Abstract
This paper presents a nonlinear solution of a radial subgrade reaction–displacement (p
k
–u
r
) curve for circular tunnel lining design in undrained clay. With the concept of soil shear strength nonlinearly mobilized with shear strain, an analytical solution of p
k
is obtained using the mobilized strength design method. Two typical deformation modes are considered, namely oval and uniform. A total of 197 orthogonally designed cases are used to calibrate the proposed nonlinear solution of p
k
using the finite element method with the hardening soil model. The calibration results are summarized using a correction factor, η, which is defined as the ratio of p
k_FEM
to p
k_MSD
. It is shown that η is correlated to some input parameters. If this correlation is removed by a regression equation, f, the modified solution f(p
k_MSD
) agrees very well with p
k_FEM
. Although in reality the mobilized soil strength varies with principal stress direction, it is found that a simple average of plane strain compression and extension results is sufficient to produce the above agreement. The proposed nonlinear p
k
–u
r
curve is applied to an actual tunnel lining design example. The predicted tunnel deformations agree very well with the measured data. In contrast, a linear p
k
model would produce an underestimation of tunnel convergence and internal forces by 2–4 times due to the overestimation of p
k
at a large strain level.