Viscous Pore Fluid Research Articles

Wave propagation at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid

PurposeThe purpose of this paper is to investigate propagation characteristics of seismic waves at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid.Design/methodology/approachA theoretical formulation of partially saturated poro-thermoelastic solid is used in this study established by Zhou et al. (2019). The incidence of two primary waves (P and SV) is taken. The incident wave from the elastic solid induces two reflected waves and five refracted waves. Due to viscous pore fluids, partially saturated poro-thermoelastic solid behave dissipative, whereas elastic solid behaves non-dissipative. As a result, both reflected and incident waves are homogeneous. However, all the refracted waves are inhomogeneous. A non-singular system of linear equations is formed by the coefficients of reflection and refraction for a specified incident wave. The energy shares of various reflected and refracted waves are determined by using these reflection and refraction factors. Finally, a sensitivity analysis is performed, and the effect of critical variables on energy partitioning at the interface is observed. The numerical example shows that throughout the process of reflection/refraction, the energy of incidence is conserved at all angles of incidences.FindingsThis study demonstrated two refracted (homogeneous) and five refracted (inhomogeneous) waves due to the incident wave from elastic solid. The reflection and refraction coefficients and partitioning of incident energy are acquired as a part of diverse physical parameters of the partially saturated poro-thermoelastic media. The interference energies between unlike pairs of refracted waves have been discovered due to the dissipative behavior of unsaturated poro-thermoelastic solid.Originality/valueThe sensitivity of different energy shares to various aspects of the considered model is graphically analyzed for a specific numerical model. The energy balance is maintained by combining interaction energy and bulk wave energy shares.

Reflection and refraction of elastic waves at the interface of an elastic solid and partially saturated soils

The present problem deals with the reflection and refraction of plane waves at the interface of an elastic solid and partially saturated soils. A mathematical model of partially saturated soils developed by Ghasemzadeh and Abounouri (Soil Dyn Earthq Eng 51:1–8, 2013) is employed. The incidence of two main waves (P and SV) is considered. As a result of the incident wave, two reflected waves (in an elastic solid) and four refracted waves (in partially saturated soils) are generated. The elastic solid behaves non-dissipative, while partially saturated soils behave dissipative due to the presence of viscous pore fluids, as a result of which the incident and reflected waves are homogeneous and all the refracted waves are inhomogeneous. The coefficients of reflection and refraction for a given incident wave result in a non-singular system of linear equations. Further, these reflection and refraction coefficients are used to obtain the energy shares of various reflected and refracted waves. This study has been numerically tested to determine the effects of various properties of partially saturated soils on the various energy shares. The numerical example confirms that during the reflection or refraction process conservation of incident energy is obtained at each angle of incidence.

Consolidation effects on monotonic and cyclic capacity of plate anchors in sand

This study investigated the change in monotonic and cyclic capacity of a plate anchor across different degrees of consolidation in dense sand. To quantify the effect of consolidation on anchor capacity, a framework is introduced and validated using centrifuge model anchor test data. The centrifuge tests considered a rectangular plate loaded at varying rates in dense sand, under both monotonic and irregular cyclic conditions, at a fixed embedment depth and with a horizontal load inclination (at the seabed). In order to vary from drained to undrained conditions, the sand was saturated using both water and a viscous pore fluid with viscosity approximately 700 times higher than water. The anchor's ultimate monotonic capacity in dense sand increased by up to 173% as the consolidation response evolved from drained to undrained with generation of dilation-induced suction. This increase in capacity across the consolidation regime can be adequately quantified using the proposed framework; however, uncertainty arises in achieving the theoretical undrained capacity. Both drained and undrained irregular cyclic loading resulted in anchor capacity increases of up to 33%, attributed to soil volume changes associated with cyclic densification under drained cyclic loading and excess pore pressure dissipation under undrained cyclic loading.

