Moment tensor analysis of transversely isotropic shale based on the discrete element method

In this study,the moment tensor of transversely isotropic shale was analyzed using a discrete element method-acoustic emission model(DEM-AE model).Firstly,the failure modes of the shale obtained from the acoustic emission(AE) events and physical experiments were compared.Secondly,the relationships between AE events and seismic magnitudes,and AE events and the resulting cracks were analyzed.Finally,a moment tensor T-k chart describing the seismic source was introduced to demonstrate the differences in the transversely isotropic shale.The results showed that,for different anisotropy angles,a linear logarithmic relationship existed between the cumulative AE events and the seismic magnitude in the concentration area of the AE events.A normal distribution was observed for the number of AE events as the seismic magnitude changed from small to large.The moment tensor T-k chart indicated that the number and proportion of linear tension cracks in the shale were highest.When θ = 30°,the peak seismic magnitude was at a minimum.The average seismic magnitude in the concentration area of the AE events was also relatively small.Points close to the U=-1/3V line and the number of cracks included in a single AE event were at a minimum,and the corresponding peak stress also reached its lowest level.In contrast,when θ=90°,all related parameters were contrary to the above θ = 30° case.The DEM-AE model and the moment tensor T-k chart are suitable for analyzing the distribution of shale cracks appearing during the loading process.This study can provide constructive references for future research on the fracturing treatment of shale.

In this study, the moment tensor of transversely isotropic shale was analyzed using a discrete element method-acoustic emission model （DEM-AE model）. Firstly, the failure modes of the shale obtained from the acoustic emission （AE） events and physical experiments were compared. Secondly, the relationships between AE events and seismic magnitudes, and AE events and the resulting cracks were analyzed. Finally, a moment tensor T-k chart describing the seismic source was introduced to demonstrate the dif- ferences in the transversely isotropic shale. The results showed that, for different anisotropy angles, a lin- ear logarithmic relationship existed between the cumulative AE events and the seismic magnitude in the concentration area of the AE events. A normal distribution was observed for the number of AE events as the seismic magnitude changed from small to large. The moment tensor T-k chart indicated that the num- ber and proportion of linear tension cracks in the shale were highest. When 0 = 30~, the peak seismic magnitude was at a minimum. The average seismic magnitude in the concentration area of the AE events was also relatively small. Points close to the U ~ -1/3 V line and the number of cracks included in a single AE event were at a minimum, and the corresponding peak stress also reached its lowest level. In contrast, when 0 = 90°, all related parameters were contrary to the above θ =-1/3 V case. The DEM-AE model and the moment tensor T-k chart are suitable for analyzing the distribution of shale cracks appearing during the loading process. This study can provide constructive references for future research on the fracturing treatment of shale.