Effect of the Transition Zone on the Bulk Modulus of Concrete

1994 ◽  
Vol 370 ◽  
Author(s):  
Melanie P. Lutz ◽  
Paulo J. M. Monteiro
Keyword(s):  
Bulk Modulus ◽  
Transition Zone ◽  
Cement Paste ◽  
Power Law ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Closed Form Expression ◽  
Form Expression ◽  
Effective Bulk Modulus ◽  
Model Predictions

AbstractIn concrete, non-uniformities in the hydration process, due to the the “wall effect” produeed by the aggregate (inclusion) particles, lead to an interfacial transition zone (ITZ) that is characterized by an increase in porosity near the inclusions. This increase in porosity may in turn be expected to cause a local decrease in the elastic moduli. We have modeled the effect of the ITZ by assuming that the elastic moduli vary smoothly in the vicinity of the inclusions, according to a power law. The exponent in the power law is chosen based on the estimated thickness of the ITZ. For this model, a closed-form expression can be found for the overall effective bulk modulus. The predicted bulk modulus of the concrete depends on known properties such as the elastic moduli of the bulk cement paste and the inclusions, the volume fraction of the inclusions, as well as on the elastic moduli at the interface. By comparing the model predictions to measured data, we can obtain estimates of the elastic moduli at the interface. Application of this inverse procedure to a set of data from the literature on mortar containing sand inclusions leads to the conclusion that the modulus at the interface is about 15-50% lower than in bulk cement paste.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

2010 ◽  
Vol 74 (2) ◽  
pp. 341-350 ◽  
Author(s):  
E. K. H. Salje ◽  
J. Koppensteiner ◽  
W. Schranz ◽  
E. Fritsch
Keyword(s):  
Bulk Modulus ◽  
Porous Materials ◽  
Power Law ◽  
Master Curve ◽  
Elastic Moduli ◽  
External Stress ◽  
Effective Elastic Moduli ◽  
Critical Porosity ◽  
Elastic Instabilities ◽  
Linear Decay

AbstractThe collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity ϕc at which small stresses will lead to the collapse of the sample. For several samples we find ϕc ~0.5 with an almost linear decay of the bulk moduli with porosity at ϕc <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law κ ~ (1–ϕm, m>2, between ϕ = 0.5 and ϕ = 1.

Closed Form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Mei-Feng Liu ◽  
Tai-Ping Chang
Keyword(s):  
Closed Form ◽  
Thin Plate ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Plate Theory ◽  
Transversely Isotropic ◽  
Closed Form Expression ◽  
Transverse Displacement ◽  
Form Expression ◽  
Thin Plate Theory

A closed form expression for the transverse vibration of a magnetoelectroelastic (MEE) thin plate is derived, and the exact solution for the free vibration of a two-layered BaTiO3–CoFe2O4 composite is obtained. Based on the Kirchhoff thin plate theory, the bending problem of a transversely isotropic MEE rectangular plate is investigated, and the governing equation in terms of the transverse displacement is then presented in a rather compact form. The material coefficients for such MEE plate are expressed uniquely by the volume fraction (vf) of the two-layered BaTiO3–CoFe2O4 composite, which indicates a transversely isotropic MEE medium. The natural frequencies of such MEE plate are evaluated analytically, and the effects of different volume fractions on the natural frequency are further discussed.

Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. F13-F20 ◽  
Author(s):  
Xavier García ◽  
Ernesto A. Medina
Keyword(s):  
Cyclic Loading ◽  
Bulk Modulus ◽  
Power Law ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Hysteretic Behavior ◽  
Dynamics Simulation ◽  
Spherical Particles ◽  
Elastic Response ◽  
Power Law Exponent

When Hertz-Mindlin force laws are considered in the context of the effective-medium theory, the predictions yield a constant Poisson coefficient and bulk/shear elastic moduli that scale with pressure with a 1/3 power law exponent [Formula: see text]. This prediction contradicts early and recent experimental findings that conclude moduli grow faster with a 1/2 power law exponent ([Formula: see text]). Such a conclusion is also reached by recent second-order corrections to linear elastic theory. In this work we use a discrete-particle method to study the elastic response of a model of sand that is unconsolidated because of cyclic loading. We use a detailed molecular dynamics simulation that accounts for Hertz-type grain interactions and history-dependent shear forces. The porous sand model is constructed from spherical particles whose size distribution mimics well-sorted unconsolidated sands. The geometry of the model is obtained by simulating critical processes in sedimentary rock formations. Hysteretic behavior and relations between the sample bulk modulus, strain, and stress are obtained. The simulated sample reproduces experimental transient and stationary loading-unloading behavior. We find good correspondence of pressure and strain dependence of elastic moduli in our model with semilinear elasticity theory predictions. Simple arguments explain low coordination numbers observed on force-transmitting samples and the tendency to reduce dissipation under cyclic loading. Our approach clearly shows that a Hertz-Mindlin grain interaction is not inconsistent with the experimental [Formula: see text] behavior of the bulk modulus.

