Anchor bolts, such as rock bolts and concrete anchors, are widely used in civil, geotechnical, and mining engineering for anchorage and ground support. They are used in retaining walls, dry docks, dams, mines, and prestressed concrete structures. Evaluating the grouting condition of anchor bolts is essential to ensure the safety of these applications. Spectrum techniques have been used to develop non-destructive methods for estimating the grouting quality of grouted anchor bolts. The spectrum methods include fast Fourier transform, time–frequency analysis, wavelet transform analysis, and empirical mode decomposition. In this study, we introduce the parameter-optimized variational mode decomposition (VMD) method for the spectrum analysis of impact echo signals of anchor bolts. This method overcomes the difficulty of conventional spectrum methods that cannot separate highly coupled natural modes for advanced analysis. The parameter-optimized VMD method enables the generation of a new evaluation index for quantifying bolt grouting conditions, which has the potential to significantly enhance the quality evaluation of anchor bolts compared with conventional analysis of natural frequencies. This study uses impact response to establish a new benchmark for the integrity diagnosis of anchor bolts, paving the way for more accurate and reliable safety assessments.
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