Aseismic smart building isolation systems under multi-level earthquake excitations: Part I, conceptual design and nonlinear analysis

Abstract

As a novel structural control strategy, tuned mass damper (TMD) inspired passive and semi-active smart building isolation systems are suggested to reduce structural response and thus mitigate structural damage due to earthquake excitations. The isolated structure’s upper stories can be utilized as a large scaled TMD, and the isolation layer, as a core design point, between the separated upper and lower stories entails the insertion of rubber bearings and (i) viscous dampers (passive) or (ii) resettable devices (semi-active). The seismic performance of the suggested isolation systems are investigated for 12-story reinforced concrete moment resisting frames modeled as “10+ 2” stories and “8+ 4” stories. Passive viscous damper or semi-active resettable devices are parametrically evaluated through the optimal design principle of a large mass ratio TMD. Statistical performance metrics are presented for 30 earthquake records from the three suites of the SAC project. Based on nonlinear structural models, including P-delta effects and modified Takeda hysteresis, the inelastic time history analyses are conducted to compute the seismic performances across a wide range of seismic hazard intensities. Results show that semi-active smart building isolation systems can effectively manage seismic response for multi-degree-of freedom (MDOF) systems across a broader range of ground motions in comparison to uncontrolled case and passive solution.

Keywords

tuned mass damper / smart building isolation / resettable device / non-linear / statistical assessment

Introduction

Structural control strategy makes an additional energy dissipation mechanism to improve seismic structural performance. Generally accepted goal of this seismic design approach is to achieve the desired structural performance with a minimal control effort. Based on this point of view, many structural isolation strategies have demonstrated the validity of the realistic seismic control systems for consideration in future design and construction, and the details and results of a set of comparative studies are used to assess the feasibility and effectiveness of such isolation systems. From the results of these comparative studies, it is found that various types of control scheme may reasonably reduce the seismic response of a structure.

As for a modified systematic approach and alternative structural control strategy, a series of new developed structural systems have been made, focusing on the use of structural partial mass. More specifically, to expand effective application of isolation techniques, it is proposed to make roof or top floor acts as a vibration absorber for the lower stories of low- and medium-rise buildings [ 1– 3]. Furthermore, more studies [ 4– 10] sought to evaluate the effect of using segmental structures, where isolation devices are placed at various heights in the structures, and this approach has an advantage of increasing the sub-mass of the structures, making it possible to control high-rise buildings.

Conceptually, the above modified isolation approaches seem to be expended concept of tuned mass damper (TMD) system with a relatively large mass ratio. However, it is difficult to convince the system’s effectiveness since the design of these upper masses (isolated roof, top floor and upper segment) is not based on the “optimal” design approach, such as optimal TMD system. In the design of any control device for the suppression of undesirable vibrations, the aim would be to provide optimal damper parameters to maximize its effectiveness.

Recently, to overcome this reliability related problem and support the availability of the use of large TMDs, considerable studies have been devoted to the optimal design of TMD-like building isolation systems to enable proper selection of absorber parameters [ 11– 15]. Especially, the authors of this study suggested the TMD principle-based design of the “TMD (passive and semi-active) building systems” and its seismic performances were evaluated over three probabilistically scaled suites of earthquake records parameters [ 16– 18]. The results showed that the suggested TMD modified systems provide more effective and robust response mitigation over a range of ground motions within each earthquake suite. However, in spite of the reliable performance results of the TMD building systems obtained, the building models in the studies were assumed to remain elastic during seismic excitations. Due to the fact of this linearity assumption, the validity and applicability of the results could be quite limited for seismic application when damage is expected. Therefore, a series of the inelastic analyses of the systems are necessarily required to provide realistic information regarding the cumulative damage to the structure, which may be more important in evaluating potential damage and degradation.

Nonlinear smart building isolation system

Comparative building models

To demonstrate the potential and beneficial effects of the suggested smart building isolation system, a realistic 12-story reinforced concrete framed structure [ 19], which was previously investigated in the linear analysis, is chosen as a target building structure. This model was designed originally according to the New Zealand Loadings Code [ 20] based on “capacity design” and revised several times following the requests of the structural upgrades and code revisions [ 21– 23]. For the smart building isolation systems, the upper “two” and “four” stories of the 12-story target structure are isolated from the “ten” and “eight” stories lower structure, respectively. Thus, the resulting comparable structure configurations are presented as 12-story, “10+ 2” story and “8+ 4” story, which differ by the mass ratio used as a function of isolated stories, as shown in Fig. 1.

