Poroelastic Properties Research Articles

Poroelastic properties of anisotropic cylindrical composite materials

The present work is devoted to the determination of the effective poroelastic properties of anisotropic materials, such as porous nanocomposites and microbiotissues. The poroelastic field of composite materials in a transversely isotropic medium is determined by using the general self-consistent method (GSCM), and the dependence of material properties of the composites on porosity is considered. A hexagonal transversely isotropic model is used and treatment processes are proposed for application to microstructures or macrostructures. Several numerical examples are presented to validate the proposed model, and the results obtained from the model are compared with those obtained from a random-array model, a hexagonal-array model using the strain energy approach (SEA), the dilute suspension of the GSCM, the self-consistent method (SCM) and the effective self-consistent method (ESCM). An explicit solution of poroelasticity is provided, and the effects of the solid matrix anisotropy and pore space on the effective poromechanical properties considered. The numerical results for the hexagonal microstructure using the GSCM agree much better with those obtained from experimental investigation in both wet and dry situations than those obtained from other methods. Finally, the influences of fatigue on micromechanical properties for wet and dry conditions are also described.

Porous materials with two populations of voids under internal pressure: I. Instantaneous constitutive relations

This study is devoted to the mechanical behavior of uranium dioxide (UO 2) which is a porous material with two populations of voids of very different size subjected to internal pressure. The smallest voids are intragranular and spherical in shape whereas the largest pores located at the grain boundary are ellipsoidal and randomly oriented. In this first part of the study, attention is focused on the effective properties of these materials with fixed microstructure. In a first step, the poro-elastic properties of these doubly voided materials are studied. Then two rigorous upper bounds are derived for the effective poro-plastic constitutive relations of these materials. The first bound, obtained by generalizing the approach of Gologanu et al. (Gologanu, M., Leblond, J., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids-case of axisymmetric oblate ellipsoidal cavities. ASME J. Eng. Mater. Technol. 116, 290–297) to compressible materials, is accurate at high stress-triaxiality. The second one, which derives from the variational method of Ponte Castañeda (Ponte Castañeda, P., 1991. The effective mechanical properties of non-linear isotropic composites. J. Mech. Phys. Solids 39, 45–71), is accurate when the stress triaxiality is low. A N-phase model, inspired by Bilger et al. (Bilger, N., Auslender, F., Bornert, M., Masson, R., 2002. New bounds and estimates for porous media with rigid perfectly plastic matrix. C.R. Mécanique 330, 127–132), is proposed which matches the best of the two bounds at low and high triaxiality. The effect of internal pressures is discussed. In particular it is shown that when the two internal pressures coincide, the effective flow surface of the saturated biporous material is obtained from that of the drained material by a shift along the hydrostatic axis. However, when the two pressures are different, the modifications brought to the effective flow surface in the drained case involve not only a shift along the hydrostatic axis but also a change in shape and size of the surface.

Earthquake slip between dissimilar poroelastic materials

A mismatch of elastic properties across a fault induces normal stress changes during spatially nonuniform in‐plane slip. Recently, Rudnicki and Rice showed that similar effects follow from a mismatch of poroelastic properties (e.g., permeability) within fluid‐saturated fringes of damaged material along the fault walls; in this case, it is pore pressure on the slip plane and hence effective normal stress that is altered during slip. The sign of both changes can be either positive or negative, and they need not agree. Both signs reverse when rupture propagates in the opposite direction. When both elastic and poroelastic properties are discontinuous across the fault, steady sliding at a constant friction coefficient, f, is unstable for arbitrarily small f if the elastic mismatch permits the existence of a generalized Rayleigh wave. Spontaneous earthquake rupture simulations on regularized slip‐weakening faults confirm that the two effects have comparable magnitudes and that the sign of the effective normal stress change cannot always be predicted solely from the contrast in elastic properties across the fault. For opposing effects, the sign of effective normal stress change reverses from that predicted by the poroelastic mismatch to that predicted by the elastic mismatch as the rupture accelerates, provided that the wave speed contrast exceeds about 5–10% (the precise value depends on the poroelastic contrast and Skempton's coefficient). For faults separating more elastically similar materials, there exists a minimum poroelastic contrast above which the poroelastic effect always determines the sign of the effective normal stress change, no matter the rupture speed.

