Was asking to do this install. My question is not sealing the RCP joints, but rather scouring around the pipe, leading to another washout. Materials and access will be tricky. I've heard of everything from rubber membrane, then rock on the inlet, to just digging up some good clay. I just don;t know what the velocity in that creek will be. It is dry now, but generally these vanes can move in a big rain. I will have to run some flow calcs in the pipe but wanted to see if anyone has experience on these "back 40" type deals.
I've never used RCP, but I had to install a 3' plastic culvert in a running stream a few years ago. I had to use the excavator bucket to hold it down so it didn't float away, while shoveling material around the inlet until all the water flowed through the pipe. I used bigger rocks first, then smaller ones to fill the cracks between those, and on down to fine sand and whatever clay type material I could find. Once the water was going through, the rest of the backfill was as normal.
Don't reinvent the wheel here. Doesn't matter a single bit whatsoever how fast that water is going through the pipe. Hand-tamp some dirty sand about a 1/4 way up the pipe, making sure to get it packed in tight under the full bottom radius, then jumping jacks to over halfway up the pipe. After that, you can switch to native fill, compacting in 6" lifts, always making sure to not pack too much to lift the pipe.