Here I have posted 2 fulwave rectifiers attached to mains, one with and another without mains neutral attached to ground.
without ground
with mains ground
Without mains ground common to R-Load is R-Load considered floating? Is it safer to use mains earth grounding for all ground references in this circuit?
With mains GND:
Look at D3. Both sides are GND-ed. This makes D3 useless.
And when you simulate the circuit .. you will see what happens.
Without mains GND:
You have the - often discussed - problem of floating circuit parts (here: supply). --> use the recommended 1Gohms (or other very high value) solution to prevent the circuit part from floating.