A 3D Analytical Approach for Determining Natural Frequency of Retaining Walls

Most of the proposed methods for obtaining the free vibration natural frequency of the retaining wall have been presented, assuming the behavior of the wall in two-dimensional domain, and they are not able to express the three-dimensional behavior of these structures in a satisfying manner. In this paper, the plate theory is employed to analyze the free vibration of wall-soil system in three-dimensional domain. So the retaining wall is modeled as a clamped-free plate and the stiffness of the soil existing behind the wall is modeled as a set of springs. Using the approximate Rayleigh method, new analytical expression for obtaining the free vibration natural frequencies for the three first modes of the wall is represented. The results of the proposed model are compared with both the results of the other researchers and the ones from finite element method (FEM). They are also compared with the results of a full-scale experiment and it shows a good agreement. The comparison shows that modeling the wall in two-dimensional form is not accurate enough to calculate all the natural frequencies of the wall. The results of this paper show that there is a considerable difference between two- and three-dimensional behavior of the walls. The proposed method also gives the free vibration natural frequencies of the wall extensional modes with an acceptable accuracy. Finally, the effect of tensile and compressive behavior of the soil on the fundamental frequency is studied. This research can be considered as a new field in three-dimensional calculation of the retaining walls.