Analysis on thin plate model of basic roof at elastic foundation boundary(I):First breaking

By establishing the basic roof mechanical model of elastic thin plate at elastic foundation boundary and using the finite difference method of partial differential equation,this paper researched the effect of the step length,e- lastic foundation coefficient,basic roof thickness and elastic modulus on the basic roof main bending moment and frac- ture positions. It is concluded that with the increase of basic roof thickness or elastic modulus,the maximum main ben- ding moment Mz of the middle roof section increases,and the absolute maximum main bending moment Mc ,Md of roof long side and short side decrease;with the step length increasing,the Mz ,Mc and Md increase,while the growth rate of the Mz is smaller;and when the elastic foundation coefficient increases,the Mz decreases,while the Mc and Md in- crease. According to the breaking criterion of the main bending moment,when the step distance or elastic foundation coefficient is small,the middle of basic roof fractures first,whereas the roof long side ahead of the coal wall breaks first;if the basic roof thickness or elastic modulus is small,the long side breaks ahead of the coal wall,whereas the central fractures first. The greater the basic roof thickness or elastic modulus,the farther the pre-breaking distance of main roof;the greater the elastic foundation coefficient or step distance,the smaller pre-breaking distance of main roof. There are three types of basic roof breaking sequence:① long side-middle-short side;② long side-short side-middle; ③ middle-long side-short side.