Expansion of Blast Vibration Attenuation Equations for Deeply Buried Small Clearance Tunnels Based on Dimensional Analysis

Abstract

The conventional empirical Sadowski formula has low prediction accuracy for the vibration velocity of the mass point in the near zone of the blast source, which makes it challenging to evaluate the damage of the building structures accurately. Considering the main influencing factors of blast vibration, the blast vibration attenuation law of deeply buried small clearance tunnels is investigated using dimensional analysis, and the Sadowski expansion formula is established considering the resistance line and free face. The regression analysis and fitting results were evaluated by combining the actual blast vibration data measured at the excavation site of the three separated tunnels at Badaling Great Wall Station with the post-expansion formula and the Sadowski formula, respectively. The results show that the correlation coefficients of the blast vibration expansion formulae based on the gauge theory for the fitted predictions of blast vibration isotropic velocities in a practical engineering context (0.92, 0.81, and 0.88, respectively) are higher than those of the conventional attenuation formulae, by 12, 10.5, and 6.3%, respectively, indicating that the expanded Sadowski formulae can better predict the blast vibration attenuation generated by the described deeply buried small clearance tunneling project.