Inhomogeneous Poroelastic Medium Research Articles

Time-Harmonic Response of an Elastic Pile in a Radially Inhomogeneous Poroelastic Medium

The time-harmonic response of an elastic pile embedded in a radially inhomogeneous poroelastic medium and subjected to a torsional loading is studied in the present article. In engineering practice, the surrounding soil may be weakened due to the disturbance effect caused by pile driving. To simulate the weakened surrounding soil, a boundary zone model with the complex shear modulus of the inner disturbed soil changing in a parabolic form along the radial direction is proposed. In view of the axis-symmetric deformation of the surrounding soil under torsional load, the equation of motion of the saturated soil is solved in the cylindrical coordinate system. The vibration displacement and shear stress solutions for the inner disturbed soil are gained by expanding the displacement as a power series, and those for the outer undisturbed soil are obtained by solving the partial differential equation. By virtue of continuity conditions at the interface between inner and outer soil regions, the torsional impedance of the radially inhomogeneous soil is solved. Then, via the boundary and continuity conditions of the pile-soil system, the twist angle and torque of the pile are obtained in the frequency domain. Finally, selected numerical results are conducted to investigate the influence of the material damping, softening degree, and softening range of the inner soil on the distribution of the twist angle and torque of the pile along the depth direction.

Attenuation and dispersion phenomena of torsional waves in self-weighted, inhomogeneous, pre-stressed poro-elastic and poro-viscoelastic stratified structure

ABSTRACT This paper studies torsional wave propagation in a poro-viscoelastic medium of finite thickness. The considered medium is clamped between an inhomogeneous poro-elastic medium of finite thickness and a poro-elastic half-space. Both finite layers are initially stressed and the half-space is self-weighted. Classical dynamical coupled theories have been used to explore the problem. Interior deformations are calculated analytically. A complex frequency equation has been obtained with the aid of suitable boundary conditions. The decomposition of the complex frequency equation into real and imaginary parts provides dispersion and damping equations. These frequency equations exhibited their reliance on the variation of attenuation coefficient, dissipation factor, inhomogeneity, initial stresses, Biot's gravity, porosity and thickness ratio parameters. The impacts of the aforesaid parameters have been extensively studied and demonstrated graphically.

Application of the Fully Coupled Planar 3D Poroelastic Hydraulic Fracturing Model to the Analysis of the Permeability Contrast Impact on Fracture Propagation

In our previous works (Baykin and Golovin 2016, 2017) it is shown that inhomogeneity of the permeability of a reservoir might play a significant role in the choice of the direction of the hydraulic fracture propagation. This effect was demonstrated using the fully coupled model of the hydraulic fracture in the poroelastic medium under the restriction on the geometry of the fracture similar to the one used in the Khristianovich–Geertsma–de Klerk model. In present paper, we extend our observations to a model of the planar 3D hydraulic fracture in the inhomogeneous poroelastic medium. In a series of numerical experiments we demonstrate that, depending on the permeability contrast of different parts of a layered reservoir, the hydraulic fracture propagates either within the low-permeable or the high-permeable zones of the reservoir. This behaviour is explained by the non-uniform action of the backstress that is formed on the fracture walls due to the pressure of the pore fluid.

Modelling of hydraulic fracture propagation in inhomogeneous poroelastic medium

In the paper a model for description of a hydraulic fracture propagation in inhomogeneous poroelastic medium is proposed. Among advantages of the presented numerical algorithm, there are incorporation of the near-tip analysis into the general computational scheme, account for the rock failure criterion on the base of the cohesive zone model, possibility for analysis of fracture propagation in inhomogeneous reservoirs. The numerical convergence of the algorithm is verified and the agreement of our numerical results with known solutions is established. The influence of the inhomogeneity of the reservoir permeability to the fracture time evolution is also demonstrated.

Propagation of crack in a pre-stressed inhomogeneous poroelastic medium influenced by shear wave

A mathematical model has been developed for the analytical study of propagation of crack due to horizontally polarized shear wave (SH-wave) in an initially stressed inhomogeneous poroelastic strip. The expression of stress intensity factor for the force of constant intensity has been determined in closed form. The emphatic impact of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive or tensile initial stress, vertical compressive or tensile initial stress, heterogeneity parameter, porosity parameter and anisotropy parameter on the stress intensity factor in an initially stressed inhomogeneous poroelastic strip has been depicted by means of graphs. In order to solve the problem, Wiener–Hopf technique specified by Matczynski has been employed. Moreover, some special cases have been deduced from the procured expression of stress intensity factor for the force of constant intensity.

Seismic wave propagation in laterally inhomogeneous poroelastic media via BIEM

SUMMARY This work addresses in-plane pressure P and vertically polarized shear SV seismic wave propagation in a finite, laterally inhomogeneous, multilayered poroelastic geological region resting on the homogeneous elastic half-space. The particular approach followed here is based on a combination of the (i) viscoelastic approximation (isomorphism) to Biot's equations of dynamic poroelasticity and on the (ii) boundary integral equation method (BIEM) using frequency-dependent fundamental solutions of the governing wave equations. The problem is formulated under plane strain conditions and time-harmonic motions are assumed. Validation of the viscoelastic isomorphism and verification of the BIEM is done by solution of benchmark examples. These simulation studies reveal that the proposed methodology is able to depict a sensitivity of the seismic signals recovered to the following parameters: (i) poroelastic properties of fluid saturated layers; (ii) lateral geological inhomogeneity; (iii) surface topography and (iv) frequency content and direction of the incident wave. It is concluded that the combination of viscoelastic isomorphism with BIEM software provides an effective numerical tool for evaluating site-effect phenomena in multilayered, fluid saturated geological regions with complex geometry. The numerical results obtained demonstrate that dynamic poroelasticity interacting with other physical peculiarities of the Earth's surface layers, such as lateral heterogeneity, material properties along the wave path, local geological profile and type of elastic wave, gives rise to complex seismic signals on the free surface at the site of interest. Copyright © 2010 John Wiley & Sons, Ltd.

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.

On the Effective Constants of Inhomogeneous Poroelastic Medium

On the Effective Constants of Inhomogeneous Poroelastic Medium

Angular variation in the simulated reflection and scattering properties of granular poroelastic ocean sediments.

Reflection and scattering properties of an inhomogeneous poroelastic medium were studied via numerical simulation. The inhomogeneous medium was modeled as an ensemble average of randomly layered poroelastic material. Each layer represented a granular material of a particular grainsize. The thickness of each layer was related to the associated grainsize and porosity by a conservation of mass relationship. Lateral variations in grainsize were approximated by performing a coherent ensemble average of results from several realizations of the randomly stratified medium. Poroelastic medium parameters were chosen to represent water‐saturated sand. The mean and standard deviation of the grainsize distribution were chosen to match existing experimental data in order to test the model. Specifically, the inhomogeneous medium was modeled as bounded by a homogeneous water half‐space on the source side, and a homogeneous poroelastic half‐space of equivalent average porosity on the other side. Reflected signals were computed for high‐frequency plane waves incident at various grazing angles. Coherent and random components of the reflected signal were calculated. The coherent part was related to the reflection coefficient. The random component was related to the scattering strength of the medium. Results were compared with existing experimental data. [Work supported by ONR.]

On the correspondence between poroelasticity and thermoelasticity

An interesting and useful analogy can be drawn between the equations of static poroelasticity and the equations of thermoelasticity including entropy. The correspondence is of practical use in determining the effective parameters in an inhomogeneous poroelastic medium using known results from the literature on the effective thermal expansion coefficient and the effective heat capacity of a disordered thermoelastic continuum.