Optimized back analysis method for stress determination based on identification of local stress measurements and its application

  • Qitao PeiEmail author
  • Xiuli Ding
  • Yuankun Liu
  • Bo Lu
  • Shuling Huang
  • Jing Fu
Original Article


This paper presents an optimization method, including the identification of local stress measurements and a two-stage back analysis, to determine in situ stress under complex conditions. Firstly, the macro-regional distribution characteristics of in situ stress can be interpreted by analyzing regional geological conditions, topography, as well as rock mass failure phenomena. Then, a stereographic projection method (SPM) is used to determine the distribution features of stress tensor on an arbitrary plane. On this basis, some representative measured data, which can reflect the distribution characteristics of in situ stress in the study area can be identified. After that, a first-stage back analysis by finite difference method (FDM) is used to calculate the field stresses from the selected in situ measured data. The obtained boundary stresses are taken to consist of a constant term, a term that varies linearly with depth, and a hyperbolic term. Further, a second-stage back analysis by discrete element method (DEM) is carried out to determine the local field stresses which are significantly affected by discontinuities and excavations. The FDM back analysis results can serve as the initial input stress conditions for DEM analysis, and the optimum stress conditions for DEM analysis will be reasonably obtained by using the uniform design method through the second-stage back analysis. To show the feasibility of the optimized method, it is applied to the Wudongde Hydropower Station to determine in situ stress. Based on local stress measurements by borehole stress relief method using hollow inclusion strain gauges, some representative measured data are selected by SPM. The unknown state of stress in the station is estimated through the first-stage back analysis by FDM. For some local key areas, encountered discontinuities or excavations in the vicinity, the local field stresses are calculated through the second-stage back analysis by DEM. Finally, the results are compared with those elicited from the borehole stress relief method. It is shown that the calculated results by the first-stage back analysis agree well with the measured ones on the whole, but the discrepancy is large in the vicinity of discontinuities as well as excavation disturbance. However, the calculated results by the second-stage back analysis roughly coincide with the measured data with lower allowable error.


In situ stress Stress measurement Stereographic projection Back analysis Numerical modeling 



The authors gratefully acknowledge the financial support of the National Science Foundation of China (Nos. 51539002, 51609018, 51379022) and the National key research and development project of China (Nos. 2016YFC0401802, 2016YFC0401804). The work in this paper was also supported by funding from the Basic Research Fund for Central Research Institutes of Public Causes (No. CKSF2017030/YT, CKSF2017054/YT).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Qitao Pei
    • 1
    Email author
  • Xiuli Ding
    • 1
  • Yuankun Liu
    • 1
  • Bo Lu
    • 1
  • Shuling Huang
    • 1
  • Jing Fu
    • 1
  1. 1.Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water ResourcesYangtze River Scientific Research InstituteWuhanChina

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