砂土中柱孔扩张问题的扩孔压力与扩孔半径分析

 通过SMP屈服准则，对砂土中柱孔扩张问题进行理论分析。以柱孔扩张理论为基础，利用孔周土体塑性区的边界条件和土体体积变化规律，推导柱孔扩张问题中初始半径a0，扩孔半径a和对应的扩孔压力p三者之间的理论关系。利用上述理论公式，得到平面应变条件下柱孔扩张问题的扩孔压力的极限值pu和孔周土体的弹塑性区域应力场、位移场，进而求得塑性区半径rp与扩孔压力p和初始孔径a0的关系。分析表明，该应力场和位移场分布规律仅与柱孔的初始半径a0和扩孔压力p相关。此外，应用应力场公式，推导散体材料桩极限强度表达式。最后通过算例分析，对柱孔扩张中应力场和位移场分布、塑性区半径和扩孔压力的变化规律进行分析。

ANALYSIS OF EXPANDED RADIUS AND INTERNAL EXPANDING PRESSURE OF CYLINDRICAL HOLE

The expansion of cylindrical hole in sand was analyzed based on the yielding criterion of spatially mobilized plane(SMP). A theoretical relationship among the initial radius a0，the expanded radius a and the expanding pressure p of the cylindrical hole was derived employing the boundary conditions of plastic zone and the volumetric variation of soil around the cylindrical hole. The limit pressure of expansion pu and the stress and displacement fields in the elastoplastic zone were obtained with the theoretical relationship. A theoretical relationship among the radius of the plastic zone rp and the expanding pressure and initial radius a0 was derived under the plane strain condition. The limit bearing capacity of a pile in granular material was deduced by using the stress field formula. Finally，an example was presented to illustrate the variations of the stress and displacement fields，the radius of plastic zone a0 and the expanding pressure p.