Analytical method for calculating natural frequencies of geosynthetic-reinforced wall with full-height concrete facing

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Abstract
Based on the theory of beams on elastic foundations, a new analytical solution for calculating the natural frequencies of reinforced-soil retaining walls is presented. The assumed retaining wall is geosynthetic-reinforced, with a full-height rigid concrete facing (a GRS-FHR wall). The current study takes into account the rigid body motion of these walls for the first time, and two analytical formulae for calculating the natural frequencies of the rigid mode of deformation for reinforced retaining walls are presented through an exact solution. Next, applying the energy method, a new analytical formula for calculating the natural frequency of the flexural deformation mode is developed. Another innovation is the modeling of the foundation soil with both rotational and translational springs, which makes it possible to consider rocking and sliding deformation modes for retaining wall motion. Moreover, the effect of backfill soil interaction is taken into consideration by translational springs along the wall. The results thus obtained are then compared with numerical analysis using Ansys software, and an excellent agreement was observed.

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