Answer:
Step-by-step explanation:
Weight
The weight of the car is F = m * a. Since it is parked, the car feels the full force of m*g where g is 9.81, the gravitational constant.
Weight = 1000kg * 9.81
Mud
Mud is not a pure solid. It is diluted by a certain amount of water. The amount of water depends entirely on the nature of the soil containing it.
By diluting the soil and letting it have some liquid properties, mud can be moved around. That's why the car sinks. There is enough liquid to transport the soil away from the tire, and so the tires sink.
Prevention
I know this is not the answer, but it is what you should do. Don't park where there is mud. Surely there must be some part of the field that is dry.
On the other hand, what you could do is extract some of the water from the dirt. You would need a very clever device to do that. I think this is the physics answer.
You could also park on wide boards to put the force evenly spread out.