Data from dynamic analyses consist of plots of response quantities directly related to the specific objectives of this study. The results and discussions are given for each earthquake input and then an overall analysis for the CDMG suite is given at the end to analyze the effect of ground motion parameters on the peak response of base isolated structures.
El Centro 1979 (Array#6 station) \(230^o\) The maximum structural acceleration (roof acceleration) and maximum base displacement of base isolated structures subjected to the El Centro 1979 \(230^o\) are shown in Fig. 14 (double axis plots) for fixed values of \(1/\alpha \). It can be seen from these plots that for low yield strength levels (\(\mu =4\)% to 6%), the degree of nonlinearity, \(1/\alpha \) and hence the preyield stiffness \(k_e\), has no noticeable effect on maxima of base displacement and structural acceleration, in this case, the response is controlled mostly by the yield strength level. Figure 15 which shows the plots of maximum base shear with variation of base isolation system parameters, prove the above interpretation. The reduction in maximum base shear observed when increasing \(\mu \) from 4 to 5% (but we still in the same region of low yield strength levels) is due mainly to the amount of extra damping, this is well seen in Fig. 16, even the effective period is slightly reduced (see Fig. 17).
Contrarily, at high yield strength levels (from \(\mu =8\)% to 15%), the degree of nonlinearity, and hence the preyield stiffness controls the maximum base shear, and no noticeable effect of \(\mu \) in this range is observed. In addition, the maximum acceleration and interstory drift are slightly constant in this case. The situation is slightly different for maximum base displacement, where the yield strength level continues also to control. Furthermore, in this case, the increase in effective damping has no significant influence in reducing the base shear and structural acceleration even it reaches values higher than 20%.
It is clear from these figures that, even the preyield stiffness controls the peak response in the region of high level of yield strength, a small change in 1/\(\alpha \) does not change dramatically the results, and it changes them with very small amounts. So, it is evident that a value of \(\mu \) in this case and any value of \(1/\alpha \) give approximately the same magnitude of peak response.
The optimal seismic isolation design parameters are normally those with when the base displacement, structural acceleration and base shear are found to be the smallest. Based on this criteria and Figs. 14, 15, 16, 17, it can easily realized that the region of optimal design parameters is located exactly between \(\mu =10\)% and 15% with any value of preyield stiffness (or \(1/\alpha \)), since it does not dramatically change the results.
A value of \(\mu =15\)% and \(1/\alpha =7\) are the optimal design parameters, since for this pair we have the smallest structural acceleration, the smallest base displacement, the second smallest base shear and a small interstory drift.
Figure 14Peak responses of BI-structures subjected to El Centro 1979.
Full size image
Figure 15Maximum base shear for various isolation system parameters (El Centro 1979).
Full size image
Figure 16Effective damping for various isolation system parameters (El Centro 1979).
Full size image
Figure 17Effective period for various isolation system parameters (El Centro 1979).
Full size image
Loma Prieta 1989 (Hollister station) \(0^o\) The maximum structural acceleration (roof acceleration) and maximum base displacement of base isolated structures subjected to the Loma Prieta 1989 earthquake recorded at Hollister station are shown in Fig. 18 for fixed values of \(1/\alpha \). Also, is shown in Fig. 19, the maximum base shear for different seismic isolation parameters, and Figs. 20 and 21 show the variation of effective damping and effective period with the same parameters.
Low yield strength levels cause large base displacement (Fig. 18) because of the small amount of effective damping \(\beta _{eff}\) (Fig. 20); even the largest effective period \(T_{eff}\) (Fig. 21) is located in this region. As the yield strength level increases, maximum base displacement becomes smaller; this is due mainly to the added hysteretic damping.
A base isolation system with large yield strength levels induces greater base shear, great structural acceleration, and small base displacement. The increase in base shear is due mostly to the shorter effective period. In general, for base isolated structures subjected to this earthquake, the influence of the degree of nonlinearity is not significant on the peak response. The yield strength level has a noticeable effect on the maximum base displacement and maximum base shear, but its influence reduces for maximum structural acceleration; since the largest and smallest maximum structural acceleration are close (difference of \(0.77\;m/sec^2\)).
