Similarity solution for cavity expansion in thermoplastic soil |
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Authors: | Hang Zhou Gangqiang Kong Hanlong Liu Lyesse Laloui |
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Institution: | 1. Key Laboratory of New Technology for Construction of Cities in Mountain Area, School of Civil Engineering, Chongqing University, Chongqing, China;2. State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, China;3. School of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China;4. School of Civil Engineering, Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, China;5. Soil Mechanics Laboratory, Ecole Polytechnique Fédéralede Lausanne (EPFL), Lausanne, Switzerland |
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Abstract: | This paper presents an analytical solution for cavity expansion in thermoplastic soil considering non‐isothermal conditions. The constitutive relationship of thermoplasticity is described by Laloui's advanced and unified constitutive model for environmental geomechanical thermal effect (ACMEG‐T), which is based on multi‐mechanism plasticity and bounding surface theory. The problem is formulated by incorporating ACMEG‐T into the theoretical framework of cavity expansion, yielding a series of partial differential equations (PDEs). Subsequently, the PDEs are transformed into a system of first‐order ordinary differential equations (ODEs) using a similarity solution technique. Solutions to the response parameters of cavity expansion (stress, excess pore pressure, and displacement) can then be obtained by solving the ODEs numerically using mathematical software. The results suggest that soil temperature has a significant influence on the pressure‐expansion relationships and distributions of stress and excess pore pressure around the cavity wall. The proposed solution quantifies the influence of temperature on cavity expansion for the first time and provides a theoretical framework for predicting thermoplastic soil behavior around the cavity wall. The solution found in this paper can be used as a theoretical tool that can potentially be employed in geotechnical engineering problems, such as thermal cone penetration tests, and nuclear waste disposal problems. |
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Keywords: | cavity expansion ordinary differential equations thermoplastic soil |
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