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Calibrating and validating a soil constitutive model through conventional triaxial tests: an in-depth study on CSUH model

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Abstract

This paper presents an approach for calibrating and validating a constitutive model via conventional triaxial tests. First, the consolidated drained triaxial compression test results are used for model calibration. The particle swarm optimization algorithm based on multiple adaptive strategies is then adopted to calibrate the best fitting parameters. Subsequently, the constitutive model is validated by considering its performance in modeling the consolidated undrained triaxial tests. The unified hardening model for clays and sands (CSUH model) proposed by Yao et al. (Comput Geotech 110:326–343, 2019. 10.1016/j.compgeo.2019.02.024) is considered. The results demonstrate that the CSUH model can well describe the dilatancy of clays and sands with different densities in both drained and undrained triaxial tests.

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Abbreviations

\(C_{ij}\) :

The element of elastic matrix \(\left[ {C_{ij}^{e} } \right]\) or elastoplastic matrix \(\left[ {C_{ij}^{ep} } \right]\); i and j = 1, 2, 3

e :

Current void ratio

e 0 :

Initial void ratio

e c0 :

Void ratio on the critical state line (CSL) at p′ = 0 kPa

E :

Elastic modulus

H :

Hardening parameter

m :

Dilatancy parameter

M :

Critical state stress ratio: slope of CSL in p′–q coordinates

M c :

Characteristic state stress ratio

M f :

Potential failure stress ratio

MRE :

Assessment criteria: mean relative error

N :

Void ratio of the asymptote of normal compression line (RNCL) at p′ = 1 kPa in the e ~ lnp′ coordinates

p′:

Mean effective stress \(p^{\prime} = \frac{{\sigma^{\prime}_{1} + 2\sigma^{\prime}_{3} }}{3}\) in conventional compression test

\(p^{\prime}_{x}\) :

Intersection of current yield surface with the p′-axis

\(p^{\prime}_{x0}\) :

Initial value of \(p^{\prime}_{x}\)

p s :

Compressive hardening parameter

\(p^{\prime}_{y}\) :

Intersection of plastic potential surface with the p′-axis

q :

Deviatoric stress \(q = \left( {\sigma^{\prime}_{1} - \sigma^{\prime}_{3} } \right)\) in conventional compression test

R :

Assessment criteria: the determination coefficient

R :

Search area of exemplar Xi

u :

Excess pore pressure

V i :

Velocity of exemplar

X i :

Exemplar or potential solution of the optimization problem

Z :

The void ratio of the normal compression line (NCL) at p′ = 1 kPa for sands in the e ~ lnp′ coordinates

κ :

Slope of the unloading line in the e ~ ln(p′ + ps) coordinates

λ :

Slope of the NCL in the e ~ ln(p′ + ps) coordinates, is also the slope of the RNCL in the e ~ lnp′ coordinates

η :

Stress ratio \(\eta = \frac{q}{{p^{\prime}}}\)

ν :

Poisson’s ratio

χ :

Critical state parameter

ξ :

State variable describing the current density

ε i :

The maximum, medium and minimum principal strain when i = 1, 2, and 3, respectively

\(\varepsilon_{v}\) :

Volumetric strain

\(\varepsilon_{v}^{p}\) :

Plastic (unrecoverable) volumetric strain

\(\sigma^{\prime}_{j}\) :

The maximum, medium and minimum effective principal stress when j = 1, 2, 3, respectively

\(\sigma^{\prime}_{3i}\) :

Initial confine pressure in the shear stage

\(\sigma^{\prime}_{c}\) :

Pre-consolidation pressure

Λ :

Total error: the average value of all individual error MRE(Xi)

Δε i :

The ith principal strain increment, i = 1, 2, 3

\(\Delta \sigma^{\prime}_{j}\) :

The jth principal stress increment, j = 1, 2, 3

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Acknowledgements

This study was supported by the National Key R&D Program of China (Grant No. 2018YFE0207100), the National Natural Science Foundation of China (Grant No. 51979001), and the National Key Basic Research Development Plan of China (Grant No. 2014CB047006). Thanks to Professor Enlong Liu for the discussion and experimental data. Thanks to Professor Xuewen Xia for providing the source code of the MAPSO algorithm. Thanks to Professor Erxiang Song and Xu Li for their valuable advice. Thanks to Dr. Shun Wang, Jian Han and Wenjie Cui for the excellent correction and polishing to this manuscript.

Funding

National Key R&D Program of China (Grant No. 2018YFE0207100), Innovative Research Group Project of the National Natural Science Foundation of China (Grant No. 51979001), National Basic Research Program of China (973 Program) (Grant No. 2014CB047006).

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Authors and Affiliations

  1. School of Transportation Science and Engineering, Beihang University, Beijing, 100191, China

    Binglong Zhu

  2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Institute of Water Resources and Hydropower Research, No. 20, West Chegongzhuang Rd., Beijing, 100048, China

    Zuyu Chen

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  1. Binglong Zhu
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Zhu, B., Chen, Z. Calibrating and validating a soil constitutive model through conventional triaxial tests: an in-depth study on CSUH model. Acta Geotech. 17, 3407–3420 (2022). https://doi.org/10.1007/s11440-021-01432-1

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