Abstract: To characterize the distribution law of vertical earth pressure for a trench-buried culvert, backfill soils were subdivided into distinct regions with varying effects of the soil arching direction, which referred to the analytical method of vertical stress for silo granular materials. The formula of vertical earth pressure for a trench-buried culvert was then presented based on the binomial distribution mode for backfill soil load transfers, and its application steps were outlined along with determining both the load transfer coefficient and the height of an equal settlement surface. Finally, discussions were carried out on the thin layer thickness, comparing verifications, and influencing factors. The results show that the proposed formula of vertical earth pressure with the maximum uniform thickness of thin layers is not only straightforward and practical without complex integrals, but also it reasonably accounts for comprehensive influences of soil arching, backfill soil partitions, load transfers, and an equal settlement surface. The validity of the proposed formula is demonstrated by comparing it with the theoretical formula, model tests, and numerical simulations. At the culvert top, the vertical earth pressure increases with increasing the trench width or the backfill soil height, and its distribution is not uniform on the horizontal plane. However, it changes in contrast to that of the load transfer coefficient, when the internal friction angle of backfill soils increases. In addition, the height of the equal settlement surface is not constant, and it should be evaluated against the backfill soil height to choose the proposed formula under different conditions.

Key words: trench-buried culvert, vertical earth pressure, binomial distribution mode, effect of soil arching, load transfer coefficient