| Rock acoustic emission b value is one of the essential characteristic parameters to establish the scale distribution law between rock acoustic emission and earthquake,which can predict rock failure precursors and probabilistic seismic hazard analysis.However,different from the b value calculation by frequency-magnitude distribution in earthquake,the apparent amplitude distribution collected by the acoustic sensor on the rock border often used to calculate acoustic emission b value,and the apparent amplitude distribution will inevitably deviate from the exponential distribution due to the attenuation of acoustic emission signal in the medium.Therefore,revealing the fundamental reason that why attenuation changes the source scale distribution law and analyzing the essential law that the apparent frequency-amplitude distribution of rock acoustic emission deviates from the G-R relationship have become the key problem to explore the b value calculation method of apparent amplitude distribution.Therefore,based on the doubly truncated exponential distribution and the specifically designed acoustic emission simulation tests,this study uses a series of generated synthetic acoustic emission data to research the effects on the accurate calculation of b value from many aspects,and finally proposed a b value calculation process suitable for the apparent amplitude distribution characteristics of rock acoustic emission.Then,the newly proposed b value calculation method is applied to the specially designed non-explosive fracturing agent expansion rock acoustic emission test,and the scientificity and accuracy of this method are verified according to the relationship between the composition of rock mineral particles and structural characteristics and the scale failure law obtained in the transparent refractive index experiment of various rocks.The main research contents and key results are as follows:（1）For the problem that the apparent frequency-amplitude distribution of rock acoustic emission deviates from the exponential distribution,it is found that the b value of apparent amplitude calculated with doubly truncated exponential distribution is very close to the theoretical b value.However,from the uncertainty analysis of various b value calculation methods,it can be seen that the 95%confidence interval and residual distribution calculated by the generalized linear regression assuming Poisson error are more in line with the fluctuation of amplitude distribution than the least square regression assuming Gaussian error.The maximum likelihood method and repeated median method cannot be compared with generalized linear regression for uncertainty analysis,because the two methods do not have the theoretical basis for calculating the confidence interval of doubly truncated frequency-amplitude distribution.And the theoretical b value will also affect the selection of the minimum data volume for the b value calculation:the larger the theoretical b value is,the greater the minimum data volume is required,which vary from 200 for b<1.5 to 300 for b>1.5.（2）Various attenuation will cause the source scale distribution to deviate from the G-R relationship,while retaining the special log-linear amplitude range of the source scale distribution characteristics,and the special log-linear amplitude range will decrease with the increase of attenuation,and the distribution law of source failure scale shows the same trend.In addition,the log-linear amplitude range will also increase with the increase of the width of the source amplitude range,that is,the smaller the influence of attenuation on the distribution law of source failure scale.In addition,the special log-linear amplitude range will also increase with the increase of the width of the source amplitude range,that is,the effect of attenuation on the source failure scale distribution law will decrease with the increase of the source amplitude range.Therefore,it can be inferred that when the source amplitude range tends to infinity,the limited attenuation will not affect the source failure scale distribution law.Moreover,the b value of the log-linear segment is very closed the theoretical b value,so we can take the b value represented by the log-linear segment as the true b value of the source amplitude distribution.Therefore,reasonably truncated the linear segment of the logarithmic frequency-amplitude distribution is the key to accurately calculate the b value of rock acoustic emission.（3）The data incompleteness also exists in the amplitude distribution of rock acoustic emission that is similar to seismic catalog,and the data incompleteness is mainly concentrated in the low amplitude range and has no effect on the high amplitude segment.The research shows that the completeness method in earthquake is also suitable for the calculation of acoustic emission completeness amplitude,among which the completeness amplitude point Ac calculated by MAXC method is the most accurate,and FGS is more suitable for calculating the auxiliary discontinuous point A0 of frequency-amplitude distribution.Based on these discussions,we proposed a new b value estimation procedure MFBG that can better identify log-linear amplitude distribution and calculate b value from apparent amplitude.（4）Using MFBG method to calculate the b value in the non-explosive fracturing agent expansion rock acoustic emission test,it is found that the b value of red sandstone>marble>granite>limestone.The results are consistent with the relationship between rock mineral particle composition and structural characteristics and scale failure law obtained in the transparent refractive index experiment of various rocks.Moreover,the temporal b value calculated by MFBG has a good corresponding relationship with energy,amplitude and strain,which can reflect the development of scale distribution law in the process of rock failure,and has the precursory characteristics of predicting rock instability and failure. |
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