Geotechnical and Geological Engineering

, Volume 31, Issue 4, pp 1011–1025 | Cite as

Response Surface Method of Reliability Analysis and its Application in Slope Stability Analysis

  • Xiao-hui Tan
  • Meng-fen Shen
  • Xiao-liang Hou
  • Dan Li
  • Na Hu
Original paper


The response surface method (RSM) is a powerful approach for carrying out reliability analysis for complicate engineering with implicit limit state functions. The quality of a response surface mainly depends on the choice of response surface function and the selection of sample points. To investigate the influence of the types of response surface functions and to reduce the computation efforts, two new sampling methods and a hybrid RSM are proposed. In the hybrid RSM, four types of response surface functions and three sampling methods are involved, and each Response surface function can be connected to each sampling method. The four response surface functions are quadratic polynomial without cross terms (PN1), quadratic polynomial with cross terms, radial basic function network (RBFN) and support vector machine (SVM). The three RSMs using the traditional sampling method, the new iterative sampling method and the new experiment design method are RSM1, RSM2 and RSM3, respectively. The accuracy and efficiency of different RSMs are illustrated through three examples. When an iterative method is used for locating sample points, the PN1-based RSM2 is proposed for its accuracy and efficiency. And when an experiment design method is used for locating sample points, the RBFN- or SVM-based RSM3 is suggested because the RBFN or SVM is suitable for global fitting.


Reliability analysis Response surface method (RSM) First-order reliability method (FORM) Radial basis function network (RBFN) Support vector machine (SVM) Slope stability analysis 



Response surface method


Response surface function


Limit state function


Quadratic polynomial without cross terms


Quadratic polynomial with cross terms


Radial basic function network


Support vector machine


First-order reliability method


Monte–Carlo simulation method


Traditional sampling method


New iterative sampling method


New experiment design method



The financial supports from the National Natural Science Foundation (40972194), China Postdoctoral Science Foundation (2011M501039) and the Center for Post-doctoral Studies of Geology, Hefei University of Technology are greatly acknowledged. The authors appreciate the valuable comments from the anonymous reviewers.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Xiao-hui Tan
    • 1
  • Meng-fen Shen
    • 1
  • Xiao-liang Hou
    • 1
  • Dan Li
    • 1
  • Na Hu
    • 1
  1. 1.School of Resources and Environmental EngineeringHefei University of TechnologyHefeiChina

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