There appear to be solid reasons for semantically equating SHEOL and hADHS--one of the strongest reasons is because the LXX utilizes hADHS in texts about the condition of the dead.
hOTI OUK EGKATALEIYEIS THN YUXHN MOU EIS hADHN OUDE DWSEIS TON hOSION SOU IDEIN DIAFQORAN (Ps. 15:10 LXX).
hOTI OUK ESTIN POIHMA KAI LOGISMOS KAI GNWSIS KAI SOFIA EN hADHi hOPOU SU POREUHi EKEI (Eccl. 9:10 LXX).
Additionally, Ps. 15:10 (16:10) prophetically speaks of the Messiah not being forsaken in SHEOL. On the day of Pentecost, Peter quoted those words, and when recording this speech Luke employs the Greek hADHS to describe what the Hebrew Scriptures call SHEOL (Acts 2:27-36). This passage indicates that the words are synonymous (they semantically overlap).
Gesenius' Hebrew-Chaldee Lexicon also equates hADHS and Sheol, as does Thayer's Greek-English Lexicon which says: "In the Sept. the Hebr. SHEOL is almost always rendered by" hADHS.
While disagreeing with my theological views, Spiros Zodhiates yet writes: "hADHS . . . Most probable derivation is from hADW, all-receding. It corresponds to SHEOL in the OT" (Complete NT Word Study).
Obviously, one can believe that SHEOL and hADHS are semantically identical without believing they both represent a place of inactivity, but I happen to think that both places are domains of inactivity.