基于能量耗散的球孔扩张理论解答

以空间准滑动面（SMP）准则为基础，推导了扩底桩扩孔压力的理论解。从能量耗散的角度分析球孔扩张的全过程，利用应力不变量推导了符合球孔扩张的屈服准则；化简微分方程得到了弹塑性区应力表达式，进而求出位移、应变表达式；分别利用体积守恒和能量守恒性推导出扩孔压力的表达式。该法考虑了塑性区弹性变形，并得到了扩孔压力p、塑性区半径R与扩孔半径a的关系。算例分析表明，该方法计算的扩孔压力与现场试验得出的结果较好地吻合，塑性区半径和扩孔压力均随扩孔半径的增加而增大，但增幅逐渐减小而趋于稳定值，剪胀角对塑性区半径和扩孔压力影响显著，随着剪胀角的增加，塑性区半径和扩孔压力明显增加。

An analytic solution for spherical cavity expansion based on energy dissipation theory

On the basis of the spatially mobilized plane (SMP) theory, a theoretical solution for the spherical cavity expansion pressure of belled piles is derived. Energy dissipation principles are applied to analyze the whole process of spherical cavity expansion. A yield criterion of spherical cavity expansion is obtained by using stress invariant. Then an elastic-plastic zone stress expression is developed by simplifying differential equation to derive the displacement and strain expressions. The solutions of the expansion pressure are derived by the volume conservation and energy conservation separately. The elastic deformation of the plastic zone is considered and the relation among the pressure p, plastic zone radius R and the expansion radius is established. The analyses demonstrate that the calculated value of expansion pressure agrees well with field testing results. The results also show that the plastic zone radius and expansion pressure increase with the increase of the expansion radius, but the growth rate gradually slows down and tends to be stable. The dilatancy angle of soil has significant influence on the plastic radius and expansion pressure. The plastic zone radius and expansion pressure increase greatly with the increase of dilitancy angle.