I've created a turtle farm according to the youtube link below and and, while the turtles mate, there is no digging and egg laying. 

https://youtu.be/NhgEnoRl66Q

Also I found some eggs and have been watching them and they are not hatching after several minecraft weeks.

I've verified there is sand 2 layers deep and have expanded the design to a 5X5 sand region and added a 3rd turtle + mated it to one of the original 2. 

It seems after mating, one turtle becomes unmatable (not accepting grass with hearts)  while the other will accept grass after aperid of time. 

So now I have two turtles that do not accept sea grass and one that still does in the pen.