Roots are one of the most vital parts of a tree. They are responsible for nutrient and water uptake, store energy, and anchor the plant. Feeder roots are responsible for absorbing the majority of essential nutrients and water. Because they are so important, it is critical that you protect roots that lie in the path of construction. For all trees, avoid needless or excessive damage. If possible, protect the tree roots to the dripline.
When dealing with trees that naturally have a narrow growth habit, an approach called the "critical root radius" is more accurate than the dripline method for determining the protective root zone. This is particularly true for columnar trees.
To calculate critical root radius, begin by measuring the diameter at breast height (DBH). This is done by measuring the tree's trunk diameter (thickness) at a point 4.5 feet above the ground. The measurement should be done in inches. For each inch of DBH, allow for 1.5 feet of critical root radius for sensitive, older, or unhealthy trees, or 1.0 feet for tolerant, younger, healthy trees. For example, if an older tree's DBH is 10 inches, then its critical root radius is 15 feet (10 x 1.5 = 15). The protective root zone for the tree is then 2x the critical root radius or 2 x 15 = 30 feet. So 30 feet is the area in which a critical amount of the tree's roots may be found. Whenever possible, isolate this area from construction disturbance.
Construction activities often alter the amounts of water received by trees. Thoroughly water plants before and immediately after they receive any kind of direct damage (e.g., severed roots). Continue periodic watering (at least four to five times per summer) throughout the next several growing seasons. Be careful not to overwater your trees. Soaking the soil to a depth of 8-10 inches throughout the protected root zone is a good rule-of-thumb.
Two to four inches of mulch (wood chips or bark) spread over as much of the root system as practical will help the tree retain water and stimulate root regeneration. Living ground covers over the root system will have a similar effect, and may be more aesthetic. Apply these techniques to any deciduous tree exhibiting wilted leaves or any coniferous tree dropping excessive amounts of needles from the inner branches.
Injured trees may need additional nutrients to replace damaged root systems. Fertilizers containing phosphorus and nitrogen can help stressed plants recover since these nutrients promote root and plant growth. Avoid excessive nitrogen; increased stem and foliage growth can cause stress, especially during hot, dry weather or if the tree has been stressed due to construction activities. Because of this problem, many experts recommend waiting two years after damage has occurred before fertilizing the trees.
Here are some publications you may find useful.

https://www.extension.umn.edu/garden/yard-garden/trees-shrubs/protecting-trees-from-construction-damage/#root

http://aggie-horticulture.tamu.edu/earthkind/landscape/protecting-trees/

Hope this helps!