This paper is concerned with the study of a poroelastic soil layer under impulsive horizontal loading. Building upon Biot's general theory of poroelasticity, a comprehensive set of governing equations addressing three-dimensional transient wave propagation problem are established. Explicit general solutions for displacements and pore-pressures are derived by employing a sophisticated mathematical approach, incorporating decoupling transformation, Fourier series expansion, and Laplace-Hankel integral transform techniques. Subsequently, physical-domain components are numerically obtained by an enhanced Durbin method coupled with inverse Hankel transform. Comparisons the existing transient solutions for the ideal elastic half-space are made to validate the proposed formulations' reliability and precision. Through representative analyses for time-domain results, it is illustrated to study the influence of the soil thickness and types of loading pulse on the transient dynamic response of finite-thickness poroelastic soil layers. The results in comparative analysis show that the magnitudes of the horizontal displacement and pore water pressure can be affected and become more fluctuant when the thickness of the poroelastic soil layer decreases. The basic solutions may be attributed to a variety of wave propagation problems due to transient dynamic loading and illustrate the corresponding distinct wave features elegantly.

This work presents an analytical method for determining vertical dynamic impedance and displacement response factor of a rigid cylindrical foundation embedded in unsaturated poroelastic soils. The foundation is assumed to be perfectly boned to its surrounding soil and its overlying half-space of unsaturated poroelastic soil, subjected to harmonic vertical loadings. The soil surrounding the circumference of the cylinder is modeled as a number of infinitely thin horizontal soil layers. Based on the Biot-type soil constitutive model, the equations governing the interaction of unsaturated soils with the cylindrical foundation are derived. Solutions are obtained by solving ordinary differential equations transformed from partial differential governing equations using the Hankel transform. The proposed solutions are verified against existing solutions of benchmark elastodynamic problems for embedded cylindrical foundations in dry and saturated soils. Using the derived solutions, several influencing parameters defining the stiffness and mass of the foundation system are examined to investigate the dynamics of the foundation interacting with it adjacent soils. It is concluded that the dynamic displacement response factor is sensitive to soil saturation. It is believed that the proposed solution should be beneficial to dynamic design with cylindrical foundations embedded in unsaturated soils.

Three approximate analytical solutions for the problem of the seismic response of two rigid cantilever walls retaining a transversely isotropic poroelastic soil layer over bedrock are presented under conditions of plane strain and time harmonic ground motion. These approximate solutions come as a result of various reasonable simplifications concerning various response quantities of the problem, which reduce the complexity of the governing equations of motion. The method of solution in all the cases is the same with that used for obtaining the exact solution of the problem, i.e., expansion of response quantities in the frequency domain in terms of sine and cosine Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations with respect to the vertical coordinate in conjunction with the boundary conditions. The first approximate solution is obtained on the assumption of neglecting all the terms of the equations of motion associated with the fluid acceleration. The second approximate solution is obtained on the assumption that the fluid displacements are equal to the corresponding solid displacements. The third approximate solution is obtained as the sum of the second approximate solution for the whole domain plus a correction inside a boundary layer at the free soil. All three approximate solutions are compared with respect to their accuracy against the exact solution and useful conclusions pertaining the approximate range of the various parameters, like porosity, permeability and anisotropy indices, for minimization of the approximation error are drawn.

Post-construction surface settlement can be a significant proportion of the total one, ranging from 30% to 90%. This settlement does not only affect the safety of tunnels, but also causes damage to adjacent buildings and underground infrastructures, posing a number of environmental, geological and geotechnical challenges. This study delves into the consolidation behavior of a soft soil around a circular tunnel, subjected to cyclic loading at the ground level. The Boltzmann growth function is introduced to characterize the exacerbation phenomenon in the lining permeability, while the stress-strain characteristics of the soft soil are described by a generalized Kelvin model. The governing equations for the consolidation of the soft soil around the tunnel are obtained based on the Terzaghi-Rendulic theory, and the dissipation of the excess pore water pressure (EPWP) is investigated. The results indicate that higher load frequencies accelerate the disappearance of cyclic load-induced EPWP fluctuation but, overall, cyclic loading prolongs the consolidation process. The local permeability coefficient predominantly affects the EPWP dissipation in the later consolidation stages. The viscous properties of the soil lead to an incomplete dissipation, and a higher number of Kelvin bodies in the adopted rheological model is associated to a slowdown of the consolidation process. The distribution of the EPWP in the upper part of the tunnel vault is also shown to depend on the ratio between the initial permeability coefficients of the lining and of the soil.

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.

Prediction of the fatigue life of steel catenary risers (SCR) in the touchdown zone is a challenging engineering design aspect of these popular elements. It is publically accepted that the gradual trench formation underneath the SCR due to cyclic oscillations may affect the fatigue life of the riser. However, due to the complex nature of the several mechanisms involving three different domains of the riser, seabed soil, and seawater, there is still no strong agreement on the beneficial or detrimental effects of the trench on the riser fatigue. Seabed soil stiffness and trench geometry play crucial roles in the accumulation of fatigue damage in the touchdown zone. There are several studies about the effect of seabed soil stiffness on fatigue. However, recent studies have proven the significance of trench geometry and identified the touchdown point oscillation amplitude as a key factor. In this study, a boundary layer solution was adapted to obtain the dynamic curvature oscillation of the riser in the touchdown zone on different areas of seabed trenches with a range of seabed stiffness. The proposed analytical model was validated against advanced finite element analysis using a commercial software. A range of seabed stiffness was examined, and the corresponding fatigue responses were compared. It was observed that in the elastic seabed, the effect of soil stiffness is attributed to the curvature oscillation amplitude and to the minimum local dynamic curvature that SCR can take in the touchdown zone. The proposed analytical model was found to be a simple and reliable tool for riser configuration studies with trench effects, particularly at the early stages of riser engineering design practice.