Thanks you for answer to my question. The goal of my work is find one Analytical Method for calculate Bending Moment and axial forces internals in one ring of tunnel lining in 2D, that allows me to compare with the results obatained of the same ring in 2D from Sap2000.
I found any equations elastic of ITA2000, but i can´t understand this...
Article Ovaling deformations of circular tunnels under seismic loadi...
There analytical solution of Wang and Penizen, its simple equations that you can find even calculations in the paper. I do not know why you are using SAP, as you can not model soil as a continuum material in SAP. I am not sure that there is any analytical solution for structural forces of circular tunnel with soil springs. I suggest you to use soil vision software ( FEM (PLAXIS, ABAQUS, LS-DYNA, OPENSEES) or FDM (FLAC) ) to compare structural forces with analytical solution.