With improving technology, the idea of using energy dissipater equipment has been strengthened in order to control the structures response in dynamic loads such as wind and earthquake. In this research, we dealt with seismic performance of base isolated structures with lead-rubber bearing (LRB) using incremental dynamic analysis (IDA). For this purpose, 3- and 9-story buildings have been utilized in the SAC project undergoing 22 earthquake records which were far-fault. Plotting the fragility curve for various states of design time period and isolator damping of LRB, it is observed that, by increasing damping, the isolator has not been activated in small spectrum acceleration, which shows that the annual exceedance probability is increased in immediate occupancy (IO) performance level and decreased in life safety (LS) performance level. The results show the reduction of determined failure probability in fragility curves for two levels of performance of uninterrupted use and lateral safety. Likewise obtained results show that, with increasing design time period of isolator, the amount of failure probability is decreased rather than the isolator with smaller design time period, for both LS and IO states. And the isolator illustrates better performance.
Earthquake as a destructive phenomenon threatens its habitants in most of life areas so that decreasing the earthquake irreparable damage has been the final goal of researchers and earthquake scientists. By passing time and changing the viewpoint of plotting based on force to plotting based on performance, the use of nonlinear analyses has been increased. The design method based on the performance is the new one that has mostly been used in new regulations and instructions [
Zhang and Huo [
The use of isolators with similar performance of horizontal springs decreases the amount of earthquake forces and resonance phenomenon with dominant frequency content through the change in inherent time period of structure. The act of increasing time period of structure is the same concept of using isolators [
(a) General form of Rubber isolators with lead core, (b) calculation model, and (c) force-displacement diagram [
The first detached building with rubber-lead supports was in New Zealand in 1981. Afterward it was used in other buildings in various countries. Detached buildings with lead supports performed satisfactory performance in Northridge and Kobe earthquake [
The method of incremental dynamic analysis (IDA) contains a collection of several dynamic analyses of nonlinear time history of structure where undergoing different severity of earthquakes is incremental. One of the most important subjects in incremental dynamic analysis method is the selection of intensity criterion and suitable damage in which structures are set under one or several seismographs of earthquake record which have been measured in different magnitude levels. After doing the analysis, one or several IDA curves will be made in parametric response against intensity levels. Ultimately by defining Load and Resistance Factor Design states and combining results with risk analysis curves, we dealt with evaluation of structures [
In this study, 3- and 9-story structures [
Plan and elevation of selected (a) 3-story building and (b) 9-story building.
In this study, firstly, base isolated structure with lead core and then fixed base structure has been studied. Afterwards the influence of isolator has been compared over the structure's response under IDA analysis.
In this study, the used isolator system is the rubber isolator with lead core. To design the isolators, the proportion of effective damping
Design of base isolation (
3-story structure
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9-story structure
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According to Table
In this study, the OpenSees finite element software has been used to model and to analyze nonlinear dynamic of structures. The OpenSees software has been provided by a research team under Mazzoni supervision in the earthquake engineering and soil dynamic field based on finite element method, in PEER engineering research center at California Berkeley University in 1990 [
Analytical model for component spring (LRB model) [
Also, in order to control LRB displacement “truss” element was employed at both ends of structure and “ElasticPPGap” material has been assigned (Figure
Physical model for control of LRB displacement.
One of the important issues in incremental dynamic analysis is determining the entered records to the structure. Therefore, suitable numbers of earthquake record should be selected to cover the range of structure response. Regarding study of Shome [
Ground motion database.
