where K is called the bulk modulus. Note that G and K are related to E and < as follows 2.2 Dynamic Elastic Constants The Young''s modulus, Poisson''s ratio and shear modulus can be determined by dynamic methods. Dynamic elastic properties are obtained by rapid application of stress to a rock …
Chapter 5 Engineering Properties of Soil and Rock 5 .1 Overview The purpose of this chapter is to identify, either by reference or explicitly herein, appropriate methods of soil and rock property assessment, and how to use that soil and rock property data to establish the final soil and rock parameters to be used for geotechnical design.
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.
· 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 ...
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 ...
(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)
1-F Rock Strength Surface Finish and Flaws If the strength of rock in beam-bending depends on the surface finish… Beam-bending is of little value to engineering design issues The strength of rock in tension is dependent on the size of the flaw These observations, combined with the fact that rock masses have many discontinuities…
modulus M and/or bulk modulus K for many chalk samples from the Valhall and Hod fields. Results of the tests show a very clear correlation between porosity and elastic modulus. Modulus decreases with increasing porosity, as shown in Figure 3.5. This trend is also …
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 ...
Substep 1.3: Calculate the dry-rock bulk modulus from the rock bulk modulus as K dry = K mineral 1 − (1 − )K log / K mineral − K log /K fluid 1 + − K mineral / K fluid − K log / K mineral, where is total porosity, and K mineral is the bulk modulus of the mineral phase (for calculating K mineral.
· The data needed to compute mechanical rock properties are: Compressional and shear velocities (slowness) Density. Shear and compressional velocities are a function of: Bulk modulus. Shear modulus. Density of the formation being measured. The Vp / Vs ratio, combined with formation density, ρ, is used to calculate:
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.
4 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 Bulk Modulus (GPa) Porosity SOLID GLASS Frame-Supported Foam Disintegrated Foam Honeycomb Structure A critical porosity value exists which is typical for a given class of porous materials. Each class is defined on the basis of common mineralogy and/or diagenetic porosity reduction
For most rocks, varies between 0.8 and 0.5. A value of 0.60 would be a good number for general use. Glass on glass 0.4 Rubber on concrete 0.75 Steel on steel 0.55 Angle of internal friction ( Rock 30 Sand 30-40 Gravel 35 Silt 34 Clay 20 Loose sand 30-35 Medium sand 40 Dense sand 35-45
· 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.
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.
· Rigid rocks with a high value of Young''s modulus will result in narrower fractures than rocks with a lower rigidity. Shear Modulus. The shear modulus, µ (Pa) or G describes the rigidity of a material, its resistance to shear strain/angular distortions. ... Bulk Modulus. The bulk modulus, K (Pa) of a material describes its ability to withstand ...
· Rock-physics models output dry-rock frame moduli: bulk modulus ... In Figure 3c, I have changed the bulk and shear modulus values to get a better fit against the data. In the absence of other information, this is perfectly reasonable — and valuable — knowledge to add to the exploration puzzle.
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!
Recall the typical stress strain response curve for a specimen of intact rock under uniaxial compression (see Figure 1 in Lecture Notes 5). Pa rt OA represents the closing of existing cracks in the rock and an overall readjustment of the rock testing machine setup whereas part AB represents the elastic rock …
Rock Mechanics Properties of Typical Foundation Rock Types: Summarizing physical and mechanical tests of rock samples from several types of foundation sites ... ENGINEERING PROPERTIES OF ROCK CORE SAMPLES STATIC MODULUS OF ELASTICITY SPECIFIC GRAVITY ABSORPTION,% No. No. spec. avg 2.94 range 0.16 ~g 0.1 range 0.1 spec. stressrange psi 0-2000 0 ...
Bulk modulus 10 9 Pa Shear modulus 10 9 Pa Density, g/cm 3; Solid quartz 37 44 2.65 Feldspar (ave) 37.5 15 2.62 Plagioclase 76 26 2.63 Clay variable* variable* variable* Calcite 77 32 2.71 Dolomite 95 45 2.87 Anhydrite 45 29 2.98 Siderite 124 51 3.96 Pyrite 147 132 4.93 Hematite 100 95 5.24
Calculate Bulk Modulus from Youngs Modulus and Poisson''s Ratio; Typical Values of Some Materials; See Also; Summary. The bulk modulus measures a substance''s elastic resistance to change in volume when under uniform loading in all directions. It can be thought of as an extension of the Youngs Modulus into three dimensions. The formula for ...
Rock as an Engineering Material Rock as an Engineering Material ... Typical Porosity Values of Intact Rocks Porosity (n) – ratio of void or pore volume, Vv to the total volume, V of the rock. ... The bulk modulus K can be determinedThe bulk modulus K can be determined .
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.
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.
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
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.
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.
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 ...
Shear modulus and bulk modulus Shear or rigidity modulus: σS =GεS =µεs Bulk modulus (1/compressibility): −P =Kεv Can write the bulk modulus in terms of the Lamé parameters λ, µ: K = λ+ 2µ/3 and write Hooke''s law as: σ= (λ+2µ) ε Young''s or stiffness modulus: σn =Eεn Mt Shasta andesite
Material required. The sample should be sufficient to permit 5 test scratches (10 mm) at least 5 mm from the edge of the rock surface and each test should be 5 mm apart. If it is a core, the diameter should be less than 76 mm and length less than 150 mm. Ideally size is like a tennis ball.
· Poisson''s Ratio of Rock. Poisson''s ratio measures the ratio of lateral strain to axial strain at linearly elastic region. For most rocks, the value of Poisson''s ratio ranges in between 0.15 to 0.40. Typical values of modulus of elasticity of some common are given in the table below.
· 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):