Officers have liased with colleagues at Strathclyde Fire and Rescue and are now on the hunt for those responsible for the damage at Croy Quarry.
They torched one of the huts once used by workers on the site near Auchenstarry.
The first incident took place on Thursday, November 22, at 6.30pm.
It has emerged that fireraisers were once again at large at the isolated site on Saturday, December 1, when a different hut was set alight at 5.50pm.
Firefighters raced to the site where the blaze was extinguished.
Thankfully nobody was hurt in either incident.
Police are now trying to find the culprits and anyone with further information relating to this incident is asked to contact them on 503900.
Alternatively Crimestoppers can be called free and in confidence on 0800 555 111.