Escape Tunnel

An Escape Tunnel is one of the many ways a prisoner will attempt to escape. Prisoners will generally only dig escape tunnels when their freedom need is high enough. They are reasonably difficult to detect, especially for a less advanced prison without Dog Handlers - which are pivotal in the detection of Escape Tunnels. If a prisoner reaches an unsecured area of the prison, they will pop out of the ground and run to the edge of the map, where they will have officially escaped.

Mechanics

Escape Tunnels will always be dug from the toilet of a cell during sleep time. A prisoner will gather contraband with the trait "tool", sometimes collaborating with other prisoners in nearby cells to increase their collective digging speed. Prisoners will avoid walls if they can, especially perimeter walls, as these take an immense amount of time to dig through. Once out of a building they no longer need a digging tool, and can dig with their bare hands, although it's marginally slower.

As of Alpha 34, multiple prisoners digging the same tunnel yields diminishing returns. 4 prisoners will dig twice as fast as 1, and to dig 3 times as fast, there needs to be 11 prisoners digging together.

Detection

Escape Tunnels can be detected when a guard searches a prisoner's cell; however, that will only have a chance of working. Also, they can be spotted when a Guard Dog walks over the tunnel, which will show a yellow flag with a trowel sign next to it. However, there can be false alarms and there might not be an actual tunnel. There is only one way to be absolutely certain about an escape tunnel; dismantling or directly searching a suspected toilet.

Prisoners lacking sleep may be a sign of an escape tunnel in progress. If you suspect someone for digging a tunnel you can search the prisoner at sleeping time by selecting him and searching. A tunnel will be found.

As of Alpha 34, manually searching a toilet will reveal any escape tunnels stemming from that toilet. Searching the whole cell or block will not work: specifically searching the toilet is required. This does not get rid of the random chance that tunnels will be found on a blanket search, but now if you want the check a specific toilet, you don't have to dismantle it.

Slower and faster routes

When a prisoner is digging, they will have a preset path from their cell to the border of the prison. This is determined by a rule of "path of least resistance". Prisoners will have difficulty digging through the foundations of a building, meaning digging underneath one will take much longer and require a tool to advance, unlike digging outside, which is faster and doesn't strictly require a tool, though they do still help. Because of this, prisoners dig paths attempting to avoid buildings as much as possible, as they do with all obstacles. The order of smallest to biggest obstacles, in terms of how long it takes a prisoner to dig underneath, is building foundations, walls, and perimeter walls, which are specifically designed to stop prisoners getting through as well as possible. It isn't all just hardships for the aspiring prisoner though. Water pipes give a speed boost to digging prisoners, and will be aimed for to speed up escape attempts. Big water pipes give a really big speed boost when dug along, being the main reason for the usage of small pipes to connect cells to water. Small pipes do also give a boost when dug along, though nowhere near as big as that of big pipes, and will not always be aimed for, if there is a still quicker route to the prison border.

Cleanup

When, inevitably, you find tunnels, the cells they intersect will be invalid until the tunnel is filled in. To remove the tunnels select the materials overlay, blue button along the bottom of the screen, and use the remove tunnels tool, bottom right of the menu. Tunnels cost twenty in-game dollars to remove for every square the tunnel covers.

Tips & Tricks

If you find a yellow flag stuck in the ground, wait for the dog to patrol there again, and if yellow flags appear again, find someone who is losing sleep (they will normally have capitals for sleep if they are digging)
Pipes are good candidates for escape tunnels, plan your dog patrols along them to maximize discovery chance. Also avoid placing water utilizing facilities (including pump station) close to the perimeter if they have a short pipe route from cell blocks.
When you find a suspected person - search them, so you can find out if they are digging tunnels.
A surefire way to find out if someone is digging an escape tunnel is to search the toilet in the suspect's cell. Note that you still have to do this manually.
When you find an escape hole outside the prison remove it using the remove tunnels action in the materials tab. This will show where the tunnel begins so you can prevent more prisoners from escaping.
Since prisoners mainly dig during the night, doing a shakedown during the night yields a higher probability of discovering tunnels since the prisoners who are currently digging will be absent from their cell when a guard comes in to check them. Calling a shakedown once all prisoners enter their cells for the night is the most opportune time for a shakedown.
Switching to the 'Deployment' view is a clear way of seeing tunnels in your prison as they will be more visible against the white background and without the furniture in the way.
As of Alpha 34, fences no longer slow down digging prisoners. Build concrete, brick, or perimeter walls around problem cell blocks to slow down diggers.
To remove tunnels completely change sleep in regime to free time as prisoners can only tunnel during sleep and can still sleep during free time.