On the Proper Estimation of the Confidence Interval for the Design Formula of Blast-Induced Vibrations with Site Records

Blast-induced ground vibration has received much engineering and public attention. The vibration is often represented by the peak particle velocity (PPV) and the empirical approach is employed to describe the relationship between the PPV and the scaled distance. Different statistical methods are often used to obtain the confidence level of the prediction. With a known scaled distance, the amount of explosives in a planned blast can then be determined by a blast engineer when the PPV limit and the confidence level of the vibration magnitude are specified. This paper shows that these current approaches do not incorporate the posterior uncertainty of the fitting coefficients. In order to resolve this problem, a Bayesian method is proposed to derive the site-specific fitting coefficients based on a small amount of data collected at an early stage of a blasting project. More importantly, uncertainty of both the fitting coefficients and the design formula can be quantified. Data collected from a site formation project in Hong Kong is used to illustrate the performance of the proposed method. It is shown that the proposed method resolves the underestimation problem in one of the conventional approaches. The proposed approach can be easily conducted using spreadsheet calculation without the need for any additional tools, so it will be particularly welcome by practicing engineers.