Giant dome concepts are beautiful, but I can't help but wonder how they could be so fragile. If there is even the tiniest rip, the whole thing would rapidly decompress. How would you protect against decompression?
Why have only one layer of dome? If you have two layers of dome, this is much more durable. Three is more durable yet.
Internally divided cells
Airships do not have a single inflated envelope. Instead, the internal structure of a blimp is divided into a bunch of different cells. A Martian dome could, instead of being a hemisphere, be a icosahedron with an internal structure dividing it into neat polyhedral sections. If one or more of the outer sections decompressed, the residents could still be safe in the inner sections.
If you keep air pressure low, then decompression won't happen as fast. People can make it in 50% of Earth's air pressure; this happens at roughly 4000 meters altitide, where there are large cities like El Alto in Bolivia. This means the rupture does not have as much pressure on it, and failures will be gentler than they would at higher pressure. This can also decrease the time needed to make repairs: ruptures at a lower pressure differential tend to be less catastrophic.
Decompression would not be rapid in most cases.
This is assuming that you have a relatively small hole in a relatively large dome, kept at or around one atmosphere of pressure. It turns out this is a situation that people think of a lot in the context of airplane safety. (Though airplanes are a fair bit more complex, since they often encounter problems at a cruising speed of several hundred miles per hour. Windstorms on Mars can be intense but they're not that intense.)
Anyway, while looking into some persistent myths about air travel, the Mythbusters contacted NASA who gave them the following estimates:
A one-foot hole in the side of a 747 will take about 100 seconds to empty it of air, provided nothing is replacing it.
The maximum force exerted by the air leaving is about half a ton; this falls off with distance.
Plugging in my own rough estimate of the size of a 747, that's about 200 cubic meters of air per second. Which sounds like a lot, and in some respects it is, but cities are huge, and therefore it follows that dome cities have to be huge too. Let's say your primary dome is a mile across (1600 meters) and is a perfect hemisphere. Its internal volume is a hair over a billion cubic meters. If you poke a one-foot hole in a one-mile dome, it will take almost two months to drain all the air out. Needless to say, that's plenty of time to get a maintenance crew in place.
The size of the hole makes a big difference, of course. If instead of roughly 30 cm across, it's more like 30 meters across, you're going to lose air correspondingly faster. (In about 10 minutes, in that case.) Your engineers should take that into consideration, designing the system to mitigate and contain impacts. But it certainly isn't the case that "the tiniest rip" will lead to all the air vanishing in a matter of seconds, as is sometimes seen in fiction.
The pressure also plays into how quickly air will leave the hole, obviously. (In a sense, air pressure is how much the air "wants" to escape. In a system in equilibrium, where the pressure is the same on both sides, there's no impetus one way or the other.) 1 atm is not that much pressure, but you could go lower to limit the escape rate if you wanted to. Your municipal air cyclers might be programmed to only feed out a certain amount of air after a breach, to sustain life in certain parts of the dome while limiting the amount of perfectly good oxygen wandering off into the atmosphere.
There's also the consideration of debris. In an airplane, one of the hazards of decompression is that objects can strike the edge of the breach, tearing it wider. A half-ton of force sounds pretty intimidating, but remember that that's only near the breach itself. If the breach is high up on the dome's side, the force is highly attenuated by the time it reaches any loose objects on the ground. You should also contrast it with the weight of the dome itself: if it can withstand all of that downward force all the time, an additional upwards force is not likely to be catastrophic. (You shouldn't take that on faith, of course; your engineers should make sure the dome can handle secondary impacts relatively gracefully.)
So how would you protect against decompression? By using the size of your dome to your advantage. Construct the dome in sections or tiles, supported by a rigid frame that's capable of limiting impact damage to one or a few tiles. It's no good to have a huge glass surface that can crack in one go, no matter how unlikely that is. Your frame should take the brunt of any really big impacts, like stray meteors or crashing space elevators, leaving the tiles themselves with smaller hits.
When an impact occurs, maintenance teams will first isolate the gap using a caisson: in this case, basically a big tarp that gets epoxied in place. It doesn't have to be pretty and it doesn't have to last, it just has to keep the air in while they remove and replace the damaged tile(s). It would be good practice to keep spares on hand so you don't have to wait. However, although critical, this isn't an emergency procedure.
Let's say what we are afraid of is small metiors
Step 1, controlled failure
Make the points of the dome weaker than the glass. Let's say each square of glass is about 1 by 1 meter. This way when the glass is hit hard enough instead of breaking, a small section is knocked out. There are no cracks, no spreading damage. In a perfect world 1/4 of the connection could even be a hinge so the broken tile does not fall off, and may instead be sucked back closed.
Step 2, Repair cannons
Now we know that we only lost a couple of square meters of dome. We simply need cannons to fire 10x10 meter patches. These patches are desired to stick to the grid which is now exposed as we have a clean break. They also are easy to aim as all airflow guides them tot he hole. A couple of shots, and you can wait for an emergency crew that just needs to install a few standardized tiles to replace the broken ones.
The biggest problem is the 1 square meter tiles crashing to the ground. People may get hurt, but not as bad as a full depressurization of the base.
For a more massive failure, all buildings should also be emergency shelters. Once an emergency is detected. all airtight doors should enable keeping people inside safe. People outside would need to seek shelters that feature airlocks. Many locations outside should feature oxygen masks. These would allow people to keep breathing as they head to a shelter.
Logan's Run world had its perks, but you are right - those domes are too fragile. I want to live under a durable dome. I want to live under a
Self healing bubble dome.
