DYork - Focht3 brings up a good point, in rather dramatic fashion, the total load on the stucture you descibed will be higher that just the static lateral pressure from the material. You certainly have to consider factors such as the "impact" of both placing (by falling from a conveyor belt?) and later removing the material (maybe with a front end loader?). However your question about how to find the lateral pressure from (static) material is nicely handled (for us structurals) by Rankine Theory.
Other factors to consider would be the shape of the pile (flat, sloping, conical, etc). and environmental conditions (does the material get wet from rain, dust control, etc.) while in storage. As usual, there are many ways to look at a problem.
There is also a nice side benefit to you for learning Rankine Therory. At this time (may change later of course) the Geotechnical portion of the Civil (Structrual) PE exam is based on Rankine. Geotech makes up 20% of the morning session. This may be helful (in a few years) when you take the Principals & Practice Exam.
Best Wishes