A curing-dependent hybrid Popovics–Thorenfeldt constitutive model for geopolymer-stabilized lateritic soil under uniaxial compression

Constitutive models are useful for describing the stress–strain response of stabilized soils in geotechnical analysis. However, existing models for geopolymer-stabilized soils often have difficulty reproducing brittle post-peak behavior or require specimen-specific calibration. This study develops a curing-dependent hybrid Popovics–Thorenfeldt model for geopolymer-stabilized lateritic soil under uniaxial compression. The model uses the Popovics equation for the ascending branch and a Thorenfeldt-type function for post-peak softening. Calibration and internal cross-validation were based on 18 stress–strain curves covering three fly ash contents (20%, 30%, and 40%), three curing regimes (open-air, sealed, and saturated), and two curing ages (28 and 91 days). A hierarchical procedure was used to relate the curvature parameter β to compressive strength. Compared with the constant-β Popovics model, the proposed formulation reduced the average Root Mean Squared Error (RMSE) from 0.525 to 0.464 MPa (11.5%) and increased the mean coefficient of determination (R 2 ) from 0.748 to 0.803. The normalized ascending branch followed β(y)=3.42 + 2.20y, with comparable coefficients across curing regimes. Cross-validation indicated that the shared parameters were transferable within the tested experimental domain, although independent validation using other materials and curing histories is still needed. The current formulation addresses only uniaxial compression and does not explicitly account for confinement effects, strain-rate dependence, or cyclic loading behavior. Extension toward triaxial stress states would likely require incorporating pressure-dependent modifications to peak strain and softening parameters.

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Publication Details

Journal
Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications
Published
2026-11-02
DOI
https://doi.org/10.1177/14644207261503040
Primary Topic
Geotechnical Engineering and Soil Stabilization
Type
article
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article

A curing-dependent hybrid Popovics–Thorenfeldt constitutive model for geopolymer-stabilized lateritic soil under uniaxial compression

Loi Van Bui, Lanh Si Ho
2 links
Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications
Geotechnical Engineering and Soil Stabilization
article

A curing-dependent hybrid Popovics–Thorenfeldt constitutive model for geopolymer-stabilized lateritic soil under uniaxial compression

Loi Van Bui, Lanh Si Ho
article en

Abstract

Constitutive models are useful for describing the stress–strain response of stabilized soils in geotechnical analysis. However, existing models for geopolymer-stabilized soils often have difficulty reproducing brittle post-peak behavior or require specimen-specific calibration. This study develops a curing-dependent hybrid Popovics–Thorenfeldt model for geopolymer-stabilized lateritic soil under uniaxial compression. The model uses the Popovics equation for the ascending branch and a Thorenfeldt-type function for post-peak softening. Calibration and internal cross-validation were based on 18 stress–strain curves covering three fly ash contents (20%, 30%, and 40%), three curing regimes (open-air, sealed, and saturated), and two curing ages (28 and 91 days). A hierarchical procedure was used to relate the curvature parameter β to compressive strength. Compared with the constant-β Popovics model, the proposed formulation reduced the average Root Mean Squared Error (RMSE) from 0.525 to 0.464 MPa (11.5%) and increased the mean coefficient of determination (R 2 ) from 0.748 to 0.803. The normalized ascending branch followed β(y)=3.42 + 2.20y, with comparable coefficients across curing regimes. Cross-validation indicated that the shared parameters were transferable within the tested experimental domain, although independent validation using other materials and curing histories is still needed. The current formulation addresses only uniaxial compression and does not explicitly account for confinement effects, strain-rate dependence, or cyclic loading behavior. Extension toward triaxial stress states would likely require incorporating pressure-dependent modifications to peak strain and softening parameters.

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications
University Of Transport Technology (VN)
Openalex Percentile: Top 21%
Geotechnical Engineering and Soil Stabilization
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