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Accurate prediction of blasting vibration associated with tunnel engineering is essential to ensure the safety and stability of tunnel excavation and to prevent any damage or distress to adjacent existing tunnels. Based on the dimensional analysis principle, this paper deduces the classical Sadovsky formula, analyzes its limitations from a mathematical point of view, and proves the feasibility of using this principle to derive a prediction model of blasting vibration. On this basis, considering the influence factors of blasting vibration such as the rock density, delay initiation time, and number of free surfaces, a new prediction model that can simultaneously consider the influence of the vibration in near-field and far-field blasting is proposed, and its rationality is explained. Combined with a case study, comparative analysis, variance analysis, and Akaike information criterion, the results show that the new prediction model can effectively solve the difference in blasting vibration in different types of blast holes and different areas, and the calculated results are in better agreement with the monitoring data than is the Sadovsky formula. Overall, this study provides a new solution and reference for more accurate prediction of blasting vibration.