ON THE DEPENDENCE OF THE ELASTIC PROPERTIES OF A POROUS ROCK ON THE COMPRESSIBILITY OF THE PORE FLUID

Geophysics ◽  
1975 ◽  
Vol 40 (4) ◽  
pp. 608-616 ◽  
Author(s):  
Robert J. S. Brown ◽  
Jan Korringa
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Fluid Pressure ◽  
Reciprocity Theorem ◽  
Pore Fluid ◽  
Pore System ◽  
Porous Rock ◽  
Special Cases ◽  
The One ◽  
Interconnected Pore

An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility [Formula: see text], the compressibility κ* of the closed container is given by [Formula: see text] Here [Formula: see text] is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of [Formula: see text]. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, [Formula: see text] and [Formula: see text], of the material exclusive of the pore fluid. When this material is homogeneous, one has [Formula: see text], and the equation reduces to a well‐known relation by Gassmann. For the other elastic properties, we also obtain expressions which generalize Gassmann’s work and which also differ from it only in the appearance of [Formula: see text] instead of [Formula: see text] in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.

Fibers of Bamboo and Hem Palm Tree

2001 ◽  
Vol 702 ◽  
Author(s):  
Shigeyasu Amada
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Simple Procedure ◽  
High Strength ◽  
Tensile Tests ◽  
Palm Tree ◽  
Bamboo Fibers ◽  
The One

ABSTRACTBamboo is a typical composite material which is axially reinforced by very strong fibers. So that, the fibers play an important role for the bamboo structure. The elastic properties of the bamboo culm have been measured only by tensile test so far, which needs a large specimen. Recently ultra-sonic technique, which has a simple procedure and uses a small specimen, has been applied to woods as well as metals. This report reviews about the elastic properties of bamboo and Hemp palm fibers. The Young's modulus and Poisson's ratio of the bamboo fibers are measured by ultra-sonic method with a transmitting wave. On the other hand, the strength of the bamboo and Hemp palm fibers are measured by the tensile tests. Using the volume fraction of fibers in the specimen and mixture principle, the Young's modulus and strength of the fibers and parenchyma were obtained. The fiber has a high strength up to 1GPa and an strong anisotropic property because its axial Young's modulus has 7 times higher than the one in the transverse direction.

Theory and Analytical Solutions to Coupled Processes of Transport and Deformation in Dual-Porosity Dual-Permeability Poro-Chemo-Electro-Elastic Media

2018 ◽  
Vol 85 (11) ◽  
Author(s):  
Chao Liu ◽  
Amin Mehrabian ◽  
Younane N. Abousleiman
Keyword(s):  
Analytical Solutions ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Dual Porosity ◽  
Coupled Processes ◽  
Electrical Potentials ◽  
Solid Deformation ◽  
Special Cases ◽  
Time Variations ◽  
Electrically Charged

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

Deriving Biot-Gassmann relationship by inclusion-based method

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D657-D667 ◽  
Author(s):  
Yongjia Song ◽  
Hengshan Hu ◽  
John W. Rudnicki
Keyword(s):  
Porous Material ◽  
Bulk Modulus ◽  
Effective Strain ◽  
Strain Tensor ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Effective Modulus ◽  
Pore System ◽  
Pore Microstructure ◽  
Stress Dependent

The quasi-static theory of poroelasticity presented by Biot and Gassmann provides a relationship between the drained and undrained elastic constants of an isotropic fluid-saturated porous material in terms of the porosity of the material, bulk modulus of the solid grains, and bulk modulus of the pore fluid. We have developed an alternative approach to derive the Biot-Gassmann (BG) relationship while including the effects of the pore microstructure. First, the Eshelby transformation is used to express the local inclusion/pore strain tensor in terms of the applied strain tensor and reference material elastic properties by the superposition of a void strain and a perturbation term due to induced inclusion stress. Second, the inclusion strain expression and Hill’s average principles are combined with the Mori-Tanaka/Kuster-Toksöz scheme to obtain inclusion-stress-dependent effective elastic moduli of porous materials. For an isolated pore system, the effective modulus tensor corresponds to the original Mori-Tanaka/Kuster-Toksöz’s expression. Although for communicating pore system, it is proven to satisfy the BG relation. In the second case, the deformation is assumed to occur so slowly that the infiltrating fluid mass has sufficient time to diffuse between material elements and, consequently, the pore fluid pressure is equilibrated within the whole pore system. It is noteworthy that we arrive at a BG relationship without applying reciprocity theorem and that the porous material effective strain is defined from Hill’s principles instead of solid phase average strain. A potential application of the stress-independent effective modulus is to help develop a dynamical modulus model of rock physics for a specific pore microstructure.

