Ooh! Time to back up to Strength of Materials class. Draw a Mohr circle with compressive strength qu on one side, and air (i.e., zero normal stress, zero shear stress) on the other. Then remember that the failure surface in frictional material is, in theory, inclined (45 deg + phi'/2) away from vertical, rather than 45 degrees. In theory, shear strength = [(qu/2)*cos(phi')], usually simplified as [qu/2] with no real loss of accuracy; in practice, there is sample disturbance, anisotropy, etc. that overshadow that. In the Hegedus and Peterson correlation, the data were pretty scattered of course, and I assume the same is true for the ones shown in DM-7, although I haven't actually seen the dots. Don't take the numbers too seriously.
Great Lakes area? I think H&P's data came from along south shore of Lk. Erie. (The paper shows H&P as being from Cleveland.)