If you're digging out a room underground, how often and by what means should you place supports to prevent a cave in?

Okay, so here’s the scenario:

I’m digging in soft clay, up against the outside edge of some tennis courts (by hand). My primary reason for placing the hole there, is because I figured a pre-existing concrete ceiling would lessen the chance of a cave-in. Currently, the hole is a 5’ x 4’ rectangle, 6’ deep. I’m getting to the point where I’m just about ready to start digging horizontally underneath the tennis courts. However, I’m unsure if, and for how long, the concrete above will be able to support itself without additional shoring. Does anyone know the the method and spacing for shoring up things like this?
By the way, the court slab looks like it’s about 6” thick.

Thanks!