scholarly journals Effective elastic properties of one-dimensional hexagonal quasicrystal composites

2021 ◽  
Vol 42 (10) ◽  
pp. 1439-1448
Author(s):  
Shuang Li ◽  
Lianhe Li
Keyword(s):  
Composite Materials ◽  
Explicit Expression ◽  
Elastic Properties ◽  
Function Method ◽  
Volume Fraction ◽  
Effective Properties ◽  
Elliptic Cylinder ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

AbstractThe explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

scholarly journals A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

2014 ◽  
Vol 470 (2170) ◽  
pp. 20130820 ◽  
Author(s):  
David L. George ◽  
Richard M. Iverson
Keyword(s):  
Debris Flow ◽  
Adaptive Mesh Refinement ◽  
Volume Fraction ◽  
Critical Role ◽  
Solid Volume Fraction ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Flow Dynamics ◽  
Pore Fluid Pressure ◽  
Numerical Predictions

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model's five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here, we recapitulate the equations and analyse their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations, we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

Preparation of Electron Transparent Metal-Matrix Composites

1968 ◽  
Vol 26 ◽  
pp. 334-335 ◽  
Author(s):  
M. R. Pinnel ◽  
A. Lawley
Keyword(s):  
Stainless Steel ◽  
Load Transfer ◽  
Volume Fraction ◽  
Steel Wire ◽  
Initial Step ◽  
Interfacial Region ◽  
Matrix Composites ◽  
Specific Test ◽  
The Matrix ◽  
The One

Numerous phenomenological descriptions of the mechanical behavior of composite materials have been developed. There is now an urgent need to study and interpret deformation behavior, load transfer, and strain distribution, in terms of micromechanisms at the atomic level. One approach is to characterize dislocation substructure resulting from specific test conditions by the various techniques of transmission electron microscopy. The present paper describes a technique for the preparation of electron transparent composites of aluminum-stainless steel, such that examination of the matrix-fiber (wire), or interfacial region is possible. Dislocation substructures are currently under examination following tensile, compressive, and creep loading. The technique complements and extends the one other study in this area by Hancock.The composite examined was hot-pressed (argon atmosphere) 99.99% aluminum reinforced with 15% volume fraction stainless steel wire (0.006″ dia.).Foils were prepared so that the stainless steel wires run longitudinally in the plane of the specimen i.e. the electron beam is perpendicular to the axes of the wires. The initial step involves cutting slices ∼0.040″ in thickness on a diamond slitting wheel.

scholarly journals Comparative study of elastic properties and mode I fracture energy of carbon nanotube/epoxy and carbon fibre/epoxy laminated composites

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Jyotikalpa Bora ◽  
Sushen Kirtania
Keyword(s):  
Carbon Nanotube ◽  
Carbon Fibre ◽  
Fracture Energy ◽  
Elastic Properties ◽  
Volume Fraction ◽  
Laminated Composites ◽  
Laminated Composite ◽  
Fe Analysis ◽  
Mode I ◽  
Mode I Fracture

