Layered unsaturated soils exhibit complex mechanical and physical properties. Owing to the roughness between unsaturated soil interfaces and the presence of irregularly distributed micro-pores, this study explores the laminar flow of pore water and counter-cyclonic flow of pore air through these channels at low velocities. In response to the complex consolidation behavior of unsaturated soils influenced by the flow and air contact resistance, an improved model is developed. The model incorporates the flow contact transfer coefficient (R-omega), flow partition coefficient (eta(omega)), air contact transfer coefficient (R-a) and air partition coefficient (eta(a)). Semi-analytical solutions for pore water pressure, pore air pressure and settlement in layered unsaturated soils are derived by employing the Laplace transform and its inverse transform. The rationality of the model is validated through comparative analysis with existing solutions. Analysis of the improved model yields critical insights: the presence of flow and air contact resistance leads to the development of relative pore pressure and air pressure gradients at interfaces, which diminishes the influence of the permeability coefficients of the water phase (k(omega)) and air phase (k(a)) on the consolidation process. Moreover, neglecting the flow and air contact resistance effects may lead to an overestimation of settlement.

Under the framework of Biot porous media theory, the fractional order Kelvin model is used to describe the rheological effect of soil skeleton, considering the coupling effect of pore pressure dissipation and skeleton rheology. By establishing a spatiotemporal analytical function for periodic cyclic loads, a three-dimensional axisymmetric dynamic consolidation control equation for a half space saturated clay foundation is constructed in a cylindrical coordinate system. The analytical solution of the control equation in the transformed domain is derived using Hankel-Laplace joint transformation and tensor operations, followed by numerical inversion to acquire the spatiotemporal solution of the physical field. By analyzing numerical examples, the dynamic consolidation characteristics of a saturated clay foundation under cyclic loading are studied. The results indicate that the settlement rate of saturated clay is slower during primary consolidation but faster during secondary consolidation. With cyclic loading, the soil's cumulative settlement development accelerates as the rheological properties of the soil skeleton strengthen. The amplitude of soil displacement fluctuations decreases as the order of viscosity increases, and the more significant the order of viscosity, the more pronounced the displacement hysteresis becomes. The rheological properties of the soil skeleton lead to a lag in pore pressure response compared to effective stress, resulting in horizontal movement of the spiral curve between pore pressure and effective stress under cyclic loading. In the unloading stage of cyclic loads, due to the decrease of normal stress with the decrease of external load, but the increase of shear stress, the soil undergoes shear dilation phenomenon, resulting in negative pore pressure in the soil.

Existing solutions for axisymmetric consolidation of viscoelastic soil are derived based on equal strain assumptions, which cannot account for soil deformation along the radial direction. This study develops a general solution for axisymmetric consolidation of viscoelastic soil under free strain conditions. The fractional -derivative Merchant model is introduced into the governing equations to account for the viscoelastic behaviour of soil around the vertical drains. The general solutions consisting of eigenfunctions and eigenvalues are proposed. Subsequently, the Laplace transform is utilized to convert the time variable tin partial differential equations into the Laplace complex argument p. Based on the boundary condition and continuity condition, the solution in the frequency domain is derived. By using Abate's fixed Euler Algorithm, the solutions in the time domain are obtained. The proposed solution is verified with finite element simulation and experimental data in the literature. Then, a series of parametric studies are conducted to investigate the influences of soil permeability, elastic modulus, viscosity coefficient, and fractional order on the axisymmetric consolidation of viscoelastic soils under free strain conditions.

Due to the presence of tiny gaps at the interface of two layers of saturated soil, water seepage occurs at a slower rate within these gaps, resulting in laminar flow at the interface. Based on the Hagen-Poiseuille law, a general imperfect flow contact model was established for layered saturated soil interfaces by introducing the flow contact transfer coefficient R omega and the flow partition coefficient eta omega. The investigation focused on the thermal consolidation behavior of layered saturated soil foundations under variable loadings considering the flow contact resistance effect at the interface. By employing the Laplace transform and its inverse transform, a semi-analytical solution for the thermal consolidation of layered saturated soil foundations was derived. In the context of a two-layer soil system, the effects of R omega, eta omega, and permeability coefficient k on the consolidation process were examined. The obtained results were then compared with three other interfacial contact models, thereby confirming the rationality of the presented model. The study findings revealed that the flow contact resistance effect leads to a clear jump in the pore water pressure. Furthermore, an increase in R omega and a decrease in eta omega were found to significantly enhance displacement and pore water pressure, while having minimal impact on the temperature increment. These insights contribute to a more comprehensive understanding of the thermal consolidation behavior of layered saturated soil foundations and underscore the significance of accounting for the flow contact resistance effect in such analyses.

The current analytical solutions for predicting the ground settlements induced by small curvature tunneling in soft ground are generally conducted on the assumption of linear elastic foundation and provide little attention on the soil rheology. This paper introduces a mathematical model to estimate the small curvature tunneling induced adjacent ground settlement considering the soil viscoelasticity. By introducing the Boltzmann viscoelastic ground model under the Laplace transform, the time domain parameters converted from Poisson's ratio and shear modulus are derived to further obtain the viscoelastic ground loss solution and the Mindlin solution. Then, the proposed viscoelastic solutions are employed for the ground settlement caused by the overexcavation and imbalanced loads for the small curvature tunnel, which accounts for the soil rheology influence. The accuracy of the mathematical model is then verified by comparisons with in-situ observed data and 3D numerical simulation results, as well as good agreement is obtained. Finally, the parametric analyses are performed to estimate the influence for transverse and longitudinal surface settlements, including tunnel curvature radius, shield cutterhead face radius, over-excavation value, creep time and shear modulus ratio of viscoelastic ground.

Under the framework of Biot porous media theory, a fractional order Kelvin model is used to describe the rheological effects of soil skeletons, and a coupled vibration model of saturated clay and a pile foundation is constructed. The Laplace transform is used to derive the analytical solution of the control equation in the transformation domain, and then the time-domain solution is obtained through numerical inversion. By analyzing numerical examples, the displacement and internal force response of pile foundations under horizontal vibration loads, as well as the influence of parameters, are studied. The results show that the displacement and internal force response of pile foundation vibrations in saturated clay foundations have a delayed effect. The stronger the rheological properties of the foundation soil, the more obvious the delay, the lower the load frequency, and the more significant the influence of the rheological properties on the delayed effect. The stronger the rheological properties of the soil, the smaller the displacement amplitude of the pile foundation vibration, and the higher the load frequency, the greater the decrease in displacement amplitude. The stronger the rheological properties of the soil, the smaller the positive bending moment of the pile body, while the negative bending moment increases. Both positive and negative shear forces increase, but the shear force at the top of the pile is not affected. Therefore, when designing pile foundations in saturated clay foundations, it is necessary to appropriately increase the pile foundation or increase the reinforcement to meet the shear resistance of the pile foundation. The results of this study can provide a valuable reference for geotechnical and seismic engineers in pile foundation design.