Closed-form solutions to investigate the nonlinear response of foundations supporting operating machines under blast loads

Machine foundations are subjected to significant dynamic impacts. These impacts could spread to the surrounding regions, affecting workers, sensitive equipment in the same institution, or nearby areas. This study analyzes the response of machine-supporting foundations to harmonic and explosive loads under operational conditions and provides closed-form solutions for predicting responses in terms of displacement, velocity, and acceleration time-histories to two common types of blast loads: a more accurate typical profile and simplified triangular profile. The soil-machine foundation system is regarded as a single-degree-of-freedom (SDOF) system that exhibits elastic–perfectly flexible resistance behavior. For the analysis of the SDOF system, two cases are considered: one assumes that the supporting soil keeps elastic during the explosion, and the peak displacement is less than the elastic one, while the other assumes that the blast occurs in an elastic state, and the peak displacement occurs in a plastic state. By using the closed-form analytical solutions, a detailed parametric analysis is carried out to evaluate the impacts of significant soil-foundation system characteristics such as mass, stiffness, and damping ratio on the response-time history of machine foundations. The findings are compared to those reported in the literature, and relevant conclusions are derived. Obtained results demonstrated that, despite its simplicity and usage of only positive phase to simulate blast loads, the simplified model's response behavior differs significantly from the typical one. Furthermore, the derived solutions are utilized to design the foundations supporting vibrating machines for both harmonic and blast loads in a variety of conceivable scenarios depending on the blast magnitude.