Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary
Abstract
:1. Introduction
2. Rectangular Pipe Jacking Excavation Cross-Section Modeling
2.1. Semi-Infinite Plane Strain Model
2.2. Conformal Transformation
2.3. Potential Function and Boundary Condition
3. Potential Function Solution and Stress–Displacement Calculation
3.1. Potential Function Solution
3.2. Stress–Displacement Calculation
4. Comparative Verification
4.1. Comparison with Numerical Solutions
4.2. Comparison with Engineering-Measured Data
5. Parametric Analysis
5.1. The Effect of the Control Points of the Mapping Function on the Accuracy of Analytic Solutions
5.2. The Effect of Model Parameters on Settlement and Stress
6. Conclusions
- The displacements and stresses of the analytical solution are consistent with the corresponding finite element solution, and the differences between the analytical solution and the engineering-measured data are acceptable in surface subsidence patterns, maximum values, and ranges.
- For the top pipe excavation, the midpoints and corners of the top boundary and the midpoints and corners of the bottom boundary can be used as the four control points of the mapping function. The accuracy of the calculation results can meet engineering requirements.
- The surface subsidence increases with the increase in the stratum loss rate, the span, and the stratum unit weight. Moreover, it decreases with the increase in the buried depth, but it will eventually tend to a constant value.
- The major principal stress at the top boundary of the pipe jacking excavation and near the corner points changed obviously with the change in the stratum loss rate, span, buried depth, and the stratum unit weight. Nevertheless, the change in the major principal stress at the other locations was not obvious. The stress concentrations at the four corners and the center of the top boundary of the excavation were more obvious.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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m = 2 | m = 3 | m = 4 | m = 5 | m = 6 | |
---|---|---|---|---|---|
−7.07103 | −7.56903 | −7.79914 | −7.79835 | −7.79811 | |
0.17157 | 0.08030 | 0.26592 | 0.26573 | 0.26569 | |
−0.30093 | −0.56187 | −0.58143 | −0.58425 | ||
−0.10561 | −0.10527 | −0.10516 | |||
0.00139 | 0.00149 | ||||
−0.00002 |
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Wang, Y.; Xiang, Y. Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary. Appl. Sci. 2024, 14, 1154. https://doi.org/10.3390/app14031154
Wang Y, Xiang Y. Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary. Applied Sciences. 2024; 14(3):1154. https://doi.org/10.3390/app14031154
Chicago/Turabian StyleWang, Yaze, and Yanyong Xiang. 2024. "Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary" Applied Sciences 14, no. 3: 1154. https://doi.org/10.3390/app14031154
APA StyleWang, Y., & Xiang, Y. (2024). Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary. Applied Sciences, 14(3), 1154. https://doi.org/10.3390/app14031154