# An Analysis of Rock Bolt Dynamic Responses to Evaluate the Anchoring Degree of Fixation
## 4 Discussion  
An investigation of the different causes and mechanisms of the poor anchorage quality of rock bolts was out of the scope of this research; it can be argued that inappropriate control of the grouting preparation and injection processes, the leakage of grouting because of fractures in rocks along the borehole, or an insufficient length of the bolts could be the main factors resulting in poor-quality anchorage. In this scenario, the development of an easy-to-use investigation method to estimate the quality of rock bolts remains a matter \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock Bolt** & **Signal** & **f1 (Hz)** & **f2 (Hz)** & **Notes** \\ \hline R2R2 & & 250 & 600 & \\ \hline \multirow{4}{*}{R15L2} & sig1 & 20 & 270 & \\  & sig2 & \textless{}10 & - & \\  & sig3 & 470 & 700 & Poor-quality record \\  & sig4 & 30 & - & \\  & sig5 & 30 & - & \\ \hline \multirow{4}{*}{R21L2} & sig1 & 1600 & - & \\  & sig2 & 1500 & - & \\ \cline{1-1}  & sig3 & 1400 & - & \\ \cline{1-1}  & sig4 & 1600 & - & \\ \cline{1-1}  & sig5 & 1400 & - & \\ \hline \multirow{4}{*}{R21L4} & sig1 & 390 & 1050 & \\  & sig2 & 420 & - & \\ \cline{1-1}  & Sig3 * & 1000 & 1500 & \\ \cline{1-1}  & sig4 & 330 & 570 & \\ \cline{1-1}  & sig5 & 390 & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Resonance frequency detected for each experiment. * Indicates the only one of the series with high frequency values, an anomalous behavior within the data set. of debate. Wave propagation-based methods are widely used for non-destructive tests of rock bolts because of their low cost and low complexity as well as their application in complex logistical conditions. In this study, we used a method based on a modal analysis that appeared to be extremely robust and suitable for the accurate analysis of the rock bolt response. The deformation state under service should also be considered: in [11], the deformation characteristics of a roof bolt of a mine roadway were examined under the constant pretension force of the bolts, providing evidence that high-pretensioning bolts can not only limit the opening of weak surfaces in the structure, but also increase the shear strength of the structural joints. Modal analyses require an accurate interpretation based on a comparison of the spectral response in the experimental record with the synthetic modeled response. It is necessary to build a theoretical modal model of a rock bolt, and different cases of grouting weaknesses or discontinuity could be modeled as well. The results of a theoretical modal analysis performed using a validated FE model could constitute a reference base for unknown cases where correlation and comparison techniques could be adopted to validate the model response. Methods based on an analysis of reflection events are promising but they are affected by certain drawbacks; direct waves and multiple reflections can mask weak reflection events from grout defects and the bolt end when only one sensor is adopted. Reference [12] focused on a stress wave reflection non-destructive test method for rock bolts using a two-sensor acquisition method. They defined the integrated instantaneous phase difference (IIPD) as an index that could characterize any estimated instantaneous phase difference at the sensors. The method appeared to be promising, but the uncertainty associated with the data processing remained a concern because of the complexity in the accurate detection of the reflected wave arrivals at the two sensors. The accurate and automatic identification of the arrival times of effective reflected waves is challenging. The modal method does not require the adoption of high sonic or ultrasonic frequencies, as in reflection methods, where the wavelength of the waveform should be in the order of few centimeters to ensure the desired spatial resolution.