There are hundreds, if not thousands, of buried potable water tanks in service. Mosr are designed under AWWA standards, State Health Division standards and structural standards of ASCE, CRSI, and others. I have designed dozens, mostly conventionally reinforced concrete, although some pre-stressed tanks exist below grade. Most are placed on hillsides or hilltops where groundwater, if any is present, will flow away from the tank.
They come in all shapes and sizes from a few hundred gallons to millions of gallons. All are leak tested periodically. Some have their roofs exposed and are used for recreation areas such as tennis courts, urban parks, etc.
I have never heard of a case of contamination by groundwater leaking into the tank. If such cases exist they appear to be very rare.
Among the advantages if burying a tank include:
stable temperature in hot climates
no need to repaint or recoat the tank exterior
ease of monitoring leakage into or out of the tank
aesthetics
long life ( some such tanks have been in service without problems for over 100 years)
Burying half the tank appears to be arbitrary and accomplishes what ?
At one time in history, the Ten State Standards were strictly wastewater standards but, it appears, they have grown in scope over the last 40 years since last I looked at them. In Oregon, where I live and work, and in California and Washington the Ten State standards do NOT apply.
None of this answers the original posters question which was about the structural design of such tanks so I apologize to him or her for digressing.