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.