Hi Robert,
I cannot see the picture, it will not expand.  Being that the berry canes are dying and depending on what is wrong with the plants, it may transfer to the other berries you have planted.
Please send pictures of the splitting canes again.  We only received one picture.
And, look at the bottom of the canes for small round holes.  That would be indicative of a burrowing pest. 
I will wait to see the pictures before trying to solve the issue.  Are there any more signs of plant disease or pest involvement.  What do the leaves look like, are the berries continuing to grow?  Is it on a few canes per plant, and is it on every giant blackberry plant? 
Check all your berries for small round holes at or near the bottom of the canes.  
I look forward to your answers.

Dear Robert,
You are correct in assuming this is a cane blight.  The pictures still do not enlarge but I transferred them to another program and was able to look closely.  The dots look purple and the stems are definitely purple.  Spots usually turn brown and/or white later. This is an ongoing disease and was most likely transferred from your other diseased berry bushes.

There are several things to do.  First, cut all infected canes to the ground, burn or throw away.  Use clean clippers and dip the clippers in alcohol EACH TIME YOU CLIP.  You could have two sets of clippers and a bucket of alcohol or hydrogen peroxide and put one set in and clip with the other, then use the next one, etc.  That will give the clippers more time in the solution.  This is a very important step and of course clean them before cutting any unaffected canes.

The leaves in the picture look purple and the one pix with two canes also looks purple.  I state this because sometimes colors do not come through on the Internet correctly.  Once you have taken the affected canes off, you can spray with lime sulfur or something called Oxidate - found online.  Actinovate is another fungicide.  These are organic sprays. However, remember that they will kill pollinators so do this in the late evening when the pollinators are not there.  They will not contain the entire disease.  Careful timing of pruning, cleaning the area and burning or trashing the canes is needed. 

Each time you prune, the cane cut is fair game for the fungus.  You might dab some of the fungicide on the open cuts when you do prune.  Or just use hydrogen peroxide undiluted.

If the problem is severe you can mow the mounds completely and dig out the soil around the plants replacing with unaffected soil like the bags of soil for raised beds that have not been opened.  

Some of the soil sold in bags at big box stores now have the OMRI stamp on it meaning that a sample of that soil has been tested for all kinds of issues and found to be uncontaminated.  OMRI - Oregon Materials Research Institute. 

This disease overwinters on old canes so remove them all and burn/or trash them.  Remove the floricanes after they have produced a crop.  Best disease control is right after harvest even if some of the canes have green leaves.  Leaving the debris in the area leaves new spores to infect other plants.  

Try not to injure the canes.  It is like cutting your skin, you are allowing spores to enter the plant material.

You can mow all the canes in late winter - another way to rid the plants of the disease. This is drastic but it should severely limit the disease growth when new shoots appear.  

Best cultural practices:   you should prune to allow airflow and use drip irrigation, keeping the bulk of the plants dry.  Both of these methods save a lot of plants especially with our rain a few days, warm weather and then back to rain again.  Good airflow restricts a lot of fungal growth.

If your raspberries are having this problem, same methods apply.
I am sending you a link from Oregon State on growing berries, very detailed and talks about cane blight.
https://extension.oregonstate.edu/catalog/pub/ec-1303-growing-blackberries-your-home-garden
This publication recommends synthetic fertilizers.  We now know that while they will feed the plant, they do not feed the microbes in the soil.  You need organic fertilizers and compost for the soil microbes to digest and make available to the plant roots. Synthetic fertilizers do not feed soil microbes.

There are many organic fertilizers on the market now.  After reading the publication and comparing the recommendations to the fertilizers you will find many organic ones that would work for your berries if indeed you need fertilizer.

If you have further questions, please contact us again and good luck with your plants this summer.

You are welcome.  Good luck with the plants.