I think first question for apsix.
Think of the pier as a pencil. You can hold the "pencil" between your two hands, and even if your hand was resting on a table, it is the side support that will do most of the pencil holding.
Brom had a method, Teng had another approach and I think brinch Hansen yet had another methof of analysing piers and lateral loads.
The passive resistance is Kp x Y x D, where Kp is the passive earth pressure coefficient, Y is the soil unit weight and D is the embedded portion of the pier. So if we draw the Free Body Diagram with a lateral load coming from the left side, then we draw a triangle on the right side. The base of the triangle is then equal to 3x Dia x Kp x y x D according to Teng's method of piers in Sand.
Looks like you are very interested in this topic. So try to purchase both texts below for more info:
"Design of Foundations for Buildings" by Johnson & Kavanagh, 1968 and
"Foundation Design" Teng, 1962