Poroelastic Soil Research Articles

Dynamic Response of Poroelastic Soil Adjacent to an Axially Vibrating Pile

Dynamic Response of Poroelastic Soil Adjacent to an Axially Vibrating Pile

An analytical solution to the soil’s dynamic response induced by wave interaction with a marine current characterized by a non-uniform vertical profile

In this work, we obtain an analytical solution to the soil’s dynamic response induced by wave interaction with a marine current with a prescribed non-uniform vertical profile. The control volume used to analyze the present problem is divided into a water region and another composed of a poroelastic soil region. The governing equations for the water hydrodynamics are presented in its dimensionless version and they are simplified for the limit of linear water waves. The velocity field in the water region is determined from the continuity equation and the “inviscid Orr-Sommerfeld linear equation”. We obtain a dispersion equation for wave-current interaction. For modeling the soil’s dynamics response, we adopt the u-p approximation. Considering a characteristic criterion for soil liquefaction, the maximum liquefaction depth is obtained as an eigenvalue problem. The analytical estimations, valid for the limit of linear water waves, provided by the present analysis show that, marine currents traveling in the same direction to the wave propagation induces larger values of the liquefaction depth than those obtained for currents opposite to wave propagation. As a first approximation, the present analysis may help understand the dynamic response of poroelastic soil induced by the wave-non-uniform marine current interaction.

Vertical Vibration of a Rigid Cylindrical Foundation Embedded in a Half-Space of Unsaturated Poroelastic Soil

Vertical Vibration of a Rigid Cylindrical Foundation Embedded in a Half-Space of Unsaturated Poroelastic Soil

Ground motion amplification by twin circular tunnels for obliquely incident seismic waves: Effects of saturated poroelastic soil parameters

Underground structures can significantly affect the ground motion and further influence the seismic design of aboveground structures around them. Although this issue has been well recognised and studied, it is not thoroughly addressed as a large number of factors are involved. This paper focuses on ground motion amplification induced by twin circular tunnels embedded in saturated poroelastic soil. The saturated poroelastic soil is modelled as a two-phase medium to consider parameters characterising the fluid phase. Three-dimensional scattering features of the twin tunnels for obliquely incident seismic waves are numerically investigated by a 2.5D finite element and boundary element hybrid model. It is shown that the presence of the twin tunnels can lead to significant modifications of the free-field motion, in terms of its magnitude and distribution. The three-dimensional oblique incidence scenario presents a more general perspective on the ground motion amplification. Moreover, the effects of saturated poroelastic soil parameters on the ground motion amplification, including soil permeability, groundwater levels, and the degree of saturation, are parametrically investigated. The differences in ground motion amplification patterns between the saturated poroelastic and dry poroelastic soil scenarios are notable, highlighting the effects of parameters characterising the fluid phase.

Axisymmetric Consolidation of a Poroelastic Soil Layer with Impermeable Surface

Axisymmetric Consolidation of a Poroelastic Soil Layer with Impermeable Surface

Dynamic impedances of multiple strips on multi-layered transversely isotropic poroelastic soils

Geo-materials naturally display a certain degree of anisotropy due to various effects such as deposition. Besides, they are often two-phase materials with a solid skeleton and voids filled with water, and commonly known as poroelastic materials. In the past, despite numerous studies investigating the vibrations of strip foundations, dynamic impedance functions for multiple strip footings bonded to the surface of a multi-layered transversely isotropic poroelastic half-plane have never been reported in the literature. They are first presented in this paper. All strip foundations are assumed to be rigid, fully permeable, and subjected to three types of time-harmonic loadings. The dynamic interaction problem is investigated by using an exact stiffness matrix method and a discretization technique. The flexibility equations are established by enforcing the appropriate rigid body displacement boundary conditions at each footing-layered soil interface. Numerical results for dynamic impedance functions of two-strip system are presented to illustrate the influence of various effects on dynamic responses of multiple rigid strip foundations.

