Blasting-induced dynamic loads are a primary risk factor for failure in underground support structures. Based on the wave-function expansion method, this study develops a dynamic response model of a surrounding rock-anchoring agent-bolt system subjected to cylindrical P-wave incidence. A dimensionless dynamic stress concentration factor (DSCF) is introduced to characterize the stress within the system. The influences of blasting source frequency, impact distance, anchoring agent thickness, and material impedance mismatch on the evolution of DSCF are systematically analyzed. Parametric analyses reveal that low-frequency excitation leads to lower and more uniformly distributed DSCF. The thickness and shear modulus of the anchoring agent significantly affect the magnitude and directional distribution of DSCF. The LS-DYNA simulations validate the model's ability to capture wave propagation, interface reflections, and stress concentration, confirming that reflected shear waves govern circumferential stress and make the 90° direction most prone to tensile failure. Physical model tests further verify this trend, with higher 90° strain and stronger internal interface response, supporting the model's engineering applicability. A three-dimensional response surface is established, incorporating frequency, impedance, and thickness. Based on this surface, a quantitative optimization strategy is proposed: within the parameter space examined here, thickness ratios in the range of 1.4–1.8 reduce DSCF, combined with suitable impedance matching, can effectively minimize DSCF under multi-frequency excitation under the adopted model assumptions. This study establishes an analytical framework and validated failure mechanism for radial dynamic stress concentration, and proposes a quantifiable design criterion that enables more reliable optimization of anchorage systems under blasting loads.
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