Sequential Measurement of Compressional and Shear Velocities of Rock Samples Under Triaxial Pressure

1969 ◽  
Vol 9 (04) ◽  
pp. 378-394 ◽  
Author(s):  
K.P. Desai ◽  
D.P. Helander
Keyword(s):  
Acoustic Wave ◽  
Resonant Frequency ◽  
Wave Velocity ◽  
Resonance Method ◽  
Shear Velocity ◽  
Berea Sandstone ◽  
Rock Samples ◽  
Wave Velocities ◽  
Compressional Velocity ◽  
Wave Properties

Abstract A laboratory measuring system was designed that can precisely and sequential measure both compressional and shear velocities of rock samples under identical conditions of stress distribution and stress history. This is required if accurate and realistic dynamic elastic properties of rocks are to be determined. The hysteresis effect on velocity pressure characteristics of rock was determined to pressure characteristics of rock was determined to illustrate this point. Lead titanate zirconate transducers were used for measuring compressional wave velocity, and AC-cut quartz transducers were used for measuring shear wave velocity. The system was tested using samples of standard material such as aluminum, steel, brass and lucite. Measurements obtained were accurate within 1 percent. percent. Compressional and shear velocities were measured sequentially on 10 samples of Berea sandstone and two samples of Bartlesville sandstone. It was found that 1. Both compressional and shear velocities increased with an increase in applied external pressure. pressure. 2. Compressional velocity depends upon both external (Pe) and internal (Pi) pressure. 3. Shear velocity depends only upon the differential pressure (Pne-Pe-Pi). 4. The nature of the fluid saturant had little effect on compressional velocity. 5. Shear velocity decreased with an increase in the density of the saturant. 6. The Berea sandstone indicated very little anisotropy. 7. The Bartlesville sandstone showed definite anisotropy. Introduction The various properties of an acoustic wave trainvelocity, amplitude, frequency, etc. may be modified, sometimes quite severely by the media through which the wave has traveled. This suggests the use of wave properties to determine, at least in part, the nature of the material through which the part, the nature of the material through which the wave has passed. To accomplish this successfully requires a reliable technique to for obtaining accurate values of all acoustic wave properties. One purpose of this paper is to describe a recently developed system that can precisely and sequentially record acoustic compressional and shear energies as functions both of time and of frequency. One example of the utility of this system is the accurate measurement of compressional and shear velocities through rock samples subjected to triaxial, i.e., simultaneous but independent vertical, circumferential and pore pressure. Since acoustic velocity and elasticity are closely interrelated, such a system would help to determine realistically the elastic properties of rock samples in the laboratory. METHODS FOR THE INDEPENDENT MEASUREMENT OF COMPRESSIONAL AND SHEAR WAVE VELOCITIES Currently there are two suitable nondestructive laboratory techniques for measuring wave velocity through a rock sample under pressure. One is by the resonance method and the other is by the pulse technique. In the resonance method a sample, in the form of a thin wire, rod, or plate, is make to vibrate in the longitudinal, torsional or flexural mode. Resonant frequency is determined by recording the amplitude of vibration as a function of applied frequency; the amplitude is maximum at resonant frequency. For isotropic materials the relationships between resonance frequencies, elastic moduli and acoustic wave velocities are well known. SPEJ p. 378

scholarly journals Theoretical investigation of acoustic wave velocity of aluminum phosphide under pressure

2019 ◽  
Vol 7 (1) ◽  
pp. 3
Author(s):  
Salah Daoud ◽  
Abdelhakim Latreche ◽  
Pawan Kumar Saini
Keyword(s):  
Acoustic Wave ◽  
Wave Velocity ◽  
Elastic Constants ◽  
Structural Parameters ◽  
Theoretical Data ◽  
Aluminum Phosphide ◽  
Semiconducting Material ◽  
Wave Velocities ◽  
Knoop Microhardness ◽  
Good Agreement

The bulk and surface acoustic wave velocities of Aluminum phosphide (AlP) semiconducting material under pressure up to 9.5 GPa were studied. The structural parameters and the elastic constants used in this work are taken from our previous paper published in J. Optoelec-tron. Adv. M. 16, 207 (2014). The results obtained at zero-pressure are analyzed and compared with other data of the literature. In addition, the acoustic Grüneisen parameter and the Vickers and Knoop microhardness are predicted and analyzed in detail. Our calculated results are in good agreement with the experimental and other theoretical data of literature.   

Acoustic wave propagation in a fluid‐filled borehole surrounded by a formation with stress‐relief‐induced anisotropy

Geophysics ◽  
1993 ◽  
Vol 58 (9) ◽  
pp. 1257-1269 ◽  
Author(s):  
Lasse Renlie ◽  
Arne M. Raaen
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Shear Wave ◽  
Transverse Isotropy ◽  
Shear Velocity ◽  
Stress Relief ◽  
Stoneley Wave ◽  
Acoustic Wave Propagation ◽  
Damaged Zone ◽  
Compressional Velocity

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the [Formula: see text] plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave with radial polarization. As a result, acoustic logging in an RTI formation, will indicate a higher [Formula: see text] ratio than that existing in the virgin formation. It also follows that the shear velocity may be a better indicator of a mechanically damaged zone near the borehole than the compressional velocity. The Stoneley‐wave velocity was found to decrease with the increasing degree of RTI.

