Numerical simulation of torsional guided wave propagation in grouted rock bolt

Numerical simulation was conducted to study the propagation properties of torsional guided wave in grouted rock bolts. Finite element models of a free bolt and a grouted bolt were established; and torsional guided waves with frequencies of 20-60 kHz were excited at the top of the bolts. The numerical results of guided wave velocities in the free bolt and in the anchoring section of the bolt agree well with the theoretical results. The result proves that the finite element method is an effective way to simulate torsional guided wave propagation in grouted rock bolts. The results of numerical simulation show that both the attenuation values of torsional guided waves in the free bolt and in the anchoring section of the bolt increase linearly with the increase of excited wave frequency. Meanwhile, the reflection amplitude of guided waves from the upper interface of the grouted rock bolt decreases. Torsional guided waves attenuate greatly in the anchoring section of the bolt; and reflected waves from the embedded end of bolt are not able to be captured; as a result, torsional guided waves are not applicable for bolt length testing. When the elastic modulus of grout material increases, the amplitude of upper interface reflected wave increases; so the upper interface reflected wave can be used to evaluate the elastic modulus of grout material.