*Mining. I just had the thought as I was cycling home from work this evening that one way to randomise mining in a game where you couldn't find an umpire would be to establish the line of approach you wanted to take at the start of a strategic turn then roll a scatter die and prodeed in that direction. Perhaps that's a little extreme. Perhaps instead you could lay a right angled template at the mine-head, with each of the arms of the 'L' diverging at 45 degrees. Roll a D6. 1-2 takes you down the left-hand path, 3-4 takes you in the desired direction and a 5-6 takes you down the right-hand path.
Mines will only move at the slowest sapping rate. Only one working party may be working at a mine and this needs to be under the supervision of an Officer of the Engineers.
*Sapping. Every sap must at it's base line at the first parallel be either 18" from an adjacent sap or 6" from either the end of the parallel or an adjacent redoubt. Ths space is assumed to be where troops might assemble or stores might be kept.
Every strategic turn you lay a certain number of lengths of sap. As you get closer to the fortress, the length of each sap you can lay down gets shorter. Each new length of sap must proceed at a 90 degree angle to that which preceedes it. Perhaps in the range band of 72-48" you could sap forward at the rate of 12" per strategic turn; for that of 48-12" you could only proceed at 8" per turn and; in the final 12-0" (0" being the very top of the glacis) perhaps as little as 4" every strategic turn.
*Parallels. Could always be built at the rate of 12" per eight figure working party, with every three working parties needing to be under the supervision of an Officer of Engineers. As do saps, parallels give cover to beseiging troops.
*Engineering. The eight man working party is the basic engineering unit. One of these may throw a length of sap if supervised by an engineering officer. One may also throw up either a battery position or redoubt in two strategic moves if so supervised. Two may throw up a battery position or a redoubt in one move if supervised by two officers. One officer can supervise three working parties at the construction of 36" of parallel because this is relatively less demanding work.
Example: The first parallel has been determined to of necessity be 72" wide. The stern general directs that this must be completed in one strategic move. It will have a redoubt at either extremity. Thus he will devote ten working parties to the task under the supervision of six Engineering Officers. It can theoretically support as many as four saps.