Sensitivity analysis of permeability parameters of bovine nucleus pulposus obtained through inverse fitting of the nonlinear biphasic equation : effect of sampling strategy

Permeability controls the fluid flow into and out of soft tissue, and plays an important role in maintaining the health status of such tissue. Accurate determination of the parameters that define permeability is important for the interpretation of models that incorporate such processes. This paper describes the determination of strain-dependent permeability parameters from the nonlinear biphasic equation from experimental data of different sampling frequencies using the Nelder–Mead simplex method. The ability of this method to determine the global optimum was assessed by constructing the whole manifold arising from possible parameter combinations. Many parameter combinations yielded similar fits with the Nelder–Mead algorithm able to identify the global maximum within the resolution of the manifold. Furthermore, the sampling strategy affected the optimum values of the permeability parameters. Therefore, permeability parameter estimations arising from inverse methods should be utilised with the knowledge that they come with large confidence intervals

Isogeometric analysis of fluid-saturated porous media including flow in the cracks

An isogeometric model is developed for the analysis of fluid transport in pre-existing faults or cracks that are embedded in a fluid-saturated deformable porous medium. Flow of the interstitial fluid in the porous medium and fluid transport in the discontinuities are accounted for and are coupled. The modelling of a fluid-saturated porous medium in general requires the interpolation of the displacements of the solid to be one order higher than that of the pressure of the interstitial fluid. Using order elevation and Bézier projection, a consistent procedure has been developed to accomplish this in an isogeometric framework. Particular attention has also been given to the spatial integration along the isogeometric interface element in order to suppress traction oscillations that can arise for certain integration rules when a relatively high dummy stiffness is used in a poromechanical model. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd

Ultrasonic Characterization of Cement and Concrete

Ultrasonic velocity measurements are used to control the quality of fresh Concrete and to monitor the concrete mixtures during hardening or curing process. The goal of this research is to determine the time required for a given mixture of Concrete to be hard enough for form removal in a construction site. Currently the concrete form removal time is not accurately known. The early removals of the concrete forms results in weaker concrete and the late removal of the concrete forms prolong the construction time. The shear and rigidity moduli of freshly mixed concrete increases with time and this change can be monitored by measuring the ultrasonic velocity in the concrete as a function of time. In this paper we investigate the evolution of ultrasonic pulse wave velocity as a function of time in the concrete mixtures, with different water to cement ratio. The results obtained can be used to predict the setting time of concrete and also to control the quality of the concrete in the construction industry. The curing process is a series of chemical reactions by which the concrete mixture, when not stirred, gradually increases its viscosity and hardens industry, knowledge of the setting-time of the concrete for form removal or for the addition of a new edifice is crucial for speeding up the construction. Although there are published guidelines such as tables from the American Concrete Institute, currently this time interval cannot be accurately predicted. It depends on the uncontrollable parameters such as ambient temperature and humidity, among other factors

Theoretical Simulation of Experimental Observations of Surface Wave Propagation on a Fluid-Saturated Porous Material

Wave propagation in fluid-saturated porous materials presents very particular features like the appearance of a second compressional wave, the so-called slow compressional wave, in addition to the conventional P (or fast compressional) and the shear wave [1,2]. First experimental observation of the slow compressional wave was carried out by Plona in 1980 in water-saturated porous ceramics at ultrasonic frequencies [3]. In 1983 Feng and Johnson predicted the existence of a new surface mode along a fluid/fluid-saturated porous solid interface, in addition to the well-known leaky-Rayleigh and true Stoneley modes [4,5]. Feng and Johnson introduced the so-called surface stiffness, T, as a parameter which describes the boundary conditions at the interface. For a value of T=0 the pores at the surface are considered open, whereas for a value of T=∞ they are considered to be closed. However, according to the theory this new surface mode appears only when closed pores boundary conditions prevail at the interface. This last restriction renders the observation of the new mode problematic, because the extreme difficult in closing the surface pores without clogging all the pores close to the surface (e.g. by painting). In 1992 Nagy observed experimental evidence of the slow surface wave [6]. Nagy demonstrated that capillary forces can extend an ideally thin membrane over the surface pores at the interface between a porous solid saturated with a wetting fluid (e.g. water or alcohol) and a non-wetting fluid (e.g. air). Under this conditions, experimental evidence of a simple form of the new surface wave mode predicted by Feng and Johnson during alcohol saturation of a sintered glass beads specimen was obtained. However, due to problems inherent to the excitation of surface waves in fluid-saturated porous solids (e.g. extremely high attenuation, small propagation lengths, etc.) the results were not conclusive. In this work we will show that the experimental evidence of slow surface wave can be predicted by the analytical method of Feng and Johnson [5], if slight modifications are introduced into the calculation technique in order to account for some of the particular characteristics of the experiment

