Poromechanics V: Proceedings of the Fifth Biot Conference on Poromechanics

This paper presents analytical and experimental studies of the effects of supercritical CO₂ injection on the seismic velocity of sandstone initially saturated with saline water. The analytical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible fluids. The experimental study used a high pressure and high temperature triaxial cell to clarify the seismic response of samples of Berea sandstone to supercritical CO₂ injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO₂ injection in the sandstone sample showed the effects of pore fluid distribution in the seismic velocity of porous rocks. CO₂ injection was shown to decrease the P-wave velocity with increasing CO₂ saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO₂ and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus.

In the present study, an analytical method for calculating dynamic response of a cylindrical cavity in an infinite cross-anisotropic porous medium is presented. The basis of the method is the Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u-w formulation of Biot's equations are solved. The stress, displacement, and pore pressure fields are evaluated in the vicinity of the cylinder in complex plane. Also the effects of many parameters ( k_h / k_v, E_h / E_v and ν_hh ) on the responses are evaluated by numerical examples.

A two-dimensional semi-analytical solution to the dynamic response of saturated porous media is presented considering a number of heterogeneous layers. The governing equations proposed by Biot are written in their fully dynamic form and possible simplifications of quasi-static and partially dynamic formulations developed in terms of the presence of inertial terms are also introduced. The analytical solutions for a plane strain saturated porous layer developed before by the author are extended to multi-layers for all formulations in terms of non-dimensional parameters. Dynamic response of the system is evaluated in terms of displacements, pore pressure as well as effective and shear stress variations in the medium. Since inertial terms in the equations associated with both the solid and the fluid part play a significant role in the dynamic response, applicability of these terms for a variety of problems is investigated. It is found that accelerations due to relative motion of pore fluid to that of solid skeleton becomes more important as higher frequencies are present in the medium. The applicability of formulations for the problems involving multi-layer porous media is determined in terms of maximum discrepancy in magnitude between the responses. As it is found quite useful by both researchers and engineers, the response is studied for different conditions and the regions of validity of the formulations are identified in a non-dimensional parametric space indicating the effect of multi-layering.

We measured seismic attenuation in the frequency range from 1 to 100 Hz and transient fluid pressure in a partially saturated rock sample. The pressure sensors were located 4.2 cm apart and, therefore, provided information on pressure gradients in the mesoscopic scale. The sample was of Berea sandstone and was saturated with 97% water (3% air). The measurements were performed at room pressure and temperature. The laboratory results suggested that that wave-induced fluid flow in the mesoscopic scale is dominant in partially saturated samples. To verify that, we performed numerical modeling to compute attenuation and transient fluid pressure on a three-dimensional poroelastic model representing the rock sample. The finite-element method was used to solve Biot's equations of consolidation by performing a quasi-static creep test. Wave-induced fluid flow in the mesoscopic scale is the only attenuation mechanism accounted for in the numerical solution. The numerical results reproduced the laboratory data for transient fluid pressure. Likewise, the numerically calculated attenuation, superposed to the frequency-independent attenuation measured in the dry sample, reproduced the attenuation measured in the laboratory in the partially saturated sample. These results show that wave-induced fluid flow in the mesoscopic scale is the dominant mechanism for frequency-dependent seismic attenuation in fluid-saturated Berea sandstone.

An important characteristic of fractured rocks is their very high seismic attenuation, which so far has been assumed to be mainly produced by wave-induced fluid flow between the fractures and the embedding matrix. As this fluid pressure equilibration process is strongly controlled by the hydraulic properties of the heterogeneous rock sample, the resulting seismic attenuation must also be expected to contain information about fracture connectivity. To date, however, the importance of fracture connectivity with regard to the observed seismic attenuation is largely unknown. Using numerical oscillatory compressibility simulations based on Biot's quasi-static poroelastic equations we show that an important, and as of yet non-documented manifestation of wave-induced fluid flow arises in the presence of fracture connectivity. We demonstrate that this additional energy loss is mainly due to fluid flow within the fractures and operates only in the presence of connected fractures. We also show that this phenomenon is sensitive to the lengths, permeabilities, and intersection angles of the fractures. Correspondingly, it contains key information on the governing hydraulic properties of fractured rocks and hence should be accounted for whenever realistic seismic models of such media are needed.

Partially saturated rocks are considered to be major sources of seismic wave velocity dispersion and attenuation in recorded real data. From the physical description of partially saturated gas-water reservoirs, we use upscaling theories to compute an equivalent frequency-dependent porous medium. These homogenization methods are associated with mesoscale description of attenuation and dispersion coming from wave-induced flow phenomena. To compute wave propagation, we use numerical codes in the frequency domain that allow us to take into account all the frequency-dependent parameters. In this way, the Biot slow compressional wave, is well modeled and its partially diffusive, partially propagative behavior is completely considered. The waves attenuation and dispersion in such media is coming partly from the wave mode conversion into diffusive slow waves, not visible on seismograms. But the amplitude of propagative P- and S-waves are mainly affected by these energy losses at interfaces. So, thanks to a full waveform modeling, we investigate the AVO attributes with respect to saturation and frequency. For a simple three layer case, we compute poroelastic wave propagation, extract maximum amplitude with respect to angle and through a least-square fitting method, we obtain the AVO attributes for PP and PS reflected events. Due to the influence of mesoscale induced fluid flow phenomena and relatively to the regime of the Biot slow wave, the main results show a strong variability of the AVO attributes with the frequency and a lower variability with the saturation for reflected PP or PS events. Then, we conclude that these AVO attributes carry information about the saturation (through the reflection coefficients) and can be utilized in a poroelastic inversion process.

Based on the generalized variational principle (GVP) the system of the generalized Biot's equations is derived for consistent account of fluid shear relaxation. Account of shear viscosity relaxation leads to existence of additional degree of freedom and hence to additional second shear wave similar to a couple of longitudinal waves in the original Biot's approach. At this the one shear wave is an acoustical one, while the other shear wave has diffusive behavior with linear dependence of phase velocity and attenuation factor at low frequencies. This behavior is different from analogous behavior of diffusive longitudinal wave with the root frequency behavior of the same values. The dispersion properties of the second shear wave are calculated for the whole frequency domain. The frequency dependences of phase velocity and attenuation factor of the second diffusive shear wave in porous medium with Maxwell's fluid behavior are presented for different relaxation times.

Gas and water patchy-saturation in heterogeneous natural gas reservoirs causes significant seismic velocity dispersion and attenuation. The Biot-Rayleigh double-porosity model is used here to describe the seismic properties of these reservoirs and design a multi-scale rock physics template that relates the wave responses at different scales to the lithology and pore fluids. This approach is applied to limestone reservoirs located at the right bank of Amu Darya river. By performing pre-stack inversion and using the template, gas saturation and porosity are estimated.

Tight sandstone gas with abundant reserve and wide distribution will be the key field in seismic prospecting. We introduce the digital characterization for the micro pore structures in tight sandstone based on high-resolution CT scanning technology, and then build a pore geometry model with several types of pore shapes and two types of pore connectivity. When elastic wave propagates in this kind of porous medium, fluid in pores with different shapes and connectivity will respond differently, which affect the elastic properties of tight sandstones. Therefore, we apply Biot-Gassmann equation and Mori-Tanaka model to analyze the connected and isolated pores respectively, and then formulate a new rock physics model. By comparison with experimental data, this model can give more reasonable explanation.

By means of a Biot-like model with isotropic stress-strain relations but anisotropic permeability monochromatic waves in a two-component poroelastic medium are analyzed. The anisotropy is induced by the anisotropy of the tortuosity which is introduced by a second order symmetric tensor. The model describes for a certain choice of orientation of the propagation direction four modes of propagation: a decoupled transversal S1-wave, a pseudo transversal mode S2 and two pseudo longitudinal modes P1 and P2. Phase speeds and attenuations of these waves are shown in dependence on the orientation of the principal directions of the tortuosity.

Krauklis waves are a special wave mode bound to and propagating along fluid-filled fractures. They are of great interest because when propagating back and forth a fracture, they may fall into resonance and emit seismic signals with a characteristic frequency. This resonant behavior can lead to strongly frequency-dependent propagation effects for seismic waves and may explain seismic tremor generation in volcanos or affect micro-seismic signals in fractured fluid reservoirs. All existing studies assume a Krauklis wave initiation inside a fracture, for example by hydro-fracturing. Here, Krauklis wave initiation by an incident plane P-wave is studied. The P-wave is scattered at the fracture, but also, two Krauklis waves are initiated, one at each fracture tip (i.e., diffraction-points of the fracture). The initiation of Krauklis waves strongly depends on the fracture orientation with respect to the incident P-wave. High-amplitude Krauklis waves are initiated at moderate (12°-40°) and high (>65°) incident angles with a distinct gap at around 50°. The initiated Krauklis waves are only visible within, but not outside the fracture. Nevertheless, the fact that P-waves can initiate Krauklis waves has important implications for earthquake signals propagating through fluid-bearing fractured rocks (volcanic areas, fluid-reservoirs) or for active seismic surveys in fractured reservoir situations.

P-wave propagation in porous rock is a fundamental problem in geophysics. Both skeleton and fluid are spatially heterogeneous, which cause wave dispersion and attenuation. Here we develop a triple-layer patchy model to predict P-wave dispersion/attenuation in double-porosity materials with dual-fluid. The model consists of spherical porous inclusions embedded in a homogeneous host medium. The inclusions are homogeneous and their radii are much smaller than the wavelength but larger than the pore size (mesoscopic). The interface between inclusion and host medium is open and fluids can flow through it. The skeletons are saturated by two types of fluids. There is an interface between the inner fluid pocket and outside fluid patch. The fluid interface is independent of inclusion-host interface. Wave equations are derived following the Lagrangian formulation. Plane wave analysis is used to achieve relation between frequency and wave number. P-wave dispersion/attenuation are calculated and compared with both theoretical models and experimental data.

Linear and nonlinear acousto-electric waves in porous solids in the presence of an electric field are investigated. The pores are filled with an electro-conductive liquid. In (Shekoyan, 2011) nonlinear equations are derived from the variational principle that take into account the motions of solid and liquid phases and changes in porosity. In order to describe the seismo-electric effects, Maxwell equations are added to those equations (Shekoyan, 2011). This system is investigated using the method described in (Bagdoev, et al, 2009). The resulting self-consistent problem is solved while all the factors accompanying the wave are taken into account. Formulae for the wave's linear and nonlinear speeds and absorption coefficients are derived. Both 1-dimensional and 3-dimensional cases have been considered. Nonlinear evolutionary and Schrodinger equations are derived. Their solutions are obtained and investigated in detail. It is shown that there can be soliton-shaped waves in the medium.

Seismic and electromagnetic wavefields are coupled in subsurface rocks due to the seismoelectric effect occurred in the electric double layer at the grain/fluid interface of porous formations. In this study, we simulate and investigate the borehole seismoelectric wavefields under logging while drilling (LWD) environment. An acoustic multipole source is assumed to radiate acoustic energy on the surface of the steel drilling collar located in the fluid-filled borehole. The seismoelectric field is calculated by solving a modified Poisson's equation, whose source term is the electric disturbance induced electrokinetically by the traveling seismic wave. The seismic wavefield itself is obtained by solving Biot's equations for poroelastic waves. By comparing the amplitudes of the collar wave in the acoustic-pressure and electric-filed full-waveforms, we found that the former is significantly weakened compared with the latter, in terms of its amplitude relative to the other wave groups in the full waveforms. Thus less and shallower grooves are required to damp the collar wave if the seismoelectric LWD signals are recorded for extracting formation compressional and shear velocities.

In this paper we have studied the influence of rock elastic properties, porosity and permeability on the reverberation of acoustic waves in a borehole drilled in a poroelastic formation. The modeling has shown that, in the case of low permeability rocks, the time of acoustical reverberation is determined by the seismic impedance of borehole wall (V_pρ), where V_p is the compressional wave velocity of the rock and ρ is the rock density. In the case of permeable rocks, the time of borehole acoustic reverberation depends on their permeability. The results obtained demonstrate the feasibility of the considered sonic log modification to estimate the rock permeability.

The elastic and anelastic parameters of dry and distilled water-saturated sandstones with low (~7.8 mD) and high (~590 mD) permeabilities were measured at various confining pressures and room temperature (22° C). The both sandstones were quarried in Donnybrook, Western Australia. The experiments were performed with a new laboratory apparatus utilizing stress-strain relationship, which was developed to measure the complex Young's moduli of rocks at seismic (1-100 Hz) and teleseismic (≤1 Hz) frequencies, confining or uniaxial pressures from 0 to 70 MPa, and strain amplitudes 10^-8-10^-7. The measurements in water-saturated sandstones reveal a prominent peak of attenuation in the sample with low permeability at frequency ~0.8 Hz, whereas the attenuation in the high permeable sample remains similar to the attenuation measured under dry conditions. These results demonstrate that for low-permeability rocks seismic frequencies do not necessarily correspond to the low frequency limit of acoustic wave dispersion.

The variation of the drained bulk modulus with frequency is examined by taking into account the local flow between cracks and pores. The magnitude of dispersion of the drained bulk modulus depends on crack density, while the relaxation frequency depends on aspect ratio. An expression of the underrelaxed drained bulk modulus on full frequency range is derived by assuming that the liquid pressure in cracks is underrelaxed and the pressure in the pores is zero. The underrelaxed drained bulk modulus is a complex quantity with its real part increasing with frequency. The liquid pressure in cracks approaches zero in the low-frequency limit and is thus relaxed. In the high-frequency limit, the drained bulk modulus is unrelaxed and its value is approximately equal to that predicated by Mavko-Jizba's relation.

Borehole seismic experiments are very sensitive to the source and receiver geometry, the presence or absence of a casing, and to heterogeneities in the formation surrounding the borehole. For applications that go beyond the use of first-arrival times, analytical solutions are generally not sufficient and numerical methods are needed. Here, we present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. We consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center followed by the casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction and Fourier expansions in the other directions. Time stepping is performed through a Runge-Kutta integration scheme. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. For the cylindrical case, the equations of motion can be solved by using spectral operators in all dimensions, thus allowing for 3D heterogeneity and arbitrary receiver and source geometries, or by applying a Fourier decomposition in the azimuthal direction assuming rotational symmetry of the model.

Acoustoelastic theory for a dissipative fluid-saturated porous rock (FSPR) is investigated based on the finite deformation theory of the continuum and poroelastic theory. The assumption of a small dynamic motion superimposed on a largely static pre-deformation of the FSPR yields natural, initial, and final configurations. The consideration of homogeneous pre-deformation, dissipation induced by the Poiseuille-type fluid-solid relative motion, the plane harmonic form of the small dynamic motion according to the constitutive relations and equations of motion of the dissipative FSPR gives acoustoelastic equations, which provide the analytical formulations for the relation of the velocities of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with the solid-skeleton stresses and the fluid pore-pressure. Taking a rock under open-pore jacketed condition as an example, the detailed discussions about the characteristic of wave dispersion and attenuation for the shear waves are shown that the characteristic of wave dispersion and attenuation for the dissipative FSPR is usually influenced by the pre-deformation. The pre-deformation has little effect on the characteristic of wave dispersion and attenuation for dissipative FSPR only when the components of the applied initial principal stresses are equal.

Recent advances in Differential Acoustic Resonance Spectroscopy (DARS) techniques have given rise to novel applications in the field of poromechanics. We derive the quasi-static expression for the bulk modulus of a fluid saturated spherical sample with open pores due to an external fluid pressure p^_e. Under the assumption that the frequency is never so high to violate the quasi-static condition, the high-frequency limit of this modulus approaches the Biot-Gassmann modulus. The frequency-dependent modulus is compared with the value of the bulk modulus from DARS measurements on unjacketed porous samples at 1 kHz. Quantitative agreement is found between the experimental value and the theoretical prediction.

The properties of a generalized Stoneley wave, a symmetric trapped mode in a fracture filled with a viscous Newtonian fluid embedded into either poroelastic or a purely elastic rock, are derived. Symmetric mode is considered. Full dispersion relation corresponding to linearized Navier-Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions is rigorously written down. A cubic equation for wavenumber is found that provides analytical approximation of the exact solution. In the frequency range of 10^-2 - 10³ Hz and for layer width less than 10 cm, the analytical approximation is verified vs. numerical solution of the full dispersion relation by comparing phase velocity and attenuation, and found to be one of high quality. Comparison to earlier results addressing viscous fluid in either porous rock with rigid matrix or in a purely elastic rock is made, and our formulae are found to better match the numerical solution.

An acoustic method is proposed for measuring the low frequencies parameters of porous materials having a rigid frame. The Biot equivalent fluid model is considered, in which the viscous losses are described by the static viscous permeability and an additional viscous parameter. The inertial interactions between fluid and structure are taken into account by the inertial factor. The thermal couplings are modeled using the thermal permeability and the thermal tortuosity. The proposed method is based on a solution of the direct and inverse problems for the propagation of transient audible frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The physical parameters are determined from the solution of the inverse problem using experimental reflected and transmitted waves by porous samples, in a wave guide (pipe). The minimization of the objective function, defined as the difference between experiment and theory, is done in the time domain. Tests are performed using industrial plastic foams. Experimental and theoretical data are in good agreement. Furthermore, the prospects are discussed.

Numerical pore-scale simulation of elastic wave propagation is an emerging tool in the analysis of static and dynamic elastic properties of porous materials. The dry rock moduli (shear modulus & bulk modulus) and the tortuosity are derived by those simulations. The rotated staggered-grid (RSG) finite difference method has proved to be particularly effective in modeling porous media saturated with ideal , i.e. non-viscous fluids. This method has been extended to viscoelastic (gernalized Maxwell) media, which allows simulation of wave propagation in porous solids saturated with Newtonian fluids. The capability of the viscoelastic RSG algorithm in modeling wave dispersion and attenuation was confirmed by simulations for an idealized porous material, namely a periodic system of alternating solid and viscous fluid layers. Revisiting these results give the perspective to determine the permeability with dynamic wave propagation simulations and to better understand a simulated signature of a theoretically predicted slow S-wave.

The compressional and shear wave speeds of a fully CO₂-saturated porous ceramic are measured as functions of pore fluid pressure and temperature. The wave speeds show considerable variation dependent upon the phase state of the CO₂. The observations are further in good agreement with Biot's model of wave propagation. The ability to change the CO₂'s compressibility, density, and viscosity by relatively modest changes in temperature and pressure provides for a somewhat 'tunable' fluid that can be used to study fluid induced variations of wave propagation behavior.

We study Biot's slow wave propagation in the presence of strong hydraulic conductivity fluctuations in the low-frequency range. The latter condition implies that the slow wave is a diffusion process. To elucidate the characteristics of the diffusion wave in an inhomogeneous medium, we perform numerical simulations. These simulations demonstrate that the diffusion wave field does not only depend on the spatial distribution of the inhomogeneities but also on the frequency. Therefore, if we seek to replace the inhomogeneous medium by an effective, up-scaled medium, the corresponding effective hydraulic conductivity will become frequency-dependent. Based on a strong-contrast approximation, suggested in the context of an effective dielectric constant, closed form expressions for the effective, frequency-dependent conductivity are derived. These expressions yield in 1D the exact low- and high-frequency bounds, while in 3D the frequency limits for certain optimal microstructures can be obtained.

Predicting seismic velocities in isotropic fluid-saturated rocks is commonly done using the isotropic Biot-Gassmann theory. For anisotropic media, the Biot-Gassmann solution is expressed in terms of stiffness or compliance, which does not provide an intuitive understanding on the impact of fluid on anisotropy. To analyse how the pore fluid affects wave propagation in weakly anisotropic media, we rederived these expressions in terms of dimensionless anisotropy parameters. Besides, we study the effect of fluid on two anisotropy patterns, the one caused by aligned fractures embedded in an isotropic porous background and the stress-induced anisotropy pattern. By deriving an approximation of the anellipticity parameter η, we show that if the dry medium is elliptical, the saturated medium is also elliptical but only if the porosity is not too small. This result can provide a way of differentiating between stress- and fracture-induced anisotropy.

When cracks and pores are connected within a rock, stress can induce fluid flow from one inclusion to another one. Because cracks are more compliant than equant pores, a stress wave builds up a higher fluid pressure within a crack than within a pore and, consequently, fluid flows from crack to pore at a local scale. At low frequencies, fluid pressure has time to reach equilibrium. The elastic moduli are in that case relaxed moduli, those moduli are defined within the framework of poroelastic theory (drained or undrained moduli). Such a situation can be expected at seismic frequencies. However, in laboratory conditions, most of elastic waves data are obtained in the MHz range. Clearly, in such a high frequency range, there is no time for fluid pressure equilibrium to take place (even at local scale). The elastic moduli are unrelaxed moduli in that case. They are not those accounted for by poroelasticity, but they may be calculated from effective medium theory.

The attenuation of seismic waves is an important material parameter which contains potentially valuable information on key properties of the probed medium. An inherent complication arising in the interpretation of such measurements is, however, that there are multiple physical mechanisms contributing to the dissipation of seismic energy, such as wave-induced fluid flow at the micro-, meso-, and macroscopic scales. In addition to this, the relative contribution and importance of the various mechanisms are generally unknown and difficult to unravel. To address this problem for the practically relevant case of unconsolidated surficial sediments, we analyze multi-frequency sonic logs with dominant source frequencies ranging between 1 and 30 kHz. In order to estimate appropriate corrections for near-field and geometrical spreading effects, which are essential to obtain reliable estimations of attenuation, we model our experimental setup using a numerical solution of the poro-elastic equations in cylindrical coordinates. After having applied the thus inferred corrections, this broadband dataset, in conjunction with a comprehensive suite of complementary logging data, allows for building a realistic rock physics model. This, in turn, provides the basis for simulating the various seismic attenuation mechanisms and for assessing their relative importance. We demonstrate that, while the levels of attenuation due to the presence of mesoscopic heterogeneities expected for the considered case are negligible, the energy losses produced by fluid flow at microscopic and macroscopic scales can be very significant. Results based on Monte-Carlo-type inversions indicate that the Biot's intrinsic macroscopic attenuation allows for obtaining a good representation of most of the data, while refinements provided by including microscopic loss are locally meaningful.

Compliant porosity in the form of cracks is known to cause significant attenuation and velocity dispersion through pore pressure gradients and consequent relaxation, dubbed "squirt flow". Squirt flow from cracks vanish at high confining stress due to crack closing. Studies on clay-bearing sandstones, however, show high attenuation and velocity dispersion remaining at high confining stress. Such dispersion is proposed to be caused by pressure gradients induced by compliant porosity within clay inclusions. By modeling the response of two extreme systems, we quantify the possible effects of such clay-squirt flow on the bulk modulus of a clay-bearing sandstone. The predicted magnitude of the clay-squirt effect on the bulk modulus is compared with experimental data. The clay-squirt effect is found to possibly account for a significant portion of the deviances from Gassmann fluid substitution in clay-bearing sandstones.

This study concerns the ultrasonic wave propagation in fractional dimensional rigid porousmedia. A Biot equivalent fluid model with a non-integer dimensional space is developed using the Stillinger-Palmer-Staravinou formalism. A generalized lossy wave equation is derived and solved analytically in time domain. The coefficients of the propagation equation are constant and depend only on the fractional dimension and the acoustical parameters of the porous material. As in the integer dimension case, the obtained propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method.