Analytical method for a tunnel with periodically jointed lining in the poroelastic soil under seismic waves

In this study, a longitudinal equivalent periodic shell (LEPS) model and corresponding continuous joint model are proposed for the periodically jointed lining (PJL) tunnel. Based on the LEPS model for the PJL tunnel, an analytical method for the PJL tunnel under seismic waves is established. The surrounding soil of the PJL tunnel is assumed to be the poroelastic medium, and described by the Biot's theory. The lining of the PJL tunnel is assumed to be composed of a series of lining rings linked periodically by ring joints along the longitudinal direction, which are simplified as a LEPS and described by the cylindrical shell theory. Due to the periodicity of the LEPS lining, the tunnel-soil system is treated as a periodic structure in this study. Based on the periodicity condition for the tunnel-soil system as well as the wave function expansion method, the representation for the scattering wave field in the soil is established. By using the aforementioned cylindrical shell theory and Fourier series expansion method, the Fourier space equations of motion and convolution type constitutive relations for the LEPS lining are derived. By using the lining-soil continuity conditions, the Fourier space equations of motion and convolution type constitutive relations for the LEPS lining as well as the representation for the wave field in the soil, the coupled equations for the tunnel-soil system are established, with which the Fourier components of the displacements of the LEPS lining and wave function coefficients for the scattering waves in soil can be solved for. Numerical results indicate that the presence of the ring joint in the LEPS lining of the tunnel will affect the distribution of the internal forces in the lining considerably, and it will also enhance the maximum internal forces occurring in the lining.

Effects of pulse-like ground motions on tunnels in saturated poroelastic soil for obliquely incident seismic waves

It has been widely recognised that near-fault ground motions can be distinctly different from far-fault ground motions, in terms of their amplitudes and spectral characteristics, and there are a number of studies investigating the effects of near-fault ground motions on the structural response. However, only a few studies focus on underground tunnels, and most of them consider vertically incident seismic waves, neglecting the wave passage effect which is critical for long tunnels. This paper investigates the consequences of near-fault pulse-like ground motions on the seismic tunnel response, with an example of a tunnel embedded in saturated poroelastic soil. The input motions are represented by obliquely incident P1 waves, and the wave passage effect along the longitudinal direction is considered by a 2.5D modelling technique. The seismic tunnel response for near-fault pulse-like and far-fault ground motions is compared. Additionally, artificial ground motions, which have consistent acceleration response spectra with the near-fault pulse-like ground motions, but without velocity pulses, are generated to gain further insight into the contribution of velocity pulses. It is shown that the near-fault pulse-like ground motions can noticeably increase the tunnel internal forces, due to large seismic energy associated with the velocity pulses. For pulse-like ground motions with similar acceleration response spectra, the fling-step velocity pulse can be more detrimental to the tunnel than the forward-directivity velocity pulse. Moreover, the amplification effect of the near-fault pulse-like ground motions on the tunnel internal forces tends to be more prominent for large vertical angles of incidence, highlighting the significance of considering the oblique incidence case for seismic design.

Vertical dynamic response of single floating piles in poroelastic soil

This paper presents a closed-form formulation for the time-harmonic response of single floating piles that are embedded in a saturated soil layer of finite thickness. The frictional force of surrounding soil to pile vertical motion is first established, considering the soil layer as homogeneous isotropic poroelastic medium that obeys Biot’s governing equations. The pile and the soil column underlying the pile tip are modelled using one-dimensional rod theory, and then closed-form solution is obtained from the boundary and continuity conditions, instead of numerically solving complicated integral equations that are used in the common boundary integral methods. Finally, we use arithmetic examples to identify the sensitivity of the dynamic pile impedance and of the soil reactions to the main geometrical and material problem parameters.

Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

AbstractIn the previous studies of rigid disk–soil dynamics, the soil under the foundation is usually treated as a poroelastic half‐space medium. However, the waves due to the vibration of rigid disk can reflect and refract back and forth between the finite soil layer and rigid bedrock, which would significantly influence the soil deformation and flow of the rigid disk–soil system. In order to overcome the shortcoming, this paper presents an analytical solution to determine the response of the rigid disk subjected to harmonic horizontal loads resting on poroelastic soil layer overlying rigid bedrock. The displacements and stresses field of the disk and soil are obtained by virtue of the Hankel transform method, dual integral equations method. Furthermore, the rationality and accuracy of the developed solution are confirmed in comparison with the previous studies. Based on the obtained solutions, numerical examples are performed to the effects of the thickness and permeability of poroelastic soil layer on the dynamic response of the rigid disk–soil system in the physical domain.

