Energy-Based Analysis of Laterally Loaded Caissons with Large Diameters under Small-Strain Conditions
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Volume 22, Issue 8
Abstract
To better predict the response of laterally loaded caissons and the displacement distribution around the foundations, three different beam theories [Timoshenko beam theory with vertical (z) displacement in soil, Timoshenko beam theory without z displacement, and rigid beam theory with z displacement] were compared in the energy-based variationally method, and two caissons from real projects under the initial loading state were studied. The results from the three methods are compared with measured data from field tests and three-dimensional differential analysis. From the study, the method of the Timoshenko beam theory that considers z displacement in the soil domain produces the most accurate results. The rigid beam theory produced the worst prediction when estimating caisson displacement, rotation, and bending moment. Therefore, for the structure–soil interaction of a laterally loaded caisson, the suggested structure is a Timoshenko beam, and the vertical soil movement around the beam should be considered.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (the response of laterally loaded caissons from MATLAB code, FDM, and the field test).
Acknowledgments
The study presented herein is supported by the National Natural Science Foundation of China (Nos. 51878160 and 52078128) and the Natural Science Foundation of Jiangsu Province (BK20180155). The authors are grateful for their support.
Notation
The following symbols are used in this paper:
- D
- outer diameter of caisson;
- dw/dz
- rotation of the beam section;
- Ep
- Young’s modulus of the caisson;
- Esi
- elastic modulus of the ith layer of soil;
- Fa
- lateral force at the head of caisson;
- Fb
- lateral force at the end of caisson;
- Hi
- thickness of soil layer i;
- Ip
- second moment of inertia of cross section;
- L
- domain of the beam element;
- Lp
- embedment depth of caisson;
- Ma
- moment at the head of caisson;
- Mb
- moment at the end of caisson;
- p
- horizontal soil reaction per unit length;
- rp
- radius of the caisson;
- t
- wall thickness of caisson;
- tm
- thickness of the closed end of caisson;
- UD
- strain energy density of a soil element;
- Up
- energy density of a caisson segment;
- uz
- vertical displacement;
- w
- lateral displacement of the beam central line;
- y
- corresponding lateral displacement;
- Ω
- soil domain that participates in the structure–soil interaction;
- ψ
- rotation of plane section caused by the bending of the beam;
- ψ
- shear rotation of the plane section;
- κ
- shear correction factor;
- σpq
- stress in soil domain;
- εpq
- strain in soil domain;
- λsi, Gsi
- Lame’s constants of the ith layer of the multilayered continuum;
- vsi
- Poisson’s ratio of the ith layer of soil;
- ϕr
- dimensionless decay functions of the displacement components in the r- directions;
- ϕθ
- dimensionless decay functions of the displacement components in the θ- directions; and
- ϕz
- dimensionless decay functions of the displacement components in the z-directions.
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Published In
International Journal of Geomechanics
Volume 22 • Issue 8 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Oct 3, 2021
Accepted: Feb 6, 2022
Published online: Jun 1, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 1, 2022
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Cited by
- Abhisek Paul, Dipanjan Basu, Analysis of Laterally Loaded Large-Diameter Rigid Piles Considering Vertical and Horizontal Soil Displacements, Geo-Congress 2024, 10.1061/9780784485323.006, (48-58), (2024).
- Xiaojuan Li, Guoliang Dai, Closure to “Energy-Based Analysis of Laterally Loaded Caissons with Large Diameters under Small-Strain Conditions”, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-8980, 23, 10, (2023).
- Dipanjan Basu, Abhisek Paul, Discussion of “Energy-Based Analysis of Laterally Loaded Caissons with Large Diameters under Small-Strain Conditions”, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-8414, 23, 10, (2023).