We use a conventional vertical shock tube to generate and study wave propagation in a borehole intersected by a single horizontal permeable fracture. A mandrel sample is used to create a variable-aperture fracture in a cylindrical sample. A theoretical description for fracture zones is derived based on the introduction of an effective borehole fluid bulk modulus, connecting the wave attenuation to the borehole wall impedance. This impedance can be calculated for fracture zones adjacent to the borehole, thus predicting borehole wave propagation, transmission and reflection over such zones. The transmittivity of a borehole tube wave over a 5-mm fracture is correctly predicted, thus showing the potential of borehole wave experiments for fracture detection and characterization.

Phase velocities and dispersion of acoustic waves in residual saturated porous rocks are affected by material properties of the solid skeleton (porosity, skeleton and grain stiffness) and properties of the inherent pore fluids (viscosities, bulk moduli), as well as the morphology of saturation. A multiscale continuum model describing acoustic waves in porous rocks saturated with a continuous gas phase and a discontinuous liquid (water or oil) phase is analysed. Dispersion relations for the P-waves are shown and compared with Biot's poroelastic approach. It is observed that negative partial densities occur close to the resonance frequency of the liquid phase. The analogy with acoustic metamaterials is discussed.

In this paper, we present numerical results suggesting that the Biot slow wave predicted by poroelastic theory could indirectly be observed in the diffuse regime, thanks to its electric field signature generated through electrokinetic coupling. This seismo-electromagnetic coupling phenomenon was theoretically described in terms of dynamic equations which coupled seismic wave propagation theory in saturated porous media with Maxwell electromagnetic equations via transport equations of electrical charges and fluid's. A numerical code was developed ten years ago using a generalized reflectivity approach in the frequency-wavenumber domains to model the coupled seismo-electromagnetic waves in saturated stratified porous media. Based on this code, we present here new synthetic studies clearly suggesting that electrokinetic wave conversions could make it possible to record and study the Biot slow wave in real conditions and at low frequencies (diffuse regime), a goal that has never been achieved until now due to its low seismic signature. These synthetic observations are then theoretically explained after deriving electric/seismic transfer functions for a wide frequency range.

We designed and developed an experimental setup in which acoustic to electromagnetic (EM) wave conversions at interfaces can be measured. Experimental results are compared with a full-waveform theoretical model based on the Sommerfeld approach. After amplitude scaling, the measured spatial distribution of the electric wave field is in excellent agreement with the theoretical prediction. A strong dependency of the reflected electric signal on the sample thickness was recorded. This dependency is not present in the acoustic signal.

The conversions between seismic energy and electromagnetic energy have been studied by geophysicists as far back as the 1930s, both experimentally and theoretically, but are still in an experimental stage. In this contribution, we address some unresolved questions concerning the coseismic effects and interface response recorded in seismo-electric field experiments. Our investigations rely on Pride's generalized theory for frequency-dependent streaming potentials in porous media and its implementation in a simulation code yielding the seismo-electric response of a layered poro-elastic medium to a point source excitation. We successively address the problem of the transfer function between seismic and electric fields for surface waves, the electrode spacing when doing seismo-electric measurements in the field, and a possible super-resolution of very thin layers by the converted seismic-to-electro-magnetic wave conversions.

When a porous medium is permeated by open fractures, wave-induced flow between pores and fractures can cause significant attenuation and dispersion. Most studies of this phenomenon assume that pores and fractures are saturated with the same fluid. In some situations, particularly when a fluid such as water or carbon dioxide is injected into a tight hydrocarbon reservoir, fractures may be filled with a different fluid (with capillary forces preventing fluid mixing). Here we develop a periodic stratified poroelastic model for wave propagation in a porous medium with aligned fractures where pores and fractures are filled with different fluids. A dispersion equation for the P-wave propagating through such medium is derived by taking the simultaneous limits of zero thickness and zero normal stiffness of the thin layers. The simulation results show that in the low-frequency limit the elastic properties of such a medium can be described by Gassmann's equation with a composite fluid, whose bulk modulus is a harmonic (Wood) average of the moduli of the two fluids. At high frequencies, the dispersion is relatively high when the fluid in both pores and fractures is liquid, and also when the pores are filled with a liquid but fractures are filled with a highly compressible gas. However, an intermediate case exists where no dispersion is observed. This can be explained by observing that when the medium is uniformly saturated with a liquid, wave-induced compression causes flow from fractures into pores due to high compliance of the fractures. Conversely, when pores are filled with a liquid but fractures are filled with gas, flow will occur from pores into fractures due to high compressibility of gas. Thus an intermediate case exists where there is no flow and, hence, no dispersion or attenuation.

Modelling seismic wave propagation in poroelastic media is based on macroscopic equations, such as proposed by Biot. It is clear, however, that some microstructural information must enter into the computation of the macroscopic parameters. One example is the flow permeability in Biot's theory. Though it is a macroscopic quantity, it is commonplace to find permeability estimates using microstructural descriptors. From a wave-propagation point of view, there is also a temporal upscaling involved. If the wave frequency is high enough, then the flow permeability will lose its meaning. This phenomenon is often captured by postulating a generalized Darcy law with a frequency-dependent (so-called dynamic) permeability. Within the viscosity-extended Biot framework, the dynamic permeability can be modelled as conversion scattering process from the Biot slow compressional wave into the slow shear wave. The latter accounts for viscous dissipation through vorticity diffusion in the fluid phase. This stochastic dynamic permeability model accounts for pore-scale heterogeneity through the two-point correlation function. Using digitized images of a limestone sample, we extract the correlation function and predict the dynamic permeability.

The initial boundary value problem of wave propagation in a half-plane filled with a fluid-saturated porous solid is considered. The Biot medium is isotropic, homogeneous, and with open pores on the boundary. Using complex analysis techniques, explicit formulas for the components of displacement vectors in elastic and fluid phases are obtained.

Biot theory has predicted a second P-wave that can propagate in a fluid-saturated porous material. This wave can be regarded as a propagating wave predominantly through the fluid saturating the medium. For this wave, the fluid moves opposite to the solid and is highly attenuated. Consequently, it is hard to detect and has only been observed in laboratory experiments so far. Several boundary conditions for the reflection and transmission of plane waves at plane interfaces separating media involving porous rocks have been proposed since the Biot theory was introduced in the 1950's. However, there is a controversy on which set of boundary conditions should be employed for such media. Only experimental tests can warrant a definitive answer to this controversy. In this contribution, forward numerical models for the reflection-transmission in porous media will be presented at both high and low frequencies. These models are based on wave propagation using Biot theory and various sets of boundary conditions. Converted waves from and to a slow P-wave mode will be given particular attention. Models, obtained at an interface between a water-saturated porous rock and water using the open boundary conditions, show converted slow P-waves with moderate amplitudes. However, models derived from boundary conditions that restrict relative fluid movement with respect to the solid, such as those used in the case of a porous-solid interface, lead to weak, converted, slow P-waves. This confirms that the slow P-wave is predominantly a flow process. However, recent reflectivity experiments from a porous-solid interface exhibit converted slow P-waves with significant amplitudes that cannot be explained by the closed boundary conditions. The modeling also shows that the slow P-wave can convert to both a fast P-wave and to an S-wave (or vice versa) with relatively significant amount of energy when the relative fluid-solid motion is not restricted at the interface.

The Biot theory of seismic wave propagation is formulated in terms of two displacement vector fields. These are the displacement fields for the average motions of the solid phase and the fluid phase. In this theory, every representative volume element, i.e. a material point, is ascribed with two constituent mass densities and has six translational degrees of freedom. Clearly, such a framework is incompatible with any wave field recording where only three independent components of a vector field can be ascribed to and measured at a given location. By defining the material point to be the center-of-mass of the constituting solid and fluid masses, this unconformity can be reconciled. The motion of this material point is determined by the vector center of the constituting masses, which we refer to as the center-of-mass or mean field. Realizing that the dynamics of the constituting masses is like a two-body problem, to this material point, the field associated with the relative acceleration between the phases is ascribed as the other field. We refer to it as the internal rotational field, or simply the internal field. It is taken as a weighted relative motion between the two phases, where the dimensionless weighting factor is the product of the reduced mass density of the poro-continuum with the difference of the reciprocal of the densities of the two phases. The mean field and the internal field are taken as the fundamental vector fields. We find that the total mass of the poro-continuum is conserved with the mean field. The total linear momentum is expressed completely in terms of the mean field. Thus, it is the mean field that is associated with three translational degrees of freedom of the material point. Geophones and seismometers are total linear momentum measuring devices thereby tracking the mean field. Therefore, recorded seismic data correspond to the mean field. The internal field is linked to the angular momentum about the center-of-mass (spin) and the rotational kinetic energy of the material point; hence, it represents the three rotational degrees of freedom of the material point. A simple linear transformation recasts the Biot equations of motion in terms of the mean and internal fields. These are be the appropriate equations of motion for wave propagation problems.

Sandy sediments have been shown to follow the Biot model with extensions to account for the squirt flow at the grain contacts. While the frequency dependence of acoustic attenuation in well sorted sands and glass beads in laboratory conditions has been shown to follow the Biot model, it is much more variable in poorly sorted sands and silts, and sediments that are found in-situ. Yamamoto and Turgut have shown that the pore size distribution can have a profound effect on the frequency dependence of the attenuation. The Yamamoto and Turgut model was combined with the Revil, Glover, Pezard and Zamora (RGPZ) model of permeability to produce a new variant of the Biot model that could be adjusted to fit a wide variety of sediment types. By adjusting the width of the pore size distribution, it is possible to smoothly change the frequency dependence of the attenuation. This suggests that pore size distribution may be a critical parameter in the determination of sound attenuation in the seabed, and in the classification of sediment types. Model predictions are compared to measurements from the Shallow Water 2006 experiment as an illustration.

The volume changes of grains (solids) are usually neglected in numerical geomechanical simulations of production from - or injection into - reservoir rocks, assuming that all rock volume changes translate into porosity changes. When grain compressibility is taken into account, it is usually done by modifying the pore pressure changes with the so-called Biot factor (α). Rock failure criteria, like fracturing or pore collapse, are fully dependent on (Terzaghi's) effective stress and not on total stress or Biot-modified effective stress. This pore pressure modification provides a wrong estimation of plasticity and fracturing and, hence, is not suitable for these types of analyses. In this paper we propose a different method for incorporating grain compressibility in Finite Element modelling. The effect of stress, pressure and temperature changes on the volume of the grains can be calculated separately and translated into a total volume change and a pore volume change. These effects can be incorporated into the constitutive model of plasticity, which uses standard effective stresses for plastic behaviour. The mismatch of elastic volume changes between total stress and pore pressure changes is corrected for by a volume strain loading that is equal to pore pressure change (Δp) divided by the Grain Bulk Modulus (K_g). For linear elasticity, the equations reduce to poro-elasticity. This volumetric strain can be directly calculated when the fluid pressure change is known or for undrained materials. The pore volume changes are also computed since they are relevant for undrained behaviour and for the amount of expelled fluids in the drained situation, which is an input for Reservoir Engineering (fluid flow) computations. This method has been incorporated in Shell's propriety FEM application GEOMEC, based on TNO-Diana FEM. In this paper, we explain the method above fully, starting from poro-elasticity theory.

We investigate the effect of spatially varying density and degree of saturation on the triggering of a persistent shear band in unsaturated porous materials. Recent papers (Borja et al. 2013a, 2013b) have shown that these two types of heterogeneity can have first-order effects on the ensuing shear band. Advances in non-invasive testing have now allowed accurate measurement and quantification of density and degree of saturation variations in granular materials; hence, these two types of heterogeneity can now be input deterministically into a hydromechanical model for more realistic modeling and simulation. We show a representative numerical simulation illustrating the triggering of a persistent shear band in soils with spatially varying density and degree of saturation.

A theoretical framework for modeling the chemo-mechanical behavior of porous media with multiphase and multispecies is developed. The new theory addresses coupled processes (such as skeletal deformation, fluid flow, heat conduction, diffusion, chemical reaction, and phase transition) in a consistent and systematic manner. Central to the theory is a general expression for the chemical potential of a species, based on which the colligative properties of porous media are discussed, including osmotic phenomenon, Donnan effect, Kelvin effect, supercooling and superheating. In particular, the components of pore pressure are identified and formulated, and the concept of effective stress is discussed. It is found that whenever electro-chemical effect comes into play, the total pore pressure cannot be directly measured via a traditional transducer.

Under the center of a wide embankment, the ratio and orientation of principal stresses are relatively constant as the embankment grows, while under the side slopes where loading is non-uniform, horizontal stresses increase. This study examines variations in vertical preconsolidation pressure (P_c,v) in overconsolidated clay under a large embankment 20 years after its construction. Although stresses in the clay from loading were less than P_c,v in the undisturbed formation, clay under side slopes showed an increase in P_c,v up to 162% greater than the applied vertical loading. These variations were positively related to the angle of Principal Stress Rotation (PSR) and the ratio of vertical to horizontal normal stress. This implies that by taking advantage of PSR, P_c,v of a soil could be increased to a greater degree; or, with less effort, using non-uniform preloading than by spatially monotonic loading.

Taking threshold gradient and variation of permeability coefficient with void ratio into account, a 1-D finite strain consolidation equation for saturated soils can be derived in reduced coordinate. Using the two empirical relations proposed by Mesri, a new governing equation is obtained. On the basis of test data for Ningbo soft clay, an example is analyzed by applying finite element method. The results show that excess pore water pressure at different depths slightly increases at the beginning of consolidation progress and then dissipates gradually after reaching the maximum. This phenomenon is similar to Mandel-Cryer effect. It will be more significant if threshold gradient is greater or location of soil is deeper. It is worth noting that the increment of excess pore water pressure is too tiny to observe in laboratory experiments and engineering practices. Therefore, there is no need to consider threshold gradient in majority of actual projects. In other words, classical Darcy's law is applicable. Our research shows that it is important to consider threshold gradient, geometric nonlinearity and material nonlinearity in the study of Mandel-Cryer effect.

During compaction band formation various mechanisms can be involved at different scales. Mechanical and chemical degradation of the grain skeleton and grain crushing are important factors that may trigger instabilities in the form of compaction bands. Compaction bands can be seen as an instability of the underneath mathematical problem leading to localization of deformation. Here we explore the conditions of compaction banding in quartz-based geomaterials by considering the effect of chemical dissolution. As the stresses/deformations evolve the grains of the geomaterial break into smaller ones. As a result, the total available surface of the grains is increased, their dissolution is accelerated and chemical softening is triggered. By accounting for (a) the mass diffusion of the system, (b) a macroscopic failure criterion with dissolution softening and (c) the reaction kinetics at the micro level, a model is proposed and the conditions for compaction instabilities are investigated.

The characterization of time-dependent brittle rock deformation is fundamental to understanding the long-term evolution and dynamics of the crust. Here we report results from a study of brittle creep in Darley Dale sandstone under triaxial stress conditions. We present new results from a series of constant strain rate experiments and conventional brittle creep experiments. We then apply a micromechanical model for brittle creep in rocks to our experimental data. This model shows that the acceleration of the strain rate observed experimentally prior to failure is due to the increasing importance of crack interactions. Finally, if we compare long-term creep failure under a constant stress with short-term failure under an imposed constant strain rate, we find a mechanical work deficit. The magnitude of the deficit in the mechanical work rate is by definition a stress deficit. Our analysis implies that rock deformation under both constant stress (creep) and constant strain rate conditions are controlled by the same underlying chemo-mechanical processes.

Fluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope failure, and large earthquakes. Terzaghi's principle of effective stress predicts that liquefaction occurs when the pore pressure within the layer becomes equal to the applied normal stress on the layer. However, under dynamic loading and when the internal permeability is relatively small the pore pressure is spatially heterogeneous and it is not clear what measurement of pore pressure should be used in Terzaghi's principle. Here, we show theoretically and demonstrate using numerical simulations a general criterion for liquefaction that applies also for the cases in which the pore pressure is spatially heterogeneous. The general criterion demands that the average pore pressure along a continuous surface within the fluid-saturated granular or porous layer is equal to the applied normal stress.

A comparison of the original elastic solution for the center of dilation with the classic Lamé solution reveals an unexpected dependence of the center of dilation solution on Poisson's ratio. This inconsistency is investigated by means of two alternative representations of the singularity which lead to the identification of a compressed zone inside the singularity. The poroelastic equivalent to this nucleus of strain is shown to be the superposition of the elastic one with drained material parameters and an instantaneous point fluid source associated with a finite volume of fluid that is expelled from the compressed region inside the singularity and is injected in the porous medium.

This study analyses the tip region of a fluid-driven fracture in a permeable poroelastic medium, by considering the stationary problem of a steadily moving semi-infinite hydraulic crack. The model accounts for the existence of a tip cavity filled with pore fluid sucked from the porous medium and the build-up of a low-permeability cake on the walls of the fracture associated with leak-off of the fracturing fluid. The paper summarizes the general solution of the stationary problem, as well as the near- and far-field asymptotes.

Compaction of porous rock is an important process in the oil and gas industry, as well as for CO₂ storage. Mechanical compaction may occur because production or injection changes the pore pressure. The effective pressure, defined by the relation of Terzaghi as the difference between the mean pressure and the pore pressure, is the key parameter. In the field, mechanical compaction can lead to seafloor subsidence (for example, the extraction of oil and gas in the Ekofisk field in the North Sea has produced a subsidence of more than 4 meters), cause casing failures, or can decrease significantly the permeability of the reservoir.

Consistent approach for description of multiple-phase media can be formulated on the basis of the generalized variational principle for dissipative continuum mechanics. An important element of this approach is a physical mean of variables in which terms the theory is formulated. The consistent statement has to be formulated in terms of variables dealt with integrals of motion of material points, representing a continuum. The various definitions of mean velocities of phases are available for multiple-phase media in dependence on interpretation of temperature. [The correct account of this circumstance allows to overcome contradictions of the Biot's theory dealt with non-additive forms of kinetic and potential energies and to evaluate simultaneously some coefficients which should be determined experimentally in the framework of the original Biot's theory.] As illustration of the new approach, the simplest double-phase media (such as suspension and rod structures filled by fluid) are considered by uniform way in the report.

We employ laws of poro-elasticity (Modified Cam Clay) to predict the stresses and pore pressures around inclined hydrocarbon reservoirs (e.g., dipping structures). We show that, at the crest, the localized flow field increases the horizontal and vertical stresses above the lithostatic value. Therefore, very high least principal stresses, even greater than the overburden value, are possible around the shallower end of dipping structures. At the deeper end of such structures, the local flow field loads the surrounding sediments, leading to elastoplastic strains and notable increase in porosity. We show that both the vertical and the horizontal total stresses decrease locally near the base. Traditional basin modeling approaches assume a horizontal-to-vertical stress ratio, so they cannot fully capture the stress changes around dipping structures. We illustrate that poromechanical analyses are essential to predict changes in pore pressure and the associated stress changes, especially in the vertical direction. The poromechanical results can significantly increase confidence in the trap integrity of inclined hydrocarbon reservoirs and provide a more reliable evaluation of borehole stability.

In this article, we present a numerical method to model the propagation of a fluid-driven fracture in a poroelastic medium in the finite element framework. We developed a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model. The fluid flow within the crack is described by the lubrication equation and the fluid pressure in the fracture acts as an hydraulic and mechanical boundary condition on the lips of the crack. The bi-dimensional pressure diffusion equation and the equilibrium equation in the surrounding porous medium are fully solved numerically. We compare the results of our numerical model with asymptotic analytical solutions. Our numerical model captures very well the analytical solutions in all the asymptotic propagation regimes. In addition, our zero-thickness element method gives access to a finer description of the fluid diffusion in the porous medium and of its coupled mechanical response.

The coupled mechanics of fluid-filled granular media controls the behavior of many natural systems such as saturated soils, fault gouge, and landslides. The grain motion and the fluid pressure influence each other: It is well established that when the fluid pressure rises, the shear resistance of fluid-filled granular systems decreases. As a result, catastrophic events such as soil liquefaction, earthquakes, and accelerating landslides may be triggered. Alternatively, when the pore pressure drops, the shear resistance of these systems increases. Despite the great importance of the coupled mechanics of grains-fluid systems, the basic physics that controls this coupling is far from understood. We developed a new multi-scaled model based on the discrete element method, coupled with a continuum model of fluid pressure, to explore this dynamical system. The model was shown recently to capture essential feedbacks between porosity changes arising from rearrangement of grains, and local pressure variations due to changing pore configurations. We report here new results from numerical experiments of a continuously shearing layer of circular two-dimensional grains, trapped between two parallel rough boundaries. The experiments use a fixed confining stress on the boundary walls, and a constant velocity applied to one of the boundaries, as if this system was the interior of a sliding geological fault filled with 'fault gouge'. In addition, we control the layer permeability and the drainage boundary conditions. This paper presents modeling results showing that the localization of shear (into a narrow shear band within the shearing layer) is strongly affected by the presence of fluids. While in dry granular layers there is no preferred position for the onset of localization, drained systems tend to localize shear on their boundary. We propose a scaling argument to describe the pressure deviations in a shear band, and use that to predict the allowable positions of shear localizations as a function of the fault and gouge properties.

The unjacketed bulk modulus of sandstone, K_s', is often considered to be equal to the bulk modulus of quartz, the main mineral which forms it. However, preliminary tests and some other works show that for Berea sandstone this assumption might be violated. Three different types of laboratory experiments were performed on the rock to measure K_s' and Biot's coefficient α: unjacketed plane strain compression, drained compression with water collection, and jacketed/unjacketed hydrostatic compression. The values of these parameters are reported at 5 MPa mean Terzaghi effective stress; α is found to be in the range of 0.64 - 0.74 and K_s' = 27.2 - 30.9 GPa. The latter value is significantly smaller than the measured bulk modulus of quartz, K_quartz = 37.0 GPa. It can be explained by the presence of clays or the existence of non-connected pore space in the rock.

Analytic solutions for consolidation problems are often derived using displacement functions. For plane strain and torsion-free axisymmetric consolidation problems, the most successful displacement functions appear to be the ones proposed by McNamee and Gibson. Their original expressions were derived for consolidating media with incompressible constituents, and were later generalised by Verruijt to account for material compressibility. This paper presents a new derivation of the generalised solution of McNamee and Gibson, using techniques of the classical theory of elasticity. The advantage of this derivation is that at the same time it proves the completeness of the solution.

Slow slip and tremor in subduction zones take place where there is abundant evidence for elevated, near lithostatic pore pressures along the plate interface. In Japan and Cascadia, these depths (~30-45 km) are such that the main source of fluids must be attributed to chemical dehydration reactions. Here, we model the condsolidation of low porosity (~5%) oceanic crust subducting through the slow slip and tremor zone in the presence of pressure and temperature-dependent dehydration reactions. We use parameters consistent with the geometry of the Cascadia subduction margin and bulk rock permeabilities in the range 10^-25 ≤ k₀ ≤ 10^-21 m². The generation of pore pressures in excess of lithostatic values, and hence negative effective stresses, is a robust feature of our simulations. These results indicate that hydraulic fracturing likely occurs at relevant depths, and have implications for the generation mechanism of non-volcanic tremor in subduction zones.

This paper presents a hypothesis of compressed methane gas expansion and migration in crustal rocks and faults for the cause of earthquakes. An earth quaking is an adiabatic process of kinetic interaction between rapid upward expansion and migration of compressed natural gas and its surrounding crustal rocks and ground soils. The natural gas is produced in core and/or mantle. It is escaped from its traps in deep fault zones of the lower crustal rocks. The interaction is instantaneous and flashing. It can be complete within few to tens and to hundreds seconds. The gas expansion and migration are confined and constrained by the inward gravity, the tectonic stresses, and the rigidness and strengths of the crustal rocks. The kinetic energy of earth quaking is mainly the physical expansion energy of the highly compressed methane gas. The gas expansion work causing the 2008 Wenchuan Earthquake and the 2011 Off the Pacific Coast of Tohoku Earthquake are estimated.