Changes in soil conditions before and after earthquakes at a repetitive soil liquefaction site in Taiwan

Geophysics ◽  
2022 ◽  
pp. 1-49
Author(s):  
Yu-Tai Wu
Keyword(s):  
Shear Modulus ◽  
Wave Velocity ◽  
Shear Velocity ◽  
Soil Condition ◽  
Soil Liquefaction ◽  
Soil Conditions ◽  
S Wave ◽  
Liquefaction Potential ◽  
Wave Velocities ◽  
Low Shear

Beishih Village of Hsinhua Township in southern Taiwan is a unique location for studying soil liquefaction. Soil liquefaction was observed at the same site after earthquakes in 1946, 2010, and 2016, each of which had a Richter magnitude greater than six. This recurrence provides an opportunity for analyzing soil condition variations resulting from soil liquefaction. Seismic data sets were collected in 2011, 2014, 2016, and 2017. We used seismic refraction tomography and the multichannel analysis of surface waves to estimate P- and S-wave velocities. In S-wave velocity profiles, low shear velocity zones were located beneath sand volcanoes shortly after two earthquakes and disappeared 4 years after a 2010 earthquake. However, the P-wave velocity is less sensitive to soil condition changes, possibly because groundwater obscures the effect of soil liquefaction on velocity profiles. In addition, we used seismic wave velocities to determine the importance of soil properties such as Poisson’s ratio, shear modulus, and porosity to identify the cause of the low shear velocity zone. Notably, although porosity decreased after soil grain rearrangement, sand and clay mixing increased the Poisson’s ratio, reducing the shear modulus of the soil. In addition, a soil layer between 2 and 7 m and a deeper layer below 10 m that resulted in sand volcanoes were both liquefied. We also considered how the evaluation of soil liquefaction potential could be affected by long-term variations in soil conditions and changes resulting from liquefaction. The factor of safety was used to evaluate the liquefaction potential of the site. The results revealed that the assessment conducted long after the earthquake underestimated risk because the soil developed shear strength after the earthquake.

How Can Be Realized High Piezoelectricity from Measuring Acoustic Wave Velocities ?

2014 ◽  
Vol 90 ◽  
pp. 33-42
Author(s):  
Toshio Ogawa
Keyword(s):  
Acoustic Wave ◽  
Wave Velocity ◽  
Piezoelectric Materials ◽  
Piezoelectric Ceramics ◽  
Measuring Method ◽  
Lead Free ◽  
Material Research ◽  
Thickness Gauge ◽  
Wave Velocities ◽  
Lead Free Ceramics

Material research and development on piezoelectric ceramics, especially lead-free ceramics, was proposed from a viewpoint of relationships between piezoelectricity and elastic constants such as Young’s modulus and Poisson’s ratio. We developed a method to be convenient to measure acoustic wave velocities by an ultrasonic thickness gauge with high-frequency. From the change in longitudinal and transvers wave velocities before and after DC poling, it was found that the ceramic bulk density was important to improve the piezoelectricity in lead-free ceramics. As a result, the candidates of lead-free ceramic compositions with higher piezoelectricity were proposed. Furthermore, the ratio of transvers wave velocity to longitudinal wave velocity was clarified to estimate compositions with higher piezoelectricity. The measurement of sound velocities was an effective method for researching and developing piezoelectric materials, and it was possible to design the material compositions of lead-free piezoelectric ceramics as well as lead-containing ceramics by the novel measuring method.

Characterization of Stress at a Ceramic/Metal Joined Interface by the Vz Technique of Scanning Acoustic Microscopy

2002 ◽  
Vol 124 (3) ◽  
pp. 336-342 ◽  
Author(s):  
Chiaki Miyasaka ◽  
Bernard R. Tittmann ◽  
Shun-Ichiro Tanaka
Keyword(s):  
Acoustic Wave ◽  
Surface Acoustic Wave ◽  
Wave Velocity ◽  
Dissimilar Materials ◽  
Acoustic Microscopy ◽  
Scanning Acoustic Microscopy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Wave Velocities

It is well known that the process of heating and then cooling dissimilar materials introduces considerable stress at and near the interface. In this article, first, the surface wave velocity distributions obtained with the Vz curve technique were found to compare well with residual stress distribution measured by the finely collimated X-ray diffraction technique. Second, a delamination was introduced at the interface. The Vz curve technique was then used again to measure the surface acoustic wave velocity along the interface. The defective specimens showed significantly different patterns of surface acoustic wave velocities. Thus, this study presents useful guidelines in discriminating between sound and defective ceramic/metal joints by scanning acoustic microscopy.

