Investigation on the inner and outer analogous hyperbola model (AHM) of strata movement

The traditional strata movement pays attention to the strata movement law of the overlying part of the working face,and the mining surface settlement pays more attention to the surface subsidence.These two different research directions are essentially related to the overall movement behavior of the overlying strata and the surface soil layer after mining.It is necessary to develop an overall movement model of the mining strata which can better describe the laws of the overlying strata movement and surface subsidence.Through theoretical and experimental analysis,the initial and periodic fracture patterns of the rock beam trapezoid block structure are obtained,and the caving conditions and judgment methods of the trapezoid “inverted funnel” caving arch and fissure arch are established.Based on the analogous hyperbola model (AHM) of strata movement boundary proposed by the authors,the AHM inside and outside is further proposed to describe the laws of strata movement and surface subsidence.The internal AHM model refers to the AHM of mining overburden caving fracture arch and surface subsidence moving arch,which is symmetrical about the key layer “up and down”.The external AHM refers to the “quasi hyperbolic” model of rock movement boundary,which is approximately “left and right” symmetrical about the coordinate axis working surface near the vertical line.The inner AHM exists inside the overlying rock,which can be approximately detected by geophysical detection methods.The outer AHM is reflected in the surface subsidence,rock collapse and other external forms.Through theoretical analysis,case study and discrete element UDEC method,the unified analogous hyperbola model of strata movement and surface subsidence is verified,and the formation conditions,influencing factors and overall migration rules of AHM of conjugate internal and external are analyzed.The results show that the error between the theoretical prediction value and the actual value of the analogous hyperbola model is small,which reflects the rationality of the AHM of the overall movement of the strata.