Procedures to couple reservoir and geomechanical models are reviewed. The focus is on immiscible, compressible, non-compositional reservoir - geomechanical models. Such models require the solution to: coupled stress, pressure, saturation and temperature equations. Although the couplings between saturation and temperature with stress and fluid pressure are "weak" and can be adequately captured thru staggered (fixed point) iterations, the coupling between stress and pressure equations are "strong" and require special procedures for accurate integration. Issues related to both simultaneous integration and sequential integration of pressure and stress equations are investigated. It is shown that simultaneous integration can be achieved by computing the contribution to the coupled Jacobian matrix through finite differencing of the residual equations. Forming the Jacobian matrix can also be avoided thru a partitioned CG iterative solution procedure of the Schur complement matrix. Iterative sequential integration (fixed point iterations) of pressure and stress equations are then discussed, and detailed algorithms are provided. Assessment of the accuracy of such iterative procedures is made through comparison with available exact analytical solutions for the half-space consolidation (McName and Gibson [1960]). The iterative sequential procedure (one-way coupling iteration) is shown to require an unreasonably large number of iterations (>50) to capture accurately coupling effects. Finally, the coupling effects in a field case are investigated: CO2 injection at In Salah, Algeria where CO2 is injected at a temperature (50 dgC) below the resident brine reservoir (90 dgC) temperature. Surface uplift displacements and induced tensile stresses in the caprock computed with both a fully two-way coupled scheme versus a one-way scheme are compared.

Liquefaction instabilities have been studied extensively for the last five decades. Since then, a number of models to predict the onset and the evolution of liquefaction have been proposed. Also, recently, some theoretical criteria have been proposed and used to predict the onset of static and dynamic liquefaction, based on plasticity theory and the concept of diffuse instabilities. However useful these criteria might be, they only predict liquefaction as a macroscopic phenomenon and cannot explain why it happens from micromechanical processes. The objective of this work is to take a first step into opening the hood behind the macroscopic process of liquefaction instability, by looking at the corresponding underlying micromechanical processes. In this way, we will unravel the micromechanical origin of liquefaction. To do this, we use continuum elastoplasticity at the macro scale and discrete element methods at the granular scale to simulate particle mechanics under undrained conditions. We hope this work will shed further insight into the origin of instabilities in general and would result in more predictive physics-based models in the near future.

A novel model about mechanic and chemo-poroelastic (osmosis) coupling of fluids and solutes in fluid-saturated porous media is here presented. This model is focused on non linear phenomena and does not apply the Osanger symmetry. Analyzing the action of a strong external stress, we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutant) concentration. Their solutions in clay or shales unveil an unexpected presence of quick, non-linear, strong transients of coupled pressure and solute, known in physics as Burger solitons. The presence of solitons may shed new light on flow processes, as about the origin of large hyperpressures. We also tested our model for sandstones assuming that a small, or very small, osmotic behavior could be there present. We found that Burgers solitons can be present in sandstones or other higher permeability rocks, as some Calabria rocks.

An exact steady-state closed-form solution is presented for coupled axisymmetric flow and deformation of an isotropic homogeneous saturated poroelastic layer with a finite radius due to a point sink. The flow-deformation coupling process is governed by Biot's consolidation theory. Boundary conditions of the side surface were specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of partial differential equations. Ordinary differential equations in the transformed domain were solved, and then the analytical solutions in the physical space for displacements and pore fluid pressure were finally obtained by finite Hankel inversions. Moreover, the long-term subsidence and radial displacement of the upper surface were given. The proposed analytical solution is highly applicable to testing the accuracy of axisymmetric poroelasticity related numerical schemes, and can also be of great use to further investigate the behaviour of flow and deformation coupling within finite axisymmetric porous materials.

An analytical solution was derived for Biot's consolidation within a finite rectangular poroelastic media due to a uniform normal loading. Appropriate Fourier and Laplace transforms and the corresponding inversions were implemented to obtain the exact solution. In particular, the boundary conditions for the displacements field were chosen with care to match the above integral transforms and inversions. The presented solution is in terms of summations of infinite series and very simple in its form. The presented analytical solution can be used to calibrate numerical algorithms for two-dimensional poroelasticity. Besides, it can provide us in-depth insights into flow and deformation coupling due to surface loading in finite two-dimensional porous materials.

This study presents prelimenary results of modelling of hydraulic fractures growth. The hydro-fractures are modelled by 2D cracks in elastic plane. The problem is reduced to a system of singular integral equations. The latter is solved by the standard method of mechanical quadratures. The analysis of fracture characteristics for different initial crack configurations has been performed in order to simulate possible hydro-fracture trajectories. It is shown that peripheral cracks penetrating into the rockmass tend to divert from the vertical direction, which is due to the interaction with the other cracks.

Adopting the linear comparison composite (LCC) method within the framework of yield design theory [1], this paper presents a novel multi-scale strength homogenization procedure for a three-phase, partially-frozen soil composite where the solid particle phase (S) and the crystal ice phase (C) are assumed to be characterized by two different Drucker-Prager strength criteria and the liquid water phase (L) has zero shear strength capacity. Based upon a multi-scale thought model shown in Fig. 1, the macroscopic strength criterion for partially frozen soil can be upscaled through a two-step homogenization process. For each step, the LCC methodology is implemented by estimating the strength criterion of a two-phase nonlinear matrix-inclusion composite in terms of an optimally chosen linear thermo-elastic comparison composite with a similar underlying microstructure. In addition, the pressure melting of ice is considered in this model by incorporating a temperature and pressure dependent phase transition between ice and water. The predicted macroscopic strength criterion for partially frozen soil shows qualitatively a good agreement with observed phenomena, such as strengthening of soil during freezing and weakening of soil during pressure melting.

Soils consist of a porous soil skeleton filled by fluids like air and water. The accurate description of their mechanical behaviour requires a coupled solid-fluid approach. The analysis is based on a set of balance equations for mass and momentum, kinematic equations and constitutive equations, the latter including a material model for partially saturated soils. In this contribution we present a constitutive model for partially saturated soils developed as an extension of the cap model proposed by Kohler and Hofstetter (2008). The elasto-plastic model is formulated in terms of two independent stress variables, generalised effective stress σ*_ij and matric suction p^c. The yield surface includes a shear failure and a hardening cap surface. The evolution of the yield surface in terms of matric suction is controlled by the load collapse (LC) yield curve and parameters defining the suction-dependent intersection of the shear failure envelope with the I*₁-p^c-plane, where I*₁ = tr(σ*_ij). We introduce an improved LC yield curve to enable a better representation of wetting/drying paths and to allow a smooth transition from partially to fully saturated state. An efficient and reliable projection algorithm is proposed for determining the stresses and internal variable at the integration point level. It includes the solution of separate scalar nonlinear equations for the hardening cap and the shear failure surface. Numerical results for a silty sand are in good agreement with experimental data.

Cracking behavior of concrete caused by early age drying shrinkage is simulated based on a multi-scale computational system. The original analysis indicates that the deformation of a restrained concrete cannot be well simulated, and micro-crack status at surface is greatly overestimated. Therefore, a local tensile strength model treating micro-pore water pressure as prestress is proposed and applied to the cracking criterion. Furthermore, the influences of nonlinear creep and water diffusion speed on cracking are discussed by means of sensitivity analysis. With the optimized coefficients related to the above influences, finally cracking process of restrained concrete can be reasonably simulated.

We present a novel formulation of the data structure needed for finite elements (FE) in a data model based on the mathematics of fiber bundles. This formulation allows integrating of FE data into a context of generic data processing operations, in particular tools for multivariate data visualization. Our approach is showcased using a real-world application dataset describing drying concrete. Total stress, displacement, mean stress and drying shrinkage strain are illustrated, combining direct visualization methods for scalar-, vector- and tensor fields. Eventually this approach allows for new insights into these rather complex and otherwise opaque FE datasets and supports optimizing the underlying simulations code.

Cementitious materials are aging materials which transform from a fluid-like state to a solid. These changes are brought about by the hydration reaction between cement and water, which results in a continuous evolution of the microstructure of the material. There is a continuous decrease in the porosity and an increase in elastic stiffness of the matrix with time. Determination of the changes in the microstructure of hydrating cement through setting, and early strength gain of the material have remained major experimental challenges. Methods used for studying cement microstructure either alter the microstructure during sample preparation or sample preparation time exceeds the time associated with changes in microstructure. An ultrasonic test procedure for continuously monitoring changes in hydrating cementitious materials through setting using horizontally polarized shear waves (SH) is presented. A theoretical framework based on the poro-elastic idealization of the hydrating cement paste is developed for interpreting the ultrasonic reflection data. The wave response obtained from the poroelastic two-phase idealization of hydrating mortar as a water-filled solid matrix is shown to provide a realistic interpretation of the experimental response. The observed changes in the ultrasonic signal are shown to be related to changes in the porosity and the elastic modulus of the skeleton within the aging material.

The work discusses the approaches to the determination of the effective modules of multiphase composite materials with the coupling of physico-mechanical fields based on the effective moduli method for the mechanics of composites, modeling of the representative volumes with account for microstructure and the finite element technologies for solving the problems for the representative volumes. In order to provide an example, the models of porous elastic media that represent interest for some problems of bio and geomechanics are considered.

The paper proposes a numerical model for predicting moisture and temperature evolution in concrete at early age along with the accompanying shrinkage. In particular, the model includes an approach for simulating the evolution of the porosity. It is suggested that the introduction of a porosity development model, which is linked to the moisture mass-balance equation, is important because if the porosity development is described independently of the moisture mass balance then inconsistent results can arise. An algorithm for computing autogenous shrinkage is presented and the performance of the model is assessed by considering its ability to reproduce the behaviour of a standard code equation as well as some data from a recent experimental investigation. The comparisons show good matches in both cases.

Breathing transitions represent recently discovered adsorption-induced structural transformations between large-pore and narrow-pore conformations in bistable metal-organic frameworks, such as MIL-53. We present a multiscale physical mechanism of the dynamics of breathing transitions. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the crystal level occur via layer-by-layer shear.

In this work, I review how pressure effects in pores affect both the physics of the confined fluid and the properties of the host porous material. I first report some molecular simulations in which high pressure effects have been observed. We will see how the strong pressure dependence of the freezing temperature of a fluid confined in nanopores can be explained by important variations of the mechanical pressure within the pore. I will also show practical applications of these pressures effects where gas adsorption in microporous solids (pore size < 2 nm) allows enhancing their mechanical properties by increasing by a factor 4 the elastic modulus.

Metal Organic Frameworks (MOFs) are porous materials made of inorganic clusters coordinated by organic linkers. These materials are mainly used as adsorbents for either gas or liquid separation. Some of them show spectacular changes of structure that may be evidenced by mechanical stress. We developed an experimental device which was placed in a microcalorimeter allowing both the measurement of heat and work during compression/decompression cycles of the material in the presence of a suited liquid. A clear step in the volume/pressure curve can be interpreted as the large pore-to-narrow pore transition of MIL-53 (Al) under the effect of pressure. The pressure induces a reversible transition with hysteresis. The internal energy balance can be calculated from the mechanical work and the heat involved. This constitutes the first direct measurement of the energy associated with the transition. This particular property of MOFs could be also used to store mechanical energy

CO₂ injection in coal can modify the petro-physical properties. Indeed, the coal matrix swelling reduces the porosity and the permeability of coal on the one hand. On the other hand, the increase in gas pressure induces the decrease in the effective stresses and, therefore, the increase in the spacing between the matrix blocks. We used a theoretical model for the variation of the Eulerian porosity which takes into account the adsorption process. This process is classically modeled with the Langmuir's isotherm. After implementation in Code_Aster (EDF), we investigated through numerical simulations (1D and 2D axisymmetric) the influence of the Biot's coefficient and the Langmuir's adsorption parameters during CO₂ injection in coal. These simulations showed that the increase in Langmuir's parameters, as well as the increase in the Biot's coefficient, promotes the reduction of the porosity when the gas pressure increases.

Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids fully or partially saturated with a fluid phase. When dealing with fully saturated nanoporous materials, which exhibit pores of the nanometer size, effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid, the so-called "swelling" phenomenon. The present work investigates how the poromechanical theory may be refined in order to describe such adsorption and confinement induced effects in nanoporous solids. The new formulation introduces an effective pore pressure, defined as a thermodynamic variable at the representative volume element scale (mesoscale), which is related to the overall mechanical work of the confined fluid. Accounting for the thermodynamic equilibrium of the system, we demonstrate that the effective pore pressure depends on measurable variables, such as the bulk fluid pressure, the temperature and the total and excess adsorbed mass of fluid. As an illustrating example, we compute the strains in the case of the methane and carbon dioxide sorption-induced swelling of an activated carbon. The fits provide a good agreement with material parameters (apparent and matrix compression moduli, porosity) available in the literature, with a close agreement with experimental data.

Recent experimental work has shown that coal and shale material subjected to a change in differential or hydrostatic effective stress can deform in a time-dependent manner. Final strains are partly irrecoverable, but may be recoverable in the case where fluids are used. The latter strains appear to be strongly dependent on the type of fluid used. One possible explanation for this may lie in the fact that coal and shale layers interact with reservoir fluids (e.g. H₂O, CO₂ or CH₄) via stress-dependent adsorption reactions that operate at the micro- and mesopore scale. In this contribution, we consider the time-dependent aspects of this behavior and, hence, the impact on long-term reservoir performance. We propose a theoretical/thermodynamic model that explains how changes in stress state affect adsorption and can lead to deformation in a direct, but time-dependent manner. Identifying relevant fluid-rock interaction mechanisms at the micro- and mesopore scale, and the manner in which these are expressed as a function of time will, foremost, contribute to understanding the long-term in-situ mechanical behavior of coal and gas shale reservoirs. In particular, it may be crucial for solving the problems encountered during hydraulic fracturing of (adsorbing) clay- and organic matter-rich horizons.

The use of low field Nuclear Magnetic Resonance (NMR) to determine petrophysical properties of reservoirs has proved to be a good technique. Together with sonic and electrical resistivity measurements, NMR can contribute to illustrate the changes on chalk elasticity due to different pore water composition. In this study we relate NMR data to changes in P-wave velocity and electrical resistivity. Core plugs from outcrop Stevns chalk, of 44% porosity, were divided into groups of three and saturated with deionized water, calcite equilibrated water, as well as sodium chloride and magnesium chloride solutions of the same ionic strength. Saturation with a solution that contained divalent ions caused a major shift on the distribution of the relaxation time. The changes were probably due to precipitates forming extra internal surface in the sample. Sonic velocities were relatively low in the MgCl₂ solution saturated plugs.

In this work, using molecular dynamics simulations, we have explored the swelling/shrinkage of a simple slit nano-pore immerged in a Lennard-Jones liquid reservoir induced by shear. It is shown that the pore can swell or shrink when the solid walls are displaced in a direction parallel to the fluid-solid interface. This is due to the fact that the normal pressure of the confined fluid appreciably varies with the relative structural ordering between the solid (crystalline) surfaces for a given pore size. Thus, when the solid walls are moved at a constant velocity, the instantaneous pore size oscillates with time and yields, on average, a shear-induced swelling/shrinkage.

Freezing and melting of water in the cylindrical pores of ordered mesoporous silica was studied by differential scanning calorimetry. For MCM-41 silica materials well-resolved melting and freezing peaks were obtained for pore diameters down to 3.0 nm, but not in 2.5 nm pores. The enthalpy of melting and the hysteresis connected with the phase transition in the pores both vanish at a pore diameter D* @ 2.8 nm, indicating that D* represents a lower limit for first-order freezing/melting of water in the pores. A more complex freezing behavior was observed in partially filled pores of SBA-15 materials (pore diameters 6 to 11 nm), where the adsorbed water film under-goes a delayering transition at a temperature below the freezing point of pore water. Our work suggests that studies of the sorption and phase behavior of water in the pores contribute to a better understanding of the pore lattice deformations caused by water in the pores.

Microporous materials such as zeolites and amorphous carbons show a characteristic signature in terms of deformation as a result of micropore filling. Here we present analysis of synthetic microporous carbons with different annealing temperatures and consequently different average micropore sizes by gas adsorption combined with in-situ dilatometry. Measurements performed with N₂ (77 K), Ar (77 K), CO₂ (273 K) and H₂O (298 K) all reveal the same general trends with respect to sorption-induced deformation, i.e. contraction of the samples at low micropore filling followed by a phase of monotonic expansion up to complete micropore filling. However, the extent and ranges in relative pressure related to contraction and expansion, respectively, are found to clearly differ for the specific combination of micropore size and analysis gas. Our results indicate that adsorption of different gases and vapors in slit shaped micropores with pore width below 0.9 nm yield a net expansion of the sample while adsorption in micropores with pore width above 0.9 nm results in contraction and expansion of similar extent.

In this work we measure the effect of water on the elastic and swelling properties of thin smectite clay films. The thin films exhibit a well organized structure with parallel clay particles and are about 40 μm thick. We measure the swelling potential of the films by analyzing Environmental Scanning Electron Microscopy pictures. We carry out tensile tests at various relative humidities to evaluate the impact of the water content on the elastic modulus of the films. In particular, the effect of the nature of the counter-ions is investigated. In parallel, we perform molecular dynamics simulations of clay layers with various water contents. At each water content, the thickness of the platelet and its elastic stiffness tensor are computed. We compare those numerical results at the scale of a clay layer with the experimental results at the scale of a clay film and discuss their relevance.

Recently, there were several attempts in the mechanical engineering community to adopt the language of poromechanics to the problems of adsorption-induced deformation in nanoporous solids. However, some important specifics of these phenomena, which are currently well understood in the adsorption community, are lost in this translation. In this paper, I attempt to present a reverse translation starting form the molecular thermodynamics of adsorption coupled with the elasticity theory. This approach aims at a unified description of the various physico-chemical mechanisms of adsorption deformation, which depend on the size of pore confinements and adsorption interactions. These effects are treated on the atomistic level by using molecular simulation tools that are currently standard in adsorption science and calculating the adsorption stress that is coupled with the strain via the linear elasticity ansatz. Our main goal is to derive a rigorous thermodynamic framework for accounting for the above-mentioned deformation mechanisms, which would result in a close system of poromechanical equations for nanostructured solids.

The growth of natural gas recovery from unmineable coal seams has motivated the investigation of the gas adsorption and swelling properties of coal, since those properties play a critical role on the evolution of seam permeability. Indeed, while advective fluid flow occurs through coal fractures at the seam scale, adsorption in nano-sized coal matrix pores induces swelling. Hence, fracture permeability depends on both confining stresses and adsorption. We developed an experimental device to measure the adsorptive-mechanical properties of coal cores, such as the specimen stiffness, the macroscale Biot coefficient, and the tangent Biot coefficient which quantifies adsorption. The device consists in a triaxial cell controlled by electromechanical pumps to manage stresses and CO₂ injection and flow, and permits specimen characterization at in-situ relevant stresses, fluid pressure, and temperature. The device fits specimens 38 mm diameter and slenderness 2:1. We show the results of a preliminary test on naturally fractured coal cores from Forzando mine in South Africa. Together, the experimental characterization and theoretical framework let us understand better the geomechanics of coal seams in views of Coal Bed Methane recovery.

A poromechanical model is presented for estimating swelling of nano-porous media fully saturated with a fluid phase. From the Gibbs adsorption isotherm, the effective pore pressure and the volumetric strain are estimated incrementally taking into account the variations of porosity upon swelling and therefore the variations of the poromechanical properties (apparent modulus, Biot coefficient, Biot modulus). Moreover the interaction between swelling and the adsorption isotherms are examined by proposing a correction to the Gibbs formalism to estimate the truly exceeding adsorbate quantities upon swelling. First comparisons with experimental data found in the literature are performed and a fair agreement is observed.

The anisotropic swelling behavior of cellular solids is investigated with a poromechanics approach. The general expression for the macroscopically observable free swelling strain is derived by upscaling the constitutive equations of a microscopic poroelastic medium. The swelling coefficient is dependent on stiffness, Biot coefficients and Biot modulus. We found that the anisotropy in swelling behavior of honeycomb-like cellular materials with low relative density, which is observed experimentally for earlywood, can be related to the anisotropy of elastic properties at the cell wall level and the geometry of honeycombs. The proposed approach provides a more physically relevant description of swelling behavior which originates from the coupled interaction of fluid and solid within the porous cell walls of cellular materials like wood.

This paper focuses on the origin of the irreversibility of the condensation-evaporation process in mesoporous materials. We report on experimental and theoretical arguments which show that the adsorption-induced strains of the pore walls is a key parameter in the physics of adsorption which could couple the pores during the evaporation process.

Nanoporous silica materials with cylindrical pores of some nanometres in diameter on a highly-ordered hexagonal pore lattice are used as a model system to assess the melting behaviour of water in confinement experimentally. Synchrotron radiation-based small-angle X-ray scattering (SAXS) is used to investigate in-situ the melting of ice in pores of 3.9 nm and 8.9 nm diameter. Besides the well-known melting point depression, the confinement-induced interaction of water with the solid pore walls manifests itself in a temperature-dependent, non-monotonous deformation of the solid host material. This deformation can be monitored as a function of temperature by measuring the pore lattice strain with small-angle X-ray diffraction, allowing to extract nanomechanical properties of the materials. The melting-induced pore lattice deformation is interpreted by a curved phase boundary between the liquid pore water in contact with the solid bulk water phase outside the pores, due to the preferred wetting of the pore walls by the liquid water. Using a simple model based on the generalized Laplace-pressure acting as a negative pressure on the pore walls, the Gibbs-Thomson equation allows a satisfactory description of the experimentally observed strains. Comparison of deduced elastic constants with those obtained from strains induced by capillary condensation for the same samples shows, however, quantitative differences up to 30%. These differences are discussed with respect to possible influencing factors.

All the carbon atoms in single-wall nanocarbons, such as single-walled carbon nanotubes (SWCNT) and single-walled carbon nanohorn (SWCNH), are exposed at the surface, making them quite sensitive to the nanoscale environments. Adsorption of alcohol molecules gives a higher frequency shift of the radial breathing mode (RBM) of the Raman spectrum, which corresponds to a compression effect by several GPa. Encapsulation of methylene blue molecules in the internal tube spaces of SWCNT leads to a higher frequency shift of the RBM peaks. The pentagon and heptagon in the carbon hexagon walls bring about the flexible motion in the SWCNT and SWCNH, which can be detected by surface enhanced Raman scattering (SERS).

The growth rate of salt crystals in stone is slower than would be predicted on the basis of growth rates observed in free solution. To account for this observation, it has been proposed that salt crystals have difficulty changing their growth direction at junctions in the pore network. To test this idea, pore channels were prepared in a hexagonal pattern in PDMS and covered with a glass sheet. The pores were filled with sodium sulfate solution and cooled to create supersaturatio, so that crystals would grow in the channels. It was observed that the crystals jumped between junctions but hesitated for long intervals before passing them. This is consistent with the prediction. However, the pressure of crystallization was localized in the most recently invaded pore, and this is believed to be an artifact related to the deformability of the PDMS. To give a true representation of the growth of salt in stone, the experiments must be performed in a rigid host.

The aim of this study is to estimate the stress induced by salt crystallization in a reservoir rock during an injection of supercritical CO₂ operation. A "pore-scale" model is used to calculate the nucleation and growth of salt crystals within brine solution submitted to a drying out process. The induced crystallization pressure is then estimated through a generalized Correns law. This information is finally imported into a poromechanical model that allows calculating the local strain induced by the crystallization process. The stress state within a representative elementary volume of the host rock is then estimated through the equivalent tensile stress to which the solid matrix of the rock is subjected.

