After rereading a second time, some of my words above are only applicable if the earth is very wet and is wet all of the time. If, instead, it's a time transient situation, then the reality would be as follows:

1. You bury the pipe and for all intents and purposes, it acts like normal underground piping.
2. At some other time, water seeps in and permits buoyancy effects that are offset by the mixture's viscosity, which is very significant. At this time, the soil-spring model is compromised due to change of ground composition.
3. The ground may or may not dry out again, leaving your pipe in a pre-stressed cold-spring state, but otherwise now behaves like underground piping from step 1 (or perhaps not. The soil model may be in a third state).
4. Repeat steps 2 and 3 ad infinitum.

If you assume that given enough time, the pipe will end up in a configuration that's identical to regular water, then you can calculate stresses as though it's in water. Assuming there's nothing to keep the pipe from floating, any sufficiently long length of underground piping is going to fail.

Perhaps the solution is not to try to get CAESAR to accurately depict stresses in the route, but to develop an administrative approach and simplify the problem with concrete sleeves that keep the pipe relatively neutrally buoyant. I would suggest sizing your concrete sleeves for spans equal to normal supports for the pipe so as to maintain consistency, as well as to act as regular supports for the pipe before it's buried.

However, I'll note that without water/earth consistency information, it'll be difficult to target the density you need when designing your sleeves.