Richard Marjoram, 57, from Deeping St Nicholas, died following an "industrial accident" involving an HGV at Stainby Quarry, near Grantham.
Police were called to the quarry at about 11:00 BST on Monday.
Lincolnshire Police said it is investigating the incident together with the Health and Safety Executive.
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In a statement, Mr Marjoram's son Ben said: "We are deeply shocked and upset at the death of my father, who was a very special husband to mum and also a fantastic father and much loved grandfather.
"Words cannot describe how much we will miss him."
The family of a man who died after an incident at a quarry have paid tribute to a "special husband, fantastic father and much loved grandfather".