Abstract
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.
Highlights
Retaining walls are widely used in slope protection engineering. e mechanical model of the retaining structure is suitable for backfill stability assessment in underground mining [1,2,3] and storage bins in the warehouse. e calculation of the earth pressure on the retaining wall is essential for the economical and safe design of the retaining wall. e distribution of the active lateral earth pressure on the retaining wall may be affected by the movement mode of the wall, the backfilling property [4], and the geometric layout of the backfill. is paper focuses on the active earth pressure on a horizontally translating rigid vertical wall supporting a cohesionless backfill
Selection of Slip Surface Shape. e linear slip surface proposed by Rankine [5] and Coulomb [6] is based on the failure criterion, concerning only the backfill property φ and the wall-soil friction angle δ; the slip surface of Tsagareli [8] only concerns the height at which the slip surface intersects the wall, yet the aspect ratio is omitted. e parabola equation of Goel and Patra [7] considers the reduction of the width at the top of the slip body, but how to choose the reduction factor is not clear. erefore, these slip surface equations do not adequately consider the geometric layout of the backfill
If the width of backfill is smaller than this value, the backfill is considered a confined backfill; and, if the width of backfill is larger than this value, the backfill is considered a general backfill. e slip surface formed when the confined cohesionless backfill is in the active state should be a function of the backfill geometry, the backfill property, and the wall-soil friction angle
Summary
Among the methods for calculating active earth pressure, the theories of Rankine [5] and Coulomb [6] have been used widely Both of them are based on a linear slip surface, and the obtained earth pressure distribution is linear. Handy [11] calculated the active earth pressure on walls based on an assumed minor principal stress trajectory with the shape of catenary. Khosravi et al [4] adopted the arc-shaped minor principal stress trajectory to obtain the two-dimensional analytical solution of the active earth pressure on the retaining wall based on the assumption that the vertical stress is uniformly distributed in Advances in Civil Engineering horizontal direction. Khosravi et al [4] adopted the arc-shaped minor principal stress trajectory to obtain the two-dimensional analytical solution of the active earth pressure on the retaining wall based on the assumption that the vertical stress is uniformly distributed in Advances in Civil Engineering horizontal direction. ese methods for calculating active earth pressure all achieved good results with respect to experimental data
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