ANALYTIC SOLUTION OF TIGHT ROOF?S BENDING MOMENT AND DEFLECTION UNDER SWELLING DISTRIBUTIVE SUPPORTING PRESSURE
PAN Yue1，GU Shitan2，QI Yunsong1
(1. School of Civil Engineering，Qingdao Technological University，Qingdao，Shandong 266520，China；2. College of Resources and Environmental Engineering，Shandong University of Science and Technology，Qingdao，Shandong 266590，China)
Abstract：Coal seam and immediate roof ahead of the coal face are considered as an elastic foundation；and because of that the damage and fracture of tight roof start at the advanced position of the middle axis of working face，so unit width rock stratum structure at middle part of the working surface can be taken to study and then the indeterminate deflection simultaneous differential equations of tight roof which are under the combined action of uniform load，advanced swelling distributive supporting load and support resistance are established. On the basis of all natural boundary conditions and continuity conditions being satisfied，the expressions about tight roof?s deflection，bending moment are derived ahead of the coal face and over the gob before the periodic weighting. According to these expressions obtained above，using Matlab software?s calculation and drawing functions，tight roof?s deflection and bending moment with the change of load，strata rigidity，flexural rigidity，support resistance and gob span are analyzed. Both the obtained four-part bending moment and deflection curves connect smoothly above the investigation interval，the peak positions of the bending moments lie ahead of the coal face and the tight roof?s subsidence values are coincident with the field experimental data. The expressions of tight roof?s deflection and bending moment are only theoretical solutions under ideal roof model，which can be used to be aroused from the calculation example of the theoretical solutions and to obtain regularity understanding for the variation in the roof?s deflection and bending moment when the relational parameters are changed；and to make reasonable qualitative judgment on the changes of the mine roof status. The analytic solution can also offer basis for further study about the damage and fracture of tight roof before the periodic weighting，the releases of the roof strain energy and the energy source of rockburst caused by the fracture of tight roof.
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2012, Vol. 31 
