The empirical equation that i'm looking for, is required to be able to calculate the amounts of cohesion and internal friction angle by using Uniaxial compressive strength and elastic modulus.
The findings of answer for your question is a great problem if we take into account a numerous factors influencing cohesion and internal friction differentiation. Probably, the data which is available in your case at moment (uniaxial compressive strength and elastic modulus) isn't sufficient. To my opinion, we must assume the additional tests, for example, energy dissipation measuring for obtaining of empirical equation under consideration. Good luck!
„Friction angle or angle of internal friction is the angle under which a solid or a granular material may be loaded, without to slide or to fail. It is a measure of the friction-ability of its surfaces (friction and roughness or smoothness). The internal friction angle of granular media is not the same as the "dump angle" of bulk or the "slope angle" of a landfill."
“Under cohesion or adhesion, in the soil mechanics one understands the cohesive forces in cohesive soils. It is only in soils markedly containing which have very small grains, i.e. in which the surface properties of the individual grains are stronger as the properties that are caused by its mass, such as clay. The cohesion makes in soil or fine grain loose rock to the internal bond of the individual particles to each other.
The cohesion has mostly the character c and the physical unit of a stress; it is a shear stress. It is a special case of the shear strength."
Apparent cohesion
Once the grains of sand are surface dried, the sand has no cohesive properties longer, but is only held together by friction forces. Wet sand has an apparent cohesion. It is bonded by capillary forces between the sand grains.
Internal friction and cohesion are two different properties of loose rocks, its shear strength both together determine. Wet sand: In the determination of the apparent cohesion, can be found empirically a relationship between apparent cohesion, water content, pore pressure and angle of friction. However, this relationship is not universal. It is important amongst other things to distinguish between the individual sizing of sand at in situ conditions. In situ can be used the Cone Penetration Tests with radiometric probe, see figure.