Developing a unified nonlinear strength (UNS) criterion for geomaterials

  • Sui Wang
  • Zuliang ZhongEmail author
  • Yifei Fan
  • Xinrong Liu
Original Paper


There is a need for a unified strength criterion, which is a variable suitable for describing the different strength properties of different types of geomaterials. In this study, a unified nonlinear strength (UNS) criterion is proposed based on the Lade-Duncan criterion for the sake of versatility to capture the complex strength behaviors of geomaterials under three-dimensional (3D) stress paths. The strength curves in this theory are a series of continuous and smooth conical loci that covers wide ranges of the meridian and octahedral planes to describe the nonlinear strength behaviors of soils. The strength curves are located between von Mises and Lade-Duncan strength curves in the deviatoric plane in the principal stress space. Verifications between the proposed criterion and experimental data from triaxial tests found in the literature show that this new criterion is able to reasonably reflect the three-dimensional (3D) strength properties and strength nonlinearity of a variety of geomaterials.


Strength criterion Strength nonlinearity Unified strength theory Intermediate principal stress ratio 



The following symbols are used in this note:

I1I2I3three stress invariants

σ1σ2σ3three principal stresses

Ca model parameter

φ0granular material internal friction angle

J1J2J3three deviatoric principal stresses

qgeneral shear stress \( q=\sqrt{3/2}\sqrt{s_{ij}{s}_{ij}} \)

pmean principal stress p = σijδij/3

θLode angle

L2parameters of UNS criterion related to φ0

L3parameters of UNS criterion related to φ0

δa dimensionless parameter

g0(θ)shape function of the Lade-Duncan criterion

Mcoefficient of friction

σ0spherical stress

γθpolar radius of UNS criterion on the octahedral plane

γ0polar radius of UNS criterion on the octahedral plane and that with θ = 0°

αa model parameter

prthe reference stress pr = 101kPa

Mfreflects the frictional property of the nonlinear material

ncurvature parameter

bthe intermediate principal stress ratio

Funding information

The work presented in this study was financially supported by the National Natural Science Foundation of China (Grant No. 51108485) and the Natural Science Foundation Project of Chongqing (CSTC2013JCYJA30005).


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Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  • Sui Wang
    • 1
    • 3
  • Zuliang Zhong
    • 1
    • 2
    Email author
  • Yifei Fan
    • 1
  • Xinrong Liu
    • 1
    • 2
  1. 1.College of Civil EngineeringChongqing UniversityChongqingChina
  2. 2.National Joint Engineering Research Center of Geohazards Prevention in the Reservoir AreasChongqingChina
  3. 3.School of Civil and Transportation EngineeringNingbo University of TechnologyNingboChina

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