Cauchy problem of three‐dimensional critical slip surfaces of slopes |
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Authors: | Hong Zheng Guan Hua Sun Chun Guang Li |
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Institution: | 1. China Three Gorges University, Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, Yi Chang 443002, People's Republic of China;2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China |
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Abstract: | Using the continuum‐based finite element approach in conjunction with the strength reduction technique, one can easily find out the factor of safety of a slope with rather high precision, but will encounter some obstacles in the accurate location of the corresponding three‐dimensional critical slip surface (CSS). On the basis of the Mohr–Coulomb failure criterion and the stress field in the limit equilibrium state of the slope, it is deduced that the three‐dimensional CSS is the solution of the Cauchy problem of a quasi‐linear partial differential equation (PDE) of first order. By means of the method of characteristics for the problem, the three‐dimensional CSS that may take any shape can be determined without the specification of its geometry. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | slope three‐dimensional critical slip surface Cauchy problem finite element method |
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