Aseismic smart building isolation systems under multi-level earthquake excitations: Part II, energy-dissipation and damage reduction

Abstract

Based on the performance results of the previously suggested smart building isolation systems (1st companion paper), this following study verifies the control effects of the systems from the view point of energy dissipation and damage level metrics. Several different model cases of the strategically isolated multi-story building structures utilizing passive dampers and semi-active resettable devices are analyzed and the energy-based target indices are compared. Performance comparisons are conducted on statistically calculated story/structural hysteretic energy and story/structural damage demands over realistic suites of earthquake ground motion records, representing seismic excitations of specific return period probability. Again, the semi-active solutions show significant promise for applications of resettable device, offering advantages over passive systems in the consistent damage reductions. The specific results of this study include the identification of differences in the mechanisms by which smart building isolation systems remove energy, based on the differences in the devices used. Less variability is also seen for the semi-active isolation systems, indicating an increased robustness.

Keywords

smart building isolation / story and structural / energy-dissipation / damage assessment

Introduction

In the previous 1st companion paper (Part I), the design details and performance results of the newly suggested ‘Smart building isolation systems’ were produced to assess those fundamental feasibility and seismic effectiveness. According the performance results, it is found that the suggested isolation systems significantly reduce the displacement-based seismic response of a structure, even if the structure is nonlinear. All the isolation systems reduced the interstory drift of the isolated upper stories, as well as the lower stories, especially highlighting the systematic advantage of the semi-active systems.

However, it is well known that seismic damage to a multistory frame is not only caused by maximum response, such as force or lateral displacement. Inelastic excursions below the maximum response can still cause significant damage to structures [ 1]. This duration-related damage, which can be expressed as the energy absorbed in a structure, should also be considered in the evaluation of structural performance [ 2, 3].

Actually, the structural vibration procedure under earthquake excitation is an energy transferring process in nature. The energy dissipation in a building is the capacity of the structural member to dissipate energy through hysteretic behavior. An element has a limited capacity to dissipate energy in this manner prior to failure. As a result, the amount of energy dissipated serves as an indicator of how much damage has occurred during seismic loading.

In particular, the energy criterion postulates that the structure collapses when it is demanded to dissipate, through inelastic deformations, an amount of energy larger than that supplied. To extend the energy-based analysis method to multistory frames, therefore, a procedure for the estimation of energy demand in a multi-degree-of freedom (MDOF) system is essentially required. In the last few years this approach has been largely accepted [ 4− 6].

Furthermore, detection of damage to structures has recently received considerable attention from the view point of maintenance and safety assessment. In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the local and whole building. Capturing the accumulation of damage sustained during dynamic loading is of particular interest to structural engineers. This process is usually accomplished through a low-cycle fatigue formulation or calculation of the energy absorbed by the system during loading. In both those cases, inelastic behavior is assumed before any damage is considered.

Thus, in this 2nd companion study, more accurate seismic performance evaluations are conducted for the suggested different types of the smart building isolation systems involving consideration of the dissipated hysteretic energy and damage based assessments. These more practical performance indices are necessarily recommended to be developed to provide information regarding the cumulative damage to the proposed smart isolation building structures, and this may be more important in evaluating reduced potential damage and degradation.

Comparative models and analytical methodology

Figure 1 shows five different models of the smart building isolation systems compared, clearly producing very different mode shapes. The newly suggested smart isolation configurations entail the insertion of rubber bearings (passive solution) and resettable device (semi-active solution) to segregate two or four stories from the rest of the lower structure, creating a large capacity tuned mass damper without burdensome additional mass. Especially, the alternatively developed semi-active isolation strategy provides the broad adaptability that cannot be obtained from passive systems. This brings the benefits of passive isolation to taller structures where it would not ordinarily be suitable, such as the high-density residential apartment structures that are becoming much more commonplace in urban centers. For the stiffness of the isolation layer, the derived optimal stiffness values have been shared to the stiffness of resettable device and rubber bearings with the same portion, which is based on the previously investigated numerical results of the linear system design and application [ 7− 9].