Sodium sulfate is known as one of the most destructive salts leading to the deterioration of porous materials such as monuments, sculptures and civil engineering structures. While sodium sulfate crystals are growing in a porous material, a crystallization pressure will build up. In this study we compare two approaches for determining the crystallization pressure (i.e., a thermodynamic and a poromechanic). The thermodynamic pressure is related to the supersaturation of the crystals growing in a material, whereas the poromechanic pressure is related to the expansion of the material as a reaction to the crystal growth. In this study we have combined the non-destructive measurement of the concentration of the pore solution in a material by using Nuclear Magnetic Resonance (NMR) with an optical measurement of the dilation of the material during crystallization. This gives the possibility to simultaneously determine the crystallization pressure using both approaches. Here we have focused on the crystallization induced by cooling of a saturated fired-clay brick. In the experiments, first heptahydrate is formed which is supersaturated with respect to decahydrate and a transformation to decahydrate has to be induced. It was found that, for fired-clay brick, the thermodynamic crystallization pressure is larger than the poromechanic crystallization pressure. In a final equilibrium condition with no dynamical crystallization and a constant concentration, the thermodynamic and poromechanic crystallization pressure are equal. The highest crystallization pressure for sodium sulfate is obtained just after the transformation from heptahydrate into decahydrate.

We derive expressions relating the physical properties of plate interfaces to the propagation velocity of slow slip earthquakes. This relationship, analogous to the classical Stokes velocity of a rising buoyant sphere, resolves the intermediate velocity enigma and implies that the effective viscosity is low, the permeability is high, and the migration direction of episodic tremor and slip events provides constraints on the mean stress gradients inside active plate boundaries.

This article is a focus on the anisotropic behavior of concrete under Alkali-Silica Reaction. In this article, we assume that the dense aggregates of a loaded concrete are attacked and progressively replaced by a swelling gel. Part of the gel escapes in the cement paste porosity, but a pressure build-up still occurs. The pressure exerted first leads to decohesion between the aggregate and the cement paste, and second to a cracking of the cement paste. Microcracks are computed through an energy minimization algorithm, taking into account the effect of an external loading. The energy used is a modified poromechanics-type energy, taking the external loading and the reaction extent as state variables, which coefficients are determined through closed form solutions adapted from classical Eshelby solution-based micromechanics estimates.

Precipitation of salts in confined space is the key mechanism for rock weathering and damage to building materials. If a repulsive force or disjoining pressure acts between the growing crystal in a pore and the pore wall, a thin layer of aqueous solution remains between crystal and pore wall. Supersaturation of this confined solution is responsible for the crystallization pressure that leads to tensile stresses in the material and eventually to material failure. With an extended surface forces apparatus, we have studied the surface forces acting between two mineral surfaces (mica) across potassium nitrate solution up to concentrations close to bulk saturation. The measured surface forces in the selected model system are related to the disjoining pressure between mineral and crystal surface, which is the upper limit for the crystallization pressure. Besides, these force measurements reveal new insights into in-pore crystallization concerning the properties of the confined solution between the crystal and the pore surface that influence the crystallization pressure.

Deformation that results from crystallization in material pores commonly requires the supply of constituents through a fluid phase. With frost damage, the gradients in chemical potential necessary to drive transport are often caused by gradients in temperature. For submarine hydrates, compositional diffusion of methane is typically aligned with solubility gradients produced by the background temperature and pressure fields. Here, we show that under nearly isothermal and isobaric conditions, changes in the distribution of pore sizes can instead be the dominant cause of the potential gradients responsible for constituent supply. We illustrate the consequences and character of isothermal frost damage using the results from simple laboratory experiments. Field observations of hydrate anomalies in a submarine sand layer motivate comparison with a model for the diffusive growth of such deposits. These simple examples motivate further examination of the role of pore space heterogeneities in the development of other mineral systems.

In this paper we present recent and ongoing results of research on crystallization pressure and the reaction-driven cracking process that can result when hydration, carbonation, and/or oxidation reactions produce large changes in volume, viscosity is high (low temperature) and reaction rates are fast (large chemical potential, catalysts present, etc). Our focus is on natural processes involving reaction of olivine - the primary mineral constituent in the Earth's upper mantle - with surface waters, and on analogue experiments intended to maximize reaction rates at low temperature (up to ~ 300°C) in a laboratory setting. We show that crystallization pressures can reach 100's of MPa, enough to fracture rocks in the upper crust. Studies of natural and laboratory systems show that reaction-driven cracking produces fracture spacing down to 10's or 100's of microns, less than the diffusion distance on time scales of years, sufficient to produce 100% alteration of mantle rocks.

A fast numerical solver to compute effective properties of porous elastic composites is presented. Pores can be treated as a material phase with vanishing stiffness (vacuum) or as a compressible or incompressible material phase (e.g. air, water, oil). For the numerical homogenization (of porous materials), the equations of elasticity are reformulated as volume integral equations of Lippmann-Schwinger type for the local strain. This approach is particularly suited for 3D digital images (CT images) of complex microstructures and needs much less computational effort than finite element schemes to predict the effective properties [1]. As new application of this method we calculate amongst other the pore pressure coefficient for digital rocks. For validation the numerical results are compared with results of finite element schemes and measurements.

A lot of applications, especially in geomechanics, require the computation of waves in porous media, e.g., earthquake waves in soil. Soil and other geomaterials are partial saturated poroelastic materials. Having waves in semi-infinite domains in mind, a boundary element formulation for such materials seems to be preferable. A linear theory for partial saturated poroelasticity is formulated based on the mixture theory, resulting in a set of coupled partial differential equations for the solid displacements and the pore pressures of both fluids. For such a system, fundamental solutions are derived in Laplace domain with the method of Hörmander. The integral equations can be deduced based on the weighted residual technique. A standard discretisation in the spatial variable and the convolution quadrature for time discretisation yield, finally, a time-stepping procedure for dynamic processes in partial saturated poroelastic media. The validation of this method is done with the help of a 1D semi-analytical solution for a column. Finally, waves in a poroelastic half space are studied.

Porous materials are known to be effective in mitigating the impact of shock/blast waves. Nano-structured materials appear to have an even greater potential for such mitigation because of their high surface-to-volume ratio, a property which attenuates shock wave propagation substantially. Molecular dynamics was used to explore the effects of this remarkable characteristic on the behavior of traveling shocks impacting on solid materials with and without a porous structure attached. The materials involved were represented by realistic interaction potentials. Cases with various values of porosity have been investigated and the results indicate that the presence of a nano-porous material layer in front of a target wall reduces the energy deposited inside the solid by about 30 percent, while at the same time considerably decreasing its loading rate.

This paper aims at obtaining an advanced formulation of the time-domain Boundary Element Method (BEM) for two-dimensional dynamic analysis of unsaturated soil. Unlike the usual time-domain BEM the present formulation applies a Convolution Quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of the suction-based mathematical model. In this formulation, the solid skeleton displacements, water pressure and air pressure are presumed to be independent variables. As there is no analytical solution for the 2D wave propagation in unsaturated soils in the literature, to verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is partially verified by comparison with the elastodynamics problem.

The nonlinear compressibility, permeability, and changes in yield stress induced by soil structure and their effect on consolidation behavior of clays is studied using the Gibson-Lo rheological model. Variations in compressibility and permeability of structured clays are captured using bi-linear e-log σ' and e-log k_v models with the break in behavior controlled by the yield stress. The resulting nonlinear governing equation for consolidation is solved using a hybrid combination of analytical and numerical methods. The relative magnitude of the applied stress to the yield stress of clays is found to influence the rate of consolidation as well as the ultimate settlement. In addition, the ratios of the model parameters C_c/C_k, C_e/C_c and C_ke/C_k are shown to have different effects on the consolidation behavior of clays.

In this paper we present an isogeometric approach for calculating fluid flow in a fractured porous medium. The fluid flow away from the crack is modelled using Darcy's relation. A similar relation is assumed for the fluid flow inside the crack. Here, the higher porosity is modelled using a different permeability. An isogeometric analysis approach with B-splines is used for both the parametrisation of the geometry and the discretisation of the weak form of the equilibrium equations. The crack is described in a discrete manner by using the continuity reduction property of the B-splines. To ease the integration into existing finite element technology, a finite element data structure based on B'ezier extraction is used. The B'ezier extraction operator decomposes the B-spline based elements to B'ezier elements which bear a close resemblance to Lagrange elements. The global smoothness of B-splines is localized to an element level similar to finite element analysis, making isogeometric analysis compatible with existing finite element codes while still exploiting the excellent properties of the spline basis functions. The results of the new model are demonstrated in an example in which the fluid flow is considered around a crack in a specimen under mode-I loading.

The use of poroelastic materials on the surfaces under flows-part of the Collaborative Research SFB 880, "Fundamentals of high-lift for future commercial aircrafts"- is investigated. Besides the positive influence that porous surfaces have on aeroacoustics, a poroelastic layer may also help reduce the impact sound. An approach to model the interface between a flow and a poroelastic material, which tracks the propagation of flow-induced structure-borne sound into the poroelastic medium, is illustrated. Firstly, the overall simulation approach and the selected material model is presented, followed by an explanation of the coupling conditions for the interface between the fluid and the poroelastic material. To illustrate the plausibility of this coupling, flow-induced structure-borne sound entry into an airfoil-like structure, layered with a porous material, is examined. The analysis is carried out on a finite element method-based in-house code.

There are many applications involving geomaterials where not only the coupling of pore fluid flow and solid skeleton deformation in the bulk porous geomaterial is important, but the additional coupling of fluid flow and deformation in cracks, joints, or interfaces is equally or more important. A short list of examples includes: (1) rock joints with higher permeability than the surrounding rock mass, encountered during large concrete arch dam construction and performance; (2) cracks in rocks generated during oil and natural gas exploration; (3) cracks in rocks generated or encountered during geologic carbon sequestration; (4) base cracks propagated between concrete gravity dams and porous foundation rock; (5) energy concrete pile foundations interfacing soil under thermal cycling and partially saturated conditions; and (6) cracks and fragments in overconsolidated clay soils generated during buried explosive loading. In some of these examples, the interface between dissimilar materials (e.g., concrete and rock, or concrete and soil) make the application of cohesive surface elements particularly meaningful, as opposed to embedded discontinuity formulations [Armero and Callari, 1999] which are deficient in this regard. Previous research has been conducted on determining the proper formulation and finite element implementation of poromechanical cohesive surface elements (CSEs) [Segura and Carol, 2004, Segura and Carol, 2007a] (this list is by no means complete). We extend this approach to what we believe is a more general continuum strong discontinuity formulation, that allows an extension to include thermal effects and partially saturated conditions more seamlessly, when starting with the continuum coupled physics equations (e.g., thermo-poro-mechanics of partially saturated soil or rock). The formulation and finite element implementation are at small strain, and we assume two-dimensional plane strain condition for now, with extension to axisymmetric condition to soon follow. More details can be found in [Sweetser, 2012]. Two numerical examples will demonstrate the CSE implementation.

The theory of Biot is most commonly used to model the behaviour of poroelastic materials. Nowadays, the Finite Element Method is the most well-established method to predict the dynamic response of those materials. This method subdivides the problem domain into a large number of small elemental domains in which the dynamic behaviour is approximated using simple polynomial shape functions. Due to the high number of unknowns per node and the fine meshes required to accurately capture the wave fields, the use of FEM is practically limited to low-frequency applications. Recently, an efficient Wave Based Method has been proposed to solve the Biot equations. This method is based on a Trefftz approach and takes the physics of the three wave types existing in poroelastic media into account, resulting in a faster convergence. This paper discusses applications of this method for multilayered structures and axisymmetric problems.

Pile foundations are integral parts of many civil engineering structures and pile foundations are routinely constructed in soft clays. The seismic behavior of pile foundations is a very complex problem with interactions between soils (solid skeleton, pore water, and pore air), piles, and superstructure. This complexity is further increased when weak soils, such as soft clays, surround the pile foundation. Seismic behavior of pile foundations in soft clays may be improved using ground improvement techniques such as Cement Deep Soil Mixing (CDSM). The seismic behavior of pile foundations in improved ground is, however, poorly understood. A fully coupled finite element computer code, TeraDysac, is used to study the influence of CDSM ground improvement around pile foundations in saturated soft clays during earthquakes. TeraDysac considers the coupled differential equations governing the behavior of the solid skeleton, pore water, and piles. Bounding surface elastoplastic constitutive models are used to simulate the stress-strain behavior of soils in TeraDysac. TeraDysac simulations of a centrifuge model test involving pile foundations in unimproved and CDSM improved soft clays are presented. The prototype of the centrifuge model test consisted of 10 m of soft clay underlain by 8 m of dense sand with single piles and various extents of CDSM ground improvement around the piles. TeraDysac simulations show that improving the ground around the piles is an effective way to reduce displacements, accelerations, and bending moments in piles during an earthquake. The dimensions of the ground improvement, however, have to be sufficiently large for these reductions to be realized.

In the numerical simulation of the Biot model numerical oscillations may occur if the spatial and discretization parameters are not properly chosen. When the time-step is too small, the grid has to be fine enough to resolve the boundary layers that appear in the early stages of the simulation. In this work, we extend a strategy that has been successfully employed in the one-dimensional case for the detection of a critical time-step, below which instabilities appear. The idea is to study under which condition the Schur complement of the poroelastic system enjoys a discrete maximum principle property. Differently from the one-dimensional case, in the vectorial case the shear modulus plays a fundamental role for the computation of the Schur complement and the maximum principle argument can be applied only for small shear. We will also investigate the sign of the entries of the Schur complement when the shear and the bulk modulus are of the same magnitude.

Three different methods are considered for integration of an elastoplastic model for clays: cutting-plane method, a semi-implicit integration technique with sub-incrementation, and a fully-implicit return mapping method. The three methods are compared in numerical simulations of triaxial and plane strain tests on K₀-consolidated clays, as well as in finite element simulation of a geotechnical boundary value problem involving over-consolidated saturated clays. The simulations show the superior performance of the fully implicit method over the other techniques. It is also shown that, while the accuracy and robustness of the implicit integration technique is clearly superior to the other two methods, the semi-implicit technique presents a reasonable alternative for the use in finite element simulations that involve a large number of integration points.

The requirement of C⁰ continuity for the pressure interpolation in coupled u-p formulations necessitates the presence of pressure degrees of freedom along element edges (for two-dimensional elements) and faces (for three-dimensional elements) in continuous pressure elements. This translates into a larger number of pressure degrees of freedom per element as compared to mixed elements with discontinuous pressure interpolations. Not surprisingly, the number of potential mixed elements that exhibit stable response, particularly under incompressible or nearly incompressible conditions, is smaller than in the case of elements with discontinuous pressure interpolations. Traditionally, u-p finite element analyses of geomaterials employed two- and three-dimensional mixed finite elements with linear pressure interpolations and a quadratic displacement interpolation. Since such elements are known to generally yield stable results, they have been used rather extensively in the past and form a basis against which to compare the performance of newer mixed elements with continuous pressure approximations. To a lesser degree, two- and three-dimensional mixed finite elements with continuous pressure interpolations that employ a so-called displacement "bubble" function have also been used in u-p finite element analyses of geomaterials. "Bubble" functions are additional displacement degrees of freedom that are included at an interior node in the element. In both "Taylor-Hood" and "bubble" function elements, the pressure interpolation is linear. Higher-order pressure interpolations are relatively rare, being confined to quartic triangular u-p elements (in displacement) with a quadratic pressure interpolation. Not surprisingly, systematic assessments of such elements have not appeared in the literature. This paper describes the preliminary phases of just such an assessment for two-dimensional elements.

Results from an experimental investigation into the dynamic response of cement foams subjected to blast pressure loading are reported in this paper. Cement foams with a cellular structure consisting of large entrained porosity in the form of uniformly distributed air cells were used in the study. The quasi-static response of such foams exhibits a distinctive concave shape associated with crushing of cell, which follows an initial linear elastic response. Experimental results from cement foam subjected to different blast pressure loadings using a shock tube are presented. Experimental results show a clear beneficial effect in reducing the amplitude of the transmitted stress. Results indicate that crushing of foam produces a continuous decrease in the amplitude of the stress wave produced in the foam. The blast pressure loading applied at one end of foam specimen is transmitted to the substrate as a stress pulse of reduced amplitude. When sufficient length of the foam is present, the transmitted stress history due to an applied blast pressure wave resembles a rectangular stress pulse of amplitude slightly higher than the crushing strength of the foam. The transmitted stress amplitude to the structure can effectively be controlled by varying the crushing strength of the foam.

New explosive threats face civilian populations each day; therefore, continuous upgrade of the defenses surrounding infrastructure and inhabited buildings is good practice. Today, barriers lack certain abilities such as mitigating shock waves, preventing the creation of secondary debris and the ability to take an impact from a vehicle. Better technology is needed. Testing provides a means to determine empirically, with less time, important parameters being sought for new advances. Several barriers have been built and tested to create a base line to see what a standard concrete barrier is able to do. Testing will then move on to test individual components that make up the barriers to determine how much of an impact they will have. When testing is complete, this research hopes to be able to determine the amount of pressure that can be mitigated using media confined inside of a concrete barrier. This research also seeks to develop new methods of building barriers in such a way that a blast impulse will be mitigated by the barrier, reducing the distance needed between the barrier and protected structure.

The response of cellular cementitious flat plates of circular shape, with or without additives to shock wave loading, has been investigated experimentally in the CCNY Shock Tube Research Facility. Cementitious cellular foam plates with and without polypropylene fiber reinforcement, were tested. The traveling shock wave generated by the rupture of an aluminum diaphragm exits the shock tube, and subsequently expands and impacts the specimen in the form of blast wave. This interaction generates a reflection of the incoming shock wave propagating in the opposite direction and, at the same time, triggers waves within the cementitious specimen which eventually initiate the appearance of cracks. The experiments have indicated that the cellular plates develop cracks initially in the radial direction which then branch out into irregular directions leading to the break of the plates. These cracks start at the high-stress concentration region close to the center or are aligned with pre-existing cracks.

Explosions on the ground surface induce strains on underground structures, such as tunnels and pipelines. Depending on the size of the explosion, distances involved, and the nature of the intervening material, these strains can be relatively high, thus causing severe damage to the structure. Barriers may be used to protect a structur, by reducing the strains created as a result of the explosion. The role of compressible protective barriers (made of polyurethane foam) and rigid barriers (made of concrete) in reducing the impact of a surface explosion was studied. Results of physical model experiments conducted on geotechnical centrifuge are presented and analyzed to evaluate the effectiveness of different types of barriers. Numerical model analyses were also conducted to further understand the behavior of different types of protective covers as compared to a soil cover. Results of such studies can help design barrier systems capable of mitigating effects of explosions, thus protecting essential components of underground infrastructure.

When saturated granular soils are subjected to blast loading, their responses are governed by their poro-elastic and poro-plastic properties. Particularly, the pore water pressure could increase significantly and, after the blast loading, residual pore water pressure could exist due to the plastic deformation of the soil skeleton. For granular soils, this could result in soil liquefaction. In this study, the poro-plastic responses of isotropic granular soils were discussed assuming that the concept of effective stress can be used to describe the plastic deformation. The cap model for granular soils, originally proposed by DiMaggio and Sandler, was extended to take into account the porous characteristics of the material and the solid-fluid coupling. The material was assumed to experience undrained loading due to the fast blast loading process. This study focused on the theoretical aspect of the constitutive modeling. Outcome of this study can be easily incorporated into existing computer subroutines of cap models to reproduce the undrained responses of granular soils with compressible solid grains.

An enhanced anisotropic elastoplastic bounding surface model with non-associative flow rule has been proposed (Ling et al., 2002; Jiang et al., 2012). The model has great potential to realistically describe the behavior of different types of cohesive soils, whether strain hardening or strain softening, under general stress paths and under drained and undrained conditions. This study integrates and demonstrates the application of the enhanced anisotropic bounding surface model with non-associative flow rule in finite element analysis (FEA) of deep excavation. To illustrate the importance of adopting a bounding surface, a built-in inviscid Sekiguchi-Ohta model in PLAXIS is employed for comparison with the measurements obtained at the Convention Center of the Taipei World Trade Center (WTC) Complex.

A parametric study was performed using an anisotropic elastoplastic bounding surface model for New York Bay Clay. The effects of material parameters on the stress path, stress-strain, and excess pore water pressure response were investigated. The set of traditional material parameters of New York Bay Clay was carefully evaluated based on a series of one-dimensional consolidation and triaxial experimental results. It was found that the mechanical behavior of New York Bay Clay was better captured when it was simulated for the tests close to normal consolidation. The traditional material parameters (λ and λ), bounding surface configuration (N_c and N_e), and hardening (w) parameters played a key role in determining the basic shape of stress path, and the elastic nucleus configuration (C and s) and plastic modulus (h) parameters controlled the stress response to reach the critical state line.

The aim of this paper is to investigate the stress wave propagation in saturated porous medium, e.g. soils, under heavy dynamic loading. This investigation is of great significance in practical engineering, e.g. coastal engineering [3]. Several one-dimensional problems are tested, e.g. dynamic generation of pore pressure wave, the effect of spatial discretization on the results or the evaluation of time step sensitivity. Finally, the consolidation process of the soil column is modeled and the numerical results obtained from the one-dimensional dynamic FEM algorithm are compared with the well-known analytical solution of Terzaghi [4]. Also wave propagation is investigated for the case of heavy dynamics when not only total stress but also pressure is applied. Again the numerical and analytical solutions are in good agreement, thus showing that the FEM algorithm successfully models the solid-water interaction.

Since its inception over thirty years ago, the bounding surface model for cohesive soils has been progressively improved and expanded to a three-invariant, elastoplastic formulation that accounts for the initial and stress-induced anisotropy. More recently, a simplified version of the model served as the basis for a simplified form of the anisotropic model. In order to more accurately simulate the softening of natural clays, the associative flow rule used exclusively in all earlier versions of the model was recently extended to include a non-associative flow rule. In an effort to unify the aforementioned versions of the bounding surface model for cohesive soils, a generalized model framework has been developed. The present paper describes this framework.

In recent years, porous materials have been attracted by biomedical engineers as load bearing scaffolds due to their mechanical properties which can be similar to those of body tissues. Among such materials, cellular sandwich structures are of more important because of their regular micro-structure. One can design the internal microstructure to achieve the desired mechanical properties. The elastic modulus of a scaffold is one of the most important mechanical properties in practical applications. In this paper, a beam finite element model is developed to predict the elastic modulus of a Ti6Al4V scaffold with regular micro-structure fabricated by Selective Laser Melting (SLM). At first, the mechanical properties of annealed Ti6Al4V are attributed to the struts material. But the obtained elastic modulus is not satisfactory in comparison with experimental one. In the second model, the mechanical properties of Ti6Al4V fabricated by SLM with the same processing parameters as those applied to manufacture the scaffold are assigned to the struts material. Using this model, the predicted elastic modulus of the scaffold is in good agreement with experimental one.

