Core(ie.core lamination stack) and core clamping structure are separately brought to cover terminal box through bushings and then grounded to earth at tank cover. Insulation resistance of core to G and core clamp to G and Core to core clamp are measured separately. As per C57.152-2013,minimum IR value recommended is 500 megohms at 1kV DC for new transformers. In old transformers it may come down to even 10 meghoms. When any of above IR value is zero, it means double grounding and circulating current may occur. Out of these three readings, core clamp to G is most significant and other two may not create much problem.When transformer is loaded, leakage flux from windings will impinge core clamps and induce voltages. When there are two grounds,this will result in heavy current flow, overheating metal. In large transformers, it may even melt metal at joints. Normally this will be detected by DGA check. If DGA is OK, it means, additional grounding is not creating damaging current flow.
So when above situation arises, there is no need for immediate shut down, but better to reduce load as much as possible so that circulating current will come down. Solutions: Open out the grounding at cover so that double earthing is prevented. With low IR values, some times cover grounding is done through a resistor to limit the circulating current, if any.