Application of Closed-Form Solution for Normal Surface Displacements on Impacted Half Space: Quantification of Impact-Echo Signals

In order to investigate the feasibility of deducing a simulated transfer function based on the Rayleigh wave form in an Impact-Echo signal, the analytical solution for the normal surface displacement due to a heaviside force at the half-space was reviewed and used to compute the surface displacement responses resulted from various types of impulse forces. Based on a series of numerical studies on the characteristics of Rayleigh wave form in the surface displacementresponses, this paper presents the idea of using an equivalent impact force to derive an intentionallyscaled transfer function. The pseudo force can be obtained from using Rayleigh wave form as a pseudo force or by generating an equivalent half-sine impact force accordingly. The effect of using such pseudo and equivalent force functions was discussed in details. In the proposed method, the force amplitude was first estimated from an amplitude curve established from numerical simulations using half-sine force functions. The recovery of a simulated transfer function was next achieved via the use of an estimated force amplitude and a selected force function. The proposed procedure also results in steady thickness amplitudes when measurements on two concrete plates were taken for various impacts associated with different steel balls and different impact locations. The success in recovering constant thickness amplitudes for plate-like structural members proved that the derivation of simulated transfer function is a useful tool in extending the Impact-Echo test. The quantitative evaluation of the interfacial property of the substrate layer will also benefit from this simulated transfer function.