Statistical models for ground vibration and airblast

Abstract

It is becoming increasingly important to be able to predict and reduce ground vibration and airblast so that mine operations may achieve their environmental requirements. The observed vibration and airblast at any monitoring location is influenced by variables such as the weight and type of explosive used per delay, the delay time sequence, scatter in that sequencc. the spatial pattern of blastholes and properties of the transmitting medium. The present work shows how the separate influence of these variables may be analysed using a Monte Carlo model that has a predictive power superior to that of the traditional charge weight scaling laws.Charge weight scaling laws have sometimes been observed to give acceptable predictions at a fixed monitoring location for the consistent use of a particular blast design. However, unlike the Monte Carlo model, such laws cannot be used to predict the likely changes in vibration due to any planned changes in blast design.Monte Carlo predicted contours of airbhst and vibration show that the blasthole locations and the direction of initiation have a considerable effect at any monitoring location. This is due to influences such as the finite travel time of the disturbance as well as thc screening effect. The travel time delay between blastholes is more significant for airblast since the velocity (334 m/s) of sound in air is typically 10 times lower than the speed of vibrational waves through the ground. It is also well known that previously fired blastholes may provide a screen for both airblast and Vibration produced by a current hole as it initiates. In the case of airblast, screening may occur due to thc airborne particulate matter produced by previous holes; in the case of vibration, screening may occur due to ground fractured by these previous holes.

Non-linear superposition models of blast vibration

“…The second mechanism is attenuation due to vibration screening whereby the severe and localised damage zone of some of the previously initiated holes lies in the direct path between the initiating hole and the vibration monitor. Such vibration screening has already been given in a previous model [7], which, incidentally, transforms it into a non-linear superposition model. However, an improved screening model is given in the present work.…”

“…In this process, each seed waveform representing each single blasthole is displaced in time according to the delay sequence and appropriately added. The complete description of this model is given in [7] and will not be repeated here except for that detail relevant to the present work. Under linear superposition, each blasthole contributes to the total vibration independently of any other hole.…”

“…The screening contribution from the offaxis hole located at B can then be given by a Gaussian Bell factor, exp(Àk nj 2 ), where k ¼ p nj /s P . The treatment on blasthole screening reported in [7] yielded the following screening function, S n , to describe the degree of screening of vibration from the nth hole along a direct path to the monitor:…”

“…Experimental data on vibration screening for holes located along the line OM has been reported in [7], and a simple two-dimensional model was used to calculate the screening effect in which all holes lying within a specified rectangular area contributed equally to the screening. This model is now upgraded to estimate screening in three dimensions and also to account for off-axis holes (using the Gaussian Bell).…”

“…To mimic a full-scale blast, linear superposition models have also been used to predict the total vibration due to a collection of blastholes [4][5][6][7]. However, it is well known that blasting induces a highly non-linear response in the near-field of the material under consideration, and thus non-linear superposition might be appropriate.…”