This paper presents a nonlinear solution of a radial subgrade reaction–displacement (pk–ur) 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 pk 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 pk 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 pk_FEM to pk_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(pk_MSD) agrees very well with pk_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 pk–ur 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 pk model would produce an underestimation of tunnel convergence and internal forces by 2–4 times due to the overestimation of pk at a large strain level.
ESTIMATE OF COEFFICIENT OF HORIZONTAL SUBGRADE REACTION FOR PILES IN SAND
