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Figure 5. Measured bulk modulus as a function of oscillation frequency for the heavy-oil-saturated Uvalde and OB8 rock samples. Figure 6. Comparison of pressure-cycling technique with other measurements of bulk modulus for the Uvalde heavy-oil-saturated rock. The magnitude of the cycling technique is correct, but the trend with frequency disagrees.
For the sake of completeness, the typical subgrade reaction modulus are listed below in Tables 1 and 2. Note that these values are valid for a 12″ plate resting on uniform soils. If there is no potential for creep and long-term consolidation, the following equations can be used in order to account for different foundation sizes (Terzaghi, 1955):
(PMT), or Dilatometer (DMT) should be considered for evaluating the elastic modulus of the soil strata. Typical elastic modulus values of predominately granular materials are shown in Table 3. Table 3: Typical elastic modulus values for granular s oil (modified after Sabatini, 2002) . soil type range of equivalent elastic modulus ksf / (kPa)
Todd (1980) reports values of K z / K r ranging between 0.1 and 0.5 for alluvium and possibly as low as 0.01 when clay layers are present. Representative Values. The following table shows representative values of horizontal and vertical hydraulic conductivities for selected rock types (from Domenico and Schwartz 1990):
where k is the bulk modulus of rock. Values of Poisson ratio σvary from 0.0 to 1.0 Either expression tells us that the compressional velocity will always be greater than the shear velocity in a given medium. If σis 0.25, the Vp/Vs ratio equals to √3. It is worth noting that for most consolidated rock materials, Vp/Vs is
1 GPa = 10 9 Pa (N/m 2); Stainless steel with Bulk Modulus 163 10 9 Pa is aprox. 80 times harder to compress than water with Bulk Modulus 2.15 10 9 Pa.. Example - Density of Seawater in the Mariana Trench - the deepest known point in the Earth's oceans - 10994 m.. The hydrostatic pressure in the Mariana Trench can be calculated as. p 1 = (1022 kg/m 3) (9.81 m/s 2) (10994 m)
The bulk modulus (or ) of a substance is a measure of how resistant to compression that substance is.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to ...
t50 value of a rock vs the unconfined compressive strength gives a visual comparison of the strength and modulus values of different rocks. ! M R= E t50 / σ a (unconfined compressive strength) - Modulus Ratio – and Miller Classification 50%! Strain! s! Slope of the line tangent at 50% of the ! unconfined compressive strength = E t50! 34!
to certain rock units in a given locale by actual laboratory measurements on core samples of the rock or soil. It is observed from seismic surveys that velocities generally increase with depth. Densities also increase with depth so it must be that the bulk and shear modulii increase faster than the density. In seismic exploration
The question is why the decrease in bulk modulus of a rock is not as rapid as it is after 10% of gas saturation. Attached is a general bulk modulus vs water saturation/ gas saturation graph.
The effect of Poisson's ratio is one of the parameters used for the calculation of modulus value in an in situ test. Sharma and Singh (1989) found that it is not much variation in the values of the deformation modulus if the value of the Poisson's ratio is between 0.1 and 0.35.
In continuum mechanics, Lamé parameters (also called the Lamé coefficients, Lamé constants or Lamé moduli) are two material-dependent quantities denoted by λ and μ that arise in strain-stress relationships. In general, λ and μ are individually referred to as Lamé's first parameter and Lamé's second parameter, respectively.Other names are sometimes employed for one or both parameters ...
Among elastic rock properties one may mention: Young’s modulus, shear modulus, bulk modulus and Poisson’s ratio. As the shear modulus and bulk modulus are functions of Young’s modulus and Poisson ratio the last two parameters are the most * Corresponding author. Tel.: +48 604 055 842; fax: +48 12 617 20 59.
Rock Salt Elastic Modulus / Mineral Modulus Clean Sandstone Porosity/Critical Porosity 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 Compressional Modulus (GPa) Porosity Cracked Igneous Rocks with Percolating Cracks Pumice with Honeycomb Structure KDry = KSolid (1 −φ/ φc) GDry = GSolid (1 −φ/ φc) Total Porosity Dry-Rock Bulk Modulus Dry-Rock Shear ...
Variations in rock mass elastic modulus are qualitatively similar (values vary from 1 to 2 GPa up to the elastic modulus of the intact rock, 40 GPa). Our study highlights that macrofractures and joints reduce rock mass strength and should be considered when assessing the rock mass for well stability and rock mass deformation due to stress ...
Next, K dry is calculated using three different methods: using measured sonics and density with Gassmann, a rigorous computation using differential equation medium (DEM) theory, and a rock physics modeling strategy that assumes saturated and dry bulk modulus values are very similar to each other. This assumption is acceptable because in ...
