Blasting pattern design using dominant frequency and permissible peak particle velocity

The energy released from an explosion propagates through the surrounding rock-mass in wave forms, causing structural vibrations in the vicinity of the explosion blocks. The waves are spread as body as well as surface waves. Resonance occurs when the frequency of the explosion wave is the same as the associated structures, leading to increase the damage to them. Hence, in designing the explosion patterns, the allowable peak particle velocity of these structures should be considered. Several correlations (Pears, 1955; Allsman, 1960; Speath, 1960) presented in the literature, express the parameters involved in evaluating the explosion effects including the explosive characteristics and the rock-mass strength. Ash (1968), proposed a simple relation based on the diameter of blast-hole to determine the burden required and Livingston (1956) suggested a relation on the basis of “crater theory” to determine the spacing. However, the influence of blast-wave has not been considered in the conventional explosion design patterns. In this study, a neural network was trained in order to design a explosion pattern based on the maximum allowable vibration. This network tried to design a blasting pattern by special attention to the allowable peak particle velocity and the natural frequencies of the buildings adjacent to blasting area. For this purpose, the ground vibration data from 11 blasts were recorded by PDAS-100 digital seismographs and 3-C L-4C seismometers. Seismographs were installed in three vertical, tangential and radial directions. 47 of the recorded vibrations were employed in a neural network training which used a back propagation algorithm for training. The network consisted of four hidden layers and one output layer composed of three neurons. The training algorithm of each hidden layer was a Levenberg- Marquardt designed to approach a second-order training speed without having to compute the Hessian matrix; Tan-sigmoid transfer function was employed for the hidden layers and a linear transfer function pureline was used for the output layer. For adequate network training process, a series of appropriate response should be ensued. During the training, in order to minimize the performance, the network weights and biases were corrected. In this study the network performance was evaluated using a mean-square error when compared to the output and the real data. The input parameters included the peak particle velocity, frequency, volume of the extraction block and the explosive density, while the outputs included the burden, spacing and the total charge weight. The other parameters of the blasting pattern such as stemming, sub-drilling were calculated by empirical equations and the blasting delay was determine by the blasting designer. The network was trained successfully at the 8920th epoch with a mean square error of 6.1910−16. To ensurecorrect training, the network was tested using the test data and was able to achieve the total charge weight, burden and spacing with coefficient correlations of 0.65, 0.77 and 0.96, respectively.