This problem goes beyond the simple child’s game of stacking objects; it is a scientific challenge with major implications. From the construction of dry masonry walls to the optimization of automated storage systems, understanding the probabilistic nature of these collapses can improve safety and efficiency in a variety of fields.

“As blocks are added, random misalignments gradually modify the stack’s center of gravity. When this exceeds a critical limit, the stack collapses.”

This approach revealed two main areas of vulnerability: the base of the stack, where cumulative errors become unsustainable, and an intermediate zone, where hidden instabilities accumulate insidiously.

The maximum height of a pile before it collapses is inversely proportional to the square of the amplitude of the positioning errors. Thus, small errors allow much greater heights to be reached, while larger errors lead to rapid collapse. Monte Carlo simulations, used to validate the theoretical model, were used to visualize the behavior of the piles. These simulations confirmed the bimodal nature of the failure points, for a given drop height, and highlighted the distribution of weak interfaces within the piles.