How to detect a fault for an earthed electric motor?

Every motor is to be protected with back up MCB / fuse and overload and single phasing protection. The motor is to be earthed properly. Once protective relays are connected in the system the system get tripped when the live terminal of any phase get earthed. Once tripping happens proper Megger check to be carried out for cable and Motor, to find the cause of tripping. The tripping can be due to Earth fault.

First, the motor body should have a "hard" connection to ground to keep the exposed surface "touch safe" for personnel. If this is the case, shorting a phase lead (connection cable) to the motor frame will result in a phase-to-ground fault, which should be picked up by the protection.

If the cable is a neutral lead (e.g. connects to the winding neutral point) - and the motor frame is appropriately grounded - there maybe a "ground loop", which would have some amount of current flowing through it. A reasonably sensitive protection device looking at neutral currents should be able to discern this.

Protection looking at either voltage or current unbalance in the primary phases (e.g. current transformers feeding a relay) should spot the difference resulting from the unintentional grounding.