Hello. In this sequence, we shall move from soil nonlinear behavior in the lab to seismic soil response in the field. First of all, the seismic shaking generates an incident motion propagating upwards. It is reflected and refracted at the rock sediments interface. If a borehole is drilled down to the interface, we may get the so-called borehole motion. Then at the free surface, the seismic response may be either considered at the alluvial site where amplification is expected or at the outcropping bedrock where small changes should be observed. Finally, the seismic response of the structures may be assessed. For a natural quake, such as the Tohoku event in Japan, the seismic soil response may be studied for a specific seismological station here, MYG013. For the Tohoku event, the acceleration is huge since it is found to be larger than 1g at this station. Analyzing the seismic motion in the time-frequency domain, we may assess the time delays for various frequency ranges. For the first arrivals at 50 seconds, the frequency range appears to be higher than for the second arrival at 90 seconds. This is due to the nonlinear behavior of the soil, leading to a modulus degradation and thus, a frequency shift in the response. If we consider a weak event recorded by K-NET in Japan, the amplification is found to be strong at 15 hertz. For a strong event, the amplification is lower due to the nonlinear effects. There is also a significant frequency shift of the amplification peak down to 8 Hz. All these results are onsite observations. How can we model the seismic soil response? The simplest type of model is the 1D analysis. We consider a soil column, the seismic wave propagates vertically, and we generally choose a single motion component. For weak quakes that is linear range for the soil behavior, we may write our favorite transfer function, T*(omega) with respect to the layer thickness, h, and the mechanical contrast, Chi. For strong quakes, this expression is no more valid. Let's consider the Tohoku earthquake in Japan. The soil column may now be modeled numerically through a 1D finite element method for instance. We may consider a vertically propagating wave with either one, two or three motion components. For station FKS011, a so-called 1D-3C FEM model involving three motion components gives the shear stresses with respect to the shear strains in both the xz plane at the top and the yz plane at the bottom. As shown on these plots, the nonlinearities for such a strong event are huge. Is this 1D approach sufficient? In the case of a deep alluvial basin in the French Alps, this 2D analysis through the finite difference method shows the discrepancy between weak and strong motion simulations. The weak response is shown by a solid line and the strong motion by a dotted line. Combining the basin effects and the nonlinear effects, the amplitude for the strong event appears much smaller than that for the weak event. For strong events, are lower amplitudes, beneficial or detrimental. What are the practical effects of such nonlinearities in the soil? We may, for instance, observe settlements due to plasticity, but extensive damages may also be experienced, as in the case of Niigata in Japan in 1964. The buildings have been tilted with respect to their foundations as if the soil has been removed. Why is that? It is due to a peculiar phenomenon occurring in saturated sands. Due to the numerous loading/ unloading cycles, the pore water pressure may increase significantly in the saturated soil. If this excess pore water pressure is large enough, liquefaction can be triggered. It means that the sand particles will float in the water and that the bearing capacity of the soil will be drastically reduced. This was the case in Niigata in 1964. Let's now reproduce the Niigata earthquake in the studio. We first fill this aquarium with water. It is the original sea and the Pangea. Then the tectonic plates move upward. We pour some fine sand in the water. It is similar to the sedimentation process of particles along rivers. We may build this bridge pier with a deep foundation then pour some more sand so we get the free surface with loose sand fully saturated with water. Then, we can build a small house with a shallow foundation. Here it is, we have a soil constituted of loose sand, fully saturated with water, our bridge pier, our small house. Then, we'll move the aquarium on the skateboard to reproduce the seismic shaking. The seismic shaking generates loading cycles, loading and unloading cycles, leading to a pore pressure increase. Above a given threshold, the pore pressure is too large, and the liquefaction process is triggered. As you can see, the small house is drowning into the soil, the liquefied soil. In the lab, we may study liquefaction through a cyclic triaxial test but with a saturated specimen. The cyclic loading plotted in green induces cyclic axial strain in red. After several cycles, the axial strain in red increases significantly due to the pore pressure build-up in blue. After 200 seconds, the saturated sand specimen is fully liquefied. Its bearing capacity is thus nearly zero. What happens in case of an actual seismic shaking? Here is a video taken in the center of Tokyo during the Tohoku event. As you can see, 250 kilometers far away from the epicenter, the shaking is both strong and slow. The loading/unloading cycles generate a pore pressure build-up into the soil. The excess water pressure mixed with sand is ejected at the free surface, creating small geysers and sand boils. As far as seismic soil response is concerned, liquefaction is probably one of the most dangerous consequences of strong quakes.
