of a single event generally leads to lower peak values, in comparison to aftershock sequences of earthquakes, due to the initial displacement offset.
• Both the initial offset and the residual displacements do not increase as all the subsequent aftershock events occur, but numerical values remain limited and do not gain over the application of the seismic sequence.
• The variation percentage between the single event and the aftershock chains peak displacement responses at all levels is averagely equal to −20% at the isolation system, and decreases to −10% as upper floors are considered.
• This behavior can be assessed, regardless of the location of a single-event within the adopted aftershock chains.
• Concerning the building response, limited variations were computed for interstory drifts at all levels, bounded between ±5%, which suggests that the superstructure is not significantly affected by the application of sequences of seismic events rather than single ground motions.

The outcomes of the present work seem to suggest that initial displacement offsets could lead to a certain unexpected discrepancy between the single-event and seismic chain responses, with consequent limitations in the total stroke of the isolation devices. Nonetheless, this issue would need further investigations, especially from the experimental standpoint, by also analyzing also other seismic isolation systems commonly adopted in real applications, together with several case study structures, in order to come up with generalized conclusions. A better understanding of the recentering behavior of isolation devices would be valuable for the revisions of the main standard codes for both anti-seismic devices and structural analysis.