Different from the previous linear quantitative analysis [ 17], in this study, the seismic performances of the semi-active building isolation models (10+ 2 and 8+ 2) including realistic ‘nonlinear’ properties are compared with those from the corresponding uncontrolled (12-story) and passive building isolation models (10+ 2 and 8+ 2). Figure 1 shows the schematic description of the reinforced concrete framed structure used and the installed isolation layer including rubber bearings (for passive and semi-active systems), viscous damper (for passive system) and resettable device (for semi-active system).

Table 1 and 2 respectively show the frame sizes and dynamic properties used for the 12-story target model and two different building isolation models. The modeling technique associated with the models adopted has been developed by the inelastic time-history analysis program, RUAUMOKO [ 24]. Overall, the 12-story target building model is considered as a realistic nonlinear structure that is broadly representative of tall framed structures in New Zealand and internationally.

Resettable device

The resettable device adopted in this study has same dynamic properties as previously used in linear analysis [ 17]. The resettable device stiffness, and thus force (k), is modeled as a variable stiffness spring element based on the relative motion between the upper and the lower structures. The ideal device acts like a linear pneumatic or hydraulic spring and develops force due to displacement and the resulting compression of a working fluid. At any specified point of device reset the compressed working fluid is released, thus dissipating energy, and resetting the effective spring length to zero.

Figure 2 shows how these devices can be used in a novel two-valve configuration to resist selected motions while providing only minimal air damping for other motions [ 25]. The end result is customized hysteretic behavior of the device. The quadrants are labeled in the first panel, and F_B is the total base shear while F_S is the base shear for a linear, undamped structure. Thus, F_B>F_S indicates an increase in base shear due to the damping added.

Two added nonlinearities are included in the ideal model to better represent the physical reality of these devices:

1) Nonlinear reset: The device reset is not instantaneous or vertical as in Fig. 2. Instead the device loses 5% of its force every 0.01 s based on experimental data [ 26, 27]. The result is that some energy or force is returned to the system aiding re-centering and creating a sweeping or curved reset line on the hysteresis loop.

2) Return friction: A constant return friction or sliding friction force is used, which is approximately 3%–5% of the peak device force seen in initial simulations. This level is based on experimental device data to date. It also serves to limit base and thus structural velocities at the cost of some increased transfer of forces.

Overall, these two nonlinearities are based on experimentally observed data from full size devices. They also provide a more optimal isolation result. Note that friction force could readily be controlled via using more than one valve per chamber or variable orifice valves, thus creating an active air damper from the device when it was not resisting motion.

Design of the isolation layer

The design parameters for the smart isolation layer are basically based on and derived from the previous linear design and application studies [ 16– 18]. For example, the tuning ratio for this multi-degree-of freedom (MDOF) system is nearly equal to the tuning ratio for a two-degree-of freedom (2-DOF) system for a mass ratio of μΦ, where Φ is the amplitude of the first mode of vibration for a unit modal participation factor computed at the location of the upper isolated stories. Thus, the tuning and damping ratios are obtained from the equations for the 2-DOF system by replacing μ by μΦ.

The resulting optimum parameters are listed in Table 3. The stiffness of isolation layer (k₂) is equally allocated to rubber bearing stiffness and the stiffness of the semi-active resettable device. This equivalent combined stiffness was chosen for simplicity and examined as a suitable stiffness value representing a nearly optimal isolation design approach.

Exact design and optimization criteria for semi-actively controlled structures are not possible due to nonlinearity of device. However, the previously investigated optimal passive stiffness (k₂) can be contributed to semi-active systems [ 16]. The efficacy of balancing stiffness between resetable devices and rubber bearings can be considered and, finally, the general validity of the optimal derived parameters has been adopted.

Nonlinear time history analysis

Motivation

Linear structural model usually overestimates the effectiveness of the structural system when comparing controlled performance with uncontrolled response. The inelastic characteristics of the structural behaviors, however, critically effects on the actual seismic responses of a building for possible earthquake excitations. This analytical ability of nonlinear model produces the real prediction of seismic responses and the accurate evaluation of seismic performance of a building structure. Thus, a reliable evaluation of the effect of nonlinear behavior on the demands resulting from time history analyses is required and, finally leads to accurate evaluation of the seismic performance not only for the global nonlinear behavior of a building but also for its local nonlinear seismic responses.

