San Jose Mine, Chile ? Rescue workers on Sunday rushed to reinforce an escape tunnel that will be used to free 33 trapped miners in Chile. If all goes according to plan, the first miner is expected to be lifted to safety early Wednesday morning, more than two months after the accident that left the men sealed off from the world above.

Sixteen steel tubes are being inserted into the top of the nearly 700-yard-deep shaft in an effort to prevent the rock walls from crumbling in and blocking the escape route.

Using video cameras, officials with the Chilean government-led rescue operation continued to analyze the entire length of the shaft Sunday. Those videos have also been viewed by a team of eight geologists. Thus far, the geologists have determined that much of the tunnel is solid rock, meaning there is a relatively low chance of it caving in. Given the numerous curves in the tunnel, however, officials are worried that the capsule may become struck in the lower sections of the shaft.

“We are going to double-check everything that is necessary until we are convinced that the system functions,” said Laurence Golborne, Chile’s mining minister.

During telephone conversations with the miners Sunday, rescue officials advised the men that they must determine the order in which they will be hauled up the rescue shaft. Jaime Manalich, the Chilean health minister, told reporters that several men expressed a desire to be the last to abandon the mine in what he called “a completely admirable show of solidarity.”

The miners later told rescue officials, however, that the true reason they were fighting to be the last one up the shaft was to be listed in the Guinness World Records for the longest time a miner has been trapped underground. Given the complexity of the 10-week-long rescue operation, it would be a record that many consider insurmountable.

Aboveground, workers on Sunday dismantled a drilling rig to make space for a platform that will be used to support the Phoenix, the bullet-shaped rescue capsule that will hoist the miners one by one to the surface.