Earthquakes propagate from the bedrock to the surface through the overlying soil deposit,which acts as a filter and modify the ground motion characteristics. The variation of the seismic waves in terms of amplitude, duration and frequency content at any depth can be evaluated through a ground response analysis. The local soil stratigraphy, the material properties, the site topography, the ground water table depth and the characteristics of the earthquake (for example, duration, peak acceleration, frequency content) have a high influence on the ground response and on the modelling strategy. The ground response analysis of a soil deposit can be considered as a necessary preliminary study for the dynamic analysis of a structure, since its seismic response is influenced by the geological and geotechnical properties of the supporting soil. Due to its filter effect, the soil deposit modifies the seismic waves by amplifying the signal at some specific frequencies and damping it at some others. If the frequency at which the maximum amplification of the ground motion occurs is close to the natural frequency of the overlying structure, the building and the ground motion are in resonance with one another. This means that the system oscillates with very high amplitudes that can cause great damages in the building.

This example (with elaborated background information) concerns the one-dimensional wave propagation analysis through a clay deposit 40 m thick above the bedrock. One-dimensional analysis can be performed when the soil layers and the bedrock surface are horizontal and they extend to infinity, and the seismic waves coincide with shear waves propagating vertically from the underlying bedrock. This last assumption can be justified considering that the seismic waves, propagating from the earthquake source through the soil, are bent by successive refractions into a nearly vertical path (according to Snell's law of refraction). The problem can be modelled through a soil column with specific features, as described in the attached document.

This example presents the results of a one dimensional site response analysis performed with PLAXIS 2D, aimed at modelling the non-linear dissipative behaviour of soils subjected to an earthquake loading. In this respect, an important role is played by the choice of the constitutive model for the soil. The results of the fully dynamic analysis performed with PLAXIS 2D are compared to an equivalent-linear site response analysis performed with EERA, where the secant shear modulus and the damping ratio are updated in subsequent iterations to be consistent with the level of strain induced in each layer. In PLAXIS , the Hardening Soil model with small strain stiffness has been chosen showing that, for earthquakes characterized by moderate peak accelerations, it is capable to capture the soil behaviour during earthquake shaking. The results from both approaches are compared showing a good agreement.

Relative displacement response spectrum at 3.6 m from the surface level.
Comparison PLAXIS - EERA