Numerical analysison the fracture of hard roof based on unbalanced force

Revealing the fracture mechanism of hard roof makes a significant contribution to the analysis of hard roof weighing during a mining process. The fracture of hard roof is the manifestation of uncoordinated deformation，so it is necessary to carry out numerical modelling on the possible uncoordinated deformation area of the structure. An idea of finite element numerical simulation was proposed. The equivalent nodal force of the stress outside the yield surface was calculated when the conventional elasto⁃plastic finite element method was unsolvable，and called it unbalanced force. The significance of unbalanced force and the theoretical basis for indicating the uncoordinated deformation area through the distribution of the unbalanced force were elucidated. An elasto⁃plastic finite element method，which indicated the uncoordinated deformation area by unbalanced force，was formed considering the influence of uncoordi⁃ nated deformation in interlamination by resetting meshes. No. 8102 working face of the Tongxin Mine was taken as re⁃ search object，and the numerical simulation of the fracture of hard roof during the mining process was carried out. The comparison with the model test and field measured data verified the effectiveness of the numerical method. The re⁃ sults were as follows: 1 The case where boundary value problems of continuum mechanics have no solution indicates that the structure cannot maintain continuity，meaning the equilibrium condition，deformation compatibili⁃ ty condition and constitutive relation cannot be satisfied at the same time and leading to the appearance of uncoordinat⁃ ed deformation and unbalanced force. 2 The unbalanced force is the measure of the deviation of stress state from the equilibrium position，the distribution of the unbalanced force can be used to indicate the development of uncoordinat⁃ ed deformation area during mining process，then offer the guidance to the judgement of the fracture of hard roof. 3 The distribution of unbalanced force is mainly affected by the mining distance and specific layers which may be thick and hard. In No. 8102 working face，there are two specific layers play periodic controlling roles in the development of unbalanced force. 4 When the mining progress reaches 110 m and 270 m， the distribution of unbalanced force breaks through the thick and hard layers and develops upward，which means the corresponding layers are fractured and the stress is released，which may be a significant factor for weighting.