Conclusions from the analysis of the results by participants

All participants, for all calculations cases, predicted a high efficiency of the seismic isolation system and a significant reduction of the horizontal response spectra in the superstructure, in comparison to what they would have been without isolation. The maximum basemat acceleration is always predicted to be significantly lower than the maximum ground acceleration (0.5 g for DBE and 0.837 g for BDBE) and amplification for higher elevations in the superstructure are low. In this qualitative aspect, results from all participants are fully consistent.

In a more quantitative way, Table 18 and Table 19 summarize the calculated maximum basemat accelerations for all participants and all cases analysed in the present Section. The mean value is also presented in these tables as well as the ‘coefficient of variation’ (COV), which is the ratio of the standard deviation to the mean. The COV is directly comparable with the logarithmic standard deviation (β) used in Seismic Probabilistic Safety Assessments (S-PSA) to introduce uncertainties, as far as it is less than about 40%. To have some reference value, note that in S-PSAs uncertainty in the seismic response results due to variability in structural modelling and damping effects is introduced by a composite β the order of 0.20 (Ref. [30]).

For all cases where the vertical excitation does not too significantly affect the horizontal response (case 1, 2 and 6 with LRB isolation system and case 1 with EQSB isolation system), the COV remains below 0.15, highlighting a rather good convergence of the different participants models, despite strong structural modelling differences for both the superstructure and the isolation system. These differences appear more stringently in other cases with COV values reaching, for example, 0.29 in case 12 with LRB isolation system.

4.5.2 Maximum displacements and hysteresis curves

Analysing the displacement curves and the force-distortion curves in the horizontal directions for all cases, it was observed that yielding and non-yielding time intervals, or sliding and non-sliding time

88

intervals, are always fully in phase in all participants’ results. All models predict the onset of yielding or sliding and the end of yielding or sliding at the same time.

TABLE 18. SUMMARY OF CALCULATED BASEMAT MAXIMUM ACCELERATION IN THE X DIRECTION

Maximum basemat acceleration along X (g)

LRB isolation system EQSB isolation system

TABLE 19. SUMMARY OF CALCULATED BASEMAT MAXIMUM ACCELERATION IN THE Y DIRECTION

Maximum basemat acceleration along Y (g)

LRB isolation system EQSB isolation system

With the LRB system, the overall shape of the horizontal force-displacement curves is also the same for all participants. Significant differences are only observed when the excitation level is increased, and a separation occurs between the results of participants who modelled the lead heating phenomenon (P1 and P2) and the others.

With the EQSB system, significant differences in hysteresis curves are obtained between the participant who did include a dependency of the friction force on the vertical load (P5) and those who did not (P3 and P7). This difference is observed in all benchmark cases and is further amplified when the excitation level is increased. Even though it did not occur in the present simulations, it is expected to have an even more important effect if uplift occurs within the EQSB isolators.

The displacement amplitude in the yielding or sliding phases is predicted differently by the different participants, with one group (P1, P2, P5, P6 and P7) predicting significantly larger isolators distortions

89 and upper basemat displacements than the other (P3, P4 and P8). This difference is mainly explained by different modelling of damping forces. The group of participants predicting lower displacement has either implemented some equivalent viscous dampers acting in parallel to the lead cores or has used a mass proportional damping matrix on the superstructure, which is known to have the effect of artificially damping its rigid body motions.

Selecting only the results of the first group of participants, considered to be more representative, Table 20 and Table 21 summarize the computed basemat relative displacements respectively in X and Y directions. The mean value is also presented in these tables as well as the COV, as defined in the previous paragraph. In all cases, the COV is found to be lower than 0.12, most of the time significantly. This highlights the fact that, even with different tools, different models and different hypotheses, provided that no undue damping is added in the analysis, there is very limited scatter in the prediction of the maximum displacement values. When results of all participants are considered, the overall COV is in excess of 0.40.

TABLE 20. SUMMARY OF CALCULATED BASEMAT MAXIMUM DISPLACEMENT IN THE X DIRECTION, FOR A SELECTED GROUP OF PARTICIPANTS

Maximum displacement along X (m)

TABLE 21. SUMMARY OF CALCULATED BASEMAT MAXIMUM DISPLACEMENT IN THE Y DIRECTION, FOR A SELECTED GROUP OF PARTICIPANTS

Maximum displacement along Y (m)

4.5.3 Floor response spectra at higher elevations

The difference between the two above mentioned groups is also observed on response spectra in the 0 to 3 Hz frequency range. Particularly, for higher excitations, a peak appears at the isolation frequency for the first group while it does not appear for the second group. Instead, the second group always predict a higher peak between 1 and 2 Hz, with the LRB as well as with the EQSB system. For frequencies higher than 3 Hz, in all directions, the influence of structural modes is predominant and the differences between participants results are not anymore due to their different isolation system modelling but to different superstructure modelling and to the use of different simplifying hypotheses.

