Settlement Analysis of Fractional-Order Generalised Kelvin Viscoelastic Foundation under Distributed Loads

Abstract

A solution is proposed for ground surface settlement induced in fractional-generalised Kelvin semi-infinite space by distributed loads, based on the fractional differential theory. The effects of four main parameters—the differential order, the two shear moduli and the coefficient of viscosity—on the settlements are analysed using a numerical example, and a parametric-sensitivity analysis is conducted. The results show that the fractional-order generalised Kelvin model is more flexible than the conventional integer-order generalised Kelvin model since it can account for the rate of the deceleration creep phase; therefore, a wider range of mechanical properties of viscoelastic materials can be described with fewer parameters, and the differential order has a higher sensitivity than the other three parameters. Finally, the model is used to identify and fit the parameters to the data of the field-bearing plate rheological tests. The fit results of the fractional-order generalised Kelvin model, unlike those of the integer-order generalised Kelvin model, are closer to the measured results and can more accurately describe the rock’s rheological behaviour at the test location.