Overall, modal analysis shows that the investigated isolation models have the unique modal features to isolate the structure to be controlled effectively. Specifically, the response clearly shows a far different dominant structural period of response compared to the uncontrolled case. Hence, the modal response between the building isolation systems used shows that the large-scaled TMD functioned designs reduce structural response by different mechanisms, which is an interesting and unique result of its own. It is apparent that the upper stories above the isolation interface of the semi-active building modes are more effectively controlled due to the proper interrupting function of the resettable device from the seismic energy. The details of the numerically evaluated modal properties, including modal mass, modal frequency and participation factors (modal and mass), are described in the previous linear study [ 8].

In creating a nonlinear structural dynamic model, the level of detail of the nonlinear modeling needs to be matched with the quantities that are of interest. This study is more concerned with the amount of energy dissipation (or demands) followed by the resultant index of damage on the story and global level, for which a lumped plasticity model of the frame elements is appropriate. Therefore, the frame members are modeled as linear elastic beam-column elements and recommended ‘modified Takeda hysteretic models’ for the restoring force of an inelastic structure was adopted. Also, the other nonlinearity of ‘P-delta’ effects is considered, and this geometric nonlinear property is considered to be included to obtain accurate nonlinear structural behavior.

Same as the 1st companion study, structural performance will be assessed by statistically enumerating seismic response improvements compared to an uncontrolled multi-story structures for a series of input ground motions. The development of the three earthquake suits was presented, with a brief description of 2%, 10%, and 50% in 50 years according the USGS Los Angeles probabilistic seismic hazard maps [ 10]. It should be noted that the structural hysteretic energy does not follow a lognormal distribution, unlike maximum drift and absolute acceleration. To define a statistical measure of the energy dissipation response and damage index values, the standard “counted” mean and 84th percentiles are applied in this study

Seismic energy demand and damage assessment

Hysteretic energy indices

The input energy due to a ground motion depends mainly on the elastic period of the structure and on the seismic record, while it is much less dependent on the viscous damping and characteristics of the plastic response like the hysteresis and the ductility. The assessment of the input energy represents a good starting point to develop a seismic design method based on energy criteria.

Ductile moment resisting framed structures of reinforced concrete designed using the capacity design philosophy allow energy to be dissipated at any of the beam ends at any level, as well as at the base of the first story columns, via inelastic hysteretic behavior. The hysteretic energy dissipation capacity of a member can be expressed by a hysteretic energy dissipation index, E_h, which can be obtained from Eq. (1) with the hysteretic model for the member [ 11]. The index, E_h, is defined to be the amount of hysteretic energy dissipated, ∆ω, per cycle during a displacement cycle of equal amplitudes in the positive and negative directions divided by 2πF_md_m, where 2πF_md_m is the critical viscous damping energy of an equivalent elastic member of stiffness k_eq = F_m/d_m.

(1) E_{\mathrm{h}}={\displaystyle \frac{\mathrm{\Delta }\omega }{\mathrm{2}\mathrm{\pi }{F}_{\mathrm{m}}{d}_{\mathrm{m}}}},

where F_m is the resistance at the peak displacement d_m, shown in Fig. 2. The value of the index is equal to the equivalent viscous damping ratio of a linearly elastic system which is capable of dissipating an amount of energy, ∆ω, in one cycle under “resonant steady-state” oscillation. The fore, F could be concentrated force and bending moment. The displacement, d, could be deflection, rotation and curvature. All of the forces and displacements related to hysteresis models refer to bending moment and curvature.

Based on the energy index described above, in this study, the more realistic and practical hysteretic energy dissipation index using the ‘modified Takeda model’ is used as defined in Eq. (2). This energy dissipation model is a function of the unloading and reloading stiffness degradation parameters, the ratio of post-yielding stiffness to the initial elastic stiffness, and the curvature ductility factor, as shown in Fig. 3.

(2) E_{\mathrm{h}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}\mathrm{\pi }}}\left\{\mathrm{2}-[R_{\mathrm{p}}(\beta -\mathrm{2})(\mu -\mathrm{1})-\mathrm{2}]{\mu }^{\alpha -\mathrm{1}}+{\displaystyle \frac{\mathrm{2}\beta (\mu -\mathrm{1})R_{\mathrm{p}}}{\mathrm{1}+R_{\mathrm{p}}(\mu -\mathrm{1})}}+\beta \left(\mathrm{1}-{\displaystyle \frac{\mathrm{1}}{\mu }}\right)\right\},

where, R_p: ratio of post-yield stiffness to initial stiffness; α: unloading stiffness degradation parameter

β: reloading stiffness degradation parameter; μ: ductility factor (ratio of maximum displacement to the initial yield displacement)

Damage indices

The degree of seismic damage for the member, the stories, or the whole structure can be predicted or evaluated using damage models. Such models are used in order to either adjust the preliminary structural design under the design level earthquake, make an engineering decision to demolish or repair an existing structure after an extreme or moderate earthquake excitation, or to access the potential damage to a structure in a future earthquake.

