Can you dig down straight always in the same diameter? I mean if you dig down in 10x10, will you end digging in 10x10?Only theoretically. Only serious answers.
Do you mean a rectangular, 10 x 10 hole? If so: No... at least not very deep. The excavation wall in most earth materials loses structural stability, and so excavation below some practical depth must be sloped to prevent failure. Even in a very competent rock, you cannot go very deep... I'm also neglecting the practicalities of the usual excavation equipment, like a backhoe or excavator, which are limited by the mechanical-arm length and geometry. I guess if you wanted to dig a 10 x 10 hole by HAND (or jackhammer or something), and you progressively reinforced the excavation walls above you as you went, then yes, I suppose you could go pretty deep. OSHA might have something to say about it, but I'm being theoretical as you asked, or semi-theoretical. Now, if you are DRILLING, so that your circular boring is 10 units (inches, feet, whatever) in diameter, then your hole stays more or less the same diameter, although there is wallow-out at the top, and maybe some small percentage of variability throughout- depending on the competence of the earth-material. Even then, you would case a deep boring to prevent wall-failure when you withdraw the augers. What you case it with depends upon your purpose- steel, PVC, cast in-place concrete, whatever. There are also cool boring machines that can drill lovely, round holes of consistent diameter through rock. There's probably plenty of other tech that I'm not experienced or familiar with with, too.
