Uncertainty Estimation in Blast Vibration Attenuation Model Using Bayesian Probabilistic Approach - Mining, Metallurgy & Exploration (2021)

The drill and blast method is the most prominent rock excavation method used in mining and civil engineering projects. The ground vibration is the most undesirable effect of the blasting and needs to be controlled. The blasts are designed so that ground vibration at nearby structures must remain under the prescribed limit. Various empirical blast vibration attenuation models have been presented to estimate the ground vibration for designing purposes. These models assume ground vibration as a function of distance and maximum charge per delay. United States Bureau of Mines (USBM) model is most commonly used for the blast design. However, the uncertainty associated with these models is seldom characterized, thus diminishing its reliability. The probabilistic Bayesian approach associated with the Monte Carlo method can easily quantify uncertainties associated with the model and its parameters. Thirty-three blast vibration observation data from a granite quarry in Kerala, India, is used to estimate the probability distribution of model parameters. Markov Chain Monte Carlo (MCMC) approach is used for sampling 12,000 samples for obtaining the posterior distribution of parameters. The uncertainty associated with model parameters is quantified from the posterior distribution, and this is further used to estimate the credible and prediction limits of the model. The point estimate of the most optimum value of the parameter is estimated using maximum-aposteriori or MAP estimate. The model parameters are also obtained using the commonly used least-square error method, which is a maximum likelihood estimation or MLE approach. It has been observed that the accuracy of the model obtained using both MAP and MLE approach is almost equal. However, the MAP estimate as per Bayesian probabilistic analysis has the added advantage that it can estimate the uncertainty of parameters as well as the model, which is not possible using the MLE approach.