Effective porothermoelastic properties of transversely isotropic rock-like composites

The present work is devoted to the determination of the overall porothermoelastic properties of transversely isotropic rock-like composites with transversely isotropic matrix and randomly oriented ellipsoidal inhomogeneities and/or pores. By using the solution of a single ellipsoidal inhomogeneity arbitrarily oriented in a transversely isotropic matrix presented by Giraud et al. [A. Giraud, Q.V. Huynh, D. Hoxha, D. Kondo, Effective poroelastic properties of transversely isotropic rocks-like composites with arbitrarily oriented ellipsoidal inclusions, Mechanics of Materials 39 (11) (2007) 1006–1024], it is possible to observe the effect of the shape and orientation distribution of inhomogeneities on the effective porothermoelastic properties. Based on recent works on porous rock-like composites such as shales or argillites, an application of the developed solution to a two-level microporomechanics model is presented. The microporosity is homogenized at the first level, and multiple solid mineral phase inclusions are added at the second level. The overall porothermoelastic coefficients are estimated in the particular context of heterogeneous solid matrix. The present model generalizes to transversely isotropic media a recently developed two-level model in the simpler case of isotropic media (see Giraud et al. [A. Giraud, D. Hoxha, D.P. Do, V. Magnenet, Effect of pore shape on effective thermoporoelastic properties of isotropic rocks, International Journal of Solids and Structures 45 (2008) 1–23]). Numerical results are presented for data representative of transversely isotropic rock-like composites.

Effective Poroelastic Properties of Transversely Isotropic Porous Medium with Aligned Spheroidal Inhomogeneities

A two-component poroelastic composite material is considered. This material consists of a homogeneous transversely isotropic poroelastic matrix and aligned spheroidal inclusions filled with material having different poroelastic properties. The effective poroelastic characteristics are obtained by the effective field method. All the formulas are presented in explicit ready-to-use form.

Dynamic torsional response of an end bearing pile in saturated poroelastic medium

A comprehensive analytical solution is developed in this paper to investigate the torsional vibration of an end bearing pile embedded in a homogeneous poroelastic medium and subjected to a time-harmonic torsional loading. The poroelastic medium is modeled using Biot’s two-phased linear theory and the pile using one-dimensional elastic theory. By using the separation of variables technique, the torsional response of the soil layer is solved first. Then based on perfect contact between the pile and soil, the dynamic response of the pile is obtained in a closed form. Numerical results for torsional impedance of the soil layer are presented first to portray the influence of wave modes, slenderness ratio, pile–soil modulus ratio and poroelastic properties. A comparison with the plane strain theory is performed. The selected numerical results are obtained to analyze the influence of the major parameters on the torsional impedance at the level of the pile head. Finally, the dynamic torsional impedance of this study is compared with that for floating pile in elastic soil.

Effect of pore shape on effective porothermoelastic properties of isotropic rocks

The present work is devoted to the determination of the macroscopic poroelastic and porothermoelastic properties of geomaterials or rock-like composites constituted by an isotropic matrix with embedded ellipsoidal inhomogeneities and/or pores randomly oriented. By considering the solution of a single ellipsoidal inhomogeneity in the homogenization problem it is possible to observe the significant influence of the shape of inhomogeneities on the effective porothermoelastic properties. In the particular case of microscopic and macroscopic isotropic behaviors, a closed form solution based on analytical integrate of the Eshelby solution for the single ellipsoidal inhomogeneity can be obtained for the randomly oriented distribution. This result completes the well known solutions in the limiting cases of spherical and penny shape inhomogeneities. Based on recent works on porous rock-like composites such as shales or argillites, an application of the developed solution to a two-level microporomechanics model is presented. The microporosity in homogenized at the first level, and multiple solid mineral phase inclusions are added at the second level. The overall porothermoelastic coefficients are estimated in the particular context of heterogeneous solid matrix. Numerical results are presented for data representative of isotropic rock-like composites.

Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions

The present work is devoted to the determination of the macroscopic poroelastic properties of transversely isotropic geomaterials or rock-like composites with arbitrarily oriented ellipsoïdal inhomogeneities. The key problem to solve is to separate respective effects of matrix anisotropy and of inhomogeneities’ orientation distribution and shape. Based on a numerical integration of the exact Green function provided by Pan and Chou [Pan, Y.C., Chou, T.W., 1976. Point force solution for an infinite transversely isotropic solid. Journal of Applied Mechanics 43, 608–612] for the transversely isotropic media, the Hill tensor P is obtained for an arbitrarily oriented oblate spheroidal inclusion. The integrate of the Hill tensor is performed in an intermediate system coordinate attached to the inhomogeneity and with one axis equal to the symmetry axis of the transversely isotropic matrix. This choice of system coordinate allows to simplify numerical calculations and to gain accuracy because partial integrate can be performed analytically. The obtained Hill tensor is next used to study the effect of matrix anisotropy, pores systems and microstructure-related parameters on the overall effective poroelastic properties in transversely isotropic rocks. As an example, a two step-homogenization scheme is presented to test the ability of the proposed model in the evaluation of effective Biot tensor and Biot modulus and stiffness tensor. With the help of an orientation distribution function (ODF) the anisotropy due to the pore systems is also accounted. Numerical applications are finally carried out for anisotropic porous rocks both composed of a matrix with solid minerals constituents and a pore space.

Unsaturated poroelasticity for crystallization in pores

This paper shows how poroelasticity provides a quantitative explanation of the role of the pore size distribution in the deformation of porous materials subjected to the frost action. Unsaturated poroelasticity is the natural extension of saturated poroelasticity, once recognized that any crystallization process within a porous material results from two distinct physical processes: (i) an invasion process by the forming crystal, which is driven by surface energy effects; (ii) a deformation process under the crystallization pressure, whose intensity is governed by the poroelastic properties of the porous solid and by the current liquid saturation. The analysis reveals that the origin of the expansion is twofold: (i) the pressure build up of the unfrozen part of the porous network, that originates from the action of the excess of liquid expelled from the freezing sites; (ii) the cryo-suction process that constantly drives the liquid back towards the frozen sites as the cooling further increases. This explains the long known efficiency of air-voids against the frost action. These voids act both as expansion reservoirs and as cryo-pumps. The analysis finally provides an assessment for the recommended spacing factor between adjacent air-voids.

Effect of geometrical imperfections in confined compression tests on parameter evaluation of hydrated soft tissues

Experimental tests, such as the confined and unconfined compression and the indentation tests, are traditionally used to determine the poroelastic properties of hydrated soft tissues (HSTs). The purpose of this study was to quantitatively evaluate the reliability of H A and K values as identified from experimental confined test data, estimating the errors that could occur in several situations with more realistic sample geometry and boundary conditions. Finite element models of the step-wise stress–relaxation confined compression tests on HSTs were developed including geometrical imperfections of the sample and the presence of a gap between the piston and the confining chamber. The errors occurring when H A and K were estimated by means of the analytical solution of the 1-D confined compression problem were assessed. Results of the analysis indicate that errors in the parameter estimation due to geometrical inaccuracies of the sample can be eliminated by applying a 5% strain pre-compression to the sample. Gap errors are negligible for H A, can reach 20% for K, and cannot be eliminated by a pre-compression of the sample.

Inclusion of regional poroelastic material properties better predicts biomechanical behavior of lumbar discs subjected to dynamic loading

Understanding the relationship between repetitive lifting and the breakdown of disc tissue over several years of exposure is difficult to study in vivo and in vitro. The aim of this investigation was to develop a three-dimensional poroelastic finite element model of a lumbar motion segment that reflects the biological properties and behaviors of in vivo disc tissues including swelling pressure due to the proteoglycans and strain-dependent permeability and porosity. It was hypothesized that when modeling the annulus, prescribing tissue specific material properties will not be adequate for studying the in vivo loading and unloading behavior of the disc. Rather, regional variations of these properties, which are known to exist within the annulus, must also be included. Finite element predictions were compared to in vivo measurements published by Tyrrell et al. (1985) of percent change in total stature for two loading protocols, short-term creep loading and standing recovery and short-term cyclic loading with standing recovery. The model in which the regional variations of material properties in the annulus had been included provided an overall better prediction of the in vivo behavior as compared to the model in which the annulus properties were assumed to be homogenous. This model will now be used to study the relationship between repetitive lifting and disc degeneration.