In a soap bubble, the soap-to-water ratio isn't homogeneous. Some places have a little more soap than others. Those places with mostly water, have a higher surface tension. The molecules pull together there, and as they pull together, they bring more soap molecules into the mix. Meanwhile, places with too much soap stretch out until the soap molecules are so thinly dispersed that it starts pulling together again. Simple as it is, a soap bubble is a self-healing, or at least self-stabilizing, structure
This bubble dome will not be a geodesic dome, or a giant fishbowl like the dome over Springfield in the Simpsons. This stately pleasure dome will be flexible, maintained with a constant infusion of the molecules which comprise it. Penetration will be met with aikido-like fluidity and regeneration.
How, you may ask, can a humble bubble contain higher pressure on the inside than on the outside? That is material for another question...
The risk of rapid decompression is quite low from a tine hole (tiny in comparisson to the whole structure), as others already mentioned.
One possible method would be a three layered dome: The inner and outer layer are made from transparent tiles, where each tile would crack individually if something struck it hard enough.
The middle layer is made of breakable containers filled with a liquid that resembles building foam: Expanding and then solidifying when the container is broken, and thus filling the breach.
For further security, every tile and container should be equipped with sensors so damage control knows exactly where a breach occured.
I want to preface my answer by stating that the "dome", per se, is volumetrically inefficient. But it is certainly more attractive to humans than what is currently planned. Also, if we're going to fill something like an O'Neill cylinder with air, why not a dome?
As has already been said, decompression probably would not be rapid. Anything that would punch a hole big enough to cause rapid decompression would also cause a lot of other damage.
I went and found a napkin on which to scribble some rough calcs, and it looks like a 1 metre hole punched through a meager dome only 1km in diameter and about 450m in height would take about two weeks to totally empty of air. I used no calculus in this answer; as the pressure slowly decreases less air will leak out per minute and it would actually take much longer to totally empty the dome of air.
A 2 metre hole would require about 3 days; an 8 metre hole would be fairly substantial but would still require 5 hours. Again, no calculus. Note that's the diameter of the hole; an 8 meter hole would have a cross-sectional area just over 50 sq. metres.
And remember that's for a 1km diameter area. That's not really such a large area as far as towns here on Earth are considered. The town of Grimsby, Ontario, has a population around 27,000 in an area roughly equivalent to a 4km circle, but it would be reasonable to assume that a planned dome community would have a much higher population density and be better organized.
It's also reasonable to consider that not all activity would take place under the dome, or possibly under a single dome. Perhaps there are multiple domes for different activities, such as agriculture, or for community expansion.
To get on to answering your question, I'm sure the colony will be constructed in such a way as to provide shelter in the event of any kind of pressure loss, such as air-tight domiciles or underground facilities, and that there will be a civil plan on file in the event of decompression.
As far as fragility goes, I question that assumption. You use the word "rip", but I doubt that an inflatable dome large enough to house a town-sized population would be considered. Probably something more like the traditional "glass dome" like structure often portrayed in old science fiction, or a dome-like structure with a "roof" consisting of a number of smaller dome-ish structures. Mars seems to have an abundance of silicon to support such a construction.
Whether an actual dome would actually be both feasible and viable is a different consideration, but you asked about a dome so I'm answering about a dome.
Hope this helps.
A colony on another planet could live in a dome structure without necessarily living in a dome like you imagine. Instead of a vast dome covering a city with separate buildings, there could be a city inside a vast dome shaped building with multiple floors and walls inside.
The building could be as wide as the Pentagon and as tall as the Empire State Building. Each of the lower floors could have as many rooms as the Pentagon, and the number of rooms would get smaller in the narrower higher floors. Various businesses and households would occupy different rooms.
And perhaps every single room in the vast building could be sealed off from other rooms. Thus if there is a leak all compartments affected by the leak could be sealed off to prevent further air losses - preferably after everyone in them was evacuated.
A spherical shape has the least amount of surface that can be pierced and lose air relative to the volume enclosed, so a semi spherical dome is a good shape for an airtight building containing an entire colony that fears having their air leak outside.
And here is another design idea for a domed colony on a world with little or no air, that is a bit more similar to your original idea.
A hole like a flat cylinder is dug in the Martian soil, deep enough to build building several stories tall in it. Buildings several stories tall that can be individually pressurized are build in it, with their roof level near the original ground level before the hole was dug. Sections of roof are built from building to building, so that the entire settlement has an airtight roof to hold atmosphere in.
Some of the excavated material from the hole is put on top of the common roof, piled several feet deep, to help insulate the settlement and to keep out dangerous radiation.
Each building should have a penthouse structure sticking up above the common roof, with airlocks, passenger and/or freight elevators, and/or stairs down to the building below.
And at the sides of the cylindrical hole there should be several long ramps gradually descending to the bottom level of the hole, for vehicles.
Outside the radius of the cylindrical hole and the ramps there should be a dome. It is good to have as much atmosphere as possible in the settlement, so that severe changes in the atmospheric composition, which would be dangerous, would be less likely. The more air there is, the harder it is to change its composition. The dome should have a wall at its bases with airlocks big enough so the vehicles can go through.
So they would fill up the dome with a thick, Earth like atmosphere, just like inside the underground community, in order to have that extra amount of atmosphere.
But the entire underground settlement can be quickly sealed up airtight if there is a leak in the dome, and will have enough air to survive for a period several times as long as the estimated time to repair the doom and fill it up with Earth like air again.
The same way that we do in submarines. Training. In fact my first underway involved a duct tape affrair on the shaft seal that only started running to the bilge pump at 300ft. I think a Mars colony that is leaky by nature but troubleshooting is the status quo is not only more realistic but also more interesting. Have everyone trained in damage control so that the things that seem awful that are going wrong constantly are handled nonchalantly by the locals