Hi Evan, Welcome!
How thick are theses travertine pavers?
When I was setting brick pavers in AZ, we would add dry portand cement to the sand, which would stiffen up the base a bit over that wonderful AZ soil.
Thanks for posting the photos!
I'm not seeing any signs of efflorescence in your photos.
Do you hose down the patio for cleaning (under the covering)? I didn't remember AZ getting much rain (except during the monsoon season).
My guess is that problem you are experiencing is just do to the actual quality of the stone. It's also possible that the corners are getting pinched due to movement and them being but jointed. Have you placed a straight edge over the affected areas? Don't forget to consider thermal expansion can be an issue. As you stated, the area covered is the worse. Two different rates of expansion between the covered and uncovered stone.
Two corrective measures (if the issue isn't caused by thermal expansion) are replacement (least expensive), or consolidate the stone, which done properly is a very extensive procedure. Having your stone TESTed is very expensive, and it only pertains to the actual piece of stone TESTed. No guarantees from one stone to another.
If this is a thermal expansion issue, there is not easy solution, except to remove and space the stone at a proper distance to allow for espansion and contraction. It wouldn't be practical to place expansion (soft) joints in a dry set application.
Do you have extra material on hand?