In evaluating seismic damage in a reinforced concrete, ductile framed structure, the damage indices for the structure and stories are regarded as more rational indicators than the structure and story ductility. Although the structural and story displacement ductility are strongly related to the overall damage in the structure and stories, they cannot reflect the contribution of the dissipated energy due to inelastic cyclic behavior and the stiffness deterioration in members to the overall damage in the structure and in its stories. There is a linear relationship between the structural damage indices and the structural displacement ductility [ 13]. This relationship may alter for long durations of strong shaking due to large number of cycles of inelastic behavior giving larger accumulated energy dissipation to the structural damage index.

From the inelastic step-by-step integration time history analyses, the member damage indices for every inelastic member end can be obtained. From this data, the story and structural damage indices are calculated as the weighted average energy of all inelastic member ends.

Member damage index

The damage index for the member is calculated at each member end. The original equation of Park and Ang’s damage index is represented as a linear combination of the maximum deformation and the total dissipated energy caused by repeated cyclic loading [ 14, 15]. The index is expressed:

(3) DI={\displaystyle \frac{{\delta }_{\mathrm{m}}}{{\delta }_{\mathrm{u}}}}+{\displaystyle \frac{\beta }{Q_{\mathrm{y}}\times {\delta }_{\mathrm{u}}}}{\displaystyle \int \mathrm{d}E},

where, δ_m : maximum response deformation under an earthquake; δ_u : ultimate deformation capacity under monotonic loading; Q_y : calculated yield strength; dE: incremental dissipated hysteretic energy; ∫dE: total dissipated hysteretic energy; β: experimental constant ( = 0.05 for reinforced concrete members).

The first term in Eq. (3) represents the damage due to maximum deformation experienced during seismic loading, and the second term reflects the influence of the total absorbed hysteretic energy on the local or member damage.

The constant parameter β = 0.05 is found experimentally. According to Park et al., β was determined using a regression equation obtained from experimental results with 400 reinforced concrete columns and beams. The value of β obtained by Park et al. [ 14] was 0.05 for reinforced concrete members, and this value is used in this study.

For reinforced concrete structures, an equivalent form of the Park and Ang’s damage index is modified to use the member curvature [ 16] that is obtained from the program RUAUMOKO [ 12]. This modified damage index is calculated at each member end of the suggested building isolation systems compared and the damage index for the plastic hinge locations at the ends of a member is defined as Eq. (4).

(4) D{I}_{\mathrm{m}}={\displaystyle \frac{{\phi }_{\mathrm{m}}}{{\phi }_{\mathrm{u}}}}+{\displaystyle \frac{\beta }{M_{\mathrm{y}}\times {\phi }_{\mathrm{u}}}}{\displaystyle \int \mathrm{d}E},

where, {\phi }_m : maximum positive or negative curvature; {\phi }_u : ultimate curvature capacity under monotonic loading; M_y : calculated yield moment

The member damage index is represented by the index DI_m with DI_m≥1.0 representing failure of the member. The ultimate curvature ductility of a member under monotonic loading has a strong influence on the member damage index and is an indicator of the curvature deformation capacity. Hence, it is very important to accurately evaluate the ultimate curvature capacity for the designed member. However, it should be noted that it can be difficult to define the ultimate state of a given member.

The curvature ductility for reinforced concrete members depends strongly on the confinement in the plastic hinge region of the member. The curvature ductility is about four times the deflection ductility [ 13]. Therefore, in this study, the ultimate curvature ductility was assumed to be 30 for all beam members and 20 for column members at 1st floor.

