**5. Conclusions**

An experimental study including determination of a correlation between grouting percentage and first three natural frequencies of a laboratory rock models was conducted. In total, 94 di fferent combinations of di fferent grouting percentages and positions were tested. Prior to testing, a data acquisition setup was established consisting of a custom-made nut for positioning of the accelerometer, a hammer made of soft steel for the generation of a dynamical impulse, a vibration input module, and a developed software program. By analyzing the statistical distribution of the data and by establishing a regression function (second order polynomial functions were employed) and regression coe fficients, it was shown that a high correlation exists between the natural frequencies and the grouting percentage. This clearly demonstrates the benefits of analyzing first, second, and third natural frequency for determination of grouting percentage along the rock bolt and provides better understanding of rock bolt dynamic response when compared to previous studies which analyzed only dominant frequency. Following experimental testing, the objectives of the numerical simulation included comparison with experimental results, as well as the analysis of the e ffect of the grou<sup>t</sup> sti ffness on the frequency response of rock bolts. When comparing the results of numerical analyses with the results of experiments, a similar general increasing trend of the first three natural frequencies with a reduction in grouting percentage is clearly visible. Moreover, the values of the natural frequencies obtained by numerical analysis have approximately the same values as the natural frequencies obtained by experimental testing. Numerical analyses have also shown that the reduction of the modulus of elasticity of the grouting mixture, leads to the reduction of the values of the natural frequencies while the variation of the elastic modulus does not a ffect the general trend of increasing natural frequencies with the reduction in grouting percentage, whereby the shape of the natural frequency—the grouting percentage curve is independent of the modulus of elasticity. The potential of using numerical methods, which are properly calibrated, for analysis of more complex grouting defects is therefore evident. Overall findings of this study are in establishing a clear correlation between first, second, and third natural frequency of rock bolt and the percentage of grouting along the rock bolt. After the proposed grouting evaluation method is validated in situ condition, it can be used as a control quality measure to check whether the installation procedures conform with the design requirements. However, because of the change of natural frequencies with rock bolt load increase, the method is applicable only to non-loaded rock bolts, tested immediately after their installation.

**Author Contributions:** Conceptualization, M.B. and M.S.K.; Data curation, M.B.; Formal analysis, M.B. and M.S.K.; Investigation, M.B. and D.J.K.; Methodology, M.B. and M.S.K.; Validation, M.B. and D.J.K.; Visualization, M.B. and D.J.K.; Writing—original draft, M.B. and M.S.K.; Writing—review & editing, D.J.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Commission Innovation and Networks Executive Agency, project DESTinationRAIL (Decision Support Tool for Rail Infrastructure Managers), gran<sup>t</sup> number. 636285.

**Conflicts of Interest:** The authors declare no conflict of interest.