Soil element testings on the sand grains could result in successive drops in stress-strain relationships. These successive drops and formations give a stick-slip nature to the fluctuations, which might be attributed mainly to the jamming through particles, rate of loading, effective stress, pore fluid characteristics, and the compliance in the apparatus. During the sticking phase, the sand grains are more closely packed and the sample exhibits a gradual increase in stress; however, when the soil matrix becomes relatively unstable, some grains slide out of the column resulting in the stress to sharply drop. The main reason of the jamming might lie in fact that the internal forces do not uniformly propagate through the specimen, but are localized through force chains of strained grains. This motion is periodic and might be because of some periodic arrangement of the grains. Following a brief review of the fluctuations observed during shear tests on granular materials, the Gutenberg-Richter law has been adapted to illustrate this relationship between the return period of fluctuations and the deviatoric stress amplitude data from a series of triaxial testing results. It has been seen that a plot of logarithm of the return period of fluctuations against deviatoric stress amplitude gives a linear relationship.

Laboratory experiments and numerical simulations were used to study the effect of pore structure on stress-porosity-permeability relations. It has been hypothesized that a heterogeneous multi-porosity system, with the permeability-controlling porosity more compressible than the other porositie,s would demonstrate a high stress-sensitivity in the permeability. The porosity and permeability of carbonate, sandstone, and fractured cores were measured under isostatic stress conditions. A power law was used to correlate the change in permeability to the change in porosity. While the power law exponents for the sandstones were similar to that expected from a Kozeny-type correlation, carbonate and fractured cores showed much higher stress-sensitivity. The pore structure of a tested carbonate, examined by X-ray computed tomography, showed strong heterogeneity. Numerical simulation of porosity and permeability reduction during a uniaxial compression of an artificial vuggy porous medium, using discrete-element and lattice-Boltzmann methods, directly confirmed the influence of the pore structure on the stress-sensitivity.

A modified cluster structure-dependent (CSD) drag coefficient model is employed to investigate the effects of flow structure on the determination of drag coefficient from the multi-scale aspect by taking momentum and energy balance of dense phase dilute phase into account. The proposed modified model of CSD drag coefficient is on the basis of transportation and suspension energy-minimization method by heterogeneous drag. The modified drag coefficient closure considers flow behavior of both liquid and particles on the wall. Implementation of the calculation was done from the approach of the energy dissipation minimization incorporating into the two-fluid model to simulate the behavior of liquid-particle flow in a riser. The flow behavior of particles is predicted to be affected by the solid down-flow near the walls of the riser in the cluster formations and the wall friction of particles results in an increase of the concentration of particles near the walls. The predicted concentration and axial velocity of particles inside the riser compared reasonably well with experimental data.

Plastic strain caused by the rotation of principal stress is one of the important contributing reasons of wave-induced seabed liquefaction. Based on the generalized plasticity theory, a constitutive model for sand incorporating the effects of rotation of principal stress and state-parameter-dependant dilatancy has been proposed. The new sand constitutive model has been included into the finite element program DIANA-SWANDYNE II to simulate the wave-induced dynamic response of level seabed. The excess pore pressure generation due to rotation of this effect has been investigated in order to validate the new constitutive model

By means of graph theory, we analyze the changes in topology of a granular assembly during deformation. The elementary mechanism of diffuse deformation consists of intermittent flips. We show that dilatancy is the direct result of an increasing number of flips and elastic relaxation of particles upon flips. Both are dependent on particles' elastic potential energy prior to flip and after the flip. The latter is the result of nonuniform distribution of interparticle forces in force chains. Next, we consider shear bands in granular materials. Formation of shear bands is accompanied by massive rolling of particle. Since rolling is constrained by neighbors, a characteristic rolling correlation length appears. The transmission of rotations in a particular direction depends on the strength of the force chain branches in the direction of propagation and across. The maximum propagation distance is comparable to observed widths of shear bands.

This paper presents a unified framework for constitutive modelling of the axial stress-volumetric strain behaviour of granular soils using an evolutionary polynomial regression technique. It is a data-driven method based on evolutionary computing, aimed to search for polynomial structures representing a system. A procedure is presented for construction of the model. The main advantage of the proposed model over conventional and neural network-based constitutive models is that it provides the optimum structure for the material constitutive model representation, as well as its parameters, directly from raw experimental (or field) data. It can learn nonlinear and complex material behavior without any prior assumptions on the constitutive relationship. The proposed algorithm provides a transparent relationship for the constitutive material model. Merits and advantages of the proposed technique are discussed in the paper.

Influence of grading on the stress-strain and critical state behavior of granular materials is investigated by employing the three-dimensional discrete-element method (3D-DEM) through conventional drained triaxial tests in compression and extension. It is found that, under the same initial conditions (same e₀, p'₀), samples with a wider particle distribution exhibit more contractive. For each grading, a unique critical state line is achieved under different stress levels. The results from different gradings highlight that the critical state of the granular samples are significantly affected by the grading: the critical state line shifts down as the coefficient of uniformity (C_u) increases. A relationship between the location of CSL and the grading index C_u is then established. Micromechanical analyses are finally performed to confirm the macro finding of the grading dependency of mechanical behavior of granular materials.

This work focuses on the Lacunar Canalicular Porosity (PLC) of cortical bone which includes the osteons. Osteons are semi-cylindrical, porous structures saturated with fluid within the bone and are approximately 250 micrometers in diameter. Their outer boundary is called the cement line. The first objective of this work is to introduce an experimental protocol to determine the permeability of the cement line in cortical bone. Osteons will be extracted with and without the cement line. Designing a less expensive system to isolate micro structural components, osteons (diameter 200 - 250 micrometers), and designing a micro mechanical loading system is very challenging. The isolation system will be built into the inverted microscope to allow mechanical isolation while looking at the specimens in the inverted microscope which will improve the accuracy and speed of the isolation process. Osteons will be extracted with and without the cement line. Osteons will be subjected to sinusoidal loading. Experimental results will be compared to theoretical solutions of unconfined compression of poroelastic, fully saturated, annular cylindrical disk that is previously developed by the authors in number of publications. Results will determine the degree of permeability of the cement line. The analysis will show the sensitivity of the poroelastic properties of the cortical bone to the flow through the cement line.

We outline the mathematical model of the time-harmonic ultrasonic response of wet cortical bone. Using two-scale asymptotics, we derive an effective model of acoustic wave propagation in a two-phase medium modeling a fine mixture of linear piezo-elastic solid and a viscous, Newtonian, ionic bearing fluid. Following the works of Moyne and Murad, and Lemaire et. al. for the quasi-static case, we develop a two-scale homogenization method for the dynamical system, albeit the time harmonic case. The idea is to connect the bulk pressure to the small displacement by an assumption used in acoustics, i.e. the pressure p ≈ - ρ_fa²_f divu; where ρ_f is the fluid density, a_f the speed of sound in the fluid, and u is the displacement. We investigate several time scales; one is associated with high frequency domination which leads to different hierarchies. The ratio ε of a typical size of the microstructural inhomogeneity and the macroscopic length scale is a small parameter of the problem. Another possibly small parameter is the Peclet number which influences the type of effective equations which are obtained. A brief asymptotic analysis is presented.

The mechanical stimuli in bone at the micro-scale maybe better characterized with poroelastic micro-computed tomography (μCT)-based, finite element (FE) models. The objective of this study is to estimate the material properties of the solid bone phase and the inter-trabecular bone marrow by fitting sample-specific, μCT-based, FE models to mechanical tests. Trabecular bone cubes were prepared and 3D FE meshes were obtained from μCT images. Bone and marrow were simulated using the poroelastic formulation and both confined and unconfined experiments were simulated. The total stress predicted for the unconfined models varied between 21.29 and 21.5 MPa according to the simulated strain rate. For the confined simulation, the total stress predicted after relaxation was 28.28 MPa with a relaxation time of 6 s. Mechanical experiments to determine the material constants by tuning the models are in progress. These kinds of models will allow studies on the effect of subject-specific micro-architecture on the poroelastic response of trabecular tissue, and have the potential to be performed based on in vivo μCT imaging.

Cancellous bone is strongly dependent upon the orientation of trabecula. One way to describe the orientation of trabecula is the fabric tensor. In the expression of fabric tensor, we introduce two unknown anisotropic coefficients, A_i^E and A_ij^P. The introduced anisotropic coefficients A_i^E and A_ij^P, which are determined by fabric tensor, are expressed by three unknown coefficients d₁, d₂, and d₃, and the porosity φ. In this calculation, three unknown coefficients are reduced to two unknown coefficients, d₁ and d₃, and the variation of anisotropic coefficients A_i^E and A_ij^P are illustrated. As a conclusion, the anisotropic coefficient A_i^E, which is related to the elastic modulus, is mostly determined by unknown coefficient d₁, but the anisotropic coefficient A_ij^P, which is related to Poisson's ratio, is mostly determined by unknown coefficient d₃.

In this paper we firstly illustrate the measurement of the swelling of a single trabecula from human femur heads during water imbibition. Moreover, since the swelling is caused by water diffusing from external surfaces to the core of the sample, by measuring the sample swelling over time, we obtained direct information about the transport of fluids through the intimate constituents of bone, where the mineralization process takes place. We developed an apparatus to measure the free expansion of the tissue during the imbibition. In particular, we measured the swelling along three natural axes (length L, width W, and thickness T) of the trabecula. To this aim, a 3D analytical model of the water uptake by the sample was performed according to Fickian transport mechanism. The results have been utilized to fit the measured swelling along the three sample directions (L, W, T) and the apparent diffusion coefficients D_T, D_W, and D_L.

Current theoretical and experimental evidence suggests that the sensory bone cells are activated by the induced drag from fluid flowing through the lacunar-canalicular porosity (PLC). One of the most important parameters of the interstitial fluid flow is the PLC permeability. However, the reported measurements of this permeability span over eight orders of magnitude in literature. In this work, innovative analytical and experimental approaches were proposed to accurately estimate the PLC permeability that was determined in a single human osteon, a domain in which the PLC can be separated from the vasular porosity (PV). Based on the curve fitting of the experimental measurements of loss tangent on cyclically loaded osteons at different frequencies to the analytical model, the PLC permeability was preliminary determined to be on the order of 10^-22 m².

Adaptation of bone is sensitive to mechanical loading frequency and to rest periods between consecutive load cycles. The time dependence of mechano-adaptation may be caused by a time-varying stimulus such as fluid flow. In vitro studies have shown that interstitial fluid flow (IFF) is osteogenic for bone cells. We investigated how bone permeability and rest insertion affect mechanical stimuli in the lacunar-canilicular system in simplified 3D poroelastic finite-element model of a beam in bending, representing mouse cortical bone. Load cycles with a 10 Hz haversine wave as amplitude were applied, with rest-insertion times ranging from 0-10 seconds. Intrinsic permeability values ranging from 10^-23-10^-18 m² were tested. IFF was determined in the centroid of the model. We found there is an optimal rest insertion time necessary to maximize fluid motion, which depends on permeability. These findings may be utilized in developing maximally effective loading protocols.

The determination of lacunar-canalicular permeability is essential to understand the mechano-transduction mechanism of bone. Murine models are widely used to investigate skeletal growth and regulation, but the value of lacunar-canalicular permeability is still unclear. To address this question, a poroelastic analysis based on nanoindentation data was used to calculate the lacunar-canalicular permeability of wild type C57BL/6 mice of 12 months. Cross-sections of three tibiae were indented using spherical fluid cell indenter tips of two sizes. Results suggest that the value of lacunar-canalicular intrinsic permeability of B6 female murine tibia is in the order of 10^-24 m². The distribution of the values of intrinsic permeability suggests that with larger contact sizes, nanoindentation alone is capable of capturing the multi-scale permeability of bone. Multi-scale permeability of bone measured by nanoindentation will lead to a better understanding of the role of fluid flow in mechano-transduction.

The paper deals with the two-level homogenization procedure which provides a computational tool for modelling multi-porous media. For subsequent upscaling consequently two levels we employ the periodic homogenization. The effective poroelastic coefficients are computed using characteristic responses, solutions of local problems imposed in representative volume elements describing the poroelastic medium at various level of heterogeneity. Such a procedure can be reiterated while combining the poroelastic equations from preceding levels and various geometries of pores at different levels. In the present work, we apply this approach for modelling the bone tissue taking into account geometrical features of the canalicular and lacunar porosities. In particular, the Biot continuum coefficients are obtained which describe the double porous medium. Further extensions of this model for non-steady problems are being considered.

This work aims to investigate the influence of the bone microctructure (bone matrix properties as well as porosity) on response of ultrasonic wave propagation in cortical bone plates when using the axial transmission test. The bone is modeled by using the Biot's theory [1] for anisotropic poroelastic media. A micromechanics model is used to estimate poroelastic properties of bone in the macro-scale from its matrix properties and porosity. A semi-analytical finite element method has been developed for simulating the ultrasonic waves propagating in a cortical bone plate coupled with soft tissues. It is shown that the method is efficient to investigate the dynamic behavior of bone plates in both time and frequency domains.

This article focuses on the mathematical problem of reconstructing dynamic permeability K(ω) of two-phase composites from data at different frequencies, utilizing the analytic structure of K(ω). To numerically simulate the data by solving the unsteady Stokes equations in the 3D domain reconstructed from μ-CT scans of the composites, the issue of segmentation is also addressed in this paper and an efficient segmentation scheme is suggested and implemented for cancellous bone.

In this paper the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric - a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone. Current diagnosis of bone loss and osteoporosis is based on the measurement of the Bone Mineral Density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction; 2) only the first wave arriving to the ultrasound probe is characterized; and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as Speed of Sound (SOS) and Broadband Ultrasound Attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory.

Propagation of two waves (fast and slow) in trabecular bone has been reported by several laboratories around the world. This is an unequivocal signature of poroelastic wave propagation accordingly to Biot's theory. Velocity and attenuation of fast and slow waves in Biot's poroelasticity theory depend on the porosity, physical properties of the solid and fluid constituents of the porous medium, and the frequency of the wave. Importantly, ultrasound is sensitive to the directionality of pore microarchitecture, which was not taken into account until recently, when a fabric-dependent anisotropic poroelastic wave propagation theory was developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium (Cowin and Cardoso 2011). Key to this development was the addition of the fabric tensor (a quantitative stereological measure of the degree of structural anisotropy of bone) into the linear poroelasticity theory. This framework was further extended to the propagation of quasi-wave modes along an arbitrary direction in porous media (Cardoso and Cowin 2011). In the present study we use this poroelastic ultrasound (PEUS) model of wave propagation to predict the porosity and fabric microarchitecture from measurements of ultrasound wave velocities. Predicted values of microarchitecture are compared to microCT measurements of microarchitecture in the human calcaneum. We have found that the porosity and fabric components of bone microarchitecture derived from PEUS approach are highly correlated to microCT measurements of the same parameters. Therefore, the anisotropic poroelastic ultrasound wave propagation model developed by Cowin and Cardoso (2011) has the potential to assess porosity and microarchitecture directionality which cannot be assessed by DEXA, thus representing a bone quality assessment beyond BMD.

Biot's theory of wave propagation in porous media predicts the genesis of two waves (fast and slow) due to the in-phase and out-of-phase motion of the solid and fluid constituents of the porous medium. In Biot's theory, the loss of energy (attenuation) of both fast and slow waves is modeled to occur due to absorption and dispersion processes. However, Biot's approach does not take into account the effect of the pore microstructure on the elastic scattering of fast and slow waves. Scattering of elastic waves generally to the loss of energy associated to the change in direction of the wave ray as a consequence of inhomogeneities in the medium. The directionality of pore microarchitecture was recently introduced into the linear anisotropic poroelastic wave propagation theory (Cowin and Cardoso 2011, Cardoso and Cowin, 2011) using the fabric tensor, a quantitative stereological measure of the degree of structural anisotropy of bone. This recent approach thus allows investigating the relationship between the fabric tensor and directional-dependent attenuation of elastic waves in anisotropic porous media. In particular, the contribution of both absorption and scattering on the attenuation of the fast and slow waves in anisotropic porous media was investigated. The absorption and scattering attenuation processes are compared, finding the scattering to be the dominating mechanism of attenuation for ultrasound waves in the 1MHz range of frequency.

The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are to be applied to the problem of determining the exchange of pore fluid between the vascular porosity and the lacunar-canalicular porosity in bone tissue due to cyclic mechanical loading and blood pressure oscillations. The result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells.

The microarchitecture of trabecular bone results from adaptation by the mechanical milieu applied to it. Characteristics of such anisotropic mechanical property can further understand adaptive response of bone to the particular mechanical loading and predict risk of fracture. Quantitative ultrasound (QUS) has demonstrated its ability to predict the principal structural orientation (PSO) of trabecular bone. It remains unknown whether the structural orientation would associate with mechanical strength of bone. The objective of this study was to evaluate the mechanical properties in different PSOs predicted using various methods (i.e., QUS and μCT), thus, to investigate the ability of QUS as a means to predict the PSO of trabecular bone noninvasively. Seven trabecular bone balls from distal bovine femurs were used for QUS tests, and to generate finite element analysis based on the 3-D μCT images. The stiffness in the PSOs predicted by QUS were highly correlated with the stiffness in the MIL tensor orientation (ATT vs. MIL, R²=0.97, p<0.001; UV vs. MIL, R²=0.92, p<0.001).

In this study, the local variability of microarchitecture of human trabecular calcaneus bone is investigated using high-resolution microCT scanning. Our results show that strong correlation exists between most scalar architectural parameters and volumetric bone mineral density (vBMD). However, no statistical correlation was found between vBMD and the fabric components. Therefore, only fabric components explain the data variance that cannot be explained by vBMD. This study demonstrates that a multi-directional, fabric-dependent, poroelastic ultrasound approach has the capability of characterizing anisotropic bone properties beyond bone mass, and could help better understand anisotropic changes in bone architecture using ultrasound. Moreover, the apparent modulus of elasticity, yield strain and stress of trabecular human calcanei along multiple directions are measured using microFEM. The results show that fabric tensor is highly correlated to the modulus of elasticity (R² = 0.62) and yield stress (R² = 0.58), but poorly correlated to yield strain (R² = 0.16).

In real-world applications involving complex, 3D, heterogeneous domains, the use of advanced numerical algorithms is of paramount importance to solve stably, accurately and efficiently the coupled system of partial differential equations (PDEs) governing the mass and the energy balance in deformable porous media. The present paper discusses a novel coupled 3D numerical model based on a combination of Finite Elements (FE) and Mixed FE (MFE) developed with the aim at stabilizing the numerical solution.

This paper presents an analytical investigation on the stability of multiphase porous media subjected to changes in fluid pressures and/or saturation conditions. For this purpose, we revisit the concept of second-order work and explore its relation with the incremental energy input in partially saturated media. Our analytical results show that second-order work contributions do not involve only effective stresses and skeletal deformation, but also depend on the changes in fluid pressures and degree of saturation. This result provides a novel approach to address unstable processes in unsaturated porous media and enables a number of theories originally conceived only for fluid-saturated compounds to be extended for unsaturated media.

A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the Fast Fourier Transform (FFT) based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin-Shtrikman which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent discretization of Green operators and of the viscosity of heterogeneous voxels comprising both solid and fluid.

Fluid infiltration is typical of many physical phenomena including, among others, geologic CO₂ sequestration, rainfall induced infiltration, drying and desiccation. All of these phenomena are interesting to be studied, per se, but also because of the macroscopic occurrences which they trigger (for instance, CO₂ displacement in aquifers, capillary trapping, drying, desiccation cracking or wetting collapse). Apparently, the infiltrating fluid is different for each of these phenomena. However, the common aspects rely on the role of capillarity in the characterisation of the partially saturated porous material. Several mathematical models have been proposed which attempt to simulate these mechanisms through suitable upscaling procedures and, consequently, at a characteristic scale much larger than that of capillarity. On the other hand, the so-called phase-field models are less common. Following Coussy's approach to a thermodynamically consistent deduction of poromechanics, and extending some previous results by the author, an enhanced poromechanical model involving gradients of strain and saturation degree is presented and discussed. Preliminary results for a biphasic van der Waals-like fluid flowing through a rigid matrix are presented aiming at capturing fingering during desiccation.

The implementation of suitable carbon capture and storage (CCS) technologies is a mandatory requirement for reducing anthropogenic emissions of greenhouse gases (GHG) and obtaining a sustainable power generation from fossil fuels, especially coal. Carbon dioxide (CO₂) sequestration within deep underground reservoirs is indicated as one of the most promising techniques which, however, implies a complex multidisciplinary effort involving a number of hydrological, geomechanical and geochemical issues. In the present contribution, a geomechanical modeling study of the CO₂ disposal into an offshore multi-compartment saline aquifer located at about 1500 m depth in the Northern Adriatic Sea, Italy, is discussed. The study assumes a CO₂ injection rate of 1×10⁶ ton/a and shows that a safe and permanent containment may be secured over a few years only for the considered distributions of the petrophysical properties and initial in-situ stress and pore pressure.

This paper analyzes the problem of a sink segment extracting fluid from a poroelastic layer bounded by two semi-infinite impermeable elastic strata. This problem can be reduced to one of the classic elasticity theory, with the gradient of the pore pressure field in the reservoir acting as a pseudo-body force, and the jumps of pore pressure at the interfaces between the reservoir and the adjacent layers inducing pseudo-tractions. The solution of this elastic problem is obtained using integral transforms. The asymptotic behaviors are then emphasized and conceptual models are introduced that capture the salient features of the small and large time asymptotes.

In this paper, we extend the poroelastic solution of a single poroelastic inclusion proposed by Rudnicki (2002) to two interacting poroelastic inclusions with arbitrary shape and orientations with respect to each other. The methodology used in this paper is a combination of Rudnicki works for a poroelastic inclusion and Moschovidis and Mura's approach to include interactions between inclusions with different poroelastic and fluid pore pressure properties. In the present work, the interacting poroelastic inhomogeneities are replaced with equivalent inclusions. This problem has a lot of application in geomechanics and biology. As an example, we used the derived solution to calculate fracture gradient changes in a formation with multiple compartments, where one of the compartments is already depleted (low pore pressure) due to fluid production. The results were tested with a numerical finite difference model to check the accuracy of the proposed solution.

This paper deals with the time-dependent behavior of rocks in the vicinity of underground cavities. Our approach is analytical and addresses different stages of the life cycle of a cavity. The theoretical framework is taken up from previous works [1-4] and completed to account for an irreversible viscoplastic behavior, which has been experimentally evidenced [5-9]. Other attempts to account for creep are available in the literature. Some of them use the viscoplasticity theory [10-14 for instance]. Most often, they require numerical tools. However, analytical approaches are useful to check the consistency of more complex numerical simulation and to make it possible to obtain practical estimations of the behavior of underground structures. To our knowledge, Pouya [13] provided an approximate analytical solution in the case of an unlined tunnel accounting for a monophasic rock mass obeying to a Norton-Hoff's creep law in the particular case of incompressible elasticity (v = 0.5). Cosenza et al. [14] analytically dealt with the long-term behavior of a spherical cavity inside a saturated poro-viscoplastic rock mass in the borderline case of stationary state, neglecting the transitional stages.

We summarize recent results of coupled, non-isothermal, fluid flow and geomechanical modeling associated with the In Salah CO₂ storage operation at the Krechba gas field, Algeria. At In Salah, significant geomechanical changes associated with the CO₂ injection have been observed, especially through satellite-based monitoring of ground surface deformations. The ground surface deformations observed during the few years of injection were modeled by poro-elastic expansion of the injection reservoir. Moreover, the simulation results showed that the highest potential for injection-induced micro-seismicity occurs along the horizontal injection wells caused by the combined effects of injection-induced cooling and pressure. Much recent modeling efforts have been dedicated to analyzing injection-induced, coupled fluid flow and geomechanical responses of a deep fracture zone or fault that has been inferred from an analysis of a double-lobe pattern of the ground surface deformations and then confirmed by a 3D seismic survey. A detailed modeling with comparison of model results to observations of the transient evolutions of surface uplift and injection was conducted for constraining the height of the fracture zone.

