The dynamic response magnitudes of retaining walls under seismic loadings, such as earthquakes, are influenced by their natural frequencies. Resonances can occur when the natural frequency of a wall is close to the loading frequency, which could result in serious damage or collapse. Although field percussion tests are usually used to study the health state of retaining walls, they are complicated and time consuming. A natural frequency equation for retaining walls with tapered wall facings is established in this paper using the transfer matrix method (TMM). The proposed method is validated against the results of numerical simulations and field tests. Results show that fundamental frequencies decrease gradually with wall height; soil elastic modulus exerts a great influence on the fundamental frequency for walls with smaller facing stiffness; fundamental frequencies are smaller for a hinged toe than a fixed toe condition, and this difference is smaller in taller walls.

With the increase of the spatial degree of freedom (DOF), the radar system achieves multi-channels data processing and improves the survivability of the radar in the complex jamming environment. When the direction of arrival (DOA) of the jamming is close to that of the target, the conventional method will be ineffectiveness. In this paper, a DOA estimation method with high precision for multiple mainlobe jammings based on sparse reconstruction is proposed. The steering vectors are estimated based on the maximize signal-noise-ratio (MSNR) criterion. Besides, the oblique projection with ℓ 1 -norm singular value decomposition (OP- ℓ 1 -SVD) is performed to accomplish the jamming suppression and DOAs estimation of the target. The proposed method can be applied to the uniform linear array (ULA) model of a practical radar system and can resist at least two mainlobe jammings.