In order to solve the problem that current theory models cannot accurately describe thick-hard roof（THR） elastic energy and assess the mine tremor disasters,a theoretical method,a Timoshenko beam theory on Winkler foundation was adopted to establish the THR’s periodic breaking model.The superposition principle was used for this complex model to derive the calculation formulas of the elastic energy and impact load on hydraulic supports.Then,the influence of roof thickness h,cantilever length L1,and load q on THR’s elastic energy and impact load was analyzed.And,the effect of mine tremor disasters was assessed.Finally,it is revealed that:（1） The THR’s elastic energy U exhibits power-law variations,with the fitted relationships U=0.0096L13.5866,U=5943.9h-1.935,and U=21.049q2.（2） The impact load on hydraulic supports FZJincreases linearly with an increase in the cantilever length,thickness,and applied load.The fitted relationships are FZJ=1067.3L1+6361.1,FZJ=125.89h+15100,and FZJ=10420q+3912.6.（3） Ground hydraulic fracturing and liquid explosive deep-hole blasting techniques effectively reduce the THR’s cantilever length at periodic breakages,thus eliminating mine tremor disasters.

supportedbytheChongqingPostdoctoralSpecialSupport(No.2022CQBSHTB1022)；theAutonomousGeneralProjectsofStateKeyLaboratoryofCoalMineDisasterDynamicsandControl(No.2011DA105287-MS202209)；theStateKeyLaboratoryofCoalMineDisasterDynamicsandControlFacesthe2030project(No.2011DA105287-MX2030-202002)；thefinancialsupportfromtheorganization；

1. Introduction
2. Engineering background
3. Theoretical method
3.1.Theoretical modeling
3.2.Theoretical calculation process
3.2.1.THR’s periodic breaking step distance
3.2.2.THR’s elastic energy
3.2.3.Impact load on hydraulic supports
3.3.Verification of theoretical method
3.3.1.Periodic breaking step distances and working resistances of hydraulic supports by the theoretical method
3.3.2.Comparison of working resistance from theoretical calculation and on-site monitoring
4.Results
4.1.Periodic breaking step distance and bending moment of THR under different factors
4.2.Elastic energy (density) of the THRs under different factors
4.3.Impact load on hydraulic supports during periodic breakage
5.Discussion
5.1.Control mechanism of the mine tremor disaster induced by the THR’s periodic breakage
5.2.Control technology of the mine tremor disaster induced by the THR’s periodic breakage
5.2.1.Liquid explosive deep-hole blasting techniques
5.2.2.Ground hydraulic fracturing technology
5.3.A case
6.Conclusions

[1]Yu B ,Peng M ,Tai Y , et al.Assessment and control of the mine tremor disaster induced by the energy accumulation and dispersion of thick-hard roofs[J].International Journal of Mining Science and Technology,2024,34(07):925-941.