Dynamic impedance and compliance surfaces of twin adjacent surface foundations under synchronous and asynchronous loads

The 3D dynamic response of twin rigid massless foundations under concurrent time-harmonic loads in a finite soil region resting on a homogeneous visco-elastic half-space is studied. The mechanical model is based on an efficient approach combining the boundary element method (BEM) for the semi-infinite far-field zone and the finite element method (FEM) for the finite near-field geological region. The accuracy and convergence study of the hybrid computational scheme based on the macro-element concept is presented. A parametric study revealing the sensitivity of the dynamic response to the following key model parameters: (1) Poisson’s ratio of the semi-infinite zone; (2) separation distance between foundations; (3) material damping; (4) the foundations’ geometry; and (5) the phase shift between the acting harmonic loads is presented. The obtained results show resonance patterns as a result of the mutual play between foundations’ geometry, their spatial arrangement, and soil properties. Approximation formulae are proposed to estimate the resonance states. The results also show that the effect of material damping cannot be fully decoupled from the impedance functions using the conventional formula. ... mehrFurther, the presence of a phase between harmonic loads acting on the foundations influences the resonance state, and negligence of it may lead to unexpected responses of the foundations. An efficient optimization of the dynamic design of structures with adjacent foundations, such as bridges, offshore and onshore infrastructures with multiple foundations, machinery, or adjacent structures, could be performed using the obtained results. For better accessibility, the solutions are presented in the form of 3D impedance and compliance surfaces, and they are readily downloadable as interactive figures. A calculation example is given in the appendix.