Weeds ... stop getting in to my garden !!!!

In my backyard I put in some metal stripping and divided my yard from the garden, but a bunch or grass and weeds crept in there from my neighbors yard.
I had some asian jasmine ground cover as well and now there is a bunch of grass (burmuda) in there.
I am peeved about having to re-do it again.
Here is what I am thinking:
1) I guess I have to build a barrier all the way around it and I guess 12" deep so the grass doesn't come in again.
2) I'm thinking that after I dig out my area I'll have to pour the barrier with cement and make it continuous so grass can not weave its way back in.
3) I'm thinking that all my jasmine and all my other plants are infused with grass and it would be a waste of time trying to replant them or save them.
Anyone been here before and have any advise?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file

HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.