ID | Earthquake | Recording station | ||
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Number | M | Year | Name | Name |
1 | 6.7 | 1994 | Northridge | Beverly Hills-Mulhol |
2 | 6.7 | 1994 | Northridge | Canyon Country-WLS |
3 | 7.1 | 1999 | Duzce, Turkey | Bolu |
4 | 7.1 | 1999 | Hector Mine | Hector |
5 | 6.5 | 1979 | Imperial Valley | Delta |
6 | 6.5 | 1979 | Imperial Valley | El Centro Array #11 |
7 | 6.9 | 1995 | Kobe, Japan | Nishi-Akashi |
8 | 6.9 | 1995 | Kobe, Japan | Shin-Osaka |
9 | 7.5 | 1999 | Kocaell, Turkey | Duzce |
10 | 7.5 | 1999 | Kocaell, Turkey | Arcellk |
11 | 7.3 | 1992 | Landers | Yermo Fire Station |
12 | 7.3 | 1992 | Landers | Coolwater |
13 | 6.9 | 1989 | Loma Prieta | Capltola |
14 | 6.9 | 1989 | Loma Prieta | Gllory Array #3 |
15 | 7.4 | 1990 | Manjil, Iran | Abbar |
16 | 6.5 | 1987 | Superstition Hills | El Centro Imp. Co. |
17 | 6.5 | 1987 | Superstition Hills | Poe Road (temp) |
18 | 7.0 | 1992 | Cape Mendocino | Rio Dell Overpass |
19 | 7.6 | 1999 | Chi-Chi, Taiwan | CHY101 |
20 | 7.6 | 1999 | Chi-Chi, Taiwan | TCU045 |
21 | 6.6 | 1971 | San Fernando | LA-Hollywood Stor |
22 | 6.5 | 1976 | Friuli, Italy | Tolmezzo |
In this study, firstly the IDA curves of structures have been plotted under 22 records. Then the structures have been assessed under the same records with LRB isolators in the columns base, though the gap material has been used to control the isolator displacement.
Three states have been considered for each structure in isolators design and the analysis of structures for different time period has been dealt with (
According to Figure First state: design time period of 2.5 seconds' isolator Second state: design time period of 4 seconds' isolator Third state: design time period of 5.5 seconds' isolator
IDA curves for 3-story frame (ISO 1 to 9 are related to damping ratios 0.1, 0.26, 0.48, 0.19, 0.52, 0.78, 0.3, 0.71, and 1.0, resp.).
According to Figure
Furthermore, it is seen that, by increasing damping percentage, the relative displacement amount of structure—in constant amount of Sa—is declined and the relative displacement amount of isolated structure—with each damping ratio—is less than the structure without isolator.
Figure
IDA curves for 9-story frame (ISO 1 to 9 are related to damping ratios 0.1, 0.26, 0.48, 0.19, 0.52, 0.78, 0.3, 0.71, and 1.0, resp.).
As it is observed in Figure
It should be mentioned that for both 3- and 9-story structures the maximum interstory drift has occurred at bottom stories which indicates the shear behavior (shear building) of structures.
IDA curves for 3-story structure for various design time periods have been presented in Figure
Summarized IDA curves for 3-story frame.
In Figure
In Table
Periods and spectral accelerations of 3-story frame at IO and LS states.
Period = 2.5 s
Structure | Fixed base | Base isolated 1 (2.5 s) | Base isolated 2 (2.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.11 | 1.5 | 1.37 |
Sa(IO (g)) | 0.59 | 0.30 | 0.39 | 0.43 |
Sa(LS (g)) | 0.89 | 0.44 | 0.59 | 0.65 |
Period = 4 s
Structure | Fixed base | Base isolated 1 (4 s) | Base isolated 2 (4 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.35 | 1.72 | 1.54 |
Sa(IO (g)) | 0.59 | 0.25 | 0.34 | 0.38 |
Sa(LS (g)) | 0.89 | 0.38 | 0.52 | 0.58 |
Period = 5.5 s
Structure | Fixed base | Base isolated 1 (5.5 s) | Base isolated 2 (5.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.52 | 1.93 | 1.71 |
Sa(IO (g)) | 0.59 | 0.23 | 0.31 | 0.35 |
Sa(LS (g)) | 0.89 | 0.35 | 0.46 | 0.52 |
As it is observed in Figure
Likewise it can be concluded that, by raising damping in structure, the intensity magnitude with immediate occupancy performance levels and lateral safety is increased and by raising time period of designed isolator, these quantities are declined.
