Setting an expandable polystyrene (EPS) board on box culverts can reduce the vertical earth pressure (VEP) acting on the culvert roof. However, long-term backfill load will induce creep in both the EPS board and the surrounding soil, resulting in a change in the stress state of the culvert-soil system. A mechanical model for the long-term interaction of backfill-EPS board-box culvert was established, and theoretical formulas were derived for calculating the earth pressure around the culvert. Numerical simulation was employed to validate the accuracy of the proposed theoretical approach. Research indicates that, with EPS board, the VEP decreases rapidly then slightly increases with time and eventually approaches an asymptotic value, ultimately decreasing by 33%. However, the horizontal earth pressure (HEP) shows the opposite pattern and ultimately increases by 15%. The foundation contact pressure (FCP) increases nonlinearly and reaches a stable value, ultimately increasing by 10.2%. Without the EPS board, the VEP and HEP are significantly different from those with the EPS board. Although EPS boards can reduce the VEP on the culvert, attention should be paid to the variation of HEP caused by the creep of the EPS board and backfill.
