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In this paper, wave propagation in a poroelastic thick-walled hollow cylinder is investigated in the framework of Biot’s extension theory. Biot’s theory of poroelasticity is valid for isotropic porous solids saturated with non-viscous fluid. The bulk and shear viscosities are not considered in the classical Biot’s theory. Biot’s extension theory takes all these into an account. Biot’s extension theory is applied here to investigate the radial vibrations in thick-walled hollow poroelastic cylinder. The paper aims to discuss these issues.

By considering the stress-free boundaries, the frequency equation is obtained in the presence of dissipation. Limiting case when the ratio between thickness and inner radius is very small is investigated numerically. In the limiting case, the asymptotic expansions of Bessel functions are employed so that frequency equation is separated into two parts which gives attenuation coefficient and phase velocity. If the shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory.

For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically.

Radial vibrations of thick-walled hollow poroelastic cylinder are investigated in the framework of Biot’s extension theory. Due to the mathematical complexity, limiting case is considered. The complex valued frequency equation is discussed numerically which gives the attenuation coefficient and phase velocity. If shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. The comparison has been made between the current results and that of classical results.

Develop a local radial point interpolation method (LRPIM) to analyze the dissipation process of excess pore water pressure in porous media and verify its numerical capability.

Terzaghi's consolidation theory is used to describe the dissipation process. A local residual form is formulated over only a sub‐domain. This form is spatially discretized by radial point interpolation method (RPIM) with basis of multiquadrics (MQ) and thin‐plate spline (TPS), and temporally discretized by finite difference method. One‐dimensional (1D) and two‐dimensional consolidation problems are numerically analyzed.

The LRPIM is suitable, efficient and accurate to simulate this dissipation process. The shape parameters, q=1.03, R=0.1 for MQ and η=4.001 for TPS, are still valid.

The asymmetric system matrix in LRPIM spends more resources in storage and CPU time.

Local residual form requires no background mesh, thus being a truly meshless method. This provides a fast and practical algorithm for engineering computation.

This paper provides a simple, accurate and fast numerical algorithm for the dissipation process of excess pore water pressure, largely simplifies data preparation, shows that the shape parameters from solid mechanics are also suitable for the dissipation process.

The purpose of this paper is to present a semi-analytical solution to one-dimensional (1D) consolidation induced by a constant inner point sink in viscoelastic saturated soils.

Based on the Kelvin–Voigt constitutive law and 1D consolidation equation of saturated soils subject to an inner sink, the analytical solutions of the effective stress, the pore pressure and the surface settlement in Laplace domain were derived by using Laplace transform. Then, the semi-analytical solutions of the pore pressure and the surface settlement in physical domain were obtained by implementing Laplace numerical inversion via Crump method.

As for the case of linear elasticity, it is shown that the simplified form of the presented solution in this study is the same as the available analytical solution in the literature. This to some degree depicts that the proposed solution in this paper is reliable. Finally, parameter studies were conducted to investigate the effects of the relevant parameters on the consolidation settlement of saturated soils. The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils.

The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils. Consolidation behavior of viscoelastic saturated soils could be reasonably predicted by using the proposed solution with considering variations of both flux and depth because of inner point sink.

The governing equations for dynamic transient analysis of a fluid‐saturated two‐phase porous medium model based on the mixture theory are presented. A penalty finite element formulation is derived with the general Galerkin procedure of the finite element method (FEM), and the obtained dynamic system equation can be solved with implicit or explicit time integration method, which is discussed in this paper. Using this method, a porous medium column under impulsive loading is analyzed and the results reveal the phenomena of one‐dimensional wave propagation, which are consistent with analytical solutions. Furthermore, two numerical examples of two‐dimensional problems demonstrate the existence of two body waves, i.e. longitudinal (P‐type) and transverse (S‐type) waves in porous media, and the Rayleigh wave in the vicinity of the surface of porous media.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The purpose of the article is to extend the node-based smoothed point interpolation method (NS-PIM) for soil consolidation analysis based on the Biot’s theory.

The shape functions for displacements and pore pressures are constructed using the PIM separately, leading to the Kronecker delta property and easy implementation of essential boundary conditions. Then, a benchmark problem of 2D consolidation under ramp load is solved to investigate the validity of this application. Meanwhile, convergence features of different solutions are studied. Furthermore, the incompressible and impermeable condition under instant load is investigated. The results calculated by the NS-PIM solution with different orders of shape functions are compared. Finally a 2D consolidation problem in construction period is solved. An error estimation method is applied to check the mesh quality.