IDA curves for 9-story structure have been presented in Figure
Summarized IDA curves for 9-story frame.
In Figure
To investigate the structure, the amount of spectral acceleration should be extracted from the related response spectrum in various levels of performance. In Figure
Simplified hazard spectrum.
For quantitative expression of structural and nonstructural various components vulnerability, the exceedance probability can be expressed from a special amount of damage based on a reference characteristic of earthquake such as PGA, PGD, and PGV, according to the amount of earthquake risk. Repetition of this operation for various amounts of PGA (or other parameters) gets the normal curves to be produced, which are prevalent as the fragility curve. These curves consider uncertainties, related changes to the capacity curve characteristic, failure states, and earth motion.
A fragility curve can be usually produced with the use of a mathematical function related to seismic capacity and demand of the structure, accounting for their uncertainties [
Following that it has been dealt with fragility curves to obtain the vulnerability amount of 3- and 9-story structures.
In Figure
Fragility curves of 3-story frame (ISO 1 to 9 are related to damping ratios 0.1, 0.26, 0.48, 0.19, 0.52, 0.78, 0.3, 0.71, and 1.0, resp.).
As can be seen from Figure
Values of annual exceedance probability for 3-story frame.
Period = 2.5 s
Structure | Fixed base | Base isolated 1 (2.5 s) | Base isolated 2 (2.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.11 | 1.5 | 1.37 |
Prob(IO) | 100% | 35% | 40% | 45% |
Prob(LS) | 68% | 35% | 32% | 26% |
Period = 4 s
Structure | Fixed base | Base isolated 1 (4 s) | Base isolated 2 (4 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.11 | 1.5 | 1.37 |
Prob(IO) | 100% | 24% | 26% | 28% |
Prob(LS) | 68% | 23% | 22% | 17% |
Period = 5.5 s
Structure | Fixed base | Base isolated 1 (5.5 s) | Base isolated 2 (5.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 1 | 2.11 | 1.5 | 1.37 |
Prob(IO) | 100% | 10% | 18% | 24% |
Prob(LS) | 68% | 22% | 21% | 13% |
The exceedance probability for two levels of performance in 3-story structure is as follows.
In Figure
Annual exceedance probability of 3-story frame at IO and LS levels.
Comparison of the amounts of exceedance probability for 3-story structure in Figure
In Figure
Fragility curves of 9-story frame (ISO 1 to 9 are related to damping ratios 0.1, 0.26, 0.48, 0.19, 0.52, 0.78, 0.3, 0.71, and 1.0, resp.).
In Table
The amounts of annual exceedance probability; 9-story structure.
Period = 2.5 s
Structure | Fixed base | Base isolated 1 (2.5 s) | Base isolated 2 (2.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 2 | 3 | 2.65 | 2.52 |
Prob(IO) | 100% | 65% | 92% | 98% |
Prob(LS) | 78% | 40% | 32% | 22% |
Period = 4 s
Structure | Fixed base | Base isolated 1 (4 s) | Base isolated 2 (4 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 2 | 3.17 | 2.72 | 2.62 |
Prob(IO) | 100% | 55% | 69% | 83% |
Prob(LS) | 78% | 38% | 23% | 14% |
Period = 5.5 s
Structure | Fixed base | Base isolated 1 (5.5 s) | Base isolated 2 (5.5 s) | Base isolated 3 |
---|---|---|---|---|
Period(s) | 2 | 3.3 | 2.87 | 2.72 |
Prob(IO) | 100% | 33% | 53% | 79% |
Prob(LS) | 78% | 36% | 19% | 12% |
The exceedance probability in two levels of performance in 9-story structure is as follows.
In Figure
Annual exceedance probability of 9-story frame at IO and LS levels.