Application of results on Eshelby tensor to the determination of effective poroelastic properties of anisotropic rocks-like composites

The present work is devoted to the determination of the macroscopic poroelastic properties of anisotropic elastic porous materials saturated by a fluid under pressure. It makes use of the theoretical results provided by Withers [Withers, P.J., 1989. The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium, and its relevance to composite materials. Philosophical Magazine A 59 (4), 759–781.] for the problem of an ellipsoidal inclusion embedded in a transversely isotropic elastic medium. The particular case of a spherical inclusion is very important for rock-like composites such as argillite and shales. The implementation of these results in a micromechanical theory of poroelasticity allows to quantify the effects of the solid matrix anisotropy and of pore space on the effective poromechanical properties. Closed form expressions of Biot tensor and of Biot modulus are presented as well as numerical applications for anisotropic shales.

Effective normal stress alteration due to pore pressure changes induced by dynamic slip propagation on a plane between dissimilar materials

Recent, detailed examinations of fault zones show that walls of faults are often bordered by materials that are different from each other and from the more uniform material farther away. In addition, they show that the ultracataclastic core of mature fault zones, where slip is concentrated, is less permeable to flow across it than the adjoining material of the damage zone. Inhomogeneous slip at the interface between materials with different poroelastic properties and permeabilities causes a change in pore pressure there. Because slip causes compression on one side of the fault wall and extension on the other, the pore pressure on the fault increases substantially when the compressed side is significantly more permeable and decreases when, instead, the extended side is more permeable. This change in pore pressure alters the effective normal stress on the slip plane in a way that is analogous to the normal stress alteration in sliding between elastically dissimilar solids. The magnitude of the effect due to induced pore pressure can be comparable to or larger than that induced by sliding between elastic solids with a dissimilarity of properties consistent with seismic observations. The induced pore pressure effect is increased by increasing contrast in permeability, but the normal stress alteration due to elastic contrast increases rapidly as the rupture velocity approaches the generalized Rayleigh velocity. Because the alteration in effective normal stress due to either effect can be positive or negative, depending on the contrast in properties, the two effects can augment or offset each other.

Poroelastic Bulk Properties of the Tectorial Membrane Measured with Osmotic Stress

The equilibrium stress-strain relation and the pore radius of the isolated tectorial membrane (TM) of the mouse were determined. Polyethylene glycol (PEG), with molecular mass (MM) in the range 20–511 kDa, added to the TM bathing solution was used to exert an osmotic pressure. Strain on the TM induced by isosmotic PEG solutions of different molecular masses was approximately the same for MM ≥ 200 kDa. However, for MM ≤ 100 kDa, the TM strain was appreciably smaller. We infer that for the smaller molecular mass, PEG entered the TM and exerted a smaller effective osmotic pressure. The pore radius of the TM was estimated as 22 nm. The equilibrium stress-strain relation of the TM was measured using PEG with a molecular mass of 511 kDa. This relation was nonlinear and was fit with a power function. In the radial cochlear direction, the transverse stiffness of the TM was 20% stiffer in the inner than in the outer region. TM segments from the basal region had a larger transverse stiffness on average compared to sections from the apical-middle region. These measurements provide a quantitative basis for a poroelastic model of the TM.

A constitutive and numerical model for mechanical compaction in sedimentary basins

The aim of the paper is to provide new elements concerning the constitutive behavior of sedimentary rocks and the numerical aspects for basin simulators. A comprehensive model for mechanical compaction of sedimentary basins is developed within finite poroplasticity setting. Particular concern is paid to the effects of large porosity changes on the poromechanical properties of the sediment material. A simplified micromechanics-based approach is used to account for the stiffness increase and hardening induced by large plastic strains. A key challenge for numerical assessment of sedimentary basin evolution is to integrate multiple coupled processes in the context of open material systems. To this end, a numerical approach inspired from the ‘deactivation/reactivation’ method used for the simulation of excavation process and lining placement in tunnel engineering, has been developed. Periods of sediments accretion are simulated by progressive activation of the gravity forces within a fictitious closed system. Fundamental components of the constitutive model developed before (hydromechanical coupling, dependence of poroelastic properties on large plasticity, impact of irreversible porosity changes on the hardening rule, evolution of permeability with porosity) are included into our finite element code. Illustrative examples of basin simulation are performed in the one-dimensional case. Various aspects of the constitutive model are investigated. Their influence on the corresponding basin response is analyzed in terms of compaction law, porosity and fluid pressure profiles.

