Well, putting shavings on her back is normal behavior for some layers. They are "hiding" themselves. Although I like to think they are prettying themselves up, because they are proud of having laid eggs.
If she is not moving from that spot during the day and night, she's going broody. Whether or not there are eggs, fertile or not, they can still go broody.
Here are Bandit's green eggs - I believe this is her 3rd egg as one of the EE laid a green egg on New Year's Eve while we were away. The other EE hasn't done much except sit in the nest box so I don't believe it was hers.