Dynamic elastic moduli of a suspension of imperfectly bonded spheres

Author(s):  
A. K. Mal ◽  
S. K. Bose

AbstractAn isotropic elastic material containing a random distribution of identical spherical particles of another elastic material is considered. The bonding between the spheres and the matrix is imperfect, so that slip may occur at interfaces when stress is applied to the medium. The shear stresses at the interface is assumed to be proportional to the amount of slip. The velocity and attenuation of the average harmonic elastic waves propagating through such a medium are calculated. The results are valid to the lowest order in frequency for wave lengths long compared with the radius of the sphere. The dynamic elastic moduli are obtained from these results and are compared with available results for welded contact. The variations in the P and S wave velocities for propagation across earthquake faults is discussed.

Solid Earth ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 25-44 ◽  
Author(s):  
M. J. Heap ◽  
P. Baud ◽  
P. G. Meredith ◽  
S. Vinciguerra ◽  
T. Reuschlé

Abstract. The accuracy of ground deformation modelling at active volcanoes is a principal requirement in volcanic hazard mitigation. However, the reliability of such models relies on the accuracy of the rock physical property (permeability and elastic moduli) input parameters. Unfortunately, laboratory-derived values on representative rocks are usually rare. To this end we have performed a systematic laboratory study on the influence of pressure and temperature on the permeability and elastic moduli of samples from the two most widespread lithified pyroclastic deposits at the Campi Flegrei volcanic district, Italy. Our data show that the water permeability of Neapolitan Yellow Tuff and a tuff from the Campanian Ignimbrite differ by about 1.5 orders of magnitude. As pressure (depth) increases beyond the critical point for inelastic pore collapse (at an effective pressure of 10–15 MPa, or a depth of about 750 m), permeability and porosity decrease significantly, and ultrasonic wave velocities and dynamic elastic moduli increase significantly. Increasing the thermal stressing temperature increases the permeability and decreases the ultrasonic wave velocities and dynamic elastic moduli of the Neapolitan Yellow Tuff; whereas the tuff from the Campanian Ignimbrite remains unaffected. This difference is due to the presence of thermally unstable zeolites within the Neapolitan Yellow Tuff. For both rocks we also find, under the same pressure conditions, that the dynamic (calculated from ultrasonic wave velocities) and static (calculated from triaxial stress-strain data) elastic moduli differ significantly. The choice of elastic moduli in ground deformation modelling is therefore an important consideration. While we urge that these new laboratory data should be considered in routine ground deformation modelling, we highlight the challenges for ground deformation modelling based on the heterogeneous nature (vertically and laterally) of the rocks that comprise the caldera at Campi Flegrei.


Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6001
Author(s):  
Sheyore John Omovie ◽  
John P. Castagna

Sonic log compressional and shear-wave velocities combined with logged bulk density can be used to calculate dynamic elastic moduli in organic shale reservoirs. We use linear multivariate regression to investigate modulus prediction when shear-wave velocities are not available in seven unconventional shale reservoirs. Using only P-wave modulus derived from logged compressional-wave velocity and density as a predictor of dynamic shear modulus in a single bivariate regression equation for all seven shale reservoirs results in prediction standard error of less than 1 GPa. By incorporating compositional variables in addition to P-wave modulus in the regression, the prediction standard error is reduced to less than 0.8 GPa with a single equation for all formations. Relationships between formation bulk and shear moduli are less well defined. Regressing against formation composition only, we find the two most important variables in predicting average formation moduli to be fractional volume of organic matter and volume of clay in that order. While average formation bulk modulus is found to be linearly related to volume fraction of total organic carbon, shear modulus is better predicted using the square of the volume fraction of total organic carbon. Both Young’s modulus and Poisson’s ratio decrease with increasing TOC while increasing clay volume decreases Young’s modulus and increases Poisson’s ratio.


Author(s):  
L. Skakal's'ka

Research into the behavior of elastic waves in thin-layered gas-bearing geological structures depends on the choice of geophysical and mathematical models of natural geological media and the numerical methods of problem solving. Hence the efficiency of a quasi-homogeneous, isotropic fractured-porous two-phase medium with given physical and mechanical properties. We have suggested a method of calculating empirical relationships between volumetric compression, porosity and pressure in porous rocks of an arbitrary geological region. Data on Zaluzhany wells were used to calculate the correlation and empirical relationships between reservoir properties and parameters of elastic waves and to distinguish dry and oil-gas saturated rocks. The least square technique made it possible to determine the correlation between the compressibility factor of fluid-saturated rocks and their porosity and pressure. Discrimination between oil and water was based on the density parameter. An algorithm has been suggested to do the corresponding calculations. The theoretical and practical implications of this study are as follows: – developing a numerical analytical predictive model for interpreting acoustic data on thin-layered rocks which is based on the correlations between their dynamic physical (effective wave propagation velocities, amplitude attenuation coefficients and their energy absorption) and reservoir (porosity, fracturing, compressibility) properties; – applying the proposed model and software products in geophysical exploration to interpret the geological and geophysical data on the structure and physical characteristics of sections and the physical properties of gas-bearing basins. In seismic acoustic exploration, the numerical model has to include experimental geological and geophysical data on the peculiarities of rock occurrence in the investigated area, with the physical and mechanical properties of different territories showing considerable variation. Such input data, as well as structural features and scattering properties of rocks (density, bedding, microporosity), ensure a significant increase in the accuracy of the numerical analysis. Preliminary testing was based on the data on the elastic moduli and S-wave velocities for dry and fluid-saturated rocks. Calculations were made of the elastic moduli and P-wave velocities for dry and fluid-saturated rocks of the Western oil and gas region of Ukraine (Zaluzhany-18 and Zaluzhany-19 wells). The aim of this work was to demonstrate the efficiency of the predictive method by examining the reservoir rock properties of the wells and to evaluate their gas saturation using the acoustic logging, geophysical and petrophysical data.


