I don't know if it is technically correct, but of the thousands of belled piers I have designed (we call them piers as we consider piling as those driven into the ground)
all of them did not consider the ground above.  However, the older engineers who trained me some years ago also, as a standard practice, didn't deduct the weight of the earth displaced by the drilled pier but simply added the weight of the pier itself.

Most of the geotechnical reports I've seen for pier foundations do not indicate any issue with the weight of the earth above the bell.  Since a great deal of load is placed on the pier, the tendency is for the pier to settle downward relative to the earth around it.  The bell is usually limited to 3 times the shaft diameter so there is usually a capacity of the earth to arch over the bell anyway.

In high swell (plastic) clays, the clays actually grab and lift the pier upward.

Typically allowable bearing capacity is given as the net allowable bearing capacity which means that you do not need to account for the weight of soil above the bell.

Bearing capacity is almost always given as the net allowable bearing capacity which means that you do not need to account for the weight of soil above the bell.  You only need to account for "new load" on the soil.

Hi JAE,

When I design drilled concrete piers for vertical downward load I typically design it for end bearing or skin friction depending on which one is greater.  The way I see it for design is that once friction is overcome we can no longer use it as resistance and thus all the load goes to end bearing.  Though simplified, is this typically how you approach this particular design?

Regards

VOD

Most Geotechnical Engineers will provide design parameters for straight drilled shaft piers that include both end bearing and skin friction.  For belled piers - the skin friction is ignored typically.