The results of the NS-PIM solution show good agreement with those certified results. Useful convergence features are found when comparing the results of the NS-PIM and the FEM solutions. A simple method is introduced to estimate the errors of the model with rough grids. The convergence features and error estimation method can be applied to check the mesh quality and get accurate results. More stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions under the incompressible and impermeable condition.

It cannot be denied that the calculation of NS-PIM solution takes more time than that of the FEM solution, and more work needs to be carried out to optimize the NS-PIM solution. Also, in further study, the feasibility of more complicated and practical engineering problems can still be probed in the NS-PIM solution.

This paper introduced a method for the consolidation analysis on the situation of construction loads (“ramp load”) using the NS-PIM which is quite indispensable in many foundation problems. Also, more stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions than that with same order of shape functions.

This study first focuses on the situation of construction loads (“ramp load”) in the NS-PIM consolidation analysis which is quite indispensable in many foundation problems. An error estimation method is introduced to evaluate the mesh quality and get accurate values based on the convergence features of the FEM and NS-PIM solutions. Then, the incompressible and impermeable condition under instant load is investigated, and the analysis show that the NS-PIM with lower order of pore pressure shape functions can get stable results in such conditions.

The implementation of the finite element solution of Biot's consolidation theory on a low‐cost microcomputer is described. A two‐dimensional linear elastic model is solved using bilinear rectangular elements and a fully implicit timestepping algorithm. The machine used is the Acorn Computers model B, BBC microcomputer, a popular low‐cost engineering applications machine. The program is written in Basic but to increase speed of computation certain sections of the solution procedure involving matrix manipulation are written in Assembly language. The results obtained are encouraging from the point of view of accuracy, problem size and computational time. It is concluded that there is scope for the use of the present generation of low‐cost microcomputer, as typified by this machine, in the numerical solution of the more straightforward, but still realistic, consolidation problems.

This paper aims to present the investigation of the linear and nonlinear seismic site response of a saturated inhomogeneous poroviscoelastic soil profile for different soil properties, such as pore-water saturation, non-cohesive fines content FC, permeability k, porosity n and coefficient of uniformity C_u.

The inhomogeneous soil profile is idealized as a multi-layered saturated poroviscoelastic medium and is characterized by the Biot’s theory, with a shear modulus varying continuously with depth according to the Wichtmann’s model. Seismic response analysis has been evaluated through a computational model, which is based on the exact stiffness matrix method formulated in the frequency domain assuming that the incoming seismic waves consist of inclined P-SV waves.

Unlike the horizontal seismic response, the results indicate that the vertical one is strongly affected by the pore water saturation. Moreover, in the case of fully saturated soil profile, the same vertical response spectra are found for the two cases of soil behavior, linear and nonlinear.

This research is a detailed study of the geotechnical soil properties effect on the bi-directional seismic response of saturated inhomogeneous poroviscoelastic soil profile, which has not been treated before; the results are presented in terms of the peak acceleration ratio, as well as the free-field response spectra and the spectral ratio (V/H).

This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.

First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.

The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.

Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

The paper aims to propose a rate‐dependent model of structural concrete in combination with the kinematics of condensed water.

First, the paper proposes the coupling model of water versus cracked concrete with a mathematical completeness of equilibrium and deformational compatibility. The proposed model deals with anisotropy of structural performance and of permeability, which is a particular issue of concrete caused by cracks. The governing equation for saturated concrete in this study is based on Biot's theory that deals with particle assembly as a two‐phase composite. Second, the paper shows the possible reduction of the fatigue life of real‐scale bridge RC decks owing to the water residing in structural cracks under moving wheel‐type loading.

The paper shows that the existence of water possibly has an influence on the rate‐dependency of structural performance. The comparison of transition of pore pressure and principal strain indicates that damage to the concrete skeleton is accelerated by internal stress caused by high pore pressure. It suggests that the existence of water can reduce the fatigue life of bridge decks, especially when the upper layer is saturated.

This paper clarifies the effect of pore water on structural concrete by using numerical model considering kinematics of water.