Previous control evaluation research into the effect of nonlinear aspects has highlighted the necessity to include two main types of nonlinear effects if models are to accurately represent real and actual structural demands [ 28, 29]. The inclusion of the effect of geometric nonlinear P-delta effects of flexural stiffness is the one of these aspects, while the other is a nonlinear hysteretic model to account for structural energy dissipation and yielding during large motions.

To demonstrate the accurate and valid controlled performances of the suggested smart building isolation systems with the uncontrolled building model, the inelastic dynamic time history analyses based on nonlinear structural models, including (i) P-delta effects and (ii) modified Takeda hysteresis, are carried out in RUAUMOKO [ 24].

P-delta effects

In most analyses, the first order moments and deflections are determined on the assumption of linear elastic behavior. However, as the frame sways laterally the vertical loads acting through the deflected shape cause additional moments and deflections. These added moments and deflections are second order effects that are not predicted by the first order analysis, but may be important in large structural responses. More specifically, these effects produce a second order stiffness called the geometric stiffness, which may be assigned to augment the first order stiffness.

When large deflections are present, the strain-displacement equations contain nonlinear terms that must be included in calculating the stiffness matrix k. The nonlinear terms in the equations modify the element stiffness matrix k so that the total stiffness is defined:

(6) k=k_{\mathrm{E}}+k_{\mathrm{G}},

where k_E is the standard elastic stiffness matrix and k_G is the geometric stiffness matrix.

The geometric stiffness matrix (k_G) is presented in Eq. (7) where the formulation was based on the lateral deformation shape along the beam being a cubic function of the position along the length.

(7) k_{\mathrm{G}}=\left[\begin{array}{l}{V}_{\mathrm{1}}\hfill \\ M_{\mathrm{1}}\hfill \\ V_{\mathrm{2}}\hfill \\ M_{\mathrm{2}}\hfill \end{array}\right]={\displaystyle \frac{P}{L}}\left[\begin{array}{cccc}{\displaystyle \frac{\mathrm{6}}{\mathrm{5}}}\hfill & {\displaystyle \frac{L}{\mathrm{10}}}\hfill & -{\displaystyle \frac{\mathrm{6}}{\mathrm{5}}}\hfill & {\displaystyle \frac{L}{\mathrm{10}}}\hfill \\ {\displaystyle \frac{L}{\mathrm{10}}}\hfill & {\displaystyle \frac{\mathrm{2}{L}^{\mathrm{2}}}{\mathrm{15}}}\hfill & -{\displaystyle \frac{L}{\mathrm{10}}}\hfill & -{\displaystyle \frac{L^{\mathrm{2}}}{\mathrm{30}}}\hfill \\ -{\displaystyle \frac{\mathrm{6}}{\mathrm{5}}}\hfill & -{\displaystyle \frac{L}{\mathrm{10}}}\hfill & {\displaystyle \frac{\mathrm{6}}{\mathrm{5}}}\hfill & -{\displaystyle \frac{L}{\mathrm{10}}}\hfill \\ {\displaystyle \frac{L}{\mathrm{10}}}\hfill & -{\displaystyle \frac{L^{\mathrm{2}}}{\mathrm{30}}}\hfill & -{\displaystyle \frac{L}{\mathrm{10}}}\hfill & {\displaystyle \frac{\mathrm{2}{L}^{\mathrm{2}}}{\mathrm{15}}}\hfill \end{array}\right]\left[\begin{array}{l}{\delta }_{\mathrm{1}}\hfill \\ {\theta }_{\mathrm{1}}\hfill \\ {\delta }_{\mathrm{2}}\hfill \\ {\theta }_{\mathrm{2}}\hfill \end{array}\right],

where P is the axial fore, V is the shear force, M is the bending moment, θ is the stability coefficient and L is the member length, respectively.

