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Derivation and application of an analytical rock displacement solution on rectangular cavern wall using the inverse
Mingzhong Gao1,2, Bin Yu3, Zhiqiang Qiu1,2
1State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu, China.
This study introduces a novel complex variable method to accurately calculate rectangular cavern wall rock deformation. The approach simplifies complex calculations, improving accuracy and aiding in controlling underground structure stability.
Area of Science:
- Geotechnical Engineering
- Computational Mechanics
- Applied Mathematics
Background:
- Rectangular caverns are crucial in underground engineering, but their failure mechanisms are complex due to unique stress distributions.
- Conventional methods for analyzing rectangular cavern wall rock deformation are computationally intensive and yield multiple solutions.
- Understanding and predicting wall rock deformation is vital for ensuring the stability and safety of underground structures.
Purpose of the Study:
- To develop a more efficient and accurate computational method for analyzing rectangular cavern wall rock deformation.
- To address the limitations of conventional methods, specifically the long computational processes and multiple displacement solutions.
- To provide a theoretical framework for predicting and controlling cavern wall rock failure.
Main Methods:
- Utilized Laurent series complex method and complex variable function theory for mapping function expression.
- Integrated Schwarz-Christoffel method to determine mapping function coefficients and calculate cavern wall rock deformation.
- Employed inverse mapping concepts to establish relationships between coordinate systems and analyze displacement fields.
Main Results:
- Developed a theoretical formula to calculate wall rock boundary deformation and displacement fields.
- Demonstrated the validity of the theoretical method by comparing results with ANSYS numerical software, showing identical trends.
- Significantly improved computational accuracy and reduced the complexity of solving for cavern boundary and internal wall rock displacements.
Conclusions:
- The proposed complex variable method offers a valid and efficient approach for analyzing rectangular cavern wall rock deformation.
- This method provides a valuable theoretical guide for managing and mitigating cavern wall rock deformation and failure in underground engineering projects.
- The findings contribute to enhanced safety and stability in the design and construction of underground structures.
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