New Analytical Solutions for Cohesive–Frictional Soils above Deep Active Trapdoors
Publication: International Journal of Geomechanics
Volume 22, Issue 12
Abstract
Even though extensive research works have been carried out to understand the trapdoor responses in frictional materials, those in cohesive–frictional materials have not yet been well studied due to the complexities involved. This paper focuses on formulating new analytical solutions for cohesive–frictional soils above deep active trapdoors. Finite-element limit analyses (FELA) were conducted to study the failure mechanisms of a deep active trapdoor considering various cover ratios, soil cohesion, and soil friction angles. Three distinct failure modes could be observed, depending on various combinations of cover ratio and soil strength parameters: internal, vertical, or external collapses. The analytical solutions, allowing the failure mechanisms and load-transfer mechanisms to be taken into account, were further proposed to calculate the modified lateral earth-pressure coefficient and vertical stresses in soils. The results from previous works and FELA solutions were compared with validate the proposed solutions. A parametric study was performed to explore the effects of cover ratios and soil-strength parameters on soil-arching ratio. The proposed solutions provide a theoretical guideline available for the initial design of geo-infrastructures spanning voids.
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Acknowledgments
The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant No. 42177121), the Project of Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources (Fujian Key Laboratory of Geohazard Prevention, No. FJKLGH2020K001).
Notation
The following symbols are used in this paper:
- B
- width of trapdoor (m);
- Bz
- width of horizontal soil layer element at depth z (m);
- c
- soil cohesion (kPa);
- dW
- gravity of soil-layer element (kPa);
- E
- Young’s modulus (MPa);
- H
- height of covered soils (m);
- H1
- height of upper vertical zone in external failure mode (m);
- H2
- height of lower spiral zone in external failure mode (m);
- K0
- coefficient of earth pressure at rest;
- Ka
- Rankine active earth-pressure coefficient;
- Kh
- lateral earth-pressure coefficient;
- modified lateral earth-pressure coefficient;
- Kp
- Rankine passive earth-pressure coefficient;
- O
- pole of polar coordinate;
- P
- surcharge on the fill surface (kPa);
- Pu
- multiplier downward load (kPa);
- r
- rotation radius (m);
- ra, rb
- end and start points of rotation radius (m);
- v
- Poisson’s ratio;
- α
- angle between slip surface and horizontal surface (°);
- α0
- initial rupture angle (°);
- ΔP
- fixed upward load (kPa);
- γ
- unit weight of covered soil (kN/m3);
- η
- rotation angle of major principal stress (°);
- ηw
- rotation angle of major principal stress exerted on the slip surfaces (°);
- θ
- rotation angle of logarithmic spiral (°);
- ρ
- soil-arching ratio;
- σ1,
- major principal stresses in original and new coordinates (kPa);
- σ3,
- minor principal stresses in original and new coordinates (kPa);
- σh, σv
- horizontal and vertical stresses in the soil element (kPa);
- σnw,
- normal stresses on the slip surface in original and new coordinate (kPa);
- average vertical stress (kPa);
- τw,
- shear stresses on the slip surface in original and new coordinates (kPa);
- τxy
- shear stress in soil element (kPa); and
- ϕ
- soil friction angle (°).
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© 2022 American Society of Civil Engineers.
History
Received: Nov 9, 2021
Accepted: Jun 30, 2022
Published online: Sep 28, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 28, 2023
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Failure analysis
- Failure modes
- Finite element method
- Forensic engineering
- Friction
- Geomechanics
- Geotechnical engineering
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Methodology (by type)
- Numerical methods
- Parameters (statistics)
- Soil analysis
- Soil mechanics
- Soil properties
- Soil strength
- Solid mechanics
- Statistics
- Structural engineering
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