Since Su depends on the rate of loading; is it considered an index of soil strength or a material property? My recollection is that it is an index of soil strength.
It is a material property but the test conditions need to mimic or somehow account for the field conditions such as rate, anisotropy, extension/compression, palne strain, etc.
su is stress dependent; therefore it is typically normalized to the effective stress of the overburden at depth of the sample. you're going to get different su for different test methods as well.