Estimating the propagation delay of a direct or reflected wave in a large concrete caisson by impact with an impulse hammer

Abstract

We present a method for estimating the propagation delay of a direct or reflected wave in a large concrete caisson. When striking a concrete structure with a small impulse hammer, reflection waves are generated from the concrete structure boundary and from a crack if a crack exists. Previously, we assumed that a direct or reflected wave can be represented approximately by a modeled vibration wave. We proposed a convolution between the hammer force and the impulse response expressed by an exponentially decaying sinusoidal wave. Then we used the finite-difference time domain (FDTD) method to investigate details of the vibration wave. The results show that the estimation error in detecting a small reflection wave is not negligible. Therefore, the sensor output should be modeled as the sum of a significant modeled vibration wave and two smaller modeled vibration waves. The propagation delay of the estimated significant modeled vibration wave is equal to the value calculated theoretically from the shape. As described herein, the propagation delays of a direct or reflection wave were estimated for two real caissons situated on land and in the sea. The results show that the estimated propagation delays coincide well with those expected from the concrete structure shape.