饱和土体中椭圆孔扩张弹塑性解

Elasto-plastic solution for elliptical cavity expansion in saturated soils

圆孔扩张理论作为一种相对成熟的理论工具已经广泛的运用于岩土工程中的各类问题,但是很多问题并非圆孔扩张而是椭圆孔扩张。基于保角变换的方法将原物理平面上的椭圆孔映射到像平面的单位圆上,将原物理平面上由于椭圆孔扩张所产生的速度边界条件转换到像平面上,利用复变函数的理论得到了一种新的位移控制的椭圆孔扩张弹塑性解。通过基于该法计算传统圆孔扩张并且与Gibson的传统的圆孔扩张的弹塑性解进行对比分析,验证了解的可靠性。续而,利用该方法计算竖向排水板(PVD)打入饱和土体中所产生的超静孔隙水压力,并与Indraratna的模型试验结果进行对比分析。研究结果表明,本文的解在退化到圆孔扩张问题后与传统的圆孔扩张弹塑性解完全一致;采用本文的解能够很好地模拟竖向排水板(PVD)打入饱和土体中所产生的超静孔隙水压力。

The cavity expansion theory has been widely used in geotechnical engineering as a mature theoretical tool. However, many practice problems are related to elliptical cavity expansion rather than cylindrical cavity expansion. The elliptical cavity on the physical plane is mapped to the unit circle on the phase plane by conformal mapping method, and the velocity boundary condition caused by the elliptical cavity expansion on the physical plane is transformed to the phase plane. The elasto-plastic solution of displacement-controlled elliptical cavity expansion is presented by the plane complex variable elasticity method. This solution is compared with the Gibson's elasto-plastic cylindrical cavity expansion solution, and the reliability of this study is verified. Then, the proposed solution is used to calculate the excess pore water pressure induced by the PVD installation using a mandrel. The theoretical prediction of the excess pore water pressure is compared with the model tests by Indraratna. The results show that this solution is consistent with the conventional cylindrical cavity expansion method when this study is degenerated to the cylindrical cavity. The proposed solution can simulate the excess pore water pressure induced by the PVD installation very well.