Active earth pressures against rigid retaining walls for finite soil under the grading condition

The active earth pressure against rigid retaining walls with narrow backfill adjacent existing surrounding buildings or basements has widely been studied. However, the finite soil under the grading condition behind the retaining walls of excavations, embankments and cutting slopes is seldom examined. In this paper, the rigid body limit equilibrium theory is introduced. The influence parameters, such as the soil cohesion, the cohesive force between soil and wall, the wall friction, the inclination angle of walls, and the surcharge on top of the backfill are considered in this study. The plane sliding failure surface is analyzed under the translation mode, combining with the characteristics of the finite soil under the grading condition behind the retaining walls. The formulae for calculating the active pressure for the finite soil is presented, which can easily be solved by using the numerical calculation method. The calculation example analysis and parameter analysis about the active earth pressure for the finite soil under the grading condition are put forward. The results show that the limit rupture angle is not constant and it will decrease with the increasing ratios of the width to height, the soil cohesion, the inclination angle of walls, and the wall friction. The limit rupture angle will tend to the value based on the Coulomb’s active earth pressure formulae considering the soil cohesion with the increasing ratios under different soil cohesions. The threshold of the limited width varies with soil cohesion. Meanwhile, the active earth pressure will decrease with the increasing soil cohesion, the inclination angle of wall, the wall friction. It will increase with the increasing ratios, which will gradually tend to the value with the Coulomb’s method. The calculated rupture angle approaches the tested angle through the model test, and the threshold of the ratios of the width to height tested by the PIV test system approaches the value with the Coulomb’s method.