A numerical procedure for determining three-dimensional terrain subsidence caused by underground cavities is proposed. The Litwiniszyn's idea, according to which the movement of cavities upwards is treated as a random process, constitutes the basis of the procedure. The proposed algorithm is based on the assumption of an imagined three-dimensional device analogous to the so called Galton's two-dimensional board. Small balls falling down in the device are randomly directed into particular cells below with the probability equal to 1/4. Complex three-dimensional problems are solved.
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