A Complex Variable Solution for Shallow Rectangular Tunnel in Semi-Infinite Plane
Publication: Journal of Engineering Mechanics
Volume 148, Issue 4
Abstract
The rectangular pipe jacking method, as a new type of shallow tunnel excavation technology, is increasingly widely used in practical engineering due to its advantages of higher space utilization and fewer impacts on the surrounding environment. The construction process of pipe jacking will cause stress change and deformation of the surrounding soil. In this paper, on the basis of the complex variable elasticity, an analytical solution for a shallow rectangular pipe jacking tunnel under the action of rectangular cavity contraction and inner uniform pressure is proposed. Through the conformal mapping technique, the rectangular cavity in a semi-infinite plane is first transformed as a unit concentric ring. Then, the stress functions for the stress and displacement around the rectangular cavity under two types of boundary conditions are derived, which allows the stress change and deformation of the surrounding soil to be determined. The proposed analytical solutions are verified by comparison with the results of finite-element numerical simulations. Parametric studies are conducted to investigate the influence of the Poisson’s ratio effects of soil, tunnel aspect ratio, and tunnel burial depth on the stress and displacement of soil. The proposed analytical solution can be potentially applied to the problem of a rectangular tunnel using pipe jacking.
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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
The work was supported by the National Natural Science Foundation of China, Grant/Award Nos. 51978105 and 52027812; the Chongqing Youth Top Talent Plan, Grant/Award No. cstc2021ycjh-bgzxm0132; and the Innovation Group Science Foundation of the Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-cxttX0003).
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 4 • April 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 25, 2021
Accepted: Dec 13, 2021
Published online: Jan 17, 2022
Published in print: Apr 1, 2022
Discussion open until: Jun 17, 2022
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