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moment in the joint of pile and foundation

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Use XY Data features for that. You can save and plot moment values for selected nodes. Either create a node set with history output request for moment or create XY Data from Field Output and select nodes in viewport manually.
 
You should request the variable called RM - reaction moment. There are 3 components of this variable (in 3 rotational direction).
 
As a mechanical engineer I don't know much about soil mechanics but if it's possible to analyze the reaction forces in such, probably sort of elastic, foundation manually with sufficient accuracy then it would be good to do it in order to verify your results.
 
Can you tell me more?
In your opinion,how can I to get the connection rigidity?
 
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