You haven't really identified what the problem is - other than you don't think that the normal procedures for determining end bearing and side friction capacities apply and I am not sure why. I suggest you see Tominson's Founatiopn Design and Construction (I have the 6th edition) - it gives a very good discussion and has a sample problem of pile into dense sand. He has a very good figure (7.7 in my edition) that shows Limiting value of ultimate end-bearing resistance (MN/m2) vs calculated value of ultimate end-bearing resistance, qb (MN/m2). The limiting value depends on the OCR of the sand - with your very dense sand, I would think that the OCR is in the range of 3 to 4 (possibly more) - in any event, he recommends a maximum limit for cohesionless soils of 15 MN/m2.
Secondly, you haven't identified the structure or any settlement criteria - i.e., how sensitive is the structure. Nor have you identified the stratigraphy that you are driving through other than you have 10 ft of very dense sand overlying bedrock nor why you think that you have to "go to rock".
There is no question when driving the close-ended pile, you will refuse in the very dense sand, and not far into it. Is the soil above the very dense sand poor as far as support goes? Are you requiring lateral capacity? These are additional considerations. I would think that you would determine the ultimate bearing and side friction in the "traditional way" - following discussions of maximum values - and go from there. One thing to keep in mind is that even with a pile driven into dense to very dense sand, much of the actual load being carried will be in skin friction/adhesion (which is why I was wondering what the soils above the very dense sand are) with only a limited load carried down to the pile tip. This can be seen in Tomlinson's Figure 7.13 . . . as it takes less movement to mobilized skin friction and more movement to mobilize end-bearing. Unless there was very good reasons not to found in the very dense sand, I am not sure why you wouldn't.
Then, during construction, checks can be made as to confirm your design capacities. Of course, pile load tests are preferred - but that would be on a limited number of piles. As a quick check, the use of the modified Gates dynamic pile driving formula could be used. (
I realize that many will not like the use of a dynamic formula but as a check - it can be done on the spot at the end of each driven pile.