Variational calculus method for passive earth pressure on rigid retaining walls with strip surcharge on backfills

摘要

In light of the limit equilibrium conditions of soil mass retained by rigid retaining walls with distanced strip surcharge on its top surface, a variational calculus method is provided to calculate the passive earth pressure on the wall. By establishing the functional relationship between the earth pressure and potential slip surface as well as normal stress on it under a specified action point of the resultant force of the earth pressure, a unified closed-form solution to the passive earth pressure is derived and preformed easily by an implicit solution tactic via Matlab. It can quantitatively exhibit the influences of fundamental parameters on the force and corresponding critical slip surface including the soil properties, soil-wall interface friction angle, dip angle of the wall back, dip angle of the top surface of the retained soil, strip surcharge, net distance from the wall back to the surcharge, distribution width of the surcharge, and so on. These parameters except for unit weight, cohesion of soil and strip surcharge have nonlinear influence on the value of the passive earth pressure. Analysis results of some examples indicate the passive earth pressure by the proposed method is usually less than that by traditional limit equilibrium methods, and equal to the Coulomb's solution under certain conditions.