How can we obtain the calculation method of the maximum force（F) of the cattle when it forced to get back?

Your “problem” has too many contradictions. You say the wall is rigid, but then it leans. Does it lean toward the water or away from it? Is the ground level or slanted?

Are you saying the cow (cattle is plural, but you seem to be talking about only one animal) is leaning against the wall as the water rises? Once the water rises, the cow would not be leaning against the wall, it would be swimming.

F=mA. There is very little acceleration, but how much mass for the cow?

The cow would cause more force on the wall by swimming away while tied to the top. But the stronger force of the current in the river would create the most force.

The cow will drown.

The picture http://screenshot.net/4l99wt9

The picture doesn’t help. There is no cow in the picture!

The wall would not move like that, it would be held in place by the soil. You give no indication of the density of the soil behind the wall.

This is a false problem.

Force on the water side is easy: p = rho * g * h, then integrate over the width * height. Max is when the water reaches the top of the wall. But if the water goes over, it will want to push back and zero out the water force!

Force on the dirt side is very hard: there is no definition of force to deform a unit volume of dirt. If known (or assumed), then integrate over width * height * angle.

When does the wall start to move? What height is the water during the movement?

@zenvelo ，we can imagine a cow is tied by a rope which is fixed to the top of the wall. The density of the soil can be assumed. The shape of soil will change because of the force by wall which applied by the cow.
@RocketGuy ，we can assume that the water goes over，the cow drag the wall through the rope. The wall leaned with an angle of 30 degrees when the cattle made great efforts (During drag process). We assume the leaned wall is just the result of the maximum force. The height can be representd by a letter.