Abstract: Based on the basic concepts and principles of the theory of probability, the transfer of additional stress in geomaterials is viewed as a probability event, and without adopting any model and assumption the probabilistic solution to additional stress is derived under point loads in the two-dimensional space. Then the solution is extended to the uniform loading condition in the two-dimensional space. Furthermore, both of the proposed solutions are extended into the three-dimensional space. Finally, all these solutions are compared to the Boussinesq solution. The results match with each other very well, showing that the proposed probabilistic solution to additional stress in geotechnical media is reliable and reasonable.

Key words: probabilistic solution, additional stress, Boussinesq solution, probability event