## Abstract

In this study, large-scale triaxial compression tests are conducted on gravelly soil material. The experimental investigation shows that gravelly soil exhibits complicated volume-dilatation/contraction behaviours that are dependent on stress level. To better describe the mechanical behaviours, an elastoplastic constitutive model is proposed within the frameworks of generalised plasticity and the critical state soil mechanics. An evolution equation of the void ratio is incorporated into the model to describe the effect of a relatively dense or loose state on the volume-change behaviours. The model has 10 material constants that could be determined using a few large-scale conventional triaxial tests. The model is then used to simulate the mechanical behaviours of gravelly soil. Comparisons between the numerical simulations and the test data show that the model is capable of capturing the mechanical behaviours of gravelly soil under various confining pressures. This research can be beneficial for understanding the mechanical behaviours of gravelly soils.

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## Funding

The work presented in this paper were financially supported by Open Funds at the Key Laboratory of Geological Hazards on Three Gorges Reservoir Area (China Three Gorges University), Ministry of Education (Grant No. 2015KDZ16 and 2015KDZ15) and by Open Fund Research at the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (Grant No. SKHL1725).

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Responsible Editor: Abdullah Al-Amri

## Appendix: Notations and definitions

### Appendix: Notations and definitions

In this study, some important qualities related to stress and strain are defined. The mean stress *p*, deviatoric stress *q* and Lode’s angle *θ* are respectively calculated using:

where *σ*_{kk} with a subscript of double “kk” denotes the sum calculation of the tensor, namely, *σ*_{kk} = *σ*_{11} + *σ*_{22} + *σ*_{33}, *s*_{ij} is the deviatoric stress tensor, namely, *s*_{ij} = *σ*_{ij} − *pδ*_{ij}, *δ*_{ij} is the Kronecker tensor, with i = j, *δ*_{ij} = 1; i ≠ j, *δ*_{ij} = 0, and *J*_{3} is the third invariant of the deviatoric stress tensor, namely, *J*_{3} = det *s*_{ij}.

The volumetric strain *ε*_{v} and equivalent shear strain \( {\overline{\gamma}}_{\mathrm{s}} \) are calculated using:

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Zhang, JC., Li, Y., Xu, B. *et al.* Testing and constitutive modelling of the mechanical behaviours of gravelly soil material.
*Arab J Geosci* **13**, 523 (2020). https://doi.org/10.1007/s12517-020-05385-9

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DOI: https://doi.org/10.1007/s12517-020-05385-9