Below is the most common way of calculating the numerical value of G as secant modulus.

Gmax = density* (Vs)^2

For a given displacement/strain you will need G.

G is obtained as follows:

1. Obtain G/Gmax vs. strain curve from literature

2. Calculate strain for a given displacement

3. Using value in step 2 find G/Gmax from step 1

4. G is obtained by multiplying the value from step 3 with the Gmax obtained from Vs known.

5. Repeat steps for other displacements.

You can obtain the Maximum shear modulus using Gmax=(Density)*(Vs2)

Vs Being Shear Wave Velocity.

This article might help you ===>>>>>

http://tarjomefa.com/wp-content/uploads/2017/11/8112-English-TarjomeFa.pdf

Hope you find it helpful.

As Sami Arsoy and Nima Haghidhat have mentioned the maximum small-strain shear modulus of a soil can be determined by the above mentioned formula. However, it is worth mentioning that some companies, like Fugro, present their shear wave velocity measurements as having been performed in either unsaturated or saturated conditions. Therefore, the density will have to be adjusted to a saturated one, which complicates things somewhat, since you now would need the in-situ void ratio (or porosity) to calculate the saturated density. Nevertheless, I am not certain if there is a very distinct difference in measurements, since I have not had the chance to compare dry or saturated shear wave velocity measurements from the same site.

Hope this helps complement a bit the previous answers.

Regards,

Hugo Portugal

Mear Mahdi:

The relation Between the Shear Modulus of the Soil and the Shear Wave Velocity is:

G = ρ * (Vs)2

I hope this help you

Dr. Carlos Jurado

the same formula given by Sami and by Carlos

You could use the same formula provided by above experts. However, you could also go to the section 4.2.3 of the EN 1998-5 code and it contents table that provide average soil damping and reduction factors for shear wave velocity and shear modulus, which can be used in the absence of specific measurement.

G = ρ * (Vs)2 same given by Carlos

Shear wave velocity is a function of density and related with shear modulus. The low strain shear modulus is usually the product of density in kg/cum and square of the shear wave velocity in m/s

G = ρ * (Vs)2