I am designing a concrete box that is 13.5 m long by 4.5 m wide by 5.1 m deep. The box will be buried 5 m in the ground.  I am using a soil weight of 16 kN/m3 and a concrete weight of 24 kN/m3 and the walls will be 0.3 m thick. I need to calculate the moments of each wall and the moments acting on the floor.  A simple moment calculation if the force x distance where the force is acting.  Now I have read a couple of books where they have used weigth of wall/floor (wf) x span (ln) squared x 1/8.  I am a little confused and could use some insite into this.

wL^2/8 is the maximum midspan moment for uniformly loaded condition.

Design consideration should also include lateral pressure due to soil on all sides, upwards force induced by buoyancy depending on the watertable for the bottom, and vertical live load in addition to the soil and concrete dead weight.

Based on how the question is worded, I would recommend you get more direction from your immediate supervisor.

It's conservative to design the walls as simple spans.  However, to get a complete picture of this problem you'll need to obtain (beg, borrow, copy or steal) a copy of "Moments and Reactions for Rectangular Plates" by the United States Department of the Interior, Bureau of Reclamation (Engineering Monograph No. 27; Water Resources Technical Publication).  It solves the exact problem you're describing for a wide variety of edge support conditions and loadings and presents them in an easy to use format (well, it's easy after a while).  It gives edge reactions (shears) also.  It's out of print, but most old-timers have a copy.
PCA (Portland Cement Association) has a similar publication in print called "Design of Rectangular Tanks", but it's mostly worthless.

whyun is correct -- you need to talk to your immediate supervisor about your load sequence and modeling assumptions.

You're asking the simplest of about 14 other questions that need answering....

DBD

Get a copy of the Portland Cement Association's tank publications. It has a series of tables for different loading and fixity criteria.

I agree with the last post.  Also, using appropriate FEM software with appropriate modelling and appropriate interpretation of results will solve your problem.

If your tank is empty most of the time the vertical load transferred from your roof slab to the walls will, depending on bearing soil conditions, also induce a hogging moment in your base slab.  You may also need to consider how any moment from lateral earth pressure against the wall transfers into the base and vice versa.  You may need to do a bit of moment distribution.

Will someone please define "hogging moment" for me?

Hogging moment; negative moment, resulting here from the soil bearing pressure against the slab.
Sagging momant; positive moment.

apsix-

Are "hogging moment" and "negative moment" synonomous?