Background
Accurately predicting the dynamic interactions occurring, in the event of an earthquake, between structures and the underlying geological formations helps increasing the safety of structures while reducing construction or rehabilitation costs. The first effect that must be taken into account is the modification of the input signal due to the kinematic interaction and in particular to the induced swing and torsion, the latter being potentially dangerous because of the weakness of the building with regard to this type of load. The second effect, known as inertial interaction, concerns the increase of the structure’s natural period and the corresponding changes in its vibration modes.
For simple buildings these effects often reduce the vulnerability due to a transfer of deformations to the surrounding soil, which also provides additional damping. However, some specific cases should be avoided, including breaches in the foundation. On the other hand, for large structures such as electric and/or nuclear power plants, among others, soil-structure interaction can become important. This interaction can be taken into account via a detailed analysis using numerical models. These techniques have proven to be very reliable compared to field experiments in the high seismic zone.
During an earthquake, seismic waves propagating in the ground set the foundations of structures in motion by shaking them mainly horizontally. Accelerated at its base, each building is subjected to inertial forces that its structure must withstand. To maintain its balance, the structure exerts significant forces on the surrounding soil. If this floor is very resistant, the initial movement of the support is not modified. There is no interaction and to ensure the maintenance of the structure, the designer can limit his analysis to the structure alone; but at the cost of internal efforts and sometimes considerable demand for resistance. If, on the other hand, the ground is of lower resistance, the support will deform and the movement of the foundation will be modified, as well as sometimes the movement of surrounding foundations. We are dealing with a phenomenon of soil-structure interaction and the designer must therefore include the soil as well as sometimes the surrounding structures in his analysis. While he faces additional difficulties, related not only to the seismic waves propagation in the ground but also to its imprecise knowledge of the geological environment, the presence of these interactions often leads to a reduction of internal structural stresses through their transfer to the foundation ground; if, however, the adjacent structure does not increase its own movements. On the other hand, this effort transfer can also threaten the performance of the surrounding soil, either by exceeding its load-bearing capacity or by gradually reducing its capacity, for example by soil liquefaction. Finally, it should be noted that this effort transfer leads generally to larger movements of the structures, generating increased stresses on the connecting elements or on the various water, gas or electricity networks.
The main consequences of the soil-structure interaction
The main consequence of the SSI is to break the sequential scheme in which seismic movement is first defined and then the structure is sized. This rupture is of two orders classically called: kinematic interaction and inertial interaction.
The kinematic interaction reflects the incompatibility between the incident wave field and the potential movements of the foundation. Indeed, the foundation is often more rigid than the surrounding soil and can therefore only move, as a first approximation, in translation and rotation. Since only part of the displacements induced by the incident seismic waves can be accommodated, part of the waves are reflected, causing significant stresses on the foundation, but reducing the energy penetrating into the structure. This kinematic interaction is also beneficial for the structures with deep foundations because seismic waves are amplified at the top of the geological formations, and the search for a deeper support point for the structure reduces the seismic loading. In order to precisely characterize this complex effect, as it depends on the nature of the subsoil and the geometry of the foundation, it is usual to focus on the dynamic response of the foundation in the absence of the building, which, in the case of a rigid foundation, means finding the displacements and rotations of the foundation. While a major swinging is rather beneficial for the structure itself because it reduces bending forces in the structure, it can be highly damaging to the foundation soil, which can break and cause the entire structure to tip over (see Figure 1). Torsion, on the other hand, is much more dangerous for the superstructure and the symmetrical properties of the foundation reduce these detrimental effects.
In summary, the kinematic interaction induces a filtering, sometimes significant, of the seismic movement during its transfer to the building but causes overall rotations of the foundation whose effects on the structure must be studied. The response of the foundation without superstructure to incident seismic movement provides the designer with the inertial forces necessary for the design of the structure. Finally, in the case of surface foundations and vertically incident waves, there is no kinematic interaction and the movement of the foundation without superstructure is equal to the movement of the ground without structure.