Instead of using the cubic function, a linear function was used in this study, as seen in Fig. 3. The net effect is the same as subtracting the geometric stiffness from the member stiffness, but is computationally more efficient. This is based on the assumption that the same displacement as the cubic function (δ) is a function of shear force (V) and the member length (L). Such an assumption implies the use of an average slope over the whole length of the structure. When this assumption is used, the simplified geometric stiffness matrix is defined:

(8) k_{\mathrm{G}}=\left[\begin{array}{l}{V}_{\mathrm{1}}\hfill \\ M_{\mathrm{1}}\hfill \\ V_{\mathrm{2}}\hfill \\ M_{\mathrm{2}}\hfill \end{array}\right]={\displaystyle \frac{P}{L}}\left[\begin{array}{cccc}\mathrm{1}\hfill & \mathrm{0}\hfill & -\mathrm{1}\hfill & \mathrm{0}\hfill \\ \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \\ -\mathrm{1}\hfill & \mathrm{0}\hfill & \mathrm{1}\hfill & \mathrm{0}\hfill \\ \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \end{array}\right]\left[\begin{array}{l}{\delta }_{\mathrm{1}}\hfill \\ {\theta }_{\mathrm{1}}\hfill \\ {\delta }_{\mathrm{2}}\hfill \\ {\theta }_{\mathrm{2}}\hfill \end{array}\right].

The above geometric stiffness matrix of Eq. (8) is usually referred to as the string stiffness.

To represent the second order effects due to the lateral displacement of the gravity loads, in this study, the simplified P-delta option was used in RUAUMOKO [ 24]. Here, the displacements are assumed to be small and the coordinates are unchanged, but the beam and column stiffness are adjusted for the axial forces from the static analysis. This allows for the lateral softening of the columns due to the gravity loads. The P-delta effect is assumed to be constant as the increase in stiffness on one side of the structure is matched by a decrease in stiffness on the other side of the structure under lateral loading, where the sum of the vertical forces is assumed to be constant.

Modified Takeda hysteresis

The “Takeda” hysteresis model includes stiffness changes at flexural cracking and yielding, hysteresis rules for small cycle inner hysteresis loops inside the outer loop, and unloading stiffness degradation with deformation. When compared to the “bilinear” hysteresis Model, this model is more complicated, but also more realistic in simulating the nonlinear behavior of reinforced concrete members.

To minimize this complexity of the “Takeda” hysteresis model, the primary curve of this hysteresis model has been modified by Otani [ 30] to be bilinear, by choosing the yield point to be the origin of the hysteretic loop instead of original tri-linear back-bone. Such a model is called as the “Modified Takeda” hysteresis model, as shown in Fig. 4, where α is an unloading stiffness degrading factor and β is a reloading stiffness degrading factor. Increasing α decreases the unloading stiffness and increasing β increases the reloading stiffness. The unloading stiffness after yielding is (d_y/d_m)^α times the initial elastic stiffness, k₀, which is similar to the approach used by Emori and Schnobrich [ 31]. The response point during reloading moves toward the point, whose displacement is (d_m−βd_p), where d_m is the displacement of the previously maximum inelastic response point. α usually ranges from 0 to 0.5, while β is from 0 to 0.6. An alternative that is modeled on the Drain-2D program [ 32] for the unloading stiffness is available in the program RUAUMOKO [ 24].

For post 1970s structures, where typical hysteresis loops are available, it is suggested that the “modified Takeda” model be used. The equivalent unloading and reloading stiffness degradation parameters α and β should be determined for the experimental hysteresis loops of the similar members, as shown in Eqs. (9) and (10).

(9) \alpha =\ln {\displaystyle \frac{k_{\mathrm{u}}}{k_{\mathrm{0}}}}/\ln {\displaystyle \frac{d_{\mathrm{y}}}{d_{\mathrm{m}}}},

(10) \beta ={\displaystyle \frac{\beta d_{\mathrm{p}}}{d_{\mathrm{p}}}},

where k₀ and k_u are the initial and degraded unloading stiffness at maximum displacement, d_m respectively, and d_y is the yield displacement. Finally, d_p = d_m−d_y and βd_p refer to the definitions in Fig. 4.

Considering that the modified Takeda hysteresis model is able to use different unloading and reloading stiffness degrading parameters, and better represents realistic hysteretic behavior of reinforced concrete members, this hysteresis model is recommended when carrying out a series of the inelastic time history analysis of the suggested smart building isolation systems.

Statistical methodology

Probabilistically scaled suites ensure that appropriate hazard curves can be generated from groups of results. As a result, the median likely outcome and its variability or variation can be readily defined. This overall approach leads to the generation of hazard curves and emerging probabilistic performance-based design methods.

