I am writing a fiction about Mars, 300 yrs after colonization. Earth turns hyper-fundamental and cuts off all communication, so they've been on their own for the past two centuries. In constructing this world, I think perhaps the place to build the three redundant settlements is in the interiors of hills or mountains, rather than on the surface with all the radiation, dust storms, and very low temperatures. Is this feasible? Also, rather than the old moon-buggy or hab-lab transports, what about underground tunnels. Sound way better. Thanks
If you want to live on Mars, tunnels are a great idea. The radiation is one very good reason, and insulation efficiency until you can raise surface temperatures is another. You don't HAVE to live in tunnels, but if your civilization is xenophobic and trying to survive on its own, then tunnels are a great low tech way to make your life more pleasant.
The be-all-end-all of Mars colonization information is Red Mars. Its probably the most widely read fiction on the topic, and has all the science you want and more. If you are writing a story about Mars colonization and haven't read that, you are wrong. There are two sequels (Green Mars and Blue Mars) that are alright, but I wouldn't say are required reading.
You can but why would you go to all the effort of burrowing underground?
The dust storms are not that bad http://www.nasa.gov/feature/goddard/the-fact-and-fiction-of-martian-dust-storms
YEs you also have to protect against radiation and cold, which make your walls thicker and more expensive.
But even underground you would need to pressurize your tunnels. Mars's Atmosphere is 1% as dense as earth's so you tunnels will either leak atmosphere or explode unless you lined them with a strong pressure resistant wall. A wall that will resist the pressure change could be as expensive as one to resist the temperature change, and you have already incurred the cost of digging.
Tunneling under mountains is possible, but quite difficult and energy intensive for the desired results.
Thermal and radiation protection from the Martian environment could be easily done through the simple expedient of digging a trench, building a barrel vault inside and then covering the trench over with the spoil from the digging.
Barrel vaults are strong, easy to build and can be easily extended, so the colonists won't have much difficulty keeping up with expanding needs. Tunnelling between the different colony sites for transportation is simply an extension of this technique, but the expense of digging long distance tunnels for transportation might be counterproductive unless there is a lot of traffic.
Economics will be a strong driving force for the colonists, since they will need to economize on their use of time, resources and energy, so unless there is every compelling reason, colonists will avoid tunnelling into mountains and dig trenches instead.