scholarly journals Porosity dependence of elastic moduli of snow and firn

2021 ◽  
pp. 1-9
Author(s):  
Colin M. Sayers
Keyword(s):  
Elastic Wave ◽  
Elastic Moduli ◽  
Elastic Wave Velocity ◽  
Velocity Measurements ◽  
Critical Porosity ◽  
Shear Moduli ◽  
Potential Applications ◽  
Non Destructive ◽  
Seismic Measurements ◽  
Good Agreement

Abstract Measurements of elastic wave velocities enable non-destructive estimation of the mechanical properties, elastic moduli and density of snow and firn. The variation of elastic moduli with porosity in dry snow and firn is modeled using a differential effective medium scheme modified to account for the critical porosity above which the bulk and shear moduli of the ice frame vanish. A comparison of predicted and measured elastic moduli indicates that the shear modulus of ice in snow is lower than that computed from single crystal elastic stiffnesses of ice. This may indicate that the bonds between snow particles are more deformable under shear than under compression. A partial alignment of ice crystals also may contribute. Good agreement between elastic stiffnesses of the ice frame obtained from elastic wave velocity measurements and the predictions of the theory is observed. The approach is simple and compact, and does not require the use of empirical fits to the data. Owing to its simplicity, this model may prove useful in a variety of potential applications such as construction on snow, interpretation of seismic measurements to monitor and locate avalanches and estimation of density within compacting snow deposited on glaciers and ice sheets.

ELASTIC‐WAVE VELOCITY MEASUREMENTS IN ROCKS AND OTHER MATERIALS BY PHASE‐DELAY METHODS

Geophysics ◽  
1975 ◽  
Vol 40 (6) ◽  
pp. 955-960 ◽  
Author(s):  
E. A. Kaarsberg
Keyword(s):  
Elastic Wave ◽  
Wave Velocity ◽  
Path Length ◽  
Shear Velocity ◽  
Elastic Wave Velocity ◽  
Phase Delay ◽  
Velocity Measurements ◽  
Multiple Reflections ◽  
Low Velocity ◽  
High Attenuation

The phase delay of a continuous sinusoidal elastic wave after transmission through a medium may be used to determine the velocity of propagation of the wave in the medium. The change in path length for a given frequency, or the change in frequency for a given path length, required to change the phase delay by integral multiples of 360 degrees is measured in the laboratory by the use of source and receiver piezoelectric transducers whose signals are applied to the horizontal and vertical deflection circuits of an oscilloscope. The accuracy of the method depends upon the accuracy with which the frequency of the transmitted wave and its path length through the medium (or change in path length) can be determined, provided the effect of extraneous signals (e.g., boundary reflections, multiple reflections, alternate modes of propagation, etc.) is negligible. The phase‐delay methods are illustrated and compared with conventional pulse methods by using both to make compressional‐velocity measurements in water and compressional‐ and shear‐velocity measurements in a high velocity basalt and in a low velocity dried mud sample. The results of the two methods agree to within a few percent. It is suggested that these phase‐delay methods may be especially well‐suited for making elastic‐wave velocity measurements in media with high attenuation of the waves propagated in them.

Anisotropy of elastic wave velocities in deformed shales: Part 1 — Experimental results

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. D75-D89 ◽  
Author(s):  
Joël Sarout ◽  
Yves Guéguen
Keyword(s):  
Elastic Wave ◽  
Wave Velocity ◽  
Elastic Anisotropy ◽  
Ambient Pressure ◽  
Transversely Isotropic ◽  
Elastic Wave Velocity ◽  
Velocity Measurements ◽  
Wave Velocities ◽  
In Situ Conditions ◽  
Triaxial Cell

Elastic wave velocity measurements in the laboratory are used to assess the evolution of the microstructure of shales under triaxial stresses, which are representative of in situ conditions. Microstructural parameters such as crack aperture are of primary importance when permeability is a concern. The purpose of these experiments is to understand the micromechanical behavior of the Callovo-Oxfordian shale in response to external perturbations. The available experimental setup allows for the continuous, simultaneous measurement of five independent elastic wave velocities and two directions of strain (axial and circumferential), performed on the same cylindrical rock sample during deformation in an axisymmetric triaxial cell. The main results are (1) identification of the complete tensor of elastic moduli of the transversely isotropic shales using elastic wave velocity measurements, (2) assessment of the evolution of these moduli under triaxial loading, and (3) assessment of the evolution of the elastic anisotropy under loading in terms of Thomsen’s parameters. This last outcome allows us to use the anisotropy of the elastic properties of this rock as an indicator of the evolution of its microstructure. In particular, [Formula: see text] in the dry case decreases from 0.5 (ambient pressure) toward 0.37 [Formula: see text], while [Formula: see text] and [Formula: see text] are almost insensitive to pressure. In the wet case, [Formula: see text] decreases from 0.3 (ambient pressure) toward 0.2 [Formula: see text]. Deviatoric stresses have a strong effect on [Formula: see text], [Formula: see text], and [Formula: see text] variations. In this case, [Formula: see text] drops (both for the dry and wet conditions) when failure is approached.