Abstract A comparative study of elastic properties and mode I fracture energy has been presented between conventional carbon fibre (CF)/epoxy and advanced carbon nanotube (CNT)/epoxy laminated composite materials. The volume fraction of CNT fibres has been considered as 15%, 30%, and 60% whereas; the volume fraction of CF has been kept constant at 60%. Three stacking sequences of the laminates viz.[0/0/0/0], [0/90/0/90] and [0/30/–30/90] have been considered in the present analysis. Periodic microstructure model has been used to calculate the elastic properties of the laminated composites. It has been observed analytically that the addition of only 15% CNT in epoxy will give almost the same value of longitudinal Young’s modulus as compared to the addition of 60% CF in epoxy. Finite element (FE) analysis of double cantilever beam specimens made from laminated composite has also been performed. It has been observed from FE analysis that the addition of 15% CNT in epoxy will also give almost the same value of mode I fracture energy as compared to the addition of 60% CF in epoxy. The value of mode I fracture energy for [0/0/0/0] laminated composite is two times higher than the other two types of laminated composites.

scholarly journals When to Substitute a Missing Upper Lateral With a Canine: A Simplified Approach

2021 ◽  
pp. 030157422098054
Author(s):  
Renu Datta
Keyword(s):  
Anterior Segment ◽  
Specific Treatment ◽  
Simplified Approach ◽  
Special Cases ◽  
Randomized Control ◽  
The One ◽  
Individual Presentation ◽  
Available Information ◽  
Missing Tooth ◽  
Made In

Introduction: The upper lateral incisor is the most commonly missing tooth in the anterior segment. It leads to esthetic and functional imbalance for the patients. The ideal solution is the one that is most conservative and which fulfills the functional and esthetic needs of the concerned individual. Canine substitution is evolving to be the treatment of choice in most of the cases, because of its various advantages. These are special cases that need more time and effort from the clinicians due to space discrepancy in the upper and lower arches, along with the presentation of individual malocclusion. Aims and Objectives: Malocclusion occurring due to missing laterals is more complex, needing more time and effort from the clinicians because of space discrepancy, esthetic compromise, and individual presentation of the malocclusion. An attempt has been made in this article to review, evaluate, and tabulate the important factors for the convenience of clinicians. Method: All articles related to canine substitution were searched in the electronic database PubMed, and the important factors influencing the decision were reviewed. After careful evaluation, the checklist was evolved. Result: The malocclusions in which canine substitution is the treatment of choice are indicated in the tabular form for the convenience of clinicians. Specific treatment-planning considerations and biomechanics that can lead to an efficient and long-lasting result are also discussed. Conclusion: The need of the hour is an evidence-based approach, along with a well-designed prospective randomized control trial to understand the importance of each factor influencing these cases. Until that time, giving the available information in a simplified way can be a quality approach to these cases.

scholarly journals Correction to: Stress and pore fluid pressure control of seismicity rate changes following the 2016 Kumamoto earthquake, Japan

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Kodai Nakagomi ◽  
Toshiko Terakawa ◽  
Satoshi Matsumoto ◽  
Shinichiro Horikawa
Keyword(s):  
Fluid Pressure ◽  
Pressure Control ◽  
Pore Fluid ◽  
2016 Kumamoto Earthquake ◽  
Pore Fluid Pressure ◽  
Seismicity Rate ◽  
Kumamoto Earthquake ◽  
The 2016 Kumamoto Earthquake ◽  
Seismicity Rate Changes

An amendment to this paper has been published and can be accessed via the original article.

scholarly journals High concentration Brownian coagulation in jet flow using two enhancement formulations

2012 ◽  
Vol 16 (5) ◽  
pp. 1519-1523
Author(s):  
Pei-Feng Lin ◽  
Di-Chong Wu ◽  
Ze-Fei Zhu
Keyword(s):  
Volume Fraction ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
High Volume ◽  
Jet Flow ◽  
High Concentration ◽  
Brownian Coagulation ◽  
Planar Jet ◽  
Ultra Fine Particle ◽  
The One

Ultra-fine particle coagulation by Brownian motion at high concentration in planar jet flow is simulated. A Taylor-Series Expansion Method of Moments is employed to solve the particle general dynamic equation. The volume fraction gets high value, very closes to that at the nozzle exit. As the vortex pairing develops, the high volume fraction region rolls out and mixes with the low value region. The enhancement factor given by Trzeciak et al. will be less than one at some specific outer positions, which seems to be less accurate than the one given by Heine et al.

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