Consider I have a pole stuck in the ground as illustrated below:
When a force F1 is exerted on the pole, its bottom end will push against the ground it's stuck in; the ground then exerts a resistance force. Intuitively, if F1 is very strong then the pole's upper end will move in F1's direction and if F1 is very weak, the ground resistance Fr keeps the pole in place.
Given some measures of the pole, specifically, how deep it is (L2) and what radius r it has (it is a cylinder), I would like to be able to determine the magnitude required by F1 to move the pole's end.
I have asked a similar question, with more physical details on another stack exchange site, too. Here is the link.
Assume that the ground is made of only one material, with uniform density, disregarding any "dirty" effects, such as moisture, or temperature. The length of the pole, its radius (it is a cylinder), and its depth L2 are all constant.
Let's view the pole as a lever with its pivot where air, ground, and pole meet. Then we have F1 * L1 = F2 * L2 when the lever is in balance. Now, I would like to find out at what force F1 the pole starts moving; the pole is moving when F1 * L1 > Fr* L2.
The problem would be solved if we find a means to compute Fr. My idea was that as the pole (in the ground)pushes towards the right at every height 0 > L >= L2 (L = 0 on dotted area where air and ground meet), there is a resistance force Fr(L) at each height (view illustration here). For big L this force is small while for small L the force grows. I assume Fr(L) must grow in a linear fashion as it does with levers (F1 * L1 = F2 * L2). Assuming that, Fr could be computed by F2 = 0∫L2 Fr(L) dL.
The solution need not be that exact, the force need only be computed approximately: the force will be used by game simulation the physics need only appear real. All that is required is a means to compute what resistance force Fr the pulling force F1 must overcome to move the pole.