Macroscopic mechanical properties of porous rock with one saturating fluid

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

Optimization of the porous material described by the Biot model

The paper is devoted to the shape optimization of microstructures generating porous locally periodic materials saturated by viscous fluids. At the macroscopic level, the porous material is described by the Biot model defined in terms of the effective medium coefficients, involving the drained skeleton elasticity, the Biot stress coupling, the Biot compressibility coefficients, and by the hydraulic permeability of the Darcy flow model. By virtue of the homogenization, these coefficients are computed using characteristic responses of the representative unit cell consisting of an elastic solid skeleton and a viscous pore fluid. For the purpose of optimization, the sensitivity analysis on the continuous level of the problem is derived. We provide sensitivities of objective functions constituted by the Biot model coefficients with respect to the underlying pore shape described by a B-spline box which embeds the whole representative cell. We consider material design problems in the framework of which the layout of a single representative cell is optimized. Then we propose a sequential linearization approach to the two-scale problem in which local microstructures are optimized with respect to macroscopic design criteria. Numerical experiments are reported which include stiffness maximization with constraints guaranteeing minimum required permeability, and vice versa. Issues of the design and anisotropy and the spline box parametrization are discussed. In order to avoid remeshing, a geometric regularization technique based on injectivity constraints is applied.

An Analytical Solution for Capillary Gravity Drainage with Dominant Viscous Forces

The development of the capillary fringe during gravity drainage has a significant influence on saturation and pressure distributions in porous formations (Sarkarfarshi et al. in Int J Greenh Gas Control 23:61–71, 2014). This paper introduces an analytical solution for gravity drainage in an axisymmetric geometry with significant capillary pressure. The drainage process results from the injection of a lighter and less viscous injectant into a porous medium saturated with a heavier and more viscous pore fluid. If the viscous force dominates the capillary and the buoyancy forces, then the flow regime is approximated by differential equations and the admissible solution comprises a front shock wave and a trailing simple wave. In contrast to existing analytical solutions for capillary gravity drainage problems (e.g., Nordbotten and Dahle in 47(2) 2011; Golding et al. in J Fluid Mech 678:248–270 2011), this solution targets the saturation distribution during injection at an earlier point in time. Another contribution of this analytical solution is the incorporation of a completely drained flow regime close to the injection well. The analytical solution demonstrates the strong dependency of the saturation distribution upon relative permeability functions, gas entry capillary pressure, and residual saturation. The analytical results are compared to results from a commercial reservoir engineering software package (\(\hbox {CMG } \hbox {STARS}^{\mathrm{TM}}\)).

Study of pore fluid effect on the mobility of granular debris flows

Granular debris flows in nature are composed of a wide range of solids and viscous pore fluids, moving at high velocities down sloping channels. The pore fluids in a granular debris flow affect the interactions between the solid and fluid phases and thus govern the debris-flow mobility. Study of the pore fluid effect (i.e., excess pore water pressures correlated to solid structures, and the viscous shearing and dragging) is essential for understanding the high flow mobility of granular debris flows. This study critically reviews two dimensionless numbers with clear physical meanings, then demonstrates a new application of field monitoring data for identifying natural debris flows on large scales (i.e., surge and continuous debris-flows, respectively). This study illustrates that, the pore fluid viscous shearing stress dominates solid inertial stress due to solids collision. It is also found that different to continuous debris-flows, the high pore fluid pressures generated in surge debris-flow body dissipate quite slowly and mostly influence particle contact behaviour significantly. A new scientific criterion for identification of continuous and surge debris flow in nature can be given by this study.

Time-harmonic Analytic Solution for an Acoustic Plane Wave Scattering off an Isotropic Poroelastic Cylinder: Convergence and Form Function

The scattering of a plane wave incident obliquely upon an infinite poroelastic cylinder immersed in inviscid fluid is investigated in this paper. Convergence analysis of the series expansion of the solutions for various interface conditions is conducted and it provides a priori estimates on number of terms necessary for achieving a desired accuracy. In contrast to the existing results in the literature, we consider viscous pore fluid and arbitrary interface discharge efficiency [Formula: see text]. Moreover, the approach presented here does not require any restriction on the viscodynamic operator of the poroelastic equations and hence it can handle general cases beyond the dissipation models proposed by Biot and by Johnson, Koplik and Dashen. The back scattering form function is then calculated from the coefficients of the series solution. Numerical results with various incident angles and interface discharge efficiencies are also presented in this paper.

