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

• Published in: Applied Mathematical Modelling Vol. 83; pp. 526 - 551
• Main Authors: Xiao, Shiguo, Xia, Pan
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2020; Elsevier BV
• Subjects: Calculus of variations; Earth pressure; Equilibrium conditions; Equilibrium methods; Interfacial friction angle; Limit equilibrium; Mathematical analysis; Parameters; Passive earth pressure; Passive pressure; Retaining walls; Slip; Soil conditions; Soil properties; Soils; Strip; Strip surcharge; Surcharges; Variational calculus method; Passive earth pressure; Retaining walls; Strip surcharge; Limit equilibrium; Variational calculus method
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.03.008

•A unified solution to passive earth pressure on rigid retaining walls with strip surcharge on backfills is established.•An implicit solution tactic for 8 equations by variational calculus is provided to compute the force easily via Matlab.•The proposed method can quantitatively exhibit effects of 11 basic parameters on the force and critical slip surface.•Compared with some existing methods, the proposed method can obtain lower results and is safer for practical designs. 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.