Do not use fabric or pond liner of any kind. Roots of trees are no big deal. Just cut them off, pull them out and whatever is left will become organic matter. Landscape fabric was never meant to be used for any other purpose than under gravel over soil. This prevents the fines from working their way up through the larger pores of the gravel layer and you losing your gravel as it sinks into the fines. This is what landscape fabric was made for...to save your gravel. It was never meant for weeds or roots and makes no sense to even try to find other uses. Using this stuff for weeds is flat out silly...roots, big deal. Just cut the roots off when you double dig your soil. If you've got clay I'd be very careful and rethink a rototiller. Makes concrete.

Dig a trench between the trees and your garden. Those roots become organic matter. Different soils through the soil profile just need to be broken up. I spent many many hours with my guys on projects with landscape fabric beneath crappy bark mulch...getting rid of it! The client spent a bit of moola to get their soils back to normalcy. First thing I will do if I find landscape fabric under mulch is get it out of there. Period.

Additional notes:

Normally roots do not grow up from the ground unless the tree isn't getting enough water. How high are your beds? What is supporting these beds? Wood, concrete? Raised beds with structural sides are considered POTS. Using the garden soil can work for awhile but as you've noticed the clay stays. Also the critical zone for all plant roots is the top 4 to 6" of topsoil. That is where the roots are able to get air and water and sometimes chemistry (not nutrients) if that has been added by a human.

It is easier and wiser to move the raised bed than it is to replace a mature tree.

Kevinsky, roots are able to go through concrete and asphalt. Pond liner surely. You hit on the fact roots don't normally grow upwards unless that tree is desperate to find water. Planting anything under trees is not a good idea except for a few hostas or pachysandra?

A raised bed above the roots will kill the roots beneath; no air no water unless there is water the tree can get at by growing up into the raised bed to get at water and air. One raised bed should not be a big deal, right?

Yes, landscape fabric would work in this situation. I take back my first statement. ONLY if you use potting soil not garden soil above the fabric. That fabric slows the drainage and causes a barrier between the flora and fauna of the larger body of the garden. With that fabric installed, especially pond liner that raised bed becomes a pot. Literally a pot. And the hard and fast rule unless you 'make' your own soil and STERILIZE it good old potting soil is the only medium to use in pots or 'planters'.

If your raised beds are made with lumber or concrete and if you install a bottom you have created a POT.

Normally roots do not grow up from the ground unless the tree isn't getting enough water. How high are your beds? What is supporting these beds? Wood, concrete? Using the garden soil can work for awhile but as you've noticed the clay stays and compacts with little organic matter. The clay is inhibiting drainage and kind of becomes a structural bottom making the raised bed literally a pot.

The critical zone for all plant roots is the top 4 to 6" of topsoil. That is where the roots are able to get air and water and sometimes chemistry (not nutrients) if that has been added by a human. Something like 95% of all plant roots exist in the top 4 to 6" of the soil.

It is easier and wiser to move the raised bed than it is to replace a mature tree. Do you have any other space for your raised bed than under the tree? This must be on the south side of the tree to get enough light, right?

Kevinsky, you correctly hit on the fact roots don't normally grow upwards unless that tree is desperate to find water. Watering the tree would make sense. I've been able to control Quaking Aspen roots just by watering the Aspens religiously.

Planting anything under trees is not a good idea except for a few hostas or pachysandra?

Kevinsky, roots are able to go through concrete and asphalt. Pond liner surely? Grins! I've uninstalled pond liner because roots completely riddled that stuff. I never use just one layer of pond fabric always 2. I don't even think two layers would have stopped the roots of the willow above the pond.

A raised bed above the roots will kill the roots beneath; no air no water unless there is water the tree can get at by growing up into the raised bed to get at water and air. One raised bed should not be a big deal, right?

Yes, landscape fabric would work in this situation. I take back my first statement. With one caveat: ONLY if you use potting soil not garden soil above the fabric.

That fabric slows the drainage and causes a barrier between the flora and fauna of the larger body of the garden. With that fabric installed, especially pond liner that raised bed becomes a pot. Literally a pot. And the hard and fast rule unless you 'make' your own soil and STERILIZE it in the oven, good old potting soil is the only medium to use in pots or 'planters'.

Do not use fabric or pond liner of any kind. Roots of trees are no big deal. Just cut them off, pull them out and whatever is left will become organic matter. Landscape fabric was never meant to be used for any other purpose than under gravel over soil. This prevents the fines from working their way up through the larger pores of the gravel layer and you losing your gravel as it sinks into the fines. This is what landscape fabric was made for...to save your gravel. It was never meant for weeds or roots and makes no sense to even try to find other uses. Using this stuff for weeds is flat out silly...roots, big deal. Just cut the roots off when you double dig your soil. If you've got clay I'd be very careful and rethink a rototiller. Makes concrete.

Dig a trench between the trees and your garden. Those roots become organic matter. Different soils through the soil profile just need to be broken up. I spent many many hours with my guys on projects with landscape fabric beneath crappy bark mulch...getting rid of it! The client spent a bit of moola to get their soils back to normalcy. First thing I will do if I find landscape fabric under mulch is get it out of there. Period.

Do not use fabric or pond liner of any kind. Roots of trees are no big deal. Just cut them off, pull them out and whatever is left will become organic matter. Landscape fabric was never meant to be used for any other purpose than under gravel over soil. This prevents the fines from working their way up through the larger pores of the gravel layer and you losing your gravel as it sinks into the fines. This is what landscape fabric was made for...to save your gravel. It was never meant for weeds or roots and makes no sense to even try to find other uses. Using this stuff for weeds is flat out silly...roots, big deal. Just cut the roots off when you double dig your soil. If you've got clay I'd be very careful and rethink a rototiller. Makes concrete.

Dig a trench between the trees and your garden. Those roots become organic matter. Different soils through the soil profile just need to be broken up. I spent many many hours with my guys on projects with landscape fabric beneath crappy bark mulch...getting rid of it! The client spent a bit of moola to get their soils back to normalcy. First thing I will do if I find landscape fabric under mulch is get it out of there. Period.

Additional notes:

Normally roots do not grow up from the ground unless the tree isn't getting enough water. How high are your beds? What is supporting these beds? Wood, concrete? Raised beds with structural sides are considered POTS. Using the garden soil can work for awhile but as you've noticed the clay stays. Also the critical zone for all plant roots is the top 4 to 6" of topsoil. That is where the roots are able to get air and water and sometimes chemistry (not nutrients) if that has been added by a human.

Is this bed beneath the canopy of this tree? Feeder roots normally are a mirror image of the tree's canopy.

It is easier and wiser to move the raised bed than it is to replace a mature tree.

Kevinsky, roots are able to go through concrete and asphalt. Pond liner surely. You hit on the fact roots don't normally grow upwards unless that tree is desperate to find water. Planting anything under trees is not a good idea except for a few hostas or pachysandra?

A raised bed above the roots will kill the roots beneath; no air no water unless there is water the tree can get at by growing up into the raised bed to get at water and air. One raised bed should not be a big deal, right?

Yes, landscape fabric would work in this situation. I take back my first statement. ONLY if you use potting soil not garden soil above the fabric. That fabric slows the drainage and causes a barrier between the flora and fauna of the larger body of the garden. With that fabric installed, especially pond liner that raised bed becomes a pot. Literally a pot. And the hard and fast rule unless you 'make' your own soil and STERILIZE it good old potting soil is the only medium to use in pots or 'planters'.