Story and structural damage indices

The damage index for a story or a whole structure (12-story, “10+ 2” story and “8+ 4” story) is used to quantify the degree of damage to the story or to the overall structure. A story is defined as all the beams at the level under consideration and all the columns just below that level. The damage index for a story can be obtained by calculating a weighted average of the local damage indices at all the inelastic member ends in this story. Park and Ang [ 14] proposed a damage index for the stories in which the dissipated energy is used in calculating the weighting factors for every member end.

Damaged structures typically show degradation in stiffness when compared with undamaged structures. This change implies a variation in the natural periods of free vibration in every time step during the earthquake. The history of the degree of damage for the overall structure can thus be expressed by the history of variation in the stiffness [ 17, 18] or period of free-vibration [ 19] etc. The maximum damage index in this history can then be regarded as the overall damage index.

Park and Ang [ 14] proposed a global damage index defined as a weighted average of the local damage indices for all components of a structure. The weighting factor for each end of a member is proportional to the dissipated energy at the corresponding end in the element. The global damage index DI_g is thus defined as Eq. (5).

(5) D{I}_{\mathrm{g}}={\displaystyle \sum _{i=\mathrm{1}}^n({\lambda }_i\times D{I}_i)},

where,

(6) {\lambda }_i={\displaystyle \frac{E_i}{{\displaystyle \sum _{i=\mathrm{1}}^n{E}_i}}},

n: number of member ends of whole structure where the local damage index is computed; E_i : dissipated energy at end i of a member.

The story-level damage index is also obtained from Eq. (3). The only difference is that the number of members is limited to these in the story under consideration.

According to the damage assessment carried out by Park and Ang [ 14] for a prototype structure, the global structural damage index can be interpreted as follows:

DI_g≤0.4 Repairable damage

DI_g>0.4 Damage beyond repair

DI_g≥1.0 Total collapse

For context, a global damage index equal to zero denotes that the structure remains in the elastic region during the excitation.

In this study, the Park & Ang [ 14] structural damage index was used in evaluating overall structural damage when the structural displacement ductility is near the design structural ductility. Damage analyses were carried out in this research for each type of building isolation model using the results obtained from nonlinear time history analyses. As the story damage indices are weighted by the dissipated energy, the damage part in the structure is more sensitive to the story damage index than the maximum story ductility factor. The maximum story ductility factor cannot reflect the member contribution to the whole structure for the seismic resistance capacity. Therefore, the storey damage index is more suitable for the damage evaluation of the structure [ 13] in this case.

Furthermore, attention is focused on overall structural damage indices because these parameters summarily lump all existing damage in members in a single value that can be easily correlated to single-value seismic parameters. For this purpose, the program RUAUMOKO [ 12] uses a modified damage index. In this slightly modified damage model, the global damage is obtained as a weighted average of the local damage at the ends of each element, with the dissipated energy as the weighting function.

Energy dissipation and damage reduction results

While peak interstory drift provides a good indication of performance, the resulting information is incomplete as it does not take into account the cumulative damage to the structure. Experimental investigations have demonstrated that structural damage is a function of both peak as well as cumulative values. To understand the practical impact of the suggested smart building isolation systems (passive and semi-active), therefore, more realistic seismic demands for the controlled and uncontrolled systems need to be investigated and compared.

After a series of dynamic nonlinear time-history analysis of the structures under the three earthquake suites of different intensity, the hysteretic energy distributions and story damage distributions along the height of the structures were developed. Furthermore, these indices are summed (hysteretic energy distributions) and averaged (story damage distributions) to the structural energy and structural damage indices respectively as representative performance parameters.

Story and structural hysteretic energy

As hysteretic energy provides a good indication of cumulative damage in structures, 50th (median) and 84th percentile values of hysteretic energy are compared for the isolation systems for each set of ground motions. The hysteretic energy dissipated by the frame members at each floor along the height of the structures are developed in Fig. 4. As the severity of ground motions increases, the amount of hysteretic energy dissipated by the structure members increases. The comparison of the response profiles shows that the higher level of hazard produces high energy demands in the lower stories and the energy distribution patterns correspond to the drift demands of the structure.

