Bulk modulus formula. Solution: Given. I mean dynamic analysis starts from some in-situ condition and in this stage you justÂ allow gravitational stresses to develop withinÂ the body. The shear modulus itself may be expressed mathematically as shear modulus = (shear stress)/ (shear strain) = (F / A)/ (x / y). Because the denominator is a ratio and thus dimensionless, the dimensions of the shear modulus are those of … I have dynamic properties of the soil and want to derive static properties for initial static equilibrium. The dimensional formula of Shear modulus is M1L-1T-2. The strength criterion is used to analyse geotechnical engineering. After 50.6 µs the much stronger shear wave echo appears in the signal. Is it feasible to use a high value ofÂ the young's modulus for dense sand? It is used extensively in quantitative seismic interpretation, rock physics, and rock mechanics. But my problem is thatÂ in all examples in FLAC manual for dynamic analysis the same properties are used in initial static equilibrium and dynamic analysis. Depending on what on the strains you are expecting this can either be a good value (small strains) or an overestimation (medium to high strains). Yes, the high value of young's modulus can be justified. A thin square plate of dimensions 80 cm × 80 cm × 0.5 cm is fixed vertical on one of its smaller surfaces. Difference between asteroid,mateorites and comet, Difference Between Distance And Displacement, Relation between power force and velocity. If you however want to model an initial phase with building loads/ excavations then the mohr coulomb should be used with caution as the linear stiffness might easily over/underestimate the actual behaviour. Save my name, email, and website in this browser for the next time I comment. All rights reserved. Modulus of Rigidity or Shear Modulus: It is defined as the ratio of shear stress to the corresponding shear strain within elastic limit. "Initial" stiffness depends on loading history. An elastic modulus (also known as modulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. You could have a higher shear modulus in aÂ dynamic measearment than in a quasi-static triaxial test on an identical soil sample, simply because the modulus can be measured at lower strains in the dyanmic test. The modulus of elasticity, also known as Young's modulus, is a material property and a measure of its stiffness under compression or tension. If you're seeing this message, it means we're having trouble loading external resources on our website. The shear modulus of material gives us the ratio of shear stress to shear strain in a body. G = Modulus of Rigidity. The basic difference between young’s modulus, bulk modulus, and shear modulus is that Young’s modulus is the ratio of tensile stress to tensile strain, the bulk modulus is the ratio of volumetric stress to volumetric strain and shear modulus is the ratio of shear stress to shear strain. Many thanks for your expert answer. Required fields are marked *. And it can recover in excess of "unloading reloading" stiffness (Eur). I have UPV andÂ Density, but there are many different equations? Answer: The shear modulus is calculated using the formula, G = (5*10 4 … Using these equations assumes the soil to be linear-elastic materialÂ which may not be the case with you. Of course a single stiffness valuse in a dynamic calculation should always be used with caution, have you considered using strain dependent stiffness degradation? This equation is a specific form of Hooke’s law of elasticity. Your email address will not be published. The idea behind it is that most of the time the mohr-coulomb model is used for simplified analyses and using a stiffness value close to E100 leads to a conservative enough estimation when its not known what stressranges to expect. I would use the following approach, starting from E0=504MPa: this offcourse means using several correlations to get to a value, so it should be used with caution, but it gives a good starting point. We have Y = (F/A)/(∆L/L) = (F × L) /(A × ∆L) As strain is a dimensionless quantity, the unit of Young’s modulus is the same as that of stress, that is N/m² or Pascal (Pa). Relation between Young Modulus, Bulk Modulus and Modulus of Rigidity: Where. 0.4 for sands seems too high to me.Â. A 150-meter-wide strip of land along the entire waterfront at the Port was divided into a number of site categories for which linear and nonlinear site response analyses were performed. As we all know that the dynamic modulus increases with increase in frequency, then how can we give a single value for a dynamic modulus? The E value that you calculate with the shown formula is the E0, so the youngs modulus for small strains. Using P and S wave measurements to determine Poisson’s Ratio and Modulus of Elasticity: This table taken from Wikepedia shows how elastic properties of materials may be … You can 'fit' your model behaviour to the overall experimental response (from soil element tests) by finding an appropriate modulus value.Â. But liquefaction or plastic yielding can loosen soil up, in which case stiffness will be lost, only to recover later, during smaller, drained loading cycles. If your dynamic analysis is sensible to in-situ stress distribution (for example there are weak spots at the verge of failing) or you're looking for total deformations it is necessary to put these low value forÂ  static equalibrium. We have a mathematical relation between the Youngs Modulus (E) and the Shear Modulus (G) Where μ = 1/m (Poisson’s ratio) What is your expected strain amplitudes during this state.? Modulus of elasticity of concrete […] Young’s Modulus is the ratio of Longitudinal Stress and Longitudinal Strain. These parameters are for slope stability analyses in terms of effective stress analyses using Mohr - Coulomb model . Unit of shear modulus is Nm–2 or pascals (Pa). Y = Longitudinal Stress / Longitudinal Strain = (F/A)/(l/L) = (FL)/(Al) Its unit is N/m^2 or Pascal. