Equivalent granular state parameter and undrained behaviour of sand–fines mixtures

Abstract

State parameter defined using void ratio, e, and the steady-state line has been shown to be effective in predicting the undrained behaviour of sand. However, steady-state line for sand with fines is dependent on fines content. To overcome this problem, the concept of equivalent granular void ratio, e*, has been well investigated. However, the conversion from e to e* has been essentially a back-analysis process. A methodology for converting e to e* without the need of a back-analysis process was first presented. The concept of equivalent granular state parameter, ψ*, defined in terms of e*, and equivalent granular steady-state line was then developed. An extensive experimental study was conducted to investigate whether ψ* can capture the effects of fines content, and thus can be used to correlate undrained behaviour of sand–fines mixtures without the need of separately considering the effects of fines content. This study suggested that the effective stress path and deviatoric stress–strain responses in undrained shearing can be correlated with the ψ* value at the start of undrained shearing irrespective of fines content.

Appendix 1

Instability (flow and limited flow) is equivalent to dq < 0 with shearing. q = ηp′ leads to:

$$ dq = \eta dp^{\prime} + p^{\prime}d\eta $$

(9)

Based on elasto-plastic idealization, undrained shearing implies:

$$ 0 = d\varepsilon_{v}^{{}} = d\varepsilon_{v}^{e} + d\varepsilon_{v}^{p}, $$

(10)

where superscripts “e” and “p” denote elastic and plastic components, respectively. A contractant response means with shearing, $d\varepsilon_{v}^{p} > 0$ and therefore $d\varepsilon_{v}^{e} < 0$. This in turn implies dp′ < 0 (based on elasticity consideration) which guarantees the first term of Eq. 9 being negative. As the second term remains positive, dq < 0 (instability) cannot be guaranteed.