## 1 Introduction  
Both rock and soil have viscoelastic properties. The creep phenomenon of settlement increases with time under the action of long-term loads, such as building loads. Excessive settlement will compromise the building's stability. Therefore, adopting a reasonable viscoelastic model is crucial to accurately calculate and predict their deformation. Various creep models have been adopted in previous studies to describe the rheological behaviour of rock and soil, such as the Kelvin, Maxwell and general Kelvin models [1; 2; 3; 4]. These models are structurally simple, clear in mechanical parameters and easily solved. However, these models often have significant errors with the measured results when applied to displacement back analysis [5]. Researchers usually use more complex rheological models to obtain better fitting results. Based on the three-parameter generalised Kelvin model, [PERSON] [6], [PERSON] [7] and [PERSON] [8] connected a Kelvin body in series to form a five-parameter generalised Kelvin model, and the fitting curve they obtained overcame the disadvantage of rapid convergence compared with the fitting curve of the three-parameter generalised Kelvin model. Furthermore, more elements are combined to improve the fitting accuracy. However, the combined complex model will result in a more complex mathematical form of the creep equation, making it more difficult to solve and inconvenient for engineering applications. In addition, the physical meaning of some parameters becomes ambiguous when the number of parameters increases [9]. Recently, fractional-order models have been widely used to simulate the viscoelastic properties of materials [10; 11; 12; 13; 14]. Because fractional-order models have the advantages of fewer parameters, clear physical meaning and practicality, they have also been widely used in the field of geotechnical engineering [15]. The fractional-order model, unlike the traditional integer-order model, can describe a wider range of viscoelastic properties of geotechnical soils with fewer parameters, enabling the more accurate fitting of experimental data. [PERSON] [16] and [PERSON] [17] used the fractional-order Maxwell and Kelvin models, respectively, to fit the experimental creep data of tight sandstone and soft soil with higher accuracy. [PERSON] [18,19] and [PERSON] [15] used a fractional-order Nishihara model to fit the rheological data of salt rocks with constant and multi-level loading with higher accuracy. [PERSON] [20] used a fractal-order model of variable order to simulate the creep response of rock in the entire stage. The aforementioned studies are all based on the uniaxial compression tests of geotechnical soils, whereas the three-dimensional viscoelastic space problem is unaddressed. Therefore, [PERSON] [21] and [PERSON] [22] used the fractional-order Kelvin model to simulate a semi-infinite spatial body and obtained the viscoelastic solutions for the displacement when vertical and horizontal concentrated forces are applied to the surface of the semi-infinite spatial body. [PERSON] et al. [23] obtained the viscoelastic solution of the displacement in the horizontal and vertical directions when a vertical concentrated force acted on the interior of a semi-infinite space using [PERSON]'s solution and the fractional-generalised Kelvin model. [PERSON] et al. [24] used the fractional-order Kelvin model to simulate the plane strain problem for semi-infinite foundations and obtained a viscoelastic solution for foundation settlements under concentrated vertical loads. The loads involved in the aforementioned studies are relatively simple when solving the problems using fractional-order models. Therefore, the fractional-order generalised Kelvin model is used to model a half-space body under the action of vertically distributed loads in this study, and the viscoelastic solutions for the settlements of the ground surface are solved using the corresponding principle [25].