Nonlinear descriptions of vertical earth pressure against positive buried pipelines based on minor principal stress trajectory

This study presents a nonlinear solution of vertical earth pressure against positive buried pipelines with three kinds of minor principal stress trajectories, such as the circular arc, the parabolic curve, and the rotation angle linearly changed. The proposed solution accounts for the effects of soil arching and pipe-soil relative stiffness to capture the nonlinear descriptions of vertical earth pressure against the positive buried pipelines. Application steps of the proposed solution are provided along with determining the height of an equal settlement plane. Comparative validations of the results from the model tests, field measurements, and numerical simulations reported in the literatures are then performed. Finally, engineering application suggestions are discussed. It is found from this study that the proposed nonlinear solution can reasonably describe the nonlinear distribution of vertical earth pressure against the positive buried pipelines in the horizontal direction, which is of broad theoretical significance and engineering applicability value. Three solutions have different application scopes corresponding with three trajectories of minor principal stress. The solution of the circular arc trajectory is well applicable for both the shallow-filled rigid and the flexible pipelines. The solution of the rotation angle linearly changed trajectory commonly provides slightly conservative estimations of vertical earth pressures. The solution of the parabolic trajectory can be applied to high-filled flexible pipelines, yet obvious overestimations often occur.