Deformation and stress from in-pore drying-induced crystallization of salt

The deformation and the fracture of porous solids from internal crystallization of salt is explored in the framework of the thermodynamics of unsaturated brittle poroelasticity. In the first place the usual theory of crystal growth in confined conditions is further developed in order to include both the deformation and the drying of the porous solid. The thermodynamics reveals the existence of a dilation coefficient associated with the crystallization process, and provides a solute–crystal equilibrium condition which involves the relative humidity, the supersaturation, and the salt characteristics. This thermodynamic condition and the mechanical equilibrium of the solution–crystal interface combine to give the current crystallization pore radius. Upscaling this information at the macroscopic scale, and taking into account the salt mass supplied by the invading solution, the approach leads to a quantitative analysis of the role of the pore size distribution on the crystal growth under repeated imbibition–drying cycles. The deformation and the fracture of the porous solid from drying-induced crystallization are then considered in the context of brittle poroelasticity. The current unsaturated macroscopic poroelastic properties are upscaled from the microscopic elastic properties of the solid matrix and from the current liquid, crystal and gas saturations. The adoption of a fracture criterion based on the elastic energy that the solid matrix can ultimately store finally leads to the determination of how long a stone can resist repeated cycles of drying-induced crystallization of salt.

Heating and weakening of faults during earthquake slip

Field observations of mature crustal faults suggest that slip in individual events occurs primarily within a thin shear zone, <1–5 mm, within a finely granulated, ultracataclastic fault core. Relevant weakening processes in large crustal events are therefore suggested to be thermal, and to involve the following: (1) thermal pressurization of pore fluid within and adjacent to the deforming fault core, which reduces the effective normal stress and hence also the shear strength for a given friction coefficient and (2) flash heating at highly stressed frictional microcontacts during rapid slip, which reduces the friction coefficient. (Macroscopic melting, or possibly gel formation in silica‐rich lithologies, may become important too at large enough slip.) Theoretical modeling of mechanisms 1 and 2 is constrained with lab‐determined hydrologic and poroelastic properties of fault core materials and lab friction studies at high slip rates. Predictions are that strength drop should often be nearly complete at large slip and that the onset of melting should be precluded over much (and, for small enough slip, all) of the seismogenic zone. A testable prediction is of the shear fracture energies that would be implied if actual earthquake ruptures were controlled by those thermal mechanisms. Seismic data have been compiled on the fracture energy of crustal events, including its variation with slip in an event. It is plausibly described by theoretical predictions based on the above mechanisms, within a considerable range of uncertainty of parameter choices, thus allowing the possibility that such thermal weakening prevails in the Earth.

周期的な間隙水圧変動を利用した水理特性評価技術の適用深度の検討―気圧変動と波浪を利用した評価例―

Poroelastic properties, including hydraulic properties, govern fluid flow and deformation of geological formations. In this paper, we discuss the applicability of methods for estimating hydraulic properties from pore pressure response to cyclic loading such as atmospheric pressure, earth tide, ocean tide, and seawater wave in terms of loading frequencies, measurement depths, and physical properties of materials. We also show 2 case studies in which we estimate hydraulic diffusivity using pore pressure fluctuations to atmospheric loading at about 100 m in depth, and those to seawater wave loading at about 1 m below the sea floor.

A Spherically Anisotropic Microstructure Model for Fluid-saturated Poroelastic Isotropic Materials

The microstructure model proposed in this work is an assemblage of hollow spheres saturated by a fluid. The solid phase of each sphere is linearly elastic and spherically anisotropic. On the basis of this microstructure model, the effective bulk modulus, Biot’s coefficient and porosity variation are determined. It is shown that local anisotropy has important effects on the macroscopic isotropic poroelastic properties via a dimensionless material parameter which characterizes the degree of anisotropy and exponentially affects the porosity.

Microporodynamics of Bones: Prediction of the “Frenkel–Biot” Slow Compressional Wave

Understanding of ultrasonic wave propagation in bones is essential for further development of related techniques in clinical practice. As any other saturated porous medium, bone is characterized by different forms of longitudinal wave propagation, either undrained waves or fast and (Frenkel–Biot) slow compressional waves. We here study the wave propagation in the framework of poromicromechanics. A continuum micromechanics model allows for the prediction of the anisotropic poroelastic properties, Biot’s coefficients, and moduli, from tissue-specific composition data, on the basis of tissue-independent (“universal”) elastic properties of the elementary components of all bones. These poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.