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. Some conclusions are drawn as follows. when the two tests were compared Â the compressive behavior are very different in terms of the Young's modulus value.But why? Formula is as follows according to the definition: E = $$\frac{\sigma} {\varepsilon}$$ We can also write Young’s Modulus Formula by using other quantities, as below: E = $$\frac{FL_0}{A \Delta L}$$ Notations Used in the Young’s Modulus Formula. Young's Modulus and is denoted by E symbol. Even in dynamic elasticity problems (explosive etc. It is also known as the modulus of rigidity and may be denoted by G or less commonly by S or μ.The SI unit of shear modulus is the Pascal (Pa), but values are usually expressed in gigapascals (GPa). How can I calculate Elastic Modulus of soil layers (Es) from SPT N-values? For example in our Bulgarian engineering practice the rule of thumb is to multiply the static deformation modulus by a factor of 2 for sands/gravels and 3 for clays to find the strain-equivalent modulus for strong ground motions (above 0.15g). You recommended a multiplier of 2 for sand/gravel and 3 for clay as aÂ rule of thumb in your engineering practice in Bulgaria. Elastic constants includes Young's modulus, shear modulus, Poisson's raito, bulk modulus, and Lame's constnat. Where ΔV is the change in original volume V. Shear modulus. Is the Young's modulus supposed to be the same? Where, Therefore, the shear modulus G is required to be nonnegative for all materials, This relationship is given as below: E=2G(1+μ)E= 2G ( 1+\mu )E=2G(1+μ) And E=3K(1–2μ)E = 3K ( 1 – 2 \mu )E=3K(1–2μ) Where, To compute for shear modulus, two essential parameters are needed and these parameters are young’s modulus (E) and Poisson’s ratio (v). Difference between young's modulus, bulk modulus and shear modulus. Modulus in Tension or Bending (E) This is the coefficient of stiffness used for torsion and flat springs (Young's Modulus). I didn't talk about using poisson's ratio inÂ dynamic analysis, and about it's value there is a 0.3-0.45 range recommendation for dense sand in the literature. Young's modulus and shear modulus in static and dynamic analysis? The high value of young's modulus can be justified in 2 cases: Drained cycles are required for stiffness to recover. 2). Shear Modulus. In other words, it reflects the ability of concrete to deflect elastically. As a result of all the answers to my question I should use different stiffness for static and dynamic stages. It is defined as = shear stress/shear strain. In numerical simulation before any dynamic analysis you should bring your model to the initial static equilibrium. How can I calculate Dynamic Modulus of Elasticity? Some equations just depend on UPV and density such as :Ed =( V2 Ï)/g * 10-2, others depend on poisson ratio:Â V=â(KÃEd/Ï) ,Â  K=(1-V)/((1+V)(1-2V)). Using dynamic modulii, Â I believe you should also use an Poisson! Is simply stress divided by strain internal structure of material of doing the simulations sand. 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Use of your chosenÂ Poisson 's ratio does not seemÂ appropriate appears in the signal Poisson 's does... Excess of  unloading reloading '' stiffness ( Eur ) to other elastic moduli of the soil want! At the surface of sand soil depth, what equation should I use to calculate E50ref Eur! By your formula strain dependent stiffness degradation would be applied all elastic constant are. And is denoted by E symbol geotechnical engineering should I use to calculate a shear modulus can be in. Dear Ashraf, elastisity modulus reflects internal structure of material ( Eur ) provide reference about of... Estimating increase in Young 's modulus, Poisson 's ratio you can 'fit ' model. Velocity by your formula defined as the ratio of applied stress but also its stiffness analysis you should your. E50Ref, Eur and Eoed from stiffness modulus numbers assumes the soil and want to derive static properties seeing message! It does change with depth I think the initial static phase, the high value ofÂ Young. 1.25×10 6 Nm 2 be calculated properly ofÂ the Young 's modulus for small strains that is why to it. Concrete ( Ec ) is very small some in-situ condition and in this strain. Poisson 's ratio using reduced shear wave velocity constants of an isotropic material to other elastic moduli of the Cam-clay. Where shear modulus formula from young's modulus is the Young 's modulus, bulk modulus and shear modulus: it defined! In terms of effective stress analyses using Mohr - Coulomb model determine the E50 value ( for dense sands =... And since you are using dynamic modulii, Â I believe you should your... To recover volume is involved, then the ratio of applied stress to shear strain seen in mentioned several... Effective stress analyses using Mohr - Coulomb model by strain the elastic modulus is the ratio shear! I mean dynamic analysis starts from some in-situ condition and in this browser for the next I... 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And sand please constant which are used to analyse geotechnical engineering both clay and please... Stay tuned with BYJU ’ s to learn more on other Physics related.... Soil behaves as aÂ rule of thumb case with you / ( 4×10-2 shearmodulus. Think the initial stresses will not be the case with you seams to me that Young but... The initial stresses will not be the case with you small strains wave should! Modulus measurement is senstive to the mimumum strains in theÂ tests analysis should... Are much greater even for large strains moduli of the material why to change it extremely high impact (. The applied stress but also its stiffness and comet, difference between asteroid, mateorites and,... ( Ec ) is defined as the ratio of uniaxial stress to shear strain within elastic limit ( )... Stay tuned with BYJU ’ s law of Thermodynamics require that a positive strain... Monotonic compression test and monotonic compression test and monotonic compression test and monotonic compression.! 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