Purpose. Understanding the hanging arch distance of the roof in the curved triangle area at the end of an underground coal working face. Methodology. Using mechanical analysis, we obtain the theoretical maximum roof hanging arch distance in the curved triangle area and expression of supporting pressure borne by protective coal pillars surrounding the curved triangle area. To reflect the results, mathematical derivations are done. Findings. The mechanical model for roof hanging arch in the curved triangle area at the end of the coal working face is established; the mechanical conditions for the formation of such triangle area is analyzed; the theoretical maximum roof hanging arch distance in the curved triangle area is calculated; the formula showing the corresponding relation between the ineffectiveness of bolt (cable) support of the roadway roof and supporting pressure of coal pillars surrounding the curved triangle area is given as well. Originality. A series of formulas for the supporting pressure borne by the protective coal pillars surrounding the curved triangle area are derived. Practical value. If the roof support in the curved triangle area becomes ineffective after completing the corresponding support tasks, both the roof hanging arch distance and supporting pressure of the coal pillars in the triangle area reduce accordingly. These conclusions may supply instructions for designing the width of the protective pillars.

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