The primary goal of this study is to provide an efficient numerical tool to analyze the seismic performance of nailed walls. Modeling such excavation supports involves complexities due partly to the interaction of support with soil and partly because of the amplification of seismic waves through an excavation wall. Consequently, innovative modeling is suggested herein, incorporating the calibration of the soil constitutive model in a targeted range of stress and strain, and the detection of a natural period of complex systems, including soil and structure, while benefiting from Rayleigh damping to filter unwanted noises. The numerical model was achieved by simulating a previous centrifuge test of the excavation wall, manifested at the pre-failure state. Notably, the calibration of the soil constitutive model through empirical relations, which replaces the numerical reproduction of an element test, more accurately simulated the soil-nail-wall interaction. Two factors were crucial to a successful result. First, probing the natural period of the complicated geometry of the model by applying white noises. Second, considering Rayleigh damping to withdraw unwanted noises and thus assess their permanent effects on the model. Rayleigh damping was applied instead of filtering the obtained results.

This study aimed to emphasize the significance of spatial variability in soil strength parameters on the behavior of nailed walls, highlighting the necessity of probabilistic design approaches. The investigation involved a 7.2-m nailed wall reinforced with five nails, simulated using the local average subdivision random field theory combined with the limit equilibrium method and the FEM, known as the random limit equilibrium method (RLEM) and the random finite-element method (RFEM) approaches. Initially, the wall stability was evaluated by RLEM using 10,000 Latin hypercube sampling realizations. The wall was globally stable among all samples for a correlation length equal to its height (7.2 m). The wall behavior, associated displacements, moments, wall shear forces, nail axial forces, and ground settlements were examined using RFEM. The RFEM analysis reveals that different random fields influence the maximum displacement (H-max), maximum moment (M-max), and maximum shear force (Vmax) experienced by the wall. The cumulative distribution function plots were generated for the wall critical parameters, including H-max, M-max, and V-max. Leveraging the simple weighted averaging and ordered weighted averaging techniques, different combinations of H-max, M-max, and Vmax were assessed with varying weight assumptions. This allowed us to identify critical random field realizations and estimate the level of risk using a newly introduced parameter, the decision index. Finally, the effect of different correlation lengths (isotropic and anisotropic) for two different coefficients of variation of soil strength parameters on the distribution of H-max, M-max, and Vmax was studied. The findings highlight the importance of considering the spatial variability of soil properties to achieve a reliable design of nailed walls.