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The duties are clearly written in the JD of the site supervisor. and they are mentioned in the SOW. these are the duties mentioned in JD is not the only duties he had to perform he has to feel, he is the elder member of the family and he has to keep satisfy and together with the family. so the moral duties are also essential. keeping them together is the best way to keep your milestone be completed on time.
the team you are leading must have the confidence that you are the person who can solve and help him whenever they need help or solution. this moral duty make you more help to complete your task.