Successfully designing for earthquakes does not necessarily mean active damping. (That is, it is not "required" as you state.) Yes, many large structures use specially designed mass or viscous dampers for dynamic loading (Citigroup Building, NYC; Taipei 101; Millennium Bridge, London), but others are designed to fail safely such that life and structure are preserved to the greatest extent possible. Specifically for bridge structures, there is the notion of plastic hinging in visible locations. [2] This way, the failures can be identified and repaired before normal use resumes. Here are some relevant state DOT guidelines. [3]
[1] http://www.spacex.com/sites/spacex/files/hyperloop_alpha-201...
[2] https://en.wikipedia.org/wiki/Plastic_hinge
[3] http://www.dot.ca.gov/hq/esc/techpubs/manual/bridgemanuals/b...
I would respectfully disagree. The rail industry has figured out how to do Continuous Welded Rail (CWR) quite well, using the elasticity of steel.
http://blogs.agu.org/landslideblog/2011/03/08/distorted-rail...
Similarly the tube for the Hyperloop doesn't HAVE to free-float against its foundations. It might be easier or harder depending on various factors to work on expansion joints or doing the tube equivalent of CWR. You'd probably work on both to figure out which is easier in the long run.
Considering that it's a 9-11ft diameter tube with about 1" wall thickness, it's going to be pretty stiff, especially relative to traditional rails. The moment of inertia means that it should be very resistance to bending or buckling under compression and under tension steel is usually very good.
Given that there are going to be plenty of turns that the track has to make, I would look at doing a combination of two things:
1. Working towards a CWR style solution
2. Allow some movement so that the corners can take up the slack as the tube expands
The turns are very gradual and sweeping. But you could imagine that there's a virtual intersection between two straight portions that you determine by drawing lines from the straight portions until they meet. The actual turn will take place far from here, but it's instructive. So as the tube expands, the actual curve is going to move ever so slightly from the neutral position towards the virtual intersection. So long as there is enough room on the pylons to accommodate this, things will be pretty good. The tube will go from being curved 0.1 degrees per 100 feet to 0.105 degrees per 100 feet (or something like this) but this can be designed for and ensured that it doesn't cause the tube to buckle or collapse. It's engineering, not the utter unknown.
At their desired vacuum pressures, the steel doesn't need to be anything special, so I would love to see the mechanical engineering that goes into designing the 5 mile track's materials.
1. Giant foundations and just handle the thermal stress by not letting anything move
2. Figure out the slip joints really well to soak up the ~125 feet of travel and still hold a good vacuum
3. Figure them out OK and just install extra vacuum pumps since there are only ~250 joints
4. Try out some/all of these options on 500 feet of tube in parallel to see how it all performs and don't make a final decision on the whole 5 miles until you have real cost numbers
The other thing I'll mention is that you don't need the steel to be continuous in order to hold a vacuum. You need the inside face of the tube to be smooth in order to not jerk around the vehicles, but all the sealing could be done on the outside with clamp-on seals. If the average continuous tube piece is 100 feet long and the max thermal expansion is 0.5% then you only need a half-inch gap between the tube pieces.
If your air bearings are say 3 feet long each and divided into 10 sections internally which are fed through orifices so that no one section can rob all the pressurized air flow then you're never going to lose more than 10% of your bearing force and you should be able to glide right over these 1/2" gaps with no problems. And if there are some problems a few accumulators (plain air tanks or pressurized bladders) inline with the supply lines would probably increase the momentary recharge capabilities enough to negate the problem.
700mph is 1000 feet per second or 12 inches per millisecond. That means a 1/2" gap is crossed in just 40 microseconds or so.
I am no rail expert (though I am a civil/structural guy), but even continuous welded rail isn't always continuous for hundreds of miles. [1] I think that there are two factors at play: continuity in the maglev/rail structures, and continuity in the superstructure/tube. I do not know what maglev devices look like, but if they do look like traditional rail, then agreed that a CWR solution seems to be the way to go. That being said, no matter how stiff the tube is, it too will have to accommodate thermal movement. My gut reaction is to call everything tube related simply supported, allow for (6.5x10^-6x100ft.x100deg = 0.065 feet) ~= 0.75" of expansion or contraction at each pier, and surround this expansion zone with a metal sleeve of 2"+ greater diameter than the main tube. Simply supported, multi-span structures are a well-studied problem. Adding in the continuity of the rail/maglev structures are what make it hairy, IMO, and the interplay between seismic considerations and thermal considerations becomes important. As far as I can see, it's very important for the maglev structures to be continuous to ensure for smoothness and speed of the ride.
For example, given that you make the superstructure spans simply supported, you have these nearly perfect "mass-on-a-stick" seismic models with well defined, and relatively short periods. Then, you have much longer continuous sections of rail/maglev equipment that contain releases on a far fewer number of span segments. These will have much longer periods of vibration. Maybe I'm stretching here, but the connections between the maglev/rail and superstructure seem like a place that is rife with potential for failure and stress during a seismic event. (I would not want a life-safety issue being my most prominent failure point.)
[1] http://boards.straightdope.com/sdmb/showthread.php?t=471152
But thermal stresses are very small, for "normal" steel it's 13e-6 per degree C. If you figure that the temperature variations in CA aren't going to be more than say 40C (and that's probably too much) then you're looking at 520e-6 or basically 5e-4.
As far as strain goes, that's not a terribly big number at less than 0.1% especially considering that most of the stress/strain graphs will go up to 10% or more and the first 1% are usually WELL within the linear elastic region. That means that you're talking about doing perhaps only using a few ksi of the steel's strength for the thermal effects.
Anyway, you don't need active dampening to keep the structure intact, but a 750mph vehicle suddenly needing to lift 10 feet in the air you’re going to need a lot of head room not to hit the top of the tube. Not to mention rapid left right displacement. Granted, cost/benifit let em die yada yada.
I suspect that you'd see a lot of wear on the tube that's sliding over the pylon supports as it might go through at least one if not several heating and cooling cycles daily. I could see two cycles if you've got side heating after dawn, midday shade under the solar panels, and then late afternoon heating after the solar panels stop casting a shadow over the tube. You might get another cycle if you have two parallel tubes with two parallel lines of solar panels above them.