90

Among others, the structural responses were found to be significantly affected by different basemat representations: from fully stiff to significantly flexible, and by different ways to merge 486 non-linear isolators into one or several macro isolators. For cases where all 486 isolators were represented, a distinctly reduced scattering of participants response spectra is observed. Besides removing the simplifying hypothesis for macro isolators, the representation of all individual isolators effectively stiffens the basemat of those participants who represented it as unrealistically flexible.

The influence of the structural modes response on the horizontal and vertical response spectra is highly dependent on the modelling of damping forces that has been adopted by different participants. Among others, it was observed that one participant (P7) significantly overdamped its structural responses, leading to a quasi-absence of peaks at the structural modes frequencies on its response spectra. At the opposite, participant P2 seemed to have a low damping on its structural modes and possibly also on its isolators model in the vertical direction and in rocking, leading to high peaks on its response spectra.

As a consequence, a relatively high dispersion of floor response spectra was observed in the benchmark results, with COVs for ZPA in the top elevations of the different buildings sometimes exceeding 0.40.

4.5.4 Effect of seismic isolation system models

For the LRB isolation system at design basis earthquake level, the effect of introducing lead heating, reduction of vertical stiffness due to horizontal distortion and rubber cavitation into the isolators numerical models, as was done by participants P1 and P2, was not observed to be predominant.

On the other side, these effects were found to significantly affect all displacements, response spectra and hysteresis curves at beyond design basis earthquake level. The structural mode frequencies were also shifted in a noticeable manner when considering such effects. New peaks appear in the high frequency range of the response spectra due to the occurrence of cavitation, which produces impact like loads on the basemat.

Representing the dependency of the rubber horizontal stiffness to the vertical compressive force was not found to have any significant effect in this benchmark.

For the EQSB isolation system, the effect of coupling the friction force to the vertical pressure exerted on the bearing was found to be predominant on all results for both design and beyond design basis excitation levels.

4.5.5 Remarks on the dispersion of results

Only a few benchmark cases corresponding to the LRB isolator have enough contributions from participants to provide some statistically significant metrics of dispersion. Relevant statistics are those which refer to magnitudes important for a designer, such as, the maximum distortion computed at the isolators or the ZPA and peaks at floor spectra.

After reviewing dispersion between the results reported by the participants, the following points are noted:

 Maximum horizontal accelerations of the upper basemat are predicted with a relatively low dispersion. Computed COVs are between 0.07 and 0.15.

 Isolator distortion and upper basemat maximum displacements are predicted with a large scatter, for the reasons explained in the previous sections. When considering all participants, COVs are in excess of 0.40. When taking only the results of one group of participants, the COV of the predicted maximum displacement values is no greater than 0.11. This shows that if engineers follow carefully the same modelling assumptions, small dispersion of results can be obtained, thus highlighting the need for a design code sharing common practice, especially about modelling damping effects.

 For frequencies higher than 3 Hz, the influence of structural modes is predominant, and the differences are due to different superstructure modelling and to the use of different simplifying hypotheses. COVs for ZPA in the top elevations of the different buildings exceed 0.40. The

91 benchmark organization tried to avoid this source of dispersion by supplying all participants with the same structural model. However, it has proven to be very difficult that analysts use a given model without “correcting” it according to their own understanding.

When differences due to (a) different modelling of the basemat stiffness, (b) different representation of damping outside the isolators themselves, and (c) different hypotheses to merge 486 isolators into one or 5 macro-isolators are set aside, it is found that participants that have adopted the same hypotheses obtain globally similar results. This is illustrated in Figure 80 for participants P1, P2 and P5 in Case 6 with the LRB isolation system. The remaining differences on these curves, are explained by the consideration of lead plug heating and non-linear vertical isolators behaviour by participant P1 and P2 and not by participant P5.

Hence, it seems that, given the nature of this type of analyses, the role of a carefully implemented Peer Review of the modelling assumptions and results by experienced engineers, can be key to assure an acceptable reliability.