1965 ◽  
Vol 36 (9) ◽  
pp. 2666-2672 ◽  
Author(s):  
Ahmed Rassem Wazzan ◽  
M. S. King ◽  
A. A. Ahmediah

Author(s):  
A. K. Chatterjee ◽  
A. K. Mal ◽  
L. Knopoff ◽  
J. A. Hudson

AbstractThe problem of the determination of the overall dynamic elastic moduli of an elastic solid permeated by uniformly distributed penny-shaped cracks is considered. The cracks are assumed to be filled with a viscoelastic material. The orientations of the cracks may be either parallel or perfectly random. The overall velocities as well as the specific attenuation coefficients of plane harmonic compressional and shear waves are calculated for low frequencies and dilute concentration of the cracks.


2013 ◽  
Vol 5 (2) ◽  
pp. 1081-1123 ◽  
Author(s):  
M. J. Heap ◽  
P. Baud ◽  
P. G. Meredith ◽  
S. Vinciguerra ◽  
T. Reuschlé

Abstract. The accuracy of ground deformation modelling at active volcanoes is a principal requirement in volcanic hazard mitigation. However, the reliability of such models relies on the accuracy of the rock physical property (permeability and elastic moduli) input parameters. Unfortunately, laboratory-derived values on representative rocks are usually rare. To this end we have performed a systematic laboratory study of the influence of pressure and temperature on the permeability and elastic moduli of the two most widespread tuffs from the Campi Flegrei volcanic district, Italy. Our data show that the water permeability of Neapolitan Yellow Tuff and a tuff from the Campanian Ignimbrite differ by about two orders of magnitude, highlighting the heterogeneous nature of the tuffs at Campi Flegrei. As pressure (depth) increases beyond the critical point for inelastic pore collapse (at an effective pressure of 10–15 MPa, or a depth of about 750 m), permeability and porosity decrease significantly, and ultrasonic wave velocities and dynamic elastic moduli increase significantly. Increasing the thermal stressing temperature increases the permeability and decreases the ultrasonic wave velocities and dynamic elastic moduli of the Neapolitan Yellow Tuff; whereas the tuff from the Campanian Ignimbrite remains unaffected. This difference is due the presence of thermally unstable zeolites within the Neapolitan Yellow Tuff. For both rocks we also find, under the same pressure conditions, that the dynamic (calculated from ultrasonic wave velocities) and static (calculated from triaxial stress-strain data) elastic moduli differ significantly. The choice of elastic moduli in ground deformation modelling is therefore an important consideration. While we urge that these new laboratory data should be considered in routine ground deformation modelling, we highlight the heterogeneous nature of the rocks that comprise the caldera at Campi Flegrei.


Author(s):  
K.R. Porter

Most types of cells are known from their structure and overall form to possess a characteristic organization. In some instances this is evident in the non-random disposition of organelles and such system subunits as cisternae of the endoplasmic reticulum or the Golgi complex. In others it appears in the distribution and orientation of cytoplasmic fibrils. And in yet others the organization finds expression in the non-random distribution and orientation of microtubules, especially as found in highly anisometric cells and cell processes. The impression is unavoidable that in none of these cases is the organization achieved without the involvement of the cytoplasmic ground substance (CGS) or matrix. This impression is based on the fact that a matrix is present and that in all instances these formed structures, whether membranelimited or filamentous, are suspended in it. In some well-known instances, as in arrays of microtubules which make up axonemes and axostyles, the matrix resolves itself into bridges (and spokes) between the microtubules, bridges which are in some cases very regularly disposed and uniform in size (Mcintosh, 1973; Bloodgood and Miller, 1974; Warner and Satir, 1974).


1984 ◽  
Vol 20 (5) ◽  
pp. 343-350 ◽  
Author(s):  
A. N. Stavrogin ◽  
G. G. Zaretskii-Feoktistov ◽  
G. N. Tanov

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