For robustness, in this study, multiple time history records over a range of seismic levels are used from the SAC Phase II project [ 33]. Each suite has 20 pairs of records with probabilities of occurrence of 50% in 50 years (low suite), 10% in 50 years (medium suite) and 2% in 50 years (high suite). For analysis, ten records from the odd half (1, 3, …) and the 50th and 84th percentile results are presented for simplicity.

For the statistical assessments, the response measures are each defined with respect to a single seismic event. To combine these results across the earthquakes in a suite, the following log-normal based statistical tools are employed [ 34, 35], since it is widely accepted that the statistical variation of many material properties and seismic response variables is well represented by this distribution provided one is not primarily concerned with the extreme tails of the distribution [ 36]. To combine the response values of a ground motion suite, a log-normal based median of the response quantities of a suite with n earthquakes is defined as

(11) \widehat{x}=\exp \left({\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{i=\mathrm{1}}^n\ln x_i}\right),

with the corresponding log-normal based coefficient of variation defined as

(12) \widehat{\sigma }=\exp \left(\sqrt{{\displaystyle \frac{\mathrm{1}}{n-\mathrm{1}}}{{\displaystyle \sum _{i=\mathrm{1}}^n\left(\ln x_i-\ln \widehat{x}\right)}}^{\mathrm{2}}}\right).

To present a summary of the distribution change between the controlled (“10+ 2” story and “8+ 4” story) and uncontrolled (12-story) data sets, while providing accurate statistical measures that are not highly affected by changes in any single variable, the 50th percentile ( \widehat{x} ) and 84th percentile ( \widehat{x}\times \widehat{\sigma } ) results are presented.

Inelastic performance results

It is known that the critical effects of secondary moments due to the gravity load upon ductile reinforced concrete frames emerge only when large inelastic deflections occur. To understand the impact of the smart building isolation systems adopted, the seismic demands for the controlled and uncontrolled systems need to be investigated. After a series of dynamic nonlinear analyses of the structures under the three earthquake suites, the maximum relative story displacement and interstory drift ratio for all levels of structure are thus evaluated, and the response performance of “10+ 2” and “8+ 4” story smart isolation building systems (passive and semi-active) are compared with the uncontrolled 12-story structure.

Relative story displacement

The maximum displacement at a floor has been commonly used in inelastic analysis since this response quantity is directly related to the structural stiffness. Figure 5 shows the envelopes of the maximum displacement in the 12-story, “10+ 2” story and “8+ 4” story structures over three probabilistically scaled suites (low, medium and high) of earthquake records.

As expected, the isolation layer produces large relative displacement between adjacent stories and this story separation is increased for the semi-active systems due to the absence of viscous damping. From the Fig. 5, it can be seen that the floor responses below the isolation interface are reduced more than that for the uncontrolled (12-story) system. However, the reduction quantities are not so different from the isolation cases developed. The envelopes in the isolated building systems under the medium and high suites (especially under the medium suite) show the clear reduction of displacement responses and this control effectiveness is pronounced for the SA and “8+ 4” story systems. However, the “8+ 4” structures produced a little bit larger 50th and 84th percentiles of the responses at some floors under the low suite. Despite if this particular point, almost results show the ability of the semi-active device and larger mass ratio (8+ 4) to reduce overall structural displacement response measures. Referring to the maximum displacements observed, it is worth noting that all suites of motion show reasonably controlled response values compared to the uncontrolled responses, under the nonlinear effects of the systems considered.

Interstory drift ratio

The intertory drift ratio (the interstory drift normalized by the story height) has been developed as a response parameter and this value relates well with observed architectural damage after severe earthquakes. A wide consensus exists in the earthquake engineering community that for moment resisting frames the interstory drift demand is the best indicator of expected damage. As a global parameter, interstory drift is much more appropriate than the roof drift because in individual stories it may exceed the latter by a factor of two or more [ 37]. Figure 6 show the maximum interstory drift ratios resulting from the analyses.

For the low suite, the 50th percentile drifts of uncontrolled system are reasonably uniform over the height of the structure and the peak drift occurs in the 9th story (Figs. 6(a) and (d)). However, the controlled systems reduced the response of the isolated upper stories, as well as the lower stories. The location of the 84th percentile of the peak drift has migrated to the 3rd story for the “8+ 4” structures and to the 7th story for the “10+ 2” structures, as seen in Fig. 6(d). Meanwhile, a different behavior is presented in the controlled structures, where the lines for the different isolation systems cross one another in 4th floor.