Based on Figs. 18, 19, 20, 21, it is clear that the region of optimal design parameters is located exactly between \(\mu \)=6% and 10% with any value of preyield stiffness (or \(1/\alpha \)), since it has no noticeable influence on the peak response. A value of \(\mu \)=8% and \(1/\alpha \)=20 are the optimal design parameters, since for this pair we have the smallest structural acceleration, the smallest interstory drift, a small base shear and a small base displacement.
Figure 18Peak responses of BI-structures subjected to Loma Prieta 1989 (Hollister station).
Full size image
Figure 19Maximum base shear for various isolation system parameters (Hollister).
Full size image
Figure 20Effective damping for various isolation system parameters (Hollister).
Full size image
Figure 21Effective period for various isolation system parameters (Hollister).
Full size image
Loma Prieta 1989 (Lexington Dam station) \(0^o\) The maximum structural acceleration (roof acceleration) and maximum base displacement of base isolated structures subjected to the Loma Prieta 1989 earthquake recorded at Lexington Dam station are shown in Fig. 22 for fixed values of \(1/\alpha \). Also, is shown in Fig. 23, the maximum base shear for different seismic isolation parameters, and Figs. 24 and 25 show the variation of effective damping and effective period with the same parameters.
At low yield strength levels, the degree of nonlinearity, and hence the preyield stiffness has no noticeable effect on the peak response in general (Figs. 22 and 23), but has a small effect on the maximum structural acceleration and the maximum displacement (Fig. 22).
As the yield strength level increases as the maximum base shear, and the preyield stiffness (or \(1/\alpha \)) begins to influence (Fig. 23). Therefore, at large yield strength levels, the preyield stiffness controls but slightly the motion, in conjunction with the yield strength level, in this case, the base shear becomes larger and base displacement reduces but with small amount while comparing with the largest value observed at lowest yield strength level.
For yield strength levels between \(\mu \) = 4 and 5%, the effective stiffness is somewhat constant even the preyield stiffness reaches its largest value, also, the effective damping (Figs. 24 and 25), hence, a smallest energy dissipation capacity. In this case, the peak structural acceleration is influenced mainly by the yield strength level. The significant effect of the preyield stiffness is observed in the region of high yield strength levels (\(\mu \) = 8 to 15%), where the two parameters influence the peak response, but not as dramatically as the increase in the maximum base shear. In this region, the preyield stiffness reduces the structural acceleration.
The effective damping effect in general is reduced when large yield strength is given to the seismic isolation system, even the capacity to dissipate energy is higher in this case; this is due mainly to the shorter period associated to system.
Based on Figs. 22, 23, 24, 25, it is clear that the region of optimal design parameters is located exactly between \(\mu \)=4% and 5% with any value of preyield stiffness (or \(1/\alpha \)), since it has no great influence on the peak response in this region.
A value of \(\mu \)=4% and \(1/\alpha \)=20 are the optimal design parameters, since for this pair we have one of the smallest values of maximum base shear, one of the smallest interstory drift, a small structural acceleration and a small base displacement.
Figure 22Peak responses of BI-structures subjected to Loma Prieta 1989 (Lexington dam station).
Full size image
Figure 23Maximum base shear for various isolation system parameters (Lexington dam).
Full size image
Figure 24Effective damping for various isolation system parameters (Lexington dam).
Full size image
Figure 25Effective period for various isolation system parameters (Lexington dam).
Full size image
Landers 1992 (Lucerne valley station) Long. The maximum structural acceleration and maximum base displacement of base isolated structures subjected to the Landers 1992 earthquake recorded at Lucerne Valley Station (longitudinal component) are shown in Fig. 26 for fixed values of \(1/\alpha \). Also, is shown in Fig. 27, the maximum base shear for different seismic isolation parameters, and Figs. 28 and 29 show the variation of effective damping and effective period with the same parameters.
