It is important that you do not disturb the root system of your trees when installing the pavers. While most conifers have deep roots, they also have roots just beneath the surface, or, in some cases, even extending above the ground. Cutting into these roots with a shovel can severely damage a tree. Instead, use a hand trowel and carefully scoop out as much soil as you need to fit new pavers into place. If you run into a root, stop digging and select a different spot. An additional problem with root pruning is the loss of tree stability. Trees have stability against wind throw because of the lateral roots.  When the important lateral roots are pruned, tree stability can be reduced. Research at the Bartlett Tree Research Laboratories has demonstrated that cutting large lateral roots within the root plate, which is a distance from the trunk to the outside of the tree drip line, can destabilize a tree. So root pruning should only be done as a last resort when all other methods have been judged as not feasible. Also, do not use plastic landscape sheeting under your patio. This creates an impermeable barrier between the pavers and the soil. While this helps prevent weeds from growing between the pavers, it can damage trees, blocking oxygen and water from reaching the roots. A better option is to use porous landscape fabric beneath the rock layer and then pull stray weeds by hand should they appear.

Hope this helps!