First, i want to emphasize that how much radiation one would actually get on the surface of the Moon is UNKNOWN. I've scrounged for figures repeatedly on this, and went with numbers for initial designs that numbers from new sources make sound silly, which is why an initial dome design had such thin walls. Then i noticed the reference i'd happily started using seemed to have slipped a decimal over one spot to the left in the chart backing up all their statements, repeated in this video. You can tell because the starting figure for radiation on the open surface definitely shouldn't be 0.02 Sv per year. It should be 0.2 Sv/yr. That came out when i found the other reference the video mentions.
Finally today i found a paper that puts it in perspective. An exceedingly relevant snippet from the abstract of Radiation exposure in the moon environment by Reitz, Berger, and Matthiae:
On Earth, the contribution to the annual terrestrial dose of natural ionizing radiation of 2.4 mSv by cosmic radiation is about 1/6, whereas the annual exposure caused by GCR on the lunar surface is roughly 380 mSv (solar minimum) and 110 mSv (solar maximum). The analysis of worst case scenarios has indicated that SPE may lead to an exposure of about 1 Sv. The only efficient measure to reduce radiation exposure is the provision of radiation shelters.
Very recently some data were added by the Radiation Dose Monitoring (RADOM) instrument operated during the Indian Chandrayaan Mission and the Cosmic Ray Telescope (CRaTER) instrument of the NASA LRO (Lunar Reconnaisance Orbiter) mission. These measurements need to be complemented by surface measurements.*
Models and simulations that exist describe the approximate radiation exposure in space and on the lunar surface. The knowledge on the radiation exposure at the lunar surface is exclusively based on calculations applying radiation transport codes in combination with environmental models.
*That bit translates in my mind to "the results don't correlate and/or don't make sense, so we don't believe them".
The radiation figures cited should be considered in the light of these calculations being astonishingly complex, mainframe computers needed, and the models haven't really been checked against reality, so there is no saying how accurate they are.
For one last bit of pause, consider how this article by Eugene Parker sees it:
This estimate is from 2006, but its high end figure is a third of the high end in the Reitz, Berger, and Matthiae paper. It's a total non-linear, non-intuitive mess.
Nevertheless, the design approach now being used does well in any of these scenarios. The part of it i'm working on now even provides a way to have a glazed roof over large portions of a sunken hall, provided you have a recessed area for when there are solar flares, and you get the proportions of the beams right. The proportions it has right now uses the average of 0.25 Sv/yr from the paper quoted above, which matches the charts from the other reference works, as long as you shift the decimal in the spots where it has drifted.
I am posting this early, the analysis of the radiation that penetrated it isn't done, but this helped me think it through. The illustration should be ready in a few hours.