[kallistisoft]

As far as I know the plan has always been to use the martian regolith and water as primary radiation shielding -- same as the moon.

Here is a recent (2022) paper[1] on the concept, but you can easily find scholarly work on this going back many decades...

[1] https://www.sciencedirect.com/science/article/abs/pii/S00320...

[ceejayoz]

https://en.wikipedia.org/wiki/Martian_lava_tube have also been proposed as pre-existing possible shelters.

https://en.wikipedia.org/wiki/Caves_of_Mars_Project#/media/F... "HiRISE image of Mars hole 'Jeanne', about 150 meters (492 feet) across and at least 178 meters (584 feet) deep."