Analytical solutions for the internal forces of lining structure in shallow double-arched tunnel subject to unsymmetrical loads

Abstract This paper presents analytical solutions for the internal forces of lining structure in shallow double-arched tunnel subjected to unsymmetrical loads, mainly for the section of arch rings. The force method is employed during the derivation. The internal forces obtained from the analytical solutions are compared with that from the numerical simulation by FEM model utilizing the load-structure-method. It is found that the largest positive bending moment appears at the arch crown, while larger negative bending moment is located at both haunches of arch rings. The axial forces of both ends of arch rings are larger than that at the arch crown, which indicates that the side and middle walls are in larger compression than the arch crown. The larger shear forces of arch rings appear at the cross section approaching the top of side walls, which may be caused by the application of elastic resistance to the side wall. The comparison results and variation trend verify the applicability of presented analytical solutions for the double-arched tunnel subjected to unsymmetrical loads.