The maximum base displacement observed in Fig. 26 is \(7.89\;cm\), which is a very small displacement, regarding the other values observed for the remainder of suite of earthquakes; this can be interpreted by the small peak ground displacement, which is equal to \(8.82\;cm\).
At low yield strength levels, large preyield stiffness and hence high degree of nonlinearity doesn’t contribute noticeably on the maximum base shear (Fig. 27) and maximum structural acceleration (Fig. 26). This is due to the fact that the effective period and energy dissipation capacity of the structure do not change in this range (\(\mu \)=4% to 5%). Also, in this case (\(\mu \)=4% to 5%) the maximum base is constant and no effect of \(1/\alpha \) is observed.
In contrast, at high yield strength levels (\(\mu \ge \)8%), the effect of the degree of nonlinearity become noticeable in reducing the base displacement, because of the induced extra amount of effective damping (Fig. 28) and hence the capacity to dissipate more ground motion energy. In addition to the significant effect of yield strength level on the peak structural acceleration, the degree of nonlinearity (i.e., the preyield stiffness) also influences, so that for high degree of nonlinearity, the isolation system induces an extra acceleration to the superstructure, but stills small (Fig. 26). However, the maximum base shear is mostly governed by the yield strength and little by the preyield stiffness.
Based on Figs. 26, 27, 28, 29, it is clear that the region of optimal design parameters is located between \(\mu \)= [4%, 5%] and \(1/\alpha \) = [10,20]. A value of \(\mu \) = 4% and \(1/\alpha \) = 10 are the optimal design parameters, since for this pair we have the smallest maximum base shear, the smallest interstory drift, a small structural acceleration, but this pair does not give a small base displacement comparing with other pairs. However, the base displacement associated to this pair is \(6.17\;cm\), which stills small enough if the problem of pounding is under consideration also. So, in the case of small displacements, one have to be aware about the base shear and structural accelerations, those, are the better indicators of effectiveness of such a seismic isolation system.
Figure 26Peak responses of BI-structures subjected to Landers 1992 (Lucerne station).
Full size image
Figure 27Maximum base shear for various isolation system parameters (Lucerne).
Full size image
Figure 28Effective damping for various isolation system parameters (Lucerne).
Full size image
Figure 29Effective period for various isolation system parameters (Lucerne).
Full size image
Northridge 1994 (Newhall station) \(360^o\) The maximum structural acceleration and maximum base displacement of base isolated structures subjected to the Northridge 1994 earthquake recorded at the Newhall station \(360^o\) are shown in Fig. 30 for fixed values of \(1/\alpha \). Also, is shown in Fig. 31, the maximum base shear for different seismic isolation parameters, and Figs. 32 and 33 show the variation of effective damping and effective period with the same parameters.
At low levels of yield strength (\(\mu \)=4%-5%), the maximum base shear (Fig. 31) is governed mostly by the degree of nonlinearity (i.e., preyield stiffness) in this case, a high degree of nonlinearity reduces the maximum base shear, but its effect tends to be not significant for higher ranges; when the preyield stiffness becomes more than 10 times the postyield stiffness. However, in this case (low yield strength levels), the degree of nonlinearity does no more govern the maximum base displacement (Fig. 30); rather, it is the yield strength in this case that governs this response quantity. Furthermore, that is not the case for structural acceleration (Fig. 30) which is governed strictly by the degree of nonlinearity, when the preyield stiffness is less than 7 times the postyield stiffness, when this ratio becomes larger, which means high degree of nonlinearity, the yield strength begins to govern also the motion, but for higher degree of nonlinearity, the peak structural acceleration becomes strictly controlled by the yield strength level.
