
Fig. 1.
The two substructures : soil and rigid structure with soil-structure interface [38]

Fig. 2.
Substructures: unbounded soil

Fig. 3.
Model of a structure equipped with active tendons and with SSI

Fig. 4.
Flowchart of solving the state equation with active control [18]

Fig. 5.
El-centro 1940 of the N-S Components

Fig. 6.
The data of the studied model
Tab. 1
The natural frequencies of the studied model with and without SSI (rad/s)
| Floor | SSI | Fixed |
|---|---|---|
| 1 | 14,514 | 17,236 |
| 2 | 43,162 | 48,295 |
| 3 | 68,091 | 69,789 |

Fig. 7.
The displacement, b) the velocity, and c) the acceleration of the final floor of the studied model, considering the effect of SSI, compared with the fixed case without control

Fig. 8.
Variation of maximum displacement at the last floor and maximum control force as a function of S/R ratios

Fig. 9.
Maximum displacements, velocities, and accelerations a) without and b) with ISS for the three controller positions compared to the case without control

Fig. 10.
The control force-displacement relationship at the last floor of the studied model a) without SSI and b) with SSI for the three controller positions compared to the case without control