Cusp Point Condition for Estimating Ultimate Load of Pile Foundation Based on Strength Reduction Method

In order to estimate the ultimate load of pile foundation by the strength reduction method, based on the Zeeman machine of cusp catastrophe, the bearing capacity functional of pile foundation and the theory of direct shear test the catastrophe's critical condition of bearing capacity of pile foundation was advanced, and the relation between incremental displacement gradient and geotechnical material shear strength was established. And a method based on cusp-catastrophic curve was put forward to estimate the ultimate load of pile foundation. The analysis of examples shows that the cusp-catastrophic curve is almost vertical to the axis of strength reduction factor after the cusp point. A micro increment of strength reduction factor will result in the quick increase of incremental displacement gradient, indicating that the plastic deformation of geotechnical materials occurs. So the strength reduction factor corresponding to the cusp point may be determined as the strength reduction factor under ultimate load condition. The ultimate loads estimated by a cusp-catastrophic curve and a reduction factor-settlement curve are almost the same, but the physical meaning and cusp point of the former are still clearer.