At high levels of yield strength (\(\mu \ge \)8%), the latter influences noticeably the maximum base shear and maximum base displacement in conjunction with the degree of nonlinearity. However, the influence of the preyield stiffness becomes insignificant when it is larger than 10 times the postyield stiffness, this can be explained by the fact that small extra amount of effective damping is added (Fig. 32). At these levels of yield strength ,the structural acceleration is governed mostly by the degree of nonlinearity; a high degree of nonlinearity reduces the peak structural acceleration. The yield strength becomes effective just for seismic isolation systems with very high degree of nonlinearity, say more than 15%.
For this earthquake, the situation is quite difficult to pick the region of optimal design parameters that lead to best performance; because the smallest maximum structural acceleration and base displacement are reached for seismic isolation system having high yield strength level (\(\mu \)=15%) and high degree of nonlinearity (\(1/\alpha \)=20), but the maximum base shear is reached when the isolation system has a low yield strength level (\(\mu \)=5%) and a high degree of nonlinearity (\(1/\alpha \)=20). However, based on Figs. 30 to 33, the region of optimal design parameters can be located somewhere between \(\mu \)=5% and 10% with the highest degree of nonlinearity, \(1/\alpha \)=20. However, the pair (\(\mu \)=8%, \(1/\alpha \)=20) can be considered as the optimal design parameters.
Figure 30Peak responses of BI-structures subjected Northridge 1994 (Newhall station).
Full size image
Figure 31Maximum base shear for various isolation system parameters (Newhall).
Full size image
Figure 32Effective damping for various isolation system parameters (Newhall).
Full size image
Figure 33Effective period for various isolation system parameters (Newhall).
Full size image
Petrolia 1992 (Petrolia station) \(90^o\) The maximum structural acceleration and maximum base displacement of base isolated structures subjected to the Petrolia 1992 earthquake recorded at the Petrolia station \(90^o\) are shown in Fig. 34 for fixed values of \(1/\alpha \). Also, is shown in Fig. 35, the maximum base shear for different seismic isolation parameters, and Figs. 36 and 37 show the variation of effective damping and effective period with the same parameters.
As seen from Figs. 34 and 35, it is clear that the peak response is governed by the yield strength level, and the degree of nonlinearity begins to contribute in governing the peak response at the region of high yield strength levels. The maximum base shear tends to be smaller as the yield strength level reaches 5%, after that the maximum becomes larger as the yield strength level. The maximum structural acceleration follows in this case the yield strength levels. In contrast, the maximum displacement becomes smaller as the yield strength reaches its largest value (\(\mu \)=15%) at higher degree of nonlinearity.
To select the region of optimal design parameters, one must decide what is the main response quantity that will dominate the choice of the base isolation system to be used? If the base displacement is very important, when the problem of pounding is present, we have to choose isolation system with high yield strength and high degree of nonlinearity; in this case we will lose the benefits of more reducing the base shear and structural acceleration. Contrarily, if the above problem is not important, one can gain more benefits of reducing the structural acceleration and base shear at the same time with the same parameters but with larger base displacement; in this case choosing an isolation system with low yield strength level with high degree of nonlinearity is the best choice.
However, in our case, a yield strength level between 4% and 10% with any degree of nonlinearity (or \(1/\alpha \)=15−20) is the near optimal choice. The pair (\(\mu \)=5%, \(1/\alpha \)=20) can be considered as the optimal design parameters, since they cause a smallest maximum base shear, a smallest structural acceleration and the smallest interstory drift.
Figure 34Peak responses of BI-structures subjected to Petrolia 1992 (Petrolia station).
Full size image
Figure 35Maximum base shear for various isolation system parameters (Petrolia).
Full size image
Figure 36Effective damping for various isolation system parameters (Petrolia).
Full size image
Figure 37Effective period for various isolation system parameters (Petrolia).
Full size image
Northridge 1994 (Sylmar station) \(360^o\) The maximum structural acceleration and maximum base displacement of base isolated structures subjected to the Northridge 1994 earthquake recorded at the Sylmar station \(360^o\) are shown in Fig. 38 for fixed values of \(1/\alpha \). Also, is shown in Fig. 39, the maximum base shear for different seismic isolation parameters, and Figs. 40 and 41 show the variation of effective damping and effective period with the same parameters.
