## 3 Numerical and Experimental Verification
### Experimental Verification
Figure 10b shows a comparison of the measured arrival time of the ultrasonic pulse with that calculated using Equation (2). The error between the measured value and the theoretically calculated value was found to be within about 5%. Figure 9: Details of the specimens and the location of the transducer: (**a**) test specimen; (**b**) top view; (**c**) side A; (**d**) side B. Figure 11 plots \(x_{i}\) were obtained by substituting the measured arrival time of the ultrasonic pulse into Equation (6) with respect to the position of the receiver for the considered specimens. Here, the adopted P-wave velocities in the anchor bolt and concrete were those actually measured in the specimens and were, respectively, 5906 and 4126 m/s. For specimen E100C100, the value of 0.02 that was used in the numerical verification was applied for the regularization factor and the corresponding results are shown in Figure 10(a). However, for specimens E200C100, E300C100 and E100C200, the transferred distance of the ultrasonic pulse through the anchor did not converge within the measurement range when using 0.02 for the regularization factor and the embedment length of the anchor could not be determined. Subsequently, the regularization factor was adjusted to 0.01 to secure the convergence for the specimens E200C100, E300C100 and E100C200. This decrease in the regularization factor resulted in a slight loss of the accuracy in the estimation of the embedment length of the anchor due to the wider dispersion of the results. The results for E200C100, E300C100 and E100C200 are plotted in Figure 10(b)-d, respectively. The values of the measured arrival time of the ultrasonic pulse include noises from various variables such as the error in the P-wave velocity in concrete and the anchor, the error brought by the material heterogeneity of concrete, the error due to the regularization factor and the anchor. Figure 10: Arrival time of ultrasonic pulse in the specimen with the different embedment lengths of the anchor bolt and cover thicknesses: (**a**) the variation in arrival time of the ultrasonic pulse according to the distance of the receiver from the top surface; and (**b**) the measured value vs. calculated value. the difference in the position of the transmitter and receiver, and the error caused by the refraction and reflection of the wave at the interface between the anchor and the concrete [22; 42]. However, the results were seen to resemble the theoretical result shown in Figure 3.  
The distance of the receiver from the top surface at which the value of the transferred distance of the ultrasonic pulse through the anchor starts to converge was determined to be approximately 300 mm for specimen E100C100 by the engineer's decision. Then, the embedded depth of the anchor was estimated via the ultrasonic pulse by the average of the values of the transferred distance of ultrasonic pulse through the anchor for the distances of the receiver from the top surface larger than 300 mm. The embedment length of the anchor for specimens E100C100, E200C100, E300C100, and E100C200 estimated by this approach were, respectively, 92.7, 173.0, 255.4, and 74.4 mm of which errors were 7.3, 13.5, 14.9, and 25.6% compared to the actual depths (see Table 4). The higher accuracy of the estimation achieved for specimen E100C100 compared to the other specimens can be explained by the relatively faster convergence of the transferred distance of the ultrasonic pulse through the anchor, which provided a larger number of data to calculate the average that is used to estimate the embedment length. In addition, the utilization of a relatively greater regularization factor for E100C100 also helped in the improvement of the accuracy.