It was shown in Chapter 5 that performing SSI analysis with elastic piers could underestimate the inelastic deformation of the piers. This hints the possibility of the overestimation of the demands of the foundation. This possibility is investigated here by determining the ratio of the demands when elastic piers were used in the analyses to the demands when piers where modelled with inelastic material. This demand ratio was obtained for both the translation and the rotation of foundation. Figure 6.6 and Figure 6.7 show the distribution of the aforementioned ratios (note that the wiggled shape of the curve for T=2.0 has no specific meaning since the curve simply connects the data points) and Table 6.1 lists the mean values of the ratios with their respective standard deviations.
Figure 6.6 shows that the predicted translation of foundation is greater when elastic structure is used in the numerical model. The translation demands obtained from the SSI analyses with elastic piers are on average up to 45% greater than the translations obtained from the analyses with inelastic piers. The average rotation demands are up to 25%
greater.
Higher predicted demands from the analyses with elastic piers result from higher forces transferred by the elastic piers to the foundation. In other words, in the analysis with inelastic piers, there is a maximum limit of the forces that can be transferred by the piers to the foundation, beyond which the piers begin to yield, and therefore the yielding pier induces less forces on the foundation compared to its corresponding elastic pier.
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These results signify the importance of proper modeling of the structural elements for seismic demand estimation of foundations and have important implications in design and retrofit of pile foundations as the overestimated demands can add to the cost of the construction of the foundation. It is common to evaluate the seismic demand of foundations by using elastic structure in the analysis and therefore the preceding observations suggest that proper material modeling of structures in SSI analysis can result 1n savings.
— Oo Qo oo i
© Nn J
S + J
Cumulative Frequency
OQ nN Ị
S OQ
S 2 © ws 1.0 1.5 2.0 2.5 3.0
Ratio of Translations
Figure 6.6: Ratio of foundation translation demands estimated from analyses with elastic piers to those estimated with inelastic piers
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—smmeT=( ,Ố S
>azz==e']=Q ẹ g |
ô=sseesstJ= | 0) g
—seesese [2=] ,5 § |
—— T=2.0s
Cumulative Frequency
2.5 3.0
Ratio of Rotations
Figure 6.7: Ratio of foundation rotation demands estimated from analyses with elastic piers to those estimated with inelastic piers
Table 6.1: Mean ratio of foundation demands estimated from analyses with elastic piers to those estimated with inelastic piers
Translation Rotation
Period Mean Standard os Mean Standard ơa
Deviation Deviation
0.3 N/A* N/A N/A N/A
0.6 1.04 0.08 1.00 0.07
0.8 1.22 0.23 1.14 0.20
] 1.12 0.18 1.08 0.15
1.5 1.11 0.11 1.15 0.20
2 1.44 0.52 1.24 0.28
* No yielding of the pile-supported pier was observed
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6.6 Summary
In this chapter the seismic demands of the foundations were studied by obtaining the translations and the rotations of the foundations and by determining their contribution into the total displacement demands of the piers. Also studied were the effects of the inelastic behaviour of the piers on the response of the foundation and how the lack of its direct consideration in SSI analysis would affect the estimated demands. The following was observed:
e Translation of foundation contributes significantly in displacing the stiffer piers with shorter natural periods, but it becomes less significant with increasing period of the piers. Therefore, the role of SSI through translation of foundation increases as the pier-to-foundation stiffness increases.
e The contribution of the foundation rotation in the total displacements of the piers increases with decreasing natural periods, however, the difference is not as pronounced as is for the translation of foundation.
e For shorter piers with shorter periods, the interaction is more in the form of translation of foundation rather than the rotation of foundation. For taller piers with longer periods, rotation is the more dominant form of SSI.
e SSI analysis with an elastic structure may overestimate the foundation demands.
This signifies the importance of the proper modeling of the inelastic behaviour of structural elements in SSI analysis for seismic demand estimation of foundations and the potential for reducing the cost of the construction of the foundation.
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7 EFFECTS OF SOIL-STRUCTURE INTERACTION ON THE SEISMIC DEMANDS OF PIERS
In Chapters 4 to 6, nonlinear dynamic analyses and estimated seismic demands of the piers and the foundations were presented. The demands of piers were studied with and without consideration of SSI, by obtaining the response of both the pile-supported piers and their corresponding fixed-base piers. Effects of SSI on the behaviour of the system were explored and the contribution of foundation response in the overall response of the piers was demonstrated. In this chapter the relevance of including SSI in seismic demand estimation of pile supported bridge piers is further discussed by comparing the demands of the flexible-base systems to those of the corresponding fixed-base systems when SSI was ignored. This chapter aims at demonstrating the effects of SSI in a format useful for structural design to effectively demonstrate when SSI must be accounted for, and what would be its effects on the response of the piers. Ductility and total displacement demands of the piers are examined and it is shown how the response without SSI is different than the response when the effects of SSI are accounted for. The significance of SSI is discussed and conclusions are made on the relevance of SSI in seismic design of pile-supported bridge piers. The comparisons are made through various response ratios which are introduced and explained in the following sections.
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