The water retention curve expressed in terms of water content or degree of saturation and suction is hysteretic, stress path dependent (on void ratio), and depends on pore network. To properly describe its evolving nature, a multimodal retention model is proposed by considering a linear superposition of two subcurves of the Van Genuchten type. The model is constructed based on PSDs obtained with Mercury Intrusion Porosimetry (MIP) data at specified initial state, and thus, is representative of this initial pore network configuration. Based on the WRC model proposed above, the evolution of parameter χ will be evaluated based on the microstructural evolution of the pore network. The model is validated based on a series of oedometer samples performed at constant water content and then saturated at different initial void ratio and the same water content.

Soil-shredded tire mixture is examined to reduce frost heave and force due to effective prevention against intrusion of cold air from atmosphere to ground. Frost force called as frost earth pressure occurs when ground temperature decreases under 0 °C and soil volume expands. Soil expansion proceeds in a horizontal direction as well as a vertical direction, which causes roadway and buried pipeline failure. In this study, experimental investigation was performed with soil-shredded tire mixture to prevent buried pipeline from being damaged by frost force.

Many theoretical and computational models have been frequently used in the past to estimate the frost depth of frozen soil, but these models require accurate data for the atmospheric environments and soil properties which is generically diverse with respect to locations. Compared to the models, field measurements directly provide the frost depth, including atmospheric environments and soil propertie;, but, it is hindered by expensive cost. A frost indicator with methylene blue solution has been used to measure the frost depth due to simplicity and cost efficiency, but accuracy of the frost indicator has not been evaluated. This study presents experimental investigation of the accuracy of the frost indicator and frost depths measured in South Korea.

Tunnels are often driven at shallow depth in urban areas where unsaturated soils may be encountered. Capillary rise from the water table, causing partial saturation of the material, increases the cohesion of the soil mass. The stiffening effect of partial saturation can stabilize the tunnel face in such way that open-face tunnelling can be performed and settlement minimised. However, the effect of capillary cohesion is difficult to quantify. Centrifuge testing has proven to be an appropriate technique to assess the face stability of shallow tunnels (Mair and Taylor, 1997), and several studies have been conducted, both in cohesive and frictional material (Idinger et al., 2011). However, little attempt has been made to extend centrifuge testing to shallow tunnelling in partially saturated soils. In this paper, some centrifuge tests on model tunnel in unsaturated soil are presented.

The offshore foundations may exhibit a relatively high liquefaction susceptibility due to the full saturation of the porous seabed and the cyclic nature of the typical offshore loads. Here, the particular relevance of some of the main factors that affect the liquefaction susceptibility of an offshore monopile will be addressed, focusing on the possibility of a progressive accumulation of residual pore water pressure within the saturated soil around a monopile under cyclic lateral loading. The discussion is based on numerical results obtained with a coupled FE model of the offshore foundation which includes the Biot-Zienkiewicz u-p model. A constitutive model of the Generalized Plasticity type has been used for the soil in order to reproduce important features of its behaviour under cyclic loading. This paper presents the findings derived from a parametric study of the problem and shows that the accumulation of residual pore pressure can produce significant changes of the pile's behaviour under external loading. The paper also investigates the effects caused by the loading from a realistic storm of moderate magnitude and the consequential transient degradation of the foundation's stiffness.

The paper starts with a historical review on primary and secondary consolidation referring to pioneers as K. Terzaghi, O.K. Fröhlich, P. Fillunger and A.S.K. Buisman. The main part of this contribution focuses on long-term oedometer tests lasting up to 42 years and performed on silty sand, (organic) clayey silt, peat and pre-treated sewage sludge. Secondary consolidation (creep) could be observed in all cases, lasting over many years and occurring widely linear with the logarithm of time. This long-term phase is followed by tertiary creep, which indicates a long-lasting fading-out period. In addition to the laboratory tests, results of field observations are presented showing the influence of ground improvement on the creeping behaviour of very soft fine-grained soils (partly organic). Soil improvement comprised temporary surcharge loading, deep dynamic compaction/consolidation (heavy tamping) and deep soil displacement (vibroflotation). The data were collected from a highway junction on highly compressible, heterogeneous ground, constructed between 1972 and 1974, and monitored since.

The construction of infrastructure projects in urban area is typically associated with tunnelling-induced settlements. These settlements are caused by the stress relief and the overcut (ring space between cutting diameter and final lining diameter) of the Tunnel Boring Machine during the excavation and frequently exceed the tolerable settlements of the above located structures. The main parameters influencing the development of total and differential settlements are: ≤ Soil conditions ≤ Effective stress level ≤ Overburden - distance between foundation level and tunnel crown ≤ Tunnel diameter ≤ Volume loss of TBM

Ground improvement techniques play an important role in extending the infrastructure in countries where soft soil deposits play an important role. Two practical examples are presented in this paper. Vertical drains combined with preloading have become common practice and are amongst the most effective procedures for ground improvement, accelerating the consolidation process and decreasing the time for reaching final settlements. In the first example, a comparison of field measurements and a numerical model for calculating settlements due to construction of an embankment on soft soil for the Cirebon Power Plant Project in Indonesia is presented. Good agreement between field measurements of settlements and numerical prediction could be achieved. In the second example, a field trial of a stone column reinforced foundation for an embankment is considered. Here settlement and pore water pressure measurements have been utilized to back calculate material parameters of the soil by means of an optimisation procedure. It could be shown that reasonable agreement could only be achieved when employing a constitutive model incorporating creep effects.

The extension of our infrastructure in urban areas and also in rural embossed areas is often linked with the design and construction of complex geotechnical structures. Especially the design of the temporarily required excavation structures with the plurality of construction phases and the varying deformation states and stress situations has to be mentioned. In the most cases, examination of the bearing and deformation behavior in plain strain models is preferred to the detailed three-dimensional investigation of the soil-structure interaction. In reality, deep excavations are spatial systems significantly influenced by the geometric and geotechnical boundary conditions [Chiou et. al. (1993)]. The three-dimensional soil-structure interaction and the influence on the bearing and deformation behavior of nearly rectangular excavations in cohesive soils are investigated by the analysis of several field measurements and the execution of a parametric study. The stiffening effect of the corners and its influence on the bearing behavior of the structure is apparent and leads to a more realistic and more economic design. The realistic approach of the acting earth pressure is contrary to the approach formulated in the technical guidelines, e.g. EAB (2012). Further investigations of the bearing and deformation behavior of deep excavations with special ground shape under consideration of the geotechnical and the structural boundary conditions shall lead to more realistic design approaches.

An experimental program was planned to investigate the effect of confining stress on the air entry and air expulsion values in the drying and wetting process, respectively. For this purpose, soil-water retention curve of the soil is determined under two different applied net stresses. A novel miniature pressure plate apparatus is designed to determine the SWRCs under different net stresses. The soil specimens are then sheared in a suction -controlled triaxial apparatus and the shear stress of the soil is determined. The measurements were carried out under net confining stresses identical to the net stresses for which the SWRCs were obtained. Finally, variations of the χ-parameter during drying and wetting process are presented.

The poro-mechanical and chemical effects of fluids are responsible for the subcritical micro-cracking (i.e., brittle creep). The focus of this work was to dissociate and quantify, using uniaxial creep tests, both the fluids effects on subcritical stress corrosion cracking in a porous rock. Different fluids with increasing chemical influence (i.e., oil, ethanol and water) were tested. The evolutions of acoustic activity indicate that micro-cracking plays the main role in the creep process. The poro-mechanical effect, which predominates under partially saturated (water/ethanol) conditions, decreases the rate of subcritical cracking through capillary forces. The chemical effect of fluids is related to stress corrosion reactions in minerals at crack tips. Immersion in water/ethanol annihilates capillary forces and decreases the activation energy of the chemical reactions, thus increasing the rate of stress corrosion cracking. Under saturated conditions, long-term strength and time to failure increase as the chemical influence of the fluid decreases.

In this paper we use a thermomechanical approach to study inelastic processes in unsaturated granular matter. The paper extends the breakage mechanics theory to unsaturated conditions, investigates the physical roots of hydro-mechanical coupling and elucidates the interplay between yielding locus and degree of saturation. For this purpose, energy storage mechanisms are hypothesized to consist of the sum of an elastic energy potential and a hydraulic contribution inspired by the capillary theory. Microscopic arguments are then used to define suitable grainsize scaling laws. These assumptions are finally combined with a statistical homogenization procedure, thus deriving a macroscopic Helmholtz free energy. The paper shows that such procedure, together with the breakage dissipation, is able to capture salient couplings between mechanics and hydraulics. The results provide a novel theoretical explanation for the approaches commonly used in plasticity models for unsaturated porous media.

This work presents constitutive thermodynamic formulations for modeling poromechanical behaviors of saturated microcracked rocks. The Mori-Tanaka homogenization scheme is adopted to determine the effective properties of the matrix-inclusion system. Continuity conditions in both stress and strain energy are used to determine unknown constants. The friction criterion is formulated in terms of the macroscopic stress, the back stress and the pore pressure. The present study can improve and extend our researches along this line. A numerical prediction of true triaxial mechanical behaviors of Westerly granite is finally presented.

Information on the poroelastic response of rock transport properties to changes in effective pressure is of importance for sustainable use of underground resources, e.g. geothermal reservoirs. Here, we report experimental results of permeability and electrical rock conductivity measurements performed during hydrostatic (confining) pressure cycling. In addition, the use of high precision pore fluid pumps allowed direct and concurrent quantification of changes in pore volume. Thus, porosity at constant pore pressure 0.1 molar NaCl-solution was used as the pore fluid. Three different types of sandstone (Fontainebleau, Bentheimer, and Flechtinger) were tested at a maximum confining pressure of 70 MPa, a constant pore pressure of 5 MPa, and three different temperatures (25, 40, and 150°C). The measurements permitted to monitor and evaluate the respective permeability-conductivity-porosity relationship over the full pressure range explored. Finally, the high precision of conductivity and porosity measurements allowed to constrain a pressure dependence of the cementation coefficient in Archie's 1^st Law.

A novel form of Terzaghi's effective stress principle is proposed to describe electro-chemo-mechanical couplings in unsaturated swelling clays characterized by two porosity levels (nanopores saturated by an aqueous electrolyte solution and micropores partially saturated with water and air). Under mechanical equilibrium, the three-scale model is derived using the homogenization procedure. Macroscopic constitutive laws are derived within the framework of work-conjugated stress-strain variables leading to a set of three pairs of state variables. In addition to the contact stress between particles and a Bishop component-type related to capillarity effects along with the skeleton strain and water saturation, the novel form includes salinity as an additional strain variable and a three-scale swelling stress directly correlated with the electrochemical phenomena at the nanoscale. Numerical results illustrate the potential of the multiscale approach in capturing the complex features of unsaturated expansive clays.

The interaction between mechanical deformation, pore fluid pressure, temperature and fluid flow determines the thermo-hydro-mechanical behavior of a geothermal reservoir rock. Both elastic and transport properties of a rock such as Flechtinger sandstone are controlled to a large extent by porosity. The poroelasticity theory and crack closure theory were employed to estimate the porosity change at drained conditions. Hydrostatic compression tests and steady state fluid flow tests were carried out. Permeability measurements were carried out while cycling confining pressure at a constant downstream pressure of 1 MPa. Meanwhile the temperature was increased stepwise from 28 °C to 140 °C. While the volumetric change of the crack-like cavities is not significant, they control the fluid flow pathways and, consequently, the permeability of the rock. The new permeability model correlates the microstructure of porosity, volumetric strain and permeability. The permeability dropped sharply until a characteristic pressure and was leveled off afterwards.

Thermo-hydro-mechanical (THM) coupling processes in unsaturated soils are very important in both theoretical and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from the Taylor's series expansions. Constitutive relationships of the THM coupled behavior for unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closed problem is formed. In addition to the modification of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling of elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are derived.

The paper presents both macroscopic and microstructural evidence of the water sensitivity of a low porosity clayey rock from Northern Spain. Particular emphasis is focused on the effects of water sensitivity at micro level. Results obtained from Environmental Scanning Electron Microscopy (ESEM) using the common procedure of sample preparation show that this procedure of sample preparation is not enough to evaluate in a proper way the irreversible changes induced at micro level by hydraulic effects. An alternative procedure is described, which seems to improve the evaluation of rock degradation at micro scale.

The paper presents the results from a preliminary study focused on the influence of pore fluid salinity on the shear strength of a soft clay from New South Wales (Australia). Direct shear tests (DST) were carried out on natural specimens using pore fluids with different salt concentrations. Electrical conductivity measurements were performed on the squeezed pore water after shearing to quantify changes in salinity of the soil pore water. Strength parameters showed a clear dependency of the pore fluid. Changes in c' and φ appear to be controlled by two factors: (i) initial salinity, and (ii) extent of the concentration gradient. Results from mercury intrusion porosimetry tests demonstrated the influence of changes in pore water salinity on the evolution of the dominant pore size. It was in agreement with macroscopic observations. Implications for further laboratory testing are highlighted in the paper.

This paper proposes a coupled chemo-poromechanical model for the excavated damaged zone located at the interface between the injection well cement and the caprock in the context of CO2 geological storage. The model relies on a simplified chemistry of carbonates precipitation induced from the well cement carbonation. Crystallization pressure induced by calcium carbonates produces tensile stress concentration at cement-caprock interface in the cement sheath which may lead to permanent damage. This poromechanical model relates a macroscale formulation with an insight into material microstructure through pore size distribution changes induced by crystallization.

Liquefaction of cargo in a bulk carrier can cause the cargo to shift, which in turn can cause a ship to list and eventually can cause the ship to capsize. When liquefaction occurs, a material undergoes a transition from a solid to a liquid state and, in general, it is caused by the pore water pressure increasing above the total stress and overcoming the effects of cohesion (i.e. shear strength becomes negligible). In this paper, a number of iron ore samples, representing loosely the range of iron ore cargos from around the world, are characterised and tested. The grain size distribution and particle density were determined along with the tests which are prescribed by the International Maritime Solid Bulk Cargoes (IMSBC) code to assess the liquefaction potential: the Proctor/Fagerberg test, the penetration test and the flow table test. It is found that the results from these test methods correspond reasonably well; however, they are not applicable for all ore types and the conditions at which the tests are performed do not correspond with the conditions encountered in the ship. Therefore, one cannot quantify the risk of liquefaction based on the results of these tests alone, and further investigations on the liquefaction mechanism and the factors which influence this process are required. Part of these investigations have shown that the liquefaction behaviour is strongly linked to the grain size distribution, both in terms of particle size and grading. It is anticipated that the permeability, compaction and water retention behaviour are also of influence in determining liquefaction potential and are governed, in part, by the grain size distribution. Examples of these properties are presented, although the experimental programme is still ongoing.

The presence of a moving fluid in porous media modifies their mechanical response. In particular, the deformation of rocks originate from lithostatic compression, pore-fluid pressure and thermal stresses. This paper introduces an original application of the hypercomplex numbers known as Quaternions to model non-isothermal processes in porous rocks. The general thermoporoelastic linear theory is introduced in four dimensions and reformulated as a set of quaternions. The need of the fourth dimension appears naturally because of the pores' presence. It is shown that a minimum set of four independent experimental coefficients are necessary for the coupling of four strain tensors: two for the bulk porous medium, one for the fluid, and one for the total thermal expansion. Once a basic set of parameters are defined, any other coefficient can be deduced algebraically. This formulation could become a new mathematical tool to represent thermoporoelastic phenomena because includes both, the fluid pressure changes and the temperature changes.

The analytical solutions for the inception of strain localization in unsaturated elastic-plastic porous materials have been implemented into the constitutive driver for bounding surface plasticity model (Khalili et al., 2008). The solutions are based on the definition of effective stress proposed by Khalili and Khabbaz (1998), which is backed up by a substantial amount of experimental evidence. The strain localization behavior of unsaturated soils is further illustrated on the example of Bourke silt from Bourke region of New South Wales, Australia. To this end, the silt is subjected to three series of drained plane strain compression tests whereby the initial net mean stresses and suctions correspond to the range of initial overconsolidation ratios between 1.26 and 6.67. It is found that the axial strain at the inception of strain localization sharply decreases in a nonlinear fashion with the increasing overconsolidation ratio.

An effective pore pressure model is used to predict the mechanical effect induced by in-pore partial freezing of a liquid phase initially saturating a cohesive porous solid. This allows discussing the influence of the thermodynamic and poroelastic properties of the different constituents of the unsaturated porous material on its strain under drained or undrained conditions.

The combined effect of flow induced by the increment of vertical stress and by the presence of a constant electrical potential is analysed using one-dimensional consolidation theory. Electro-hydro-mechanical coupling is considered. Data from oedometer tests performed on saturated white kaolin specimens, in which a DC voltage was applied during the entire loading period, are analysed. The long-term displacements observed are explained considering the contribution of voltage, constant in time, after the end of the hydrodynamic consolidation. This corresponds to consider the validity of the classic one-dimensional consolidation theory, assuming hydro-mechanical coupling, to which the term for voltage is added.

This paper describes a field-scale experiment on gas transport mechanisms performed at the Andra Underground Research Laboratory in a clay rock. The experimental layout consists of two parallel boreholes that are equipped with multiple packer completions delimiting three intervals each and which continuously monitors the pore pressure evolution of the clay rock. Nitrogen gas is injected in the middle test interval of one of the boreholes at increasing constant rates. The experimental data collected so far are presented along with their interpretation by means of 1D and 3D numerical modeling of the boundary value problem. The numerical results show that a predictive model as two-phase flow approach is able to reproduce experimental observations in large scale system, as far as the injection flow rate and the gas pressures remain moderate. Moreover, permeability is not modified by gas injection, which indicates that the rock mass is not damaged by the gas pressure increase during the test.

Because of their mineralogy, active clays are very sensitive to changes in the type and concentration of species dissolved in the pore water. At a molecular level, this sensitivity can be explained by variations in the short range interaction forces acting between clay platelets immersed in the pore water. While models based on equilibrium of short range interaction forces can be used to predict the volumetric behavior of dilute clay suspensions, different approaches must be invoked for real soils. Natural and compacted soils react differently from dilute suspensions to chemical changes because of their fabric. It is, therefore, not possible to derive reliable relationships (at least from the quantitative point of view) describing the chemo-mechanical behavior of active soils solely on the basis of mineralogical and chemical properties. Both microscopic experimental evidences and modeling approaches are used here to analyze the effects imparted by fabric on the coupled hydro-chemo-mechanical behavior of an active clay soil.

The factors that contributed to the initiation of a triggering mechanism in a shallow landslides induced by rainfall are investigated in this work at laboratory scale. The aim of the work was to characterise the behaviour of the soil in triaxial tests, in the light of the possible failure mechanisms in a slope subjected to rainfall. The material study is a silty sand from a steep slope in Ruedlingen in the North-East of Switzerland, where a landslide triggering experiment was carried out. Conventional drained and undrained triaxial tests for the water phase were conducted to detect critical state conditions as well as peak shear strength as a function of confining pressure for three different water content related to the in situ one. Soil specimens with three different gravimetric water contents were exposed to stress paths simulating the in situ anisotropic compression followed by a decrease of mean effective stress at constant axial load. Possible unstable response along the stress paths analysed was investigated by means of second order work.

This paper presents an alternative approach for interpreting unsaturated soil behaviour, which is built in the space of stress versus degree of saturation. A new volume change equation is proposed in terms of stress and degree of saturation, to give a better explanation to the non-linear change of soil compressibility under constant suctions. An alternative approach to simulate hydraulic hysteresis and hydro-mechanical interaction is then introduced, which enables the calculation of the effective degree of saturation under complex stress and suction paths. The loading-collapse yield surface is derived based on the proposed volume change equation in the plane of the effective degree of saturation and the Bishop effective stress. The proposed volume change equation and the corresponding yield surface are generalized to three-dimensional stress states by incorporating with the Modified Cam-clay model. The proposed model is validated against a variety of experimental data in literature.

To elucidate the question of evolution of effective unsaturated permeability of porous media with cracking, an original numerical approach is developed in this work. It consists of a discrete modeling of pores network as a connected channels (1D elements) of various shapes. While number studies and observations confirm an increase of intrinsic permeability of porous materials when an increasing cracking takes place, little is known about evolution of unsaturated characteristics such as isotherm absorption curve or relative permeability of a porous material when cracking state evolves. Spatial distribution of pores, as well as the distribution of hydraulic conductivity and specific surfaces of pores, follows some chosen statistical laws empirically defined from observations and characterization of the structure of studied material (mercury porosimetery, image analysis and so on). In fully saturated conditions, the hydraulic conductivity of a tube is defined using a Kozeny-Carman like-equation. In partially saturated conditions, only tubes with smaller radius that the critical one defined by Kelvin-Laplace law could be fully or partially water-filled. In that case, the flow through a pipe depends not only on the hydraulic load difference on the pipe extremities and its section but also on the capillary forces of meniscus. We use this procedure to quantify the impact of crack evolution on effective properties of a partially saturated stone. In order to account for the cracking evolution, whose origins are not accounted for in this paper, an increasing number of tubes is introduced into the initial pores network. The partially saturated effective properties of damaged stone are then identified numerically. The results of numerical simulations show that cracking modifies significantly not only the intrinsic permeability of stone but also the retention curve and its relative permeability. These modifications are such that close to saturation for a given suction, the damaged material is under-saturated as compared to healthy one. In the simulations performed here, the intrinsic permeability of damaged material is up to three orders greater than the one of undamaged material. Otherwise, the relative permeability of damaged stone is found to be smaller than that of undamaged material.

The soil water retention curve (SWRC) represents the relationship between capillary pressure (matric suction) and water content. It is one of the fundamental characteristics of unsaturated soils. Basic properties of unsaturated soils such as shear strength, volume change behavior, and coefficient of permeability are closely related to the SWRC. SWRC is, usually, determined at zero confining pressure and is used, afterward, to describe soil behavior such as shear strength at both zero and nonzero confining pressures. As determination of SWRC is a time consuming task, there is a great appeal to find suitable numerical schemes and simulation tools which can estimate the retention behavior of soil at different mechanical and hydraulic conditions. One of the newly introduced simulation techniques for two-phase flow in porous media is pore network modeling. Pore network modeling has not yet been much introduced in unsaturated soil mechanics. In this study, pore network modeling is used to study the effect of stress level on SWRC. For this purpose, first, the main characteristics of a 3-D pore network model which affect its efficiency in SWRC modeling are found. Coordination number, mean pore radius, aspect ratio, and pore distribution standard deviation were found to highly influence the simulated SWRC. Based on these findings, a pore network is constructed so that it can resemble the real soil pore structure. The best matching parameters were obtained by comparison of the simulated SWRC and the experimental one. This was done by an error minimization process. In order to generate the pore network, available experimental data of SWRC (at zero confining pressure) is used and SWRC at other stress levels is subsequently generated using the initial pore network model. The SWRC results of the pore network model for each stress level are in good agreement with the experimental data. Thus, a suitable pore network generated from SWRC (at zero confining pressure), can be used to simulate SWRC at other stress levels. It is observed that the structural parameter controlling throat radii as well as coordination number have to be changed when stress level changes in order to be able to match SWRC at other stress levels.

