Dynamic Poisson's Ratio Research Articles

Poisson's ratios of crystalline rocks as a function of hydrostatic confining pressure

The hydrostatic pressure (P) dependence of dynamic Poisson's ratios (υ) has been investigated for 54 samples of the crystalline rocks from the Sulu‐Dabie orogenic belt (China) using pulse transmission techniques. The Poisson's ratio of each sample was calculated from its mean P and S wave velocities from three orthogonal directions corresponding to the tectonic framework (X‐Y‐Z) defined by foliation and lineation. The experimental results display two typical categories of υ – P relationship in the range of 40–800 MPa: (1) with increasing pressure, υ increases rapidly below ∼200 MPa and then becomes quasi‐constant at higher pressures, and (2) υ shows little variation with P. Types 1 and 2 are observed in 32 and 22 samples, respectively. The origin of type 1 can be reasonably interpreted by a small volume fraction (0.1–0.5%) of randomly distributed and randomly oriented thin disk‐shaped microcracks that are progressively closed during pressurization. Type 2 is originated from the combined effects of microcrack orientation, crystallographic preferred orientations, and compositional layering. The present study confirms that the crystalline rocks at pressures above ∼200 MPa show no significant changes in Poisson's ratio with increasing pressure. Below 200 MPa, however, both modal composition and confining pressure play a critical role in influencing the Poisson's ratio.

Relation of bulk to shear loss factor of solid viscoelastic materials

The relation between the bulk and shear loss factors of isotropic, homogeneous, linear solid viscoelastic materials is investigated in this paper by means of the complex modulus concept. It is shown that the bulk and shear loss factors can be related through the dynamic Poisson's ratio provided that the shear loss is low enough. Bounds on the ratio of the bulk to shear loss factor are derived, and the respective lower bounds are given as a function of the dynamic Poisson's ratio. The ratio of the bulk to shear loss factor is predicted to decrease with the increase of dynamic Poisson's ratio, and it is shown that the decrease may obey a simple power law if the Poisson's ratio is close to either 0 or 0.5. Experimental data on solid polymeric materials are presented which support the theoretical findings.

Application of low-profile piezoceramic transducers for health monitoring of concrete structures

Using piezoceramic patches bonded on concrete beams to perform structural health monitoring is investigated in this paper. To evaluate the performance of piezoceramic sensors and ultrasonic wave methods, two series of tests were carried out on 100×100×500 mm 3 concrete prisms. In the first series of tests, the influence of the frequency of the input signal on the waveforms was investigated and the optimum frequency to generate ultrasonic waves was evaluated. From the velocity of Rayleigh waves and longitudinal waves, the dynamic modulus of elasticity and dynamic Poisson's ratio of the concrete were obtained. In the second series, the effect of uniaxial compressive stress and the resulting internal cracking of the concrete on the amplitude of the waveforms received by piezoceramic sensors was investigated. It is shown that differences in amplitude between two wave packets are sensitive to the cracking process of concrete with externally applied loads. The results confirm that piezoceramic sensors and corresponding ultrasonic waves methods have the potential to monitor cracking and the long-term deterioration of concrete structures.

The Poisson's loss factor of solid viscoelastic materials

The complex Poisson's ratio plays an important role in characterizing the linear dynamic behaviour of solid materials, and occurs in a number of equations used for acoustical and vibration calculus. The ratio of the imaginary part to the real part of complex Poisson's ratio is referred to as Poisson's loss factor. The magnitude of the Poisson's loss factor is investigated in this paper for homogeneous, isotropic, linear solid viscoelastic materials with positive Poisson's ratio. The relation of the Poisson's loss factor to the material damping is determined. It is shown that the magnitude of the Poisson's loss factor is approximately proportional to the difference between the shear and bulk loss factors, and is a rational fractional function of the dynamic Poisson's ratio. In addition, relationships are developed which enable one to determine the approximate magnitude of the Poisson's loss factor from knowledge only of the shear loss factor and the dynamic Poisson's ratio. It is shown that the Poisson's loss factor is smaller than the shear loss factor usually by one order of magnitude at least. Moreover, it is pointed out that the Poisson's loss factor of a high loss and a low loss material may be about the same. Experimental data on two rubbers and a hard plastic are presented to verify the theoretical conclusions.

