Use can refer to any code of practice (British standard) for the definition of the dynamic modulus from which you can calculate the shear modulus.

Yes, the high value of young's modulus can be justified.

As you noted - "shear modulus decreases by cyclic strain amplitude increasing". Meaning - stiffness can change. "Initial" stiffness depends on loading history,

The high value of young's modulus can be justified in 2 cases:

Drained cycles are required for stiffness to recover. And it can recover in excess of "unloading reloading" stiffness (Eur). Eur is some times proposed to be used instead of "initial stiffness" in designing of off shore wind turbine foundations, as exposure to long term cyclic loading stiffens the soil, effectively changing the "initial state" to a stiffer one.

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.

Dear college, it seams to me that Young modulus but not shear modulus is correlated with sound velocity by your formula.  Second formula is correct.

Dear Hossein, it is convinuent for dynamic elasticity to assume static and dynamic moduli be equal

Hey,

What exactly you mean by initial static equilibrium? What is your expected strain amplitudes during this state.? Using these equations assumes the soil to be linear-elastic material which may not be the case with you. Also, the use of your chosen Poisson's ratio does not seem appropriate. Static Poisson's ratio are different from the dynamic ones. and since you are using dynamic modulii, I believe you should also use an appropriate Poisson's ratio. 0.4 for sands seems too high to me. 

 Dear Saeed,

In numerical simulation before any dynamic analysis you should bring your model to the initial static equilibrium. I mean dynamic analysis starts from some in-situ condition and in this stage you just allow gravitational stresses to develop within the body. So in this stage strain amplitudes are very small and soil behaves as a linear-elastic material.

I didn't talk about using poisson's ratio in dynamic analysis, and about it's value there is a 0.3-0.45 range recommendation for dense sand in the literature.

Dear Hossein,

What you've seen from prof. Das's textbook I assume (given the values) are the deformation moduli of the soil for settlement analysis. 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 for  static equalibrium. The dynamic moduli are much greater even for large strains. 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).

Dear Hossein,

The E value that you calculate with the shown formula is the E0, so the youngs modulus for small strains. 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).

When you are looking for youngs moduli in the regular strain range (exavations etc.) 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. Of course a single stiffness valuse in a dynamic calculation should always be used with caution, have you considered using strain dependent stiffness degradation? FLAC has that option if I rememeber correctly.

Dear Stoyan Andreev,

Thank you for your helpful answer. You recommended a multiplier of 2 for sand/gravel and 3 for clay as a rule of thumb in your engineering practice in Bulgaria. Is there any reference for your recommendation?

Best regards.

Dear Korneel,

Many thanks for your expert answer. Is there any reference for your third correlation?

Yes, as you stated in FLAC by using hysteretic damping, strain dependent stiffness degradation would be applied. But my question is about static analysis. I have dynamic properties of the soil and want to derive static properties for initial static equilibrium. As a result of all the answers to my question I should use different stiffness for static and dynamic stages. But my problem is that in all examples in FLAC manual for dynamic analysis the same properties are used in initial static equilibrium and dynamic analysis.

Best regards.

Dear Hossein,

I dont have an exact reference for it but I have seen in mentioned in several papers as rule of thumb. 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.

In the case of FLAC it makes sense to use the same stiffness in the inital phase as the dynamic one as the initial stress generation using k0 should not be dependend on the stiffness. 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.

Best regards and good luck with the calculations

Dear Korneel,

Thank you for your helpful reply.

Best regards.

Dear Hossein it is just a rule of thumb. You may also calculate the strain-equivalent G-modulus using reduced shear wave velocity.

Dear Stoyan,

Many thanks for your helpful response.

Best regards.

Dear Mr. Khaleghi

I think the initial static phase of these type of problems should be analyzed with static properties. If you use the dynamic E in the static phase, the initial stresses will not be calculated properly.

Regards   

Dear Ashraf, elastisity modulus reflects internal structure of material. That is why to change it extremely high impact loading (wave) should be applied to deformal solid. Even in dynamic elasticity problems (explosive etc.), static modulus is used

Dear Hossein,

The soil modulus measurement is senstive to the mimumum strains in the tests. You could have a higher shear modulus in a 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. Just bear in mind the stated when you compare your modulus values with those in the literature.

Is it feasible to use a high value of the young's modulus for dense sand? Well, it all depends on your purpose of doing the simulations. If you'd like to replicate your lab experimental results, then you may not want to use the high value young's modulus in the FLAC mohr-coulomb model where the elastic behaviour is simply assumed linear. You can 'fit' your model behaviour to the overall experimental response (from soil element tests) by finding an appropriate modulus value. 

Regards,

Yang

Dear Yang,

Many thanks for your expert answer.

Best Regards.

Hello friends,

I have a small doubt regarding dynamic modulus. 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?