L 0 L A F E ∆ ∆ = This modulus reflects the stiffness of earth materials. E is the ratio of stress to strain.If our aim is to lengthen or shorten a rock without actually breaking it, the greater the value of E, the larger the stress that is needed to achieve the deformation.
rock - rock - Mechanical properties: When a stress σ (force per unit area) is applied to a material such as rock, the material experiences a change in dimension, volume, or shape. This change, or deformation, is called strain (ε). Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression).
observed, providing a Young's modulus of (75 ±7) GPa and a Poisson's ratio of (0.28 ±0.02). These values are characteristic of Calcare Massiccio in undamaged condition. Key words: elastodynamics, laboratory measurement, moduli. 1 INTRODUCTION Elastic constants are relevant parameters whenever stresses and strains are considered.
Table of Fluid Bulk Modulus (K) Values There are bulk modulus values for solids (e.g., 160 GPa for steel; 443 GPa for diamond; 50 MPa for solid helium) and gases (e.g., 101 kPa for air at constant temperature), but the most common tables list values for liquids.
The maximal value of T 1 is obtained in the bulk fluid: in shales the longest T 1 values may be tens or hundreds of times smaller than the bulk fluid value for water, reflecting the fact that all of the water is confined and influenced by surface interactions. Download : …
The bulk modulus of any pore fluid must be used to inter-pret the seismic response and perform a fluid substitution for Direct Hydrocarbon Indicator analysis. However, fluids will have losses and show dispersion as a result of the viscoelas-tic behavior of the bulk modulus. This behavior can be de-scribed through the bulk viscosity.
A measured B-value that is constant and independent of the magnitude of the back pressure indicates full saturation. Once the air is driven into solution, the air-water mixture behaves as a fluid with a bulk modulus equal to that of pure water [8,18], so dissolved air in the water has no influence on Kf. Hence, pore fluid bulk modulus
In general, the soil stiffness and elastic modulus depends on the consistensy and packing (density) of the soil. Typical values of soil Young's modulus are given below as guideline. Typical values of Young's modulus for granular material (MPa) (based on Obrzud & Truty 2012 complied from Kezdi 1974 and Prat et al. 1995)
) and deformation modulus of rocks Average values from tests of intact rock samples Tests of rocks world-wide Scandinavian rocks tested at SINTEF c E E c of tests Number c E c Number ROCK MPa GPa MPa GPa of tests ure Dolomite 86 38 443 8 110 49 443 2 Limestone 107 47 441 81 74 71 961 25
Where k is bulk modulus, µ shear modulus and ρ density of a rock. Although the actual rocks are not isotropic and homogeneous, elastic equivalency exists between the two to a great extent in Layered media when the velocities are approximated as Interval, Average and RMS. Velocity ratio (Vp/Vs) and Acoustic Impedance (AI) can be expressed as
bulk volume may at times be less than true values of bulk volume is shown by the fact that the computed apparent porosity occasionally exceeds the computed total porosity where bulk volume is obtained by mercury displacement, and where there is no evidence that adsorp tive effects have resulted in erroneously large determinations of pore volume.
Typical values for Ct are 3 to 25 * 10^-6 psi-1. Ct varies inversely with porosity and pressure, and numerous authors have published correlations applicable to specific rock types. The inverse of a compressibility is a bulk modulus, for example Kc = 1 / Ct is the composite bulk modulus of the porous rock.
K sat1 is the bulk modulus of a porous rock saturated with fluid-1 (bulk modulus K f1), K sat2 is the rock bulk modulus saturated with fluid-2 (bulk modulus K f2), K m is the mineral bulk modulus, K sk is the dry frame bulk modulus, and ϕ is the porosity. The relation provides the necessary recipe for fluid substitution. When the velocities in the porous medium saturated with a known fluid ...
Table 1. Range in Values for Bulk Modulus of Compression (E) and Specific Storage . S s =γ w α [After Domenico and Mifflin (67)]. I have expanded the calculations of Table 1 to utilize a formula for S s that includes the compressibility of water. This formula is S s =γ w (α +nβ), where n is porosity (dimensionless) and β is the compressibility of water (M-1 LT 2).
The initial straight-line portion of the curve is the elastic range for the steel. If the material is loaded to any value of stress in this part of the curve, it will return to its original shape. Thus, the modulus of elasticity is the slope of this part of the curve and is equal to about 207,000 MPa (30,000,000 psi) for steel.
material. By using the M,-0 (bulk-stress) relationships developed, a nonlinear elastic-layered analysis was undertaken on 40 different pavement cross sections to establish typical bulk-stress and resilient-modulus values. The correlations between modulus and layer coefficients (a;) and composite modulus …
deformation modulus of rock masses was made by Hoek and Diederichs (2006). ... is the value of the Hoek-Brown constant m for the rock mass, s and a are constants which depend upon the rock mass characteristics, and V ci is the uniaxial compressive strength of the intact rock pieces.
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