Spatial predictions of geological rock mass properties based on in-situ interpretations of multi-dimensional seismic data

The article presents a statistical approach to characterize and predict engineering geological conditions in the up to 2000 m deep Faido tunnel and Gotthard base tunnel in Switzerland. Seismic investigations were conducted to improve the technology of interpreting seismic tomographic images. Overall, the goal of this study was to predict spacial maps of geological rock mass properties, such as, uniaxial compressive strength or total fracture spacing, by using up to six seismic features in combination, e.g., compression-wave and shear-wave velocities and dynamic Poisson's ratio. Self-Organizing Mapping (SOM), an artificial intelligent method, was used for the purposes of interpreting multi-dimensional geophysical attributes derived from seismic profiles of tomographic images along tunnel sidewalls. The SOM-method was applied in the Faido tunnel to delineate complex physical relations between the geological and seismic parameters. Then, the method was applied to predict geological properties around a segment of the Gotthard base tunnel with unknown geological–geotechnical conditions. The results illuminate that correlation analyses (pairwise parameter classification) are substantially less powerful than the SOM-method (multi-parameter classification) in order to interpret geological features from seismic in-situ data. Moreover, predicted spatial distributions of the total fracture spacing and the uniaxial compressive strength, for example, corresponded well with drill core and tunnel mapping results. The SOM-approach was a helpful tool for practitioners in predicting zones of instabilities and geological complexity during underground excavation processes of the Gotthard base tunnel. It is suggested to use such an interpretation method as decision support for purposes of sub/surface exploration and long-term geophysical monitoring of large-scale geoengineering projects, such as, disposals of nuclear waste and greenhouse gases or geopower plants for renewable energy (geothermal, biosoils).

How depositional texture and diagenesis control petrophysical and elastic properties of samples from five North Sea chalk fields

Chalk samples from Dan, Tyra, South Arne, Valhall and Ekofisk fields were collected from hydrocarbon-bearing intervals in the Cretaceous Tor and Palaeogene Ekofisk formations in the central North Sea. The samples were compared with respect to stable isotope ratios, lithotype, texture, porosity, permeability, capillary entry pressure, as well as the dynamic elastic Biot's coefficient and Poisson's ratio. The depositional texture and present grain-size distribution were quantified by petrographic image analysis. Oxygen isotope ratio and Biot's coefficient were used as indicators of cementation. Porosity varies more than 20 porosity units within each hydrocarbon field and is controlled by three parameters: (1) sorting as expressed by Dunham texture, so that mudstones tend to have highest porosity and packstones the lowest; (2) sorting of the carbonate mud, where a mixture of clay-size chalk particles and silicates tend to reduce porosity; and (3) by pore-filling cementation. The relative significance of these parameters varies with field and formation. The presence of chalk clasts as an indicator of re-deposited chalk seems to have no relationship to porosity. Permeability and capillary entry pressure depend on porosity and mineral content as expressed in specific surface. Prediction of permeability and capillary entry pressure may be aided by information on carbonate content or on Poisson's ratio.

