Relationship between small and large strain solutions for general cavity expansion problems in elasto-plastic soils |
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| Institution: | 1. Division of Geotechnical and Tunnel Engineering, University of Innsbruck, Austria;2. Department of Mathematics, University of Innsbruck, Austria;1. Seazen Holdings Co., Ltd. Shanghai Second Branch, Shanghai 201800, China;2. Key Laboratory of Rail Infrastructure Durability and System Safety, Tongji University, Shanghai 201804, China;3. Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Cao An highway.4800, 201804 Shanghai, China;4. Department of Civil Engineering, McMaster University, Main Street West.1280, L8S4L7 Hamilton, Canada;1. Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, School of Civil Engineering, Chongqing University, Chongqing 400045, China;2. College of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China;3. School of Computer Science, Engineering and Mathematics, Flinders University, 1284 South Road Clovelly Park, South Australia, 5042, GPO Box 2100, Adelaide 5001, South Australia, Australia;4. College of Civil Engineering, Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing 400045, China;1. Marine and Land Geotechnics and Geomechanics, Institute for Geoscience, Kiel University, Ludewig–Meyn–Str. 10, 24321 Kiel, Germany;2. Faculty of Science, Charles University in Prague, Albertov 6, 12843 Prague 2, Czech Republic;1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;2. Department of Civil Engineering, Shanghai University, Shanghai 200444, China |
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| Abstract: | This paper presents a closed-form relationship between small and finite strain cavity expansion solutions. Its derivation is based on the non-linearly elastic–perfectly plastic cylindrical (or spherical) problem considering a general Mohr’s criterion and constant plastic dilatancy. It is shown, however, that it is sufficiently accurate for general expansion problems not obeying plane-strain rotationally (or spherically) symmetric conditions and involving strain-hardening/softening constitutive behaviour. Therefore, this relationship quantifies the error stemming from the computational assumption of small deformations and provides a simple and efficient way of accounting for geometric non-linearity based entirely on conventional computational methods: ‘self-correction’ of small strain analyses results. |
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| Keywords: | Cavity expansion Deformation Hyperbolic function Plasticity |
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