The proposal actually details what would happen in a number of emergency situations, but indicates the Hyperloop would be built to withstand an earthquake with “the necessary flexibility” and tube alignment.
"A ground based high speed rail system is susceptible to Earthquakes and needs frequent expansion joints to deal with thermal expansion/contraction and subtle, large scale land movement," it says. "By building a system on pylons, where the tube is not rigidly fixed at any point, you can dramatically mitigate Earthquake risk and avoid the need for expansion joints. Tucked away inside each pylon, you could place two adjustable lateral (XY) dampers and one vertical (Z) damper."
"These would absorb the small length changes between pylons due to thermal changes, as well as long form subtle height changes," it says. "As land slowly settles to a new position over time, the damper neutral position can be adjusted accordingly. A telescoping tube, similar to the boxy ones used to access airplanes at airports would be needed at the end stations to address the cumulative length change of the tube."
In a lengthy description of the tube section of the system (the part in which the capsules travel through), earthquakes are mentioned again:
The tube will be supported by pillars which constrain the tube in the vertical direction but allow longitudinal slip for thermal expansion as well as dampened lateral slip to reduce the risk posed by earthquakes. In addition, the pillar to tube connection nominal position will be adjustable vertically and laterally to ensure proper alignment despite possible ground settling.
It says the Hyperloop's capability to withstand earthquakes has been demonstrated in structural simulations.
If an earthquake did strike while the Hyperloop was in operation, the proposal suggests the capsules (in which passengers ride) would be controlled remotely with emergency braking systems being deployed.