Dispite what my what has been said above, there is no relationship between poisson's ratio, modulus of elasticity and friction angle. Many times over the course of 40 years have people tried to find relationships. Realistically, the resistance of a penetrometer to penetration is related to the 'strength' of the soil and nothing else. Strength can be determined as 'undrained strength' or 'friction angle for a soil of a specified density at a k0 of bla bla...". Any correlation is indirect. A more dense soil is stronger, for example.
The standard penetration value was intended to be an index value of strength and density. It was never intended to be the ultimate design parameter. Move on to some tests that actually measure strength or density.
jim