Surface Wave Inspection of Porous Ceramics and Rocks

The most interesting feature of acoustic wave propagation in fluid-saturated porous media is the appearance of a second compressional wave, the so-called slow compressional wave, in addition to the conventional P (or fast) wave and the shear wave [1,2]. The slow compressional wave is essentially the motion of the fluid along the tortuous paths in the porous frame. This motion is strongly affected by viscous coupling between the fluid and the solid. Therefore, both the velocity and the attenuation of the slow wave greatly depend on the dynamic permeability of the porous frame. It was not until 1980, that Plona first experimentally observed the slow compressional wave in water-saturated porous ceramics at ultrasonic frequencies [3]. Only three years later, Feng and Johnson predicted the existence of a new slow surface mode on a fluid/fluid-saturated solid interface in addition to the well-known leaky-Rayleigh and true Stoneley modes [4,5]. The slow surface mode is basically the interface wave equivalent of the slow bulk mode, but there is a catch: the surface pores of the solid have to be closed so that this new mode can be observed. Otherwise, a surface vibration can propagate along the fluid/fluid-saturated porous solid interface without really moving the fluid since it can flow through the open pores without producing any significant reaction force. All previous efforts directed at the experimental observation of this new surface mode failed because of the extreme difficulty of closing the surface pores without closing all the pores close to the surface (e. g., by painting). On the other hand, it has been recently shown that surface tension itself could be sufficient to produce essentially closed-pore boundary conditions at the interface between a porous solid saturated with a wetting fluid, such as water or alcohol, and a non-wetting superstrate fluid, like air [6]

Numerical Investigation on the Fixed-Stress Splitting Scheme for Biot’s Equations: Optimality of the Tuning Parameter

We study the numerical solution of the quasi-static linear Biot equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We investigate numerically the optimality of the parameter and compare our results with physically and mathematically motivated values from the literature, which commonly only depend on mechanical material parameters. We demonstrate, that the optimal value of the tuning parameter is also affected by the boundary conditions and material parameters associated to the fluid flow problem suggesting the need for the integration of those in further mathematical analyses optimizing the tuning parameter.acceptedVersio

Coherent and Incoherent Scattering Mechanisms in Air-Filled Permeable Materials

Ultrasonic evaluation of porous materials can take advantage of some very specific acoustic phenomena that occur only in fluid-saturated consolidated solids of continuously connected pore structure. The most interesting feature of acoustic wave propagation in such media is the appearance of a second compressional wave, the so-called slow wave [1,2]. The slow compressional wave represents a relative motion between the fluid and the solid frame. This motion is very sensitive to the kinematic viscosity of the fluid and the dynamic permeability of the porous formation. Certain material properties such as tortuosity, permeability, porosity, and pore size, shape and surface quality are inherently connected to the porous nature of the material and can be evaluated best from the propagation properties of the slow compressional wave.</p

Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

This article presents a novel finite element formulation for the Biot equation using low-order elements. Additionally, an extra degree of freedom is introduced to treat the volumetric locking steaming from the effective response of the medium; its balance equation is also stabilized. The accuracy of the proposed formulation is demonstrated by means of numerical analyses.Peer ReviewedPostprint (author's final draft

Fiber Acoustic Waveguide : A Sensor Candidate

Sensor development plays a key role in the field of nondestructive evaluation and process control. The annual fiber optic sensor market alone is a multimillion dollar business (1). Acoustic waves are about five orders of magnitude slower than optical waves and can also be guided in cladded glass fibers, similar to optical fibers, with low loss and low dispersion (2–7). Fiber acoustic waveguides are believed to be a very attractive and basic component for further sensor development (8). In this paper a brief theoretical description of a weakly guiding acoustic fiber (7) is given. The material selection criteria for the core and the cladding of the fiber guide, the properties of single-mode operation, and some sensing mechanisms for temperature and pressure variations are discussed. The acoustic waveguide with a liquid core is also considered

Generalized Lamb Modes in Fluid-Saturated Porous Plate

Since analysis by Rayleigh [1] and Lamb [2], the vibration modes for an elastic homogeneous infinite solid thin plate are well understood. These so-called “Lamb modes” result from a pure compressional wave and pure shear wave. Similarly, excitation of “leaky Lamb modes” in elastic plates immersed in a fluid, caused by incident acoustic waves, has been extensively described theoretically [3–7] and experimentally [8,9]. Results are generally presented as dispersion curves which relate the phase velocity of the mode to the product of frequency and plate thickness