An analytical accurate analysis for uniform and damped soil supported on elastic rock

Prediction of ground motion by earthquakes is still the main issue for seismologists, engineers, and researchers. In this paper, the site response analyses (SRAs) have been carried out by considering the homogeneity, heterogeneity, and non-linearity of the soil, and the randomness of the seismic input. Analytical differential equations have been solved by calibrating boundary conditions. In this sense, the analyses can be considered accurate since the different effects have been studied separately in a more advanced way. The calibration has been made by using previous published studies and reliable software. Results are expressed in terms of horizontal displacements, accelerations, shear strains, and stresses. Results show that the heterogeneity effects depend on the shear wave velocity reaching, for heterogeneous soil, a value 10 times greater than that for homogeneity soil. Regarding the non-linearity and dynamic effects are more complicated to be framed by a unique conclusion. However, for some cases, the results appear similar to previous studies. In a more global way, it was possible to estimate direct approximations for non-linear homogeneous, dynamic homogeneous and heterogeneous soil in function of input data regarding the earthquake, usually known, as peak ground accelerations (PGAs) and maximum frequencies.