Some geomembranes are easier to repair than others, simple tears or punctures can be patched or sewn; others quickly lose their structural integrity, and need to be replaced. This will also depend on the extent of the damage. Stress cracks point to a structural weakness within the material, and likely can't be fixed via simple repairs.
On the other hand, a small tear thanks to a particularly stubborn rock, is much more likely to be fixed with a simple patch or by sewing the material back together.
