Explicit solution of the three-layer soil period, based on the theory of wave vibration equations

The soil’s natural period has been simulated in more realistic conditions in recent years using complex equations. In previous studies, the natural period of soils made of bilayer soils with different characteristics has been determined and formulas have been presented. For three-layer soils, the proposed relations are complex and performed by approximate methods. Those methods are inappropriate to fast and precise calculation. In this study, the natural period of the soil has been solved using explicit and closed solution of wave propagation method. The final equations are simplified to utilize the advantages of this method are providing simple relations and high accuracy of answers. Likewise, the natural period of twolayer soil is determined based on the proposed method. the natural ground period of the layers around Karaj alluvium has been determined using the above method. Additionally, considering a few ordinary conditions (depth of layers and soil qualities), the natural period of the soil has been determined and introduced by graphs. As indicated by the outcomes, weak layer cause to increase the ground natural period, while stiff layer decreases the period. The rate of ground period sharply reduces by considering the strong soil in bottom of the layers. In general, increasing the layers specification ratio, reduce ground natural period; excluding the case where the order of the layers is strong to weak. The difference between the values of period in both states are significant.