Estimation on Embedment Length of Anchor Bolt inside Concrete Using Equation for Arrival Time and Shortest Time Path of Ultrasonic Pulse

The bearings or the seismic isolation bearings that play a critical role in bridge structures are fixed to the substructure by anchor bolts. However, the embedment depth of the constructed anchor bolts does often not reach the designed one and may lead to safety issues. The present study proposes an ultrasonic non-destructive testing (NDT) method to verify the embedment depth of the anchor bolts installed on bridges in-service. The P-wave of 50–100 kHz that is usually used in the NDT of concrete was transmitted from the head of the anchor bolt and its arrival time on the concrete cover was measured. The shortest arrival time of the ultrasonic pulse and the corresponding path were then analyzed to formulate their relationship and obtain the distance traveled by the ultrasonic pulse along the anchor by inverse analysis using the equation error estimation. The instability occurring in the inverse analysis is settled by regularization. Finally, the embedment depth of the anchor bolt can be estimated by the analysis of the graph plotting the position of the ultrasonic transmitter and the distance traveled by the pulse along the anchor. The proposed method is validated numerically and experimentally. The method is expected to contribute to the NDT of civil structures by making it possible to estimate the embedment depth of anchor bolts by the means of ultrasonic transducers using P-waves of 50–100 kHz.