I agree with Richard. Not sure where you are in the country, but does look like Diaprepes Root Weevil, (link re-posted, as there was some coding attached that rendered the link as incorrect):
http://www.ipm.ucdavis.edu/EXOTIC/diaprepescitrus.html
I would send your photos to your local county extension office or MG group and have them take a look. Check in the evening to see if you can find any of the adult weevils at work, to confirm.
And I also agree to get rid of the grass around your citrus trees. Hopefully? they're not planted in a lawn that is being sprinkled. Citrus really do not like to be sprinkled, and will not do well in that environment. You want to create a nice water well, and place your drips in the well. Fertilize with a fertilizer as close to 5-1-3 NPK as possible. Top with some compost, keeping it clear from the trunk. That will discourage pests. And, I have to say, it looks like your poor little citrus tree is "tied up to a post", lol!! You might want to unwind the twine a wee bit. Try using padded twist ties, and let the trunk had a little bit of "wiggle" room, so the trunk is stimulated by the wind to develop. If you lash your citrus to a stake like that, you're going to end up with a weak, skinny trunk