I would like to know how to get rid of the rings that occurs around upper transition zone without mechanically breaking by stopping the kilns

There are various options, but if you cannot avoid the problem by better control of the kiln feed chemistry or burning conditions in the kiln then there are two possibilities:
(i) install the equipment to fire Cardox charges in the region where you have persistent problems, and
(ii) by an industrial gun and shoot the rings out.

What are the relationships between clinker hard burning and grindability of clinker. Is hard burned clinker hard to grind? Finally what is the relation between silica mudulus(SM), iron modulus, time of storage of clinker, size of the clinker.

When clinker is hard burnt the amount of liquid phase increases and the clinker becomes very dense and fused together. This is the reason why hard burnt clinker is hard to grind. High silica modulus means low liquid content therefore softer clinker. High iron content means more liquid so possibly denser and harder clinker. If clinker is stored for a long time then it can become hard to grind due to "relaxation" of the clinker. Large clinker implies hard burning and agglomeration into large balls so might well be hard to grind.