“…Notations: C a , interactive constant with respect to air phase; C w , interactive constant with respect to water phase; C a vx , coefficient of volume change with respect to air phase in x-direction; C a vz , coefficient of volume change with respect to air phase in z-direction; C w vx , coefficient of volume change with respect to water phase in x-direction; C w vz , coefficient of volume change with respect to water phase in z-direction; g, gravitational acceleration; h, thickness of soil layer; k ax , coefficient of air permeability in x-direction; k az , coefficient of air permeability in z-direction; k wx , coefficient of water permeability in x-direction; k wz , coefficient of water permeability in z-direction; l, length of soil layer; M, molecular mass of air; m a 1 , coefficient of air volume change with respect to a change in σ − u a ; m a 2 , coefficient of air volume change with respect to a change in u a − u w ; m s 1 , coefficient of volume change with respect to a change in σ − u a ; m s 2 , coefficient of volume change with respect to a change in u a − u w ; m w 1 , coefficient of water volume change with respect to a change in σ − u a ; m w 2 , coefficient of water volume change with respect to a change in u a − u w ; n 0 , initial porosity; q 0 , initial surcharge; R, universal gas constant; S r0 , initial degree of saturation; s, complex number; t, time; u a , excess pore-air pressure; u atm , atmospheric pressure; u 0 a , initial excess pore-air pressure; u w , pore-water pressure; u 0 w , initial excess pore-water pressure; w, settlement; w*, normalized settlement; x, investigated distance; z, investigated depth; γ w , unit weight of water; ε v , total volumetric strain; Θ, absolute temperature boundaries. Lately, Zhou et al 28 obtained the analytical solutions for the axisymmetric consolidation in an unsaturated soil stratum on the basis of the assumption of free and equal strain, respectively. And Shan et al 29,30 gave implicit analytical solutions of the 1D consolidation equations for the single layer and multilayer unsaturated soils, respectively.…”