Vertical vibration of rigid strip footings on poroelastic soil layer of finite thickness

This paper presents a numerical solution that describes the response to forced vertical vibrations of rigid strip footings founded on the surface of a poroelastic soil layer of finite thickness. To mathematically describe this mixed boundary value problem, we relax the boundary conditions and cast it as a pair of dual integral equations, which are transformed to a system of linear equations by means of Jacobi orthogonal polynomials. The system is solved numerically to provide the frequency-dependent footing compliance, and the associated nearby soil displacement. Results obtained with the model at hand underline the important contribution of standing waves to the response of the soil-foundation system, and draw the limits of existing solutions that consider the foundation soil as infinite half-space, where standing waves cannot form.

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

AbstractThe large size embedded foundation is widely used in the engineering, but the finite thickness of soil layer underlying this foundation is usually neglected in design, which leads to the non‐negligible error of calculation. By virtue of Biot's elastodynamic theory, this paper proposes a simple method to discuss the horizontal dynamic response of the cylindrical rigid foundation partially embedded in a poroelastic soil layer. First, based on the Novak plane strain model, the shaft resistance from the surrounding soil is simulated and solved. Second, the foundation end soil is assumed as a continuous medium of finite thickness, whose initial mechanism is derived from the dynamic interaction between the rigid disk and soil. Finally, the horizontal dynamic response factor is calculated by adopting newton's second law. Several cases are set to verify the rationality of the presented solution and to develop the analysis of key parameters. The numerical results suggest that the soil layer thickness has a significant influence on the dynamic vibration of the embedded foundation, and its effect is consistent with that of poroelastic half‐space when the thickness exceeds certain value.

Consolidation settlement of vertically loaded pile groups in multilayered poroelastic soils

Pile groups are commonly used as the foundations of many structures including those used in transportation infrastructures. Consolidation settlement of a pile foundation is an important design parameter. A theoretical model is developed in this study to estimate the consolidation settlement and axial load transfer of vertically loaded pile groups in multilayered poroelastic soils. The multilayered saturated soil is modeled according to Biot’s poroelasticity theory. In order to determine quasi-static response of pile groups, the interaction problem is first formulated in the Laplace transform domain. Vertical displacement compatibility is enforced at the pile-soil interface to simulate the pile group-soil interaction. Axial deformation of each pile is represented by an exponential series with undetermined coefficients, which are obtained from a variational approach. Vertical displacement influence functions due to a buried uniform vertical load applied to the layered soil are required in the formulation. The application of an exact stiffness matrix method yields the required influence functions. Time-domain solutions are obtained by employing a numerical Laplace inversion method. Numerical results for time-dependent vertical stiffness and consolidation settlement are presented for different pile group configurations, layer profiles, pile elastic moduli and pile lengths.

Analytical solution for the vertical vibration of a pipe pile embedded in poroelastic soil

This paper presents an analytical method to investigate the vertical vibration of a pipe pile in layered poroelastic soils due to a harmonic load. The relationship of general displacement and stress is obtained through a stiffness matrix which is derived by applying analytical layer element method. The pipe pile with a thick wall is governed by vibration theory of a one-dimensional bar. By considering the compatible conditions at the inner-surface and outer-surface of a pipe pile and soil, the vertical vibration performance is obtained. The proposed method is proved correct by comparing with the existing solutions. Parametric studies are carried out to illustrate the influences of wall thickness of the pipe pile, soil permeability and pile-soil stiffness ratio on the vibration characteristics of the pipe pile.

Kinematic responses of a pipe pile embedded in a poroelastic soil to seismic P waves

Kinematic responses of a pipe pile embedded in a poroelastic soil to seismic P waves

Coupling Soil–Fluid–Structure Domains by Localized Lagrange Multipliers Mixed Formulation (u, p) for Modeling Offshore Wind Turbine Vibration

