I'm confused by this question. "UC triaxial" test. I'm used to "UC" as an unconfined compression test - it's triaxial, with sigma 3 as the atmospheric pressure.
Also, I'm not clear on the "dilation" angle. Dense granular materials will dilate during shear due to the effects of interlocking of the material. Is this "dilation angle" the difference in failure envelope angle between the material sheared with no volume change (no dilation, no contraction) versus dilation?
In most applications, psi (and phi) will be a lot smaller than Batiste's values. She was working at very low confining stresses. It would, as McCoy suggests, be very uncommon to see psi used in practice.
Talking simply about direct shear
Dilation Angle is the ratio of the (shear stain /dilative or contractive strain). When doing analyses or design you should consider it. It is important when dealing with frictional materials;e.g Sand. e.g. Row (1966) has shown that actual friction angle is directly influenced by dilation angle. I appreciate that some practictioners do not know what it is since in Soil Mechanics there is (unfortunately) huge gap between research and industry.
Bolton's Paper posted By Mccoy is also very good