Do you mean Skemptons B? If yes you can do triaxial tests, close the drainage valve, increase confining pressure and measure the increase of the pore water pressure. The ratio of the increase of pore water pressure and confining pressure equals Skempton's B in triaxial tests.
I am thinking the Hollow Cylinder test could be an option? Allows complete and smooth control of the rotation of principal stress. Also, noting where your University is, I know they have a Hollow Cylinder apparatus at Tehran Universtiy - perhaps that helps.
The parameter b you mention, I am thinking you mean (sigma2' - sigma3')/(sigma1'-sigma3'), which is one of the stress parameters that can be directly controlled in the HCA test using the GDS software. You can measure Skemptons B also.