Analysis and Calculation of Passive Earth Pressure of Vertical Layered Soil

Based on the limit equilibrium theory and the associated flow rule,a mathematical model of the passive earth pressure of the vertical layered soil behind the retaining wall with respect to the sliding surface angle was established.According to the static equilibrium relationship of the sliding soil wedge,the calculation expression and distribution of passive earth pressure of vertical layered soil were derived.Then,the function curve of passive earth pressure changing with the angle of sliding surface was made by using Matlab calculation software,and the passive earth pressure and its corresponding limit rupture angle were determined according to the minimum points on the curve.The rationality and feasibility of this method were verified by comparison with existing theoretical calculations.Finally,the influence laws of layered soil property parameters and geometric and physical parameters of retaining structures on passive earth pressure E_p and rupture angle θ_cr were analyzed.The results show that the classical Rankine and Coulomb earth pressure theories and literature solutions are special cases of the research method in the case of a single soil layer.The passive earth pressure E_p increases with the increase of wall-soil friction angle δ,backfill soil friction angle φ₁,wall-soil cohesion C_w,backfill soil cohesion C₁,backfill weight γ₁,and fill surface load q,and decreases with the increase of wall back slope angle α.The rupture angle θ_cr decreases with the increase of δ,φ₁,C_w,C₁,γ₁,and increases with the increase of α.The influence of backfill distance b on passive earth pressure E_p and rupture angle θ_cr is jointly affected by the properties of backfill layer and original soil layer.Finally,from the perspective of engineering design,the vertical and rough back of the retaining wall is more conducive to the passive earth pressure.