A design methodology is developed based on analysis of the practical consequences for intersection /junction of underground openings. Mechanism of interaction support with rock mass is simulated based on theoretical solution. Empirical correction factors are introduced into the solution to account geomechanical and technological factors. The 3D problem for intersections is solved as 2D problem by introduction an effective depth. The effective depth takes into account additional stress from the adjacent opening.
Some of the less investigated fields in geomechanics are the junctions/intersections of underground constructions. Theoretical approach for this problem is limited by elastic or plastic model for the unsupported openings. They are strictly based on empirical hypotheses and statistical analysis of the field measurements. The hypotheses are often not justifiable and the statistics are usually rather poor. This is why recommendations beyond conditions of the field measurements are unreliable, especially for predicting loads on the support structures. These consequences do not confirm the verisimilar formula (1). The value of the coefficient fjU shall depend on the stress state and strength of rock mass, not only on geometry of the junction. Substantial influence of the relative stress on displacement in openings at junction is confirmed by shaft measurements of displacement in development openings at zone of productive long wall openings, Reva (1985). Measured displacements in these zones at junction were 2–3 times more than at the same junction of the opening located away from long wall.
There are many analytical 2D solutions for stress analysis around parallel openings with equal or different diameters and there is only one analytical solution for 3D problem. It is the elastic Soloviev's solution (1969) for toroidal opening located in homogeneous rock mass with hydrostatic initial state of stress equal to γH.