基于SMP准则柱孔扩张问题相似解

以柱孔扩张理论为基础，将柱孔扩张后塑性区半径b作为时间刻度，引入扩孔速度概念，将塑性区内任意一点的应力、应变描述成塑性区半径b和柱孔扩张后扩张体单元距孔心距离r的函数，采用平面应变条件下无黏性土的SMP准则和不相关联流动法则，考虑到无黏性土的剪胀性，推导出柱孔扩张后极限扩张力 的相似解。通过参数分析表明，土体强度和剪胀性对塑性区半径和极限扩张力产生很大的影响，即随着土体强度和剪胀性的增加，极限扩张力明显增加，相应塑性区半径却随之减小。通过与基于摩尔-库仑准则解答进行对比分析表明，考虑中间主应力影响的SMP准则所得到的极限扩张力明显高于基于摩尔-库仑准则的解答。该解答为无黏性土中进行静力触探（CPT）试验和静压桩等岩土工程问题提供必要的理论依据。

Similarity solutions of cylindrical cavity expansion based on SMP criterion

On the basis of the cylindrical cavity expansion theory,the concept of expansion velocity is introduced into the theory.The movement of the plastic boundary b is taken as the scale of "time" and the stress/strain of any point in the expansion body are described as the functions of the plastic boundary b and the current radius r.By using the spatially mobilized plane(SMP) theory of cohesionless soils in the plane strain condition,non-associated flow rule and considering cohesionless soils,shear dilation,the similarity solution of limit pressure is obtained.Meanwhile,the parametric study indicates that the influence of strength and shear dilation on the limit pressure and plastic zone radius is remarkable.With the increase of strength and shear dilation the limit pressure increases greatly while the plastic zone radius decreases.A comparative analysis shows that the limit pressure calculated from the SMP criterion which includes the effect of intermediate principal stress is obviously greater than that from the solutions based on Mohr-Coulomb criterion.The proposed solutions provide some theoretical bases for geotechnical engineering practices in cohesionless soils,such as cone penetration tests(CPT),jacked piles,and so on.