I would say if you prepared prior to the cut and done some TLC for the roots that wont be cut you'd be fine. At 16' away you wont be encountering too many structural support roots (ones over say 1" dia).
What is the dia of the tree? There's some rules of thumb like whatever the dia is then 10x that as a radius is what is termed the critical root zone (CRZ).
For example, the oak is 0.5m dia then the CRZ would be 5m, which in your case is close to 15' and you'll be cutting 16' away so all is OK.
Now if your oak is 1m dia then the CRZ is 10m and you are within that. However, a loss of up to 1/3 can be sustained provided you prepare and care. The loss has to be on the outer side of the 10m zone which you are.
It is recommended you cut the roots not tear them away with an excavator or bobcat. There's machines similar to a concrete saw that will cut a fine straight line.
Once cut it would be wise to insert a root barrier or plastic sheet. That's to prevent roots absorbing too much of that lovelly concrete water and builders slush ... it will also prevent the roots growing under your slab.
The remainder needs to be cared for, you know, mulch, water, seaweed extract, charlie carp, molasses, a little organic fertilizer but no chemical fertilizer especially NITROGEN (N)! You do not want to spur growth on the tree.
Now the timing of this is important, the root cut would be best done during dormancy, however the preparation prior to the cut for the CRZ needs to be done before hand, the tree needs to store up on those goodies before dormancy so when spring comes around next it has a full swag of goodies to go about it's business including growing new roots and sealing some of those cut ones.
Hope that helps, normally you'd pay around $150 for that advice.
There may be variances on the figures for different species of trees however the concept remains universal. Some trees can take a lot of root abuse, some little.
Also depends on the terrain, are the remaining roots in rock, soil, up hill or down hill etc all makes an impact. Other arborists on here may be able to get more specific advice from experience but at the end of the day you can only do your best. I would say at 16' away for a 50' oak (juvenile) correctly done, no worries.
