Testing and constitutive modelling of the mechanical behaviours of gravelly soil material

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.

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:

$$ p=\frac{1}{3}{\sigma}_{\mathrm{kk}},\kern1em q=\sqrt{1.5{s}_{\mathrm{ij}}{s}_{\mathrm{ij}}},\kern1em \theta =\frac{1}{3}{\sin}^{-1}\left(-\frac{27{J}_3}{2{q}^3}\right) $$

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where σ_kk with a subscript of double “kk” denotes the sum calculation of the tensor, namely, σ_kk = σ₁₁ + σ₂₂ + σ₃₃, 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 J₃ is the third invariant of the deviatoric stress tensor, namely, J₃ = det s_ij.

The volumetric strain ε_v and equivalent shear strain ${\overline{\gamma}}_{\mathrm{s}}$ are calculated using:

$$ {\varepsilon}_{\mathrm{v}}={\varepsilon}_{\mathrm{kk}},\kern1em {\overline{\gamma}}_{\mathrm{s}}=\sqrt{\frac{2}{3}\left({\varepsilon}_{\mathrm{ij}}-\frac{\varepsilon_{\mathrm{v}}{\delta}_{\mathrm{ij}}}{3}\right)\left({\varepsilon}_{\mathrm{ij}}-\frac{\varepsilon_{\mathrm{v}}{\delta}_{\mathrm{ij}}}{3}\right)} $$

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