Several Italian cities are characterized by the presence of centuries-old historic walls, which have a cultural heritage value and, due to their structural role as a retaining wall, often influence the safety of adjacent buildings and infrastructure. Ancient urban walls are increasingly subject to instability and collapse phenomena, because the greater frequency of extreme meteoric events aggravates the static condition of the walls and of the wall–soil system. Since the seismic risk in the contexts in which the historical urban walls are located is often medium-high, it is advisable to evaluate the influence of soil moisture on the seismic response of the soil–structure system. In this paper, the seismic vulnerability of historical urban walls was examined through considering scenarios of both dry and wet soil, in order to evaluate the seismic response of the structure as a function of soil imbibition. Seismic vulnerability analyses were carried out on the case study of the historical urban masonry walls of Volterra (Italy), which have been affected by two major collapses in the last ten years. Seismic vulnerability was assessed by means of the limit equilibrium method and the finite element method, and through adopting proper soil imbibition models. The results highlight which sections of the walls are at greater seismic risk due to the presence of soil moisture, as well as the influence of soil imbibition on the structural safety and failure mechanism.

Pile buckling is infrequent, but sometimes it can occur in slender piles (i.e., micropiles) driven into soils with soft layers and/or voids. Buckling analysis of piles becomes more complex if the pile is surrounded by multi-layered soil. In this case, the well-known Timoshenko’s solution for pile buckling is of no use because it refers to single-layered soils. A variational approach for buckling analysis of piles in multi-layered soils is herein proposed. The proposed method allows for the estimation of the critical buckling load of piles in any multi-layered soil and for any boundary condition, provided that the distribution of the soil coefficient of the subgrade reaction is available. An eigenvalue-eigenvector problem is defined, where each eigenvector is the set of coefficients of a Fourier series describing the second-order displaced shape of the pile, and the related buckling load is the eigenvalue, thus obtaining the effective buckling load as the minimum eigenvalue. Besides the pile deformed shape, the stiffness distribution in the multi-layered soil is also described through a Fourier series. The Rayleigh–Ritz direct method is used to identify the Fourier development coefficients describing the pile deformation. For validation, buckling analysis results were compared with those obtained from an experimental test and a finite element analysis available in the literature, which confirmed this method’s reliability.