Environmental Earth Sciences

, 77:758 | Cite as

Application of a unified linear yield criterion in plane strain to study the strength theory effect in geotechnical engineering

  • Changguang Zhang
  • Mingming Cai
  • Junhai Zhao
  • Lizhou WuEmail author
Original Article


The plane strain condition is a common, but polyaxial stress state for geotechnical structure designs, in which the selection of an appropriate yield or failure criterion is crucial to reasonably account for the intermediate principal stress. Under plane strain condition, a unified linear yield criterion for seven commonly used geotechnical yield criteria is presented in conjunction with the inductive method. These seven yield criteria considered in this study are the Mohr–Coulomb, Tresca, Drucker–Prager, Mogi–Coulomb, Extended Matsuoka–Nakai, Extended Lade–Duncan criteria, and the Unified Strength Theory. The generalized analytical solutions for earth pressure of retaining walls, critical load of strip foundations as well as stress and displacement of circular tunnels are derived on the basis of the proposed unified yield criterion, and their respective theoretical significance is analyzed. Thereafter, the critical load of strip foundations obtained herein is compared with two numerical results from the literature. Furthermore, the effect of strength theory on result differences of the three typical geotechnical problems by simply selecting constants, which conform to different yield criteria, is explored through a parametric study. It is found that the proposed unified yield criterion is convenient for investigating analytical solutions of the aforementioned geotechnical structures. The strength theory effect due to adopting different yield criteria is considerably significant, which cannot be ignored. Additionally, recommendations are provided on how to make use of these seven yield criteria for an optimum design.


Unified linear yield criterion Plane strain Effect of strength theory Intermediate principal stress Generalized analytical solution 



The financial support provided by the National Natural Science Foundation of China (NSFC 41202191 and 51878056), the Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (SKLGP2017K025), the Special Fund for Basic Scientific Research of Central Colleges (310828173402), and the China Scholarship Council (CSC 201706565020) is gratefully acknowledged. The authors would like to thank four anonymous reviewers for their constructive suggestions in improving the original manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Changguang Zhang
    • 1
    • 2
  • Mingming Cai
    • 1
  • Junhai Zhao
    • 1
  • Lizhou Wu
    • 2
    Email author
  1. 1.School of Civil EngineeringChang’an UniversityXi’anChina
  2. 2.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologyChengduChina

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