scholarly journals Velocity-Porosity-Mineralogy Model for Unconventional Shale and Its Applications to Digital Rock Physics

2021 ◽  
Vol 8 ◽  
Author(s):  
Jack Dvorkin ◽  
Joel Walls ◽  
Gabriela Davalos
Keyword(s):  
Elastic Wave ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Solid Phase ◽  
Rock Physics ◽  
Elastic Wave Velocity ◽  
Mathematical Form ◽  
Critical Porosity ◽  
Physics Model ◽  
Rock Physics Model

By examining wireline data from Woodford and Wolfcamp gas shale, we find that the primary controls on the elastic-wave velocity are the total porosity, kerogen content, and mineralogy. At a fixed porosity, both Vp and Vs strongly depend on the clay content, as well as on the kerogen content. Both velocities are also strong functions of the sum of the above two components. Even better discrimination of the elastic properties at a fixed porosity is attained if we use the elastic-wave velocity of the solid matrix (including kerogen) of rock as the third variable. This finding, fairly obvious in retrospect, helps combine all mineralogical factors into only two variables, Vp and Vs of the solid phase. The constant-cement rock physics model, whose mathematical form is the modified lower Hashin-Shtrikman elastic bound, accurately describes the data. The inputs to this model include the elastic moduli and density of the solid component (minerals plus kerogen), those of the formation fluid, the differential pressure, and the critical porosity and coordination number (the average number of grain-to-grain contacts at the critical porosity). We show how this rock physics model can be used to predict the elastic properties from digital images of core, as well as 2D scanning electron microscope images of very small rock fragments.

scholarly journals Evaluation of Static and Dynamic Residual Mechanical Properties of Heat-Damaged Concrete for Nuclear Reactor Auxiliary Buildings in Korea Using Elastic Wave Velocity Measurements

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2695 ◽  
Author(s):  
Seong-Hoon Kee ◽  
Jun Won Kang ◽  
Byong-Jeong Choi ◽  
Juho Kwon ◽  
Ma. Doreen Candelaria
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Elastic Wave ◽  
Wave Velocity ◽  
Elastic Moduli ◽  
Nuclear Reactor ◽  
Dynamic Properties ◽  
Velocity Measurements ◽  
Heating And Cooling ◽  
Dynamic Elastic Moduli

The main objectives of this study are (1) to investigate the effects of heating and cooling on the static and dynamic residual properties of 35 MPa (5000 psi) concrete used in the design and construction of nuclear reactor auxiliary buildings in Korea; and (2) to establish the correlation between static and dynamic properties of heat-damaged concrete. For these purposes, concrete specimens (100 mm × 200 mm cylinder) were fabricated in a batch plant at a nuclear power plant (NPP) construction site in Korea. To induce thermal damages, the concrete specimens were heated to target temperatures from 100 °C to 1000 °C with intervals of 100 °C, at a heating rate of 5 °C/min and allowed to reach room temperature by natural cooling. The dynamic properties (dynamic elastic modulus and dynamic Poisson’s ratio) of concrete were evaluated using elastic wave measurements (P-wave velocity measurements according to ASTM C597/C597M-16 and fundamental longitudinal and transverse resonance tests according to ASTM C215-14) before and after the thermal damages. The static properties (compressive strength, static elastic modulus and static Poisson’s ratio) of heat-damaged concrete were measured by the uniaxial compressive testing in accordance with ASTM C39-14 and ASTM C469-14. It was demonstrated that the elastic wave velocities of heat-damaged concrete were proportional to the square root of the reduced dynamic elastic moduli. Furthermore, the relationship between static and dynamic elastic moduli of heat-damaged concrete was established in this study. The results of this study could improve the understanding of the static and dynamic residual mechanical properties of Korea NPP concrete under heating and cooling.

Elastic moduli of grain boundaries in nanocrystalline MgO ceramics

2005 ◽  
Vol 20 (3) ◽  
pp. 719-725 ◽  
Author(s):  
Ori Yeheskel ◽  
Rachman Chaim ◽  
Zhijian Shen ◽  
Mats Nygren
Keyword(s):  
Grain Size ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Hot Isostatic Pressing ◽  
Velocity Measurements ◽  
Shear Moduli ◽  
Plasma Sintering ◽  
Spark Plasma ◽  
Nanocrystalline Mgo

Dense MgO ceramics with nanometer to submicrometer grain size were fabricated by high-temperature hot-isostatic pressing, low-temperature hot-pressing, and spark plasma sintering. The elastic properties were determined by sound wave velocity measurements. Young's and shear moduli of nanocrystalline MgO were lower by 13% than those with submicrometer grain size. Softening of the elastic properties was analyzed and related to the lower density and lower elastic moduli of the grain boundaries compared to the crystal interior. Young's and shear moduli of the grain boundaries were evaluated as 90 and 34 GPa, respectively. This leads to a more than 3-fold decrease in the effective elastic moduli with the decrease of grain size into the nanometer range.

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