The inertial interaction reflects, independently of the change in loading described above, the coupling between the structure and the surrounding soil. Two elements are essential here: the modification of the structure’s resonances with respect to its behaviour on a fixed base and the dissipation of energy in the ground.
Thus, the fundamental period of the soil-structure system is always higher than the one of the fixed base structure because flexibility and mass is added when the soil is taking into account. The extent of this increase depends on the relative flexibilities of the structure and the soil. The former is generally proportional to the height of the structure while the latter is proportional to the size of the foundation. As a result, soil-structure interaction can become predominant for structures of limited slenderness based on soils with low properties.
The energy dissipation increase in the system by wave radiation in the ground or by internal friction in the ground is undoubtedly the main benefit of soil-structure interaction because it will reduce the magnitude of resonances. This dissipation depends on the relative movement of the foundation in relation to the drive movement, and therefore on the ratio between the flexibility of the soil and the structure. Since dissipation is proportional to flexibility, the greater the interaction, the greater the dissipation. The part due to wave radiation in the ground also depends on the relative speed of the foundation. Thus, the larger the foundation is, the lower the wave velocity and the fundamental period will be and the more the damping will increase.
To conclude on the inertial interaction, it should be noted that if, in the vast majority of cases, it is beneficial or negligible, there are specific cases where it has a harmful effect, particularly for a relatively light structure based on a massive foundation whose fundamental period is close to the one of the light structure; the seismic movement then undergoes two successive amplifications.
Outstanding structures
Due to their mass and the large size of the foundations, structures such as power plants, storage tanks, dams or large bridges are likely to interact strongly with the surrounding soil. In addition, these structures, whose safety is essential, are not subject to the usual design rules and justification methods adapted to earthquake must be implemented. They include detailed finite element modelling including a part of the surrounding soil. The justification is then done by numerically approaching the dynamic response of the structure for several imposed seismic signals. In addition, as precise knowledge of the properties of foundation soils is not available, several studies are being carried out taking into account extreme values for the properties of materials. For each of these studies, it is necessary to check not only the strength of the structure but also the levels of deformation obtained in the soil. When the latter are high, an adaptation of the stiffness and damping values is necessary, the procedure being iterated until convergence. These calculation methods were calibrated from experiments conducted on models built in highly seismic regions (see Figure 2).
Interaction between structures and city effect
When the waves radiated into the ground by a building become significant, interactions between structures can occur. Locally, the vibration of a structure on its foundation can induce additional loading on the surrounding structures, which is particularly damaging when the latter are smaller in size. On a more global scale and for highly urbanized areas, all the structures are vibrated in a coherent or inconsistent way. This is called the city effect. This effect is still not well known because there is little experimental data to quantify its importance. Recent work suggests that amplifications occur occasionally as well as increases in the duration of seismic signals (see Figure 3). However, analyses carried out in districts of Mexico City or Nice show that these effects are generally rather beneficial since the amplification due to the resonance of the geological site tends to be reduced in the presence of buildings. In addition, the presence of buildings prevents the propagation of surface waves, thus reducing seismic movement in highly urbanized areas.
Bibliography
- P.-Y. Bard et al. (2004) Site-City Interaction. Chapter 5 of the book « Assessing And Managing Earthquake Risk », C.S. Oliveira et al. Editors, Kluwer, 2004.
- Clouteau et al. (2001), Modifications of the ground motion in dense urban area, Journal of Computational Acoustics,n°9-4,p. 1.
- Clouteau et al. (2003), Computational soil-structure interaction, Chapter 2 of « Boundary Element Methods for soil-structure interaction », Olivetto et al. editors, Kluwer, 2003.
- Clouteau et al. (2002), Uplift of foundations under seismic loadings : time v.s. time-frequency methods, Revue Eur. des Elements finis, n°11-1, p. 185.
- Pecker (1984) Dynamique des Sols. Presse des Ponts et Chaussées, Paris, France, 1984.