At low yield strength levels, the degree of nonlinearity has no effect on the peak response of base isolated structures (Figs. 38 and 39); the control in this case belongs to the yield strength level alone. A great decrease of the peak responses is observed from \(\mu \)=4% and 5%.
At high yield strength levels, the degree of nonlinearity has a negligible effect on the maximum base displacement and maximum structural acceleration. The effect of the degree of nonlinearity is noticeable in the case of case of very high yield strength levels in reducing the maximum base shear. However, in general, the peak response of base isolated structures subjected to this particular earthquake is governed mostly by the yield strength level. The effective damping is not as great as when subjected to other earthquakes, in this case the maximum effective damping is around 10%, which is small.
The capacity to dissipate more energy is very great in this case; regarding that the energy dissipated per cycle is around \(2824.25\;kN.m\), that is a great while comparing to the same structures subjected to other earthquakes. A severe earthquake having the character of Northridge 1994 (recorded at Sylmar County) causes the structure to dissipate more energy, so that it can reduce the maximum base shear to 15% of the corresponding fixed base structure. This level of reducing the base shear is the best reduction observed for the entire CDMG suite of earthquakes.
The region of optimal seismic isolation parameters can be selected simply in this case, we can arrive at the smallest maximum base shear with the smallest base displacement, with the pair of isolation system parameters ranging from: \(\mu \)=10%−15% and a very high degree of nonlinearity, say \(1/\alpha \)=15−20. The peak structural acceleration varies slightly in this range. The pair [\(\mu \)=15%, \(1/\alpha \)=20] gives the smallest maximum base shear, which constitutes 15% of the maximum base shear of the corresponding fixed base structure, and the smallest maximum base displacement, also, this pair gives the smallest interstory drift.
Figure 38Peak responses of BI-structures subjected to Northridge 1994 (Sylmar station).
Full size image
Figure 39Maximum base shear for various isolation system parameters (Sylmar).
Full size image
Figure 40Effective damping for various isolation system parameters (Sylmar).
Full size image
Figure 41Effective period for various isolation system parameters (Sylmar).
Full size image
Landers 1992 (Yermo station) \(270^o\) The maximum structural acceleration and maximum base displacement of base isolated structures subjected to the Landers 1992 earthquake recorded at the Yermo station \(270^o\) are shown in Fig. 42 for fixed values of \(1/\alpha \). Also, is shown in Fig. 43, the maximum base shear for different seismic isolation parameters, and Figs. 44 and 45 show the variation of effective damping and effective period with the same parameters.
At low yield strength levels, low degree of nonlinearity has small effect on the peak response of base isolated structures (Figs. 42 and 43). In this case, the small augmentation in yield strength causes larger maximum base shear, as well as for base displacement and structural acceleration, because the effective period is shortened (Fig. 45), and a very small added effective damping has not effect.
However, an isolation system with high degree of nonlinearity does not affect the peak response, namely the maximum base shear, maximum base displacement, and peak structural acceleration, when high yield strength is used for the isolation system, this is due to the fact the effective damping doesn’t change significantly as well as the effective period, that seem to be constant for a constant high yield strength, and they do not change with the degree of nonlinearity (Figs. 44 and 45).
Because of the small variation of the maximum structural acceleration, which its variation is banded between 0.25g and 0.36g, and because the larger maximum base displacement is in a reasonable range \(19.5\;cm\), the maximum base shear in this case is the main performance indicator of a seismic isolation system.
Based on the above consideration, the region of optimal design parameters may be located between \(\mu \)=4%−5% and any value of \(1/\alpha \), or between \(\mu \)=4%−8% with a high degree of nonlinearity (say \(1/\alpha \)=10−20). The pair [\(\mu \)=4%, \(1/\alpha \)=20] gives the smallest maximum base shear, which constitutes 37.4% of the maximum base shear of the corresponding fixed base structure and the smallest interstory drift.