Figure 6, overall, clearly reflects the systematic advantage of the semi-active isolation systems. Though increasing the level of seismic hazard increases the interstory drift, the increased ratios of the drift in the isolated upper stories are still small and again the peak drift locations are shifted to the lower stories, as seen in Figs. 6(d), (e) and (f). For the low and medium sets of motion, all the drift demands of the isolation systems are less than the life safety limit of 2.5% for the numerical time history analysis specified in NZS4203 (1992).

Again, the better control effects of the higher mass ratio (8+ 4) structures compared to the less mass ratio (10+ 2) structures can be seen in the response of interstory drift at almost floor levels, especially under the low and medium suites. This performance advantage of larger mass ratio (8+ 4) can be seen for both semi-active and passive controlled structures. Meanwhile, as the earthquake intensity increases, the effectiveness of the drift reduction of semi-active structures becomes less effective, particularly compared to the passively controlled structures. This is because the semi-active strategy is not so better able to cope with the detuning effects of nonlinear response than was expected under higher intensity environment.

Absolute acceleration

Acceleration demands are of concern for the nonstructural components of the building. In general, added seismic control systems have the benefit of being capable reducing the acceleration demands on the structure, while also reducing drift demands. More traditional methods, such as increasing the building stiffness, cannot achieve this behavior motivating these more enhanced control approaches.

From Figs. 7(a) to (f), it can be seen that the accelerations at the isolated upper floors are clearly reduced. In contrast, the accelerations at the isolation layer, especially for the semi-active systems, show an abrupt increase. These performance properties are similar to those observed in terms of the displacement response. To achieve the reductions in drift desired, the semi-active system sacrifices floor accelerations at the isolation layer.

Under the low suite of ground motions, the passively controlled structures (10+ 2 and 8+ 4) produce 50th percentile floor accelerations similar to the uncontrolled structures at the lower floors. The accelerations for the semi-active structures (10+ 2 and 8+ 4) are slightly higher than those of the uncontrolled structures. However, only the semi-active (8+ 4) system slightly increases the 50th percentile floor accelerations at the lower floors under the medium suite of motions. For the high suite of ground motions, it is difficult to find the virtual control effectiveness of the acceleration responses at the lower floors under the isolation layer. Meanwhile, the passive (10+ 2 and 8+ 4) structures reduce the floor accelerations of the upper floors below those of the semi-active systems under the medium suite of ground motions and a similar pattern is observed in the high suite of ground motions.

Conclusions

Realistic and inelastic response effectiveness of isolation systems were presented as comprehensive results of suggested novel building isolation systems (“10+ 2” story and “8+ 4” story) over a range of seismic hazards. Isolated upper stories ( + 2 or+ 4) of the structure are rolled as a large scaled tuned mass. Viscous dampers and resettable devices are adopted as two core energy dissipation tools for passively and semi-actively controlled structures respectively. Optimal TMD principle based control parameters were adopted from the previously investigated design results.

The time history analysis results showed that both building isolation systems present significant reductions in all of the control indices considered for all seismic hazards. However, the cost included is an increase in the accelerations at the isolation interface, which may or may not necessarily be detrimental. Nonlinear modeling of the MDOF structures results in more realistic structural response. The difference in response between the uncontrolled, passive and semi-active building isolation systems is not as pronounced as it was for the linear structures. However, the fundamental changes in structural period and control action are still evident for both isolation systems.

Large mass ratio semi-active smart building isolation systems can effectively manage seismic response for MDOF systems across a broad range of ground motions in comparison to uncontrolled and passive solutions. The resettable devices of the semi-active systems provide a more advanced control function by anticipating the motion of the isolation layer. In particular, the semi-active building isolation systems offer unique advantages over passive systems in obtaining consistent response reductions over broad ranges and types of ground motions at realistic seismically important structural natural frequencies. They are thus more robust to ground motion variation, as they provide tighter ranges across each suite. Thus, it might be concluded that the semi-active isolation is the better choice for the seismic case where future input motions are unknown.

However, peak responses alone do not describe the possible damage incurred by the structure as cumulative damage can often result from several smaller cycles into or near the inelastic range. Thus, more accurate evaluations are necessarily required involving consideration of the dissipated hysteretic energy. Particularly, hysteretic dissipated energy and practical damage assessments are necessarily recommended to be developed to provide information regarding the cumulative damage to the structure, and this may be more important in evaluating potential damage and degradation.

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