Numerical investigation of pipeline upheaval buckling in rockfills: significance of particle scale effect

Abstract

The predictive models for uplift resistance of subsea pipelines buried in coarse-grained materials, particularly gravels or rockfills, are semi-empirical in the current design guidelines, and the impact of particle scale effect, i.e. the ratio between the pipe diameter (D) and the median particle size (d₅₀), is often not considered. To help understand this effect, this study performed a set of numerical analyses of the pipe upheaval in rockfills with various embedment ratios H_c/D (from 0.5 to 6, primarily) and D/d₅₀ ratios (from 3 to 20) using the three-dimensional Discrete Element Method (DEM). The state-of-the-art DEM simulation is believed to well capture the morphologies of coarse-grained materials by using elongated particle clumps. The DEM results show good agreement with the latest database for the uplift resistance factor, f_up (Sun et al., 2025), presenting significant particle scale effect particularly when D/d₅₀ and H_c/D are both small. A global uplift failure mechanism was presented with a larger inclination angle of the displaced soil wedge when the particle scale effect is dominant. A transition value of D/d₅₀ for the particle scale effect can be approximated between 7.0 and 10.0. A two-parameter model was proposed to help evaluate the rockfill weight and shear contributions during pipe uplift. For design purposes, high and low estimate trendlines of uplift resistance were given with the uplift zone shape factor β and shear resistance factor f_up varying between [1.0, 2.0] and [0.3, 0.8], respectively. The proposed model has shown a good coverage of data in terms of the predicted resistance.