Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application
In urban environment, it is often unavoidable for shallow tunnels to be constructed adjacent to existing pile foundations. To obtain the ground displacements and stresses induced by shallow tunneling and existing pile foundation loads, the key procedure involves superimposing the analytical solution...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2019/5739123 |
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| author | Caixia Guo Kaihang Han Heng Kong Leilei Shi |
| author_facet | Caixia Guo Kaihang Han Heng Kong Leilei Shi |
| author_sort | Caixia Guo |
| collection | DOAJ |
| description | In urban environment, it is often unavoidable for shallow tunnels to be constructed adjacent to existing pile foundations. To obtain the ground displacements and stresses induced by shallow tunneling and existing pile foundation loads, the key procedure involves superimposing the analytical solution for shallow tunneling in green-field with the analytical solution for existing structure loads. In green-field, the complex variable method provides exact analytical solutions of ground displacements and stresses caused by shallow tunneling. However, the exact analytical solutions are not directly expressed as explicit functions of the coordinates (x, y) in the physical plane (called implicit form of exact analytical solutions), whereas the displacements and stresses induced by existing structure loads are explicit functions of the coordinates (x, y) in the physical plane, which makes it difficult to superpose the displacements and stresses induced by existing structure loads. In this paper, explicit form of exact analytical solutions of displacements and stresses induced by shallow tunneling in green-field is obtained by using the inverse conformal transformation and the Cauchy–Riemann equations. Comparison with implicit form of exact analytical solutions shows that the explicit form of exact analytical solutions is intuitional and easily used by engineers, and moreover, the calculation amount is much smaller than that for the implicit form of exact analytical solutions. Then, an application involving superimposing the explicit form of exact analytical solutions with Mindlin’s solution is implemented to analyze the secondary stress field and the related potential plastic zone caused by shallow tunneling adjacent to pile foundations. Moreover, the influences of pile foundation parameters on the ranges and shapes of the potential plastic zones induced by nearby tunneling are analyzed. |
| format | Article |
| id | doaj-art-57ab043621ee43ebae44966ab570e52b |
| institution | Kabale University |
| issn | 1687-8086 1687-8094 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj-art-57ab043621ee43ebae44966ab570e52b2025-02-03T07:26:15ZengWileyAdvances in Civil Engineering1687-80861687-80942019-01-01201910.1155/2019/57391235739123Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its ApplicationCaixia Guo0Kaihang Han1Heng Kong2Leilei Shi3Department of Civil Engineering, Tsinghua University, Beijing 100084, ChinaDepartment of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095, USABeijing Municipal Construction Co., Ltd., Beijing 100048, ChinaBeijing No. 4 Municipal Construction Engineering Co., Ltd., Beijing 100176, ChinaIn urban environment, it is often unavoidable for shallow tunnels to be constructed adjacent to existing pile foundations. To obtain the ground displacements and stresses induced by shallow tunneling and existing pile foundation loads, the key procedure involves superimposing the analytical solution for shallow tunneling in green-field with the analytical solution for existing structure loads. In green-field, the complex variable method provides exact analytical solutions of ground displacements and stresses caused by shallow tunneling. However, the exact analytical solutions are not directly expressed as explicit functions of the coordinates (x, y) in the physical plane (called implicit form of exact analytical solutions), whereas the displacements and stresses induced by existing structure loads are explicit functions of the coordinates (x, y) in the physical plane, which makes it difficult to superpose the displacements and stresses induced by existing structure loads. In this paper, explicit form of exact analytical solutions of displacements and stresses induced by shallow tunneling in green-field is obtained by using the inverse conformal transformation and the Cauchy–Riemann equations. Comparison with implicit form of exact analytical solutions shows that the explicit form of exact analytical solutions is intuitional and easily used by engineers, and moreover, the calculation amount is much smaller than that for the implicit form of exact analytical solutions. Then, an application involving superimposing the explicit form of exact analytical solutions with Mindlin’s solution is implemented to analyze the secondary stress field and the related potential plastic zone caused by shallow tunneling adjacent to pile foundations. Moreover, the influences of pile foundation parameters on the ranges and shapes of the potential plastic zones induced by nearby tunneling are analyzed.http://dx.doi.org/10.1155/2019/5739123 |
| spellingShingle | Caixia Guo Kaihang Han Heng Kong Leilei Shi Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application Advances in Civil Engineering |
| title | Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application |
| title_full | Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application |
| title_fullStr | Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application |
| title_full_unstemmed | Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application |
| title_short | Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application |
| title_sort | explicit form of exact analytical solution for calculating ground displacement and stress induced by shallow tunneling and its application |
| url | http://dx.doi.org/10.1155/2019/5739123 |
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