###### Abstract  
This paper proposes a semi-analytical solution for one-dimensional consolidation of viscoelastic unsaturated soil considering a variable permeability coefficient under exponential loading. The governing equations of excess pore air pressure (EPAP) and excess pore water pressure (EPWP) were acquired by introducing the Merchant viscoelastic model. By employing [PERSON]'s correspondence principle and the Laplace transform, the solutions for EPAP and EPWP were derived under the boundary conditions of the permeable top surface and impermeable bottom surface. [PERSON]'s method was then used to execute the inverse Laplace transform, yielding a semi-analytical solution in the time domain. Through typical examples, the dissipation of EPAP and EPWP and the change of the average degree of consolidation over time under the influence of different elastic moduli, viscoelastic coefficients, and air-to-water permeability ratios were studied. The variation of the permeability coefficient and its influence on consolidation were also analyzed. The findings of this research show that the consolidation rate of viscoelastic unsaturated soil is slower than that of elastic unsaturated soil; however, an acceleration in the consolidation of the soil is observed when changes in the permeability coefficient are considered. These discoveries enhance our comprehension of the consolidation behaviors exhibited by viscoelastic unsaturated soil, thereby enriching the knowledge base on its consolidation traits. viscoelastic unsaturated soil; semi-analytical solution; one-dimensional consolidation; variable permeability coefficient; exponential loading 2020 IEEE/RSJ International Conference on Intelligent Systems (IEEE), Vol. 1, No. 1, No. constitutive relations for unsaturated soils proposed by [PERSON] and [PERSON] [7], introduced two independent stress state variables (net normal stress and matric suction) and established the widely applied 1D consolidation theory for unsaturated soils in 1979. The research presented in this paper builds upon the 1D consolidation theory of [PERSON] and [PERSON]. In recent years, scholars have conducted extensive research on the 1D consolidation of unsaturated soils. [PERSON] and [PERSON] [8] established a connection between the settlement rate of unsaturated soils and the mean degree of consolidation for both air and water phases in 1999. They proposed an equation capable of predicting the time-dependent settlement behavior of foundations. [PERSON] et al. [9] analyzed the 1D consolidation of unsaturated soils under external loads and increasing matric suction. [PERSON] et al. [10] acquired the analytical solution for 1D consolidation of unsaturated soils with instantaneous uniform loading and homogeneous boundary conditions using the Laplace transform, Cayley-Hamilton principle, and inverse Laplace transform. Considering instantaneous uniform loading, [PERSON] et al. [11; 12] applied the method of separation of variables to acquire analytical solutions for 1D consolidation of unsaturated soil foundations under one-sided drainage, two-sided drainage, and mixed boundary conditions. [PERSON] et al. [13] utilized the eigenfunction expansion method to find a semi-analytical solution for one-dimensional consolidation of unsaturated soils under one- and two-sided permeability boundary conditions considering initial excess pore pressures uniformly distributed or linearly varying along depth. Additionally, some scholars [14; 15; 16; 17; 18; 19; 20; 21] extended the research for instantaneous uniform loading to time-varying loads, obtaining analytical or semi-analytical solutions under different boundaries and initial conditions. However, these analytical or semi-analytical solutions assumed that unsaturated soils are linearly elastic, which cannot explain certain consolidation problems accurately in the case of viscoelastic unsaturated soil. In addition, they neglect the change of the permeability coefficient during consolidation progress.