Flow liquefaction instability and the permissible range of fractional order of sand

Abstract

To capture the state-dependent behaviour of granular soil, an interdisciplinary approach, fractional plasticity, was proposed. However, the permissible value of the fractional-derivative order has not been evaluated. This technical note aims to analyse the permissible range of fractional order from the perspective of modelling flow liquefaction of sand. A state-dependent fractional elastoplastic model without using predefined state parameters is proposed. Then, a series of test results of different sands under flow liquefactions are simulated. Permissible range of the fractional order is analysed by evaluating the second-order work for predicting flow liquefaction instability of sand, where it is suggested that the fractional order should be less than two.

Keywords:

• Fractional derivative
• state dependence
• sand
• liquefaction

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The invaluable inspiration by Prof. Wen Chen is highly appreciated. The financial support provided by the Natural Science Foundation of China (Grant No. 51890912, 41630638) are appreciated.