Hmm, you're right heathfield, I must get out more. I don't notice these things as I take one of my female research assistants with me to give me a hand. I just keep my hands behind my back.
I was trying to establish if there was any chance that this build up was composed of napthalene or paradichlorobenzene, both of which are major constituents of these toilet blocks. It is possible that parts of these blocks might cause a build up in the trap.
As far as what the substance is, it really depends on the overall pH of the urine going down the pipe. Acid urine usually has uric acid, cystine, oxalates and urates in it, all of which are fairly insoluble in water. Alkaline urine has insoluble phosphates and calcium carbonate present. So yes, the build up could be calcium salts and/or uric acid etc. In fact, much of this may be due to one person who uses the facilities having one of a number of medical conditions!
With regard to dissolving the build up, there are lots of laboratory chemicals that would do the job. Now obviously, these wouldn't be available for domestic/commercial use, so we have to look for a proprietary product. It seems that some of the best might include Buster Bathroom Drain Cleaner and Woodman Ammo Knockout Drain Cleaner.
i would add that you need to choose a corrosive drain cleaner rather than an enzymatic one (those that claim to "digest" the blockage). enzymatic cleaners would take forever to do a job like this and might not work at all. All the same, you need to very careful with corrosive cleaners as splashes can have very serious consequences - follow the instructions carefully.