Figure 42Peak responses of BI-structures subjected to Landers 1992 (Yermo station).
Full size image
Figure 43Maximum base shear for various isolation system parameters (Yermo).
Full size image
Figure 44Effective damping for various isolation system parameters (Yermo).
Full size image
Figure 45Effective period for various isolation system parameters (Yermo).
Full size image
Table 2 summarizes the near optimal design seismic isolation parameters (region and discrete values) for each earthquake of the CDMG suite in parallel with their characteristics (units for PGA, PGV and PGD are cm and sec. and the \(*\) character means any value) obtained from the parametric analysis.
Table 2 Near optimal design seismic isolation parameters for the CDMG suite.Full size table
Table 3 The table shows the smallest maximum base shear for each earthquake record, as well as the largest maximum base shear and the corresponding pair of isolation system parameters. The PGV controls the maximum base shear in conjunction with the PGD, but the latter has a very small effect. The PGA has no effect on the maximum base shear of base isolated structures, since they have a long period that puts them in the velocity sensitivity (for those having long isolation period) and in the displacement sensitivity (for those having very long period), also, this is clear from the table. The maximum base shear is reduced slightly for the Newhall earthquake (comparing with Petrolia) even it has greater PGV than Petrolia, this cannot be interpreted by the reduction in PGA, because it has no effect (see for example Lucerne and Yermo in the table), also cannot be interpreted by the PGD, because the reduction in this case is negligible. This can be interpreted by the frequency content.
Table 3 Isolation system parameters that give smallest max. base shear.Full size table
The base isolated structure (with \(\mu \)=4% and \(1/\alpha =10\)) subjected to the Lexington earthquake (PGV = 84.43 cm/sec.) has a maximum base shear smaller than that of the base isolated structure (with \(\mu \)=5% and \(1/\alpha \)) when subjected to the Hollister (PGV = 62.78 cm/s); this can be interpreted by the PGD, which is smaller in Lexington . In this case, we can understand why PGA has no effect, because Lexington has PGA greater than Hollister, and the maximum base shear is smaller when the structure is subjected to it.
The CDMG suite of earthquakes can be divided into two main categories; the first category includes El Centro and Sylmar and the second category includes the remainder of earthquakes. The first category has a great PGV, so it includes the severe earthquakes. The second category includes moderate and those having less severity earthquakes.
The largest maximum base shear occurs when using isolation systems with \(\mu \)=15, that means high yield strength level and \(1/\alpha =5\), that means low degree of nonlinearity for the second category. Therefore, one should select an isolation system with low yield strength level (say 4–5%) with high degree of nonlinearity (say \(1/\alpha =10-20\) or even more) in order to get smallest maximum base shear. In contrast, a base isolated structure subjected to an earthquake from the second category has a large maximum base shear when the isolation system is characterized by low yield strength level (\(\mu =4\%\)) and very low degree of nonlinearity. Therefore, the appropriate isolation system must have a high degree of nonlinearity as well as a high yield strength level, in order to meet the performance expected from the seismic isolation system.
Table 4 reports the isolation system parameters that give the smallest maximum base displacement and the corresponding maximum base displacement for each earthquake record, also is reported in the same table the largest maximum base displacement and the corresponding pair of isolation system parameters.
Table 4 Isolation system parameters that give smallest max. base displacement.Full size table
Tables 2 and 3 show that the maximum base displacement is velocity sensitive, meaning that the PGV governs the motion. The influence of PGD is not as noticeable; it affects the response when the PGV is moderate. There is a trade-off between reducing the base shear and increasing the base displacement, which can be overcome by choosing parameters according to the primary need. In our study, we selected parameters that are near optimal and were chosen to give the best performance expected from the use of an isolation system. Generally, the base shear is considered as the main parameter of interest when selecting the appropriate isolation system parameters, as well as the structural acceleration, which can be amplified (higher modes effect). The base displacement is less important, since the interstory drift is related to base shear.
Want more information on seismic isolator price, seismic isolation bearings? Click the link below to contact us.