Transverse vibration frequency and the key influence factors of fully grouted rock bolts in layered rock mass

Health monitoring of fully grouted rock bolts (FGRBs) remains challenging in geotechnical engineering, despite their widespread use as primary support elements in fractured rock masses. This study established a governing equation for the transverse vibration and derived an analytical expression for the FGRB’s transverse vibration frequency ( f ) based on beam transverse vibration theory. Case studies were performed to investigate the effects of axial bolt load ( T ) and dynamic stiffness coefficient ( K ) on the FGRB’s natural frequency ( f ). The intrinsic components of K were thoroughly analyzed for both rock and resin anchorage materials. Numerical simulations were conducted to validate the theoretical derivation results and elucidate the FGRB’s transverse vibration characteristics at different axial positions in single-layer and multi-layer rock masses. The theoretical results indicated that f varied logarithmically with K . The effect of T on f was negligible relative to that of K . This finding contrasts with partially grouted rock bolts, where T strongly influences the free segment’s transverse vibration response. The K of resin anchoring agent-rock mass composite specimens was primarily governed by the mechanical properties of the rock mass. Numerical simulations also revealed a logarithmic relationship between f and the elastic modulus ( E ) of the rock mass, which agrees with and indirectly validates theoretical predictions. The FGRB’s f in the layered rock mass varied stepwise along the longitudinal axis. This variation was accompanied by noticeable interface effects. These observations can inform estimates of layer thickness and lithology.