There is "common area" and then there is "exclusive use common area". Exclusive use common area, sometimes referred to as "restricted common area" or "limited common element," is defined as those common areas outside the owner's separate interest which are for the exclusive use of that owner. Maintenance responsibilities for exclusive use common areas are often assigned to owners but may vary from association to association depending on their governing documents.
Assuming that this tree is on your exclusive use common area, it is possible that you may be liable for some or all of the damage to the pipe. The way this is determined if this matter goes to court is through what is known as "a battle of the experts" using an expert regarding tree roots and/or the useful life of the pipe in question. Damages may be apportioned according to the depreciated value of the pipe.
That said, however, I would argue that trimming the tree roots was not your responsibility as the roots are on the association's property.
Under CA law, if roots encroach under adjacent property, the association can sever the roots if the roots are causing damage and then only if done reasonably. If the tree roots of an adjoining landowner do in fact cause damage and the association acts reasonably to sever the roots causing damage, the owner of the encroaching tree is liable for the actual out-of-pocket expenses incurred as a direct result of his tree's encroaching roots.
So, you are right to question whether this constitutes "damage by a member" as the duty to sever the roots appears to fall on the adjoining landowner which in this case appears to be the common areas of the association.
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