Experimental and theoretical rock physics research with application to reservoirs, seals and fluid processes

This paper describes a range of geophysical research activities at the Australian Resources Research Centre based around the development of an experimental capability to validate theoretical and numerical modelling predictions of geophysical properties of reservoirs and seals. Laboratory tests performed on reservoir sandstones, shales and artificial sandstones under a range of controlled triaxial stress conditions allow the full anisotropic elastic tensor to be calculated from ultrasonic measurements on a single core. The analysis of elastic properties and anisotropy in relation to varied stress, pore pressure and fluid saturation can provide significant insight for both exploration (e.g. pore pressure prediction) and production (4D seismic feasibility studies for changes in pore pressure and saturation during production). Ultrasonic data from core measurements are related to seismic response through theoretical analysis of frequency effects and the methodologies developed from this research are subsequently tested on 3D seismic data. Understanding the causes and degree of anisotropy, for example, are critical for depth conversion, imaging, fluid identification (e.g. AVO) and dynamic Poisson's ratio. Velocity hysteresis observed in shales and sandstones with different stress histories has led to an improved understanding of the concept of effective stress and its effect on seismic data. Positive correlations between effective stress and pore pressure with several instantaneous seismic attributes have been established that allow direct mapping of seismic attribute changes into absolute values of effective stress. This methodology has been tested on a 3D seismic dataset from the Northwest Shelf of Australia and shows good agreement with both the distribution and magnitude of the overpressures present. Similarly, X-ray CT images have been combined with ultrasonic measurements conducted on core samples to establish the sensitivity of instantaneous seismic attributes to various degrees of fluid saturation. These results indicate that seismic attributes can be used as an alternative approach for discrimination between pressure and saturation affects. The results from these combined research activities have improved our understanding of the impact of effective stress, anisotropy and saturation on the interpretation of geophysical data, which has implications for pore pressure prediction, 4D seismic evaluations, depth conversion and stress-saturation discrimination.

Relationship Between Physical and Mechanical Parameters of Coal Measures Rocks and Acoustic Wave Velocity

AbstractThe longitudinal and transverse wave velocity of sedimentary rock of coal measures is systematically analyzed by ultrasonic‐time dynamic testing. The parameters of dynamic elasticity are calculated. Static mechanical parameters of the rocks are synchronously tested. The qualitative and quantitative relationships between the dynamic and static elasticity parameters, and between the physical and mechanical parameters and acoustic wave velocity of the rocks are established. The research results show that there is a good positive correlativity between dynamic modulus of elasticity and the longitudinal or transverse wave velocity, but there is no such positive correlativity between dynamic Poisson's ratio of the rocks and its longitudinal or transverse wave velocity. The dynamic elastic modulus of the rocks is higher than its static elastic modulus, while the dynamic Poisson's ratio is lower than its static Poisson's ratio, and there is a linear correlativity between them. The relationships between density of the rock, uniaxial compressive strength, tensile strength and the longitudinal or transverse wave velocity are also the positive correlativity, which are best fitted by quadratic function, exponential function and linear function, respectively.

A new model for analyzing the effect of fractures on triaxial deformation

Rock is porous, with a connected network of cracks and pores. The static and dynamic behaviors of a rock sample under load depend on both the solid mineral matrix and the porous phase. In general, the configuration of the pore phase is complex; thus, most studies on the effect of the porous phase on rock deformation are conducted numerically and theoretical analyses of the constitutive relations are scarce. We have studied rock deformation under axially symmetric loading by analyzing a model where the pore phase is approximated by rough planes, randomly spaced and oriented, extending through the sample. The roughness is caused by asperities, all with the same tip radii, but having heights h with a probability density distribution given by the negative exponential e − h/ λ where λ is a length parameter. Slip at contacts under local shear stress is resisted by simple Coulomb friction, with friction coefficient f. Both static and dynamic deformation were analyzed. The effect of porosity on deformation for both modes was found to be given by the non-dimensional parameter λα j , where α j is the total area of the fault planes per unit volume. We demonstrate that stress-induced microfracturing begins as randomly oriented microslip throughout the sample. As axial load increases, microslip occurs along preferred orientations and locations, which finally leads to deformation on a single fault. The model was found to fault under static loading conditions—the axial load at faulting and the angle of the “fracture” plane agree with values of those parameters given by Coulomb's theory of fracture. Dynamic moduli and Poisson's ratio are found to be virtually elastic and independent of the friction coefficient acting at contacts. The attenuation Q E - 1 for uniaxial dynamic loading is a strong function of the friction coefficient and increases linearly with strain amplitude, in agreement with laboratory measurements.

