Analytical Solution of the Dynamic Response of Piles under Blast Waves

Abstract

Several studies have addressed the effect of blasting on piles, but none of them has used an analytical method to find the piles blast-induced peak particle velocity (PPV). In this paper, the response of piles to ground shocks induced by surface blast is presented using mathematical analysis. In order to construct mathematical model, pile was modeled as beam and its displacements were calculated under blast wave equivalent dynamic load. Mathematical modeling of the problem resulted in a fourth-order nonhomogeneous partial differential equation which had to be solved so that the pile displacements and PPV could be found. Since it was not possible to solve the problem in time domain, first, time domain was converted to frequency domain by Fourier transform, and then, the differential equation was solved. Finally, the solution was transformed to time domain and blast-induced PPV was found using a computer code. In addition to verify results of analytical solution, a finite element modeling was generated, and its results are compared with analytical solution results. The techniques applied in this paper and its findings provide valuable information to find a safe distance between blast source and piles.