Modeling is frequently used to design structures in a large range of engineering applications. Coupled models can be solved by several numerical procedures. This paper presents a soil–fluid–structure coupling analysis applied to offshore wind turbines design. The goal of this work is to develop a coupled structural finite element procedure using Localized Lagrange Multipliers (LLM) at idealized offshore wind turbines with poroelastic soil foundation. The poroelastic media theory of Biot is used to represent the soil domain as two-phase material which is considered to be fully saturated with water. The numerical model is validated through a fully coupled model at classical problems results. In this work, the mixed formulation (u,p) is used to model the interface frames between the domains. The interface domain behaves as fictitious porous material generating a nonsymmetrical coupling between elastic solid and potential fluid. The momentum equilibrium and mass continuity equations are solved by algebraic equation system imposed by Lagrange multipliers methodology. In order to fully model the coupled system, aerodynamic decoupling effects are implemented to separate the tower structure, the soil foundation and the rotor-nacelle assembly. This procedure is based on the blade aerodynamic characteristics. The force and moment vectors are assembled considering the aerodynamic damping coupling between inplane and outplane rotor motions. Finally, the equations of the tower-nacelle structure, ocean fluid and poroelastic soil are obtained by the classical finite element method. In addition, their interaction is modeled using LLM. The numerical model for monopile and jacked offshore wind turbine is developed in terms of time dynamic response which is evaluated for a range of physical parameters including the wind nature and soil type.

Vertical vibration of end-bearing single piles in poroelastic soil considering three-dimensional soil and pile wave effects

This paper presents an analytical solution developed to describe the dynamic interaction between a single end-bearing pile subjected to a dynamic axial load on its head, and its surrounding poroelastic soil. The main feature of the solution is that both the two-phase soil and the pile are treated as three-dimensional continua. This allows capturing the propagation of compressional and shear waves in three dimensions, and their effect on pile response. The soil surrounding the pile is treated as porous medium and its response is described with Biot’s poroelastic theory, while the pile is treated as linear elastic solid, considering explicitly both vertical and radial pile displacements. The solution yields expressions for the displacement and velocity admittance at the pile head in the frequency domain, and allows computing pile head velocity time histories. These are applied to study the effects of wave propagation in three dimensions on pile response in the frequency- and in the time-domain, and identify the conditions under which these effects may be important for the analysis of piles in practice.

Analytical and numerical studies on the behavior of a freezing soil layer

This paper focuses on investigating how a particular but classical configuration of a finite homogeneous soil layer, once studied by Terzaghi and currently subjected to freezing temperatures, behaves and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses. Spatial homogeneity is a strong assumption but has the decisive advantage of simplicity, allowing eventually the construction of an analytical solution, useful both to enhance understanding and as a benchmark. The essential relations on the constitutive behavior of saturated poroelastic soils are firstly recalled, in the general non-linear case where material parameters are state-dependent. Solutions to both linearized governing equations with constant material parameters and general non-linear equations with state-dependent parameters are then developed respectively by analytical derivation and by a commercial code COMSOL based on finite elements method accounting for two different sets of boundary conditions. The validity of this numerical modelling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals the important impact of ice content variations on various material parameters that modify significantly the THM responses. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks. Numerical results accounting for two different hydraulic boundary conditions at the ground surface reveal how such factors can modify significantly the THM evolution of the soil mass. In the last part of the paper, a limited parametric study on the effect of permeability relative to liquid water flow highlights how this parameter plays an important role in the development of excess water pressures hence ground movements.

Interaction of Beams with Consolidating Nonlinear Poroelastic Layered Soil

Interaction of Beams with Consolidating Nonlinear Poroelastic Layered Soil

Responses of Laterally Loaded Single Piles Subjected to Various Loading Rates in a Poroelastic Soil

Groundwater table has an important role in soil–structure interaction problems. However, analysis of laterally loaded single piles has often been conducted by solely considering the mechanics of the soil skeleton or decoupling the interactive mechanics of the soil skeleton and the fluid flux; in other words, most analyses were performed without taking into consideration the coupling effect between the soil skeleton and the fluid flux. To improve our understanding of the hydromechanical coupling effect on laterally loaded single piles, a series of finite element study on laterally loaded single piles in saturated porous media was conducted. The effect of pile cap geometries, cap widths, cap embedment depths, and pile lengths, on the response of laterally loaded single piles was also studied. The loading condition of the pile was found to have a significant effect on the generation of excess pore-water pressure. The lateral displacement and bending moment computed at the maximum excess pore water pressure, which in turn, is equivalent to an undrained analysis, produced the minimum responses among all the other loading conditions. The effect of pile cap geometries was found to be much less significant than anticipated.