Static and Dynamic Swelling Properties of Poly(N-isopropylacrylamide) Gels in the Swollen State

Static and dynamic swelling properties of cylindrical poly(N-isopropylacrylamide) (PNIPA) gels in water as well as in liquid paraffin (non-solvent for PNIPA gels) have been investigated by using a laboratory-made magnetic force-driven rheometer. In static tests (under a constant stress), the length and diameter of the gel sample in water increase with time due to stress-induced swelling. Relaxation times of the stress-induced swelling in both directions are identical within experimental error. The Poisson ratio decreases from ∼0.5 to ∼0.2 with time just after the application of the magnetic force. The dynamic tests (under sinusoidal forces) reveal large differences in the swelling behavior of the gels in water and liquid paraffin. In liquid paraffin, amplitudes of strains parallel and perpendicular to elongation (ε‖ and ε⊥, respectively) are independent of angular frequency (ω), giving the absolute value of dynamic Poisson ratio (|μ∗|=ε⊥/ε‖) of ∼0.47. On the other hand, ε‖, ε⊥ and |μ∗| in water significantly depend on ω due to the stress-induced swelling with a characteristic time. The dynamic Poisson ratio at ω→∞ (short time limit) or ω→0 (long time limit) agrees well with the corresponding Poisson’s ratio obtained by the static tests. The phase lags of ε∗‖ and ε∗⊥ seeing from the stress wave (δ‖ and δ⊥, respectively) are independent of ω in liquid paraffin whereas ε∗‖ and ε∗⊥ move with keeping |δ⊥−δ‖|=π. In water, the δ‖ curve shows a minimum while the δ⊥ curve does a maximum at the same angular frequency. A characteristic time of swelling in the dynamic tests obtained as an inverse of the frequency accords well with the relaxation time in the static tests.

Variants of the strain-amplitude dependence of elastic wave velocities in rocks under pressure

The dependence of the compressional and shear wave velocities on strain amplitude in the Madra dolomites is studied. The experiments were performed using an ultrasonic pulse transmission technique (f = 1 MHz) with a uniaxial pressure of P = 1–60 MPa. An amplitude dependence of wave velocity in the range ed ~ (1–3) × 10−6 under a pressure of 5–20 MPa is found. The compressional velocity depends on strain amplitude but the shear velocity does not depend on amplitude change. Determined by the first arrival time, the compressional velocity increases with amplitude. However, if the compressional velocity is determined by the measurement of peak time, the velocity decreases with amplitude. For the upward and downward pressure, the curve Vp(Pax) exhibits open hysteresis, yielding a residual component of velocity. An intersection of the branches of the hysteretic loop is observed in more porous dolomites in comparison with less porous dolomite. This intersection is manifested most in the residual components of the dynamic bulk modulus and Poisson's ratio. The dynamic parameters can be used as is supposed as additional criteria in a geological interpretation.

The aging of gypsum in underground mines

The aging properties of gypsum extracted from two underground mines in France (Livry–Gargan and Grozon) have been highlighted by means of observation performed using scanning electron microscopy on samples taken along horizontal boreholes drilled through to the middle of several pillars. The aging process is exhibited by the presence of traces of dissolution (edges of the dissolved crystals, corroded crystalline surfaces, important intra- and intercrystalline space). These dissolution figures decrease in number and in intensity from the wall heading towards the middle of the pillar. The “older” pillars display a greater number of dissolution traces than the “more recent” pillars. Then, the role of the aging has been assessed by determining various physical and mechanical parameters on cylindrical samples of 38 mm in diameter and 76 mm in height, machined from the set of drilled boreholes. The following parameters have been quantified: density, grains density, total porosity, porosity accessible to water, intrinsic permeability to nitrogen, velocity of ultrasonic compression and shear waves, dynamic Young's modulus, dynamic Poisson's ratio, uniaxial compressive strength and static Young's modulus. Significant variations in parameter values between the wall and the middle of the pillar were recorded and recognized as being strongly correlated with the intensity of dissolution traces, and hence with gypsum aging.

