Slip Surface and Active Earth Pressure of Cohesionless Narrow Backfill behind Rigid Retaining Walls under Translation Movement Mode
Publication: International Journal of Geomechanics
Volume 20, Issue 8
Abstract
A slip-failure surface forms in the backfill soil upon sufficient yielding or movement of the wall that retains the backfill soil. The shape of the slip-failure surface plays an important role in estimating the lateral earth pressure, including its magnitude and location of its resultant force. As retaining walls at times must be built with narrow and constrained backfill space, this study presents an analytic derivation of the slip-surface shape in narrow cohesionless soil behind a rigid retaining wall under translation movement mode of the wall. Results of a series of experimental tests were presented to demonstrate the effects of narrow backfill spaces on forming the slip surface and that the slip surfaces are curvilinear planes developed from the heel of the retaining wall to the crest of the backfill. Based on the experimental findings, a rigorous analytic derivation using a variational limit equilibrium method is conducted to determine the governing equation for the shape of the slip surface in the narrow backfill soil. The analysis reveals that the active failure plane of the narrow soil behind a rigid retaining wall agrees well with a logarithmic spiral plane. The derived log-spiral slip-surface plane is further verified by experimentally observed slip surface and measured active lateral earth pressure. Substantial discrepancy was observed in the lateral earth pressure distribution between the logarithmic spiral slip surface and the assumed linear planar slip surface, indicating that the assumption of a linear planar slip surface in narrow backfill may result in significantly erroneous estimation and lead to an overly conservative and uneconomical design. Furthermore, a threshold value of 0.5 is identified for the backfill width/height ratio that distinguishes the narrow backfill from a sufficiently wide backfill.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request, including data for Table 1 and Figs. 4–12.
Acknowledgments
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China under Grant Number 51678230.
Notation
The following symbols are used in this paper:
- B
- width of retaining wall (m);
- b
- width of the narrowed backfill or horizontal distance from the retaining wall to existing buildings (m);
- d
- vertical distance from Ea to the base of the wall (m);
- dy
- differential depth along the y-axis (m);
- Ea
- active thrust (kN/m);
- H
- height of retaining wall (m);
- r0
- polar radius of point C in the polar coordinate system (m);
- rh
- polar radius of point B in the polar coordinates (m);
- r(θ)
- sliding surface equations in the polar coordinate system;
- SABC
- area of ABC (m2);
- W
- weight of the failure wedge ABC (kN/m);
- x
- abscissa of any point on the failure surface (m);
- abscissa in the polar coordinate system (m);
- x(y)
- sliding surface equations in terms of the variable y;
- y
- ordinate of any point on the failure surface (m);
- ordinate in the polar coordinate system (m);
- γ
- unit weight of the backfill soil (kN/m3);
- δ
- soil–wall interface-friction angle (degree);
- θ
- angle of the slip surface in the polar coordinate system (degree);
- θh
- polar angle of point B in the polar coordinate system (degree);
- θ0
- polar angle of point C in the polar coordinate system (degree);
- λ1
- Lagrange multiplier;
- λ2
- Lagrange multiplier;
- σ
- normal stress on the slipping surface (kN/m2);
- σ(y)
- normal stress equation in terms of the variable y;
- τ
- tangential stress on the slipping surface (kN/m2); and
- φ
- internal friction angle of the backfill soil (degree).
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Published In
International Journal of Geomechanics
Volume 20 • Issue 8 • August 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Aug 30, 2018
Accepted: Feb 24, 2020
Published online: May 22, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 22, 2020
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