Application of Homogenized Load-Bearing Ring Hypothesis in Roadway Supporting

Table 1

Types of tangential stress and maximum location on the equivalent ellipse.

Function relationship between λ and k		X-axis		Y-axis		Position of extremum
		Type of tress in X point	Type of tress in X′ point	Type of tress in Y point	Type of tress in Y′ point
k < λ	λ > 2k + 1	Tensile stress	Tensile stress	Compressive stress	Compressive stress	Y
	λ = 2k + 1	0	0	Compressive stress	Compressive stress	Y
	k < λ < 2k + 1	Compressive stress	Compressive stress	Compressive stress	Compressive stress	Y
k = λ	k = λ	Compressive stress	Compressive stress	Compressive stress	Compressive stress	X = Y
λ < k	k/(2 + k) < λ < k	Compressive stress	Compressive stress	Compressive stress	Compressive stress	X
	λ = k/(2 + k)	Compressive stress	Compressive stress	0	0	X
	λ < k/(2 + k)	Compressive stress	Compressive stress	Tensile stress	Tensile stress	X