Waveform Analysis And Predictive Stochastic Model Study Of Bench Blasting Vibration Velocity

In this paper,a large number of blasting vibration field tests are carried out,and the characteristics of the measured blasting vibration velocity waveform are analyzed.The values below determine the empirical prediction equations of the model parameters.Combined with the seismic wave superposition theory,the stochastic model of blasting vibration waveform is extended to the prediction of the multi-hole millisecond blasting vibration velocity.Finally,the vibration reduction calculation is carried out for the equal interval delay blasting.The main research results are as follows:（1）The results of field testing and analysis of the blasting vibration velocity waveform show that despite the blasting source conditions being consistent,after propagating through the rock mass medium,both the blasting vibration velocity waveform and its vibration elements exhibit randomness;blasting vibration velocity waveforms.In the time domain and frequency domain,it shows strength non-stationarity and frequency non-stationarity:the amplitude of vibration velocity in the time domain has experienced three stages of amplitude increase,peak value,and zero reduction,frequency components contained in vibration.And the corresponding amplitude changes with time history in the frequency domain,and the frequency distribution shows an exponential decrease trend over time as a whole.（2）In order to reflect the randomness of the blasting vibration velocity waveform and the non-stationarity in the time and frequency domains,a mathematical model of modulation and filtering white noise was selected to describe the blasting vibration velocity waveform,and combined with the detailed characteristics of the blasting vibration waveform,a Gamma function was constructed as the intensity envelope function and the blasting vibration random waveform model with the pseudo-velocity response of a single degree of freedom system under unit pulse as the unit impulse response function.All parameters in the model can be divided into intensity parameters I₀,αandβ,and frequency parametersη,γ,andξ.（3）According to the source of the vibration random model parameters,the identification methods of the intensity parameters and frequency parameters are respectively determined:for the intensity parameters,the combination of the peak point position of the seismic wave and the normalized cumulative energy curve improves the previous identification method of directly fitting the cumulative energy curve of the seismic wave,Which reduces the number of regression parameters and improves the recognition accuracy;for frequency parameters,in view of the simple structure of the single-hole blasting seismic wave waveform,the frequency time-varying parametersηandγare identified based on the seismic wave half-wave frequency,and the seismic wave irregularity indexεidentification filter is introduced.The damping ratioξreduces the parameter identification error while ensuring the independence of the values between the two types of parameters.（4）Counting the values of the vibration random model parameters under different test conditions,it is found that there is indeed a correlation between the model parameters and the test conditions.Taking the blasthole charge Q,the burst center distance R and the longitudinal wave velocity c_p of the rock mass medium at the test site as independent variables,the statistical prediction equations for each parameter of the model were established.The significance test results of the regression model functions and coefficients and the normality analysis results of the regression residuals show that the selected regression model function can well describe the relationship between the data,and the regression estimates of all prediction equation coefficients are unbiased.This provides a method for determining the value of the vibration random model parameters under different test conditions,and realizes the simulation of single-hole blasting vibration velocity waveform under general conditions.（5）Combined with Anderson superposition model,a waveform linear and nonlinear superposition method based on vibration random model is proposed,which is verified by vibration simulation of open-pit 3-hole blasting and vibration prediction of group hole blasting.The results show that the waveform superposition result based on vibration random model is a set of vibration velocity waveforms including measured waveforms,The statistical characteristics of peak vibration velocity and FFT dominant frequency are consistent with the measured waveform;Compared with the linear superposition method,the nonlinear superposition method only reflects the effect on the vibration amplitude,and they still have high commonalities in waveform and vibration frequency.Considering the simplicity of calculation and the safety of structure,the linear superposition method is preferred in waveform prediction.（6）Considering the randomness distribution of blasting vibration peak velocity and the reliability of building（structure）safety evaluation results,the expression method of millisecond blasting vibration reduction rate is improved by using the upper limit of 95%unilateral confidence interval of probability density distribution.For equal interval millisecond blasting,the vibration reduction rate increases with the increase of inter hole delay as a whole,but there is an inflection point from fast to slow.Comparing the millisecond blasting vibration reduction rate under different blast hole number,blast center distance and site longitudinal wave velocity,it is found that in the case of short delay blasting,the vibration reduction effect can be improved by increasing the number of blast holes;It is difficult to reduce the vibration of far zone blasting only by changing the time delay between holes;It is easier to realize vibration reduction control for underground superimposed vibration of complete rock mass field.