Estimation of the dissipation due to radiation damping for the pile embedded in soil: A closed-form solution

In the present work, the overall energy dissipation of a pile embedded in the soil, modeled as visco-elastic springs, is thoroughly investigated. The term dissipation is used to measure the rate of decay of amplitude of displacement response in the time domain. The estimation of dissipation in piles is necessary to understand how quickly a pile reaches its steady state or equilibrium under dynamic loads or in cases of free vibration, respectively. A higher level of dissipation indicates a shorter duration of transient vibration, which is a deserving trait for vibration mitigation in extreme events, such as earthquakes, storms, blasts, shocks, etc. The dispersion relation which is a function of wavenumber and free wave frequency is obtained for the pile embedded in the soil medium by implementing the generalized form of Bloch’s theorem. The dispersion relationship is solved in the free-wave approach, in which a real wave number yields a set of complex frequencies. For predicting the overall dissipation of the system from the complex frequency values, an analytical closed-form expression is proposed in this paper. Further, the predicted dissipation is validated with a finite element-based numerical model of the soil–pile system.