Mathematical mystery for lean and stand of leaning Tower of Pisa

It is attractive to investigate why the leaning Tower of Pisa is leaning but not fallen. Center on this subject, deformation mechanisms of geomaterials and their loading order dependency are introduced at first. After checking by the necessary and sufficient condition of path independency for curvilinear integration, it is confirmed that the stress path dependency of strains in the particular Cam-clay is consistent with the tests. Exactly the same Tower of Pisa, exactly the same foundation, just the difference of construction speed makes a significant distinction of effective stress path in foundation, then greatly affects the development of general shearing strain which is stress path dependent; and finally determines whether or not the foundation is destroyed and whether or not the leaning Tower of Pisa is fallen over. From this perspective, the mathematical mystery for the lean and stand of the leaning Tower of Pisa is deeply and ingeniously revealed. As soon as the viewpoint from Burland et al. that the tower would have fallen over if had work continued is explained by stress path dependency; it is confidently pointed out that if the leaning Tower of Pisa is built more slowly, the effective stress path will be more farther to the critical state stress line; and then, the lean of the leaning Tower of Pisa today may be much little.