Abstract: In order to study the law of roadway roof separation, established a mechanical model which considered anchorage effect and horizontal stress based on Time Series Analysis theory of roof separation value and the Elastic Theory of Beams. Besides, we used Maple and SAS to analysis this problem. Based on the mechanical model, we put forward a method to determine the value of elasticity ωmax and the value of instability δmax. we could get the optimal supporting time and judge roof fall by three values, which are the predicted value Xt and the two separation values ωmax and δmax. In addition, we discussed the mechanical mechanism of surrounding rock instability by the mechanical model. Finally, we used an engineering example Dong Tan Mine 1035 roadway as an example of the model. Conclusion are drawn that the value of separation ωmax and δmax are 16mm and 35mm, and measures should be made when the value of separation reached 35mm.

Key words: Time Series Analysis, critical value of roof separation, optimal supporting time, instability, Maple, SAS