My Passport partition won't mount and needs repair

Hello all. My 500GB ‘My Passport’ has developed a fault and now the main partition will not mount on any computer. The virtual CD ‘WD SmartWare’ mounts, so the drive is not completely lost. Also, I have tried to repair the partition in Disc Utility on my Mac. This results in a message saying the Disc Utility cannot repair the disc and I should back up my files before reformatting the drive. Unfortunately, if the drive won’t mount, I can’t back up.

Is there anything anyone can recommend? I have tried running the disc utility repair multiple times, as one blog post recommended.

Two screen shots of the disc utility feedback are available here: https://www.dropbox.com/sh/u4scfold18b6exx/AABK9FUBuRJrVjzY43C_AsIza?dl=0

Your help will be appreciated. Thanks.

Hi, you can connect the drive to a Windows computer and use WD DLG to check the drive and see if it has physical damage.