An analytycal method for calculating the natural frequency of retaining walls

For calculating the natural frequency of structures such as buildings, chimneys, bridges and silos appropriate analytical formulas exist. However, in the case of retaining walls undergoing the soil pressure at one side, calculating the natural frequency is not a straightforward task and requires the effects of soil-structure interactions to be considered. By modeling the soil as series of linear springs, a new formulation is presented in this article, to calculate the natural frequency of retaining walls. This formula considers the vertical cross sectional width change, and hence, enables us to calculating the natural frequency of retaining walls with different types of backfill. The geometrical properties of the retaining walls and its bending rigidity together with the soil’s modulus of elasticity and its Poisson’s ratio are the most important parameters to calculate. A comparison of the results for retaining walls with constant cross section obtained from the suggested method with those of the software analyses was carried out and good agreement was detected. A second comparison of the results with those of other researchers revealed that the natural frequency of flexible retaining wall is an upper bound for natural frequency of rigid walls. The Selected shape function is also very close to the real shape mode.