Scaling law of static liquefaction mechanism in geocentrifuge and corresponding hydromechanical characterization of an unsaturated silty sand having a viscous pore fluid

Fast landslides induced by rainfall impose considerable damage on infrastructure and cause major casualties worldwide. Static liquefaction is one of the triggering mechanisms mentioned frequently in the literature as a cause of this type of landslide. The scaling laws required to model this mechanism in the geotechnical centrifuge are developed, and it is shown that either a reduction in the soil pore size or use of a viscous pore fluid is needed to unify the time scaling factors of contractive volume change of the saturated voids and dissipation of the excess pore pressure generated. The latter option was used in this research; therefore, the influences of the viscous pore fluid on the hydromechanical characteristics of a silty sand were investigated. Subsequently, geocentrifuge tests were conducted to compare the behaviour of a slope having a viscous solution as the pore fluid with that of a model with water as the pore fluid. Both slopes were subjected to rainfall, and the evolution of the pore pressure and surface movements were monitored.

Centrifuge and Large-Scale Modeling of Seismic Pore Pressures in Sands: Cyclic Strain Interpretation

AbstractCentrifuge modeling of pore pressure buildup in a sand deposit as a result of shaking is evaluated by comparison with a large-scale experiment. In large-scale Test SG-1, a 5.6-m-thick, mildly sloping deposit of hydraulic fill clean Ottawa sand of Dr=40%, was subjected to 5 s of low-intensity base shaking (<0.02g) that induced excess pore pressures short of liquefaction. Three centrifuge experiments using various soil deposits and saturation fluids were conducted and compared with the large-scale test. One of these centrifuge simulations used the same Ottawa sand and Dr=40% of the prototype, a viscous pore fluid, and dry pluviation deposition, which created a soil fabric stiffer than the prototype. The other two centrifuge simulations used silty sand saturated with water. The pore pressure buildup in one of the silty sand tests was in good agreement with the prototype, while the other two centrifuge deposits did not develop any excess pore pressure. The various responses in the four tests are expla...

BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium

Taking into account three important porous media mechanisms during wave propagation (the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms), we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt (BISQ) model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.

Multiphasic Intervertebral Disc Mechanics: Theory and Application

The human spine is the flexible support structure of our body. Its geometric shape is a result of the human evolutionary history, where especially the lumbar spine area (L1–L5) is most at risk of causing discomfort resulting from mechanical stresses. Herein, the intervertebral discs (IVD) between the vertebral bodies are the most susceptible elements, as these avascular structures have to provide the flexibility. It is widely accepted that the IVD are often the trigger for back pain. In the context of biomechanical research, it is therefore important to develop a model for the human lumbar spine with particular focus on the IVD. The objective of the presented work is to subject the IVD of the lumbar spine to continuum-biomechanical research. Herein, a three-dimensional (3-d) finite-element model is developed that allows to estimate the influence of lumbar spine motion, i.e., bending, torsion and compression, on the resulting stress-field inside the IVD. Following this, the model can be utilised to detect inappropriate or excessive loading of the spine. The theoretical description of the IVD is based on a multi-phase continuum approach in the framework of the well-known “Theory of Porous Media” (TPM). This is a natural choice resulting from the avascular composition of the IVD. In general, IVD tissue is categorised as charged hydrated material with mechanical and electro-chemical internal coupling mechanisms. In order to capture these couplings, the underlying model incorporates an extracellular matrix (ECM) with fixed negative charges, which is saturated by a mixture of a liquid solvent and ions. Following the basic concept of the TPM, a volumetric averaging process is prescribed leading to volume fractions for the pore space and the solid skeleton as well as molar concentrations for the ion species in the pore fluid. In detail, the IVD exhibits a gelatinous core known as the nucleus pulposus (NP), and an onion-like surrounding structure consisting of anisotropic crosswise fibre-reinforced lamellae, the annulus fibrosus (AF). Both regions are seamlessly merging into each other and consist of mostly collagen fibres of varying strength and direction as well as proteoglycans with adhering negative charges. As a result of these fixed negative charges and the fact that the interstitial fluid carries positively and negatively charged ions, a model is created that describes the mutually coupled behaviour of solid deformation and fluid flow. To illustrate the resulting coupled swelling and shrinkage process, it is sufficient to recall that the size of the human body is reduced by roughly 2 centimetres during the waking phase of the day. This change in height is triggered by mechanical loads stemming from the body weight, which squeezes the interstitial fluid out of the IVD, thereby losing altitude. Simultaneously, an electro-chemical imbalance is generated, which is compensated during the nocturnal resting phase, where the interstitial fluid is driven back into the IVD due to osmotic effects. In summary, the presented paper provides a review on IVD mechanics and can be understood as a compilation of relevant information giving valuable guidance to researchers starting to work in this challenging field. In this regard, the paper opens with anatomical and chemical fundamentals of IVD tissue with a particular focus on the inherent inhomogeneities. This is followed by an introduction to the continuum-mechanical fundamentals including an overview of the TPM as well as the inelastic non-linear kinematics and the balance equations of the resulting porous continua. Thereafter, the constitutive modelling process is illustrated with a particular focus on the thermo-dynamically consistent modelling process of the intrinsic viscoelasticity of the ECM as well as the inhomogeneous characteristics of the embedded collagen fibres and the viscous pore fluid. The resulting system of coupled partial differential equations is then numerically discretised using the finite-element method which finally allows the simulation of deformation processes of the IVD using either single- or multi-processor machines. Moreover, an automated computation scheme is presented to systematically capture the inhomogeneities of the IVD. The paper is closed with several sample applications, which embrace the capabilities of the presented computational model on the one hand and give advice for further validation in terms of the applied material parameters.

