In recent years, many pile driving analysis methods are proposed and it is applied to the analysis of actual pile driving. However, there are few papers written in detail about the separation section event (ram, anvil, adapter, pile) which occurs on an actual pile driving, and impulse force influenced by the separation section event.
 In this paper, the above-mentioned subjects proposes that it is theoretically solvable by using an advection equation. An advection equation is drawn in the process in which the general solution (d'Alembert's solution) of a one-dimensional wave equation is solved. And, how to apply an advection equation to the pile driving analysis simulation was also described. Moreover, the validity of this simulation was confirmed by comparing with two or more examples.

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 The present study proposes an estimation curve of crack-depth for the surface of a homogeneous body in terms of numerical simulations based on the impact elastic wave method, specifically the elastodynamic finite integration technique. A rectangular solid specimen with a specified opened crack is modeled for the numerical simulation. Giving Ricker wavelet to the specimen model, we observed the attenuation of wave passing through a prescribed surface crack on the specimen.
 It was concluded from the numerical investigation that the magnitude of attenuation strongly depends on the ratio of wavelength to crack-depth, but hardly on materials used. According to these outputs, the present study formulated the estimation curve of crack-depth and proposed an entire procedure to evaluate crack-depth on the surface of homogeneous body in practical use.

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