LAUSR

Abstract A numerical approach, the Hyperstatic Reaction Method (HRM), is presented in this paper to study the behavior of two kinds of U-shaped tunnel linings (with and without an inverted arch). The developed numerical HRM model is validated by a comparison with the results obtained from finite difference numerical models using FLAC3D. The results of this paper show that the behavior of U-shaped tunnel supports could be effectively estimated by the proposed HRM model. Using the HRM model, the effect of the shear springs and the toe constraint on the behavior of U-shaped tunnel linings without an invert are studied. In addition, the results of two kinds of U-shaped tunnels obtained by the HRM are compared with those of a circular-shaped kind. A parametric investigation is conducted considering the changes in the stiffness of the springs, the loads on the supports, the geometries, and the bending stiffness of the support structures.