Karst collapse and shallow tunnel construction frequently cause partially ground settlement of shallow foundations

resulting in partially developed soil arching effect. Development of approaches to quantitatively analyze the influence of partially developed arching on vertical stresses is of much importance. Through shallow trapdoor tests

it is summarized that the shape of slip plane of shallow trapdoor may be tower-shape under plane strain conditions. Analytical solutions to coefficients of lateral and vertical stresses for any depth of the shallow foundation under the action of partially developed soil arching effect are deduced and proved

which are based on the principal stress rotation and the differential settlement of soil layers. The influence of main parameters about partially developed soil arching effect is investigated. The results reveal that the larger depth-width ratio and the displacement-width ratio of trapdoor are needed to fully develop the arch. In addition

the vertical stress of fill increases with the increase in the effective angle of internal friction and angle of slip plane. The corresponding results can provide theoretical guidance for the calculation of vertical stress of shallow subsoil subject to local settlements.