Effects of testing methods and conditions on the elastic properties of limestone rock

This paper presents results of a laboratory experimental program performed on limestone rock samples, using both static and dynamic methods. The objective is to compare elastic properties (elastic modulus and Poisson's ratio) for limestone rock, determined by static and dynamic methods, under different conditions. The static elastic modulus and Poisson's ratio were determined using cylindrical specimens tested under unconfined compression using a strain-controlled loading frame. Minor cycles of unloading–reloading were made at various stress levels. The data were analyzed to evaluate the effect of stress–strain level on the secant and tangent moduli as well as on Poisson's ratio. The values of the tangent modulus and Poisson's ratio during the minor cycles at various stress levels were also obtained. The dynamic elastic modulus and Poisson's ratio were determined for rock specimens using an ultrasonic system equipped with pairs of transmitting and receiving transducers: one P-wave and two polarized S-waves. Measurements were made at different confining pressures. The effects of cyclic loading, unloading, and reloading conditions were investigated. The static and dynamic results obtained for the investigated rock were analyzed and compared. The findings were also compared with similar results available in the literature for limestone rocks. The equivalent confinement to compensate for the cohesion was introduced to have a general form for the initial modulus that can be used even for cohesive materials at unconfined condition. For unconfined condition, the initial modulus is correlated with the unconfined compressive strength.

Modelling the size of the crushed zone around a blasthole

A new model to predict the extent of crushing around a blasthole is presented. The model is based on the back-analysis of a comprehensive experimental program that included the direct measurement of the zone of crushing from 92 blasting tests on concrete blocks using two commercial explosives. The concrete blocks varied from low, medium to high strength and measured 1.5 m in length, 1.0 m in width and 1.1 m in height. A dimensionless parameter called the crushing zone index (CZI) is introduced. This index measures the crushing potential of a charged blasthole and is a function of the borehole pressure, the unconfined compressive strength of the rock material, dynamic Young's modulus and Poisson's ratio. It is shown that the radius of crushing is a function of the CZI and the blasthole radius. A good correlation between the new model and measured results was obtained. A number of previously proposed models could not approximate the conditions measured in the experimental work and there are noted discrepancies between the different approaches reviewed, particularly for smaller diameter holes and low strength rock conditions. The new model has been verified with full scale tests reported in the literature. Results from this validation and model evaluations show its applicability to production blasting.

Linear Viscoelastic Property Measurement and Its Significance for Some Nonlinear Viscoelasticity Models

Three linear viscoelastic properties of an Ashland neat urethaneadhesive were measured. Dynamic tensile compliance was found using anovel extensometer. The results were considerably more accurate andprecise than standard DMTA testing. Dynamic shear compliance wasdetermined using an Arcan specimen. Dynamic Poisson's ratio wasextracted from strain gage data that was corrected to include gagereinforcement effects. Experiments spanned three frequency decades andisothermal data was shifted by time-temperature superposition to createmaster curves spanning thirty decades. Master curves were fit to Pronyseries that originated in the time domain. Dynamic shear complianceinferred from dynamic tensile compliance and dynamic Poisson's ratiocompared well with measured values. This established the validity of thetime temperature shifting and interconversion procedures that weredeveloped for this isotropic material in its linear range. Dynamictensile compliance and dynamic Poisson's ratio were then used to obtainthe dynamic bulk compliance, which was in turn converted to the timedomain along with the dynamic shear compliance. The shear and dynamiccreep compliance functions thus obtained formed the basis of thenonlinear viscoelastic models.

