Numerical simulation of attenuation and group velocity of guided ultrasonic wave in grouted rock bolts

In this paper, the guided ultrasonic wave propagating in grouted rock bolts was simulated with finite element method. An 800 mm partially grouted cylindrical rock bolt model was created. Dynamic input signals with frequency from 25 to 100 kHz were used to excite ultrasonic wave. The simulated waveform, group velocity and amplitude ratio matched well with the experimental results. This model made it possible to study the behaviour of the guided waves in the grouted bolt along its central axis. Analysis of the simulated results showed that the group velocity in grouted rock bolts is constant along the grouted length, and the boundary effect on the group velocity is negligible. This paper also presents methods to determine the attenuation coefficient from simulation and to determine the boundary effect on attenuation at the bolt ends. The analysis showed that the attenuation of the guided wave propagating inside the grouted bolts is similar to the theoretical solution in steel bar with infinite length. After correction for the boundary effects the grout length of a grouted rock bolt can be determined using the measured attenuation, with sufficient accuracy.