[MUSIC] Hello. The foundation of structures has a very strong influence on their seismic response. As shown in this movie, depending on the type of foundation, the structural response may be totally different. Two main situations are at stake: shallow foundations for stiff soils or small structures, and deep foundations for soft soils or tall structures. The soil foundation interaction will be different in both cases Considering shallow foundations, the stability depends on the combination of various forces: the vertical force V, the horizontal force H, and the overturning moment M. For static loadings, we may identify soil foundation interaction through failure mechanisms identified by yield design approaches. If we consider the vertical force, the bearing capacity is at stake. The failure of the soil foundation system may occur if such failure mechanisms are triggered into the soil. For the horizontal force H, the sliding of the soil foundation interface may be critical. Finally, for the overturning moment M, the soil foundation interaction leads to different failure mechanisms depending on the load eccentricity. Each failure mechanism being identified, the seismic design of shallow foundations should determine the critical force combination between H, V and M, in this 3D plot. Considering the combination between the vertical force and the moment first, we get the bounding curves in red in the M/V vertical plane. It may be assessed for quasi static as well as dynamic loadings. Considering the combination between the vertical and the horizontal force, we now get the bounding curves in blue in the H/V horizontal plane. Finally, considering the combination between the horizontal force and the moment, we now get the bounding curve in green in the M/H vertical plane for a given vertical force. Changing the value of the vertical force, we get various green bounding curves, creating a bounding surface for the various failure mechanisms: bearing capacity, sliding and overturning. This may be called the "rugby ball" approach. Considering simulations of dynamic loadings by Gazetas, a single building on a shallow foundation may experience a bearing capacity failure on the left hand side at t=4s. Then the soil failure on the right hand side at 8 s occurs and finally at 17 seconds the failure mechanisms on both sides appear simultaneously. For two buildings, the results are significantly different: bearing capacity failure only on the left hand side for the left building, only on the right hand side for the right building all along the seismic sequence, that is t=4s at the top, 8 seconds at the middle and 17 seconds at the bottom. Moving from the simulations to real life, we get similar failure mechanisms for this soil-foundation-structure system. It is worth including such effects in the initial seismic design. How does it work for deep foundations? We previously mentioned the kinematic and inertial effects. Let's try to model the soil foundation interaction for single pile through its horizontal and vertical motions. For the horizontal motion, crucial under seismic excitation, we may consider several horizontal springs to model the interaction with each soil layer. They can be obtained from the so-called p-y curves estimated experimentally or numerically. For the vertical motion, a vertical spring is also added at the pile tip in green. To fully model the vertical soil foundation interaction, we should also model the shear process at the soil-pile interface. Various shear stiffnesses are estimated from the so-called t-z curves, but this is for a single pile only. How can we assess the interaction for several piles? Considering a foundation with four piles, we may wonder if the global stiffness is simply four times that of the single pile. Same question for 9 piles. We shall thus compare the horizontal stiffness of the NxN piles system to N^2 times the horizontal stiffness of the single pipe K_X^1. We shall also consider different values of the pile spacing to the ratio S/d, where S is the spacing and d is the pile diameter. Plotting the normalized global stiffness with respect to the normalized frequency omega d / Vs, the values are generally higher than that of N^2 single piles. The higher stiffness is due to the so called group effect in the pile system. It is also higher for 9 piles in gray than for 4 piles in blue. For a shorter pile spacing, S/d equals 5 instead of 10, the global stiffness is larger due to a stronger group effect. The larger stiffness values are logically obtained at higher frequencies. Let's now identify such interactions experimentally. We consider a pile foundation, including 5 piles: four at the corners and one at the center of the raft. This is a reduced scale model of the soil-foundation-structure system tested in the IFSTTAR centrifuge in France. The artificial gravity forces allow to reproduce realistic stress states with respect to the actual large scale foundation. Let's now plot the results in terms of moment at the corner of the foundation, first graph, and at the center, second graph. The acceleration is shown in red at the bottom. It corresponds to the Northridge earthquake. The moments in both piles in blue appear to be different and are not symmetrical. Following the variations of the excitation, we check the maximum moment profile in each pile. Finally, we may proceed to the seismic design of such a foundation system. Since we have identified the variations of moments with respect to the ground acceleration as well as the maximum moments in each pile. How does it work in the field for actual quakes? For the Loma Prieta earthquake in 1989, severe damages were observed at the pile-structure interface. As you can see on this bridge, some of the piles even penetrated the bridge deck, this was a very strong soil-foundation-structure interaction. So are we done with a rugby ball for shallow foundations and moment profiles for pile foundations? Not so sure when soil foundation interaction is influenced by strong liquefaction phenomena as it was observed near this house in New Zealand. In such cases, shallow foundations may suffer large settlements, and the piles can move freely in the liquefied soil, thus leading to small moments but huge lateral displacement!