Simulation of surface waves in porous media

SUMMARY We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

Dimensional analysis of natural debris flows

Debris flow is generally composed of a wide range of solid particles and viscous pore fluid. It flows at a high velocity down a slope channel. Interactions between solid and fluid phases affected by multiple parameters govern the rheological properties of debris flows. A dimensional analysis for a systematic study of the governing parameters is presented. Multiple dimensionless numbers with clear physical meanings are critically reviewed. The applications of field data to the studying of natural debris flows are demonstrated. Specific values of dimensionless numbers for classifying flow regimes of large-scale natural debris flows are obtained. Compared with previous small-scale physical model tests, this study shows that the contact friction between particles dominates in natural debris flows. In addition, the solid inertial stress due to particle collisions and the pore-fluid viscous shearing stress play key roles in governing the dynamic properties of debris flows. The channel width as a confinement to the flows can affect the solids discharge per unit width significantly. A dimensionless number related to pore-fluid pressure dissipation is also found that can satisfactorily distinguish between surge flows and continuous flows in the field.

Novel Computer-Controlled Saturation of Dynamic Centrifuge Models Using High Viscosity Fluids

Abstract The practice of saturating centrifuge models with a highly viscous pore fluid is widely used. As the fluid saturates the model, care must be taken to ensure that the hydraulic gradients are not too high to cause excessive disturbance to the model. A new computer-controlled saturation system (CAM-Sat) has been developed and implemented at the University of Cambridge to aid the saturation of soil models with a high viscosity pore fluid. Models are saturated under vacuum and pore fluid enters through ports in the model’s base. The system controls the ingress of pore fluid into the model by monitoring the fluid mass flux and then altering the pressure drop between a reservoir of pore fluid and the model. The system was found to be stable across a wide range of fluid viscosities and sand types. A further test showed that the system was able to respond to changes in mass flux demanded by the researcher.

Effect of Soil Permeability on Centrifuge Modeling of Pile Response to Lateral Spreading

This paper presents experimental results and analysis of six model centrifuge experiments conducted on the 150 g-ton Rensselaer Polytechnic Institute centrifuge to investigate the effect of soil permeability on the response of end-bearing single piles and pile groups subjected to lateral spreading. The models were tested in a laminar box and simulate a mild infinite slope with a liquefiable sand layer on top of a nonliquefiable layer. Three fine sand models consisting of a single pile, a 3×1 pile group, and a 2×2 pile group were tested, first using water as pore fluid, and then repeated using a viscous pore fluid, hence simulating two sands of different permeability in the field. The results were dramatically different, with the three tests simulating a low permeability soil developing 3–6 times larger pile head displacements and bending moments at the end of shaking. Deformation observations of colored sand strips, as well as measurements of sustained negative excess pore pressures near the foundations i...

