New mathematical model for computing natural frequencies of retaining walls considering soil–structure interaction

In this study, a new analytical model is proposed for estimating natural frequencies of retaining walls, and accordingly three closed-form formulas are presented for calculating the first three natural frequencies. In the first step, rigid body motion of retaining walls is taken into account and two closed-form formulas for calculating natural frequencies of the rigid mode of deformation are presented via exact solution. Next, applying the energy method, a new closed-form formula is developed for calculating the natural frequency of the flexural deformation mode. Another innovation of this paper is the modeling of the foundation soil with both torsional and translational springs that make it possible to consider rocking and sliding modes for retaining wall motion. Additionally, the effect of backfill soil interaction is taken into consideration by massless translational springs along the wall. The results thus obtained from the proposed formulas are then compared with numerical analysis using ANSYS software, and a good agreement was observed.