The drilling of storage tunnels generates an Excavated Damaged Zone, where clay-rock properties could change due to the presence of fractures. It's also expected that underground water seepage will contribute to argillite self-sealing. To simulate fractures responses to water seepage and mechanical loading, experimental procedures are developed on fractured samples. The specimen is then placed in a triaxial cell and the device is connected to four LVDT sensors which provide information about argillite deformation due to swelling or crushing. Under 3 MPa confining pressure, LVDT sensors exhibit the crushing of the macro-cracked sample. After water injection at a flow rate of 0.05 mL/min, the sample water permeability decreases rapidly to reach a value close to undisturbed sample permeability K_w=8.7 10^-20m² . When gas is injected, the permeability increases. At the end of experiment, the fracture was visualized using a 3D optical microscope highlighting its complete closure and the self-sealing phenomenon.

The procedure of identification of linear and non-linear drag parameters of flow of liquid in high permeability materials by U-tube method is presented. The experiments are based on measurements of pressure oscillations in liquid and direct computer data acquisition. The macroscopic model takes into account inertial forces, gravity, and interaction of oscillating liquid with porous material and U-tube walls. The calibration of the U-tube system allows to determine parameters of interaction of liquid with tube walls. The drag parameters are determined numerically for porous foams by fitting model predictions to experimental data.

This study compares minutes-long microindentation creep experiments on cement paste with years-long macroscopic creep experiments on concrete. For both cement and concrete samples, after a transient period their creep function was well captured by a logarithmic function of time. The creep modulus of various concrete samples was estimated from microindentation tests on cement pastes combined with micromechanical model. The estimated moduli were very close to those calculated directly from uniaxial compressive creep tests on concrete, which proves that minutes-long microindentation creep test can give access to the long-term creep properties of concrete. Key words: basic creep, long-term creep, microindentation, cement, concrete

The thermo-poro-elastic response of porous media to changes in effective pressure and temperature is of major interest in various fields of reservoir usage, e.g. energy storage, geothermal energy and shale gas extraction. The change of the pore pressure of an undrained rock specimen during heating can be expressed by the thermal pressurisation coefficient, which relates the induced pore pressure change to the applied temperature change. Various studies investigated the poro-elastic and thermo-elastic behaviour of reservoir rocks, separately. But in geothermal reservoirs and in reservoirs used for energy storage, temperature and pressure will change simultaneously due to the injection of fluid. The reservoir rock consists of the solid framework and the fluid inside the pore space. Due to the different thermal expansion of these components, a temperature change causes a decrease or increase the reservoir pressure. Such a thermal pressurisation is more pronounced for undrained conditions and for high effective pressures. Within this study, non-isothermal hydrostatic compression tests were performed on jacketed cylindrical rock specimens of 10 cm length and 5 cm diameter. A major focus of this study was the pore pressure build-up within the specimen, which was placed inside a high pressure and temperature test assembly. In order to measure the pore pressure build-up within the specimen during undrained experiments, a novel fibre optic pressure and temperature sensor was installed within the pressure chamber. In order to quantify the magnitude of thermal pressurisation, we induced temperature change of ~1 K due to rapid hydrostatic loading (10 MPa / 15 min) followed by a 45 min equilibration period of an undrained sample. Here the thermal pressurisation coefficient increases with an increase in effective pressure. The magnitude of the thermal pressurisation coefficient was measured to be more than 2 MPa/K even for moderate effective pressures less than 10 MPa.

The originality of this contribution is to evidence the nature of progressive passage through initially macro-cracked and water-saturated (i.e. self-sealed) COx claystone of given thickness (9.5 to 30mm), by using a mix of gases detected on the sample downstream side by a mass spectrometer accurate to 2-5ppm. We show that gas passage occurs first, by discontinuous capillary passage, i.e. snap off, followed by continuous breakthrough (i.e. permeation) whether the upstream pressure value is increased or not. Upstream gas pressure kinetics are key to observing gas passage.

The effects of internal curing in concrete and the process of delivering water for cement hydration reactions using absorptive aggregates are studied using nanomechanical test methods. Although internal curing has been a focus of research for some time, little study has been made on the microstructure of cement hydration products in internally cured concretes, particularly using direct mechanical measurements. In this paper, the grid nanoindentation technique was utilized to examine microstructural features and mechanical properties of internally cured cement hydration products in concrete materials with fly ash and blast furnace slag. Internal curing was implemented by coarse lightweight aggregates made of expanded slate. Large aggregate length scales allow for identification of interfacial transition zones near porous aggregates and zones far from porous aggregates. Results suggest that internal curing effects are observable by nanoindentation methods. A slower release of water from porous aggregates leads to the development of hydration products with lower than expected porosity and higher than expected densities compared to concrete with conventional aggregate.

Argillaceous rocks are possible host rocks for underground nuclear waste repositories. Such rocks actually exhibit multi-scales heterogeneities, among which the scale of composite microstructure (clay matrix + mineral inclusions) is particularly interesting: the complex matrix-inclusion interaction under hydric and mechanical loadings is a potential source of damage. One important interest of this work is in the in-situ investigations at such a micro-scale, based on the combination of high resolution imaging by environmental scanning electron microscope and digital image correlation techniques. The results show complex localization patterns of deformation as well as some damage phenomena, both under purely hydric and combined mechanic/hydric loadings. Based on these observations, the deformation mechanisms can be identified, and the validation of standard poromechanics to describe the hydromechanical behavior of such rocks is discussed.

This paper proposed an integrated experimental approach to the characterization of CO₂ injection chemical impact on rock dynamic poroelastic properties. Acoustic measurements have been performed on intact and homogenously altered carbonate samples. The obtained results show a decrease of both the drained bulk modulus and the shear modulus under the effect of alteration. NMR measurements and microscanner imaging performed before and after alteration have provided an insight into the alteration impacts at the microscopic scale.

The paper presents an overview of the different attempts undertaken by EDF from the 1980's to now to monitor the water content throughout time in the concrete structures of nuclear power plants. A brief review of existing techniques is proposed, associated to a focus on those chosen by EDF to be tested on site. A feedback on capacitive probes embedded in concrete is provided. An example of metrological requirement for this kind of sensor is presented, in relation with their use in structural analysis. Future research works and considered perspectives are discussed.

Many rigid plastic models, including models for soils and granular materials, are described by hyperbolic systems of equations. Solutions of boundary value problems for such models can include envelopes of characteristics. It has been already shown for several models that solutions can be singular in the vicinity of surfaces coinciding with such envelopes. In particular, the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule. It is evident that such behaviour of exact solutions can cause difficulties with their numerical approximation. Therefore, it is of importance to obtain the exact asymptotic representation of solutions near singular surfaces. In the present paper, the double slip and rotation model is considered. It is shown that plane strain solutions near envelopes of characteristics are singular and the asymptotic representation of solutions is given. In particular, it is demonstrated that the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule, as in the case of the classical rigid perfectly plastic potential model for pressure-independent materials.

By definition, cohesion is the stress (act) of sticking together. Yet, in engineering mechanics, particularly in soil mechanics, cohesion refers to shear strength under zero normal stress, or the intercept of a material's failure envelope with shear stress axis in the shear stress-normal stress space. Cohesion under saturated drained conditions is called drained cohesion and under variably saturated conditions is called apparent cohesion. This paper summarizes and extends recent work showing that there exists a unique functional relation between drained cohesion and apparent cohesion as they share common sources of physical origin, namely, van der Waals attraction, double layer repulsion, cementation, and capillary attraction. All of these forces depend on saturation and material (soil) type. Cohesion and apparent cohesion can be unified by a unified effective stress called suction stress under variably saturated conditions. Cohesion can be unambiguously de-composed into the product of tangent frictional angle and suction stress or tensile stress, and thus can be physically interpreted as the mobilized suction stress to internal frictional stress. Under such conceptualization, suction stress is the true cohesion as it is the stress of sticking granular particles together. Together with the internal friction angle, it can be used to mathematically describe cohesion of all granular materials under variably saturated conditions.

Swelling clays are found in various parts of the world. These clays cause enormous damage to infrastructure and light structures because of swelling and the exertion of swelling pressure when swelling is constrained. However, the swelling phenomenon is critical when these clays are used as barrier materials in environmental engineering applications, oil exploration, clay nanocomposites, etc. In this paper, we present the methodology and results of molecular dynamics simulations of Na-Montmorillonite clay interlayer to find the key mechanisms of swelling during early stage of hydration. Molecular models of Na-Montmorillonite clay are constructed and placed in a solvation box. Molecular dynamics simulations are conducted at room temperature and pressure. Trajectories of individual water molecules are calculated and the evolution of d-spacing and interaction energies between water molecules, cations, and clay sheets with time are computed. These simulations provide and unprecedented insight into mechanisms that lead to interlayer swelling during early stages of hydration.

When pore fluid dielectric properties differ or the composition of the clay minerals in the soil is changed, most clays in general, and swelling clays in particular, exhibit dramatic differences in swelling behavior, mechanical properties and fluid flow response. Our prior work has also shown that in swelling clays, particles "break down" as a result of exfoliation. Thus, it appears that molecular scale interactions between clay and fluids dramatically influence clay microstructure during swelling, and resulting macroscopic behavior of swelling clays. Innovative FTIR experiments have been conducted on undisturbed and disturbed clay samples. FTIR experiments were used to calculate the flow rate of water molecules in the interlayer of Na-montmorillonite. The relative "strength" of molecular interactions between clay and fluids were found and were correlated to the changes in the clay microstructure and macroscopic properties such as swelling pressure, permeability and consolidation. This paper summarizes the use of FTIR as a powerful tool to connect macroscale properties to molecular scale interactions in swelling clays.

In 2005, Hurricane Katrina landed on the southern states of the U.S. and caused more than 1000 deaths and severe property damage. The life loss and property damage were mostly caused by the failure of floodwalls that surrounded City of New Orleans. Several cases of failures were caused by so called "gap formation" and "erosion" which were believed to be due to the dispersive characteristics of expansive clay minerals contained in levee soils. The New Orleans area has wide distribution of expansive clay minerals. Some soils in this area contained as high as 5% montmorillonite soils. In this study, it turned out that the undrained shear strength and erosion resistance of these soils can drop as low as immeasurable range when wet. This paper experimentally and analytically addresses the behavior of expansive soils contained in levee soils that triggered the failure of the levees under heavy rain and overtopping condition.

This paper details the fundamental concepts of a proposed approach along with the step-by-step procedural details for modeling time-dependent deformation of natural expansive clay soils. Estimation of the soil suction variations within the active zone depth and the corresponding soil modulus of elasticity with respect to the suction variation form the key components of the proposed approach. The soil suction variations within the active zone of the expansive soil profile are estimated using the soil-atmosphere commercial model VADOSE/W. The soil deformation (shrinkage/swelling) is estimated based on the soil structure constitutive relationship for unsaturated soils considering the variation of modulus of elasticity with respect to suction. The proposed approach, which is referred to as the modulus of elasticity based method (MEBM), reasonably well reproduced the deformations of previously published field study results of a natural expansive soil caused by changes in suction over time taking account of environmental factors.

This paper presents the results of a series of carefully conducted experiments to characterize the stress-dependent permeability of tight oil and gas shales. Specifically, the applicability of the Constant Rate of Strain (CRS) consolidation test to obtain continuous stress-dependent permeability data on tight shales is rigorously investigated. The CRS method has been widely used for geotechnical testing of very compressible sediments but has never been tested for very stiff and low permeability shales. The CRS method allows only for drainage from one end of the test sample and fluid flow is blocked at the other end while the sample is being compressed at a constant strain rate. An analytical solution is used to calculate the permeability from an idealized pore pressure distribution within the test sample. The tests were performed on a sample of Mancos shale trimmed in a thin disc-shape using a modified high-pressure triaxial cell. The paper shows that the CRS method can be used to reliably obtain continuous stress-dependent permeability data during consolidation of very low permeability shales provided poro-elastic effect is accounted for in the pore pressure dissipation calculation. A simple modification of the one-dimensional consolidation equation was found to be sufficient to account for the poro-elastic effect. The permeability values from the CRS tests were found to be comparable to those obtained from the Pressure-pulse Decay Permeability (PDP) and the Constant Pressure Gradient Permeability (CPGP) tests. Klinkenberg, non-Darcy inertial flow, and pore pressure variations effects were included in the gas permeability calculations. The need to account for poro-elastic effect in the determination of stress-dependent permeability from the CRS test requires careful determination of the Biot coefficient α and Skempton's pore pressure parameter B. It is shown that both α and B-value change significantly during compaction of the shale, and these changes have to be accounted for in the determination of permeability from the CRS test.

The correspondence principle is widely used to estimate the effective behaviour of non-ageing linear viscoelastic composites, as it allows to take advantage of homogenization approaches originally developed in the elastic framework. However, this principle is no longer valid when the phases exhibit ageing. The approach proposed in this paper overcomes this limitation. It allows the use of homogenization of random media on composites made up of isotropic ageing linear viscoelastic phases. It can be applied to estimate the effective viscoelastic behaviour of solidifying composite materials, that is porous materials subjected to gradual precipitation of solids into pore space. This theory developed by Bažant shows that even if the behaviour of the precipitated material is non ageing, the effective behaviour exhibits ageing due to the microstructure evolution with time. Modelling the solidifying material as a set of fictitious ageing linear viscoelastic phases, it is possible to investigate other precipitation mechanisms than the parallel arrangement initially considered by the solidification theory.

In this paper, we are focusing on modeling plastic deformation and effects of water saturation for a class of mortar subjected to both mechanical loading and desiccation process. First, a micro-mechanics model is proposed for the mortar which is considered as a two- phase composite (cement paste and sand grain) at the mesoscale. The cement paste is a porous material with an elastoplastic behavior whose solid phase obeys the Drucker-Prager criterion. The sand grains are considered as rigid inclusions and embedded uniformly in cement paste. With a nonlinear homogenization technique, a macroscopic strength criterion is presented for the macroscopic behavior of mortar composite, considering the effects of pores and inclusions. Then the influence of saturation is considered in the modeling, and the concept of effective stress for the influence of water saturation is introduced. The model is assessed by comparing the numerical results and experimental data with different degrees of saturation and confining pressures.

A combined homogenization/thermodynamics framework is presented for constitutive modelling of friction-induced inelastic deformation and damage by microcracking as well as their coupling with the effect of pore pressure for microcracked solids. The key for thermodynamic formulations of the cracked system weakened by pores is to determine the free energy and then a complementary energy by a transformation of the former. It is shown that the pore pressure is involved in both the macroscopic stress and the local stress. A Coulomb-type friction criterion function of this local stress and a strain-energy release rate-based damage criterion are adopted respectively for describing evolution of inelastic deformation and damage propagation. The proposed unified model contains a back-stress hardening/softening term. The number of parameters in the current model can be largely reduced when compared with phenomenological models.

In this paper, we focus on the prediction of the elastic and linear viscoelastic properties of porous solids based on their microstructure for the entire range of porosity. Both analytical models, namely Mean Field theory for porous solids and beam theory for cellular solids, and Finite Elements method are used and the corresponding results are compared. For low porosity, Mean Field models yield good predictions. However, when increasing the void concentration and the pores become macroscopically interconnected, only the Differential Method continues to give good estimates. The potential of Mean Field models suitable for highly porous solids to predict the response of cellular materials is also investigated.

The generalized Maxwell's method is developed for the calculation of the static effective parameters of poroelastic medium containing a random set of ellipsoidal anisotropic poroelastic inhomogeneities (poroelastic composite material). It is shown that the Maxwell method leads to the equations for the effective poroelastic constants that coincide with equations obtained by other self-consistent methods. Moreover, the Maxwell method allows deriving the so-called "cross-property relations", i.e. relations between different effective poroelastic constants that were established earlier for some particular cases.

In the case of electrically charged porous media as clays, a precise definition of swelling pressure has already been given in our preceding works using the periodic homogenization medium for two scales (nano/macro) (Moyne and Murad, 2002, 2006). The modeling at the nanoscale is based on the Poisson-Boltzmann equation to describe the electrostatics. However, for montmorillonite clays, if for a monovalent compensating cation (eg Na), swelling is always observed. For divalent ions (eg Ca or ions of higher valence), on the contrary, shrinking phenomena can be observed. As the Poisson-Boltzmann equation always predicts swelling, a more precise description of the physics at the nanopore level is needed. Therefore, a pore-scale model is developed within the framework of Statistical Mechanics in conjunction with a thermodynamic approach based on Density Functional Theory.

An effective model is derived for periodically layered poroelastic media, where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. Each layer is homogeneous, described by Biot's equations of poroelasticity. The proposed model has only real-valued frequency-independent effective coefficients determined analytically exclusively by the physical parameters of the layers. It serves as an alternative to the existing models with frequency-dependent effective elastic properties. Homogenization is based on asymptotic expansions with multiple spatial scales and results in equations of motion containing higher-order derivatives. It is valid for wavelengths much larger than the period of the system. This approach, being widely used in elasticity, is extended to poroelasticity in this work. The exact analytical solution, obtained by the application of Floquet's theory to poroelastic composites, is used to validate the model.

Human Haversian cortical bone has a composite microstructure that is reinforced with hollowed long fibers called osteons. The biological tissue is highly heterogeneous and changes with age. Following hormonal modifications, osteoporosis is developed by nearly a third of women over 65 and the pathology significantly increases bone porosity. Treatments using biphosphonates to slow down the excessive bone resorption can lead to reduced osteon counts. We present a study of relevant morphological parameters to characterise pathological microstructural evolutions of bone and we detail its implementation into Monte Carlo synthetic bone 3D microstructures. The results are validated against explicit real bone models and show the effects of either a porosity increase or a fiber content reduction on the internal strain distribution.

The equivalent inclusion method (EIM) was initially proposed by Moschovidis and Mura [12] to find an approximate solution to the problem of two ellipsoidal inhomogeneities embedded in an infinite medium. More recently, it has been applied to large assemblies of inhomogeneities [7]. Although less accurate than traditional (e.g. finite elements) numerical techniques, the equivalent inclusion method is an attractive solution for numerical homogenization problems. Indeed, it leads to relatively small linear systems, and does not require time-consuming preliminaries (such as mesh creation). However, the standard EIM has some shortcomings which are mainly due to the fact that point collocation techniques are used to discretize the underlying integral equation [6, 12]. In contrast, the Variational Equivalent Inclusion Method (VEIM) introduced here uses Galerkin techniques to carry out this discretization. In this paper, we briefly recall the fundamentals of the standard EIM. We then present the VEIM and show that it can lead to rigorous bounds on the macroscopic properties. Finally, some illustrations of the method are presented.

To reduce the environmental impact of buildings, light-weight concrete made of renewable aggregates is a promising solution. This work aims to study hygromechanical properties of wood-aggregate concrete (composed of cement paste and wood shavings) upon drying by using both experimental and modeling approaches. To study the effect of the mechanical properties of the different constituents on the hygromechanical behavior of this concrete, we performed compression tests to determine the Young's modulus of the samples and measured shrinkage strains upon drying of mixtures with identical contents of wood but various cement-to-wood mass ratios. To analyze the compression data, we developed a first model based on homogenization theory using the self-consistent scheme which allows to link the evolution of Young's modulus over time with the volume fractions and elastic properties of the various phases of the concrete. A second model coupling desorption-induced strains and water transfer was derived to explain the measured shrinkage strains.

Biot-Gassmann relations that link the change in effective elastic properties of fluid-filled porous media to the change in pore fluid properties are not applicable for solid-filled porous media. Such problems arise when concerned with pore-filling materials with non-negligible shear modulus; examples of such materials include molten lava, cold bitumen, kerogen, clay, etc. In this paper, we discuss how effective solid-filled bulk and shear moduli of a solid-filled porous medium (or composite) are explicitly related to other effective stiffnesses and pore-filling solid elastic properties. Such relations are known as substitution equations and are particularly useful in exploration geophysics, for example in reservoir monitoring. We present new equations which improve on previously suggested solid substitution relations by Ciz and Shapiro.

Alkali-Silica Reaction is a deleterious chemical reaction which affects concrete due to the swelling of a gel close to reaction sites generally located in or at the surface of reactive aggregates. The pressure build-up due to the swelling of the gel can lead to fracture of the interface between the aggregates and the cement paste, and cracking in the cement paste. Our goal is to predict the anisotropy of the macroscopic expansion of concrete through the computation of the crack directions. The choice of the micromechanical representation of the concrete has been helped by comparison of different estimates with finite element simulations on typical crack patterns. In this article we explain the micromechanics modeling.

Hypoplastic model is becoming very popular for granular materials. Unlike elastic-plastic models, there is no clear boundary between elastic and plastic deformations in hypoplastic model. The behavior of material is described with a nonlinear tensor equation and a single set of parameters. In this paper, an updated hypoplastic model is used to simulate plane strain tests from Discrete Element Mothod (DEM) simulations. A DEM simulation of plane strain test is carried out to compare with the hypoplastic model. The material parameters of the hypoplastic model are determined according to the stress-strain curve and volume strain curve of the DEM simulation. The results of DEM simulation and hypoplastic model are compared and discussed.

Ultrasonics is an important diagnostic tool for bone diseases as it allows for a non-invasive assessment of bone tissue quality through mass density-elasticity relationships. The latter are, however, quite complex for fluid-filled porous media, which motivates us to develop a rigorous multiscale poromicrodynamics approach valid across the great variety of different bone tissues. The wave propagation problem, comprising three sets of equations (equation of motion, fluid flow, and constitutive equations for the solid and for the fluids), is solved for a double porous medium, in which the lowest scale pore space is undrained. Results show that 2.25 MHz acoustical signals transmit (low-porosity) cortical bone only in the form of fast waves, agreeing very well with experimental data, while both fast and slow waves transmit large porosity trabecular bone.

Hardwoods show a very complex, hierarchically organized microstructure. Slight structural differences at various length scales bring about a huge variety of hardwood species. This motivates the development of a micromechanical model for hardwood. Since differences in the microstructure of the material can be considered in the model, it offers the opportunity to explain the variability of mechanical properties of the whole class of hardwood. The micromechanical model is formulated in the framework of poroelasticity. In this contribution, poroelastic properties at different length scales of the material are discussed. Validation of the micromechanical model is based on an extensive experimental database covering elastic properties and microstructural characteristics of different temperate and tropical hardwood species. Exemplary parameter studies demonstrate the ability of the model to study the contribution of specific microstructural characteristics to the load transfer and the deformation characteristics of wood.

In the 1930s, Freyssinet presented a model describing that the strength of cement paste decreases with increasing capillary porosity. He proposed that uniaxial compressive strength of cement pastes is proportional to a volume quotient which is nowadays referred to as "gel-space ratio". In the 1970s, Fagerlund found out that capillary porosity is not the only governing factor because he observed that the final strength of substoichiometric cement pastes increases with decreasing initial water-to-cement mass ratio. However, due to limited microstructural insight, he could only propose an empirical description of the observed effect. We here provide more insight into how microstructural properties of cement paste influence its macroscopic compressive strength, based on the experimentally confirmed elasto-brittle micromechanics model of Pichler and Hellmich [CemConRes, 41(5) 467-476, 2011]. Gel-space ratio is shown to be equal to the solid volume fraction of a "hydrate foam" which is defined at the scale of a few microns and which exhibits a (quasi-)polycrystalline morphology of needle-shaped and isotropically oriented hydration products with capillary porosity filling the space in between. The model confirms that the material strength of cement pastes is not only determined by the capillary porosity, but unhydrated clinker grains (which are embedded, as inclusions, in the hydrate foam) act as reinforcements which increase the macroscopic strength; and that this is practically significant for substoichiometric mixes at large maturities, see Pichler et al. [CemConRes, 45(1), 55-68, 2013].