Determining P- and S-wave velocities and Q-values from single ultrasound transmission measurements performed on cylindrical rock samples: it’s possible, when…

2020 ◽  
Author(s):  
Marc S. Boxberg ◽  
Mandy Duda ◽  
Katrin Löer ◽  
Wolfgang Friederich ◽  
Jörg Renner
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
Standard Material ◽  
Rock Samples ◽  
Intrinsic Attenuation ◽  
Finite Element Software ◽  
Wave Velocities ◽  
P Wave Velocity

<p>Determining elastic wave velocities and intrinsic attenuation of cylindrical rock samples by transmission of ultrasound signals appears to be a simple experimental task, which is performed routinely in a range of geoscientific and engineering applications requiring characterization of rocks in field and laboratory. P- and S-wave velocities are generally determined from first arrivals of signals excited by specifically designed transducers. A couple of methods exist for determining the intrinsic attenuation, most of them relying either on a comparison between the sample under investigation and a standard material or on investigating the same material for various geometries.</p><p>Of the three properties of interest, P-wave velocity is certainly the least challenging one to determine, but dispersion phenomena lead to complications with the consistent identification of frequency-dependent first breaks. The determination of S-wave velocities is even more hampered by converted waves interfering with the S-wave arrival. Attenuation estimates are generally subject to higher uncertainties than velocity measurements due to the high sensitivity of amplitudes to experimental procedures. The achievable accuracy of determining S-wave velocity and intrinsic attenuation using standard procedures thus appears to be limited.</p><p>We pursue the determination of velocity and attenuation of rock samples based on full waveform modeling and inversion. Assuming the rock sample to be homogeneous - an assumption also underlying standard analyses - we quantify P-wave velocity, S-wave velocity and intrinsic P- and S-wave attenuation from matching a single ultrasound trace with a synthetic one numerically modelled using the spectral finite-element software packages SPECFEM2D and SPECFEM3D. We find that enough information on both velocities is contained in the recognizable reflected and converted phases even when nominal P-wave sensors are used. Attenuation characteristics are also inherently contained in the relative amplitudes of these phases due to their different travel paths. We present recommendations for and results from laboratory measurements on cylindrical samples of aluminum and rocks with different geometries that we also compare with various standard analysis methods. The effort put into processing for our approach is particularly justified when accurate values and/or small variations, for example in response to changing P-T-conditions, are of interest or when the amount of sample material is limited.</p>

Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks

Geophysics ◽  
1985 ◽  
Vol 50 (4) ◽  
pp. 571-581 ◽  
Author(s):  
J. P. Castagna ◽  
M. L. Batzle ◽  
R. L. Eastwood
Keyword(s):  
Bulk Modulus ◽  
Shear Wave ◽  
Wave Velocity ◽  
Velocity Ratio ◽  
Shear Velocity ◽  
Compressional Wave ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Water Saturated ◽  
Silicate Rocks

New velocity data in addition to literature data derived from sonic log, seismic, and laboratory measurements are analyzed for clastic silicate rocks. These data demonstrate simple systematic relationships between compressional and shear wave velocities. For water‐saturated clastic silicate rocks, shear wave velocity is approximately linearly related to compressional wave velocity and the compressional‐to‐shear velocity ratio decreases with increasing compressional velocity. Laboratory data for dry sandstones indicate a nearly constant compressional‐to‐shear velocity ratio with rigidity approximately equal to bulk modulus. Ideal models for regular packings of spheres and cracked solids exhibit behavior similar to the observed water‐saturated and dry trends. For dry rigidity equal to dry bulk modulus, Gassmann’s equations predict velocities in close agreement with data from the water‐saturated rock.

THE ELASTICITY OF THE LARGE ARTERIES IN HYPERTENSION

1952 ◽  
Vol 30 (2) ◽  
pp. 125-129
Author(s):  
J. P. Adamson ◽  
J. Doupe
Keyword(s):  
Blood Pressure ◽  
Pulse Wave Velocity ◽  
Wave Velocity ◽  
Pulse Wave ◽  
Diastolic Pressure ◽  
Arterial Elasticity ◽  
Large Arteries ◽  
Wave Velocities

Intra-arterial pressures and pulse wave velocities were measured in 18 subjects whose auscultatory diastolic pressures ranged from 45 to 120 mm. Hg. Various methods were used to lower the blood pressure in the hypertensive and to raise it in nonhypertensive subjects so that pulse wave velocities might be compared in all subjects at a common diastolic pressure. The pulse wave velocities were calculated for a diastolic pressure of 80 mm. Hg. No significant differences were found between hypertensive and nonhypertensive subjects. It was concluded that a defect of arterial elasticity as gauged by pulse wave velocity is not a factor in the pathogenesis of hypertension.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

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