In particular, clearly lower energy demands at upper stories which are above the isolation layer can be found due to its interception of the energy flow up from the base. This structural property produces the reduced energy demands of the lower stories too. In other words, the amount of transferred energies from the base was decreased by splitting the lump of overall structural mass and, therefore, the dissipated energy along the height is reduced. In the low suite of motions, the energy curves of the isolated upper structures lie along the y-axis, as they are very successful in isolating and maintaining the upper structure within the limits of elastic behavior as seen in Fig. 4. In the medium and high suites of motions, the isolated systems are still successful at keeping the response essentially linear, as indicated by very low values of hysteretic energy indices.

Finally, as a representative energy value, all of the dissipated energy values along the height are summed to establish a total structural hysteretic dissipated energy index, as seen in Fig. 5. Again, the control effects are shown to become significant for the larger mass ratio (8+ 4) and the semi-active isolation system, and the control effectiveness difference is pronounced from the passive (10+ 2) to the semi-active (8+ 4) systems. This result shows that the combined operation of the semi-active device and large mass ratio contributes greatly to the effectiveness of the overall control system compared to typical and optimal passive design. Overall, all the isolation systems were successful in reducing the seismic hysteretic energy demands at all hazard levels.

Story and structural damage

The distribution of story damage indices are shown in Fig. 6. Story damage indices are based on the member damage indices in a level. It can be said that the distribution of story damage has a similar pattern to that of story dissipated energy, which is used as a weighting factor for the calculation of the damage index. The only difference between these two indices is from the part of structural deformation.

From the Fig. 6, it can be seen that all of the isolation systems suffer insignificant repairable story damage up to the 50th percentile of the medium suite. Only the 1st level of the isolation systems suffers significant damage for the 84th percentile of the high suite, which gives damage indices over 1.0. The figures also show that the damage indices of the upper isolated stories for every suite are less than 0.4 at each level, which indicates again the effective interception of energy flow at the isolation layer. Overall, it seems that the main benefits of the reduced damage demands are on the upper stories for each suite, rather than for the lower stories.

The structural (global) damage indices, which indicate the damage of the whole structure, are summarized in Fig. 7. The structural damage indices are obtained as a weighted average of the local damage at the ends of each element, with the dissipated energy as the weighting function. The structural damage indices for all suites are less than 0.4 except for the 84th percentile of the high suite. Hence, all of the isolation systems are repairable for those suites. Even for the 84th percentile of the high suite, the structural damage indices are under 1.0, which indicates that the structures can survive with damage beyond repair under the high suite. The semi-active (8+ 4) system proves to be more effective than any other type of isolation system in terms of structural damage indices and this effectiveness becomes more pronounced for the lower hazard suites.

Conclusions

The details and results of a set of comparative studies were used to assess the feasibility and energy-dissipative effectiveness of the smart building isolation systems (passive (10+ 2 and 8+ 4) and semi-active (10+ 2 and 8+ 4)) over three probabilistically scaled suites of earthquake records. The estimated seismic demands, for the comparison, were based on nonlinear modeling, including geometric P-delta effects and modified Takeda hysteresis. Particularly, hysteretic dissipated energy and practical damage assessments were developed to provide information regarding the cumulative damage to the structure, which are necessarily important in evaluating potential damage and degradation.

Overall, the proposed smart isolation strategy was successful in reducing the seismic demands of energy dissipation and damage reduction in statistical point of view for both new designs (10+ 2 and 8+ 4), and the semi-active solutions provided more robust response mitigation over a range of ground motions within each suite. From these comparative results, moreover, it is found that the proposed scheme may significantly reduce the practical seismic response of a structure, even if the structure is nonlinear. In view of these findings, and the fact that they might be relatively easy to construct using these emerging semi-active devices, it is concluded that the proposed semi-active isolation building system has the potential to become a practical and effective way to reduce earthquake damage.

Especially, the development of designs suitable for implementing semi-active energy management systems ensure the proposed study remains focused on outcomes that are immediately useful. All such outcomes will advance the state of the art by providing additional knowledge and capability from which structural designers can draw in developing new structures or retrofitting existing structures. Finally, these outcomes ensure that the overall goal of taking semi-active energy management systems from a status of zero, or occasional highly specialized implementations, to a state where regular implementation may be more immediately practicable.

As a future study, furthermore, it would be interesting to investigate the effect of uncertain structure material properties on the response variability and reliability of suggested isolated structural systems with different energy dissipation mechanisms. [ 20]

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