Micromechanical model for hydroxyapatite whisker reinforced polymer biocomposites

2006 ◽  
Vol 21 (8) ◽  
pp. 2136-2145 ◽  
Author(s):  
Weimin Yue ◽  
Ryan K. Roeder
Keyword(s):  
Aspect Ratio ◽  
High Density Polyethylene ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Orientation Distribution ◽  
Ratio Distribution ◽  
Reinforced Polymer ◽  
Model Predictions ◽  
Aspect Ratio Distribution

A micromechanical model was developed to predict the elastic moduli of hydroxyapatite (HA) whisker reinforced polymer biocomposites based upon the elastic properties of each phase and the reinforcement volume fraction, morphology, and preferred orientation. The effects of the HA whisker volume fraction, morphology, and orientation distribution were investigated by comparing model predictions with experimentally measured elastic moduli for HA whisker reinforced high-density polyethylene composites. Predictions using experimental measurements of the HA whisker aspect ratio distribution and orientation distribution were also compared to common idealized assumptions. The best model predictions were obtained using the experimentally measured HA whisker aspect ratio distribution and orientation distribution.

scholarly journals AUTOCORRELATIONS OF RANDOM FRACTAL APERTURES AND PHASE SCREENS

Fractals ◽  
2017 ◽  
Vol 25 (01) ◽  
pp. 1750005
Author(s):  
JONATHAN F. SCHONFELD
Keyword(s):  
Euclidean Space ◽  
Power Law ◽  
Short Distance ◽  
New Product ◽  
Closed Form Expression ◽  
Form Expression ◽  
Product Representation ◽  
Random Fractal ◽  
Distance Behavior ◽  
Phase Screens

We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling at short distance follows almost immediately. Similar techniques provide easy constructions of objects with fractional Brownian short-distance behavior for phase screens and other applications.

Compressional-wave propagation in porous media saturated with two fluids

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. L1-L11 ◽  
Author(s):  
Igor A. Beresnev
Keyword(s):  
Porous Media ◽  
Bulk Modulus ◽  
Wave Velocity ◽  
Power Law ◽  
Empirical Data ◽  
Volume Fraction ◽  
Compressional Wave ◽  
Immiscible Fluids ◽  
The Body ◽  
Specific Class

A theory of porous media with voids filled by two immiscible fluids should comply with Laplace’s law of capillary pressure at the pore level. For the convenience of practical use, it ideally should also involve only the generic elastic coefficients of the mineral grains and pore-filling fluids and avoid the use of “bulk” coefficients of the dry solid frame, whose measurement involves idealized experiments, or poorly understood “phase-coupling” coefficients. It should be reconcilable with the body of empirical data as well. Such a theory and the resulting propagation of the conventional compressional wave can be deduced from principles of linear elasticity. Although the interfacial tension between the fluids is rigorously included, it turns out to have no effect on the velocity of seismic waves. To be reconcilable with observational data, the theory needs to be modified to (1) postulate a power-law effect of the volume fraction of the solid and fluid phases on the reduction of their elastic moduli contributing to the aggregate value and (2) honor the additivity of fluid compressibilities versus bulk moduli to form the effective bulk modulus of the fluids. Empirical calibration of the constants of the power law is necessary to make the theory applicable to a specific class of rock. Constructed this way for well-cemented rocks such as sandstones or limestones, the theory agrees well with the empirical data describing (1) the bulk modulus of the dry solid frame, (2) the bulk modulus of the solid frame filled with one fluid, both as functions of porosity; (3) the data on wave velocity in such rocks filled with one fluid, as a function of porosity, and (4) the measurements of wave velocity in such rocks filled with air and water, as a function of water saturation.

Effective elastic and transport properties of regular honeycombs for all densities

2000 ◽  
Vol 15 (9) ◽  
pp. 1985-1993 ◽  
Author(s):  
S. Hyun ◽  
S. Torquato
Keyword(s):  
Dielectric Constant ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Properties ◽  
Effective Conductivity ◽  
Property Values ◽  
Entire Volume ◽  
The Past ◽  
Point Estimates ◽  
Effective Bulk Modulus

The effective planar elastic moduli and planar conductivity (or dielectric constant) of regular hexagonal and triangular honeycombs were investigated for the entire range of volume fractions. Only the extreme limits of the volume fraction have been studied in the past. We studied the effective properties both numerically, via finite elements, and analytically, via rigorous three-point bounds, three-point approximations, and cross-property bounds. We show here that the three-point bounds and approximations are generally in excellent agreement with the simulation data and are superior to the two-point Hashin–Shtrikman bounds. Therefore, the three-point estimates provide accurate analytical predictions of the effective properties for all densities. Both the effective bulk modulus and effective conductivity are nearly extremal in the case of hexagonal honeycombs for the entire volume-fraction range, in contrast to the effective shear modulus. In the case of triangular honeycombs, all of the property values are relatively close to being optimal. Thus, the triangular honeycomb has desirable multifunctional performance for all densities in so far as the elastic moduli, conductivity, and dielectric constant are concerned.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

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