Is P-Wave Velocity an Indicator of Saturation in Sand with Viscous Pore Fluid?

It is commonly assumed that within inundated sand the Skempton B value and P-wave velocity decrease with decrease in saturation. In centrifuge tests a common saturation procedure is to inundate the specimen with carbon dioxide while under a vacuum and then slowly introduce the viscous pore fluid. The B value and related saturation is difficult to measure in centrifuge models and P-wave velocity—saturation correlations have been used for this purpose. A laboratory emulation of centrifuge saturation procedures was made using a triaxial cell with top and bottom bender elements and a viscous methyl cellulose–water pore fluid. Contrary to expectations, the laboratory tests showed high P-wave velocities indicative of full saturation when B values were low. Numerical modeling of the laboratory tests indicated that if air bubbles within the pore fluid are numerous and closely spaced then there is a good correlation between saturation, B value, and P-wave velocity. However if the air bubbles are larger and only pr...

On the interplay between the solid deformation and fluid flow during the solidification of a metallic alloy

During solidification in casting processes, metallic alloys undergo a continuous transition from liquid to solid by passing a semi-solid or mushy state. In this contribution, we present a continuum-mechanical model describing the deformation and solidification using the thermodynamically consistent theory of porous media (TPM). The model is based on two constituents, namely an elasto-viscoplastic solid skeleton and a viscous pore fluid. The balance equations are formulated on the macroscale and the exchange of mass, species, momentum and energy between the constituents is expressed. Between both constituents a local thermal equilibrium is assumed. The initial boundary value problem is solved by a numerical solution scheme based on mixed Galerkin finite elements. The velocity of the solid skeleton, the pressure of the pore fluid, the common temperature and the chemical compositions are taken as the primary unknown field variables.

Sound speed and attenuation measurements in unconsolidated glass-bead sediments saturated with viscous pore fluids

As part of a recent ocean sediment acoustics experiment, a number of independent sound speed and attenuation measurements were made in a well-characterized sandy sediment. These measurements covered a broad frequency range and were used to test both Biot-Stoll theory and Buckingham’s more recent grain-to-grain shearing model. While Biot theory was able to model the sound speed well, it was unable to predict the attenuation measured above 50kHz. This paper presents a series of measurements made in the laboratory on a simple glass-bead sediment. One goal of these measurements was to test the hypothesis that the attenuation measured at-sea was a result of scattering from shells within the sediment. The laboratory sediments used were saturated with fluids with different viscosities in order (assuming that Biot-Stoll theory is correct) to shift the dispersion into the frequency range of the measurement system. The measured attenuation in the glass-bead sediments exhibited the same frequency dependence as observed in the ocean experiment even though no shells were present. The laboratory results motivated development of a sediment model which incorporates both fluid viscosity and grain-to-grain interactions as embodied in a simple frequency-dependent, imaginary frame modulus first suggested by Biot.

Shear Strength and Stress-Strain behavior of Contaminated Soils

Abstract A series of unconfined compression tests performed on fine-grained soils contaminated with varying amounts of chemicals showed a decrease in shear strength and stress-strain behavior. These observations were attributed to changes in dielectric constant and pore fluid viscosity. Consolidated drained triaxial tests performed on a granular soil showed a similar behavior, even though granular soils do not show a physicochemical interaction between soil and pore fluid. This is attributed to mechanical interactions at particle contacts, caused by enhanced lubrication by viscous pore fluids. For fine-grained soils, the observed reduction in shear strength is attributed to physicochemical effects caused by a reduction in dielectric constant and mechanical interactions caused by high pore fluid viscosities. Observations show that the reduced physicochemical interactions seem to have been overshadowed by mechanical interactions. The clayey silt tested showed a marginal reduction in shear strength, indicating that the net effect is insignificant.