Passive Earth Pressure in Narrow Cohesive-Frictional Backfills
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
A narrow backfill zone is formed when retaining walls are built near existing stabilized structures (e.g., rock faces). In such circumstances, the classical passive earth pressure coefficient is no longer applicable, and a correction factor is required for the design. This paper aims to develop analytical solutions for estimating the passive earth pressure problem of narrow cohesive-frictional backfills behind retaining walls. The novel arched differential element method considers both effects of the horizontal shear stress in backfills and the soil arching, and it is employed to estimate the passive earth pressure distribution along with wall depth. The solutions are compared against those published experimental data, analytical approaches, and finite-element limit analysis solutions. The factors influencing the distribution of passive earth pressure are also undertaken using a series of parametric studies. To implement the derived solutions into a routine design, a modified practical design equation is presented following the standard Coulomb’s solutions. This work provides a theoretical guideline for the initial design of retaining walls with narrow soils, and it should be of great interest to practitioners.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study was supported by a CSC grant, the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX20_0118), and the Scientific Research Foundation of Graduate School of Southeast University (Grant No. YBPY2041).
Notation
The following symbols are used in this paper:
- B
- bottom width of narrow soils behind retaining wall (m);
- c
- soil cohesion (kPa);
- D1 − D22
- abbreviations used in the derivation process;
- abbreviations used in the derivation process;
- dz
- thickness of the arched element (m);
- Ep
- passive earth thrust acting on rotating retaining wall (kN);
- ,
- horizontal forces at the wall–soil interface involved in the element in the upper zone (kN);
- ,
- horizontal forces on upper and lower boundaries of the element in the upper zone (kN);
- ,
- vertical forces at the wall–soil interface involved in the element in the upper zone (kN);
- ,
- vertical forces on upper and lower boundaries of the element in the upper zone (kN);
- G1
- gravity of arched differential element in the upper zone (kN);
- H
- retaining wall height (m);
- H1
- height of the upper zone (m);
- H2
- height of the lower zone (m);
- Kp
- passive thrust coefficient;
- Kp,Coulomb
- passive earth pressure coefficient calculated by Coulomb’s theory;
- length of A1E1 (m);
- curve length of E1E1′ (m);
- N
- ratio of major to minor principal stresses;
- p1 − p7
- optimal constant coefficients;
- radius of major principal stress trajectory (m);
- z
- buried depth of arched element (m);
- Δz
- vertical distance between points A1 and i (m) ;
- αf
- sliding angle of the slip surface (°);
- β
- angle of the slope (°);
- γ
- unit weight (kPa);
- δ1
- wall–soil interface friction angle (°);
- δ2
- slope–soil interface friction angle (°);
- η
- correction factor;
- θr
- rotation angle of major principal stress of the rock–soil interface in Mohr’s circle (°);
- θr1
- rotation angle of minor principal stress on slope surface to the horizontal (°);
- θs
- rotation angle of minor principal stress on the slip surface to the horizontal (°) ;
- θw
- rotation angle of minor principal stress at the wall–soil interface to the horizontal (°);
- rotation angle of minor principal stress at the wall–soil interface to the vertical (°);
- ϕ
- soil friction angle (°);
- μ1
- interface roughness factor of the wall;
- μ2
- interface roughness factor of the slope;
- minor principal stresses at the wall–soil interface (kPa);
- minor principal stress at arbitrary point i on upper boundary of the element (kPa);
- , ,
- lateral earth pressure exerted in upper and lower zones (kPa);
- σr, τr
- normal and shear stresses on the rock–soil surface (kPa); and
- σs, τs
- normal and shear stresses on the slip surface in backfills (kPa).
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 15, 2022
Accepted: Aug 14, 2022
Published online: Nov 4, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 4, 2023
ASCE Technical Topics:
- Backfills
- Buildings
- Construction engineering
- Construction methods
- Continuum mechanics
- Data analysis
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Excavation
- Existing buildings
- Finite element method
- Friction
- Geomechanics
- Geotechnical engineering
- Methodology (by type)
- Numerical methods
- Research methods (by type)
- Retaining structures
- Shear stress
- Soil dynamics
- Soil mechanics
- Soil pressure
- Solid mechanics
- Stress (by type)
- Structural analysis
- Structural engineering
- Structures (by type)
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