Deep Underground Science and Engineering Lab - Topography Shielding Part III

The best way to calculate permutations for the endmember cases of muon flux at the DUSEL 8000 ft level campus. 

Best case: Say the entire depth of the lab is a full 8000 feet below the lowest ground surface. Also, assume that the rock is very dense Iron Formation with a specific gravity of 6.0. The calculation is simple, 8000ft of rock * 6.0 g/cc / 1g/cc water / 3.28 ft/m = 14,600 MWE, meters of water equivalent. This is more than double the estimated MWE.

Worst Case: Assume that the 8000 ft campus is actually 7000 feet below the ground surface because of topography. Also assume that mining methods of removed about 75% of the in-place rock and backfilled it with sand. This sand would be largely dewatered by gravity drain effects and have an air void volume of about 30%. Any water that remains trapped in the pores of the rock will increase the effective density, but we ignore that here. Finally, we could assume that the rock would be a granite-like composition with a specific gravity of about 2.85. The in-place rock would be 1,750 ft thick * 2.85 g/cc Qtz / 1 g/cc water / 3.28 ft/m = 1,520 MWE. The sand would have a thickness (7000 ft total depth-1750 ft in-situ depth)*(100%-30% sand volume) = 3675 rock in-place equivalent. The rock-in-place equivalent should have a similar specific gravity so: 3675 ft * 2.85 g/cc Qtz / 1 g/cc / 3.28 ft/m = 3190 MWE. The two values are additive so 3675 + 3190 = 6865 MWE. This is only slightly below the estimated 7000 MWE for the 8000 ft level. 

The best case scenario is more than double the published estimate for the MWE. This estimate is also likely a significant overestimate because the iron formation is not largely extensive around Homestake, it is some fraction of the total thickness of the rock over the 8000 ft level campus. 

The worst case scenario is close to the estimated value, suggesting that the DUSEL folks were being conservative. I can not imagine a case where the ground below Lead would not be actively caving in with a lower MWE (although it is subsiding). In the muon flux shielding world, more is always better, so I can confidently conclude that the the MWE shielding estimate is a good one and likely to prove more effective when the lower campus is built.