NS, We are just putting out info that will benefit some and it is just a recommendation based on research and experience plus engineering and if you are satisfied with rectangular or square shape tunnels or shafts. its your hole and you can do anything you wish.
Of course it all depends on the type of native soil of the site but I have seen tunnels of treasure hunters in the Philippines and all they have is a post on opposite walls and a beam connected to each other and a few feet further is much of the same, but nothing on the overhead and that is called Shoring, not timbering. Look at pictures of real Gold Mines, timbering on the walls and the ceiling. I have entered a tunnel on a side of a ravine, if you can call it that as it is only about 3 feet in diameter but it was something like 75 feet long and i have to be on my hand and knees, it ended on a 4'x4'x5' room but nothing was there, probably someone already beat me to it but after more than 6 decades and it was still in good shape and it was like compact sand. Where does the collapse occur in a square hole, in between corners as that is the weakest point, not on the corners but in the middle between corners and on a tunnel, where will it collapse,in the middle of the ceiling as that is your weakest point from the pressure or weight from above, again, not from the corners. The tunnel need not be round but it should be arched to better withstand the weight from above, the Romans knew that centuries ago. Whatever your preference, like the saying goes,"Just Do It".