强度折减法判定桩基础极限荷载的尖点突变条件

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

为采用强度折减法判定桩基础的极限荷载,根据突变理论Zeeman机构、桩基础承载力泛函数和直剪试验原理,建立了桩基础承载力突变的临界条件和位移增量梯度与岩土材料剪应力的关系,进而提出利用尖点突变曲线判定桩基础极限荷载.算例分析结果表明:尖点突变曲线拐点出现后,曲线近似垂直于强度折减系数坐标轴,强度折减系数的微小增量将引起位移增量梯度陡增,说明岩土材料已发生塑性变形,拐点对应的强度折减系数即为极限荷载条件下的强度折减系数;由尖点突变曲线和折减系数位移曲线得到的桩基础极限荷载基本相同,但尖点突变曲线的拐点更明显,物理意义更清晰.

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, hut the physical meaning and cusp point of the former are still clearer.