1. School of Energy and Mining Engineering,China University of Mining and Technology(Beijing),Beijing　 100083,China; 2. Department of Mathematics, Beijing University of Posts and Telecommunications,Beijing　 100876,China; 3. School of Safety Engineering,North China Institute of Science and Technology, Beijing　 101601,China

Rock mass failure and fault formation in the earth crust are related to the genesis of induced seismicity,in which the X-typed conjugate shear fracture is closely related to zones which are frequently subjected to earthquakes. Based on the stability theory of dynamic system and butterfly failure theory about rock masses around holes, a X-shaped conjugate shear fracture-seismic composite model was established. The calculation formula of fracture size was derived,and the calculation method of seismic energy was presented. The authors used the dynamical system theo- ry to explain a quantitative correspondence between the size of fracture expansion and the energy release of earth- quake,and fully elaborated the formation and evolution mechanics of X-type,V-type and Y-type conjugate fractures. The important physical mechanics phenomena and laws associated with the conjugate shear fractures and earthquakes were deduced. The research result indicated that the failure of rock mass around the underground soft anisotropic body under the action of high deviation stress field was in accordance with the Mohr-Coulomb shear failure condition,and formed a butterfly-shaped failure zone which can also be called as the petal-shaped damage zone. With the expansion of the butterfly-shaped failure zone,the dominant or recessive X-type conjugate shear fracture centered on the soft ani- sotropic body was formed. The change of strength characteristics of the rock mass around the soft anisotropic body made the conjugate fracture exhibit X-type,V-type and Y-type characteristics. Under certain in-situ stress and sur- rounding rock environment,the non-linear dynamic system comprised of soft anisotropic bodies in the earth’s crust and surrounding rock mass showed sensitivity to,and dependence on,the in situ stress and formation strength. The extend- ed size of conjugate shear fracture and the energy released by the earthquake had mutual associated exponential varia- tion characteristics. The same stress increment triggered different one-time extension scales of conjugate fractures under different tectonic stress fields to thus induce different magnitudes of earthquake,and there existed a characteristic in- flection point from non-sensitive dependence region to sensitive dependence region.

国家自然科学基金资助项目(51704294，51434006);中央高校基本科研业务费资助项目(3142018022)

QIAO Jianyong,MA Nianjie,MA Ji,et al. Conjugate shear fracture-seismic composite model based on structural stabili- ty of dynamic system[J]. Journal of China Coal Society,2019,44(6):1637-1646.