Dynamic Property Determination for Early-Age Concrete

Test results are reported of the dynamic modulus (DM) elasticity and Poisson's ratio of concrete at early age by means of nondestructive evaluation. The DM was measured by a new test apparatus that includes a free-free boundary vibration chamber and a dynamic resonance measurement system with a fast Fourier transform analyzer. The measurement was conducted on concrete cylinder specimens. The DM and Poisson's ratio were calculated using the first 2 natural frequencies of a cylinder. The measured dynamic response showed good consistency and reproducibility. This method enables a measurement of progressive changes in the stiffness of the concrete without damaging the specimen and provides reliable values of DM. It is found that the age of concrete has a significant influence on resonance frequencies; herein, the resonance frequencies shift from lower to higher values in a regular pattern with the age of concrete.

Measurement methods of complex Poisson's ratio of viscoelastic materials

The methods of measuring the complex Poisson's ratio of viscoelastic materials as a function of frequency are investigated in this paper with special respect to the accuracy of determining the relevant loss factor. The measurement methods are reviewed, evaluated and compared from the point of view accuracy and frequency range. It is shown that some contradictory beliefs on the frequency dependence of dynamic Poisson's ratio and the value of loss factor are due to experimental difficulties. It is pointed out that the measurement of two complex moduli, especially the shear and bulk moduli, may be the most effective method to determine the dynamic Poisson's ratio and loss factor over a wide frequency range. An example for determining the complex Poisson's ratio of a rubber in a wide frequency range is presented.

Experimental study on Young’s modulus of concrete

Young’s Modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young’s modulus and dynamic Young’s modulus when dynamic Poisson ratio μ d varies nearby 0.20. P-wave velocity and elastic modulus have the same varying tendency as letter N. μ, μ d decrease with the increase of loading rate and μ d has a great effect on the parameters E d and E D.

FREQUENCY DEPENDENCES OF COMPLEX MODULI AND COMPLEX POISSON'S RATIO OF REAL SOLID MATERIALS

The concept of a complex modulus of elasticity is a powerful and widely used tool for characterizing the linear dynamic elastic and damping properties of solid materials in the frequency domain. It is shown in this paper that typical characters of frequency dependences of all complex moduli (shear, Young's etc.), and complex Poisson's ratios of real solid materials can be determined by transforming the causal and real relaxation and creep responses, respectively, from the time-domain into the frequency domain, even without having to specify the processes of relaxation and creep. It is proved that all dynamic moduli monotonically increase, and the dynamic Poisson's ratio monotonically decreases with increasing frequency, and all respective loss factors pass through at least one maximum. These frequency dependences are generally valid for any real solid material regardless of the actual damping mechanisms. Some experimental results are presented and interpreted in the light of the theory. The usefulness of theoretical predictions in materials engineering, measurements of dynamic properties and in modelling dynamic behaviour is discussed.

Measured and Calculated Horizontal Stresses in the Travis Peak Formation

Summary This paper presents the results of an experimental program to determine in-situ horizontal stress magnitudes from the dynamic mechanical properties of tight-gas sand cores. These measurements were made on 47 vertical plug samples from the Gas Research Inst. (GRI) test wells, Staged Field Experiment (SFE) Wells 1 through 3. The wells were cored in the Travis Peak formation of east Texas from ≈ 6,500 to ≈ 9,500 ft deep. Vertical overburden stress gradient was measured in one well using a downhole gravimeter. The core mechanical properties were used with the Anderson and Newberry equations to calculate in-situ horizontal stress. Actual in-situ minimum horizontal stress was determined from instantaneous shut-in pressures measured during minifracture and microfracture tests. The Newberry equation was found to give results that agreed best with measured horizontal stress. A closer match was obtained between measured and calculated horizontal stress values when we used dynamic Poisson's ratio from partially gas-saturated samples. The assumptions and limitations of the procedure are presented.