People mainly due CU tests to determine effective stress parameters. This is because a CD takes way too much time and is too expensive. CU with pore pressure measurements should gave the same effective stress parameters as CD tests.
There is no undrained phi angle for cohesive soils. There as some soils, and at low confining stress you will get some phi angle. but for 99.9% of assessments, undrained phi is 0.
The shear strength you get from a CU test is also not really usable either as its not reflective of real world conditions. Check Duncan and Wight - Soil strength and slope stability latests edition. he has a section on it