deep, shallow
The body was found in a shallow grave.

open
The mourners threw flowers into the open grave.

fresh, freshly dug
unmarked
His body is buried in an unmarked grave.

common, communal (esp. BrE), mass
A mass grave has been discovered outside the town.

watery
He rescued her from a watery grave (= saved her from drowning).

early
She smoked herself into an early grave (= died young as a result of smoking).

dig
mark
The grave was marked by a simple headstone.

desecrate
Some of the graves have been desecrated by vandals.

visit
Whenever he goes home he visits his mother's grave.

beyond the grave
The old lady still influences the family from beyond the grave.

in a/the grave
I'll be in my grave by the time that happens!

on a/the grave
She puts fresh flowers on her husband's grave every Sunday.

Grave is used with these nouns:
breach, charge, concern, consequence, crime, crisis, danger, difficulty, disadvantage, disappointment, disservice, doubt, error, face, implication, injustice, insult, miscalculation, misgivings, mistake, offence, peril, problem, reservation, responsibility, risk, sin, situation, suspicion, threat, violation