Development of a cross-hole transmission wave-based non-destructive testing method for rock bolts

Non-destructive testing of rock bolt support is pivotal to operational safety and stable production in coal mining. However, in-situ characterization of critical parameters-grouting voids and effective anchorage length-remains a prominent geotechnical challenge. To address this, a novel non-destructive testing method for rock bolts based on cross-hole transmission wave theory is proposed. The propagation characteristics of stress waves in the rock bolt-grout-surrounding rock system were investigated through integrated theoretical analysis, laboratory physical modeling, and numerical simulations. By extracting cross-hole first-arrival signals and analyzing their time-history curves and differential features, the response characteristics of rock bolt embedment length, anchorage length, and grouting defects on time-depth profiles were identified. Furthermore, the influence of surrounding rock elastic modulus on the sensitivity of defect detection, the reason of first-arrival wave time lag in defective sections, and the sources of detection error in anchorage length were discussed. Results indicate that detection errors for embedment length, anchorage length, and defect length are less than 5%, 8.57%, and 6.67%, respectively, alongside accurate defect localization. Anchorage defects alter first-arrival wave propagation paths, extending travel distance and inducing arrival time lags, which serve as key diagnostic indicators. While the defect position exerts a comparatively minor influence on detection error, detection precision is positively correlated with the length of the defective section. Moreover, a higher elastic modulus of the surrounding rock enhances wave reflection and refraction at interfaces by increasing the wave impedance difference, thereby improving detection accuracy. This detection method provides an effective technical approach for quantifying anchorage length and precisely localizing grouting voids.