system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: In regards to hills and valleys, what determines whether a roadway will be a tunnel, a cutout, a bridge, or just go with the curve of the land?
gpt
Civil Engineer here.

The biggest factor in determining a tunnel, a cutout, a bridge or following the natural curve of the land has to do with....Geometrics.

Roadway geometrics deals with how a road can handle a vehicle as it speeds along pavement.  Ever notice how it feels like you are being shoved to the right or left side of a car as you round a curve while going fast?

If the intent of the roadway is to carry traffic at high speeds (70 mph posted - usually designed for 80 mph), you can't have any tight turns; otherwise vehicles will fly off the road - literally.  This is the reason why racetracks have high angled banking turns.

With that in mind, if engineers want to maintain traffic speeds, they have to maintain gradual grades over hills, through valleys and around turns to accommodate high speed vehicle flow.  This also holds true for the super fast trains that speed around central Europe and Japan.

Secondly, after geometrics, is money.  As stated earlier - cost is a huge factor when determining whether to dig out a cut section in a hill or just bore right through it with a tunnel.  Sometimes it is easier to lop a cut in a hill with some explosives and bulldozers versus the specialized equipment and personnel needed to bore through thick rock for tunnels.  

Bridges are usually resorted to when a stream can't be filled or a valley must be crossed high above the ground below.  The engineering economics associated with these projects are a new topic entirely!