Analytical Method: Convergence

These methods are based on analytical closed solutions for cases of circular openings in grounds that can be modeled with an elastic or elasto-plastic behavior. Under simplified assumptions of natural stresses and geometry, it is possible to calculate analytically the relationship between deformation and internal pressure on a circular opening in the ground (characteristic curve of the cavity). At the same time, it is possible to calculate analytically for a certain kind of support the same relationship between internal pressure and radial deformation (characteristic curve of the support). The intersection point between the two curves gives the equilibrium point (pressure and deformation) for a certain combination of cavity and support element. This method is more or less easily applicable and can draw quite good results for a support design; however, its applicability is reduced to very simplified conditions of natural stresses, geometry, geomechanical behavior and geological layoutcities.