ר אלעזר שני דברים אינן ברשותו של אדם ועשאן הכתוב כאילו ברשותו ואלו הן בור ברשות הרבים וחמץ משש שעות ולמעלה
Pesachim (6b): There are two items which are not owned by a person but which the Torah nonetheless holds a person responsible for: chameitz on Pesach and a pit dug in a reshus harabim.
Ran explains that the din of bitul chamietz stems from this statement of R' Elazar. Since technically chameitz is not yours, a minimal declaration (actually, even a verbal declaration is not necessary; a mental decision suffices according to Ran) of bitul is sufficient to offset the liability of bal yera'eh.
In other words (as many achronim explain), bitul is an act of siluk - it prevents the onset of ownerhip imposed by the special gezeiras hakasuv of chameitz. Bitul is not really the same as hefker, which is the removal of ownership which is already established.
So why is there no parallel din of bitul habor (or whatever you would call it) that would allow a person to avoid being chayav for digging a pit? Why can you not simply declare yourself immune from assuming the onset of responsibility for the bor?