Calculation of Active Earth Pressure for Narrow Backfill with a Curved Slip Surface

A method was proposed to calculate the earth pressure from a cohesionless backfill with a high aspect ratio (ratio of height to width of retaining wall). An exponential equation of slip surface was proposed first. The proposed nonlinear slip surface equation can be obtained once the width and height of the backfill as well as the internal friction angle of the backfill were given. The failure surface from the proposed formula agreed well with the experimental slip surface. Then, the earth pressure was calculated using a simplified equilibrium equation based on the proposed slip surface. It is assumed that the minor principal stress of the backfill near the wall and at its corresponding slip surface where the depth is the same is the same. Thus, based on the vertical force balance of the horizontal backfill strip, assuming the wall-soil interface and the slip surface is in the limit equilibrium state, defined by the Mohr–Coulomb criterion, the differential equilibrium equation was obtained and numerically solved. The calculated results agreed well with the test data from the published literature.

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