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

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.