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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。
As a relatively mature theoretical tool, the hole expansion theory has been widely used in various problems in geotechnical engineering, but many problems are not the expansion of circular holes but the expansion of elliptical holes. Based on the conformal mapping method, the elliptical hole on the original physical plane is mapped onto the unit circle of the image plane, and the boundary condition of velocity in the original physical plane due to the expansion of the elliptical hole is transformed onto the image plane. Based on the theory of complex variable function A new displacement-controlled elliptical hole expansion elastic-plastic solution is obtained. The reliability of the solution is verified by comparing the traditional calculation of the expansion of circular holes with the elastoplastic solution of Gibson ’s traditional circular hole expansion. In addition, the method was used to calculate the excess pore water pressure generated by vertical drainage plates (PVD) into saturated soils, and compared with the Indraratna model test results. The results show that the solution of this paper is completely consistent with the traditional circular hole expansive elastoplastic solution after degenerating to the problem of circular hole expansion. The solution of this paper can well simulate the displacement of vertical drainage plate (PVD) into saturated soil Produced by excess pore water pressure.