A stability analysis of landslides based on random fields - Part I: Toe circle slope

  • X. P. ZhouEmail author
  • B. Z. Zhu
  • Louis N. Y. Wong
Original Article


The stability analysis of toe circle slopes is studied using random field theory from the perspective of probability, and the relationship between the failure probability of toe circle slopes and the correlation length is analyzed. The closed-form solutions of the safety factor and the failure probability of toe circle slopes are derived using the integration method. The accuracy of the safety factor of toe circle slopes is improved when the slice method is replaced by the integration method. The effects of spatial correlation length on the safety factor and failure probability of toe circle slopes are investigated. The results show that the spatial correlation length significantly affects the failure probability, and the vertical integration model is more suitable for the homogeneous toe circle slopes than the horizontal integration model.


Random fields Toe circle landslides Failure probability Integration method Safety factor Closed-form solution 



The work is supported by the National Natural Science Foundation of China (nos. 51325903, 51679017) and the Natural Science Foundation Project of CQ CSTC (nos. CSTC, cstc2013kjrcljrccj0001, cstc2013jcyjys0005, cstc2015jcyjys0002, cstc2015jcyjys0009, and cstc2016jcyjys0005).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingPeople’s Republic of China
  2. 2.School of Civil EngineeringChongqing UniversityChongqingPeople’s Republic of China
  3. 3.Key Laboratory of New Technology for Construction of Cities in Mountain AreaChongqingPeople’s Republic of China
  4. 4.Department of Earth ScienceThe University of Hong KongHong KongPeople’s Republic of China

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