Abstract
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.
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Notation
The following symbols are used in this note:
I1, I2, I3three stress invariants
σ1, σ2, σ3three principal stresses
Ca model parameter
φ0granular material internal friction angle
J1, J2, J3three 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
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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Editorial Handling: C. Gokceoglu
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Wang, S., Zhong, Z., Fan, Y. et al. Developing a unified nonlinear strength (UNS) criterion for geomaterials. Arab J Geosci 12, 187 (2019). https://doi.org/10.1007/s12517-019-4379-z
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DOI: https://doi.org/10.1007/s12517-019-4379-z