IIRC they accelerated rock as the reaction mass. Gigatons of rock accelerated to well above escape velocity and launched from the ground.

In the real world their scheme is doomed as it would strip the atmosphere off of the Earth, but since they were planning to leave the solar system the atmosphere was going to freeze to a solid anyway so maybe it didn't really matter. To be honest I thought the entire scheme was an extremely elaborate cover for the fact the lead ship was the actual ark and everyone else was just plain doomed. This would have mirrored one of the themes in the 3 Body Problem where interstellar space travel is strictly forbidden until everybody can participate at once. The "launch the Earth as a spaceship" concept was so poorly thought out I thought it had to be a fraud in the story, and our somewhat dense protagonists just didn't catch on.