Let's see if I made sense of all your inputs.
T3 = operating temperature

D1 = static hogging, which would mean up/down if at the midline of the vessel, but everywhere else would mean up/down and rotate in/out, but happens once per trip.
D3 = dynamic hogging, which would mean up/down if at the midline of the vessel, but everywhere else would mean up/down and rotate in/out, and this happens all day, every day.

U1 = acceleration forward (increasing velocity forward with propellers)
U3 = deceleration forward (decreasing velocity forward with propellers)

D6 & D8 = pipe in tall structures waving around above as an effect of hogging. Are the structures capable of waving in a chaotic fashion, or strictly as a function of D3, U1, and U3, which is modified by D1?

Ultimately, your goal is to get CAESAR to simulate the shape the pipe is going to be in at any phase of its journey, calculate stresses, and as applicable, fatigue life.

I would caution you that you need to scrutinize the addition of like vectors (e.g. displacement vectors). I believe CAESAR averages them by default, and thus e.g. D1+D2 might not give you what you want.