Concrete aggregates are covered by 15-microns-thick interfacial transition zones (ITZs) exhibiting larger porosity, but smaller stiffness and strength than the adjacent bulk cement paste. This renders the immediate vicinities of the aggregates' surfaces as the weakest links within the microstructure of concrete. Onset of cracking, representing the elastic limit of the material, typically starts in these regions. Post-failure concrete fragments give insight into the debonding processes close to the aggregate surfaces: partly the aggregates have separated cleanly from the ITZ, and partly a thin layer of cement paste remains attached to the aggregates. This is the motivation to investigate the possibility of two different types of debonding: ITZ-aggregate separation and ITZ failure. Therefore, concrete is idealized as a perfectly bonded three-phase composite (consisting of spherical aggregates, surrounded by ITZs, and embedded in a cement paste matrix). At the concrete-related scale, ITZs are represented as 2D interface phases because the ITZ thickness of 15 microns is negligible as compared to the typical dimensions of the aggregates and of the cement paste matrix. At an even smaller scale, however, the ITZs are resolved as three-dimensional spherical shells. Based on this multiscale model, we derive, by means of a continuum micromechanics approach, traction vectors acting on aggregate surfaces and of full three-dimensional stress states within representative ITZ volumes. These microscopic fields of traction vectors and ITZ stresses intervene in microscopic tensile strength criteria for ITZ-aggregate separation and for ITZ failure, respectively. Comparison of model predictions with available experimental data implies that onset of concrete cracking is more likely to happen by means of ITZ failure than by ITZ-aggregate separation, if representative concrete volumes are subjected to compression-dominated types of loading; while under tension-dominated types of loading, also ITZ-aggregate separation might well govern onset of concrete cracking.

The effect of porosity on the thermal expansion coefficient of porous materials is studied for two different cases. The first case concerns the thermo-elastic evolution of the porosity of a given material for which it is shown that the drained thermal expansion coefficients increase with the porosity increase. The second case concerns porous materials with similar solid phase and different porosity which is studied using the homogenization method. A parametric study shows the coupled effect of the thermal expansions and bulk moduli of the solid constituents on the thermal expansion coefficient-porosity relationship. Depending on the combination of the parameters, the thermal expansion coefficient can increase or decrease with the porosity. The effective thermal expansion increases with the porosity when a solid constituent has higher thermal expansion but lower rigidity than the other constituent. Generally, there is no unique thermal expansion-porosity relationship that can be applied to all porous materials.

Bone tissue is a living biological entity. In particular, it is able to renew itself, which is key for maintaining its mechanical integrity necessary for fulfilling fundamental tasks such as providing protection of organs and facilitating locomotion. Moreover, bone is also able to accommodate to a long-term changing mechanical loading (as it may occur during exercise regimes, bedrest, or exposure to microgravity). The process responsible for accomplishing either task is termed bone remodeling, involving removal of mature bone tissue and subsequent formation of new bone tissue. Bone remodeling is driven by complex actions of biological cells and biochemical factors, and it is sensitive to the mechanical loads applied onto the skeleton. As for the latter, the exact mechanical stimulus, which is sensed and transduced into bone remodeling events, is still a matter of debate. In this paper, we study how hydrostatic pressure that occurs in the lacunar pore space of cortical bone (hosting osteocytes, thus the cells believed to be mainly responsible for triggering the mechanobiology of bone remodeling), accumulating due to (macroscopically applied) mechanical loading, is able to drive bone remodeling. For determination of the hydrostatic pressure, we make use of a micromechanics-based poroelasticity model. Finally, we compare simulation results with pertinent experimental and clinical data, in order to assess the role of the hydrostatic pressure in the lacunar pores for regulating bone remodeling.

It is fairly well accepted that the "lubricant effect" of water or other fluids is a key to the creep behavior of a large range of bio- and geomaterials. However, a more precise theoretical assessment is found, at best, rarely. As a remedy, we start here from 2D viscous interfaces where shear tractions trigger in plane displacement discontinuity rates and quantify their interaction with a surrounding linear elastic solid phase in the framework of continuummicromechanics, particularly bymeans of the influence tensor concept and the theory of "sharp" inclusions. This allows us to assign macroscopic creep and relaxation behavior to interface density and viscosity, thereby closing a gap between material physics and engineering mechanics.

The elaboration of green building materials is nowadays a field of intensive researches aiming at reducing human activity impact on the environment. In particular, the vegetal fibers are more and more considered to be an alternative renewable and natural raw material in building construction and thermal renovation. This work, carried out in the framework of research program PROMETHE, is devoted to the evaluation of thermo-hydro-mechanical properties of an insulated material elaborated using cereal straw and various natural mineral cements. In the objective to elaborate an optimal material in respect with its mechanic, hydraulic, thermal, economic and ecologic properties in short and long time, we performed, in one hand, a multiscale experimental characterization of constituents and, in the other hand, numerical upscaling simulations. In first glance the new elaborated material represents dense straw fibers plugged into a matrix of mineral cement. The mechanical properties (Young's modulus and Poisson coefficient), thermal properties (thermal conductivity, linear thermal expansion coefficient and thermal capacity) and hydraulic properties are evaluated using a one-step homogenization Mori-Tanaka scheme. While the insulating developed material must be an excellent thermal insulating it must match in the same time the standards in terms of mechanical and hydraulic ones. So, it is necessary to search the best mixing volume fraction of mineral matrix and straw fibers in order to satisfy simultaneously thermal, mechanical and hydraulic standards for an insulating material. The numerical simulations and the first laboratory results show that it is possible to obtain such properties for various formulations of reinforced composite using either lime-based mortar or plaster as mineral matrix and different volume fractions of straw fibers.

The behavior of a porous material on which air-solid surface tension effects are not negligible is studied experimentally and theoretically. Overall properties were measured on mixtures of foams and pastes. Theoretical estimates were obtained in the framework of an upscaling approach. It was observed and predicted that the overall properties of the porous medium depend upon the deformability of the pores in the elastic regime whereas in the plastic regime, the porous medium yield stress is the same as the matrix yield stress. Deformability of the pores is accounted for by a capillary number defined as the ratio of the matrix elastic modulus to the pore capillary pressure in the linear regime and as the ratio of the matrix secant modulus to the pore capillary pressure in the non-linear regime. This non-linear capillary number tends toward zero when the plastic plateau is reached.

The main objective of the present study is to determine the macroscopic strength of porous materials having a Drucker-Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. These two scales are assumed well separated. Based on available results by Maghous et al. (2009), we first derive a preliminary closed-form expression of the strength for a dry porous medium having a matrix obeying to a general elliptic criterion. The methodology to formulate this macroscopic strength criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. Taking advantage of these results, we implement a two-step homogenization procedure which delivers an analytical expression of the strength of a dry, double-porous media with a Drucker-Prager solid phase at microscale. Finally, we extend the obtained results to saturated double-porous media with the different pores pressures. The results are discussed and assessed by comparison to recently published results.

We present first results of a coupled hydro-mechanical modelling approach for a so-called benchmark fault zone set-up, built according to characteristic features of fault zones as they can be found in the subsurface of North-European lowlands. Several layers down, to a depth of 5000 m, are considered, separated by a fault zone, in which geothermal anomalies can expect to be found, suitable for geothermal heat production. For modelling we apply the COMSOL Multiphysics code. The two-way coupling between hydraulics and mechanics in a poroelastic approach is outlined. We conclude that using poroelastic and hydrogeological parameters in the expected range, the deformations at the ground surface are marginal and also the hydraulic gradient in the usual range is quite irrelevant.

In this paper, the extended finite element method is investigating for the solution of the plane strain problem of a hydraulic fracture propagating in an impermeable elastic medium. This proposed method is based on an integration of a standard displacement-based approximation near a crack, a field of displacement discontinuity, and a partition of unity method for the near-crack front asymptotic fields. Therefore, this technique can effectively avoid remeshing by using the mesh to represent independently the entire fracture when modeling fracture growth, and the angle of the fracture propagation is determined by the Griffith's criterion at each time step. With the model of hydraulic fracture propagation, a hypothetic numerical experiment is conducted. Results demonstrate that XFEM is an efficient tool to simulate the hydraulic fracture propagation.

Back analysis is commonly used in identifying geomechanical parameters based on the monitored displacements. Conventional back analysis method is not capable of recognizing non-linear relationship involving displacements and mechanical parameters effectively. A hybrid model for displacement back analysis which combined Least Square Support Vector Machine (LSSVM), Artificial Bee colony (ABC) and numerical analysis has been investigated for estimating the magnitude of horizontal in situ stresses based on borehole displacements. In the displacement back analysis, a hybrid LSSVM-ABC model is used to identify horizontal in situ stresses. LSSVM is used to represent the non-linear relationship between the maximum and minimum horizontal in situ stresses (σ_H, σ_h) and borehole displacement. ABC is used to search the set of unknown horizontal in situ stresses based on the objective function. Numerical analysis is used to create the necessary training and testing samples for the hybrid LSSVM-ABC model. Results of numerical experiments demonstrate that a hybrid LSSVM-ABC model for displacement back analysis can effectively identify horizontal in situ stresses based on wellbore movements during drilling.

Massive CO₂ injection into subsurface formation involves interactions among pressure and temperature change, chemical reactions, solute transport, and the mechanical response of the rock. This is a coupled thermal-hydraulic-mechanical-chemical (THMC) process. Numerical modeling of CO₂ injection around the wellbore area can provide information, such as changes in rock properties, as well as stress and pressure changes. This helps better predict injectivity evolution and leakage risk. In this paper, finite element methods are employed to analyze the transient stress, pressure, temperature and chemical solute concentration changes simultaneously around an injection well. Particularly, the stabilized finite element scheme is used to overcome these numerical oscillations in solving the transient advection-diffusion equations involved in the heat transfer and solute transport processes. Finite element analysis of stress and pressure changes in the rock around a wellbore subjected to thermal and chemical effects will be shown in a numerical experiment.

A dual-porosity model is proposed to describe low and high valence ion transport in swelling clays characterized by three separate-length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the finest (nano) scale the medium is composed of charged clay particles saturated by aqueous electrolyte solution containing monovalent and divalent ions. Assuming local equilibrium with the bulk fluid lying in the micropores, the disjoining pressure is computed exploring the tools of Statistical Mechanics based on an integral equation theory which, in contrast to monovalent ions, predicts attractive forces between particles for multivalent ions due to incorporation of the ion-ion correlation effects. At the intermediate microscale, the two-phase homogenized system is represented by swollen clay clusters (or aggregates) with the nanoscale disjoining pressure incorporated in a modified form of Terzaghi's effective principle. At the macroscale, the system of clay clusters is homogenized with the bulk fluid. The resultant macroscopic picture is governed by a dual-porosity model wherein ion transport takes place in the bulk solution and the clay clusters act as sources/sinks to the bulk fluid. The quasi-steady version of the dual-porosity model allows to build-up numerically the constitutive behavior of the retardation coefficient governing adsorption within the clay clusters. The three-scale model is applied to numerically simulate the migration of monovalent and divalent ions in a compacted clay liner underneath a sanitary landfill. Owing to the distinct constitutive behavior of the swelling pressure for each ionic species, totally different evolving regimes are observed for calcium and sodium diffusion through the clay liner.

In this paper we present the development of the macroscopic model describing the hydro-mechanical coupling of damaged porous media containing cracks or/and vugs, by using the asymptotic expansion method. The analysis starts at the mesoscopic scale, at which we assume a generic microstructure and the validity of the Biot model in the micro-porous domain saturated by a fluid. In the crack/vug domain, the Stokes equation is assumed. After estimation of orders of magnitude of different terms, the description is rendered non-dimensional and the homogenization process is carried out. It leads to an extended Biot model that possesses the same mathematical structure as the initial Biot model. However, the macroscopic poro-elasticity and the macroscopic Darcy conductivity are modified. In order to illustrate the performance of the model, numerical computations of a macroscopic boundary value problem were performed. The results show practical importance of modifications introduced in the Biot model.

Concrete carbonation is a chemical degradation mechanism compromising the service life of reinforced concrete structures. Using a homogenization approach to upscale the associated reaction-diffusion system given in a porous medium, whose microstructure undergoes an evolution in time, an effective macroscopic limit model is obtained. To lower the complexity of numerical simulations further, an efficient adaptive finite element scheme for the limit problem is presented. The approach is generally applicable to reaction-diffusion problems in porous media.

This paper deals with the acoustics of gas-saturated, rigid, porous medium consisting in damped Helmholtz resonators embedded in a porous matrix. The macroscopic description of this system is established through homogenization method. It is shown that the resonators brought a negative contribution in the effective stiffness of the gas. The atypical features of acoustic wave propagation are determined and the occurrence of a broad band gap and strongly dispersedwaves is discussed according to the characteristics of the porous matrix and of the resonators.

We study the problem of derivation of an effective model of acoustic wave propagation in a two-phase, non-periodic medium modeling a fine mixture of linear elastic solid and a viscous Newtonian fluid. Bone tissue is an important example of a composite material that can be modeled in this fashion. We extend known homogenization results for periodic geometries to the case of a stationary random, scale-separated microstructure. The ratio ε between a typical size of microstructural inhomogeneity and the macroscopic length scale is a small parameter of the problem. We employ stochastic two-scale convergence in the mean to pass to the limit ε → 0 in the governing equations. The effective model describes a biphasic, viscoelastic material with long-time history dependence. Homogenized system describes macroscopically anisotropic media and is more general than the Biot system.

Simulating porous media flows has a wide range of applications. Often, these applications involve many scales and multi-physical processes. A useful tool in the analysis of such problems in that of homogenization as an averaged description is derived circumventing the need for complicated simulation of the fine scale features. In this work, we recall recent developments of homogenization techniques in the application of flows in deformable porous media. In addition, homogenization of media with high-contrast. In particular, we recall the main ideas of the homogenization of slowly varying Stokes flow and summarize the results of [4]. We also present the ideas for extending these techniques to high-contrast deformable media [3]. These ideas are connected by the modeling of multiscale fluid-structure interaction problems.

Physical properties of porous media are inherently determined by their morphological features. Distinctive behaviors of soils, rocks, and cementitious media have traditionally divided researchers into separate communities. To unify these studies in each individual porous media application, a universal poromechanics theory should account for morphological distinctions among these porous media. In this study, the morphological parameters used in composite theory are introduced to formulate a morphologically informed poroelasticity. Corresponding to the underlying morphologies for the two bounds of the bulk modulus, the formulas for the drainage and effective stress of the porous media are derived. For those porous media commonly met in engineering application, e.g. soils, the poroelasticity formulation will be developed in next stage based on the two bound formulation, i.e. by matching the coefficient in the effective stress formula with those of Terzaghi and Biot.

A general approach to modeling chemical degradation processes in cementitious materials, due to combined action of variable hygral, thermal, chemical and mechanical loads, is presented. Mechanics of multiphase porous media and damage mechanics are applied for this purpose, and kinetics of chemical processes is described with evolution equations based on thermodynamics of chemical reactions. The mass-, energy- and momentum balances, as well as the evolution equations, constitutive relationships are briefly summarized. The mutual couplings between the hygral, thermal, chemical and mechanical processes are considered in the equations. Two examples of the model application for analyzing chemo-hygro-thermo-mechanical processes in cement based materials are presented and discussed. The first one deals with the salt crystallization during drying of a concrete wall, and the second one concerns calcium leaching from a concrete wall due to chemical attack of pure water in two different thermal conditions: with and without temperature gradient.

The aim of this paper is numerical analysis of the thermal consolidation processes in the framework of the coupled hydro-thermo-mechanical (HTM) modeling of soils due to mechanical and thermal loads. A fully coupled finite element model for non-isothermal elasto-plastic multiphase materials based on Porous Media Mechanics is therefore developed. In particular, the ACMEG-TS thermo-elasto-plastic constitutive model for variably saturated clayey soils has been implemented in the finite element code COMES-GEO for the analysis of non-isothermal deformable multiphase porous materials. The non-isothermal consolidation of a Boom clay column is studied in order to analyse the coupled effects of mechanical and thermal loads on this material, which is a candidate for an underground nuclear waste storage facility. A preliminary result of a heating case where the temperature is above the boiling value and liquid water phase change develops is also shown.

Experimentally obtained results show that the gradual loss of fine particles during internal erosion affects significantly the mechanical behavior of the soil. To simulate the behavior of sand-silt mixtures in both drained and undrained conditions, a constitutive model based on the introduction of the equivalent mean size and the evolution of the position of the critical state line with fines content for various sand-silt mixtures is proposed. This model describes the influence of the fines content from sand to silt on the overall behavior of soil mixtures and the impact of the decrease of the fines content due to internal erosion.

A three-dimensional finite-difference time-domain (FDTD) algorithm is developed to solve Pride equations to obtain the seismic waves and the accompanying electromagnetic (EM) fields excited by an underground slipping fault. The seismic waves are calculated separately by solving Biot equations using a velocity-stress FDTD algorithm and the PML technique for the truncated boundary. The accompanying EM fields are calculated by the alternating-direction implicit method, which is unconditionally stable and requires much less computation time than ordinary implicit methods. Planar free-surface boundary condition, under which analytical solutions exist, is considered. Local grid refinement is applied to model the high attenuation of the electric field near the free-surface, which is caused by the high attenuation of the slow compressional wave converted at the free-surface. Seismoelectric fields exited by a double couple are calculated as an example. Good agreements between our numerical results and the analytical results show the validity of our FDTD algorithm.

In this contribution, a finite element model for simulating coupled hydromechanic and electrokinetic flow in a multiphase domain is outlined. The model describes CO₂ flow in a deformed, unsaturated geological formation and its associated streaming potential flow. The governing field equations are derived based on the averaging theory and solved numerically based on a mixed discretization scheme. The standard Galerkin finite element method is utilized to discretize the deformation and the diffusive dominant field equations, and the extended finite element method, together with the level-set method, is utilized to discretize the advective dominant field equations. The level-set method is employed to trace the CO₂ plume front, and the extended finite element method is employed to model the high gradient in the saturation field front. The mixed discretization scheme leads to a highly convergent system, giving a stable and effectively mesh-independent model. The capability of the model is evaluated by verification and numerical examples. The numerical analysis shows that the streaming potential peak moves with the saturation front, and hence, measuring the streaming potential can be utilized for monitoring CO₂ flow remotely.

Since early stages of the unsaturated soil mechanics, a long-lasting debate has started on the choice of suitable stress state variables; this has given birth to various frameworks. A central question for the debates was the effective stress formulation for unsaturated soils and efficacy of effective stress approaches to model mechanical behavior of such soils. One important ingredient of all formulations is matric suction (capillary pressure), whether considered as a part of a single effective stress or simply as a separate stress state variable. Therefore, a relationship between matric suction and saturation will always be an inevitable part of any hydro-mechanical model in unsaturated soil mechanics. One should note that we usually measure this relationship at equilibrium state. In geotechnical engineering practice, soil water retention curves which express this dependency are usually measured under quasi-static conditions. Thus, the whole theory of modern unsaturated soil mechanics has been built around soil water retention curves at equilibrium state, which is not the case in many practical situations (e.g., there is no equilibrium during rainfall-induced landslides). It is, therefore, necessary to discuss and disclose the importance of dynamic soil water retention curves and their influence on unsaturated soil mechanics. In this paper, after a brief review of recent researches/advances on nonequilibrium theories of two-phase flow, major consequences of these advancements for unsaturated soil mechanics and potential research directions for theoretical and experimental future works are presented.

This work proposes a model for the reactive transport of CO₂ throughout cement paste under geological storage conditions. Special attention is paid to the modeling of the dissolution and precipitation of the main solid compounds: portlandite (CH), calcium silicate hydrates (C-S-H), amorpheous silica (SH_t) and calcite (CC-). A thermodynamic description of the dissolution of C-S-H is proposed to account for the continuous variation (decrease) of the C/S ratio during the dissolution reaction of C-S-H. The porosity changes induced by the precipitation and dissolution reactions are also taken into account. We simulate by using a finite volume method some experiments reported in the literature and compare our numerical results to these experimental observations.

Coupled THM processes that describe the mechanical behaviour of fluid-saturated porous media are an extension to the classical theory originally proposed by Biot [1]. This extension in now an integral part of geomechanics [2-8], where the concepts are applied in a number of areas, including the deep geological disposal of heat-emitting, high-level nuclear fuel waste, thermal stimulation of resource bearing formations and the use of geologic basins for the permanent storage of greenhouse gases converted to supercritical forms. In addition to the consideration of coupled processes of elastic deformations of the porous skeleton, fluid transport in the pore space and heat transfer encountered in a variety of disciplines in the engineering sciences, it is also essential to accurately evaluate the pore fluid pressure responses where adverse fluid pressures can induce damage in the form of microfracturing of the porous skeletal structure. Investigations dealing with the modelling of THM processes in poro-elastic fluid-saturated media are quite extensive; readers are further directed to recent literature in geomechanics, particularly those conferences devoted to poromechanics and the recent articles on nuclear waste management cited previously, for further information.

Electro-osmosis consolidation is an innovative and effective ground improvement method for soft clays. However, electro-osmosis is also a very complicated process, as the mechanical behaviour, and the hydraulic and electrical properties of the soil are changing rapidly during the treatment process. This makes electro-osmosis hard to describe and simulate. Traditional electro-osmosis consolidation theory cannot provide a satisfactory solution because it does not directly consider the mechanical behaviour, nor the nonlinearity of the mechanical, hydraulic and electrical properties of the soil. A numerical solution for the electro-osmosis consolidation of clay in multi-dimensional domains is presented, with the coupling of the soil mechanical behaviour, pore water transport and electrical fields being considered. Three fully coupled equations are solved using classical finite elements. Furthermore, the Modified Cam Clay model is incorporated to describe the elasto-plastic behaviour of clay. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, an assessment of the impact of nonlinear soil behaviour is made by comparing numerical results with the results of an electro-osmosis laboratory test. The results show that the numerical solution can well predict the nonlinear behaviour of clay during electro-osmosis consolidation.

The common understanding in up-scaling of porous media mechanics is that pore scale phenomena are well understood. Navier-Stokes, Poiseuille's law, double-layer theory, thermal convection, all are classical theories coming to our rescue to describe the pore scale events in porous media in a strictly quantitative manner. So, most researchers do not feel the need to physically look at what is really happening. In this work we study a number of poorly understood phenomena that take place at that pore scale. These phenomena include formation of hundreds of micrometers wide exclusion zones next to hydrophilic surfaces, formation of colloidal crystals, micro-convective transport and unexpected pH and electric potential gradients across the exclusion zone. Investigating these phenomena is of great benefit for our understanding of porous media and could spark a wide range of applications in different fields. Until now, there is no comprehensive understanding of why these phenomena occur. There are several possible root causes for the formation of the exclusion zone being investigated. These include formation of liquid crystals of water molecules in the exclusion zone and Frohlich-like coherent oscillations. To develop the understanding about these phenomena, we have conducted experiments where we have used a variety of techniques to measure a number of parameters such as flow velocity and viscosity. These techniques include optical microscopy, optical tweezers, multi-particle tracking and interferometry. Examples of the results of these experiments are shown.

Simulation of 2D and 3D hydraulic fracturing in fully-saturated, porous media is presented. The discrete fracture/s is/are driven by the fluid pressure. A cohesive fracture model is adopted where, in the 3D case, the fracture follows the face of the element around the fracture tip which is closest to the normal direction of the maximum principal stress at the tip. While in the 2D setting, the fracture follows directly the direction normal to the maximum principal stress. No predetermined fracture path is needed. This requires continuous updating of the mesh around the crack tip to take into account the evolving geometry. The updating of the mesh is obtained by means of an efficient mesh generator based on Delaunay tessellation. The governing equations are written in the framework of porous media mechanics and are solved numerically in a fully coupled manner. Numerical examples dealing with well injection in a geological setting and hydraulic fracture in a concrete dam conclude the paper.