According to Figure
In 3- and 9-story structure, increasing damping gets the exceedance probability to be increased in immediate occupancy level performance. Furthermore, the amounts of failure probability reduction are less in 9-story structure; in immediate occupancy level performance, it means the isolator has great proficiency in 3-story structure. For example, the exceedance probability is 26% in 3-story structure and 22% in 9-story structure, in design time period of 2.5 seconds. Therefore, the isolator has proper proficiency in immediate occupancy performance level for 3-story structure and in life safety performance for 9-story structure.
In this research, we dealt with the seismic performance of base isolated structures and its effect on the various parameters of structure response using incremental dynamic analysis (IDA). For this purpose, 3- and 9-story model of steel buildings of SAC project has been used under 22 remote records of fault, introduced in the FEMA-P695 issue. It is seen that, in the constant amount of Sa, by increasing damping percentage, the amounts of structures drift decrease. Moreover, the amount of this parameter in base isolated structures is less than fixed base structure in any damping proportion. The primary slope of IDA curves in base isolated structures is more than fixed base structure where this procedure indicates the drift reduction. Base isolated structure has lower damage probability in comparison with fixed base structure in the specific performance level. In other words, use of isolator gets the performance level of structure improved. By increasing the isolator damping, isolator does not work in the low Sa, because of increase in the lead core diameter, and by raising the isolator damping, this procedure makes the exceedance probability of IO performance level increased, that is equivalent to 0.7% relative displacement. But when the isolator starts to work in constant Sa and higher relative displacements, the inverse results are obtained in comparison of former one in LS fragility curves, though by increasing isolator damping, the exceedance probability of LS performance level is decreased, that is, equivalent to 0.25% relative displacement. The time period of structure in the fixed state is 1 second and when the structure is equipped with LRB damper, time period of structure increases. According to the results, it is seen that, by increasing damping in structures, the Sa analogous intensity parameter increases with immediate occupancy performance level and life safety and furthermore by increasing the time period of designed isolator, this amount decreases. In 3-story building, with design time period of 2.5 seconds, by increasing damping the annual exceedance probability increases in the performance level IO and decreases in LS, respectively, where in both states these amounts are less than the amounts without isolator. By increasing damping, the annual exceedance probability increases and decreases in the performance levels of IO and LS, respectively, where in both states this amount is less than the amount without isolator. In both 3- and 9-story structure in the IO state, the increase of damping gets the exceedance probability increased. Maybe this is because the area of entered force is low and the damper does not work so much. But in the LS state, the isolator has good decreasing effect, because the entered force is great. Moreover, according to the obtained results it is clear that, in the IO performance level, the amount of damage probability reduction is less in 9-story structure; it means the isolator shows the better performance in 3-story structure. But in the LS performance level, the isolator significantly decreases the amount of damage in 9-story structure in comparison with 3-story structure. For example, in design time period of 2.5 seconds, the exceedance probability is 26% and 22%, respectively, in 3- and 9-story structures. With respect to results, it can be said that in 3-story structure with design time period of 2.5, 4, and 5.5 seconds by increasing damping the annual exceedance probability increases and decreases in the performance levels IO and LS, respectively, whilst in both states these amounts are less than the amounts of fixed base structure. Although structure has an appropriate performance rather than the fixed base structure in IO performance level, by increasing damping, the amounts of annual exceedance probability are increased. In other words, the isolator shows better performance in low damping, and this situation is opposite the state that happens in LS; it means that, in higher damping, the isolator shows the better performance from itself.
The results demonstrate that, by increasing the design time period, the amount of damage probability decreases in comparison with less design time period and the isolator shows better performance.
The authors declare that they have no conflicts of interest.
This research was supported by Support for Infrastructure and Transportation Technology Commercialization Program funded by Ministry of Land, Infrastructure and Transport of Korean Government (Grant no. 15TBIP-C093001-01).