To accurately calculate primary loads for an induced trench installation culvert

the study first described the soil arching effect of unsaturated backfills above an induced trench installation culvert by using the circular-arc trajectory of minor principal stress

so as to derive a theoretical formulation of the earth pressure coefficient at a sliding surface. Then

the frictional shear stress at a sliding surface was determined based on the strength equation of two stress state variables for unsaturated soils

and an analytical solution of vertical earth pressure at the culvert top in unsaturated soils was presented. Application steps of the proposed solution were provided along with height calculation of an equal settlement plane

and comparing validations against field measurements reported in the literature were performed. Finally

load reduction rate was defined to analyze the influences of different factors including matric suction and its distributions

suction angle

compressible material thickness

and deformation modulus of compressible materials. Results show that the obtained analytical solution of vertical earth pressure could reasonably account for the comprehensive influences of matric suction and its distributions

the soil arching effect

the performance of compressible materials

and the height of equal settlement planes. Consequently

the proposed solution could improve the structural design theory of an induced trench installation culvert. The frictional effect increased and the equal settlement plane decreased simultaneously with increasing unsaturated soil strength. Both matric suction and suction angle had dual-effects on the load reduction rate

reflected by the fact that the load reduction rate increased at the beginning and decreased afterwards

and the dual-effect was more obvious for uniform suction. With the increase in compressible material thickness

the load reduction rate increased nonlinearly and tended to be stable

whereas it decreased nonlinearly with increasing deformation modulus of compressible materials.